[ { "id": "authors:yzm59-hkt87", "collection": "authors", "collection_id": "yzm59-hkt87", "cite_using_url": "https://authors.library.caltech.edu/records/yzm59-hkt87", "type": "article", "title": "Hyperbolic high-fidelity simulations of cratering on a particle bed induced by a turbulent supersonic plume", "author": [ { "family_name": "Balakrishnan", "given_name": "Kaushik", "orcid": "0000-0002-3162-6458", "clpid": "Balakrishnan-Kaushik" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "
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A recently proposed hyperbolic granular model (Balakrishnan and Bellan, 2024) has been used to investigate the problem of supersonic-jet induced cratering on a solid-particle bed. This model relies upon the concept of added mass and a fluid-mediated particle pressure to render the system of equations hyperbolic. The jet is modeled using Large Eddy Simulation (LES) and the solid phase is modeled in an Eulerian framework using a Kinetic-Theory-based model modified for dense particle collections. The formulation also incorporates pseudo-turbulent kinetic energy (PTKE) which has been shown to modify a flow field laden with particles. The results explore the influence of the jet-to-ambient fluid density ratio, of the ambient fluid density, and of PTKE. A detailed analysis of the local and time-wise evolution of the added mass is presented through quantification of convection, added mass source and velocity-difference contributions. A quantitative assessment of the PTKE equation shows that while production is mostly effective at the crater base and walls, the dissipation and source term, both of which are also effective in the ejecta, nearly balance each other. The influence of the PTKE is mostly observed in the dilute particle regions (soil/gas interface and ejecta), with no effect on the macroscopic length scales of the flow. Both the jet-to-ambient fluid density ratio, of the ambient fluid density affect the macroscopic crater features through entrainment into the jet, determined by the former, and through the density of the fluid entrained, determined by the latter. This complex interaction governs the evolution of the crater diameter, visible top-view depth, and lower depth of the compacted region.

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", "doi": "10.1016/j.ijmultiphaseflow.2024.104902", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "2024-06-25", "pages": "104902" }, { "id": "authors:g1ndv-4fk23", "collection": "authors", "collection_id": "g1ndv-4fk23", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221219-416589000.2", "type": "article", "title": "Effects of thermophoresis on high-pressure binary-species boundary layers with uniform and non-uniform compositions", "author": [ { "family_name": "Toki", "given_name": "Takahiko", "orcid": "0000-0002-3408-0681", "clpid": "Toki-Takahiko" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations of high-pressure binary-species temporal boundary layers are performed to investigate the flow physics for three situations: (1) uniform and equal composition, (2) uniform but unequal compositions and (3) non-uniform composition. Both colder- and hotter-wall situations compared with the free stream are simulated. The working fluid is a nitrogen/methane mixture. The analysis is performed at a case-specific self-similar state. Even when the initial composition is uniform, the methane mean mass fraction decreases near the colder wall, whereas it increases near the hotter wall and the mass fraction fluctuates in the entire boundary layer. Analysis of the species-mass diffusion balance and flow structures reveal that both mass-fraction variation and fluctuations are induced by the Soret effect. When the initial composition is non-uniform and the wall is colder, the methane mean mass fraction monotonically increases from the wall akin to its initial profile. However, when the wall is hotter the mean mass fraction decreases near the wall in contrast to its initial profile, a fact traced through the species-mass diffusion balance to the Soret effect being large and enriching methane near the wall. In contrast, the direction of the Soret flux is opposite for the colder wall, thus keeping the methane concentration small. Although the initial magnitude of the difference between the wall and free-stream temperature is the same in all cases, the situation is not symmetric between colder- and hotter-wall cases; the flow structure exhibits much smaller scales when the wall is hotter than when the wall is colder.", "doi": "10.1017/jfm.2022.923", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2022-12-10", "volume": "952", "pages": "Art. No. A37" }, { "id": "authors:tcatq-gss94", "collection": "authors", "collection_id": "tcatq-gss94", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210927-225706581", "type": "article", "title": "Turbulent chemical-species mixing in the Venus lower atmosphere at different altitudes: A Direct Numerical Simulation study relevant to understanding species spatial distribution", "author": [ { "family_name": "Morellina", "given_name": "Stefano", "clpid": "Morellina-Stefano" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "To evaluate a recent hypothesis of species stratification in the Venus lower atmosphere, a time-dependent, three-dimensional model is proposed for studying turbulent mixing of many species in the Venus lower atmosphere. This model is based on fundamental physics embedding non-equilibrium thermodynamics, the Onsager classical relationship between fluxes and forces, high-pressure transport property calculation and a real-gas equation of state. The conservation equations are self-contained, with no need for coefficients based on parametrizations to match Venus observations. The rationale for solving these equations in relatively small spatial domains at different altitudes in the Venus lower atmosphere is presented. The equations are solved in a temporal mixing layer configuration that is eminently suited to investigate turbulent mixing between two streams of different composition. The adopted simulation method is Direct Numerical Simulation (DNS). A substantial database of DNS realizations is generated for mixtures of two and seven species, with different levels of initial stratification, and at the realistic conditions of pressures and temperatures in the Venus lower atmosphere at three altitudes. High density-gradient magnitude regions (HDGM) are shown to form under initial high stratification conditions, with larger gradient values obtained at low altitudes where supercritical conditions occur. Independent of the altitude lower than 50 km, under low stratification conditions, mixing produces a more uniform spatial distribution of the density than at higher initial stratification. Under low initial stratification conditions, the influence of the minor species on the global behavior of the flow seems to be negligible. At high initial stratification conditions, differences in diffusion of various species play an important role in determining the mixture characteristics. The hypothesis of chemical species separation is discussed in the light of the present results which do not support the existence of stable species separation in the lower Venus atmosphere, independent of the number of species or the altitude.", "doi": "10.1016/j.icarus.2021.114686", "issn": "0019-1035", "publisher": "Elsevier", "publication": "Icarus", "publication_date": "2022-01-01", "volume": "371", "pages": "Art. No. 114686" }, { "id": "authors:ayj57-ytr29", "collection": "authors", "collection_id": "ayj57-ytr29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211123-202139721", "type": "article", "title": "Investigation of species-mass diffusion in binary-species boundary layers at high pressure using direct numerical simulations", "author": [ { "family_name": "Toki", "given_name": "Takahiko", "orcid": "0000-0002-3408-0681", "clpid": "Toki-Takahiko" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations of single-species and binary-species temporal boundary layers at high pressure are performed with special attention to species-mass diffusion. The working fluids are nitrogen or a mixture of nitrogen and methane. Mean profiles and turbulent fluctuations of mass fraction show that their qualitative characteristics are different from those of streamwise velocity and temperature, due to the different boundary conditions. In a wall-parallel plane near the wall, the streamwise velocity and temperature have streaky patterns and the fields are similar. However, the mass fraction field at the same location is different from the streamwise velocity and temperature fields indicating that species-mass diffusion is not similar to the momentum and thermal diffusion. In contrast, at the centre and near the edge of the boundary layer, the mass fraction and temperature fields have almost the same pattern, indicating that the similarity between thermal and species-mass diffusion holds away from the wall. The lack of similarity near the wall is traced to the Soret effect that induces a temperature-gradient-dependent species-mass flux. As a result, a new phenomenon has been identified for a non-isothermal binary-species system \u2013 uphill diffusion, which in its classical isothermal definition can only occur for three or more species. A quadrant analysis for the turbulent mass flux reveals that near the wall the Soret effect enhances the negative contributions of the quadrants. Due to the enhancement of the negative contributions, small species-concentration fluid tends to be trapped near the wall.", "doi": "10.1017/jfm.2021.814", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2021-12-10", "volume": "928", "pages": "Art. No. A18" }, { "id": "authors:5wkez-5vq18", "collection": "authors", "collection_id": "5wkez-5vq18", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201027-074230260", "type": "article", "title": "Investigation of high-pressure turbulent jets using direct numerical simulation", "author": [ { "family_name": "Sharan", "given_name": "Nek", "orcid": "0000-0002-7274-8232", "clpid": "Sharan-Nek" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations of free round jets at a Reynolds number (Re_D) of 5000, based on jet diameter (D) and jet-exit bulk velocity (U_e), are performed to study jet turbulence characteristics at supercritical pressures. The jet consists of nitrogen (N\u2082) that is injected into N\u2082 at the same temperature. To understand turbulent mixing, a passive scalar is transported with the flow at unity Schmidt number. Two sets of inflow conditions that model jets issuing from either a smooth contraction nozzle (laminar inflow) or a long pipe nozzle (turbulent inflow) are considered. By changing one parameter at a time, the simulations examine the jet-flow sensitivity to the thermodynamic condition (characterized in terms of the compressibility factor (Z) and the normalized isothermal compressibility), inflow condition and ambient pressure (p\u221e) spanning perfect- to real-gas conditions. The inflow affects flow statistics in the near field (containing the potential core closure and the transition region) as well as further downstream (containing fully developed flow with self-similar statistics) at both atmospheric and supercritical p\u221e. The sensitivity to inflow is larger in the transition region, where the laminar-inflow jets exhibit dominant coherent structures that produce higher mean strain rates and higher turbulent kinetic energy than in turbulent-inflow jets. Decreasing Z at a fixed supercritical p\u221e enhances pressure and density fluctuations (non-dimensionalized by local mean pressure and density, respectively), but the effect on velocity fluctuations depends also on the local flow dynamics. When Z is reduced, large mean strain rates in the transition region of laminar-inflow jets significantly enhance velocity fluctuations (non-dimensionalized by local mean velocity) and scalar mixing, whereas the effects are minimal in jets from turbulent inflow.", "doi": "10.1017/jfm.2021.524", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2021-09-10", "volume": "922", "pages": "Art. No. A24" }, { "id": "authors:ws84b-3qf64", "collection": "authors", "collection_id": "ws84b-3qf64", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210414-125248593", "type": "article", "title": "Fluid density effects in supersonic jet-induced cratering in a granular bed on a planetary body having an atmosphere in the continuum regime", "author": [ { "family_name": "Balakrishnan", "given_name": "Kaushik", "clpid": "Balakrishnan-Kaushik" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "To investigate the effect of atmospheric density and jet-fluid density during supersonic jet-induced cratering on a granular particle bed, large eddy simulation (LES) for the fluid phase coupled with a granular flow model based on kinetic theory is used. Coupling accounts for momentum and energy interaction between particles and fluid. Several simulations are conducted that enable discriminating between the crater characteristics which depend on the atmospheric (or jet) density, and those which depend on the ratio between jet-fluid density and atmospheric density. The crater cross-sectional shapes are controlled by the density ratio between jet fluid and atmosphere. For large such ratios, the craters have a parabolic cross-section shape, are relatively shallow, have large diameters and have subdued ejecta. In contrast, for ratios close to unity, the craters have a conical cross-section, are relatively deep, have relatively small diameters and have substantial ejecta; these craters also display ripples on their walls. The physics leading to these differences is explained. Considerations of particle momentum flux indicate that at same fraction of the crater depth and same radial distance from the jet axis, the radial and vertical components have larger magnitudes for conical craters than for parabolic craters. The spatial distribution of the ratio between the drag force and the force due to the particles resistance to compaction are compared and it is found to be dependent on the jet-to-atmospheric fluid density ratio. A few features of the crater, in particular its depth, only depend on the atmospheric (or jet) fluid density.", "doi": "10.1017/jfm.2021.29", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2021-05-25", "volume": "915", "pages": "Art. No. A29" }, { "id": "authors:132v5-w9v66", "collection": "authors", "collection_id": "132v5-w9v66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-122714899", "type": "article", "title": "Twenty-species and 15-species chemical kinetic mechanisms for cyclohexane using the local self-similarity tabulation method", "author": [ { "family_name": "Kourdis", "given_name": "Panayotis D.", "clpid": "Kourdis-P-D" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The 1081 species cyclohexane\u2010oxidation elementary reaction mechanism of Silke et al. (DOI:10.1021/jp067592d) is reduced in the number of species by a O(10\u00b2) factor using the local self\u2010similarity tabulation (LS2T) method. Reduced\u2010species mechanisms of both 20 (R20) and 15 (R15) species are created in the high\u2010pressure combustion regime typical of diesel engines. To evaluate the performance of R20 and R15 against the elementary kinetics, simulations are performed for cyclohexane/air mixtures at initial temperatures of 1150, 900, 750, and 680 K and constant pressures of 20 and 40 bar for a variety of equivalence ratios \u03a6 (\u03a6 = 0.5, 1.0, and 2 for 1150 and 900 K; \u03a6 = 1 for 750 K; \u03a6 = 0.5 for 680 K). Very good agreement between R20 and R15 with the elementary kinetics mechanism is demonstrated at 1150 and 900 K for which the self\u2010similarity is very well obeyed; however, only fair agreement is obtained at 750 and 680 K, a fact which is traced to the less faithful adherence to the self\u2010similarity due to the one order of magnitude increase in ignition time over the range 750\u2010680 K. These results are found to be quasi\u2010independent of the tabulation grid. Future work is proposed to improve the reduction in the cold\u2010ignition, high\u2010pressure regime.", "doi": "10.1002/kin.21368", "issn": "0538-8066", "publisher": "Wiley", "publication": "International Journal of Chemical Kinetics", "publication_date": "2020-08", "series_number": "8", "volume": "52", "issue": "8", "pages": "526-547" }, { "id": "authors:j2gs7-bep42", "collection": "authors", "collection_id": "j2gs7-bep42", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200420-153316450", "type": "article", "title": "A priori evaluation of the Double-conditioned Conditional Source-term Estimation model for high-pressure heptane turbulent combustion using DNS data obtained with one-step chemistry", "author": [ { "family_name": "Bushe", "given_name": "W. Kendal", "clpid": "Bushe-W-K" }, { "family_name": "Devaud", "given_name": "Cecile", "clpid": "Devaud-C" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "An evaluation of the submodels constituting the Double-Conditioned Source-term Estimation (DCSE) method for utilization in Large Eddy Simulation (LES) is presented which makes use of a single realization of a turbulent high-pressure reactive-flow database obtained from Direct Numerical Simulation (DNS). A filtered and coarsened DNS (FCDNS) field is first created to mimic a real LES field, and the FCDNS values for thermodynamic variables (temperature, density and species mass fractions) are used as inputs to the DCSE model to predict the FCDNS reaction rates. It is found that there are significant errors in the predictions of the filtered reaction rate compared to the template. These errors are attributed to three important aspects of the model. First, the conditional-filtered values of the thermodynamic variables are found by an inversion of an integral equation, but this inversion requires the definition of spatial ensembles in which it must be performed; these ensembles are a subset of the entire spatial domain containing the LES volumes. A drastic reduction in the number of ensembles from the number of LES volumes (i.e. the largest possible number of such ensembles) deteriorates the model, whereas a further and smaller such reduction has a small effect. Second, the procedure for the integral inversion introduces problems related to the method selected to regularize the inversion. Third, by far the largest source of error was found to be due to the modelling of the joint probability density function of the conditioning variables: assuming a \u03b2-PDF for the marginal PDF of the reaction progress variable is shown to be a particularly poor choice, as is the assumption that the conditioning variables are statistically independent.", "doi": "10.1016/j.combustflame.2020.03.015", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2020-07", "volume": "217", "pages": "131-151" }, { "id": "authors:js9b8-0qn17", "collection": "authors", "collection_id": "js9b8-0qn17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191127-092423364", "type": "article", "title": "An experimental study of the mixing of CO\u2082 and N\u2082 under conditions found at the surface of Venus", "author": [ { "family_name": "Lebonnois", "given_name": "S\u00e9bastien", "clpid": "Lebonnois-S" }, { "family_name": "Schubert", "given_name": "Gerald", "clpid": "Schubert-G" }, { "family_name": "Kremic", "given_name": "Tibor", "clpid": "Kremic-T" }, { "family_name": "Nakley", "given_name": "Leah M.", "clpid": "Nakley-L-M" }, { "family_name": "Phillips", "given_name": "Kyle G.", "clpid": "Phillips-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Cordier", "given_name": "Daniel", "clpid": "Cordier-D" } ], "abstract": "Based on the only reliable temperature profile available in the deepest \u223c10 km layer above Venus' surface (obtained by the VeGa-2 landing probe), the mixing conditions of the main constituents of Venus's atmosphere, CO\u2082 and N\u2082, have been questioned. In this work, we report the results of a series of experiments that were done in the GEER facility at Glenn Research Center to investigate the homogeneity of CO\u2082/N\u2082 gas mixtures at 100 bars and temperatures ranging from \u223c296 K to \u223c735 K. When the gas mixtures are initially well-mixed, separation of the two gases based on their molecular mass does not occur over the time scales observed; although, small systematic variations in composition remain to be fully interpreted. However, when N\u2082 is injected on top of CO\u2082 (layered fill), the very large density ratio makes it more difficult to mix the two chemical species. Timescales of mixing are of the order of 10\u00b2 hours over the height of the test vessel (roughly 60 cm), and even longer when the gas mixture is at rest and only molecular diffusion is occurring. At room temperature, close to the critical point of the mixture, large pressure variations are obtained for the layered fill, as N\u2082 slowly mixes into CO\u2082. This can be explained by large density variations induced by the mixing. For conditions relevant to the near-surface atmosphere of Venus, separation of CO\u2082 and N\u2082 based on their molecular mass and due to physical properties of the gas mixture is not demonstrated, but can not be firmly excluded either. This suggests that if the compositional vertical gradient deduced from the VeGa-2 temperature profile is to be trusted, it would most probably be due to some extrinsic processes (not related to gas properties, e.g. CO\u2082 volcanic inputs) and large mixing time constants.", "doi": "10.1016/j.icarus.2019.113550", "issn": "0019-1035", "publisher": "Elsevier", "publication": "Icarus", "publication_date": "2020-03-01", "volume": "338", "pages": "Art. No. 113550" }, { "id": "authors:tjy96-tth32", "collection": "authors", "collection_id": "tjy96-tth32", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200225-073358187", "type": "article", "title": "Future Challenges in the Modelling and Simulations of High-pressure Flows", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The study of high-pressure turbulent combustion is a relatively new field in the realm of combustion studies. The coupling between the conservation equations and the equation of state is examined here in order to highlight the existing challenges in performing accurate numerical simulations at high-pressure conditions. The multi-species mass fluxes and the heat flux contained in the conservation equations are those derived from fundamental physics and incorporate transport properties computed using models valid at high-pressure situations. The intricacies in evaluating results obtained from the corresponding simulations with experimental data are addressed. The numerical approaches that stem from either lack of experimental initial condition information or from differences between the experimental configuration versus the simulation configuration are discussed. Experimental difficulties are also addressed, particularly those related to obtaining meaningful data to discriminate between high-pressure models and atmospheric-pressure models.", "doi": "10.1080/00102202.2020.1719404", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "2020-02-17", "series_number": "7", "volume": "192", "issue": "7", "pages": "1199-1218" }, { "id": "authors:hcbev-mxg06", "collection": "authors", "collection_id": "hcbev-mxg06", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190612-082812671", "type": "article", "title": "The modeling of the turbulent reaction rate under high-pressure conditions: A priori evaluation of the Conditional Source-term Estimation concept", "author": [ { "family_name": "Devaud", "given_name": "Cecile", "clpid": "Devaud-C" }, { "family_name": "Bushe", "given_name": "W. Kendal", "clpid": "Bushe-W-K" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "With the goal of obtaining an accurate model of the turbulent reaction rate for Large Eddy Simulations (LESs), the modeling of turbulence-chemistry-thermodynamic interaction is addressed through an a priori study of a Direct Numerical Simulation (DNS) database representing high-pressure turbulent combustion. The DNS database consists of simulations of a temporal mixing layer in which a single-step chemical reaction occurs. The potential of the single-conditioned Conditional Source-term Estimation (CSE) approach to model the filtered turbulent reaction rate needed for conducting LES is examined. Evaluations conducted with the mixture fraction as a conditioning variable at two filter widths and with the probability density function (PDF) extracted from the DNS database that represents the mixture fraction, show that the deviation between the model and template is large and substantially increases with filter width. To address this deviation, the Double-conditioned CSE (DCSE) approach is explored with two different second conditioning variables, the first conditioning variable still being the mixture fraction; four filter widths are considered. The first choice of the second conditioning variable is a normalized progress variable based on the CO2 mass fraction and the second choice of the second conditioning variable is a normalized temperature. With each second conditional variable, the DCSE results represent a substantial improvement over CSE, by as much as an order of magnitude when measured by the relative error from the DNS-extracted filtered reaction rate. A quantitative test based on a root mean square identifies the reason for the DCSE success compared to CSE: unlike in CSE, the DCSE is able to substantially reduce the fluctuations of the modeled reaction rate from the filtered reaction rate over the entire range of the filtered reaction rate values, and particularly at the larger reaction rate values for which the DCSE model has higher fidelity. The results are shown to be equally favorable for the two conditioning variables. Consideration of DNS realizations at higher free-stream pressure or larger Reynolds number shows that the results are essentially equally successful at other pressure or Reynolds number values.", "doi": "10.1016/j.combustflame.2019.05.037", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2019-09", "volume": "207", "pages": "205-221" }, { "id": "authors:be0ky-kc682", "collection": "authors", "collection_id": "be0ky-kc682", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190610-095426554", "type": "article", "title": "A Multi-Species Modeling Framework for Describing Supersonic-Jet Induced Cratering in a Granular Bed: Cratering on Titan Case Study", "author": [ { "family_name": "Balakrishnan", "given_name": "Kaushik", "clpid": "Balakrishnan-K" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The dynamics of cratering caused by a multi-component supersonic jet due to its interaction with the granular soil on the surface of Titan is investigated using a two-phase model and numerical simulations. Both fluid and particles are mathematically described in an Eulerian framework. The fluid is modeled using multi-species Large Eddy Simulation accounting for the details of diffusion among species, and the solid phase is described by a Kinetic-Theory-based model. The general framework is that of a recent model that successfully predicted specific details of Mars/Earth cratering observed by the Mars Science Laboratory (Balakrishnan and Bellan, International Journal of Multiphase Flow, 99, 1\u201329, 2018), however the distinctive differences between the present and previous model allows new physics to be uncovered that is peculiar to cratering in the presence of a dense atmosphere. Unsteady, three-dimensional simulations are performed to elucidate the morphological features of the crater and the dynamics of its evolution with time. Parametric variations of the initial conditions are conducted to understand the effect of the surface evenness, jet Mach number, particle size in the granular bed, jet composition, and the inter-granular stress coefficient. The new observation of crater-in-a-crater formation at early times is discussed and explained; this phenomenon is transient and the subsequent consumption of the inner crater by the surrounding crater walls is explained in detail. The jet exhibits complex morphological features revealed by vorticity and helicity analysis. The primary-crater walls display ripples along their surface that are traced to the interaction with the dense jet fluid which, having reached the crater bottom, changes direction to exit the crater using the spaces unoccupied by the jet and rubs the crater walls. Detailed analyses of the particle volume fraction and the particle momentum revealed the detailed morphology of the craters and the ejections from the craters, and related them to the initial conditions. A larger jet Mach number results in increased erosion due to the higher momentum content of the jet. A smaller increase in the jet momentum obtained by increasing the jet-fluid molar mass jet results in a crater that is more angled at the top, this feature being due to the increased jet expansion rate. The inter-granular stress coefficient does not affect the large-scale features of the crater, but does affect the peak compaction values. Species diffusion is investigated and it is found that both regular and uphill diffusion occur, the latter being primarily concentrated in the vicinity of the jet and the depths of the crater. The presented detailed formulation and numerical methodology for investigating supersonic jet-induced cratering on granular soil are sufficiently robust to accommodate plume-induced cratering on a variety of planetary bodies having an atmosphere.", "doi": "10.1016/j.ijmultiphaseflow.2019.05.011", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "2019-09", "volume": "118", "pages": "205-241" }, { "id": "authors:q8vpr-6xn24", "collection": "authors", "collection_id": "q8vpr-6xn24", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190228-150106232", "type": "article", "title": "The influence of the chemical composition representation according to the number of species during mixing in high-pressure turbulent flows", "author": [ { "family_name": "Sciacovelli", "given_name": "Luca", "orcid": "0000-0002-2463-4193", "clpid": "Sciacovelli-L" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Mixing of several species in high-pressure (high-p) turbulent flows is investigated to understand the influence of the number of species on the flow characteristics. Direct numerical simulations are conducted in the temporal mixing layer configuration at approximately the same value of the momentum ratio for all realizations. The simulations are performed with mixtures of two, three, five and seven species to address various compositions at fixed number of species, at three values of initial vorticity-thickness-based Reynolds number, Re_0, and two values of the free-stream pressure, p_0, which is supercritical for each species except water. The major species are C_7H_(16), O_2 and N_2, and the minor species are CO, CO_2, H_2 and H_2O. The extensive database thus obtained allows the study of the influence not only of Re_0 and p_0, but also of the initial density ratio and of the initial density difference between streams, \u0394\u03c1. The results show that the layer growth is practically insensitive to all of the above parameters; however, global vortical aspects increase with Re_0, p_0 and the number of species; nevertheless, at the same Re_0, p_0 and density ratio, vorticity aspects are not influenced by the number of species. Species mixing produces strong density gradients which increase with p_0 and otherwise scale with \u0394\u03c1 but, when scaled by \u0394\u03c1, are not affected by the number of species. Generalized Korteweg-type equations are developed for a multi-species mixture, and a priori estimates based on the largest density gradient show that the Korteweg stresses, which account for the influence of the density gradient, have negligible contribution in the momentum equation. The species-specific effective Schmidt number, Sc_(\u03b1,eff), is computed and it is found that negative values occur for all minor species \u2013 particularly for H_2 \u2013 thus indicating uphill diffusion, while the major species experience only regular diffusion. The probability density function (p.d.f.) of Sc_(\u03b1,eff) shows strong variation with p_0 but weak dependence on the number of species; however, the p.d.f. substantially varies with the identity of the species. In contrast, the p.d.f. of the effective Prandtl number indicates dependence on both p_0 and the number of species. Similar to Sc_(\u03b1,eff), the species-specific effective Lewis-number p.d.f. depends on the species, and for all species the mean is smaller than unity, thus invalidating one of the most popular assumptions in combustion modelling. Simplifying the mixture composition by reducing the number of minor species does not affect the crucial species\u2013temperature relationship of the major species that, for accuracy, must be retained in combustion simulations, but this relationship is affected for the minor species and in regions of uphill diffusion, indicating that the reduction is nonlinear in nature.", "doi": "10.1017/jfm.2018.992", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2019-03-25", "volume": "863", "pages": "293-340" }, { "id": "authors:rf4qc-s8p17", "collection": "authors", "collection_id": "rf4qc-s8p17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180426-101117147", "type": "article", "title": "Side-jet effects in high-pressure turbulent flows: Direct Numerical Simulation of nitrogen injected into carbon dioxide", "author": [ { "family_name": "Gnanaskandan", "given_name": "Aswin", "clpid": "Gnanaskandan-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct Numerical Simulation realizations were generated of a round jet under high-pressure (high-p) turbulent conditions. In the simulations, a jet of nitrogen was injected into a chamber filled with carbon dioxide for three different jet-to-chamber density ratio, s, and three different chamber pressures, pch,0. The results show that for s = 0.5 and 0.35 side jets form whereas no side jets are observed for s = 1 ; thus providing, for the first time, evidence of side jet formation in high-p flows. Due to these side jets, mixing of the jet fluid and chamber fluid is promoted; although the species experience regular diffusional mixing, it is shown that due to turbulent conditions there can be effective uphill thermal conduction. Analysis of the vortical features of the side jets elucidated the process through which the enhanced mixing occurs: fluid from the jet is effectively pumped in the radial direction though the combined action of dilatation/compression and vortex stretching/shrinking. The value of s is shown to control radial and circumferential mixing versus axial mixing which occurs through jet penetration in the flow. Examination of dynamic and thermodynamic quantities indicates that side jets also promote flow unsteadiness. The pressure in the chamber is demonstrated to have negligible effect on the side jets.", "doi": "10.1016/j.supflu.2018.04.015", "issn": "0896-8446", "publisher": "Elsevier", "publication": "Journal of Supercritical Fluids", "publication_date": "2018-10", "volume": "140", "pages": "165-181" }, { "id": "authors:p6q6p-55837", "collection": "authors", "collection_id": "p6q6p-55837", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180418-103622369", "type": "article", "title": "On models for predicting thermodynamic regimes in high-pressure turbulent mixing and combustion of multispecies mixtures", "author": [ { "family_name": "Castiglioni", "given_name": "Giacomo", "orcid": "0000-0003-0278-6951", "clpid": "Castiglioni-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The thermodynamic regime of a complex mixture depends on the composition, the pressure and the temperature; the spinodal locus separates the regime of thermodynamic instability from the remainder of the phase space. Since diffusion is one of the phenomena affecting the local chemical composition, the first focus is here on evaluating diffusion models in the context of high-pressure (high-p) multispecies mixing and combustion. It is shown that the diffusion model equations previously used to create two high-p direct numerical simulation (DNS) databases can reproduce classical experimental observations of uphill diffusion in an accurate spatiotemporal manner, whereas the popular model which has a diagonal diffusion matrix and uses a velocity correction lacks spatiotemporal accuracy. Further, a mathematical formalism is used to compute the spinodal locus for mixtures for which either experimental data or previous computations from the literature are available, and it is shown that the agreement of the present calculations with that previously existing information is excellent. Using the spinodal-calculation mathematical formalism, the aforementioned DNS databases are then examined to determine the thermodynamic regime of the mixture at important stages of the simulations. In the first subset of the DNS databases that portrays mixing of five species under high-p conditions, this stage is that of the transitional state representing the individual time station at which each simulation, having been initiated in a laminar state, transitions to a state having turbulent characteristics. In the second subset of the DNS databases that portrays high-p turbulent combustion, this stage represents the individual time station at the peak achieved during the calculations. In both databases, the influence of the initial Reynolds number, the free-stream composition and the free-stream p is studied. The results show that in all cases the mixture is in the single-phase regime. The present DNS databases have only five species, but it is shown that the methodology for computing the spinodal locus can be applied to very complex mixtures, with examples given for a twelve-species mixture and surrogate diesel fuels, thereby boding well for determining the thermodynamic regime of practical mixtures in high-p turbulent flow simulations for engineering applications. According to these calculations, diesel-fuel surrogates are always in the single-phase regime at injection-conditions p and temperatures existing in diesel-engine combustion chambers.", "doi": "10.1017/jfm.2018.159", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2018-05-25", "volume": "843", "pages": "536-574" }, { "id": "authors:5mbxw-0v724", "collection": "authors", "collection_id": "5mbxw-0v724", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-092336757", "type": "article", "title": "High-Fidelity Modeling and Numerical Simulation of Cratering Induced by the Interaction of a Supersonic Jet with a Granular Bed of Solid Particles", "author": [ { "family_name": "Balakrishnan", "given_name": "Kaushik", "clpid": "Balakrishnan-K" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The dynamics of cratering caused by a supersonic jet on a granular bed of solid particles is investigated using a high fidelity, two-phase model and numerical simulations. To model the gas phase, the Large Eddy Simulation (LES) approach is used and a kinetic theory-based model is employed for the solid phase. Three-dimensional time-dependent simulations are conducted for the purpose of elucidating the morphological features of the crater and their evolution with time. Parametric variations of the initial conditions are performed to understand the effect of the initial solid volume fraction in the bed, of the coefficient of restitution, of the jet Mach number, of the particle diameter, and of the particle material density. The simulation snapshots of the cratering are in qualitative agreement with the images from the Mars Science Laboratory (MSL) mission and from Earth-based experiments. Analysis of the results shows that solid particle compaction at the crater base and side walls increases with increasing volume fraction of the undisturbed particle bed and reaches solid volume fractions close to 0.65. The coefficient of restitution is shown to have no effect on the large scale dynamics of the crater but affects the small scale features, particularly the shape of elongated bursts of solid particle clouds as well as radially aligned structures on the outer crater walls. A smaller jet Mach number results in a smaller crater characterized by ridge-like structures and walls at an angle of approximately 45 degrees with respect to the undisturbed bed whereas larger Mach number jets create craters with walls approximately perpendicular to the undisturbed bed. A smaller particle size and a lighter particle material density also result in wider and deeper craters. The formation of all morphological structures is explained in detail and is related to the physical phenomena from which they originate. Power law curve fits are also presented for the crater outer diameter as well as for the depth. The mean and rms profiles of the solid volume fraction are computed, and it is found that the peak rms in the solid volume fraction does not occur at the surface but rather in the depth of the crater. In addition, the mean and rms of the particle momentum flux are also computed and discussed. Furthermore, the sources of particle momentum are evaluated, and the viscous drag as well as the gas pressure gradient are observed to be the prominent terms. The results show that the model developed is robust and is able to simulate craters due to a range of external conditions operating over particle beds having different characteristics.", "doi": "10.1016/j.ijmultiphaseflow.2017.08.008", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "2018-02", "volume": "99", "pages": "1-29" }, { "id": "authors:kfr63-mbc53", "collection": "authors", "collection_id": "kfr63-mbc53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170710-080451483", "type": "article", "title": "From elementary kinetics in perfectly stirred reactors to reduced kinetics utilizable in turbulent reactive flow simulations for combustion devices", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "This study addresses the protocol of tests for evaluating the performance of skeletal, reduced and highly-reduced chemical kinetics mechanisms for one-dimensional (1D) laminar flame simulations and the validity of these tests for turbulent flame applications. Taking n-heptane as an example fuel, it is first shown that there are apparent disagreements regarding the elementary-reaction chemical kinetics models which should be emulated by reduced kinetic mechanisms. Further it is also shown, expectably, that the functional relationship between mass fractions and temperature is different between 0D and 1D models, and it is different among 1D models having different molecular species-transport formulations. Having identified the retention of this functional relationship as pivotal in the success of highly-reduced reaction mechanisms to accurately simulate spatial configurations, it is demonstrated that the unity Lewis-number assumption biases this functional relationship such that the highly-reduced chemical kinetic mechanism LS2T 20-species mechanism (LS2T 20) used for 1D flame simulations fails to agree with the template but provides accurate predictions in conjunction with, for example, the mixture-average diffusion model at otherwise the same initial conditions as the unity-Lewis-number simulation. The LS2T 20 success extends to the cold-ignition regime. For rich conditions the mixture-average diffusion approximation is less acceptable, and if the transport model does not include the direct effect of the heavy species (which are all modeled in LS2T) on the light species (which are all computed in LS2T), moderate departures of the 1D predictions from the template are obtained around the peak OH mass fraction, whereas CO_2 is still excellently reproduced by LS2T 20. It is then conjectured that, independent of the reduction method, the more reduced is a kinetic mechanism, the more accurate the transport formulation should be to ensure the preservation of the species/temperature functional relationship; due to the extensive investigation necessary to evaluate this conjecture, this activity is relegated to future studies.", "doi": "10.1016/j.combustflame.2017.06.013", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2017-10", "volume": "184", "pages": "286-296" }, { "id": "authors:bv3nz-exy71", "collection": "authors", "collection_id": "bv3nz-exy71", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170306-110211350", "type": "article", "title": "Evaluation of mixture-fraction-based turbulent-reaction-rate model assumptions for high-pressure reactive flows", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Several assumptions of atmospheric-pressure (atmospheric-p) single-phase turbulent reaction rate models are examined for high-p reactive flows having turbulent characteristics. The study uses a Direct Numerical Simulation (DNS) database described elsewhere (Bellan, 2017). This database was obtained with a model combining multi-species mixing under high-p conditions, a real-gas equation of state (EOS) and a single-step chemical reaction. The database, created in the configuration of a temporal mixing layer, probes the effect of the initial Reynolds number, Re_0, of the initial pressure, p_0, and of the initial composition of the two mixing-layer streams. The reaction is initiated in a turbulent flow and in each simulation the computations are pursued past a time when a maximum average-volumetric p is attained, ^(t*)pp. The examination of the vorticity and enstrophy equations at a time before reaction initiation and also at ^(t*)pp highlights the pivotal role of the high density-gradient magnitude regions (Bellan, 2017) in producing turbulence and the crucial role at ^(t*)pp of the baroclinic effect representing the misalignments of gradients of thermodynamic variables. Compared to the classical mixture fraction equation, the results show that the mixture fraction obeys an equation in which there is an additional diffusion term having a larger r.m.s. magnitude than that of the mixture-fraction typical diffusion term. An assessment of the Conditional Source-term Estimation (CSE) model assumptions found that, using an accurate mixture fraction probability density function (PDF), one can obtain a very good representation of the turbulent reaction rate in the most intense reaction regions, however the quality of the predictions of CSE deteriorated significantly when a common model for the PDF, the \u03b2-PDF, was used despite the \u03b2-PDF being constructed with the accurate moments extracted from the DNS. In the regions of minimal reaction, the CSE model using the exact PDF extracted from the DNS does not provide an accurate representation of the turbulent reaction rate, a fact which is attributed to the combined effect of lack of correlation between fluctuations of the reaction rate and of the mixture fraction, and to the strong correlation of the thermodynamic variables through the real-gas EOS in regions of colder and denser fluid.", "doi": "10.1016/j.combustflame.2017.02.004", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2017-05", "volume": "179", "pages": "253-266" }, { "id": "authors:z76ce-anc48", "collection": "authors", "collection_id": "z76ce-anc48", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170407-124745831", "type": "article", "title": "Numerical Simulation of Jet Injection and Species Mixing under High-Pressure Conditions", "author": [ { "family_name": "Gnanaskandan", "given_name": "Aswin", "clpid": "Gnanaskandan-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are performed of a round fluid jet entering a high-pressure chamber. The chemical compositions and temperatures of the jet and that of the fluid in the chamber are initially prescribed. The governing equations consist of the conservation equations for mass, momentum, species and energy, and are complemented by a real-gas equation of state. The fluxes of species and heat are written in the framework of fluctuation-dissipation theory and include Soret and Dufour effects. For more than two species, the full mass diffusion and thermal diffusion matrices are computed using high-pressure mixing rules which utilize as building blocks the corresponding binary diffusion coefficients. The mixture viscosity and thermal conductivity are computed using standard mixing rules and corresponding states theory. To evaluate the physical model and numerical method, LES is employed first to simulate a supercritical N_2 jet injected into N_2. Time averaged results show reasonable agreement with the experimental data. Then, DNS is conducted to study the spatial evolution of a supercritical N_2 jet injected into CO_2. Time averaged results are used to compute the length of the potential core and the species diffusion characteristics. Spectral analysis is then applied on a time series data obtained at several axial locations and a dominant frequency is observed inside the potential core.", "doi": "10.1088/1742-6596/821/1/012020", "issn": "1742-6588", "publisher": "IOP Publishing", "publication": "Journal of Physics: Conference Series", "publication_date": "2017-04-07", "volume": "821", "pages": "Art. No. 012020" }, { "id": "authors:qwag5-ark63", "collection": "authors", "collection_id": "qwag5-ark63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170407-132631621", "type": "article", "title": "Direct numerical simulation of a high-pressure turbulent reacting temporal mixing layer", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct Numerical Simulation realizations were created of a temporal mixing layer in which combustion occurs under high-pressure (high-p) turbulent conditions. The model combines the formulation of Masi, et al. (2013) for describing multi-species mixing under high-p conditions and a single-step chemical reaction of rate consistent with ignition prediction (Borghesi, and Bellan, 2015). In each simulation the computations are pursued past a time at which a maximum average-volumetric p is attained; most analysis is performed at this time, t^*_(pp). The ensemble of realizations explores the effect of the initial Reynolds number, Re_0, of the initial pressure, p_0, and of the initial composition of the two mixing-layer streams. The results show that the thermodynamic energy added by the reaction at the small scales is partially dissipated and partially backscattered. The formation of turbulent small scales is initiated by the morphological changes in the flow through stretching and twisting rather than vice versa. The reaction establishes primarily in the oxidizer stream and is preponderantly of diffusion type. Overwhelmingly, the higher reaction rates occur in the diffusion flame, particularly in regions of high density-gradient magnitude. At higher p_0 the reaction rate reaches higher values and occurs in regions of higher density gradients. The range of reaction rates is independent of the Re_0 value but the magnitude of the density gradients increases with Re_0. When H_2O and CO_2 are initially present, uphill diffusion dominates over regular diffusion and occurs in regions of smaller density-gradient magnitude whereas regular diffusion occurs in regions of larger density-gradient magnitude where the reaction is more vigorous. H_2O is more prone than CO_2 to regular diffusion in the larger density-gradient magnitude regions. When H_2O and CO_2 only form in the flame, both H_2O and CO_2 are subject to regular diffusion over the entire range of density-gradient values. The dissipation probability density function is a log normal distribution at large dissipation values.", "doi": "10.1016/j.combustflame.2016.09.026", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2017-02", "volume": "176", "pages": "245-262" }, { "id": "authors:sgjvc-f6968", "collection": "authors", "collection_id": "sgjvc-f6968", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160907-090126651", "type": "article", "title": "Highly Reduced Species Mechanisms for iso-Cetane Using the Local Self-Similarity Tabulation Method", "author": [ { "family_name": "Kourdis", "given_name": "Panayotis D.", "clpid": "Kourdis-P-D" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "We utilize the local self-similarity tabulation method to drastically downsize the number of species involved in a detailed kinetic mechanism of iso-cetane. Reduced-species mechanisms of 20 and 15 species are constructed, out of the 1114 species involved in the detailed mechanism, with a focus on high-pressure combustion. The performance of the two reduced mechanisms are compared to the detailed one for a lean (\u03d5 = 0.5), stoichiometric (\u03d5 = 1.0), and rich (\u03d5 = 1.5) iso-cetane/air mixture at initial temperatures of 900 and 1100 K and constant pressures of 20 and 40 bar. Good to very good agreement between the detailed kinetic mechanism and the two highly reduced species mechanisms are demonstrated.", "doi": "10.1002/kin.21029", "issn": "0538-8066", "publisher": "Wiley", "publication": "International Journal of Chemical Kinetics", "publication_date": "2016-11", "series_number": "11", "volume": "48", "issue": "11", "pages": "739-752" }, { "id": "authors:s30qz-ay684", "collection": "authors", "collection_id": "s30qz-ay684", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-140759946", "type": "article", "title": "Large-Eddy Simulation of Supersonic Round Jets: Effects of Reynolds and Mach Numbers", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Large-eddy simulations of supersonic turbulent jets are performed for Reynolds numbers of Re < 10,000 for the purpose of understanding the effects of Reynolds numbers and the Mach number M. The subgrid terms in large-eddy simulations are modeled using a combination of the dynamic Smagorinsky (\"General Circulation Experiments with the Primitive Equations. Part I, Basic Experiments,\" Monthly Weather Review, Vol. 54, No. 1, 1963, pp. 99\u2013164) and Yoshizawa (\"Statistical Theory for Compressible Turbulent Shear Flows, with the Application to Subgrid Modelling,\" Physics of Fluids, Vol. 54, No. 1, 1986, pp. 2152\u20132164) models. Simulations are performed for supersonic jets having Reynolds numbers of 1500, 3700, and 7900, and Mach numbers of 1.4 and 2.1. Two of the simulations are validated with experimental data. The Reynolds number value is observed to play a role in the transition to turbulence but, once transition is achieved, it has a subdued effect above a threshold value; that is, as seen experimentally for supersonic flows, a similarity is found here. This similarity occurs for Reynolds number values that are relatively small compared to those typical of the fully turbulent regime. The turbulent structures in the transition region are more coherent, and the potential core is longer when the Mach number is larger, which leads to a slower downstream velocity decay. The root-mean-square velocities are biased in the axial direction, as expected. In the fully turbulent regions, the computed Reynolds stress is higher for a larger-Mach-number jet. Peak pressure fluctuations occur at about half a jet diameter, radially away from the centerline of the jet, and this location is independent of both the Reynolds number and Mach number values. The pressure\u2013velocity correlations and the turbulent kinetic energy profiles are investigated along the centerline and radial directions, and it is found that the peak turbulent kinetic energy occurs at the same location as the maximum pressure fluctuations.", "doi": "10.2514/1.J054548", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2016-05", "series_number": "5", "volume": "54", "issue": "5", "pages": "1482-1498" }, { "id": "authors:3wyqv-psz61", "collection": "authors", "collection_id": "3wyqv-psz61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-153408437", "type": "article", "title": "Explicitly-filtered LES for the grid-spacing-independent and discretization-order-independent prediction of a conserved scalar", "author": [ { "family_name": "Radhakrishnan", "given_name": "Senthilkumaran", "clpid": "Radhakrishnan-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The previously proposed methodology of Explicitly Filtered Large Eddy Simulation (EFLES) predicts velocity fields that are grid-spacing and discretization-order independent for single-phase, and for two-phase compressible flows. In the current study, EFLES is tested for determining the predictability of a passive scalar evolution in turbulent flows, and the EFLES results are also compared to equivalent ones obtained with conventional Large Eddy Simulation (LES). A single Direct Numerical Simulation (DNS) realization of a temporal mixing layer is conducted with an initial Reynolds number of 1800. After an initial transient, the mixing-layer momentum thickness grows linearly with time. The DNS is continued during the linear growth period and until the momentum thickness Reynolds number reaches 6405. The filtered and coarsened DNS (FDNS) database is considered the template to be reached by LES or EFLES. Both LES and EFLES are conducted using the dynamic Smagorinsky model. Three grids \u2013 coarse, medium and fine \u2013 and three discretization orders \u2013 fourth, sixth and eighth \u2013 are used for each LES and EFLES. In contrast to conventional LES where the grid spacing and the filter width are proportionally related, in EFLES the filter width is set beforehand and independent of the grid spacing. The criteria for comparing LES and EFLES results to the FDNS encompass both averages and second-order quantities that characterize the passive scalar behavior. Homogeneous plane averages combined with time averaging past the time when the mixing layer becomes turbulent, enabled the computation of smooth statistics for comparison between FDNS and LES or EFLES. It is found that the conventional LES results are not predictive in that refining the grid or increasing the discretization order, or both, does not lead to coincidence of the results. In contrast, refining the grid past the medium spacing for the sixth- and eighth-order discretizations leads to the EFLES results collapsing on a single curve. Thus, the medium grid spacing and sixth discretization order is the most computationally economic predictive simulation. Based on these findings, EFLES computations, the predictions of which are unaffected by numerical errors, are recommended for model validation with experimental data.", "doi": "10.1016/j.compfluid.2015.01.003", "issn": "0045-7930", "publisher": "Elsevier", "publication": "Computers & Fluids", "publication_date": "2015-04-16", "volume": "111", "pages": "137-149" }, { "id": "authors:phn5k-rq606", "collection": "authors", "collection_id": "phn5k-rq606", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141001-102111535", "type": "article", "title": "High-pressure reduced-kinetics mechanism for n-hexadecane autoignition and oxidation at constant pressure", "author": [ { "family_name": "Kourdis", "given_name": "Panayotis D.", "clpid": "Kourdis-P-D" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "In previous work, a local full self similarity (LFS2) was identified between (properly) normalized thermo-kinetic quantities when plotted against a normalized temperature. The local partial self similarity (LPS2), which is the computationally efficient companion of LFS2, was coupled with a simple tabulation scheme and yielded highly-accurate twenty-light-species reduced mechanisms for constant-mass and constant-volume autoignition and oxidation of n-heptane, n-decane, n-dodecane and iso-octane. The LFS2 and LPS2 reduction framework coupled with tabulation were combined into a method here called Local Self Similarity Tabulation (LS2T). The LS2T method is here extended and validated for constructing reduced kinetics mechanisms for the constant-mass autoignition and oxidation of an even heavier hydrocarbon, n-hexadecane, but now at constant pressure conditions for a wide range of initial conditions. The method employs the same twenty light species as species progress variables as in the lighter alkanes previously studied, and tabulates through the LPS2 all information involving any heavy species. The template mechanism used for reduction is the detailed 2115-species kinetics from the Lawrence Livermore National Laboratory. Results are presented for the n-hexadecane autoignition and oxidation at the high pressures encountered during engine operation and for several initial temperatures and equivalence ratios. We show that the utilization of a real-gas equation of state (the Peng\u2013Robinson equation of state with a volume correction) is essential in obtaining accurate results. Reduced-kinetics plots of the temperature and the major species, including the OH temporal evolution, computed with the LS2T method accurately duplicated those obtained with the LLNL detailed mechanism.", "doi": "10.1016/j.combustflame.2014.09.008", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2015-03", "series_number": "3", "volume": "162", "issue": "3", "pages": "571-579" }, { "id": "authors:d4grk-tjz26", "collection": "authors", "collection_id": "d4grk-tjz26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150507-104525329", "type": "article", "title": "A priori and a posteriori investigations for developing large eddy simulations of multi-species turbulent mixing under high-pressure conditions", "author": [ { "family_name": "Borghesi", "given_name": "Giulio", "clpid": "Borghesi-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A Direct Numerical Simulation (DNS) database was created representing mixing of species under high-pressure conditions. The configuration considered is that of a temporally evolving mixing layer. The database was examined and analyzed for the purpose of modeling some of the unclosed terms that appear in the Large Eddy Simulation (LES) equations. Several metrics are used to understand the LES modeling requirements. First, a statistical analysis of the DNS-database large-scale flow structures was performed to provide a metric for probing the accuracy of the proposed LES models as the flow fields obtained from accurate LESs should contain structures of morphology statistically similar to those observed in the filtered-and-coarsened DNS (FC-DNS) fields. To characterize the morphology of the large-scales structures, the Minkowski functionals of the iso-surfaces were evaluated for two different fields: the second-invariant of the rate of deformation tensor and the irreversible entropy production rate. To remove the presence of the small flow scales, both of these fields were computed using the FC-DNS solutions. It was found that the large-scale structures of the irreversible entropy production rate exhibit higher morphological complexity than those of the second invariant of the rate of deformation tensor, indicating that the burden of modeling will be on recovering the thermodynamic fields. Second, to evaluate the physical effects which must be modeled at the subfilter scale, an a priori analysis was conducted. This a priori analysis, conducted in the coarse-grid LES regime, revealed that standard closures for the filtered pressure, the filtered heat flux, and the filtered species mass fluxes, in which a filtered function of a variable is equal to the function of the filtered variable, may no longer be valid for the high-pressure flows considered in this study. The terms requiring modeling are the filtered pressure, the filtered heat flux, the filtered pressure work, and the filtered species mass fluxes. Improved models were developed based on a scale-similarity approach and were found to perform considerably better than the classical ones. These improved models were also assessed in an a posteriori study. Different combinations of the standard models and the improved ones were tested. At the relatively small Reynolds numbers achievable in DNS and at the relatively small filter widths used here, the standard models for the filtered pressure, the filtered heat flux, and the filtered species fluxes were found to yield accurate results for the morphology of the large-scale structures present in the flow. Analysis of the temporal evolution of several volume-averaged quantities representative of the mixing layer growth, and of the cross-stream variation of homogeneous-plane averages and second-order correlations, as well as of visualizations, indicated that the models performed equivalently for the conditions of the simulations. The expectation is that at the much larger Reynolds numbers and much larger filter widths used in practical applications, the improved models will have much more accurate performance than the standard one.", "doi": "10.1063/1.4916284", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2015-03", "series_number": "3", "volume": "27", "issue": "3", "pages": "Art. No. 035117" }, { "id": "authors:vmyhq-7qv97", "collection": "authors", "collection_id": "vmyhq-7qv97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-102122597", "type": "article", "title": "Irreversible entropy production rate in high-pressure turbulent reactive flows", "author": [ { "family_name": "Borghesi", "given_name": "Giulio", "clpid": "Borghesi-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A Direct Numerical Simulation (DNS) database is created describing high-pressure reactive flows for studying the flow characteristics and the irreversible entropy production rate that must be modeled by Subgrid-Scale (SGS) models in Large Eddy Simulation. The governing equations are the continuity, momentum, total energy and species transport equations complemented by a real-gas equation of state. The molecular transport model is based on complete mass-diffusion and thermal-diffusion matrices having elements computed according to all-pressure mixing rules. The mixture viscosity and thermal conductivity are calculated from the individual species values, valid at high pressures, by using all-pressure mixing rules. The reaction is a one-step process and the values of different coefficients in the reaction rate ensure that it gives physically-correct trends for autoignition. The DNS is performed for a temporal mixing layer. Three realizations are computed and examined to reveal the influence of the initial pressure p_0 and of exhaust gas recirculation (EGR). It is found that the main flame is of diffusion type, flanked by premixed flames. As p_0 increases, the most intensive premixed-flame regions draw closer to the diffusion flame. Additionally to the well-known advantage of EGR, we found that it promotes the development of uphill diffusion which is a molecular process inducing the formation of strong species gradients that in turn induce turbulence production, i.e. the formation of dynamic small scales. Analysis of the irreversible entropy production rate revealed that its four modes \u2013 due to viscosity, mass diffusivity, thermal conductivity and reaction \u2013 operate in different spatial regions of the flow where different phenomena occur. Increasing p_0 and lack of EGR both result in an increase in the magnitude of the irreversible entropy-production rate. For the Reynolds number values achievable in DNS, the reaction mode dominates in magnitude all other modes of the irreversible entropy-production rate.", "doi": "10.1016/j.proci.2014.05.016", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2015", "series_number": "2", "volume": "35", "issue": "2", "pages": "1537-1547" }, { "id": "authors:rgc4r-x6081", "collection": "authors", "collection_id": "rgc4r-x6081", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150211-072315895", "type": "article", "title": "Models for the large eddy simulation equations to describe multi-species mixing occuring at supercritical pressure", "author": [ { "family_name": "Borghesi", "given_name": "G.", "clpid": "Borghesi-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "An existing database of direct numerical simulations (DNS) representing mixing of species under supercritical pressure (supercritical-\u03c1) conditions has been investigated for the purpose of understanding the modeling of the gradient of the filtered pressure, the divergence of the filtered heat flux, and the divergence of the filtered species mass flux, all in the context of large eddy simulation (LES). The analysis consists of two separate parts. The activities of all terms appearing in the LES equations are first evaluated, and the dominant terms for each of the transport equations are identified. These data are used to check whether the standard LES assumptions\u2212i.e., that the three above quantities are equal to the gradient of the pressure and the divergences of the fluxes computed from the filtered flow field, respectively\u2212that are routinely used for atmospheric-\u03c1 flows, continue to be valid also in the realm of supercritical-\u03c1 conditions. Having found that these assumptions do not hold under supercritical-\u03c1 conditions, alternative modeling strategies for these terms are proposed, and their accuracy with respect to the standard LES assumptions is assessed.", "doi": "10.1615/IntJEnergeticMaterialsChemProp.2014011313", "issn": "2150-766X", "publisher": "Begell House", "publication": "International Journal of Energetic Materials and Chemical Propulsion", "publication_date": "2014-10", "series_number": "5", "volume": "13", "issue": "5", "pages": "435-453" }, { "id": "authors:jzpkx-tj411", "collection": "authors", "collection_id": "jzpkx-tj411", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131223-095256414", "type": "article", "title": "Heavy-alkane oxidation kinetic-mechanism reduction using dominant dynamic variables, self similarity and chemistry tabulation", "author": [ { "family_name": "Kourdis", "given_name": "Panayotis D.", "clpid": "Kourdis-P-D" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model of local and full or partial self similarity is developed for situations in which a phenomenon exhibits a dominant variable, with the goal of applying the model to obtain reduced oxidation kinetics from detailed kinetics for n-heptane, iso-octane, n-decane and n-dodecane. Upon appropriate normalization, it is shown that the state vector for all four alkanes indeed obeys local full self similarity with respect to the dominant variable which is here a normalized temperature. Further, the vector of species mass fractions is partitioned into major species which are those of interest to calculate, and thus for which equations are solved, and minor species which are those of no interest to calculate and are therefore modeled. The goal of the chemical kinetic reduction is to provide a model which expresses the influence of the minor species on the major species. The identification of major species with the light species, and of the minor species with the heavy species leads to partitioning the energetics into computed and modeled parts. This partition of the species set is shown to lead to local full self similarity of the reaction rates between the modeled and calculated species; the local full self similarity also prevails for the energy of the modeled species and for the average heat capacity at constant volume of the heavy species. A methodology is developed to take advantage of this self similarity by considering the initial condition as a point in the three-dimensional space of the initial pressure, initial temperature and equivalence ratio, choosing eight points surrounding the initial condition in this space, developing the self similarity graphs at these eight points using the LLNL detailed mechanism in conjunction with CHEMKIN II, and calculating at each time step the modeled contributions at the surrounded point by interpolating from those known at the eight points. Once the modeled contributions are known, the conservation equations for the species and the energy, coupled with a real-gas equation of state, are solved. With a focus on the high-pressure conditions in automotive engines, extensive results are shown for the four alkanes over a wide range of initial temperatures (650\u20131000 K) and equivalence ratios (0.35\u20133.00) at 20 bar and 40 bar. The results consist of timewise profiles of the temperature and species, allowing the calculation of the ignition time and the equilibrium or maximum temperature. Comparisons between the reduced mechanism and the detailed mechanism show excellent to very good agreement for all alkanes when only 20 progress-variable light species are used in the reduced mechanism; the 20 species are the same for all fuels, and for n-decane and n-dodecane this represents a reduction in the species progress variables by factor of more than 100. As an example, calculations that excellently duplicate the elemental mechanism are also shown for n-dodecane using only 15 or 6 progress-variable light species, indicating the potential for further progress-variable reduction beyond the 20 species.", "doi": "10.1016/j.combustflame.2013.11.012", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2014-05", "series_number": "5", "volume": "161", "issue": "5", "pages": "1196-1223" }, { "id": "authors:m1aka-tvq58", "collection": "authors", "collection_id": "m1aka-tvq58", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131003-081047378", "type": "article", "title": "Prediction of premixed, n-heptane and iso-octane unopposed jet flames using a reduced kinetic model based on constituents and light species", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model of steady, quasi one-dimensional premixed laminar jet flame developing unopposed into a uniform flow has been formulated using a previously successful reduced chemical-kinetics model [10] and [11]. A detailed derivation of the steady quasi one-dimensional conservation equations revealed that it is only under very restrictive conditions \u2013 probably very difficult to achieve experimentally and the validity of which is not reported in detail in experimental studies \u2013 that the quasi one-dimensional concept is meaningful. The governing equations have been mathematically manipulated to be consistent with the framework of the reduced chemical-kinetics model which relied on constituents representing the heavy species, and on quasi-steady light species and unsteady light species. The flame model includes accurate transport property calculation for high-pressure conditions and a real-gas equation of state. Based on a found self-similarity [10] and [11] which deteriorates at increasingly rich conditions, the chemistry model consists of tables of kinetic rates, quasi-steady species molar fractions and the heavy species mean molar mass extracted from the LLNL model in the framework of the reduced kinetics. The progress variables are only the mass fractions of the unsteady light species and the temperature. The values of the dependent variables are specified at the inflow location and null gradients are specified at the outflow. Simulations were performed for both n-heptane and iso-octane air oxidation over a wide range of pressures and equivalence ratios. The limited documentation of experimental conditions not specifying the inflow velocity (or flux) made it impossible to use this data for detailed comparison. In the one case where the inflow velocity was available for a burner experiment, those conditions were adopted for the simulation and the configuration was changed to a constant-area jet to approach the burner configuration. Results from this simulation compared favorably with the data, considering the different configurations. Results from parametric studies not associated with experimental data showed that at stoichiometric conditions the flame temperature, flame velocity and strain rate are not sensitive to the pressure, although flames become increasingly thinner with increasing pressure and the yield of the unsteady light species is different. Computations conducted at 40 bar for various equivalence ratios and for velocities differing with the equivalence ratio showed that the maximum flame velocity, flame strain and flame temperature were obtained at stoichometric conditions. Finally, we discuss the limitations of utilizing a priori obtained reduced chemical-kinetic models in flames calculations.", "doi": "10.1016/j.combustflame.2013.06.005", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2013-11", "series_number": "11", "volume": "160", "issue": "11", "pages": "2404-2421" }, { "id": "authors:greny-kgs28", "collection": "authors", "collection_id": "greny-kgs28", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130627-094307167", "type": "article", "title": "Multi-species turbulent mixing under supercritical-pressure conditions: modelling, direct numerical simulation and analysis revealing species spinodal decomposition", "author": [ { "family_name": "Masi", "given_name": "Enrica", "clpid": "Masi-E" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "Kenneth G.", "clpid": "Harstad-K-G" }, { "family_name": "Okong'o", "given_name": "Nora A.", "clpid": "Okong'o-N-A" } ], "abstract": "A model is developed for describing mixing of several species under high-pressure\nconditions. The model includes the Peng\u2013Robinson equation of state, a full massdiffusion\nmatrix, a full thermal-diffusion-factor matrix necessary to incorporate the\nSoret and Dufour effects and both thermal conductivity and viscosity computed for\nthe species mixture using mixing rules. Direct numerical simulations (DNSs) are\nconducted in a temporal mixing layer configuration. The initial mean flow is perturbed\nusing an analytical perturbation which is consistent with the definition of vorticity\nand is divergence free. Simulations are performed for a set of five species relevant\nto hydrocarbon combustion and an ensemble of realizations is created to explore the\neffect of the initial Reynolds number and of the initial pressure. Each simulation\nreaches a transitional state having turbulent characteristics and most of the data\nanalysis is performed on that state. A mathematical reformulation of the flux terms\nin the conservation equations allows the definition of effective species-specific Schmidt\nnumbers (Sc) and of an effective Prandtl number (Pr) based on effective speciesspecific\ndiffusivities and an effective thermal conductivity, respectively. Because these\neffective species-specific diffusivities and the effective thermal conductivity are not\ndirectly computable from the DNS solution, we develop models for both of these\nquantities that prove very accurate when compared with the DNS database. For two\nof the five species, values of the effective species-specific diffusivities are negative\nat some locations indicating that these species experience spinodal decomposition; we\ndetermine the necessary and sufficient condition for spinodal decomposition to occur.\nWe also show that flows displaying spinodal decomposition have enhanced vortical\ncharacteristics and trace this aspect to the specific features of high-density-gradient\nmagnitude regions formed in the flows. The largest values of the effective speciesspecific\nSc numbers can be well in excess of those known for gases but almost\ntwo orders of magnitude smaller than those of liquids at atmospheric pressure. The\neffective thermal conductivity also exhibits negative values at some locations and the\neffective Pr displays values that can be as high as those of a liquid refrigerant.\nExamination of the equivalence ratio indicates that the stoichiometric region is thin\nand coincides with regions where the mixture effective species-specific Lewis number\nvalues are well in excess of unity. Very lean and very rich regions coexist in the\nvicinity of the stoichiometric region. Analysis of the dissipation indicates that it is dominated by mass diffusion, with viscous dissipation being the smallest among the\nthree dissipation modes. The sum of the heat and species (i.e. scalar) dissipation is\nfunctionally modelled using the effective species-specific diffusivities and the effective\nthermal conductivity. Computations of the modelled sum employing the modelled\neffective species-specific diffusivities and the modelled effective thermal conductivity\nshows that it accurately replicates the exact equivalent dissipation.", "doi": "10.1017/jfm.2013.70", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2013-04", "volume": "721", "pages": "578-626" }, { "id": "authors:29war-c1g21", "collection": "authors", "collection_id": "29war-c1g21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130319-150030156", "type": "article", "title": "Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation", "author": [ { "family_name": "Radhakrishnan", "given_name": "Senthilkumaran", "clpid": "Radhakrishnan-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Predictions from conventional large-eddy simulation (LES) are known to be grid-spacing and spatial-discretization-order dependent. In a previous article (Radhakrishnan & Bellan, J. Fluid Mech., vol. 697, 2012a, pp. 399\u2013435), we reformulated LES for compressible single-phase flow by explicitly filtering the nonlinear terms in the governing equations so as to render the solution grid-spacing and discretization-order independent. Having shown in Radhakrishnan & Bellan (2012a) that the reformulated LES, which we call EFLES, yields grid-spacing-independent and discretization-order-independent solutions for compressible single-phase flow, we explore here the potential of EFLES for evaporating two-phase flow where the small scales have an additional origin compared to single-phase flow. Thus, we created a database through direct numerical simulation (DNS) that when filtered serves as a template for comparisons with both conventional LES and EFLES. Both conventional LES and EFLES are conducted with two gas-phase SGS models; the drop-field SGS model is the same in all these simulations. For EFLES, we also compared simulations performed with the same SGS model for the gas phase but two different drop-field SGS models. Moreover, to elucidate the influence of explicit filtering versus gas-phase SGS modelling, EFLES with two drop-field SGS models but no gas-phase SGS models were conducted. The results from all these simulations were compared to those from DNS and from the filtered DNS (FDNS). Similar to the single-phase flow findings, the conventional LES method yields solutions which are both grid-spacing and spatial-discretization-order dependent. The EFLES solutions are found to be grid-spacing independent for sufficiently large filter-width to grid-spacing ratio, although for the highest discretization order this ratio is larger in the two-phase flow compared to the single-phase flow. For a sufficiently fine grid, the results are also discretization-order independent. The absence of a gas-phase SGS model leads to build-up of energy near the filter cut-off indicating that while explicit filtering removes energy above the filter width, it does not provide the correct dissipation at the scales smaller than this width. A wider viewpoint leads to the conclusion that although the minimum filter-width to grid-spacing ratio necessary to obtain the unique grid-independent solution might be different for various discretization-order schemes, the grid-independent solution thus obtained is also discretization-order independent.", "doi": "10.1017/jfm.2013.3", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2013-03", "volume": "719", "pages": "230-267" }, { "id": "authors:rytkg-brc05", "collection": "authors", "collection_id": "rytkg-brc05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120515-113222411", "type": "article", "title": "Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of compressible single-phase flow", "author": [ { "family_name": "Radhakrishnan", "given_name": "Senthilkumaran", "clpid": "Radhakrishnan-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "In large-eddy simulation (LES), it is often assumed that the filter width is equal to the grid spacing. Predictions from such LES are grid-spacing dependent since any subgrid-scale (SGS) model used in the LES equations is dependent on the resolved flow field which itself varies with grid spacing. Moreover, numerical errors affect the flow field, especially the smallest resolved scales. Thus, predictions using this approach are affected by both modelling and numerical choices. However, grid-spacing-independent LES predictions unaffected by numerical choices are necessary to validate LES models through comparison with a trusted template. First, such a template is created here through direct numerical simulation (DNS). Then, simulations are conducted using the conventional LES equations and also LES equations which are here reformulated so that the small-scale-producing nonlinear terms in these equations are explicitly filtered (EF) to remove scales smaller than a fixed filter width; this formulation is called EFLES. First, LES is conducted with four SGS models, then EFLES is performed with two of the SGS models used in LES; the results from all these simulations are compared to those from DNS and from the filtered DNS (FDNS). The conventional LES solution is both grid-spacing and spatial discretization-order dependent, thus showing that both of these numerical aspects affect the flow prediction. The solution from the EFLES equations is grid independent for a high-order spatial discretization on all meshes tested. However, low-order discretizations require a finer mesh to reach grid independence. With an eighth-order discretization, a filter-width to grid-spacing ratio of two is sufficient to reach grid independence, while a filter-width to grid-spacing ratio of four is needed to reach grid independence when a fourth- or a sixth-order discretization is employed. On a grid fine enough to be utilized in a DNS, the EFLES solution exhibits grid independence and does not converge to the DNS solution. The velocity-fluctuation spectra of EFLES follow those of FDNS independent of the grid spacing used, in concert with the original concept of LES. The reasons for the different predictions of conventional LES or EFLES according to the SGS model used, and the different characteristics of the EFLES predictions compared to those from conventional LES are analysed.", "doi": "10.1017/jfm.2012.73", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2012-04-25", "volume": "697", "pages": "399-435" }, { "id": "authors:3qvrk-pag21", "collection": "authors", "collection_id": "3qvrk-pag21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-153637928", "type": "article", "title": "Influence of computational drop representation in LES of a mixing layer with evaporating drops", "author": [ { "family_name": "Radhakrishnan", "given_name": "Senthilkumaran", "clpid": "Radhakrishnan-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The objective of this work is to quantify the influence of the number of computational drops and grid spacing on the accuracy of predicted flow statistics and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provides minimal error in flow prediction. For this purpose, Large Eddy Simulation (LES) of a mixing layer with evaporating drops has been performed using the dynamic Smagorinsky model and employing various numbers of computational drops. The LES were performed by reducing the number of physical drops by a factor varying from 8 to 128 to obtain the ensemble of computational drops, and by utilizing either a coarse or a fine grid. A set of first order and second order gas-phase statistics as well as drop statistics are extracted from LES predictions and are compared to results obtained by filtering a Direct Numerical Simulation (DNS) database. First order statistics such as Favre averaged streamwise velocity, Favre averaged vapor mass fraction, and the drop streamwise velocity are predicted accurately independent of the number of computational drops and grid spacing. Second order flow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor flux are predicted accurately by the fine mesh LES only when the computational drop field is reduced by a factor of no more than 32, and by the coarse mesh LES reasonably accurately for all computational drop field values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must not be significantly lower than that in the DNS.", "doi": "10.1016/j.compfluid.2011.11.018", "issn": "0045-7930", "publisher": "Elsevier", "publication": "Computers & Fluids", "publication_date": "2012-04-15", "volume": "58", "pages": "15-26" }, { "id": "authors:rq1y1-7kz29", "collection": "authors", "collection_id": "rq1y1-7kz29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-160118408", "type": "article", "title": "A new formulation of the Large Eddy Simulation composition equations for two-phase fully-multicomponent turbulent flows", "author": [ { "family_name": "Gloor", "given_name": "Michael", "clpid": "Gloor-M" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The Large Eddy Simulation (LES) composition equations for fully multicomponent two-phase flows are here reformulated compared to a previous study in order to palliate modeling issues identified with the previous formulation. These modeling issues were highlighted in an a priori study using a Direct Numerical Simulation (DNS) database of a transitional, compressible, gaseous, temporal mixing layer laden with evaporating fuel drops. The issues consisted of: (1) the dominance of resolved source terms (representing the effect of the drops on the gas) with respect to advection and (2) the important role of subgrid source terms, even when the filter width was moderate with respect to the DNS grid spacing (e.g. factor of 4). The new formulation no longer exhibits the first issue, while the second issue is only present at larger filter widths (e.g. larger than a factor of 8). The capability to model SGS effects other than those resulting from source terms is a priori tested on this new formulation for two different SGS models using the DNS database. Due to more accurate modeling possibilities and improved computational efficiency, the new set of equations is identified as better suited for LES applications.", "doi": "10.1016/j.compfluid.2011.06.017", "issn": "0045-7930", "publisher": "Elsevier", "publication": "Computers & Fluids", "publication_date": "2011-11", "series_number": "1", "volume": "50", "issue": "1", "pages": "94-103" }, { "id": "authors:4hpky-2nq70", "collection": "authors", "collection_id": "4hpky-2nq70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110921-110133253", "type": "article", "title": "The subgrid-scale scalar variance under supercritical pressure conditions", "author": [ { "family_name": "Masi", "given_name": "Enrica", "clpid": "Masi-E" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "To model the subgrid-scale (SGS) scalar variance under supercritical-pressure conditions, an equation is first derived for it. This equation is considerably more complex than its equivalent for atmospheric-pressure conditions. Using a previously created direct numerical simulation (DNS) database of transitional states obtained for binary-species systems in the context of temporal mixing layers, the activity of terms in this equation is evaluated, and it is found that some of these new terms have magnitude comparable to that of governing terms in the classical equation. Most prominent among these new terms are those expressing the variation of diffusivity with thermodynamic variables and Soret terms having dissipative effects. Since models are not available for these new terms that would enable solving the SGS scalar variance equation, the adopted strategy is to directly model the SGS scalar variance. Two models are investigated for this quantity, both developed in the context of compressible flows. The first one is based on an approximate deconvolution approach and the second one is a gradient-like model which relies on a dynamic procedure using the Leonard term expansion. Both models are successful in reproducing the SGS scalar variance extracted from the filtered DNS database, and moreover, when used in the framework of a probability density function (PDF) approach in conjunction with the \u03b2-PDF, they excellently reproduce a filtered quantity which is a function of the scalar. For the dynamic model, the proportionality coefficient spans a small range of values through the layer cross-stream coordinate, boding well for the stability of large eddy simulations using this model.", "doi": "10.1063/1.3609282", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2011-08", "series_number": "8", "volume": "23", "issue": "8", "pages": "Art. No. 085101" }, { "id": "authors:j6cc0-gnd60", "collection": "authors", "collection_id": "j6cc0-gnd60", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110801-094730278", "type": "article", "title": "Subgrid-scale models and large-eddy simulation of oxygen stream disintegration and mixing with a hydrogen or helium stream at supercritical pressure", "author": [ { "family_name": "Ta\u015fkino\u011flu", "given_name": "Ezgi S.", "clpid": "Ta\u015fkino\u011flu-E-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "For flows at supercritical pressure, p, the large-eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid-scale (SGS) fluxes but also new SGS terms, each denoted as a 'correction'. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations and represent differences, other than contributed by the convection terms, between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) which is the difference between the filtered divergence of the molecular heat flux and the divergence of the molecular heat flux computed as a function of the filtered flow field. We revisit here a previous a priori study where we only had partial success in modelling the q-correction term and show that success can be achieved using a different modelling approach. This a priori analysis, based on a temporal mixing-layer direct numerical simulation database, shows that the focus in modelling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES molecular heat-flux calculation. Furthermore, an a posteriori study is conducted for temporal mixing layers initially containing oxygen (O) in the lower stream and hydrogen (H) or helium (He) in the upper stream to examine the benefit of the new model. Results show that for any LES including SGS-flux models (constant-coefficient gradient or scale-similarity models; dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/gradient models), the inclusion of the q-correction in LES leads to the theoretical maximum reduction of the SGS molecular heat-flux difference; the remaining error in modelling this new subgrid term is thus irreducible. The impact of the q-correction model first on the molecular heat flux and then on the mean, fluctuations, second-order correlations and spatial distribution of dependent variables is also demonstrated. Discussions on the utilization of the models in general LES are presented.", "doi": "10.1017/jfm.2011.130", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2011-07", "volume": "679", "pages": "156-193" }, { "id": "authors:drk6q-jg864", "collection": "authors", "collection_id": "drk6q-jg864", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-160406159", "type": "article", "title": "Spray Control for Maximizing Energy Efficiency and Reducing Emission in Combustion Engines", "author": [ { "family_name": "Chigier", "given_name": "Norman", "clpid": "Chigier-N" }, { "family_name": "Bachalo", "given_name": "William", "clpid": "Bachalo-W" }, { "family_name": "Reitz", "given_name": "Rolf D.", "clpid": "Reitz-R-D" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Herrmann", "given_name": "Marcus", "clpid": "Herrmann-M" } ], "abstract": "Combustion engines for automotive, locomotive, land, ships, and aircraft utilize liquid fuel injected into combustion chambers. Projected increases in the price of fuel and the effects of emissions on pollution and climate change are requiring increased efforts to increase combustion and energy efficiency within combustion chambers together with minimizing emission of particulates, including oxides of nitrogen and sulfur and other pollutants, including CO_2. The question that is being addressed is how research can contribute to the objective of improving the efficiency of engines using liquid fuel and reducing the amount of pollutants generated in the energy conversion process by control of drop size, velocity, and trajectory and local air/fuel mixture ratios which have a dominant influence on ignition, combustion, and exhaust emissions. Basic predictions of global spray combustion phenomena may not result in sufficient understanding that can lead to the necessary improvements. Advancing our knowledge of the associated phenomena with careful experimentation and modeling can hold the key to a deeper understanding of the involved processes and thus can result in the required improvements. This paper provides a brief overview of the current state and challenges in some of the key research areas related to understanding the processes involved in liquid fuel combustion. It represents a summary of a Forum discussion titled \"Spray Control for Maximizing Energy Efficiency and Reducing Emission in Combustion Engines\" held at the ILASS-Americas 22nd Annual Conference on Liquid Atomization and Spray Systems in Cincinnati, Ohio.", "doi": "10.1615/AtomizSpr.2012003496", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "2011", "series_number": "7", "volume": "21", "issue": "7", "pages": "553-574" }, { "id": "authors:m34nn-p8y20", "collection": "authors", "collection_id": "m34nn-p8y20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-095549725", "type": "article", "title": "A model of reduced oxidation kinetics using constituents and species: Iso-octane and its mixtures with n-pentane, iso-hexane and n-heptane", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A previously described methodology for deriving a reduced kinetic mechanism for alkane oxidation and tested for n-heptane is here shown to be valid, in a slightly modified version, for iso-octane and its mixtures with n-pentane, iso-hexane and n-heptane. The model is still based on partitioning the species into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement in the species ensemble, and mathematically decomposing the heavy species into constituents which are radicals. For the same similarity variable found from examining the n-heptane LLNL mechanism in conjunction with CHEMKIN II, the appropriately scaled total constituent molar density still exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures in the cold ignition regime. When extended to larger initial temperatures than for cold ignition, the self-similar behavior becomes initial temperature dependent, which indicates that rather than using functional fits for the enthalpy generation due to the heavy species' oxidation, an ideal model based on tabular information extracted from the complete LLNL kinetics should be used instead. Similarly to n-heptane, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable, but here their slope variation is no longer fitted and instead, their rate equations are used with the ideal model to calculate them. As in the original model, the light species ensemble is partitioned into quasi-steady and unsteady species; the quasi-steady light species mole fractions are computed using the ideal model and the unsteady species are calculated as progress variables using rates extracted from the ideal model. Results are presented comparing the performance of the model with that of the LLNL mechanism using CHEMKIN II. The model reproduces excellently the temperature and species evolution versus time or versus the similarity variable, with the exception of very rich mixtures, where the predictions are still very good but the multivalued aspect of these functions at the end of oxidation is not captured in the reduction. The ignition time is predicted within percentages of the LLNL values over a wide range of equivalence ratios, initial pressures and initial temperatures.", "doi": "10.1016/j.combustflame.2010.06.010", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2010-11", "series_number": "11", "volume": "157", "issue": "11", "pages": "2184-2197" }, { "id": "authors:76cjw-5zz26", "collection": "authors", "collection_id": "76cjw-5zz26", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-095909602", "type": "article", "title": "A model of reduced kinetics for alkane oxidation using constituents and species: Proof of concept for n-heptane", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described and applied to n-heptane. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement in the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the LLNL skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately scaled global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The concept is tested by using tabular information from the LLNL skeletal mechanism in conjunction with CHEMKIN II. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is overpredicted. To palliate this deficiency, functional modeling is incorporated into our conceptual reduction. Due to the reduction process, models are also included for the global constituent molar density, the kinetics-induced enthalpy evolution of the heavy species, the contribution to the reaction rate of the unsteady lights from the heavies, the molar density evolution of oxygen and water, the mole fractions of the quasi-steady light species and the mean molar heat capacity of the heavy species. The model is compact in that there are only nine species-related progress variables. Results are presented comparing the performance of the model for predicting the temperature and species evolution with that of the skeletal mechanism. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure and initial temperature.", "doi": "10.1016/j.combustflame.2010.02.013", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2010-08", "series_number": "8", "volume": "157", "issue": "8", "pages": "1594-1609" }, { "id": "authors:evpb5-kgc37", "collection": "authors", "collection_id": "evpb5-kgc37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-161319825", "type": "article", "title": "Small-scale dissipation in binary-species, thermodynamically supercritical, transitional mixing layers", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The irreversible entropy production (i.e. the dissipation) has three distinct modes due to viscous, heat and species-mass fluxes. Computations of the dissipation and its modes are conducted using transitional states obtained from Direct Numerical Simulations (DNS) of O_2/H_2 and C_7H_(16)/N_2 temporal mixing layers at thermodynamically supercritical pressure. A non-dimensionalization of the mathematical expression for each dissipation mode is first performed and representative reference values computed using the DNS database are utilized to highlight the order of magnitude of each mode and their relative importance. For more quantitative results, the importance of each dissipative mode is assessed both at the DNS scale and at scales determined by filter sizes from four to sixteen times the DNS grid spacing. The subgrid-scale (SGS) dissipation is computed by subtracting the filtered-field dissipation from the DNS-field dissipation. For each species system, three layers are considered having different initial Reynolds number and perturbation wavelength. For all layers, it is found that the species-mass flux contribution dominates both the DNS and SGS dissipation due to high density-gradient-magnitude (HDGM) regions which are a distinctive physical aspect of these layers. Backscatter, indicated by regions of negative SGS dissipation, is found in a substantial portion (15\u201360%) of the domain, and decreases only slightly with increasing filter width. Regions of the most intense negative and positive SGS dissipation strongly correlate with the HDGM regions. On a domain-average basis, the proportional contribution of each dissipation mode to the total is similar at the DNS and SGS scales, indicating scale-similarity. The proportion of the species-mass dissipation mode to the total is remarkably similar in value across all simulations whether at the DNS or SGS scale. For each mode and the total, the SGS contribution to the DNS-field dissipation is only species-system and filter-size dependent but nearly independent of the initial Reynolds number and perturbation wavelength. The SGS contribution is smaller for O_2/H_2 layers than for C_7H_(16)/N_2 ones, but increases more rapidly with increasing filter width. The implications of these results for Larger Eddy Simulation modeling are discussed.", "doi": "10.1016/j.compfluid.2010.02.001", "issn": "0045-7930", "publisher": "Elsevier", "publication": "Computers & Fluids", "publication_date": "2010-08", "series_number": "7", "volume": "39", "issue": "7", "pages": "1112-1124" }, { "id": "authors:qw66w-0r713", "collection": "authors", "collection_id": "qw66w-0r713", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110510-132732647", "type": "article", "title": "A posteriori study using a DNS database describing fluid disintegration and binary-species mixing under supercritical pressure: heptane and nitrogen", "author": [ { "family_name": "Taskinoglu", "given_name": "Ezgi S.", "clpid": "Taskinoglu-E-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a 'pressure correction' (p correction) in the momentum equation. This additional term results from filtering the Navier\u2013Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.\nIn the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS p-correction term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and 'mixed' models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even better predictions in capturing vortical features are obtained with the GRD model. The GRD predictions improve when LES is initiated at a time past the initial range in which the p-correction term rivals in magnitude the leading-order term in the momentum equation. Finally, the ability of the LES to predict the FC-DNS irreversible entropy production is assessed. It is shown that the SSCP model is the best at recovering the domain-averaged irreversible entropy production. The sensitivity of the predictions to the initial conditions and grid size is also investigated.", "doi": "10.1017/S0022112009992606", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2010-02-25", "volume": "645", "pages": "211-254" }, { "id": "authors:edhbn-b2859", "collection": "authors", "collection_id": "edhbn-b2859", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090702-094013653", "type": "article", "title": "Large Eddy Simulation composition equations for\n single-phase and two-phase fully multicomponent flows", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Selle", "given_name": "L. C.", "clpid": "Selle-L-C" } ], "abstract": "The Large Eddy Simulation (LES) equations for multicomponent (MC) fuel single-phase (SP) flow and\ntwo-phase (TP) flow with phase change are derived from the Direct Numerical Simulation (DNS) equations\nby filtering the DNS equations using a top-hat filter. Additional to the equations solved for singlecomponent\n(SC) fuels, composition equations enter the formulation. The species composition is represented\nthrough a Probability Distribution Function (PDF), and DNS equations for the PDF moments\nare solved to find the composition. The TP filtered equations contain three categories of subgrid-scale\n(SGS) terms: (1) SGS\u2013flux terms, (2) filtered source terms (FSTs) and (3) terms representing the 'LES\nassumptions'. For SP flows no FSTs exist. The SGS terms in the LES equations must be either shown negligible\nor modeled. It is shown that for the composition equations, two equivalent forms of the DNS equations\nlead to two non-equivalent forms of the LES equations. Criteria are proposed to select the form best\nsuited for LES. These criteria are used in conjunction with evaluations based on a DNS database portraying\nmixing and phase change, and lead to choosing one of the LES forms which satisfies all criteria. It is\nshown that the LES assumptions lead to additional SGS terms which require modeling. Further considerations\nare made for reactive flows.", "doi": "10.1016/j.proci.2008.06.005", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2009", "series_number": "2", "volume": "32", "issue": "2", "pages": "2239-2246" }, { "id": "authors:dwh6h-m3f41", "collection": "authors", "collection_id": "dwh6h-m3f41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:OKOpof08", "type": "article", "title": "Detailed characteristics of drop-laden mixing layers: Large eddy simulation predictions compared to direct numerical simulation", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Leboissetier", "given_name": "Anthony", "clpid": "Leboissetier-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Results are compared from direct numerical simulation (DNS) and large eddy simulation (LES) of a temporal mixing layer laden with evaporating drops to assess the ability of LES to reproduce detailed characteristics of DNS. The LES used computational drops, each of which represented eight physical drops, and a reduced flow field resolution using a grid spacing four times larger than that of the DNS. The LES also used models for the filtered source terms, which express the coupling of the drops with the flow, and for the unresolved subgrid-scale (SGS) fluxes of species mass, momentum, and enthalpy. The LESs were conducted using one of three different SGS-flux models: dynamic-coefficient gradient (GRD), dynamic-coefficient Smagorinsky (SMD), and constant-coefficient scale similarity (SSC). The comparison of the LES with the filtered-and-coarsened (FC) DNS considered detailed aspects of the flow that are of interest in ignition or full combustion. All LESs captured the largest-scale vortex, the global amount of vapor emanating from the drops, and the overall size distribution of the drops. All LESs tended to underpredict the global amount of irreversible entropy production (dissipation). The SMD model was found unable to capture either the global or local vorticity variation and had minimal small-scale activity in dynamic and thermodynamic variables compared to the FC-DNS. The SMD model was also deficient in predicting the spatial distribution of drops and of the dissipation. In contrast, the GRD and SSC models did mimic the small-scale activity of the FC-DNS and the spatial distribution of drops and of the dissipation. Therefore, the GRD and SSC models are recommended, while the SMD model seems inappropriate for combustion or other problems where the local activity must be predicted.", "doi": "10.1063/1.2990758", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2008-10", "series_number": "10", "volume": "20", "issue": "10", "pages": "Art. No. 103305" }, { "id": "authors:kjrmf-9rg92", "collection": "authors", "collection_id": "kjrmf-9rg92", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SELjfm07", "type": "article", "title": "Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study", "author": [ { "family_name": "Selle", "given_name": "Laurant C.", "clpid": "Selle-L-C" }, { "family_name": "Okong'o", "given_name": "Nora A.", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "Kenneth G.", "clpid": "Harstad-K-G" } ], "abstract": "A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.", "doi": "10.1017/S0022112007008075", "issn": "0022-1120", "publisher": "Journal of Fluid Mechanics", "publication": "Journal of Fluid Mechanics", "publication_date": "2007-12-25", "volume": "593", "pages": "57-91" }, { "id": "authors:t5ysn-9wy96", "collection": "authors", "collection_id": "t5ysn-9wy96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SELpof07", "type": "article", "title": "Characteristics of transitional multicomponent gaseous and drop-laden mixing layers from direct numerical simulation: Composition effects", "author": [ { "family_name": "Selle", "given_name": "L. C.", "clpid": "Selle-L-C" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Transitional states are obtained by exercising a model of multicomponent-liquid (MC-liquid) drop evaporation in a three-dimensional mixing layer at larger Reynolds numbers, Re, than in a previous study. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete dynamic and thermodynamic coupling between phases is included. The liquid composition, initially specified as a single-Gamma (SG) probability distribution function (PDF) depending on the molar mass, is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF (DGPDF). The compositions of liquid and vapor emanating from the drops are calculated through four moments of their PDFs, which are drop-specific and location-specific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices, resulting into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions, and the effects of the initial mass loading and initial free-stream gas temperature are explored. For reference, simulations are also performed for gaseous multicomponent mixing layers for which the effect of Re is investigated in the direct-numerical-simulation\u2013accessible regime. The results encompass examination of the global layer characteristics, flow visualizations, and homogeneous-plane statistics at transition. Comparisons are performed with previous pretransitional MC-liquid simulations and with transitional single-component (SC) liquid-drop-laden mixing layer studies. Contrasting to pretransitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF. Unlike in pretransitional situations, regions of large composition standard deviation no longer necessarily coincide with those of large mean molar mass. The rotational and composition characteristics are all liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The classical energy cascade is found to be of similar strength, but the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation for MC flows. The kinetic energy and dissipation are liquid-specific and the variation among liquids is amplified with increasing free-stream gas temperature. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from, a SGPDF. Eulerian and Lagrangian statistics of gas-phase quantities show that the different observation framework may affect the perception of the flow.", "doi": "10.1063/1.2734997", "issn": "1070-6631", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "2007-06-01", "series_number": "6", "volume": "19", "issue": "6", "pages": "Art. No. 063301" }, { "id": "authors:ey7qp-vm357", "collection": "authors", "collection_id": "ey7qp-vm357", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-100315218", "type": "article", "title": "Evaluation of assumed-PDF methods in two-phase flows using direct numerical simulation", "author": [ { "family_name": "Selle", "given_name": "L. C.", "clpid": "Selle-L-C" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The hypothesis of uncorrelated temperature (T) and vapor-fuel mass fraction (Y_v), frequently made when modeling reaction rates using assumed-PDF models, is examined utilizing transitional databases from direct numerical simulation (DNS) of three-dimensional mixing-layers two-phase (TP) flows with evaporation. Because the databases do not contain chemical reaction, which would further correlate variables, finding here a correlation between T and Y_v is sufficient for invalidating reaction rate modeling of the joint (T, Y_v) probability distribution function (PDF) as a product of the marginal PDFs. The databases comprise four multicomponent fuels, two mass loadings and two free-stream gas temperatures. For comparison, databases for single-phase (SP) flows are also analyzed at two initial Reynolds numbers. The examination is conducted in the mixing layer excluding the free streams and in a more restricted part of the mixing layer constituting its core. The analysis is performed at the DNS and large eddy simulation (LES) scales, and subgrid scale (SGS). To obtain the LES database, the DNS database is filtered, and an evaluation of the examined correlation at the LES and SGS scales is made at two filter sizes. At the DNS scale, T and Y_v are practically uncorrelated for SP flows, showing the weak influence of the perfect-gas equation of state, whereas for TP flows the correlation is strong and increases with mass loading indicating the powerful effect of the phase change. At the LES scale, the findings emulate those at the DNS scale. The fluctuations of the SGS scale are uncorrelated for SP flows, but the product of the marginal PDFs is different from the joint PDF. For TP flows, the fluctuations are correlated and the correlation increases with temperature, casting doubt on current assumed PDFs used to model chemistry in reacting sprays. These results are independent of filter size. The joint PDFs for TP and SP fluctuations are successfully modeled.", "doi": "10.1016/j.proci.2006.07.004", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2007-01", "series_number": "2", "volume": "31", "issue": "2", "pages": "2273-2281" }, { "id": "authors:zn89n-z8286", "collection": "authors", "collection_id": "zn89n-z8286", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-100826494", "type": "article", "title": "Scalar-dissipation modeling for passive and active scalars: A priori study using direct numerical simulation", "author": [ { "family_name": "Selle", "given_name": "L. C.", "clpid": "Selle-L-C" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Transitional databases from direct numerical simulation (DNS) of three-dimensional mixing layers for single-phase flows and two-phase flows with evaporation are analyzed and used to examine the typical hypothesis that the scalar-dissipation probability distribution function (PDF) may be modeled as a Gaussian. The databases encompass a singlecomponent fuel and four multicomponent fuels, two initial Reynolds numbers (Re), two mass loadings for two-phase flows and two free-stream gas temperatures. Using the DNS-calculated moments of the scalar-dissipation PDF, it is shown, consistent with existing experimental information on single-phase flows, that the Gaussian is a modest approximation of the DNS-extracted PDF, particularly poor in the range of the high scalar-dissipation values, which are significant for turbulent reaction rate modeling in non-premixed flows using flamelet models. With the same DNS-calculated moments of the scalar-dissipation PDF and making a change of variables, a model of this PDF is proposed in the form of the \u03b2-PDF which is shown to approximate much better the DNS-extracted PDF, particularly in the regime of the high scalar-dissipation values. Several types of statistical measures are calculated over the ensemble of the 14 databases. For each statistical measure, the proposed \u03b2-PDF model is shown to be superior to the Gaussian in approximating the DNS-extracted PDF. Additionally, the agreement between the DNS-extracted PDF and the \u03b2-PDF even improves when the comparison is performed for higher initial-Re layers, whereas the comparison with the Gaussian is independent of the initial Re values. For two-phase flows, the comparison between the DNS-extracted PDF and the \u03b2-PDF also improves with increasing free-stream gas temperature and mass loading. The higher fidelity approximation of the DNS-extracted PDF by the \u03b2-PDF with increasing Re, gas temperature and mass loading bodes well for turbulent reaction rate modeling.", "doi": "10.1016/j.proci.2006.07.003", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2007-01", "series_number": "1", "volume": "31", "issue": "1", "pages": "1665-1673" }, { "id": "authors:h168x-cy007", "collection": "authors", "collection_id": "h168x-cy007", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-101258515", "type": "article", "title": "On possible release of microbe-containing particulates from a Mars lander spacecraft", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Due to possible planet contamination, before Earth-departure, Mars landers and/or rovers are subject to strict requirements on the maximum number of attached spores or particles that carry viable microbes. Estimates of the release rates of these particles on Mars are made considering the three mechanisms of wind shear, collision with suspended dust, and collision with saltating sand particles. The first mechanism is found to apply only to particles of size greater than 10\u03bcm, the second mechanism has a characteristic particle adhesion half life that is so long as to be of no concern, and the third mechanism is deemed of possible importance, vitally depending on attached particle size and detailed surface characteristics of sand and spacecraft. While not investigated in detail, dust devils are shown to be possible contributors to release of microbe-containing particles.", "doi": "10.1016/j.pss.2005.12.007", "issn": "0032-0633", "publisher": "Elsevier", "publication": "Planetary and Space Science", "publication_date": "2006-03", "series_number": "3", "volume": "54", "issue": "3", "pages": "273-286" }, { "id": "authors:fve1b-2y226", "collection": "authors", "collection_id": "fve1b-2y226", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-095150347", "type": "article", "title": "Global analysis and parametric dependencies for potential unintended hydrogen-fuel releases", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Global, simplified analyses of gaseous-hydrogen releases from a high-pressure vessel and liquid-hydrogen pools are conducted for two purposes: (1) establishing order-of-magnitude values of characteristic times and (2) determining parametric dependencies of these characteristic times on the physical properties of the configuration and on the thermophysical properties of hydrogen. According to the ratio of the characteristic release time to the characteristic mixing time, two limiting configurations are identified: (1) a rich cloud exists when this ratio is much smaller than unity, and (2) a jet exists when this ratio is much larger than unity. In all cases, it is found that the characteristic release time is proportional to the total released mass and inversely proportional to a characteristic area. The approximate size, convection velocity, and circulation time of unconfined burning-cloud releases scale with the cloud mass at powers 1/3, 1/6, and 1/6, respectively, multiplied by an appropriately dimensional constant; the influence of cross flow can only be important if its velocity exceeds that of internal convection. It is found that the fireball lifetime is approximately the maximum of the release time and thrice the convection-associated characteristic time. Transition from deflagration to detonation can occur only if the size of unconfined clouds exceeds by a factor of O(10) that of a characteristic detonation cell, which ranges from 0.015 m under stoichiometric conditions to approximately 1 m under extreme rich/lean conditions. For confined vapor pockets, transition occurs only for pocket sizes larger than the cell size. In jets, the release time is inversely proportional to the initial vessel pressure and has a square root dependence on the vessel temperature. Jet velocities are a factor of 10 larger than convective velocities in fireballs and combustion is possible only in the subsonic, downstream region where entrainment may occur.", "doi": "10.1016/j.combustflame.2005.07.005", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2006-01", "series_number": "1-2", "volume": "144", "issue": "1-2", "pages": "89-102" }, { "id": "authors:h87ws-nwp31", "collection": "authors", "collection_id": "h87ws-nwp31", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-145454271", "type": "article", "title": "Theory, Modeling and Analysis of Turbulent Supercritical Mixing", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Previous studies of supercritical three-dimensional mixing layers are reviewed to derive a unified understanding of supercritical turbulence and mixing. These studies consisted of Direct Numerical Simulations of mixing layers having initially a single chemical species in each of the two free streams. Each mixing layer was initially perturbed, which led to a double pairing of four initial spanwise vortices. These pairings yielded in each case an ultimate vortex within which small scales proliferated, resulting in a state having turbulence characteristics, called a transitional state. The evolution of the layer to this transitional state and the state itself were previously analyzed to elucidate the features of supercritical turbulence and mixing. This analysis is here used to classify those supercritical turbulent mixing characteristics that are species-system independent or species-system dependent. Finally, comments are offered on future prospects of developing small-scale models particularly suited for Large Eddy Simulations of supercritical turbulent mixing.", "doi": "10.1080/00102200500292241", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "2006", "series_number": "1-3", "volume": "178", "issue": "1-3", "pages": "253-281" }, { "id": "authors:3zcz7-sk846", "collection": "authors", "collection_id": "3zcz7-sk846", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-094958414", "type": "article", "title": "Direct numerical simulation of gaseous mixing layers laden with multicomponent-liquid drops: liquid-specific effects", "author": [ { "family_name": "Le Clercq", "given_name": "Patrick C.", "clpid": "Le-Clercq-P-C" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A representation of multicomponent-liquid (MC-liquid) composition as a linear combination of two single-Gamma probability distribution functions (PDFs) is used to describe a large number of MC-liquid drops evaporating in a gas flow. The PDF, called the double-Gamma PDF, depends on the molar mass. The gas-phase conservation equations are written in an Eulerian frame and the drops are described in a Lagrangian frame. Gas conservation equations for mass, momentum, species and energy are combined with differential conservation equations for the first four moments of the gas-composition PDF and coupled to the perfect gas equation of state. Source terms in all conservation equations account for the gas/drop interaction. The drop governing equations encompass differential conservation statements for position, mass, momentum, energy and four moments of the liquid-composition PDF. Simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops colder than the surrounding gas. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. During the layer evolution, the drops heat and evaporate. The results address the layer evolution, and the state of the gas and drops when layers reach a momentum-thickness maximum past the double vortex pairing. Of interest is the influence of the liquid composition on the development of the vortical features of the flow, on the vortical state reached after the second pairing, and on the gas temperature and composition. The MC-liquid simulations are initiated with a single-Gamma PDF composition so as to explore the development of the double-Gamma PDF. Examination of equivalent simulations with n-decane, diesel and three kerosenes as the liquid, permits assessment of the single-species versus the MC-liquid aspect, and of mixture composition specific effects. Global layer growth and global rotational characteristics are unaffected by liquid specificity; however, the global mixing is highly liquid-specific. Also liquid-specific is the evolution of the ensemble-averaged drop characteristics and of the volumetric averages representing the gas composition. Visualized rotational characteristics show that the small-scale vortical activity increases with increased fuel volatility, which is confirmed by analysis of the vorticity budgets. Homogeneous-plane-average budgets of the vorticity and vorticity-magnitude equations indicate that the stretching and tilting, and momentum-source terms are responsible for the difference among simulations. For all MC liquids, the gas displays a high level of composition heterogeneity, which can directly be traced to the original PDF representing the MC-liquid composition. Under most conditions, the single-Gamma PDF develops into a double-Gamma PDF; however, the extent of this transformation, indicative of vapour condensation onto drops, is not readily parametrized by the liquid volatility, initial carrier-gas temperature or trace vapour in the initial gas.", "doi": "10.1017/S0022112005003940", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2005-06-25", "volume": "533", "pages": "57-94" }, { "id": "authors:h1nsk-21v82", "collection": "authors", "collection_id": "h1nsk-21v82", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-073918068", "type": "article", "title": "Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 2. A posteriori modelling", "author": [ { "family_name": "Leboissetier", "given_name": "Anthony", "clpid": "Leboissetier-A" }, { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constant-coefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.", "doi": "10.1017/S0022112004002101", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2005-01-25", "volume": "523", "pages": "37-78" }, { "id": "authors:pradg-xm765", "collection": "authors", "collection_id": "pradg-xm765", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-152421976", "type": "article", "title": "Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 2. A posteriori modelling", "author": [ { "family_name": "Leboissetier", "given_name": "Anthony", "clpid": "Leboissetier-A" }, { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Large-eddy simulation (LES) is conducted of a three-dimensional temporal mixing layer whose lower stream is initially laden with liquid drops which may evaporate during the simulation. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, species, momentum and energy source terms. The drop evolution is modelled using physical drops, or using computational drops to represent the physical drops. Simulations are performed using various LES models previously assessed on a database obtained from direct numerical simulations (DNS). These LES models are for: (i) the subgrid-scale (SGS) fluxes and (ii) the filtered source terms (FSTs) based on computational drops. The LES, which are compared to filtered-and-coarsened (FC) DNS results at the coarser LES grid, are conducted with 64 times fewer grid points than the DNS, and up to 64 times fewer computational than physical drops. It is found that both constant-coefficient and dynamic Smagorinsky SGS-flux models, though numerically stable, are overly dissipative and damp generated small-resolved-scale (SRS) turbulent structures. Although the global growth and mixing predictions of LES using Smagorinsky models are in good agreement with the FC-DNS, the spatial distributions of the drops differ significantly. In contrast, the constant-coefficient scale-similarity model and the dynamic gradient model perform well in predicting most flow features, with the latter model having the advantage of not requiring a priori calibration of the model coefficient. The ability of the dynamic models to determine the model coefficient during LES is found to be essential since the constant-coefficient gradient model, although more accurate than the Smagorinsky model, is not consistently numerically stable despite using DNS-calibrated coefficients. With accurate SGS-flux models, namely scale-similarity and dynamic gradient, the FST model allows up to a 32-fold reduction in computational drops compared to the number of physical drops, without degradation of accuracy; a 64-fold reduction leads to a slight decrease in accuracy.", "doi": "10.1017/S0022112004002101", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2005-01-25", "volume": "523", "pages": "37-78" }, { "id": "authors:kfrj7-9t916", "collection": "authors", "collection_id": "kfrj7-9t916", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-102529921", "type": "article", "title": "Modeling of multicomponent-fuel drop-laden mixing layers having a multitude of species", "author": [ { "family_name": "Le Clercq", "given_name": "P. C.", "clpid": "Le-Clercq-P-C" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A formulation representing multicomponent-fuel (MC-fuel) composition as a probability distribution function (PDF) depending on the molar mass is used to construct a model of a large number of MC-fuel drops evaporating in a gas flow, so as to assess the extent of fuel specificity on the vapor composition. The PDF is a combination of two Gamma PDFs, which was previously shown to duplicate the behavior of a fuel composed of many species during single drop evaporation. The conservation equations are Eulerian for the flow and Lagrangian for the physical drops, all of which are individually followed. The gas conservation equations for mass, momentum, species, and energy are complemented by differential conservation equations for the first four moments of the gas-composition PDF; all coupled to the perfect gas equation of state. Source terms in all conservation equations couple the gas phase to the drops. The drop conservation equations for mass, position, momentum, and energy are complemented by differential equations for four moments of the liquid-composition PDF. The simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. The drop temperature is initially lower than that of the surrounding gas, initiating drop heating and evaporation. The results focus on both evolution and the state of the drops and gas when layers reach a momentum-thickness maximum past the double vortex pairing; particular emphasis is on the gas composition. Comparisons between simulations with n-decane, diesel, and three kerosenes show that at same initial Reynolds number and Stokes number distribution, a single-component fuel cannot represent MC fuels. Substantial differences among the MC-fuel vapor composition indicate that fuel specificity must be captured for the prediction of combustion.", "doi": "10.1016/j.proci.2004.07.023", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2005-01", "series_number": "2", "volume": "30", "issue": "2", "pages": "2011-2019" }, { "id": "authors:xfhmk-y2136", "collection": "authors", "collection_id": "xfhmk-y2136", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-103222230", "type": "article", "title": "Modeling of multicomponent homogeneous nucleation using continuous thermodynamics", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A theory of homogeneous nucleation in a multicomponent vapor is developed by combining classic nucleation and continuous thermodynamics concepts. The perfect gas equation of state is used in conjunction with this theory to obtain a model valid at low vapor pressures. The theory is applied to kerosenes used for fuels in aeronautics (Jet A, JP-7, and RP-1) at temperatures from 220 to 360 K and at vapor pressures up to 1 bar. The results show that although the overall nucleation trends regarding the dependency on vapor pressure and temperature are similar for all kerosenes, Jet A has a distinct behavior compared with JP-7 and RP-1. For all kerosenes, as pressure increases, the nucleus size rapidly decreases and is smallest at low temperatures.", "doi": "10.1016/j.combustflame.2004.08.012", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2004-11", "series_number": "3", "volume": "139", "issue": "3", "pages": "252-262" }, { "id": "authors:6d0xe-5zs38", "collection": "authors", "collection_id": "6d0xe-5zs38", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-075140238", "type": "article", "title": "Perturbation and initial Reynolds number effects on transition attainment of supercritical, binary, temporal mixing layers", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Two- and three-dimensional (2D and 3D) numerical simulations are performed for a heptane/nitrogen (thermodynamically) supercritical mixing layer initially perturbed at different wavelengths, including the most unstable incompressible wavelength. Simulations are performed with spanwise (and streamwise, for 3D) perturbations available in the literature (for direct numerical simulations of turbulent flow) superimposed on the mean flow, and the domain length is four times the perturbation wavelength. The 2D simulations are undertaken to ascertain that perturbations having the shortest unstable wavelength obtained from a linear inviscid stability analysis are unstable for the viscous non-linear flow. For 3D layers, the purpose of the perturbations is to accelerate the growth of the layer in order to attain transitional Reynolds numbers, as well as to generate structures similar to those that have been observed in spatial mixing layers. The goal of the 3D simulations is to ascertain whether perturbing the mixing layer at different wavelengths, in contrast to the most unstable incompressible wavelength as had previously been done, will affect the transition to turbulence. In particular, we inquire whether perturbing the layer at smaller wavelengths, which requires a smaller domain, will reduce the computational time. It is found that transition can be obtained at different perturbation wavelengths, provided that they are longer than the shortest unstable wavelength as determined by the 2D linear inviscid stability analysis, and provided that the initial Reynolds number is proportionally increased as the wavelength is decreased. The transitional states thus obtained display different dynamic and mixture characteristics, and show strong departures from perfect gas, ideal mixtures. The smaller wavelength perturbations were found to have similar computational requirements for transition attainment.", "doi": "10.1016/j.compfluid.2003.10.001", "issn": "0045-7930", "publisher": "Elsevier", "publication": "Computers & Fluids", "publication_date": "2004-09", "series_number": "8", "volume": "33", "issue": "8", "pages": "1023-1046" }, { "id": "authors:chybk-94q42", "collection": "authors", "collection_id": "chybk-94q42", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:LECpof04", "type": "article", "title": "Direct numerical simulation of a transitional temporal mixing layer laden with multicomponent-fuel evaporating drops using continuous thermodynamics", "author": [ { "family_name": "Le Clercq", "given_name": "P. C.", "clpid": "Le-Clercq-P-C" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model of a temporal three-dimensional mixing layer laden with fuel drops of a liquid containing a large number of species is derived. The fuel model is based on continuous thermodynamics, whereby the composition is statistically described through a distribution function parametrized on the species molar weight. The drop temperature is initially lower than that of the carrier gas, leading to drop heat up and evaporation. The model describing the changes in the multicomponent (MC) fuel drop composition and in the gas phase composition due to evaporation encompasses only two more conservation equations when compared with the equivalent single-component (SC) fuel formulation. Single drop results of a MC fuel having a sharply peaked distribution are shown to compare favorably with a validated SC-fuel drop simulation. Then, single drop comparisons are performed between results from MC fuel and a representative SC fuel used as a surrogate of the MC fuel. Further, two mixing layer simulations are conducted with a MC fuel and they are compared to representative SC-fuel simulations conducted elsewhere. Examination of the results shows that although the global layer characteristics are generally similar in the SC and MC situations, the MC layers display a higher momentum-thickness-based Reynolds number at transition. Vorticity analysis shows that the SC layers exhibit larger vortical activity than their MC counterpart. An examination of the drop organization at transition shows more structure and an increased drop-number density for MC simulations in regions of moderate and high strain. These results are primarily attributed to the slower evaporation of MC-fuel drops than of their SC counterpart. This slower evaporation is due to the lower volatility of the higher molar weight species, and also to condensation of already-evaporated species on drops that are transported in regions of different gas composition. The more volatile species released in the gas phase earlier during the drop lifetime reside in the lower stream while intermediary molar weight species, which egress after the drops are entrained in the mixing layer, reside in the mixing layer and form there a very heterogeneous mixture; the heavier species that evaporate later during the drop lifetime tend to reside in regions of high drop number density. This leads to a segregation of species in the gas phase based on the relative evaporation time from the drops. The ensemble-average drop temperature becomes eventually larger/smaller than the initial drop temperature in MC/SC simulations. Neither this species segregation nor the drop temperature variation with respect to the initial temperature or as a function of the mass loading can be captured by the SC-fuel simulations.", "doi": "10.1063/1.1688327", "issn": "1070-6631", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "2004-06-01", "series_number": "6", "volume": "16", "issue": "6", "pages": "1884-1907" }, { "id": "authors:y5x64-rfj52", "collection": "authors", "collection_id": "y5x64-rfj52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-101642932", "type": "article", "title": "Modeling evaporation of Jet A, JP-7, and RP-1 drops at 1 to 15 bars", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model describing the evaporation of an isolated drop of a multicomponent fuel containing hundreds of species has been developed. The model is based on continuous thermodynamics concepts wherein the composition of a fuel is statistically described using a probability distribution function (PDF). Following previous studies, this PDF is parametrized on the species molar weight. However, unlike in previous studies, a unified formulation is developed wherein the same PDF holds for three major homologous hydrocarbon classes. The new PDF is a double-Gamma-PDF that is parametrized on the square root of the molar weight. The additional advantage of the formulation is that it is valid in the subcritical region from 1 to 15 bars. Discrete species distributions for Jet A, JP-7, and RP-1 are fitted using this novel PDF and extensive calculations for isolated drops of these kerosenes are performed. The results show that under the quasi-steady gas phase assumption, the D^2 law is recovered after an initial transient. The evaporation constant is an increasing function of the far field temperature and pressure and a complex function of far field composition according to the values of the far field temperature and pressure. The difference between the surface and the far field vapor molar fraction is nearly independent of the far field pressure. The composition of the vapor at the drop surface is kerosene-fuel specific. A comparison between results obtained with a model assuming the drop interior to be well mixed and a model wherein the drop may evaporate either in a well-mixed mode or at unchanging composition shows that the percentage difference between the evaporation constant predicted by the two models is within the range of uncertainty in the transport properties.", "doi": "10.1016/j.combustflame.2004.01.012", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2004-04", "series_number": "1-2", "volume": "137", "issue": "1-2", "pages": "163-177" }, { "id": "authors:y9ss9-jy892", "collection": "authors", "collection_id": "y9ss9-jy892", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-134912781", "type": "article", "title": "Turbulence and fluid-front area production in binary-species, supercritical, transitional mixing layers", "author": [ { "family_name": "Okong'o", "given_name": "N.", "clpid": "Okong'o-N" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Databases of transitional states obtained from direct numerical simulations of temporal, supercritical mixing layers for two species systems, O_2\u2013H_2 and C_7H_(16)\u2013N_2, are analyzed to elucidate species-specific turbulence aspects and features of fluid disintegration. Although the evolution of all layers is characterized by the formation of high-density-gradient magnitude (HDGM) regions, due to the specified, smaller initial density stratification, the C_7H_(16)\u2013N_2 layers display higher growth and increased global molecular mixing as well as larger turbulence levels than comparable O_2\u2013H_2 layers. However, smaller density gradients and lower mass-fraction gradients at the transitional state for the O_2\u2013H_2 system indicate that on a local basis, the layer exhibits an enhanced mixing, this being attributed to the increased mixture solubility and to mixture near-ideality. These thermodynamic features are found responsible for a larger irreversible entropy production (dissipation) in the O_2\u2013H_2 compared to the C_7H_(16)\u2013N_2 layers. The largest O_2\u2013H_2 dissipation is primarily concentrated in HDGM regions that are distortions of the initial density stratification boundary, whereas the largest C_7H_(16)\u2013N_2 dissipation is located in HDGM regions resulting from the mixing of the two fluids. To understand fluid disintegration, the area production of a fluid front perpendicular to the mass fraction gradient is calculated in a coordinate system moving with the relative velocity between the front and the flow. On a cross-stream local basis, the C_7H_(16)\u2013N_2 layers produce more area, and area production increases with smaller perturbation wavelengths combined with larger initial Reynolds numbers. The most active area-producing layer also exhibits the largest probability of having perpendicular vorticity and mass-fraction-gradient vectors. Analysis of the terms in the area production equation shows a large pressure-gradient-term root mean square contribution for the C_7H_(16)\u2013N_2 layers, due to the coincidence of regions with large magnitudes of pressure gradient with HDGM regions. Such coincidence is attributed to real-gas behavior, which is species-system specific, as the alignment of the pressure gradient and density gradient is similar for both species systems. The alignment of the mass fraction gradient with the strain rate is also species-system dependent. Independent of species system and of the initial conditions, the vorticity is preferentially aligned with the intermediate strain-rate eigendirection, indicating that eddy-viscosity-type models are not adequate for turbulent supercritical mixing.", "doi": "10.1063/1.1688326", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2004-04", "series_number": "5", "volume": "16", "issue": "5", "pages": "1467-1492" }, { "id": "authors:jnfhn-hje51", "collection": "authors", "collection_id": "jnfhn-hje51", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-131503487", "type": "article", "title": "Mixing rules for multicomponent mixture mass diffusion coefficients and thermal diffusion factors", "author": [ { "family_name": "Harstad", "given_name": "K. G.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Mixing rules are derived for mass diffusion coefficient and thermal diffusion factor matrices by developing compatibility conditions between the fluid mixture equations obtained from nonequilibrium thermodynamics and Grad's 13-moment kinetic theory. The mixing rules are shown to be in terms of the species mole fractions and binary processes. In particular, the thermal diffusion factors for binary mixtures obtained by the Chapman\u2013Enskog expansion procedure are suitably generalized for many-component mixtures. Some practical aspects of the results are discussed including the utilization of these mixing rules for high pressure situations.", "doi": "10.1063/1.1650296", "issn": "0021-9606", "publisher": "American Institute of Physics", "publication": "Journal of Chemical Physics", "publication_date": "2004-03", "series_number": "12", "volume": "120", "issue": "12", "pages": "5664-5673" }, { "id": "authors:nnr4y-6mk74", "collection": "authors", "collection_id": "nnr4y-6mk74", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-145148525", "type": "article", "title": "Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 1. Direct numerical simulation, formulation and a priori analysis", "author": [ { "family_name": "Okong'o", "given_name": "Nora A.", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Large-eddy simulation (LES) models are presented and evaluated on a database obtained from direct numerical simulation (DNS) of a three-dimensional temporal mixing layer with evaporating drops. The gas-phase equations are written in an Eulerian frame for two perfect gas species (carrier gas and vapour emanating from the drops), while the liquid-phase equations are written in a Lagrangian frame. The effect of drop evaporation on the gas phase is considered through mass, momentum and energy source terms. The DNS database consists of transitional states attained by layers with different initial Reynolds numbers and initial liquid-phase mass loadings. Budgets of the LES equations at the transitional states show that, for the mass loadings considered, the filtered source terms (FSTs) are smaller than the resolved inviscid terms and some subgrid scale (SGS) terms, but larger than the resolved viscous stress, heat flux and mass flux terms. The irreversible entropy production (i.e. the dissipation) expression for a two-phase flow with phase change is derived, showing that the dissipation contains contributions due to viscous stresses, heat and species-mass fluxes, and source terms. For both the DNS and filtered flow fields at transition, the two leading contributions are found to be the dissipation due to the energy source term and that due to the chemical potential of the mass source. Therefore, the modelling effort is focused on both the SGS fluxes and the FSTs in the LES equations. The FST models considered are applicable to LES in which the grid is coarser than the DNS grid and, consistently, 'computational' drops represent the DNS physical drops. Because the unfiltered flow field is required for the computation of the source terms, but would not be available in LES, it was approximated using the filtered flow field or the filtered flow field augmented by corrections based on the SGS variances. All of the FST models were found to overestimate DNS-field FSTs, with the relative error of modelling the unfiltered flow field compared to the error of using computational drops showing a complex dependence on filter width and number of computational drops. For modelling the SGS fluxes and (where possible) SGS variances, constant-coefficient Smagorinsky, gradient and scale-similarity models were assessed on the DNS database, and calibrated coefficients were statistically equivalent when computed on single-phase or two-phase flows. The gradient and scale-similarity models showed excellent correlation with the SGS quantities. An a posteriori study is proposed to evaluate the impact of the studied models on the flow-field development, so as to definitively assess their suitability for LES with evaporating drops.", "doi": "10.1017/S0022112003007018", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2004-01-25", "volume": "499", "pages": "1-47" }, { "id": "authors:4k6k9-czh57", "collection": "authors", "collection_id": "4k6k9-czh57", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-155454998", "type": "article", "title": "High-Pressure Binary Mass Diffusion Coefficients for Combustion Applications", "author": [ { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A scaling for binary mass diffusion coefficients is developed using a corresponding states expression based on kinetic theory. The scaling is used to form nondimensional diffusion coefficients. Available data for high-pressure binary mass diffusion coefficients related to combustion applications are processed in conjunction with the scaling, leading to recommended scaled coefficient fits as a function of the reduced density. Data uncertainties and possible interpretation difficulties are examined. A means for comprehensive diffusion coefficient modeling over a broad (3 orders of magnitude) pressure range is suggested.", "doi": "10.1021/ie0304558", "issn": "0888-5885", "publisher": "American Chemical Society", "publication": "Industrial & Engineering Chemistry Research", "publication_date": "2004-01-21", "series_number": "2", "volume": "43", "issue": "2", "pages": "645-654" }, { "id": "authors:ycypa-6v540", "collection": "authors", "collection_id": "ycypa-6v540", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-084425585", "type": "article", "title": "Real-Gas Effects on Mean Flow and Temporal Stability of Binary-Species Mixing Layers", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Real-gas effects on the mean flow and inviscid stability of temporal mixing layers are examined for supercritical\nheptane/nitrogen and oxygen/hydrogen mixtures. The analysis is based on the compressible Navier\u2013Stokes equations for conservation of mass, momentum, total energy, and species mass, with heat and species-mass fluxes derived from fluctuation-dissipation theory and incorporating Soret and Dufour effects. An approximate form of the equations is used to obtain a system of similarity equations for the streamwise velocity, the temperature, and the mass fraction. The similarity profiles show important real-gas nonideal-mixture effects, particularly for the temperature, in departing from the incompressible error-function similarity solution. Realistic Schmidt and Prandtl numbers were found to be important to the similarity profiles. A linear, inviscid stability analysis is then performed using the similarity profile, as well as analytical error-function profiles, as its basic flow. The stability\nanalysis shows that the similarity profile has larger growth rates at a given wavelength and a shorter more unstable wavelength than the error-function profiles and than an incompressible flow. The similarity profile also has a larger range of unstable wavelengths than the error-function profiles.", "doi": "10.2514/2.6842", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2003-12", "series_number": "12", "volume": "41", "issue": "12", "pages": "2429-2443" }, { "id": "authors:j16f6-6n993", "collection": "authors", "collection_id": "j16f6-6n993", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-145459492", "type": "article", "title": "Statistical Model of Multicomponent-Fuel Drop Evaporation for Many-Drop Flow Simulations", "author": [ { "family_name": "Harstad", "given_name": "K. G.", "clpid": "Harstad-K-G" }, { "family_name": "Le Clercq", "given_name": "P. C.", "clpid": "Le-Clercq-P-C" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A statistical formulation is developed describing the composition in an evaporating multicomponent-fuel liquid\ndrop and in the gas phase surrounding it. When a complementary discrete-component model is used, it is shown\nthat, when drops are immersed in a carrier gas containing fuel vapor, condensation of species onto the drop results in\nthe development of a minor peak in the liquid composition probability distribution function (PDF). This peak leads\nto a PDF shape that can be viewed as a combination of two gamma PDFs, which is determined by five parameters.\nA model is developed for calculating the parameters of the two combined gamma PDFs. Extensive tests of the\nmodel for both diesel and gasoline show that the PDF results replicate accurately the discrete model predictions.\nMost important, the mean and variance of the composition at the drop surface are in excellent agreement with\nthe discrete model. Results from the model show that although the second peak is minor for the liquid PDF, its\ncorresponding peak for the vapor distribution at the drop surface has a comparable magnitude to and sometimes\nexceeds that corresponding to the first peak. Four-parameter models are also exercised, and it is shown that they are unable to capture the physics of the problem.", "doi": "10.2514/2.1894", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2003-10", "series_number": "10", "volume": "41", "issue": "10", "pages": "1858-1874" }, { "id": "authors:2zeze-jyc81", "collection": "authors", "collection_id": "2zeze-jyc81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-104249859", "type": "article", "title": "On de-coupling of Shvab-Zel'dovich variables in the presence of diffusion", "author": [ { "family_name": "Lam", "given_name": "S. H.", "clpid": "Lam-S-H" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "In multi-component reacting flows, it is well-known that significant simplifications are available when the \"all-Lewis-numbers-are-unity\" assumption can be justified. Under this assumption, certain linear combinations of the dependent variables, commonly known as the Shvab-Zel'dovich (SZ) variables, are \"decoupled\" from the chemistry terms. A derivation is presented here showing that the same simplifications can be achieved under less-restrictive conditions. The means to check whether these conditions are satisfied is provided.", "doi": "10.1016/S0010-2180(02)00519-9", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2003-03", "series_number": "4", "volume": "132", "issue": "4", "pages": "691-696" }, { "id": "authors:682rr-4xs74", "collection": "authors", "collection_id": "682rr-4xs74", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-104830532", "type": "article", "title": "A posteriori assessment of assumptions used in the modeling of dense reactive granular flows", "author": [ { "family_name": "Lathouwers", "given_name": "D.", "clpid": "Lathouwers-D" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "To describe complex granular flow in fluidized bed reactors, Lathouwers and Bellan [1] have developed a validated fundamental model accounting for the different history of the two particle classes represented by the sand (subscript s) and biomass (subscript b), and for the interaction between gas and particles. The addition of a heat transfer model and of the validated kinetic scheme of Miller and Bellan [2] by Lathouwers and Bellan [3] warrants a re-evaluation of the assumptions used to derive the hydrodynamic model. Specifically, here we assess the hypothesis that the relative velocity between particles is small in the context of calculating the granular transport properties, the assumption that the effect of the surrounding gas on the granular stress tensor and granular conductivity is negligible, and we also evaluate the importance to the heat-transfer correction factor because of mass blowing from the particles.", "doi": "10.1016/S0010-2180(02)00412-1", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2002-11", "series_number": "3", "volume": "131", "issue": "3", "pages": "353-356" }, { "id": "authors:w09gp-ea494", "collection": "authors", "collection_id": "w09gp-ea494", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-124143361", "type": "article", "title": "Direct numerical simulations of two-phase laminar jet flows with different cross-section injection geometries", "author": [ { "family_name": "Abdel-Hameed", "given_name": "H.", "clpid": "Abdel-Hameed-H" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations are performed of spatial, three-dimensional, laminar jets of different inlet geometric configurations for the purpose of quantifying the characteristics of the flows; both single-phase (SP) and two-phase (TP) free jets are considered. The TP jets consist of gas laden with liquid drops randomly injected at the inlet. Drop evaporation ensues both due to the gaseous flow being initially unvitiated by the vapor species corresponding to the liquid drops, and to drop heating as the initial drop temperature is lower than that of the carrier gas. The conservation equations for the TP flow include complete couplings of mass, momentum, and energy based on thermodynamically self-consistent specification of the vapor enthalpy, internal energy, and latent heat of vaporization. Inlet geometries investigated are circular, elliptic, rectangular, square, and triangular. The results focus both on the different spreading achieved according to the inlet geometry, as well as on the considerable change in the flow field due to the presence of the drops. The most important consequence of the drop interaction with the flow is the production of streamwise vorticity that alters entrainment and species mixing according to the inlet geometry. Similar to their SP equivalent, TP jets are shown to reach steady-state entrainment; examination of the flows at this time station shows that the potential cores of TP jets are shorter by an order of magnitude than their SP counterpart. Moreover, whereas the TP circular jet exhibits a symmetric entrainment pattern well past the streamwise location of the potential core, noncircular jets display at the same location strong departures from symmetry. Furthermore, the SP-jet phenomenon of axis switching is no longer present in TP jets. The distributions of drop-number density, liquid mass, and evaporated species are compared for different inlet cross sections and recommendations are made regarding the optimal choice for different applications.", "doi": "10.1063/1.1504712", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2002-09", "series_number": "10", "volume": "14", "issue": "10", "pages": "3655-3674" }, { "id": "authors:7hx42-y1f63", "collection": "authors", "collection_id": "7hx42-y1f63", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-081326190", "type": "article", "title": "Direct numerical simulation of a transitional supercritical binary mixing layer: heptane and nitrogen", "author": [ { "family_name": "Okong'o", "given_name": "Nora A.", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations (DNS) of a supercritical temporal mixing layer are conducted for the purpose of exploring the characteristics of high-pressure transitional mixing behaviour. The conservation equations are formulated according to fluctuation-dissipation (FD) theory, which is consistent with non-equilibrium thermodynamics and converges to kinetic theory in the low-pressure limit. According to FD theory, complementing the low-pressure typical transport properties (viscosity, diffusivity and thermal conductivity), the thermal diffusion factor is an additional transport property which may play an increasingly important role with increasing pressure. The Peng\u2013Robinson equation of state with appropriate mixing rules is coupled to the dynamic conservation equations to obtain a closed system. The boundary conditions are periodic in the streamwise and spanwise directions, and of non-reflecting outflow type in the cross-stream direction. Due to the strong density stratification, the layer is considerably more difficult to entrain than equivalent gaseous or droplet-laden layers, and exhibits regions of high density gradient magnitude that become very convoluted at the transitional state. Conditional averages demonstrate that these regions contain predominantly the higher-density, entrained fluid, with small amounts of the lighter, entraining fluid, and that in these regions the mixing is hindered by the thermodynamic properties of the fluids. During the entire evolution of the layer, the dissipation is overwhelmingly due to species mass flux followed by heat flux effects with minimal viscous contribution, and there is a considerable amount of backscatter in the flow. Most of the species mass flux dissipation is due to the molecular diffusion term with significant contributions from the cross-term proportional to molecular and thermal diffusion. These results indicate that turbulence models for supercritical fluids should primarily focus on duplicating the species mass flux rather than the typical momentum flux, which constitutes the governing dissipation in atmospheric mixing layers. Examination of the passive-scalar probability density functions (PDFs) indicates that neither the Gaussian, nor the beta PDFs are able to approximate the evolution of the DNS-extracted PDF from its inception through transition. Furthermore, the temperature\u2013species PDFs are well correlated, meaning that their joint PDF is not properly approximated by the product of their marginal PDFs; this indicates that the traditional reactive flow modelling based on replacing the joint PDF representing the reaction rate by the product of the marginal PDFs is not appropriate. Finally, the subgrid-scale temperature\u2013species PDFs are also well correlated, and the species PDF exhibits important departures from the Gaussian. These results suggest that classic PDFs used in atmospheric pressure flows would not capture the physics of this supercritical mixing layer, either in an assumed PDF model at the larger scale, or at the subgrid scale.", "doi": "10.1017/S0022112002008480", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2002-08-10", "volume": "464", "pages": "1-34" }, { "id": "authors:7bwpj-twg20", "collection": "authors", "collection_id": "7bwpj-twg20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-144446319", "type": "article", "title": "Direct Numerical Simulations of O_2/H_2 Temporal Mixing Layers Under Supercritical Conditions", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Harstad", "given_name": "Kenneth", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations of a supercritical oxygen/hydrogen temporal three-dimensional mixing layer are conducted to explore the features of high-pressure transitional mixing behavior. The conservation equations are\nformulated according to fluctuation\u2013dissipation theory and are coupled to a modified Peng\u2013Robinson equation\nof state. The boundary conditions are periodic in the streamwise and spanwise directions and of nonreflecting\noutflow type in the cross-stream direction. Simulations are conducted with initial Reynolds numbers of 6 x 10^2\nand 7.5 x 10^2, initial pressure of 100 atm, and temperatures of 400 K in the O_2 and 600 K in the H_2 stream. Each\nsimulation encompasses the rollup and pairing of four initial spanwise vortices into a single vortex. The layer eventually\nexhibits distorted regions of high density-gradient-magnitude similar to the experimentally observed wisps\nof fluid at the boundary of supercritical jets. Analysis of the data reveals that the higher-Reynolds-number layer\nreaches transition, whereas the other one does not. The transitional layer is analyzed to elucidate its characteristics.", "doi": "10.2514/2.1728", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "2002-05", "series_number": "5", "volume": "40", "issue": "5", "pages": "914-926" }, { "id": "authors:te5rv-fg152", "collection": "authors", "collection_id": "te5rv-fg152", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-105455457", "type": "article", "title": "Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Previously developed characteristic-wave-based boundary conditions for multicomponent perfect gas mixtures are here extended to real gas mixtures. The characteristic boundary conditions are derived from the one-dimensional wave decomposition of the Euler equations, and the wave amplitude variations are determined from the prescribed boundary conditions on the flow variables. The viscous conditions are applied separately. For multidimensional simulations, the boundary conditions for each coordinate direction are applied additively. These boundary conditions are tested on a representative two-dimensional problem\u2014the propagation of an incompressible vortex by a supersonic flow with outflow conditions specified as nonreflecting\u2014solved using a high-order finite-difference scheme. Simulations conducted for a heptane\u2013nitrogen mixture flow with strong real gas effects display excellent, nonreflective wave behavior as the vortex leaves the computational domain, verifying the suitability of this method for the multidimensional multicomponent real gas flows computed.", "doi": "10.1006/jcph.2002.6990", "issn": "0021-9991", "publisher": "Elsevier", "publication": "Journal of Computational Physics", "publication_date": "2002-03-01", "series_number": "2", "volume": "176", "issue": "2", "pages": "330-344" }, { "id": "authors:t1y6n-w1b17", "collection": "authors", "collection_id": "t1y6n-w1b17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-110047558", "type": "article", "title": "Modeling of dense gas\u2013solid reactive mixtures applied to biomass pyrolysis in a fluidized bed", "author": [ { "family_name": "Lathouwers", "given_name": "D.", "clpid": "Lathouwers-D" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model is presented for mathematically describing the thermofluid dynamics of dense, reactive, gas\u2013solid mixtures. The model distinguishes among multiple particle classes, either on the basis of their physical properties (diameter, density) or through their thermochemistry (reactive versus inert particles). A multifluid approach is followed where macroscopic equations are derived from the kinetic theory of granular flows using inelastic rigid-sphere models, thereby accounting for collisional transfer in high-density regions. Separate transport equations are constructed for each of the particle classes, allowing for the description of the independent acceleration of the particles in each class and the interaction between size classes, as well as for the equilibration processes whereby momentum and energy are exchanged between the respective classes and the carrier gas. Aimed at high-density suspensions, such as fluidized beds, the relations obtained for the stress tensor are augmented by a model for frictional transfer, suitably extended to multiple-class systems. This model, previously derived, is here enlarged to include heat and mass transfer, as well as chemical reactions and is therefore applicable to general gas\u2013solid combustion systems. The noteworthy novelties of the model with respect to other derivations in the literature include: (i) a systematic and consistent derivation of the solids transport equations and transport properties within the multifluid concept, allowing for non-equilibrium effects between the respective particle classes, (ii) the ability to explicitly account for the possibility of porous solid fuel particles, and (iii) the modeling of multiple chemical reactions in both gas and solid phases and the associated effects of heat and mass transfer. The model, which includes a separately validated chemistry model, is applied to high-temperature biomass particle pyrolysis in a lab-scale fluidized bed reactor and is used to obtain yield of reaction products. The results indicate that, at fixed initial particle size, the fluidizing gas temperature is the foremost parameter influencing tar yield. The biomass feed temperature, the nature of the feedstock, and the fluidization velocity all have minor impact on the yield. It is also shown that the fluidizing gas temperature can be optimized for maximizing the tar yield.", "doi": "10.1016/S0301-9322(01)00059-3", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "2001-12", "series_number": "12", "volume": "27", "issue": "12", "pages": "2155-2187" }, { "id": "authors:gac0g-xj548", "collection": "authors", "collection_id": "gac0g-xj548", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-111028665", "type": "article", "title": "Evaluation of commonly used assumptions for isolated and cluster heptane drops in nitrogen at all pressures", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A study is performed to assess commonly used assumptions in the modeling of drop behavior in moderate to high temperature surroundings and at all pressures. The model employed for this evaluation has been previously validated for isolated drops by using microgravity data, and is very general: it contains Soret and Dufour effects, does not assume mass transfer quasi-steadiness at the drop boundary, or necessarily the existence of a drop surface (i.e., phase discontinuity). Moreover, the numerical simulations are performed with accurate equations of state and transport properties over a wide range of thermodynamic variables. Consistent with low pressure conditions, the drop boundary is identified a posteriori of the calculations with the location of the largest density change. Simulations are here performed for isolated drops, and for monodisperse as well as binary size drop clusters. The results show that at locations arbitrarily near the boundary, the drop does not reach the mixture critical point within the wide range of conditions investigated (far-field temperatures of 470\u20131000 K and pressures ranging from 0.1 to 5 MPa). However, the state arbitrarily near the boundary is closer to the critical condition for smaller drops in a cluster than for the larger drops. Evaluations of the effect of the relaxation time at the drop boundary show that quasi-steadiness of the mass transfer prevails for drops of radius as small as 2 \u00d7 10^(\u22123) cm. Finally, the diameter squared exhibits a linear time variation only at atmospheric pressure. At all other pressures investigated (1\u20135 MPa), the diameter squared displays a negative curvature with time which never becomes linear. In agreement with existing experimental data, the drop lifetime increases monotonically with pressure at low far field temperatures (470 K), but exhibits a maximum as a function of pressure at high temperatures (1000 K). On an appropriate scale, the slope of the diameter squared versus time is shown to be independent of the drop size at all pressures.", "doi": "10.1016/S0010-2180(01)00292-9", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2001-10", "series_number": "1-2", "volume": "127", "issue": "1-2", "pages": "1861-1879" }, { "id": "authors:tf2pk-57q17", "collection": "authors", "collection_id": "tf2pk-57q17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-144632493", "type": "article", "title": "Yield Optimization and Scaling of Fluidized Beds for Tar Production from Biomass", "author": [ { "family_name": "Lathouwers", "given_name": "D.", "clpid": "Lathouwers-D" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A numerical study is performed in order to evaluate the performance and optimal operating conditions of fluidized bed pyrolysis reactors used for condensable tar production from biomass. For this purpose, a previously validated biomass particle pyrolysis model is coupled with a detailed hydrodynamic model for the binary gas particle mixture. The kinetics scheme is based on superimposed cellulose, hemicellulose, and lignin reactions. Any biomass feedstock can be simulated through knowledge of its initial mass composition with respect to these three primary components. The separately validated hydrodynamic model is based on a three-fluid model (gas, sand, and biomass) derived from the kinetic theory of granular flows. Separate transport equations are constructed for each particle class, allowing for the description of such phenomena as particle segregation and for separate temperatures for each particle class. The model is employed to investigate the effect of various operating conditions on the efficiency of tar collection in fluidized bed reactors. Results indicate that, at fixed particle size, the operating temperature is the foremost parameter influencing tar yield. The biomass feed temperature, the feedstock, and fluidization velocity magnitude, all have minor impact on the yield. The particle diameter has a considerable influence on the short-time tar yield, but it is inferred that it may have a more moderate influence on the steady-state tar yield. For the range of fluidizing gas temperatures investigated, optimum steady-state tar collection is obtained for 750 K under the assumption that the pyrolysis rate is faster than the feed rate; the predicted optimum temperature is only slightly higher if this assumption is not satisfied. Finally, scale-up of the reactor is addressed and is found to have a small negative effect on tar collection at the optimal operating temperature. It is also found that slightly better scaling is obtained by using shallow fluidized beds with higher fluidization velocity.", "doi": "10.1021/ef010053h", "issn": "0887-0624", "publisher": "American Chemical Society", "publication": "Energy and Fuels", "publication_date": "2001-09", "series_number": "5", "volume": "15", "issue": "5", "pages": "1247-1262" }, { "id": "authors:nmxjw-wa012", "collection": "authors", "collection_id": "nmxjw-wa012", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-154826158", "type": "article", "title": "Direct numerical simulations of supercritical fluid mixing layers applied to heptane\u2013nitrogen", "author": [ { "family_name": "Miller", "given_name": "Richard S.", "clpid": "Miller-R-S" }, { "family_name": "Harstad", "given_name": "Kenneth G.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations (DNS) are conducted of a model hydrocarbon\u2013nitrogen mixing layer under supercritical conditions. The temporally developing mixing layer configuration is studied using heptane and nitrogen supercritical fluid streams at a pressure of 60 atm as a model system related to practical hydrocarbon-fuel/air systems. An entirely self-consistent cubic Peng\u2013Robinson equation of state is used to describe all thermodynamic mixture variables, including the pressure, internal energy, enthalpy, heat capacity, and speed of sound along with additional terms associated with the generalized heat and mass transport vectors. The Peng\u2013Robinson formulation is based on pure-species reference states accurate to better than 1% relative error through comparisons with highly accurate state equations over the range of variables used in this study (600 \u2a7d T \u2a7d 1100 K, 40 \u2a7d p \u2a7d 80 atm) and is augmented by an accurate curve fit to the internal energy so as not to require iterative solutions. The DNS results of two-dimensional and three-dimensional layers elucidate the unique thermodynamic and mixing features associated with supercritical conditions. Departures from the perfect gas and ideal mixture conditions are quantified by the compression factor and by the mass diffusion factor, both of which show reductions from the unity value. It is found that the qualitative aspects of the mixing layer may be different according to the specification of the thermal diffusion factors whose value is generally unknown, and the reason for this difference is identified by examining the second-order statistics: the constant Bearman\u2013Kirkwood (BK) thermal diffusion factor excites fluctuations that the constant Irwing\u2013Kirkwood (IK) one does not, and thus enhances overall mixing. Combined with the effect of the mass diffusion factor, constant positive large BK thermal diffusion factors retard diffusional mixing, whereas constant moderate IK factors tend to promote diffusional mixing. Constant positive BK thermal diffusion factors also tend to maintain density gradients, with resulting greater shear and vorticity. These conclusions about IK and BK thermal diffusion factors are species-pair dependent, and therefore are not necessarily universal. Increasing the temperature of the lower stream to approach that of the higher stream results in increased layer growth as measured by the momentum thickness. The three-dimensional mixing layer exhibits slow formation of turbulent small scales, and transition to turbulence does not occur even for a relatively long non-dimensional time when compared to a previous, atmospheric conditions study. The primary reason for this delay is the initial density stratification of the flow, while the formation of strong density gradient regions both in the braid and between-the-braid planes may constitute a secondary reason for the hindering of transition through damping of emerging turbulent eddies.", "doi": "10.1017/S0022112001003895", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "2001-06-10", "volume": "436", "pages": "1-39" }, { "id": "authors:6f3gw-3te36", "collection": "authors", "collection_id": "6f3gw-3te36", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-111811362", "type": "article", "title": "The D^2 variation for isolated LOX drops and polydisperse clusters in hydrogen at high temperature and pressures", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A study of the d^2 variation for isolated fluid drops and for fluid drops belonging to polydisperse clusters has been conducted at a high temperature and elevated pressures. The mathematical formulation is based on a previously validated model of subcritical/supercritical isolated fluid drop behavior. Coupled with the isolated drop equations, a set of conservation equations has been developed to describe the global cluster behavior. All these equations are based on the general transport matrix including Soret and Dufour terms and they are consistent with nonequilibrium thermodynamics and at low pressure with kinetic theory. Moreover, the model also accounts for real gas effects through accurate equations of state and for correct values of the transport properties in the high pressure, high temperature regime. The model has been first exercised for isolated LOX drops in H_2 at pressures ranging from 1.5 MPa (subcritical pressure for O_2) to 20 MPa (supercritical pressure for O_2). The results show that while at subcritical pressures the d^2 variation is nearly linear, with increasing pressure it departs considerably from the linear behavior; the largest departure occurs in the vicinity of the oxygen critical point. The slope of d^2(t) was fitted using both a constant and a linear fit, and it was shown that the linear fit provides a better alternative for correlation purposes. Simulations were also conducted for clusters of LOX drops in H_2 in the range 6 to 40 MPa (reduced pressures of 1.2\u20138 with respect to pure O_2). Parametric studies of the effect of the thermal diffusion factor value reveal that it is minor at 10 MPa and moderate at 40 MPa, and that although the Soret term is dominated by the Fick, Dufour, and Fourier terms, it is not negligible. The influence of a cluster Nusselt number is also shown to be relatively small in the range 10^3 to 10^4, consistent with the supercritical behavior being essentially a diffusive one. All of the results show a nonlinear d^2 variation with curves having a positive curvature independent of the values of the thermal diffusion factor, the Nusselt number or the LOX/H_2 mass ratio. The approximation of a binary size cluster containing relatively a much larger number of small drops by a monodisperse cluster with a drop size based upon the surface average of the drops in the polydisperse cluster yields a good evaluation of the thermodynamic quantities in the interstitial drop region but an underestimate of the lifetime of the drops in the cluster.", "doi": "10.1016/S0010-2180(00)00217-0", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "2001-03", "series_number": "4", "volume": "124", "issue": "4", "pages": "535-550" }, { "id": "authors:qkc2w-16m17", "collection": "authors", "collection_id": "qkc2w-16m17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-111417758", "type": "article", "title": "An all-pressure fluid drop model applied to a binary mixture: heptane in nitrogen", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The differences between subcritical liquid drop and supercritical fluid drop behavior are shown to be a direct consequence of the length scales near the fluid drop boundary. Under subcritical, evaporative high emission rate conditions, a film layer is present in the inner part of the drop surface which contributes to the unique determination of the boundary conditions; it is this film layer in conjunction with evaporation which gives to the solution its convective\u2013diffusive character. In contrast, under supercritical conditions the boundary conditions contain a degree of arbitrariness due to the absence of a physical surface, and the solution has then a purely diffusive character. Results from simulations of a free fluid drop under no-gravity conditions are compared to microgravity experimental data from suspended, large drop experiments at high, low and intermediary temperatures and in a range of pressures encompassing the sub- and supercritical regime. Despite the difference between the conditions of the simulations and the experiments, the time rate of variation of the drop diameter square is remarkably well predicted in the linear curve regime. Consistent with the optical measurements, in the simulations the drop diameter is determined from the location of the maximum density gradient. Detailed time-wise comparisons between simulations and data show that this location is very well predicted at 0.1 MPa. As the pressure increases, the data and simulations agreement becomes good to fair, and the possible reasons for this discrepancy are discussed. Simulations are further conducted for a small drop, such as that encountered in practical applications, over a wide range of specified, constant far field pressures. Additionally, a transient pressure simulation crossing the critical point is also conducted. Results from these simulations are analyzed and major differences between the sub- and supercritical behavior are explained. In particular, it is shown that the classical calculation of the Lewis number gives erroneous results at supercritical conditions, and that an effective Lewis number previously defined gives correct estimates of the length scales for heat and mass transfer at all pressures.", "doi": "10.1016/S0301-9322(99)00108-1", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "2000-10-01", "series_number": "10", "volume": "26", "issue": "10", "pages": "1675-1706" }, { "id": "authors:mwezt-1x044", "collection": "authors", "collection_id": "mwezt-1x044", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-080716513", "type": "article", "title": "Supercritical (and subcritical) fluid behavior and modeling: drops, streams, shear and mixing layers, jets and sprays", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A critical review of recent investigations in the realm of supercritical (and subcritical) fluid behavior is presented with the goal of obtaining a perspective on the peculiarities of high pressure observations. Experiments with drops, isolated or in groups, streams, shear and mixing layers, jets and sprays are tabulated and discussed as a precursor to forming a conceptual picture of fluid comportment. The physics of fluid behavior in the supercritical and subcritical regimes is discussed, and major differences between the observations in these two regimes are identified and explained. A variety of supercritical fluid models is then examined in the context of drop studies, and salient aspects of fluid behavior are identified. In particular, a model that has been validated with microgravity drop experiments is described and summarized; in this validated model, the differences in subcritical/supercritical comportment are interpreted in terms of lengths scales and it is this difference that is responsible for the traditional Lewis number expression no longer portraying the ratio of heat to mass transfer in supercritical fluids; instead, an effective Lewis number is recommended that gives a realistic estimate of the ratio of these length scales. Furthermore, the application of various fluid models to the description of supercritical fluid in various geometric configurations is discussed for conditions relevant to liquid rocket, Diesel and gas turbine engines. Such preliminary simulations performed with the validated fluid model have already reproduced some specific experimental features of supercritical fluid jet disintegration. Finally, comments are offered regarding future areas of research.", "doi": "10.1016/S0360-1285(00)00008-3", "issn": "0360-1285", "publisher": "Elsevier", "publication": "Progress in Energy and Combustion Science", "publication_date": "2000-08", "series_number": "4-6", "volume": "26", "issue": "4-6", "pages": "329-366" }, { "id": "authors:bm66k-ph253", "collection": "authors", "collection_id": "bm66k-ph253", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-151801695", "type": "article", "title": "A priori subgrid analysis of temporal mixing layers with evaporating droplets", "author": [ { "family_name": "Okong'o", "given_name": "Nora", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a direct numerical simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using an Eulerian formulation, with Lagrangian droplet tracking. The large eddy simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by using the DNS database. Since LES of this flow requires the computation of droplet source terms, it is essential to obtain the unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points. This paper proposes to model these unfiltered gas-phase variables at the drop locations by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the subgrid scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the gradient model and the scale-similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the gradient and scale-similarity methods give results in excellent agreement with the DNS.", "doi": "10.1063/1.870405", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2000-05", "series_number": "6", "volume": "12", "issue": "6", "pages": "1573-1591" }, { "id": "authors:55zet-7y390", "collection": "authors", "collection_id": "55zet-7y390", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-142113982", "type": "article", "title": "Direct numerical simulation and subgrid analysis of a transitional droplet laden mixing layer", "author": [ { "family_name": "Miller", "given_name": "Richard S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations of a temporally developing, droplet laden mixing layer undergoing transition to mixing turbulence are conducted. The formulation includes complete two-way couplings of mass, momentum, and energy. As many as 18\u00d710^6 grid points are used to discretize the Eulerian gas phase equations and up to 5.7\u00d710^6 initially polydisperse evaporating droplets are tracked in the Lagrangian reference frame. The complete transition to mixing turbulence is captured for several of the higher Reynolds number simulations and it is observed that increasing the droplet mass loading ratio results in a more \"natural\" turbulence characterized by increased rotational energy and less influence of the initial forcing perturbations. An increased mass loading also results in increased droplet organization within the layer. An a priori subgrid analysis is then conducted which shows that neglecting subgrid velocity fluctuations in the context of large eddy simulations may result in significant errors in predicting the droplet drag force for Stokes numbers St\u223c1 (with the flow time scale based on the mean velocity difference and initial vorticity thickness). Similar possible errors of lesser magnitude are also observed for the droplet heat flux and evaporation rate when thermodynamic subgrid fluctuations are neglected. An extension of the eddy interaction model commonly used in Reynolds-averaged simulations is then proposed in order to account for the missing subgrid information. Probability density functions (PDFs) of the subgrid fluctuations calculated across homogeneous planes are shown to be highly intermittent, particularly near the laminar\u2013turbulent boundaries of the mixing layer. However, the actual subgrid PDFs calculated locally are much less intermittent and may be adequately modeled by the Gaussian distribution throughout the majority of the mixing layer. A scale similarity model is then employed to predict both the velocity and thermodynamic subgrid variances. The similarity model is well correlated with the actual subgrid variances and shows good agreement in predicting the local fluctuation intensities when a filter width-dependent model constant is used. The subgrid fluctuation variances acting on the droplets are then shown to be well modeled if the Eulerian subgrid variance model is interpolated to the droplet locations.", "doi": "10.1063/1.870271", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "2000-02", "series_number": "3", "volume": "12", "issue": "3", "pages": "650-671" }, { "id": "authors:fgyeh-evs61", "collection": "authors", "collection_id": "fgyeh-evs61", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-075841503", "type": "article", "title": "Perspectives on Large Eddy Simulations for Sprays: Issues and Solutions", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A review of the large eddy simulations (LES) methodology is presented in the context of sprays. Issues related to modeling both the drop interaction with the carrier flow and the interaction among drops are discussed. Appropriate direct numerical simulations (DNS) for use as precursors to LES, and the extraction of subgrid scale (SGS) models are both described. Particular attention is devoted to LES aspects which are different from those of single-phase flows. These include the correct portrayal of the drop interaction with small turbulent scales, the modeling of SGS stresses, SGS heat and SGS species fluxes, and the accurate representation in the carrier flow equations of the source terms associated with the presence of the drops. Recommendations for future work are also offered.", "doi": "10.1615/AtomizSpr.v10.i3-5.90", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "2000", "series_number": "3-5", "volume": "10", "issue": "3-5", "pages": "409-425" }, { "id": "authors:117ew-rpk30", "collection": "authors", "collection_id": "117ew-rpk30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-130158589", "type": "article", "title": "Entropy production of emerging turbulent scales in a temporal supercritical n-heptane/nitrogen three-dimensional mixing layer", "author": [ { "family_name": "Okong'o", "given_name": "N.", "clpid": "Okong'o-N-A" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A study of emerging turbulent scales entropy production was conducted for a supercritical shear layer as a precursor to the eventual modeling of subgrid scales (SGS: from a turbulent state) leading to large eddy simulations (LES). The entropy equation was first developed for a real, non-ideal fluid using a validated all-pressure fluid model, and the entropy flux and production terms were identified. Employing a direct numerical simulation (DNS) created database of a temporal three-dimensional supercritical shear layer using the fluid model, the different contributions to the irreversible entropy production term were evaluated. Both domain averaged and root mean square (RMS) terms were computed at three different stages of the DNS, representing the timewise ascending, culmination, and descending branches of the spatially averaged positive spanwise vorticity. The unifltered and filtered databases were compared to evaluate the relative importance of irreversible entropy production from viscous, Fourier heat diffusion, and molar fluxes terms. The results show that the average entropy production is dominated by the viscous terms at all stages of the evolution: however, the contribution to the RMS of the molar flux term for both the ascending and descending branches is non-negligible. This latter result was traced to the molar gradients tending to be smeared by emerging turbulent scales. Based on this finding a physical picture of the layer evolution was presented involving competition between large scales entraining heavy fluid from the lower stream and forming strong density and mass fraction gradients at spatially varying locations with time, and small-scale turbulent structures evolving but being damped by contact with the newly formed strong density gradient regions which act similar to material surfaces. Analysis of the results showed that the primary contribution to the molar flux dissipation for both the average and the RMS is the mixture non-ideality.", "doi": "10.1016/S0082-0784(00)80248-9", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2000", "series_number": "1", "volume": "28", "issue": "1", "pages": "497-504" }, { "id": "authors:fydms-wjf45", "collection": "authors", "collection_id": "fydms-wjf45", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-131856863", "type": "article", "title": "Modeling and simulation of bubbling fluidized beds containing particle mixtures", "author": [ { "family_name": "Lathouwers", "given_name": "D.", "clpid": "Lathouwers-D" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A comprehensive model is presented for mathematically describing the isothermal, non-reactive, fluid dynamics of a mixture of particles in a gas. A multifluid approach was followed in which macroscopic transport equations were derived by taking suitable ensemble averages of the local gas and particle dynamic equations. A standard phasic ensemble average was selected for the gas phase, whereas the particle equations were derived using a kinetic theory approach in which collisional transfer is included. Separate transport equations were constructed for each of the particle classes, allowing for the description of the independent acceleration of the particles in each class and the equilibration processes whereby momentum and energy are exchanged between each class, leading to a wider range of applicability than common mixture equations have. Closure of the particle equations was exercised by providing separate velocity distributions for each of the particle classes, here specified as Gaussian: this is a valid approach for small gradients in the mean variables, and for nearly elastic particles. In the region of very high solids volume fractions, the relations obtained for the stress tensor were augmented by a model describing frictional transfer. The model was applied to three different test cases: (1) prediction of the shear and normal stresses in a homogeneous shear flow, (2) simulation of the particle pressure along the wall of a bubbling bed, and (3) a comparison between simulations of monodisperse and binary mixtures in a homogeneously aerated bed. Where possible to compare, correspondence between simulations and available experimental data is reasonable.", "doi": "10.1016/S0082-0784(00)80640-2", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "2000", "series_number": "2", "volume": "28", "issue": "2", "pages": "2297-2304" }, { "id": "authors:4rng4-prv10", "collection": "authors", "collection_id": "4rng4-prv10", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-080217729", "type": "article", "title": "Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Direct numerical simulations are performed of a confined three-dimensional, temporally developing, initially isothermal gas mixing layer with one stream laden with as many as 7.3\u00d710^5 evaporating hydrocarbon droplets, at moderate gas temperature and subsonic Mach number. Complete two-way phase couplings of mass, momentum and energy are incorporated which are based on a thermodynamically self-consistent specification of the vapour enthalpy, internal energy and latent heat of vaporization. Effects of the initial liquid mass loading ratio (ML), initial Stokes number (St0), initial droplet temperature and flow three-dimensionality on the mixing layer growth and development are discussed. The dominant parameter governing flow modulation is found to be the liquid mass loading ratio. Variations in the initial Stokes number over the range 0.5 \u2a7d St_0 \u2a7d 2.0 do not cause significant modulations of either first- or second-order gas phase statistics. The mixing layer growth rate and kinetic energy are increasingly attenuated for increasing liquid loadings in the range 0 \u2a7d ML \u2a7d 0.35. The laden stream becomes saturated before evaporation is completed for all but the smallest liquid loadings owing to: (i) latent heat effects which reduce the gas temperature, and (ii) build up of the evaporated vapour mass fraction. However, droplets continue to be entrained into the layer where they evaporate owing to contact with the relatively higher-temperature vapour-free gas stream. The droplets within the layer are observed to be centrifuged out of high-vorticity regions and to migrate towards high-strain regions of the flow. This results in the formation of concentration streaks in spanwise braid regions which are wrapped around the periphery of secondary streamwise vortices. Persistent regions of positive and negative slip velocity and slip temperature are identified. The velocity component variances in both the streamwise and spanwise directions are found to be larger for the droplets than for the gas phase on the unladen stream side of the layer; however, the cross-stream velocity and temperature variances are larger for the gas. Finally, both the mean streamwise gas velocity and droplet number density profiles are observed to coincide for all ML when the cross-stream coordinate is normalized by the instantaneous vorticity thickness; however, first-order thermodynamic profiles do not coincide.", "doi": "10.1017/S0022112098004042", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "1999-04-10", "volume": "384", "pages": "293-338" }, { "id": "authors:3cfbd-fan30", "collection": "authors", "collection_id": "3cfbd-fan30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-144744226", "type": "article", "title": "The Lewis number under supercritical conditions", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "An effective Lewis number is calculated for situations where temperature and mass fraction gradients are very large by defining effective thermal and mass diffusivities; such situations may occur in systems where there is more than one chemical component, and in particular under supercritical conditions. The definitions evolve from a model assuming that derivatives of certain functions are small with respect to those of the dependent variables. In the model, Soret and Dufour effects are included and Shvab\u2013Zeldovich-like variables are defined to remove the coupling between the operators of the differential equations for temperature and mass fractions. Results from calculations using binary systems of chemical components, using both isolated fluid drops and interacting fluid drops, show that under supercritical conditions, depending upon the compounds, the effective Lewis number can be 2\u201340 times larger than the traditionally calculated Lewis number and that the spatial variation of the two numbers is different. For the values of the thermal diffusion factor used in the calculations, the Soret and Dufour effects are negligible; the discrepancy between the traditional and effective Lewis numbers is due to the combined effect of the small mass diffusion factor and the difference between the specific enthalpies of the two compounds. Parametric variations show that the effective Lewis number increases with increasing pressure and decreasing surrounding gas temperature. Closer drop proximity in clusters results in sharper peaks in the effective Lewis number due to the increased gradients of the dependent variables.", "doi": "10.1016/S0017-9310(98)00230-0", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1999-03-01", "series_number": "6", "volume": "42", "issue": "6", "pages": "961-970" }, { "id": "authors:0kjtm-0vj74", "collection": "authors", "collection_id": "0kjtm-0vj74", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-080951487", "type": "article", "title": "High-Energy-Density Fuel Blending Strategies and Drop Dispersion for Fuel Cost Reduction and Soot Propensity Control", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "High-energy-density (HED) liquid fuels have high soot propensity and are expensive. The idea of mitigating these characteristics by adding a less expensive, low soot propensity liquid fuel to the HED is tested through numerical simulations. The model represents an axisymmetric, polydisperse, dense cluster of binary-fuel (solvent/solute) spherical drops embedded into a vortex. Since soot propensity depends on the partial density of the evaporated fuel, this partial density is compared for uncharged and electrostatically charged drops; charging is used here as an effective way to increase dispersion and reduce sooting propensity. Results from the simulations show that while the solvent soot propensity indeed decreases with drop charging, contrary to simplistic expectations, addition of HED as a solute increases sooting propensity of the solute with increased drop dispersion. This is due to the additional dispersion maintaining the slip velocity at the drop surface and preferentially evaporating the solute. These counterintuitive but correct physical effects are independent of the initial solvent/solute mass ratio, and the soot propensity decreases with decreasing solute volatility. Based on these results, blending strategies are suggested for minimizing sooting propensity and decreasing fuel costs.", "doi": "10.1615/AtomizSpr.v9.i4.40", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "1999", "series_number": "4", "volume": "9", "issue": "4", "pages": "371-383" }, { "id": "authors:xek6k-x5373", "collection": "authors", "collection_id": "xek6k-x5373", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-073649264", "type": "article", "title": "Isolated fluid oxygen drop behavior in fluid hydrogen at rocket chamber pressures", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model has been developed for the behavior of an isolated fluid drop of a single compound immersed into another compound in finite, quiescent surroundings at supercritical conditions. The model is based upon fluctuation theory which accounts for both Soret and Dufour effects in the calculation of the transport matrix relating molar and heat fluxes to the transport properties and the thermodynamic variables. The transport properties have been modeled over a wide range of pressure and temperature variation applicable to LO_x\u2013H_2 conditions in rocket chambers, and the form of the chemical potentials is valid for a general fluid. The equations of state have been calculated using a previously-derived, computationally-efficient and accurate protocol. Results obtained for the LO_x\u2013H_2 system show that the supercritical behavior is essentially one of diffusion. The temperature profile relaxes fastest followed by the density and lastly by the mass fraction profile. An effective Lewis number calculated using theory derived elsewhere shows that it is larger by approximately a factor of 40 than the traditional Lewis number. The parametric variations show that gradients increasingly persist with increasing fluid drop size or pressure, and with decreasing temperature. The implication of these results upon accurate measurements of fluid drop size under supercritical conditions is discussed.", "doi": "10.1016/S0017-9310(98)00049-0", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1998-11-01", "series_number": "22", "volume": "41", "issue": "22", "pages": "3537-3550" }, { "id": "authors:kmj4g-ypp76", "collection": "authors", "collection_id": "kmj4g-ypp76", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-074109330", "type": "article", "title": "Interactions of fluid oxygen drops in fluid hydrogen at rocket chamber pressures", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model of fluid drop behavior in clusters has been developed including the interactions induced by the drop proximity. The model is based upon the global conservation equations for the interstitial cluster region coupled to isolated fluid drop equations previously developed. Heat and mass transfer to the cluster are modeled using the Nusselt number concept. Results from calculations for the LO_x\u2013H_2 system show the predictions to be insensitive to the value of the Nusselt number over three orders of magnitude. The results also show that at fixed pressure, increased drop proximity induces increased accumulation of LO_x in the interstitial space inside the cluster. At fixed initial drop proximity, the gradients of the dependent variables become increasingly smeared as the pressure increases; an opposite result from that obtained for isolated drops (Harstad K, Bellan J. Isolated fluid oxygen drop behavior in fluid hydrogen at rocket chamber pressure. Int J Heat Mass Transfer 1998; 41:3537\u201350). It is thus inferred that clusters of drops might be a desirable aspect in supercritical combustion because they aid interdiffusion of the reactive components.", "doi": "10.1016/S0017-9310(98)00048-9", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1998-11-01", "series_number": "22", "volume": "41", "issue": "22", "pages": "3551-3558" }, { "id": "authors:cdqqb-z4q64", "collection": "authors", "collection_id": "cdqqb-z4q64", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-110525024", "type": "article", "title": "Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A variety of liquid droplet evaporation models, including both classical equilibrium and non-equilibrium Langmuir\u2013Knudsen formulations, are evaluated through comparisons with experiments with particular emphasis on computationally efficient procedures for gas\u2013liquid flow simulations. The models considered are those used in droplet laden flow calculations such as direct numerical simulations for which large numbers of individual (isolated) droplet solutions are obtained. Diameter and temperature evolution predictions are made for single-component droplets of benzene, decane, heptane, hexane and water with relatively large initial sizes \u223c1 mm vaporizing in convective air flows. All of the models perform nearly identically for low evaporation rates at gas temperatures significantly lower than the boiling temperature. For gas temperatures at and above the boiling point, large deviations are found between the various model predictions. The simulated results reveal that non-equilibrium effects become significant when the initial droplet diameter is <50 \u03bcm and that these effects are enhanced with increasing slip velocity. It is additionally observed that constant properties can be used throughout each simulation if both the gas and vapor values are calculated at either the wet-bulb or boiling temperature. The models based on the Langmuir\u2013Knudsen law and a corrected (for evaporation effects) analytical heat transfer expression derived from the quasi-steady gas phase assumption are shown to agree most favorably with a wide variety of experimental results. Since the experimental droplet sizes are all much larger than the limit for non-equilibrium effects to be important, for these conditions the most crucial aspect of the current Langmuir\u2013Knudsen models is the corrected analytical form for the heat transfer expression as compared to empirical relations used in the remaining models.", "doi": "10.1016/S0301-9322(98)00028-7", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "1998-09", "series_number": "6", "volume": "24", "issue": "6", "pages": "1025-1055" }, { "id": "authors:x7nyp-6er09", "collection": "authors", "collection_id": "x7nyp-6er09", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-143611991", "type": "article", "title": "Numerical Simulation of Vortex Pyrolysis Reactors for Condensable Tar Production from Biomass", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A numerical study is performed in order to evaluate the performance and optimal operating conditions of vortex pyrolysis reactors used for condensable tar production from biomass. A detailed mathematical model of porous biomass particle pyrolysis is coupled with a compressible Reynolds stress transport model for the turbulent reactor swirling flow. An initial evaluation of particle dimensionality effects is made through comparisons of single- (1D) and multi-dimensional particle simulations and reveals that the 1D particle model results in conservative estimates for total pyrolysis conversion times and tar collection. The observed deviations are due predominantly to geometry effects while directional effects from thermal conductivity and permeability variations are relatively small. Rapid ablative particle heating rates are attributed to a mechanical fragmentation of the biomass particles that is modeled using a critical porosity for matrix breakup. Optimal thermal conditions for tar production are observed for 900 K. Effects of biomass identity, particle size distribution, and reactor geometry and scale are discussed.", "doi": "10.1021/ef970088a", "issn": "0887-0624", "publisher": "American Chemical Society", "publication": "Energy and Fuels", "publication_date": "1998-01", "series_number": "1", "volume": "12", "issue": "1", "pages": "25-40" }, { "id": "authors:sdbts-x2t78", "collection": "authors", "collection_id": "sdbts-x2t78", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-145141363", "type": "article", "title": "Dispersion (Electrostatic/Mechanical) and Fuel Properties Effects on Soot Propensity in Clusters of Drops", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "Soot propensity is studied numerically for an initially binary size, axisymmetric cluster of evaporating drops by defining it as the propensity for nucleation reactions to occur; the study does not address physical or chemical processes ensuing after soot nucleation, such as soot oxidation effects resulting from the fuel molecular structure. The relative magnitude of the fuel vapor partial density is taken as an indication of the soot nucleation magnitude; thus, the effect of drop dispersion on soot (precursor) formation is isolated from that of soot production resulting from formation/destruction by oxidation. The cluster is embedded in an inviscid vortex and exchanges mass, momentum, species, and energy with its surroundings. The vortical motion disperses the drops and the initial cluster evolves into a cylindrical shell with an inner and an outer boundary. In addition to the forces resulting from the vortical motion, an electrostatic force acts on the cluster when the drops are charged; in this situation, the drops might become small enough to reach the Rayleigh limit. Results are obtained for typical vortical motion times having the same order of magnitude as the drop lifetime. Analysis of the results shows that the motion of uncharged drops is determined primarily by centrifugation, whereas for charged drops the electrostatic dispersion becomes the dominant influence in the outer part of the cluster. In the range of parameters investigated, mechanical dispersion cannot rival electrostatically induced dispersion for decreasing the fuel vapor partial density. An additional feature of drop charging is the maintenance of a finite slip velocity in the outer part of the cluster, thereby compounding the advantage of increased dispersion to enhanced evaporation. The results also show that mechanical dispersion combined with electrostatic dispersion does not have a substantial advantage over electrostatic dispersion alone. For uncharged drops it has been found that the latent heat governs soot propensity at small drop dispersion, whereas the liquid density becomes increasingly important with increasing drop dispersion. Drop charging does not affect the influence of fuel physical properties on soot propensity.", "doi": "10.1615/AtomizSpr.v8.i6.10", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "1998", "series_number": "6", "volume": "8", "issue": "6", "pages": "601-624" }, { "id": "authors:17ybe-wdg67", "collection": "authors", "collection_id": "17ybe-wdg67", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-103758152", "type": "article", "title": "On the validity of the assumed probability density function method for modeling binary mixing/reaction of evaporated vapor in gas/liquid-droplet turbulent shear flow", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "An investigation of the statistical description of binary mixing and/or reaction between a carrier gas and an evaporated vapor species in two-phase gas-liquid turbulent flows is performed through both theoretical analysis and comparisons with results from direct numerical simulations (DNS) of a two-phase mixing layer. In particular, the validity and added complications of extending single-point assumed probabolity density function (PDF) methods to two-phase flows involving evaporating droplets as sources of vapor are addressed. Noting that Favre density-weighted averaging is the most convenient form for moment transport equations for these flows, algebraic relationships are derived for the ratios of the Favre and nonweighted scalar means and variances. Comparisons with the DNS results indicate that the mixing layer centerline where the root mean square (rms) density fluctuation is >12% of the mean density. It is therefore considered appropriate to use Favre moments for the nonweighted PDF closure. A transport equation for effects. The DNS results indicate that one of these terms due to scalar-source correlations is predominantly responsible for scalar variance production, whereas the remaining three terms are of negligible magnitude. Finally, the \u03b2 PDF, which is known to represent well the DNS generated mixture fraction statistics for single-phase mixing, is shown to be a poor representation for mixing of vapor resulting from droplet evaporation.", "doi": "10.1016/S0082-0784(98)80507-9", "issn": "0082-0784", "publisher": "Elsevier", "publication": "Symposium (International) on Combustion", "publication_date": "1998", "series_number": "1", "volume": "27", "issue": "1", "pages": "1065-1072" }, { "id": "authors:adc1j-z2288", "collection": "authors", "collection_id": "adc1j-z2288", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-125537950", "type": "article", "title": "Behavior of a polydisperse cluster of interacting drops evaporating in an inviscid vortex", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The dynamics and evaporation of polydisperse collections of liquid drops in an axisymmetric, infinite, cylindrical vortex are described using a statistical model. This model describes both the dense regime where inter-particle effects are important and the dilute regime. The initial size distribution is partitioned into size classes and each initial size-class is followed dynamically and thermodynamically using a class-defined, drop-frame coordinate system. Each initial-size-class develops a continuum of sizes as drops centrifuge towards hotter surroundings and evaporate. A separate coordinate system tracks the gas phase. Because larger drops experience larger centrifugal force, they approach the hotter gas faster. However, for appropriate liquid heating times, the large drops might evaporate at a faster rate, and so the size-differentiated centrifugation previously observed and calculated for cold flow situations does not occur. Instead, a radially peaked drop size distribution is developed in the gas vortex. The centrifugal motion forms a drop-free inner vortex core bound by a cylindrical shell containing all the drops. This shell of gas and drops is called the drop cluster. Numerical calculations show that more parameters control dense clusters than dilute clusters; examples of these parametric relations include: (i the gas vortex, whereas drop size distribution controls the outer region; and (ii increases the maximum mass fraction of the evaporated compound and enhances penetration of the evaporated compound into the surroundings. Except for dilute clusters, the assumption of uniform drop number distribution in the cluster is found to be inappropriate. Instead, the drop size distribution always becomes non-uniform even if the initial size distribution is monodisperse and the initial drop number distribution is uniform. This development of non-uniformity is caused by drops at the cluster peripheries preventing heat conduction/convection to drops in the central cluster.", "doi": "10.1016/S0301-9322(97)00011-6", "issn": "0301-9322", "publisher": "Elsevier", "publication": "International Journal of Multiphase Flow", "publication_date": "1997-09", "series_number": "5", "volume": "23", "issue": "5", "pages": "899-925" }, { "id": "authors:wk7ky-v8266", "collection": "authors", "collection_id": "wk7ky-v8266", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171024-144448068", "type": "article", "title": "Efficient high-pressure state equations", "author": [ { "family_name": "Harstad", "given_name": "Kenneth G.", "clpid": "Harstad-K-G" }, { "family_name": "Miller", "given_name": "Richard S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A method is presented for a relatively accurate, noniterative, computationally efficient calculation of high-pressure fluid-mixture equations of state, especially targeted to gas turbines and rocket engines. Pressures above 1 bar and temperatures above 100 K are addressed. The method is based on curve fitting an effective reference state relative to departure functions formed using the Peng-Robinson cubic state equation. Fit parameters for H_2, O_2, N_2, propane, methane, n-heptane, and methanol are given.", "doi": "10.1002/aic.690430624", "issn": "0001-1541", "publisher": "Wiley", "publication": "AIChE Journal", "publication_date": "1997-06", "series_number": "6", "volume": "43", "issue": "6", "pages": "1605-1610" }, { "id": "authors:eeyk6-53p15", "collection": "authors", "collection_id": "eeyk6-53p15", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-075242108", "type": "article", "title": "A Generalized Biomass Pyrolysis Model Based on Superimposed Cellulose, Hemicelluloseand Liqnin Kinetics", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "The pyrolysis of general biomass materials is modeled via a superposition of cellulose, hemi-cellulose and lignin kinetics. All three of the primary biomass components are modeled with multi-step kinetics involving both competetive primary pyrolysis and secondary tar decomposition reactions. Only \"typical\" (untreated) feedstocks are considered at atmospheric pyrolysis pressures. The kinetics scheme is then coupled to the porous particle model of Miller and Bellan (1996) along with appropriate properties and heats of reaction to provide a complete model for the pyrolysis of arbitrary biomass feedstocks and sample sizes. Comparisons with past isothermal and thermogravimetry experiments for a variety of biomass materials under both kinetically controlled and diffusion limited conditions show favorable agreement with the model predictions. In addition, discussions are provided which support the use of competetive char production kinetics over single and successive reaction schems which cannot currently be reconciled with observed pyrolysis behavior.", "doi": "10.1080/00102209708935670", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1997", "series_number": "1-6", "volume": "126", "issue": "1-6", "pages": "97-137" }, { "id": "authors:xdb2s-yam21", "collection": "authors", "collection_id": "xdb2s-yam21", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-074414439", "type": "article", "title": "Tar Yield and Collection from the Pyrolysis of Large Biomass Particles", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Tar yield collection from the pyrolysis of relatively large particles of biomass are investigated using the model of Miller and Bellan (1997).A variety of feedstocks are considered by varying the ratios of cellulose, hemicellulose and lignin within the biomass. Effectsof secondary tar reactions, quenching, temperature, particle size and carrier gas are assessed. Secondary tar reactions occuring in both the particle's interior and the exterior boundary layer strongly reduce the potential amount of tar available for collection compared to the maximum given by kinetic predictions. The primary effect of these reactions is the existence of an optimal reactor temperature range for maximizing tar yields. This range is a function of both the quenching location and the initial particle size. For rapid qvenching near the particle surface, tar collection is maximized at high temperatures for small particles, and at low temperatures for large particles. For delayed quenching, low temperatures slow the secondary reactions and provide larger tar yields for all particle sizes investigated. Tar yields are also dependent on the choice of the inert carrier gas; primarily due to changes in heat capacity. A sensitivity study is performed in order to assess the influence of the biomass apparent density, thermal conductivity, heat capacity and primary heats of reaction.", "doi": "10.1080/00102209708935689", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1997", "series_number": "1-6", "volume": "127", "issue": "1-6", "pages": "97-118" }, { "id": "authors:1fta3-zq381", "collection": "authors", "collection_id": "1fta3-zq381", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-080352367", "type": "article", "title": "Analysis of Reaction Products and Conversion Time in the Pyrolysis of Cellulose and Wood Particles", "author": [ { "family_name": "Miller", "given_name": "R. S.", "clpid": "Miller-R-S" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A detailed mathematical model is presented for the temporal and spatial accurate modeling of solid-fluid reactions in porous particles for which volumetric reaction rate data is known a priori and both the porosity and the permeability of the particle are large enough to allow for continuous gas phase flow. The methodology is applied to the pyrolysis of spherically symmetric biomass particles by considering previously published kinetics schemes for both cellulose and wood. A parametric study is performed in order !o illustrate the effects of reactor temperature, heating rate, porosity, initial particle size and initial temperature on char yields and conversion times. It is observed that while high temperatures and fast heating rates minimize the production of char in both reactions, practical limits exist due to endothermic reactions, heat capacity and thermal diffusion. Three pyrolysis regimes are identified: 1) initial heating, 2) primary reaction at the effective pyrolysis temperature and 3) final heating. The relative durations of each regime are independent of the reactor temperature and are approximately 20%, 60% and 20% of the total conversion time, respectively. The results show that models which neglect the thermal and species boundary layers exterior to the particle will generally over predict both the pyrolysis rates and experimentally obtainable tar yields. An evaluation of the simulation results through comparisons with experimental data indicates that the wood pyrolysis kinetics is not accurate; particularly at high reactor temperatures.", "doi": "10.1080/00102209608952004", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1996", "series_number": "1-6", "volume": "119", "issue": "1-6", "pages": "331-373" }, { "id": "authors:9nrr1-zm743", "collection": "authors", "collection_id": "9nrr1-zm743", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-080145618", "type": "article", "title": "External Cluster Combustion of Binary-Fuel Drops", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model describing external sheet combustion of a cluster of drops has been developed for clusters of binary-fuel drops. The binary-fuel is assumed to be a solvent-solute combination in which the solute is much more volatile than the solvent whose initial mass fraction within the mixture is larger than that of the solute. Both the ignition timing and location are calculated using criteria previously derived; for the range of air/fuel mass ratios considered, ignition always occurs around the cluster. Following ignition, an internal flash flame burns all the oxygen within the cluster. An external sheet flame ensues fueled by vapor released from the cluster. Results show that drop interactions are important in modifying the amount of fuel burnt. It is only for small initial cluster velocities and for large air/fuel mass ratios that the external flame behaves approximately like a classical diffusion flame in that it almost burns all the fuel released from the cluster. For all other conditions, the amount of fuel burnt is smaller than that released from the cluster. These conclusions are independent of the initial solute mass fraction and of the Arrhenius ignition parameters having assumed them identical for solvent and solute.", "doi": "10.1080/00102209608935574", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1996", "series_number": "1-6", "volume": "120", "issue": "1-6", "pages": "213-236" }, { "id": "authors:z29jt-w4435", "collection": "authors", "collection_id": "z29jt-w4435", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-132350571", "type": "article", "title": "Electrostatic dispersions and evaporation of clusters of drops of high-energy fuel for soot control", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A model is presented for the electrostatic dispersion of a poly disperse cluster of evaporating drops embedded into an inviscid vortex. Results from this model obtained for dense clusters of drops show that electrostatic dispersion decreases the mass fraction of the evaporating compound as well as the gas density in side the cluster. Since the sooting tendency of a fuel (through coagulation) is an increasing function of the partial density of the fuel vapor, it is inferred that electrostatic charging decreases the sooting tendency. Results indicate that the sooting tendency is a monotonically decreasing function of the charge. By using this model for different fuels, it is shown that the sooting tendency of a fuel is associated with two competing characteristic times: that of drop dispersion and that of drop evaporation. It is also shown that the drop evaporation time is directly related to the latent heat of the fuel, thereby providing a simple way to relate sooting propensity to fuel-specific properties.", "doi": "10.1016/S0082-0784(96)80396-1", "issn": "0082-0784", "publisher": "Elsevier", "publication": "Symposium (International) on Combustion", "publication_date": "1996", "series_number": "1", "volume": "26", "issue": "1", "pages": "1713-1722" }, { "id": "authors:jqnvh-4tf52", "collection": "authors", "collection_id": "jqnvh-4tf52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-091855457", "type": "article", "title": "Unsteady injection of sequences of drop clusters in vortices depicting portions of a spray", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A model of unsteady injection of sequences of drop clusters embedded in jet vortices was applied to describe both vortices in the shear layer of a spray and small-scale vortical structures in the core of a spray. In the first case, the vortices are large compared to the size of the spray, they rotate fast with respect to the injection rate, and their number per area of spray is small. In the second case, the vortices are small compared to the size of the spray, they rotate slowly with respect to the injection rate, and their number per area of spray is large.\nResults were obtained for injection sequences where either the drop size or the air/fuel mass ratio varied from cluster to cluster in the injection sequence. The variation was a mono-tonic increase, a monotonic decrease, or a sinusoidal variation. The results thus obtained were compared to baseline results from steady-state calculations. Additionally, both the entrainment from the ambient into the jet and the initial number of clusters per jet area were varied so as to ascertain their influence on cluster penetration and jet properties.\nThe results show that penetration of a cluster into the ambient is a function of the characteristics of the cluster sequence following the cluster, that the jet temperature is controlled by entrainment from the ambient into the jet in the shear-layer application whereas conduction also becomes important in the spray-core application, and that the fuel mass fraction in the jet is a function of the initial characteristics of the clusters as well as entrainment.", "doi": "10.1615/AtomizSpr.v5.i1.20", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "1995", "series_number": "1", "volume": "5", "issue": "1", "pages": "17-44" }, { "id": "authors:yamdh-h3j37", "collection": "authors", "collection_id": "yamdh-h3j37", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-091601090", "type": "article", "title": "Steady injection of identical clusters of evaporating drops embedded in jet vortices", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A model has been developed that describes the evaporation of clusters of drops in a flowing gaseous jet. Each one of these clusters is embedded into a coherent vortex and the drops evaporate as the clusters convect downstream together with the vortex. Because there is a continuous injection of clusters, each cluster represents in fact a statistical average of clusters at that particular location. Thus, the formulation contains a conservation equation for the cluster number density, conservation equations for the gas in the jet, and conservation equations for the drops in the cluster and the vortex containing the cluster. The cluster and vortex models are coupled to the gaseous jet model through boundary conditions. The heat necessary to evaporate the drops comes from the surroundings of the gaseous jet, and this is described through a global, diffusive entrainment model. It is assumed that the turbulent diffusion coefficient is proportional either to the local vortex strength or to the cluster velocity and the multiplier is named the entrainment coefficient.\nResults are presented here for the stationary case representing the situation when identical clusters are continuously injected and the injection rate is constant. Thus, if a \"snapshot\" of the calculation is taken at any time, the cluster is observed at that time and the clusters in its wake represent the history of the cluster at previous times. Parametric studies cover the influence of the initial air/fuel mass ratio, the entrainment coefficient, and the initial drop and gas velocities inside the vortices. The results show that quantitative predictions of the evaporation time, the penetration of the clusters into the ambient, and the temperature of the jet depend on details of the entrainment of hot gas into the jet.", "doi": "10.1615/AtomizSpr.v5.i1.10", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "1995", "series_number": "1", "volume": "5", "issue": "1", "pages": "1-16" }, { "id": "authors:znx67-xzw70", "collection": "authors", "collection_id": "znx67-xzw70", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-103852612", "type": "article", "title": "Ignition of a Binary-fuel (Solvent-Solute) Cluster of Drops", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "Evaporation and ignition of a binary-fuel cluster of drops is described by models under the assumptions that the volatile compound has infinite volatility with respect to the solvent and that the chemistries of the two compounds are independent. A Damk\u00f6hler number criterion developed for use in sprays is utilized to determine the ignition time. Another criterion is used to determine the ignition location which can be either around individual drops, or around groups of drops inside the cluster, or around the entire cluster.\n\nResults show that except for very dilute situations where the initial liquid mass fraction of the volatile is very small, ignition always occurs around the entire cluster. Otherwise, ignition occurs around groups of drops inside the cluster but never around individual drops even though the ratio of the distance between the centers of two adjacent drops by the drop diameter is greater than thirty five.\n\nStudies performed by varying the air/fuel mass ratio for a variety of parametric combinations show that: (1) At typical gas temperatures for combustion devices, the ignition of very dense and very dilute clusters of drops is evaporation-controlled for identical chemistries; it is strongly-controlled by solvent ignition in the very dense cluster regime, it is strongly-controlled by ignition of the volatile in the very dilute regime. In the intermediary regime, ignition is controlled by the relative ignition chemistries of the compounds. These conclusions are independent of the amount of volatile initially present in the liquid. (2) The concept of volatile is more strongly associated with the latent heat of evaporation in the dense regime, and more strongly associated with the saturation pressure curve in the very dilute regime. (3) By increasing the surrounding gas temperature one gradually gains control of ignition in the dense and dilute regimes through the evaporation of solvent and volatile respectively. (4) The initial slip velocity between phases affects ignition only in the very dilute regime. (5) Changes in the cluster size affect the ignition time only in the very dense regime.\n\nConclusions (3) and (4) are valid under the assumption of identical kinetics for the two compounds; when different kinetics are considered, it turns out that kinetic effects overwhelmingly dominate ignition.", "doi": "10.1080/00102209508951939", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1995", "series_number": "1", "volume": "110-111", "issue": "1", "pages": "531-548" }, { "id": "authors:69wmq-ez255", "collection": "authors", "collection_id": "69wmq-ez255", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-131442063", "type": "article", "title": "Unsteady evaporation and combustion of a drop cluster inside a vortex", "author": [ { "family_name": "Fichot", "given_name": "F.", "clpid": "Fichot-F" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A model has been developed that describes the evaporation, ignition, and combustion of a drop cluster embedded in a large vortex. The purpose of this model is to simulate the behavior of drops in large coherent vortices produced in the shear layer of a jet. The model treats the dynamic interactions between the drops and the vortex, and also takes into account the drop proximity to calculate the heat and mass transfer between drops and ambient gas. The gas phase outside the cluster is treated as an unsteady, reacting phase, whereas quasi-steadiness is assumed between the drops and surrounding gas inside the cluster. It is assumed that drops will not burn individually, but as a group. The results show a very complex interaction between the dynamics of the drop-loaded vortex, the flame, and the evaporation process. A quasi-steady state is not always reached, depending upon the drop number density or the vortex intensity. In most cases, the flame is located very close to the cluster. The mass ratio of burned fuel (at complete evaporation) to initial fuel is generally less than 10%.", "doi": "10.1016/0010-2180(94)90194-5", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1994-07", "series_number": "1-2", "volume": "98", "issue": "1-2", "pages": "5-19" }, { "id": "authors:1821h-pv885", "collection": "authors", "collection_id": "1821h-pv885", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171027-101441171", "type": "article", "title": "Entrainment and Evaporation of Drops in the Laminar Part of a Two-Dimensional Developing Mixing Layer", "author": [ { "family_name": "Fichot", "given_name": "F.", "clpid": "Fichot-F" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A formulation has been developed that combines the simplicity of an experimentally derived well-establishedcorrelation for describing the development of a mixing layer, and a rigorous approach for the description of the dynamics and evaporation of dense or dilute clusters of drops in large coherent vortices.\n\nAn extensive parametric study has been performed by varying the radius of the drops in the drop-ladenstream both for high and low air/fuel mass ratio, as well as for constant initial drop number density, but at varying air/fuel mass ratio. The air/fuel mass ratio has also been varied at fixed drop radius in the drop-laden stream. Additional parameters independently varied were the temperature of the hot air stream, its velocity, and the velocity ratio between the two streams.\n\nThe results show that it is possible to optimize the relative number of drops (with respect to the initial value) entrained into the coherent vortices of the mixing layer by using the velocity ratio as control parameter. The eventual liquid mass entrained in the cluster is an increasing function of the drop radius in the drop-carrying stream for typical drop number densities in sprays. The mass fraction of the evaporated fuel in the clusters can be optimized by using the velocity of the hot air stream as a control parameter.\n\nIt is also shown that, in agreement with existing observations, the average drop radius may increase withaxial distance from the mixing layer inception point, and the reasons for this are explained.", "doi": "10.1016/S0082-0784(06)80667-3", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "1994", "series_number": "1", "volume": "25", "issue": "1", "pages": "397-405" }, { "id": "authors:dqkrx-xe925", "collection": "authors", "collection_id": "dqkrx-xe925", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171027-160538311", "type": "article", "title": "A Model of the Evaporation of Binary-Fuel Clusters of Drops", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A formulation has been developed to describe the evaporation of dense or dilute clusters of binary-fuel drops. The binary fuel is assumed to be made of a solute and a solvent whose volatility is much lower than that of the solute. Convective flow effects, inducing a circulatory motion inside the drops, are taken into account, as well as turbulence external to the cluster volume. Results obtained with this model show that, similar to the conclusions for single, isolated drops, the evaporation of the volatile is controlled by liquid mass diffusion when the cluster is dilute. In contrast, when the cluster is dense, the evaporation of the volatile is controlled by surface layer stripping, that is, by the regression rate of the drop, which is, in fact, controlled by the evaporation rate of the solvent. These conclusions are in agreement with existing experimental observations. Parametric studies show that these conclusions remain valid with changes in ambient temperature, initial slip velocity between drops and gas, initial drop size, initial cluster size, initial liquid mass fraction of the solute, and various combinations of solvent and solute. The implications of these results for computationally intensive combustor calculations are discussed.", "doi": "10.1615/AtomizSpr.v1.i4.20", "issn": "1044-5110", "publisher": "Begell House", "publication": "Atomization and Sprays", "publication_date": "1991", "series_number": "4", "volume": "1", "issue": "4", "pages": "367-388" }, { "id": "authors:27z9t-sdv79", "collection": "authors", "collection_id": "27z9t-sdv79", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171027-101011089", "type": "article", "title": "The dynamics of dense and dilute clusters of drops evaporating in large, coherent vortices", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "The behavior of evaporating clusters of drops embedded into large, coherent vortices is described using a formulation which is valid for both dense and dilute clusters. Drops and gas interact both dynamically and thermodynamically. Dynamic coupling occurs through a force on the drops due to drag resulting from a slip velocity between the two phases The net interaction force on the gas with drops is due to a source thrust from evaporation plus drag on each drop. The drag coefficient accounts for blowing from the drop surface. Thermodynamic coupling is a result of drop heating and evaporation. Limitations due to drop proximity on heating and evaporation are taken into account.\n\nThe vortical motion of the drops in the cluster results in the formation of a core region devoid of drops at the center of the vortex, and a shell region containing the drops and surrounding the inner core. Results are presented showing the dependence of the evaporation time, the final to initial volume ratio and the final to initial shell thickness ratio upon the initial air/fuel mass ratio and as a function of the initial tangential velocities, upon the initial Stokes number, initial drop radius and initial outer cluster radius. Differences in behavior between and control parameters of dense and dilute clusters are pointed out by these new results. It is found that for dense clusters the final to initial volume ratio and final to initial shell thickness scale with the initial Stokes number, a new result which must be validated experimentally.", "doi": "10.1016/S0082-0784(06)80403-0", "issn": "1540-7489", "publisher": "Elsevier", "publication": "Proceedings of the Combustion Institute", "publication_date": "1991", "series_number": "1", "volume": "23", "issue": "1", "pages": "1375-1381" }, { "id": "authors:4jkcq-sz128", "collection": "authors", "collection_id": "4jkcq-sz128", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-123707161", "type": "article", "title": "Evaporation, ignition, and combustion of nondilute clusters of drops", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A theory of evaporation, ignition, and burning of moderately dense spherical drop clusters has been developed. The theory takes into account burning of premixed air and fuel internal to the cluster at ignition and subsequent burning of fuel emitted from the cluster by a flame sheet surrounding it. The model considers interdrop interaction, momentum exchange between drops and gas, and turbulent exchange processes between the cluster and its surroundings. Calculations are performed for varying initial air-to-fuel-mass ratios, initial cluster radii, ambient gas temperatures and initial drop temperatures. Results are presented for ratios of fuel mass burned to fuel mass lost from the cluster between drop ignition and drop disappearance, fuel burned fractions at ignition and at the moment of drop disappearance, and jump conditions at ignition.", "doi": "10.1016/0010-2180(90)90139-I", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1990-03", "series_number": "3-4", "volume": "79", "issue": "3-4", "pages": "272-286" }, { "id": "authors:f60xd-f1t97", "collection": "authors", "collection_id": "f60xd-f1t97", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-104133863", "type": "article", "title": "Transport-related phenomena for clusters of drops", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "Measurements performed in sprays characteristic of power systems show that sprays are composed of several regions [1]. Near the atomizer the drops might not be entirely formed and liquid sheets and filaments might still exist. There follows a region where the drops are already formed but have not yet been dispersed, so that they cluster together with a typical distance between the drops that is of the same order of magnitude as that of the average radius of the drops themselves. This region of the spray is called the dense spray region. Finally, further from this dense spray region there exists a region where the drops might still cluster, but in these clusters the distance between drops is much larger than the average radius of the drops. This region is called the dilute spray region.\nIn the dilute spray region drops are far apart from each other and thus when the spray is exposed to a convective flow, these drops practically behave like isolated drops in a convective flow. In contrast, in the dense spray regime, the drops are close to each other and thus their history is controlled by how much of the surrounding gas can enter in contact with them. This is to say that, unlike for drops belonging to dilute clusters of drops, transport phenomena are crucial in determining the behavior of drops belonging to dense clusters of drops because transport imposes limits on heat and mass transfer between the two phases. These phenomena pertain to indirect interactions and they can control the motion of drops, their heat-up time, evaporation, ignition and combustion.\nPrevious work [2-5] pointed out some important consequences of these indirect interactions. Two models of turbulent transport were used in ref. [5] in order to investigate the importance of turbulent transport from the surroundings to the cluster. Because of the global aspect of the model in which all the drops were assumed to behave identically, the transport from the cluster to surroundings was modeled using a 'trapping factor'. Basically, the 'trapping factor' is a weighing factor which allows the modeling of intermediary situations between those of dilute clusters where evaporated mass was assumed to be trapped in the cluster and that of dense clusters where evaporated mass was assumed to escape to ambient. It was found [5] that whereas in the dilute regime turbulence is not a controlling parameter, in the dense regime it becomes the crucial control parameter. This is a fact well known by experimentalists and design engineers who locate turbulent enhancement devices near the injector where the spray is dense, rather than further down the combustor where the spray is dilute.\nSince the transport processes between the cluster and its surroundings were found to be so important in the case of dense clusters, it was thought very important to improve the description of the transport of heat, mass and species from the cluster and its surroundings. This new model is described in detail in ref. [6] for electrostatically charged drops, and is used to calculate the results presented below for the special case of null charge. Due to the brief nature of the Technical Note, the nomenclature used here is the same as in refs. [5, 6].\nThe model developed in ref. [6] is similar to that of ref. [5] in that the drops and gas have two velocity components: a uniform axial component along the trajectory direction and a radial component. The difference between the two models is in the description of the radial velocity component. Whereas in ref. [5] a 'trapping factor' was used as discussed above, the new formulation uses the assumption of self-similarity in the radial direction as explained in detail in ref. [6].", "doi": "10.1016/0017-9310(89)90253-6", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1989-10", "series_number": "10", "volume": "32", "issue": "10", "pages": "2000-2002" }, { "id": "authors:f6gz3-y4663", "collection": "authors", "collection_id": "f6gz3-y4663", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-104721118", "type": "article", "title": "Electrostatic Dispersion of Drops in Clusters", "author": [ { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "A theory of evaporation and dispersion of electrostatically charged drops has been developed for drops belonging to a spherical cluster exposed to a flow Under the assumption of constant atmospheric pressure, the quasi-steady approximation was made for the gas phase whereas the drop-temperature history is unsteady. The model lakes into account interdrop interactions (in terms of heal and mass transfer) due to drop proximity, turbulence exchange processes between the cluster and its surroundings and electrostatic force effects due to the charge on the drops. Calculations based upon this model were made for charged as well as uncharged clusters of drops. The charge was varied from a null value to the maximum possible charge found empirically for hydrocarbon sprays. Moreover, the turbulence model was varied in such a way as to simulate the cluster embedded into a flow where turbulence develops with time (Model 1) or a flow with pre-existing turbulence (Model 2). The results show that the control parameters for the evaporation of charged drops are different from those for uncharged drops in dense clusters; turbulence levels which were shown lo be crucial for the latter in the dense cluster regime do not affect the former in the same regime. For dilute clusters turbulence is unimportant in both cases. Moreover, drop charging docs not affect dilute clusters of drops whereas dense clusters of drops are substantially affected. Based upon existing experimental data, inferences are made about how electrostatic spray dispersion can affect soot control in powersystems using fuel sprays. Limited results perlainingto the ignition of nearly-dense clusters of electrostatically charged drops are discussed as well.", "doi": "10.1080/00102208908947125", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1989", "series_number": "4-6", "volume": "63", "issue": "4-6", "pages": "169-181" }, { "id": "authors:mm82c-7wg30", "collection": "authors", "collection_id": "mm82c-7wg30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-105336722", "type": "article", "title": "Turbulence effects during evaporation of drops in clusters", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A model of droplet evaporation in clusters and the exchange processes between the cluster and the gas phase surrounding it are presented. This model is developed for use as a subscale model in calculations of spray evaporation and combustion and thus described only global features of cluster behavior. The gas pressure in the cluster remains constant during evaporation and as a result the volume of the cluster and the drop number density inside the cluster vary. Two turbulence models are considered. The first one describes cluster evaporation in surroundings initially devoid of turbulence and turbulence is allowed to build up with time. The second model describes cluster evaporation in surroundings where turbulence is present initially. The results obtained with these models show that turbulence enhances evaporation and is a controlling factor in the evaporation of very dense clusters; examples are shown where with the first turbulence model saturation was obtained before complete evaporation whereas the opposite was obtained with the second turbulence model. As the initial air/fuel mass ratio increases, both turbulence history and the initial relative velocity between drops and gases can control evaporation. It is shown that the evaporation time decreases with an initial increase in turbulence levels or relative velocity. When the initial air/fuel mass ratio increases further and the initial drop number density falls within the dilute regime, neither of the above parameters can control evaporation. Moreover, the evaporation time decreases with the decreasing size of the cluster for dense clusters of drops, whereas for dilute clusters of drops the size is not a controlling factor. The practical implications of these results are discussed.", "doi": "10.1016/0017-9310(88)90278-5", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1988-08", "series_number": "8", "volume": "31", "issue": "8", "pages": "1655-1668" }, { "id": "authors:ffbnt-a6235", "collection": "authors", "collection_id": "ffbnt-a6235", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-111155291", "type": "article", "title": "The details of the convective evaporation of dense and dilute clusters of drops", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A global model describing the convective evaporation of dense and dilute clusters of drops has been formulated starting from first principles. The volume of the cluster and the number of drops in a given cluster are fixed and the drops do not move with respect to each other. The model has been tested for three different drag models and shows less than 10% sensitivity in the prediction of the droplet lifetime. A thorough parametric study has been performed and the results show that the control parameters are very different in order of importance for dense and dilute clusters. The initial relative velocity between drops and gases is a weak control parameter in the 40\u20131000cm s^(-1) regime.", "doi": "10.1016/0017-9310(87)90038-X", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1987-06", "series_number": "6", "volume": "30", "issue": "6", "pages": "1083-1093" }, { "id": "authors:wsfce-tq129", "collection": "authors", "collection_id": "wsfce-tq129", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-111709573", "type": "article", "title": "Analysis of the convective evaporation of nondilute clusters of drops", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A model for the convective evaporation of nondilute clusters of drops has been developed. The critical parameter which controls the different evaporation modes has been identified to be the penetration distance of the outer flow into the cluster volume. A dynamic criterion has been developed to differentiate between penetration and no penetration. Convective evaporation was modeled using a Reynolds number correlation between the evaporation rate with and without convection. Other equations, previously developed [Combust. Flame51, 55\u201367 (1983)] for quiescent, nondilute-spray evaporation, have been used here as well, with the exception of a new kinetic-evaporation law at the droplet surface and a nonuniform interior temperature model which have both been developed here.\nThe model is shown to perform well for low penetration distances which are obtained for dense clusters in hot environments and low relative velocities between outer gases and cluster. For dense clusters with low penetration distances the results of the model predict that for the same initial velocity the evaporation time is shorter as the cluster becomes more dilute. For dilute clusters and large penetration distances, the opposite was found. Since for large penetration distances the predictive ability of the model deteriorates, these last trends are questionable. Furthermore, the evaporation time was found to be a weak function of the initial relative velocity and a strong function of the initial drop temperature. The initial surrounding gas temperature was found to have a strong influence in the lower temperature regime, 750\u20131500 K, whereas in the higher temperature regime the influence was very weak. The vitiation of the ambient gas by fuel vapor was found to have a very small influence upon the evaporation time for rich mixtures when the cluster is introduced in a strongly convective, high temperature surroundings. In all cases the results show that the interior drop-temperature was transient throughout the drop lifetime, but nonuniformities in the temperature persisted up to at most the first third of the total evaporation time.", "doi": "10.1016/0017-9310(87)90065-2", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1987-01", "series_number": "1", "volume": "30", "issue": "1", "pages": "125-136" }, { "id": "authors:jkshd-rbe94", "collection": "authors", "collection_id": "jkshd-rbe94", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151105-105158121", "type": "article", "title": "A Simplified Description of Char Combustion", "author": [ { "family_name": "Loewenberg", "given_name": "M.", "clpid": "Loewenberg-M" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Gavalas", "given_name": "G. R.", "orcid": "0000-0003-1468-6835", "clpid": "Gavalas-G-R" } ], "abstract": "A simplified analysis of carbonaceous particle combustion is presented that includes the effects of pore diffusion and growth as well as gas-phase heat and mass transfer. The combustion dynamics are described by time-dependent equations for particle temperature, radius and a number of intraparticle conversion variables. These are coupled to pseudosteady equations for gas-phase transport and internal reaction and diffusion. The differential equations for gas-phase transport are reduced by quadrature to a nonlinear boundary condition to the intraparticle boundary value problem. Numerical calculations are performed for conditions relevant to pulverized coal combustion. An analytical solution of the intraparticle problem, pertinent to the regime of strong diffusional limitations, reduces the intraparticle solution into a set of two quadratures which drastically simplifies the numerical calculations. The simplified intraparticle solution is in excellent agreement with the full solution at 1800 K free stream temperature and fair agreement at 1500 K.", "doi": "10.1080/00986448708911961", "issn": "0098-6445", "publisher": "Gordon and Breach", "publication": "Chemical Engineering Communications", "publication_date": "1987", "series_number": "1-6", "volume": "58", "issue": "1-6", "pages": "89-103" }, { "id": "authors:v88rj-gv063", "collection": "authors", "collection_id": "v88rj-gv063", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-111436572", "type": "article", "title": "Ignition of Non Dilute Clusters of Drops in Convective Flows", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "A global model has been developed for the qualitative prediction of ignition of clusters of drops evaporating in a convective flow. This model incorporates the description of convective droplet-cluster evaporation through a model which is valid for both dense and dilute clusters. The model takes into account drop interactions and the resulting possible limitations on evaporation in the limit of dense clusters. An Eulerian description is used to predict both drop and gas velocities. To complement the fluid mechanics model which is self-contained, the bulk interaction between the convective flow around the cluster and the cluster is evaluated using a penetration ratio criterion. The penetration distance itself is calculated in a Lagrangian frame. The model of droplet-cluster ignition can predict both the ignition time of the cluster and the location of the flame rs) at that time (under the, assumption of a spherical cluster). The ignition-timing part of the ignition criterion is valid only for diffusion-controlled ignition. The various possible combustion regimes for droplet-clusters are identified using a two dimensional map which compares convective and diffusive effects. Further numerical calculations show that in practical systems dense droplet-cluster ignition is always diffusion-dominated. The dependence of the ignition time upon both the initial drop temperature and gas temperature is studied as well. It is shown that the initial conditions determine whether a cluster ignites in anyone of the regimes previously identified.", "doi": "10.1080/00102208708947021", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1987", "series_number": "2-3", "volume": "53", "issue": "2-3", "pages": "75-87" }, { "id": "authors:ae6a1-j4b81", "collection": "authors", "collection_id": "ae6a1-j4b81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-111923147", "type": "article", "title": "Evaluation of the importance of the relative velocity during evaporation of drops in sprays", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Harstad", "given_name": "K.", "clpid": "Harstad-K-G" } ], "abstract": "Evaporation and combustion of liquid sprays in power systems invariably occurs in environments where there is a convective flow past the spray. This convective flow influences evaporation and combustion in at least to ways. First, it changes the heat and mass transfer rates between the spray as an entity, and the ambience. Secondly, it changes the geometry of the spray by entrainment of the spray periphery and recirculation of the gases surrounding the spray. These processes are all very complex and difficult to model. For this reason, guidance was sought initially from the study of individual drop evaporation and combustion. These studies [1-6] concurred with the experimental observation that a\u2026", "doi": "10.1016/0017-9310(86)90099-2", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1986-04", "series_number": "4", "volume": "29", "issue": "4", "pages": "647-651" }, { "id": "authors:jvxgt-cdd55", "collection": "authors", "collection_id": "jvxgt-cdd55", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-133931012", "type": "article", "title": "Fuel-Composition Effects on High-Temperature Corrosion in Industrial/Commercial Boilers and Furnaces: A Review", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Elghobashi", "given_name": "S.", "clpid": "Elghobashi-S" } ], "abstract": "In this review, literature relevant to the problems of deposits and corrosion in industrial/commercial furnaces and boilers is analyzed, and the facts are synthesized into a picture that addresses corrosion problems expected with the use of unconventional fuels. Corrosion is found to depend greatly on the phenomena occurring during the combustion of fuel-oil sprays introduced into the furnace. In a first step, the drops that form the spray heat up and evaporate in a way that closely resembles a batch distillation process. Eventually, ignition and combustion occur with the subsequent change of the liquid fuel drops into carbonaceous, porous, sphere-like particles called cenospheres. In a second step, these cenospheres burn and the products of this combustion step determine the majority of the deposits on metal surfaces. This observation is very important since nonvolatile, non-combustible, corrosive trace compounds existing in the initial fuel-oil drop will have a much higher concentration in the cenosphere than in the original fuel. Accordingly, it is recommended that the theoretical and experimental study of oil spray combustion, cenosphere formation, and cenosphere combustion in a cloud of cenospheres receive a very high priority. Corrosion by gases is found to be unimportant. Deposits are found to be much more corrosive when in liquid form, although corrosion by solid deposits is by no means negligible. As a result, it is suggested in the study that corrosion on highly polished metal surfaces should be studied in order to evaluate the potential of this method of inhibiting deposition and thus hindering corrosion. Recent advances in the theory of deposition from combustion gases are also outlined in this study. The literature survey shows that the main corrosion-causing fuel constituents present in unconventional fuels are sulfur, alkali, vanadium, carbon and carbon monoxide, iron, and chloride. It is found that sometimes one of these compounds might act as a catalyst in corrosive reactions initiated by another compound, and therefore great care must be taken to identify the corrosion-causing compound in the deposits on metal surfaces. It is also found that in some cases a corrosive compound will inhibit the corrosive action of another corrosive compound. It is recommended that such situations be studied further so as to investigate the possibility of an optimum concentration of two such corrosive compounds that would minimize metal wastage. The problem of performing meaningful corrosion experiments is also addressed in this report and specific recommendations are made to achieve this goal. Finally, the effects of additives and the furnace operating conditions are discussed, and potential problems with both additives and new operating conditions are mentioned. The recommendations at the end of this study present a comprehensive set of areas to be investigated in order to better understand and be able to mitigate corrosion problems associated with unconventional fuels. High-priority experimental and theoretical studies are also outlined.", "doi": "10.1115/1.3239797", "issn": "0742-4795", "publisher": "American Society of Mechanical Engineers", "publication": "Journal of Engineering for Gas Turbines and Power", "publication_date": "1985-07-01", "series_number": "3", "volume": "107", "issue": "3", "pages": "744-757" }, { "id": "authors:k0gnm-1af65", "collection": "authors", "collection_id": "k0gnm-1af65", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-135140499", "type": "article", "title": "A theory of nondilute spray evaporation based upon multiple drop interactions", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Cuffel", "given_name": "R.", "clpid": "Cuffel-R" } ], "abstract": "A theory of nondilute spray evaporation has been developed which takes into account the separation distance between drops. This theory is based upon the global conservation equations for the two-phase mixture and the conservation equations for a drop evaporating in finite surroundings. Results obtained for n-decane using this theory show that as the equivalence ratio of the two-phase mixture decreases from 200 to 10^(\u22122), four universal regimes are identified: (1) a regime of lean overall mixtures and dilute sprays where nondilute and dilute spray theories agree, (2) a regime where although both theories predict complete evaporation before saturation, the ratio of the evaporation times (onndilute/dilute) predicted by the two theories is a function of the equivalence ratio, (3) a regime where the nondilute spray theory predicts saturation before complete evaporation, whereas the dilute spray theory predicts the opposite, and (4) a regime where both theories predict saturation before complete evaporation, but at different residual drop sizes. In regimes 1 and 2 the evaporation time is a decreasing function of the equivalence ratio, whereas in regimes 3 and 4 it becomes an increasing function of the equivalence ratio. Parametric variations of the initial gas composition show that departures from the predictions of the dilute spray theory are obtained even for very dilute sprays if the overall mixture is rich. This implies that the dilute spray theory cannot adequately describe evaporation of drops injected during the later part of injection, or of larger-than-average drops in polydisperse sprays. Other departures from the dilute spray theory are obtained for sprays injected into relatively hot gases and for dense sprays initially composed of relatively cold drops. It was also shown that the evaporation time of a spray is a decreasing, nearly linear function of the initial drop temperature.", "doi": "10.1016/0010-2180(83)90083-4", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1983", "volume": "51", "pages": "55-67" }, { "id": "authors:p8cgr-2kk71", "collection": "authors", "collection_id": "p8cgr-2kk71", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-132925763", "type": "article", "title": "A new approach to soot control in diesel engines by fuel-drop charging", "author": [ { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" } ], "abstract": "Particulate formation is greatly enchanced by the\nnondiluteness of a diesel spray because it is responsible\nfor the creation of a fuel-rich vapor that accumulates without burning and instead undergoes complex chemical reactions [1, 2] which, combined with nucleation processes, [2-4] form soot. Since premixing was found to eliminate soot\n[1], it is clearly desirable to burn the nondilute spray injected in a diesel engine cylinder in a dilute\nconfiguration.", "doi": "10.1016/0010-2180(83)90090-1", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1983", "volume": "51", "pages": "117-119" }, { "id": "authors:c5jkg-m2n44", "collection": "authors", "collection_id": "c5jkg-m2n44", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-160247129", "type": "article", "title": "A model of smoldering combustion applied to flexible polyurethane foams", "author": [ { "family_name": "Ohlemiller", "given_name": "T. J.", "clpid": "Ohlemiller-T-J" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Rogers", "given_name": "F.", "clpid": "Rogers-F" } ], "abstract": "Smoldering combustion, particularly in upholstery and bedding materials, has been proven a serious life hazard. The simplest representation of this hazard situation is one-dimensional downward propagation of a smolder wave against a buoyant upflow (cocurrent smolder); the configuration treated here is identical in all respects to this except for the presence of a forced flow replacing the buoyant one. The complex degradation chemistry of the polyurethanes is here reduced to the two major overall reactions of char formation and char oxidation. The model solutions, which are in reasonable agreement with experimental results, show the smolder process to be oxygen-limited, which leads to some very simple trends. More subtle behavior aspects determine actual propagation velocity, fraction of fuel consumed, and apparent equivalence ratio (all of which are variable). The self-insulating character of the smolder wave makes it viable in a wide-ranging set of conditions if the igniting stimulus is sufficiently long. These results have significant implications regarding the problem of smolder prevention or hindrance.", "doi": "10.1016/0010-2180(79)90060-9", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1979", "volume": "36", "pages": "197-215" }, { "id": "authors:hrt28-jdy13", "collection": "authors", "collection_id": "hrt28-jdy13", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-140429082", "type": "article", "title": "Linear finite-element numerical techniques for combustion problems requiring variable step size", "author": [ { "family_name": "Sandusky", "given_name": "H.", "clpid": "Sandusky-H" }, { "family_name": "Bellan", "given_name": "J.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Ohlemiller", "given_name": "T. J.", "clpid": "Ohlemiller-T-J" }, { "family_name": "Vichnevetsky", "given_name": "R.", "clpid": "Vichnevetsky-R" } ], "abstract": "Combustion problems frequently pose situations\nin which the dependent variables (temperature,\nspecies concentrations, etc.) vary rapidly in some\nlocal domain and much more slowly throughout\nthe remaining region of interest. Such situations\narise for both fluid-mechanical (e.g., boundary-layer\nbehavior) and chemical reasons (i.e., Arrhenius-\ntype temperature dependence of chemical reaction\nrates). In any case, they present a particular\ndifficulty in the numerical solution of the governing\nconservation equations: if a fixed space-step is\nto be used, its magnitude is dictated by stability\nand/or accuracy requirements of the limited but\nrapidly varying domain. Outside this narrow domain,\nmany more space steps are taken than are required;\ncomputing costs are thus magnified.\n\nVarious means to avoid this difficulty have\nbeen used in the past, but none has proved generally\nsatisfactory or convenient. Finite-element methods\nare substantially more convenient than the classical\nfinite-difference techniques for approximating\nspatial dependencies in certain combustion problems.\nWe discuss only linear finite-element (LFE)\nmethods here. A discussion of this and more\ngeneral finite-element methods can be found in\nseveral sources [1-3]; we briefly outline the application\nof the LFE method and illustrate its advantages.", "doi": "10.1016/0010-2180(79)90059-2", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1979", "volume": "36", "pages": "193-196" }, { "id": "authors:gyf7g-fcx53", "collection": "authors", "collection_id": "gyf7g-fcx53", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171023-143538311", "type": "article", "title": "Theoretical examination of assumptions commonly used for the gas phase surrounding a burning droplet", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Summerfield", "given_name": "Martin", "clpid": "Summerfield-M" } ], "abstract": "A finite reaction-rate model is compared to three commonly used flame-sheet models. The latter differ in their treatment of the evaporation from the surface and the value used for the molecular weights in the evaporation law. All four models are applicable to both steady and unsteady burning of droplets. Further, they account for variations of droplet radii and allow for differences in ambient conditions. Numerical results (obtained forn-decane) show that if the radius of the droplet is 10^(\u22122) cm the thin-flame approximation is excellent at 10 atm if the droplet surface temperature is not close to either the boiling point or the ambient temperature. However, this approximation is unacceptable at 1 atm. Among the three flame-sheet models, the one using non equilibrium evaporation at the surface and individual molecular weights best approximates the finite reaction-rate theory. However, this agreement breaks down for smaller droplets with lower surface temperatures, or for air with a larger oxygen content. These conclusions are independent of the chosen kinetics. The Clausius-Clapeyron approximation is shown to be excellent away from the boiling point for R = 10^(\u22122) cm. However, as the droplet surface temperature approaches the boiling point, or the droplet radius decreases, this assumption leads to considerable errors in the evaporation rate and also distortion of the thermal layer. Even larger errors are obtained when an average molecular weight is used. Here, large underestimates of the evaporation rate and great distortions of the thermal layer of the droplet are obtained. In spite of these errors, all models agree well at wet-bulb conditions.", "doi": "10.1016/0010-2180(78)90054-8", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1978", "volume": "33", "pages": "107-122" }, { "id": "authors:5agj3-ywp32", "collection": "authors", "collection_id": "5agj3-ywp32", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171019-134640679", "type": "article", "title": "A preliminary theoretical study of droplet extinction by depressurization", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Summerfield", "given_name": "Martin", "clpid": "Summerfield-M" } ], "abstract": "Depressurization-induced extinction of droplets is demonstrated using an unsteady liquid-phase theory and a previously presented quasisteady gas-phase model. Numerical results show that depressurization of the gas phase causes extinction of both regressing and nonregressing droplets. For nonregressing droplets it is found that at fixed droplet size the extinction pressure is a decreasing function of the initial depressurization rate; thus results are explained in terms of the time lag needed by a droplet to respond to a change in pressure. Regressing droplets, which extinguish more rapidly than constant-size ones, show the same type of behavior. Extinction boundaries, evaluated as functions of the initial temperature profile, show that whereas for constant-size droplets the extinction pressure is a strong decreasing function of the temperature, for regressing droplets this dependence is very weak and an asymptote is reached as the temperature increases. Results obtained by varying the initial pressure show that the extinction pressure is an increasing function of the initial pressure for regressing droplets. For constant-size droplets this function is nonmonotonic and reaches a maximum at the initial pressure for which the initial temperature profile is the wet-bulb state. The thermal conductivity of the liquid phase has almost no influence on the extinction boundary.", "doi": "10.1016/0010-2180(78)90100-1", "issn": "0010-2180", "publisher": "Elsevier", "publication": "Combustion and Flame", "publication_date": "1978", "volume": "32", "pages": "257-270" }, { "id": "authors:8pa46-q3b75", "collection": "authors", "collection_id": "8pa46-q3b75", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-134801561", "type": "article", "title": "Model for Studying Unsteady Droplet Combustion", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Summerfield", "given_name": "Martin", "clpid": "Summerfield-M" } ], "abstract": "The concept of a reduced boundary condition at the surface of a droplet is used to develop a theory of unsteady droplet burning. This theory utilizes a quasi-steady gas-phase assumption, which has been shown to be realistic for a wide range of droplet sizes at low pressures. The most significant consequence of the theory is that the problem of unsteady droplet burning is reduced to the solving of a single diffusion-type nonlinear partial differential equation having one of its boundary conditions determined by an algebraic function of the quasi-steady gas-phase variables. This reduced boundary condition incorporates the entire dependence of the solution on fuel characteristics, chemical kinetics, and thermal properties of the gases. An experiment is proposed for determining this boundary condition so that the nonsteady droplet combustion problem can be solved for a realistic situation. By using additional assumptions, a numerical estimate of the boundary condition has been made.", "doi": "10.2514/3.60621", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1977-02", "series_number": "2", "volume": "15", "issue": "2", "pages": "234-242" }, { "id": "authors:28exa-zc769", "collection": "authors", "collection_id": "28exa-zc769", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-145418174", "type": "article", "title": "Quasi-steady gas phase assumption for a burning droplet", "author": [ { "family_name": "Bellan", "given_name": "Josette", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Summerfield", "given_name": "Martin", "clpid": "Summerfield-M" } ], "abstract": "[No abstract]", "doi": "10.2514/3.7172", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1976-07", "series_number": "7", "volume": "14", "issue": "7", "pages": "973-975" }, { "id": "authors:xt2qx-m6s22", "collection": "authors", "collection_id": "xt2qx-m6s22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-152237780", "type": "article", "title": "Combustion and NO Formation in a Stratified-Charge Engine: a Two-Turbulent Equations Model", "author": [ { "family_name": "Bellan", "given_name": "Josette R.", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Sirignano", "given_name": "William A.", "clpid": "Sirignano-W-A" } ], "abstract": "A theoretical model of turbulent flame propagation in reciprocating stratified-charge engines is developed and compared to a previous model. A spacial variation of mixture ratio is considered such that there is a fuel-rich region in the center of the cylinder and a fuel lean-region near the cylinder walls. The spark in the fuel-rich region results in a premixed type of flame propagating toward the walls. A diffusion-type flame results in the wake of the other flame due to the mixing of the excess air and fuel.\n\nThe first model which was presented in a previous paper is based upon a prescribed time variation of the turbulent diffusivity depending upon the piston velocity. In the present work, a two-turbulent-equations model is developed and the turbulent diffusivity varies in space and time as well. Without experimental data it is difficult to ascertain that the second model is superior to the first one. However, because of the coupling of the turbulence phenomenon to the combustion itself, the second model is believed to be better than the first one. In both models calculations of the temperature and species mass fractions as functions of time and space are made. Also, the pressure is calculated as a function of time.\n\nA parametric study is performed with the second model. Parameters concerning both the engine and the mixture are varied. In particular a comparison with an engine operating with a premixed gas mixture is made. Trends indicate methods to \"optimize\" the combustion process so that a \"satisfactory\" reduction in NO could be achieved with a \"small\" drop in the pressure level.", "doi": "10.1080/00102207608946709", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1976", "series_number": "1-3", "volume": "12", "issue": "1-3", "pages": "75-104" }, { "id": "authors:dpfr6-6fz94", "collection": "authors", "collection_id": "dpfr6-6fz94", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171025-152716727", "type": "article", "title": "A Theory of Turbulent Flame Development and Nitric Oxide Formation in Stratified Charge Internal Combustion Engines", "author": [ { "family_name": "Bellan", "given_name": "Josette Rosentweig", "orcid": "0000-0001-9218-7017", "clpid": "Bellan-J" }, { "family_name": "Sirignano", "given_name": "William A.", "clpid": "Sirignano-W-A" } ], "abstract": "A theoretical model of turbulent flame propagation in a reciprocating stratified charge engine is developed and calculations of temperature and species concentrations as functions of space and time are made. Also pressure is calculated as a function of time. A spacial variation of mixture ratio is considered such that there is a fuel-rich region in the center of the cylinder and a fuel-lean region near the cylinder walls. The spark in the fuel-rich region results in a premixed-type of flame propagating toward the walls. A diffusion-type flame results in the wake of the other flame due to the mixing of the excess air and fuel.", "doi": "10.1080/00102207308946630", "issn": "0010-2202", "publisher": "Taylor & Francis", "publication": "Combustion Science and Technology", "publication_date": "1973", "series_number": "1-2", "volume": "8", "issue": "1-2", "pages": "51-68" } ]