Direct numerical simulations (DNS) of reacting flows are routinely performed either by solving the fully compressible Navier-Stokes equations or using the low Mach number approximation. The latter is obtained by performing a Mach number expansion of the Navier-Stokes equations for small Mach numbers. These two frameworks differ by their ability to capture compressibility effects, which can be broadly defined as phenomena that are not captured by the low Mach number approximation. These phenomena include acoustics, compressible turbulence, and shocks. In this thesis, we systematically isolate compressibility effects in subsonic flows by performing two sets of DNS: one using the fully compressible framework, and one using the low Mach number approximation. We are specifically interested in the interactions between turbulence, acoustics, and flames.

The addition of detailed chemistry in the compressible flow solver required the development of a novel time integration scheme. This scheme combines an iterative semi-implicit method for the integration of the species transport equations, and the classical Runge-Kutta method for the integration of the other flow quantities. It is found to perform well, yielding time steps limited by the acoustic CFL only. Furthermore, the computational cost per iteration of this hybrid scheme is low, being comparable to the one for the classical Runge-Kutta method.

After extensive validation, the first application is the investigation of flame-acoustics interactions in laminar premixed flames. The thermodynamic fluctuations that accompany the acoustic wave are shown to significantly impact the flame response. Using the Rayleigh criterion, the flame-acoustics system is found to be thermo-acoustically unstable for various fuels, flow conditions, and acoustic frequencies. As expected, the low Mach number approximation and the fully compressible framework are in good agreement at low frequencies, since the flame is very thin compared to the acoustic wavelength. The two frameworks differ for very large acoustic frequencies only. In the high frequency limit, the gain reaches a plateau using the low Mach number approximation, while it goes to zero using the fully compressible framework. This is related to the spatial variations in the acoustic pressure field, which are not present in the low Mach number approximation. However, for practically relevant acoustic frequencies, the low Mach number framework is found to yield accurate results.

Next, a numerical methodology to simulate compressible flows in geometries that lack a natural turbulence generation mechanism is presented. It is found that, unlike in incompressible flows, special care must be taken regarding the energy equation and the presence of standing acoustic modes. When using periodic boundary conditions, forcing the dilatational velocity field promotes the growth of unstable modes. This is explained by extracting the eigenvalues of the linearized forced Navier-Stokes equations. Based on these observations, it is found necessary to force the solenoidal velocity field only. This methodology is applied first to simulations of subsonic homogeneous non-reacting turbulence. We present simulations results for turbulent Mach numbers varying from 0.02 to 0.65. The Mach number dependence of various quantities, such as the dilatational to solenoidal kinetic energy ratio, is extracted. The Mach number scaling of all quantities of interest is found to be readily explained by the low Mach number expansion, specifically the zeroth and first order sets of equations, for turbulent Mach numbers up to 0.1.

Finally, the interaction between subsonic compressible turbulence and premixed flames is investigated. Compressibility effects are isolated by comparing results obtained with the low Mach number approximation and the fully compressible framework, at the same flow conditions. Compressibility effects on chemistry are found to be limited for turbulent Mach numbers at least up to 0.4, especially when contrasted with the large impact of the Karlovitz number. Compressibility effects give rise to significant thermodynamic fluctuations away from the flame front, but these remain small compared to the large fluctuations due to the presence of the turbulent flame brush. The low Mach number approximation thus remains a valid framework for the Mach numbers considered, when the primary goal is to characterize the impact of turbulence on the chemical processes at play.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/qjfk-5q05, author = {Ruan, Joseph Y.}, title = {Streamwise Homogeneous Turbulent Boundary Layers}, school = {California Institute of Technology}, year = {2021}, doi = {10.7907/qjfk-5q05}, url = {https://resolver.caltech.edu/CaltechTHESIS:06062021-094519451}, abstract = {Boundary layers are everywhere and computing direct numerical simulations (DNS) of them is crucial for drag reduction. However, traditional DNS of flat-plate boundary layers are prohibitively expensive. Due to the streamwise inhomogeneity of the boundary layer, simulations of spatially growing boundary layer simulations require long domains and long convergence times. Current methods to overcome streamwise inhomogeneity (and allow for shorter streamwise domains) either suffer from a lack of stationarity or have difficult numerical implementation. The goal of this thesis is to develop and validate a more efficient method for simulating boundary layers that will be both statistically stationary and streamwise homogeneous.

The current methodology is developed and validated for the flat plate, zero pressure gradient, incompressible boundary layer. The Navier-Stokes equations are rescaled by a boundary layer thickness to produce a new set of governing equations that resemble the original Navier-Stokes equations with additional source terms. Streamwise homogeneity and statistical stationarity are verified through non-periodic and periodic simulations, respectively. To test the accuracy of the methodology, a sweep of Reynolds number simulations is conducted in streamwise periodic domains for Re_{δ*}=1460-5650. The global quantities show excellent agreement with established empirical values: the computed shape factor and skin friction coefficient for all cases are within 3% and 1% of empirical values, respectively. Furthermore, to obtain accurate two-point correlations, it is sufficient to have a computational domain of length 14δ_{99} and width 5δ_{99}, thus, leading to large computational savings by one-to-two orders of magnitude. This translates into increasing the largest possible Reynolds number one could simulate by about a factor of 3.

Thanks to the streamwise homogeneous nature of the simulation results, it is now possible to apply cost-efficient data-driven techniques like spectral proper orthogonal decomposition (SPOD; Towne et al. 2018) to extract turbulent structures. Particular emphasis is place on identifying structures for waves in the inner and outer layers. To interpret these structures, 1D resolvent analysis (McKeon and Sharma 2010) is leveraged. The peak location for the extracted inner wave is captured by traditional resolvent analysis, assuming a parallel flow. However, the peak location for the extracted outer wave differs from that predicted by the classic 1D resolvent analysis by 20%. Recovering the peak location requires including in the resolvent operator the mean wall-normal velocity profile and the streamwise growth of the boundary layer.

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This methodology has natural extensions to slowly growing boundary layer flows, including thermal boundary layers, rough wall boundary layers and mild pressure gradient flows.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/7SXH-V275, author = {Rah, Kyupaeck Jeff}, title = {Derivation of Realistic Forcing Schemes to Reproduce Turbulent Characteristics of Round Jets on Centerline}, school = {California Institute of Technology}, year = {2020}, doi = {10.7907/7SXH-V275}, url = {https://resolver.caltech.edu/CaltechTHESIS:08262019-191842947}, abstract = {Turbulence forcing techniques are often required in the numerical simulation of statistically stationary turbulent flows. However, the existing forcing techniques are not based on physics, but rather arbitrary numerical methods that sustain the turbulent kinetic energy. In this work, a realistic forcing technique is devised to reproduce the centerline turbulent characteristics of round jets in a triply periodic box.

A velocity forcing term is derived from the Navier-Stokes equations by applying a Reynolds decomposition with the mean velocity of the axisymmetric jet. The result is an anisotropic linear forcing term. A series of direct numerical simulations (DNS) are performed over a range of Reynolds numbers by applying the derived velocity forcing term in a 3D cubic box. The budget of the terms in the kinetic energy equation is found to be very close to the experimental measurement on the centerline. The anisotropy ratio, kinetic energy, and dissipation rate of the simulations are also comparable to experimental values. Finally, the kinetic energy spectrum in the axial direction is presented. With appropriate normalizations, the spectrum agrees well with the round jet spectrum on its centerline.

A similar procedure is applied to passive scalars to derive a scalar forcing term to simulate the centerline mixing properties of round jets. The term is derived from the scalar transport equation using a Reynolds-like decomposition of the scalar field. The equation is closed by applying the known mean velocity and scalar profiles of axisymmetric jets. The result is a combination of a mean gradient term and a linear scalar term. DNS at different Reynolds numbers have been performed with these source terms for unity Schmidt number. Scalar flux values and scaling exponents of scalar energy spectra from simulations are comparable to experimental values. In addition, a dimensional analysis shows that the normalized scalar statistics, such as variance, flux, and dissipation rate, should only be a function of Reynolds number; indeed, such quantities computed from our simulations approach constant values as the Reynolds number increases. The effects of velocity forcing on scalar fields are also investigated; changing velocity forcing terms may result in unstable scalar fields even under the same scalar forcing.

More computations on higher Schmidt number scalars are performed with the same velocity and scalar forcing terms. It is found that the scalar flux values decrease with increasing Schmidt number for low Reynolds number flows, and reach plateaus as the Schmidt number increases. The flux values also increase with the Reynolds number for all non-unity Schmidt numbers. The scaling exponents of scalar energy spectra are found to decrease with increasing Schmidt number for all Reynolds numbers.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/FW2R-BF41, author = {Krueger, Rachel Ann}, title = {Theoretical Characterization of Aromatic Exciplex Fluorescence}, school = {California Institute of Technology}, year = {2020}, doi = {10.7907/FW2R-BF41}, url = {https://resolver.caltech.edu/CaltechTHESIS:07242019-140324087}, abstract = {The negative effects of soot on the environment and human health are well known, but efforts to decrease soot production in combustion processes are hampered by the absence of accurate, transferable models for soot formation. Uncertainties about the soot nucleation mechanism, including the size and properties of the molecules involved and the relative importance of chemical and physical stabilization, have made model development difficult. Electronic spectroscopy methods such as laser-induced fluorescence (LIF) have the potential to characterize transient soot nuclei, but interpreting spectra requires a comprehensive understanding of the photoresponse of likely soot precursors, namely polycyclic aromatic hydrocarbon (PAH) dimers and clusters. To build up a picture of this photoresponse using theory, it is necessary to evaluate which methods are capable of treating the relevant molecules at reasonable cost while capturing the excited-state and noncovalent interactions involved in excimer and exciplex formation, a key excited-state process for aromatic clusters. In this work, we describe extensive benchmarking of basis set error in highly-accurate perturbatively-corrected multireference calculations of exciplex interaction strength and use the best possible multireference approach to evaluate the performance of less-expensive time-dependent density functional theory (TDDFT) results. Using the most accurate TDDFT methods, we explore how the geometric and electronic properties of the monomers influence excited-state interactions in complexes, considering a large database of complexes. A predictive model for exciplex fluorescence emissions of complexes containing six-membered ring PAHs based on monomer HOMO-LUMO gaps is proposed. We describe the contrasting photoresponse of PAHs containing five-membered rings, where nonaromatic groups produce conformational flexibility that has a strong impact on absorption and emission behavior.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/FH31-4468, author = {Dhandapani, Chandru}, title = {Using the Force: Applications and Implications of Turbulence Forcing Terms in Direct Numerical Simulations}, school = {California Institute of Technology}, year = {2019}, doi = {10.7907/FH31-4468}, url = {https://resolver.caltech.edu/CaltechTHESIS:06102019-185605511}, abstract = {Most energy requirements of modern life can be fulfilled by renewable energy sources, but it is impossible in the near future to provide an alternative energy source to combustion for airplanes. That being said, combustion in aviation can be made more sustainable by using alternative jet fuels, which are made from renewable sources like agricultural wastes, solid wastes, oils, and sugars. These alternative fuels can be used in commercial flights only after a long certification process by the Federal Aviation Agency (FAA) and ASTM International. Unfortunately, in over 50 years of fuel research, only five fuels have been certified. This research project aims to speed up the certification process with quicker testing of alternative fuels. Engine testing and even laboratory testing require large amounts of time and fuel. Simulations can make the process much more efficient, but accurately simulating highly turbulent flames in such complex geometries would need large amounts of computational resources. The goal of this thesis is to create an efficient computational framework, that can replicate different engine-like turbulent flow conditions in simple geometries with numerical tractability.

The central idea is to decompose the flow field into ensemble mean and fluctuating quantities. The simulations then resolve only the fluctuations using simple computational domains, while emulating the effect of the mean flow using “forcing” terms. These forcing terms are calculated first for incompressible turbulence, and this method is later extended to turbulent reacting flows. In incompressible turbulence, Direct Numerical Simulations (DNS) performed on simple triply periodic cubic domains reasonably capture the statistically stationary shear turbulence, that is observed in free shear flows. The simulations are also performed in cuboidal domains, that are longer in one direction and with an inflow/outflow along it. Both changes are observed to not have a significant impact on the turbulence statistics. Finally, shear convection is applied to the turbulence simulations with inflow/outflow, which has a significant impact on the turbulence. These simulations accurately capture the turbulence anisotropy in free-shear flows.

The study is extended to DNS of highly turbulent *n*-heptane-air flames performed under different flow conditions. Turbulent flames involve two-way coupling between fluid mechanics and combustion. The effects of the flame on the turbulence and the impact of the turbulent flow conditions on the flame behavior are analyzed. The focus is placed on the effects of turbulence production, shear convection, and pressure gradients. The anisotropy produced in the turbulence due to the different flow conditions and the flame are also compared and contrasted. While the global behavior and flow anisotropy were affected by these conditions, the local chemistry effects were unaffected, and depend only on the laminar flame properties and turbulence intensity. These findings can help predict turbulent flame behavior, and can expedite the search and testing of sustainable alternatives to conventional jet fuels.

The use of hydrogen as a fuel for power generation applications has been suggested as an additive to, or replacement of, hydrocarbon fuels. The safety of hydrogen combustion has also received recent attention due to nuclear power plant disasters and the rise of hydrogen refuelling stations. In these uses and scenarios, lean hydrogen–air flames are prone to thermo-diffusive instabilities which can be dangerous to equipment and personnel. These instabilities are heavily influenced by two mechanisms: transport properties (e.g., diffusion) and chemical species production rates. This thesis investigates lean premixed hydrogen combustion using direct numerical simulations. A wide range of flame configurations are considered, spanning one-dimensional steady configurations to three-dimensional unsteady laminar and turbulent flames with high curvature. In particular, the two controlling mechanisms of thermo-diffusive instabilities are carefully investigated.

The effects of transport properties, in particular the importance of thermal diffusion in these mixtures, are quantified through global and local evaluations. Thermal diffusion is found to change flame speeds in one-dimensional flat flames, and also modify species profiles due to the increased diffusivity of light reactants. The impact of thermal diffusion is greatly enhanced in the presence of flame curvature, resulting in higher flame speeds (20% to 30% for two- and three-dimensional laminar and turbulent flames), fuel consumption, and flame surface area relative to simulations neglecting thermal diffusion. The mixture-averaged thermal diffusion model proposed by Chapman and Cowling (1970) is found to accurately reproduce global and local flame statistics (including enhanced burning and local extinction) computed using multicomponent transport at significantly reduced costs. Further cost reductions of the mixture-averaged thermal diffusion method are undertaken, and a new model is developed with constant computational requirements for large (~100 species) chemical models. The resulting reduced thermal diffusion model additionally improves upon the accuracy of the mixture-averaged thermal diffusion technique.

The effects of fluctuating chemical source terms on flame instabilities are then investigated using tabulated chemistry. One-dimensional unstretched flames including non-equal diffusion and thermal diffusion are incorporated into a chemistry table. This table successfully captures the interaction of differential diffusion and flame curvature. The chemistry tabulation approach is applied to a similar set of flame configurations, and accurate predictions of global and local statistics are found. The tabulated chemistry method reproduces flame curvature, local enhanced burning, and local extinction of unstable flames using one-dimensional, flat, burning flames in its construction. The proposed reduced-order thermal diffusion and chemistry tabulation models significantly reduce computational costs while simultaneously including physical properties necessary to predict lean premixed hydrogen–air flame instabilities.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/N3VJ-BE39, author = {Burali, Nicholas}, title = {Towards a priori Models for Differential Diffusion in Turbulent Non-Premixed Flames}, school = {California Institute of Technology}, year = {2018}, doi = {10.7907/N3VJ-BE39}, url = {https://resolver.caltech.edu/CaltechTHESIS:06062018-163232775}, abstract = {In this work, progress is made towards the correct modeling of differential diffusion, both for resolved simulations, and for reduced-order combustion models. For resolved simulations, the validity and the limitations of the constant non-unity Lewis number approach in the description of molecular mixing in laminar and turbulent flames is studied. Three test cases are selected, including a lean, highly unstable, premixed hydrogen/air flame, a lean turbulent premixed n-heptane/air flame, and a laminar ethylene/air coflow diffusion flame. For the hydrogen flame, both a laminar and a turbulent configuration are considered. The three flames are characterized by Lewis numbers which are less than unity, greater than unity, and close to unity, respectively. For each flame, mixture-averaged transport simulations are carried out and used as reference data. The analysis suggests that, for numerous combustion configurations, the constant non-unity Lewis number approximation leads to small errors when the set of Lewis numbers is chosen properly. For the selected test cases and our numerical framework, the reduction of computational cost is found to be minimal. Two different methods of evaluating the Lewis numbers are tested, with both performing well, and neither consistently better than the other.

The flamelet-based chemistry tabulation technique is a popular reduced-order chemical model for non-premixed turbulent flames. In this approach, the correct choice of the species Lewis numbers in the flamelet equations plays an important role. Experimental results have highlighted that, in turbulent non-premixed jet flames, turbulent transport becomes gradually dominant over molecular mixing with (i) increasing axial distance from the burner exit plane, and (ii) increasing jet Reynolds number. In the current work, this transition is characterized and a priori models for the effective species Lewis numbers in turbulent non-premixed flames are assessed.

First, a flamelet-based methodology is proposed to extract these effective Lewis numbers from data sets of turbulent non-premixed flames. This methodology is then applied to the Sandia non-premixed methane/air jet flames B, C, D, and E (R. Barlow, Int. Work. Meas. Comput. Turb. Non-Prem. Flames, 2003). The effective Lewis numbers are found to transition from their laminar values, close to the burner exit plane, to unity further downstream. Previously-suggested scalings for the effective Lewis numbers are then assessed.

To overcome the limitations associated with the experimental data, a campaign of Direct Numerical Simulations (DNS) of Sandia flame B is carried out. A baseline grid is carefully designed, and grid independence is assessed through simulations using refined grids in the axial, radial and azimuthal directions. Radiation and differential diffusion effects are systematically isolated by considering radiating and unity Lewis number cases, respectively. The DNS database is then validated using available measured statistics for flame B, and comparisons to the higher Reynolds number flames are carried out. Effective Lewis numbers extracted from the DNS data are found to transition to unity with increasing downstream distance. Finally, the scalings for the effective Lewis numbers are re-computed from the DNS data base, and compared to the higher Reynolds number flames.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/Z90V89SW, author = {Lapointe, Simon}, title = {Simulation of Premixed Hydrocarbon Flames at High Turbulence Intensities}, school = {California Institute of Technology}, year = {2016}, doi = {10.7907/Z90V89SW}, url = {https://resolver.caltech.edu/CaltechTHESIS:05272016-105842881}, abstract = {Turbulent premixed hydrocarbon flames in the thin and distributed reaction zones regimes are simulated using both Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES). A series of DNS is performed to study the transition from the thin reaction zones regime to the distributed reaction zones regime. Differential diffusion effects, distributed burning, and local extinctions are quantified. Different fuels, chemical mechanisms, and equivalence ratios are considered. The fuel Lewis number significantly influences the chemical source terms and turbulent flame speeds. More precisely, simulations with differential diffusion effects exhibit lower mean fuel consumption and heat release rates than their unity Lewis number counterparts. However, the differences are reduced as the reaction zone Karlovitz number is increased. The turbulent reaction zone surface areas increase with the turbulence intensity but aren’t strongly affected by fuel, equivalence ratio, chemical mechanism, or differential diffusion. Unsurprisingly, changes in the integral length at a fixed Karlovitz number do not affect the chemical source terms but lead to an increase in flame surface area. Assumptions behind closure models for the filtered source term are then studied a priori using the DNS results. Using the concept of optimal estimators, it is shown that a tabulation approach using a progress variable and its variance can predict accurately the filtered progress variable source term. The filtered source terms are compared to predictions from two common presumed sub-filter Probability Density Functions (PDF) models. Both models show deviations from the filtered DNS source terms but predict accurately the mean turbulent flame speed. Finally, LES of experimentally-studied piloted premixed jet flames are performed using tabulated chemistry. Velocity and flame height measurements from simulations and experiments are compared. The LES are in good agreement with the experimental results for the four different hydrocarbon fuels and three different Reynolds numbers simulated. This corroborates that fuel and chemistry effects in turbulent flames are limited to effects present in laminar flames.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/Z9Z03649, author = {Bobbitt, Brock Douglas}, title = {Small Scale Turbulence in High Karlovitz Number Premixed Flames}, school = {California Institute of Technology}, year = {2016}, doi = {10.7907/Z9Z03649}, url = {https://resolver.caltech.edu/CaltechTHESIS:03102016-211538603}, abstract = {The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω^{2} = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τ_{η}, just as in homogeneous isotropic turbulence. As τ_{η} is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO_{2} and soot production to increasing engine efficiency.

Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot’’ exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/XKM7-7368, author = {Rabinovitch, Jason}, title = {Advancing EDL Technologies for Future Space Missions: From Ground Testing Facilities to Ablative Heatshields}, school = {California Institute of Technology}, year = {2014}, doi = {10.7907/XKM7-7368}, url = {https://resolver.caltech.edu/CaltechTHESIS:05302014-140011538}, abstract = {Motivated by recent MSL results where the ablation rate of the PICA heatshield was over-predicted, and staying true to the objectives outlined in the NASA Space Technology Roadmaps and Priorities report, this work focuses on advancing EDL technologies for future space missions.

Due to the difficulties in performing flight tests in the hypervelocity regime, a new ground testing facility called the vertical expansion tunnel is proposed. The adverse effects from secondary diaphragm rupture in an expansion tunnel may be reduced or eliminated by orienting the tunnel vertically, matching the test gas pressure and the accelerator gas pressure, and initially separating the test gas from the accelerator gas by density stratification. If some sacrifice of the reservoir conditions can be made, the VET can be utilized in hypervelocity ground testing, without the problems associated with secondary diaphragm rupture.

The performance of different constraints for the Rate-Controlled Constrained-Equilibrium (RCCE) method is investigated in the context of modeling reacting flows characteristic to ground testing facilities, and re-entry conditions. The effectiveness of different constraints are isolated, and new constraints previously unmentioned in the literature are introduced. Three main benefits from the RCCE method were determined: 1) the reduction in number of equations that need to be solved to model a reacting flow; 2) the reduction in stiffness of the system of equations needed to be solved; and 3) the ability to tabulate chemical properties as a function of a constraint once, prior to running a simulation, along with the ability to use the same table for multiple simulations.

Finally, published physical properties of PICA are compiled, and the composition of the pyrolysis gases that form at high temperatures internal to a heatshield is investigated. A necessary link between the composition of the solid resin, and the composition of the pyrolysis gases created is provided. This link, combined with a detailed investigation into a reacting pyrolysis gas mixture, allows a much needed consistent, and thorough description of many of the physical phenomena occurring in a PICA heatshield, and their implications, to be presented.

Through the use of computational fluid mechanics and computational chemistry methods, significant contributions have been made to advancing ground testing facilities, computational methods for reacting flows, and ablation modeling.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/ZED4-A872, author = {Xuan, Yuan}, title = {Progress in Numerical Modeling of Non-Premixed Combustion}, school = {California Institute of Technology}, year = {2014}, doi = {10.7907/ZED4-A872}, url = {https://resolver.caltech.edu/CaltechTHESIS:05292014-112456783}, abstract = {Progress is made on the numerical modeling of both laminar and turbulent non-premixed flames. Instead of solving the transport equations for the numerous species involved in the combustion process, the present study proposes reduced-order combustion models based on local flame structures.

For laminar non-premixed flames, curvature and multi-dimensional diffusion effects are found critical for the accurate prediction of sooting tendencies. A new numerical model based on modified flamelet equations is proposed. Sooting tendencies are calculated numerically using the proposed model for a wide range of species. These first numerically-computed sooting tendencies are in good agreement with experimental data. To further quantify curvature and multi-dimensional effects, a general flamelet formulation is derived mathematically. A budget analysis of the general flamelet equations is performed on an axisymmetric laminar diffusion flame. A new chemistry tabulation method based on the general flamelet formulation is proposed. This new tabulation method is applied to the same flame and demonstrates significant improvement compared to previous techniques.

For turbulent non-premixed flames, a new model to account for chemistry-turbulence interactions is proposed. %It is found that these interactions are not important for radicals and small species, but substantial for aromatic species. The validity of various existing flamelet-based chemistry tabulation methods is examined, and a new linear relaxation model is proposed for aromatic species. The proposed relaxation model is validated against full chemistry calculations. To further quantify the importance of aromatic chemistry-turbulence interactions, Large-Eddy Simulations (LES) have been performed on a turbulent sooting jet flame. %The aforementioned relaxation model is used to provide closure for the chemical source terms of transported aromatic species. The effects of turbulent unsteadiness on soot are highlighted by comparing the LES results with a separate LES using fully-tabulated chemistry. It is shown that turbulent unsteady effects are of critical importance for the accurate prediction of not only the inception locations, but also the magnitude and fluctuations of soot.

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/RDHJ-3X60, author = {Carroll, Phares Lynn}, title = {Towards Understanding the Mixing Characteristics of Turbulent Buoyant Flows}, school = {California Institute of Technology}, year = {2014}, doi = {10.7907/RDHJ-3X60}, url = {https://resolver.caltech.edu/CaltechTHESIS:05212014-101703985}, abstract = {This work proposes a new simulation methodology in which variable density turbulent flows can be studied in the context of a mixing layer with or without the presence of gravity. Specifically, this methodology is developed to probe the nature of non-buoyantly-driven (i.e. isotropically-driven) or buoyantly-driven mixing deep inside a mixing layer. Numerical forcing methods are incorporated into both the velocity and scalar fields, which extends the length of time over which mixing physics can be studied. The simulation framework is designed to allow for independent variation of four non-dimensional parameters, including the Reynolds, Richardson, Atwood, and Schmidt numbers. Additionally, the governing equations are integrated in such a way to allow for the relative magnitude of buoyant energy production and non-buoyant energy production to be varied.

The computational requirements needed to implement the proposed configuration are presented. They are justified in terms of grid resolution, order of accuracy, and transport scheme. Canonical features of turbulent buoyant flows are reproduced as validation of the proposed methodology. These features include the recovery of isotropic Kolmogorov scales under buoyant and non-buoyant conditions, the recovery of anisotropic one-dimensional energy spectra under buoyant conditions, and the preservation of known statistical distributions in the scalar field, as found in other DNS studies.

This simulation methodology is used to perform a parametric study of turbulent buoyant flows to discern the effects of varying the Reynolds, Richardson, and Atwood numbers on the resulting state of mixing. The effects of the Reynolds and Atwood numbers are isolated by looking at two energy dissipation rate conditions under non-buoyant (variable density) and constant density conditions. The effects of Richardson number are isolated by varying the ratio of buoyant energy production to total energy production from zero (non-buoyant) to one (entirely buoyant) under constant Atwood number, Schmidt number, and energy dissipation rate conditions. It is found that the major differences between non-buoyant and buoyant turbulent flows are contained in the transfer spectrum and longitudinal structure functions, while all other metrics are largely similar (e.g. energy spectra, alignment characteristics of the strain-rate tensor). Also, despite the differences noted between fully buoyant and non-buoyant turbulent fields, the scalar field, in all cases, is unchanged by these. The mixing dynamics in the scalar field are found to be insensitive to the source of turbulent kinetic energy production (non-buoyant vs. buoyant).

}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, } @phdthesis{10.7907/PTD9-W004, author = {Verma, Siddhartha}, title = {Velocity Resolved - Scalar Modeled Simulations of High Schmidt Number Turbulent Transport}, school = {California Institute of Technology}, year = {2014}, doi = {10.7907/PTD9-W004}, url = {https://resolver.caltech.edu/CaltechTHESIS:06042014-163735743}, abstract = {The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Blanquart, Guillaume}, }