Abstract: Poly(methyl methacrylate) (PMMA) is the synthetic polymer of methyl methacrylate (MMA), used as a solid fuel in hybrid rockets. PMMA undergoes pyrolysis into predominantly gaseous MMA (C5H8O2), which then undergoes combustion with an oxygen stream in the combustion chamber. Experimental studies of this combustion chamber have been performed in literature, and this study performs simulations, which can access more data in the combustion chamber. Simulations of laminar diffusion and laminar diffusion flames are performed using NGA, in a cylindrical domain, with gaseous MMA introduced through the cylinder walls. The rate of inflow of MMA is controlled by the temperature field in the combustion chamber, and the results from the 2D simulation are comparable to 1D counterflow diffusion flame simulations.

ID: CaltechAUTHORS:20200609-125133442

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Abstract: Reproducing hypersonic flight conditions in ground based facilities is a very challenging problem due to the high enthalpies required in the test gas, while simultaneously trying to match the post shock gas composition seen in flight. Experimental facilities have made significant progress in reproducing accurately hypersonic flows, but these facilities generally face issues associated with high operating costs and relatively short and noisy test times. This necessitates the need for high fidelity numerical simulations to aid with the investigation of these flows.

Vol.: 1
ID: CaltechAUTHORS:20170621-102011434

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Abstract: Published physical properties of phenolic impregnated carbon ablator (PICA) are compiled, and the composition of the pyrolysis gases that form at high temperatures internal to a heatshield is investigated. A 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 consistent, and thorough description of many of the physical phenomena occurring in a PICA heatshield, and their implications, to be presented.

ID: CaltechAUTHORS:20190816-144342150

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Abstract: Radiation heat transfer from gas phase species and soot particles is an important process that needs to be taken into account in numerical simulations of reacting flows for the accurate prediction of the flame structure, species yield and pollutant emission. Previous studies have included radiation effects into the tabulated chemistry approach using solutions to the unsteady flamelet equations. A new radiation model based on steady-state flamelets is proposed. This radiation model is developed based on a time scale analysis of flamelets, showing that radiation is a much slower process than chemistry and mixing in the reaction zone. This distinct time scale separation suggests that radiation could be treated in a quasi-steady fashion. In the procedure described herein, flamelets with different radiation intensities varying from non-radiating to fully radiating are pre-computed with a range of scalar dissipation rates to generate the flamelet library. An enthalpy defect is introduced in the flamelet library as a measure of the departure from the non-radiating flamelet solutions. The proposed radiation model is validated on a well-documented methane/air coflow diffusion flame. Results obtained using the tabulated chemistry approach including radiation effects are compared against experimental measurements, revealing satisfactory agreement.

ID: CaltechAUTHORS:20150723-094636869

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Abstract: The vortex-premixed flame interaction is investigated analytically for vortices of different length and velocity scales, l_v and u_v, by expanding the continuity, momentum, vorticity, temperature, and species equations. The terms are written in powers of a small parameter, ϵ. Solutions are separated based on the ratio of u_v to the laminar name speed, S_L, for a strong vortex, S_L/u_v = ϵ « 1, and for a weak vortex, u_v/S_L = ϵ « 1. They are further separated based upon the ratio of l_v to the flame length scale. L_F, resulting in four different cases. For all cases, the leading order equations describing the name and vortex are derived. The vorticity equation which describes to leading order the transformation of the vortices across the flame is solved analytically for l_v/l_F « 1, and qualitatively described for l_v/l_F » 1. This provides the leading order solution for the transformation of the size, velocity, circulation, and vorticity of the vortex across the flame. These solutions have applicability to modeling and predicting the transformation of turbulence across a flame.

ID: CaltechAUTHORS:20150723-093635097

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Abstract: In this paper, Large Eddy Simulations (LES) have been performed on an ethylene/air piloted turbulent sooting jet flame to examine the importance of chemistry-turbulence interaction. The current work focuses on the effects of turbulent transport on the formation of Polycyclic Aromatic Hydrocarbons (PAH). These species are of primary importance since their concentrations control directly the soot nucleation rates. The Flamelet/Progress Variable (FPV) approach is adopted to describe the combustion of all gas phase species except for PAH. Radiative heat transfer is considered by introducing enthalpy defect as an additional parameter in the FPV model. This parameter represents a measure of the departure from the non-radiating flamelet solutions. The FPV model accounting for radiative heat losses is closed in the current LES using a presumed subfilter Probability Density Function (PDF) approach. Given the large time scale related to PAH formation, PAH species exhibit large unsteady effects. To model these effects, transport equations are solved for these species. The chemical source terms are closed using a recently developed linear relaxation model. The importance of the interactions between turbulence and PAH chemistry is highlighted by comparing the PAH yield resulting from the LES to steady state flamelet predictions.

ID: CaltechAUTHORS:20150723-095606496

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Abstract: Numerical simulations of reacting flows often rely on direct integration of the continuity and momentum equations while transporting each chemical species and integrating their source term. However, requirements on the grid size and time step to resolve all the relevant physics is not generally well defined. In practice, information regarding convergence is gathered from the corresponding non-reacting flow, one-dimensional laminar flame, and full convergence studies. The establishment of general criteria or benchmarks relating convergence of these three aspects would decrease research and computational effort performing detailed convergence studies and increase consistency in the literature. To support this goal, studies were performed relating the convergence of the global flow field of a laminar reacting flow to the convergence, in space and time, of the corresponding one-dimensional flame and non-reacting flow. It was found that grid convergence of the global flow field was related to, but had more stringent requirements than either of the two separate cases while the required time step was the same. These results contribute to the development of satisfactory general criteria and benchmarks for determining convergence across specific flow cases, chemical mechanisms, and numerical implementations.

ID: CaltechAUTHORS:20150723-095254149

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Abstract: A simple a priori model for the effective Lewis numbers in a premixed turbulent flame is presented. This a priori analysis is performed using data from a series of direct numerical simulations (DNS) of lean (φ = 0:4) premixed turbulent hydrogen flames, with Karlovitz number ranging from 10 to 1562. Those simulations were chosen such that the transition from the thin reaction zone to the broken reaction zone is captured. The conditional mean of various species mass fraction (< Y_i | T >) vs temperature profiles are evaluated from the DNS and compared to equivalent unstretched laminar premixed flame profiles. The turbulent flame structure is found to be different from the laminar flame structure. However, the turbulent flame can still be mapped onto a laminar flame with an appropriate change in Lewis numbers. Those effective Lewis numbers were obtained by minimizing the error between the DNS results and predictions from unstretched laminar premixed flames. A transition from “laminar” Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured - equivalently, as the turbulent Reynolds number increases, given that the ratio of the integral length scale to the laminar flame thickness is fixed throughout the series of DNS. Those results suggest the importance of using effective Lewis numbers that are neither the “laminar” Lewis numbers nor unity in tabulated chemistry models without considering the impact of the turbulent Reynolds number or Karlovitz number. A model for those effective Lewis numbers with respect to the turbulent Reynolds number was also developed. The model is derived from a Reynolds Averaged Navier-Stokes formulation of the reactive scalar balance equations. The dependency of the effective Lewis numbers to the Karlovitz number instead of the Reynolds number was studied and is discussed in this paper. These changes in effective Lewis numbers have significant impacts. First, the laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used. A dependency on the effective Lewis numbers have to be introduced.

Vol.: 3
ID: CaltechAUTHORS:20141001-154719912

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Abstract: In this paper, the response of different species to turbulent unsteadiness is investigated utilizing the 1D unsteady laminar diffusion flamelet model. Turbulent effects are modeled solely through a abrupt change in the scalar dissipation rate. Steady-state flamelets are perturbed by the modeled turbulent effects. One-dimensional flamelet calculations assuming unity-Lewis number for all species are performed. Based on the numerical results, relations between the chemical source terms and species mass fractions are examined for various representative species. It is found that the smallest turbulent time scale remains much larger than that of the gaseous phase chemistry for some small species. The steady-state flamelet assumption for these species is well justified and their mass fractions can be pre-tabulated using the flamelet library legibly. On the other hand, PAH chemistry is relatively slow, and these PAH species cannot react instantaneously to the abrupt change in the local scalar dissipation rate. Based on the above considerations, a relaxation model is proposed for the chemical source terms of light species, species of moderate molecular weights, and heavy hydrocarbons. These source terms can be decomposed into a positive production term and a negative consumption term. The production term is observed to be constant for a given mixture fraction value, whereas the consumption term is found to be linearly dependent on the local species concentration. The dependence of the consumption term on the species mass fraction is found to be determined only by the scalar dissipation rate after its abrupt change. This observation suggests that the relaxation model can be fully pre-tabulated using the results of steady state flamelets. Based on the relaxation results, the validity of different chemistry tabulation models is assessed.

Vol.: 3
ID: CaltechAUTHORS:20141001-155352561

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Abstract: This study investigates the effects of curvature of mixture fraction iso-surfaces on the non-unity Lewis number transport of species in diffusion flames. A general flamelet formulation is derived mathematically for both unity and non-unity Lewis number transport and for different contours of mixture fraction iso-surfaces (i.e. non-zero curvature with varying magnitude.). These theoretical results suggest that curvature does not play a role in the transport process for unity Lewis number irrespective of the flame curvature, which was varied between highly curved and perfectly flat. On the other hand, for nonunity Lewis numbers, a curvature-related term becomes explicit for perfectly spherical flames, and this term acts as a convective term in mixture fraction space. Finally, in cases where flame curvature is not uniform, this convective term induces a non-zero diffusion flux in the direction normal to the mixture fraction gradient, which is inconsistent with the 1D flamelet assumptions. The flamelet equations accounting for curvature effects are solved considering first laminar spherical diffusion flames with different prescribed curvature at the stoichiometric mixture fraction. The results indicate that the magnitude of the curvature-induced convection term can become much larger than that of the convective term in the traditional flamelet formulation. Furthermore, the mass fraction profiles of heavy hydrocarbons, such as PAHs, are shifted significantly by the inclusion of curvature. The current work suggests a possible means to account for curvature effects via a new a priori chemistry tabulation which includes curvature for laminar and mildly turbulent diffusion flames.

Vol.: 3
ID: CaltechAUTHORS:20141001-100943831

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Abstract: We conducted an ab-initio quantum computational study to address certain issues present in current models of soot nucleation. Most models base soot nucleation upon the dimerization of gas phase polycyclic aromatic hydrocarbons (PAHs) that arises through collisions between these gaseous molecules. These models contain three major flaws and ultimately violate the second law of thermodynamics. Firstly, soot particles are formed at all temperatures, including room temperature, a phenomenon that is not observed experimentally. Secondly, these models predict that collisions between aromatic molecules of any size, including benzene, will form a soot particle. Thirdly, the dimers produced by these collisions are predicted to be infinitely stable. In an attempt to correct for the first two issues, we hypothesized that only collisions that included at least one excited state PAH, which would not be found at low temperatures, could form a stable dimer. The calculations of the excitation energy difference between excited and ground states were performed at the B3LYP level with the Dunnings Correlation Consistent basis sets. The cc-PVDZ basis set proved itself sufficient, as its excitation energy calculations differed from those of higher order Dunning’s sets by only a few percent. The results suggest that, while the excitation energy negatively correlated with molecular weight, it was strongly dependent upon the structure of the given PAH. PAHs that more closely resembled the n-acenes in structure had lower excitation barriers than other PAHs of similar mass. Using the calculated excitation energies, we evaluated the population of excited states at a given temperature assuming a Boltzmann equilibrium distribution. We found that only higher mass PAHs, particularly anthracene and tetracene, form a sufficiently large population of excited molecules at common sooting flame temperatures. Then, to tackle the third issue presented by current models, we used benzene and naphthalene as test cases to determine the stability of any dimers formed from a successful collision. Even though we found such dimers unlikely to form, they provided computationally efficient results that should generalize to higher order PAHs. These calculations were carried out using the MP2/cc-PVDZ level of theory. We compared the energy of two molecules, one in its ground and one in its excited state, an ”infinite distance” apart to two in close proximity (3-4 angstroms) and found that, for benzene, dimerization provides significant stabilization to the two molecules ( 30 kJ/mol). The present results suggest that a collision based model involving one ground state and one excited state PAH might adequately capture the physics of soot nucleation.

Vol.: 2
ID: CaltechAUTHORS:20140929-104113389

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Abstract: The interaction of a vortex with an initially planar premixed stoichiometric hydrogen-air flame is investigated to characterize the evolution of the vortex across the flame and identify the different regimes of behavior. These characteristics include vortex circulation, peak vorticity, peak velocity, and size. There are two key non-dimensional parameters. The first is the ratio of length scales, l_v/l_F, being the ratio of the vortex diameter to the laminar flame width and the second is the ratio of velocity scales, u_v/S_L, being the ratio of the characteristic velocity of the vortex to the laminar flame speed. The parameter space is explored with values of l_v/l_F ranging from 0.3 to 10 and values of u_v/S_L ranging from 0.1 to 50 corresponding to over 20 separate conditions. By performing simulations which vary these parameters over two and three orders of magnitude, the intermediary and limiting cases of each parameter are investigated. The simulations are performed using a low-Mach number Navier- Stokes solver, detailed hydrogen-air chemistry with 9 species, and unity Lewis number transport. Under stoichiometric hydrogen-air, the assumption of unity Lewis number is justified. Viscous and simulations with a reduced viscosity are preformed highlighting aspects of the coupling of the chemistry and the fluid mechanics. The results demonstrate the existence of four different regimes of the vortex-premixed flame interaction. In the limit u_v/S_L ≫ 1 and l_v/L_F ≫ 1, the vortex wraps the flame within itself and the vortex survives after passing through the flame. In the limit u_v/S_L ≫ 1 and l_v/l_F ≪ 1 the vortex mixes individual layers of the flame within itself and the vortex survives after passing through the flame. In the limit u_v/S_L ≪ 1 and l_v/l_F ≫ 1, the vortex creates sufficient flame curvature to produce baroclinic torque which destroys the incoming vortex. In the limit u_v/S_L ≪ 1 and l_v/l_F ≪ 1, the vortex has negligible effect on the flame and simply stretches in the flame normal direction. All four regimes correspond to qualitatively different vortex flame interactions and therefore the changes in vortices follow different behavior. The use of detailed chemistry for these simulations provides for additional insight into the coupling of chemistry and fluid mechanics in describing the behavior of vortex-premixed flame interactions.

Vol.: 3
ID: CaltechAUTHORS:20141001-151537412

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Abstract: Numerical simulations are carried out to study the effect of a vortex on the ignition dynamics of hydrogen/ air in a quiescent mixing layer. The problem has direct implications on the auto-ignition behavior and stabilization mechanism in turbulent non-premixed flames, recirculating burners and supersonic combustion. Similar problems have been studied in the past using different approximations like infinitely fast and single-step chemistry and large activation energy asymptotics. While useful insight is obtained, the role of multi-step reaction chemistry is neglected. More recent work utilizing detailed chemical kinetics has been limited in its scope due to computational requirements. These difficulties are overcome in the present study by utilizing a tabulated approach. Chemistry tabulations are generated utilizing steady-state solutions of the non-premixed flamelet equations. The fluid dynamic simulations are carried out using a lookup table approach. Similar calculations are also performed with detailed chemistry to demonstrate the accuracy of the tabulated approach. The reduction in computational time obtained using the tabulated approach is utilized to conduct a parametric study investigating the effects of vortex strength, characteristic size, center location, and fuel/air temperatures on ignition delay time and location. The effect of these parameters are correlated to the scalar dissipation rate to explain the physical processes leading to ignition.

Vol.: 3
ID: CaltechAUTHORS:20141001-104729934

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Abstract: Issues resulting from the rupture of the secondary diaphragm in an expansion tunnel may be mitigated by matching the test gas pressure and the accelerator gas pressure, orienting the tunnel vertically, and initially separating the test gas from the accelerator gas by density stratification. Two benefits are: 1) the removal of the diaphragm particulates in the test gas after its rupture and 2) the elimination of the wave system that is a result of a real secondary diaphragm having a finite thickness and mass. An inviscid perfect-gas analysis is performed to find the reservoir conditions available in the vertical expansion tunnel (VET) for comparison to a conventional expansion tunnel (ET) and a reflected shock tunnel (RST). A numerical inviscid perfect-gas analysis is presented to estimate the available test time in the VET. The effective reservoir conditions of the VET lie somewhere between the RST and the ET.

ID: CaltechAUTHORS:20190826-092412604

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Abstract: An experimental and numerical study was performed to investigate the behavior of a counter-rotating vortex pair as well as a single vortex in the vicinity of a wall. A wind tunnel with two NACA0012 profiles mounted vertically with an optional splitter plate in the center and a 3D PIV system were used to experimentally study the interactions between two counter-rotating vortices, as well as the interactions between a vortex and a wall. Many fundamental differences were found between the two configurations, which promote the growth of the Crow instability in the two vortex configuration, but not in the one vortex/wall configuration. The numerical results obtained re-enforced the experimental results, and emphasize the fundamental physical differences between the two configurations. While modeling a vortex wall system with an image vortex may give correct integral results for loads experienced by blades, this model does not accurately describe the downstream dynamics of the vortex system.

ID: CaltechAUTHORS:20190930-110458199

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