Abstract: To ensure numerical stability in the vicinity of shocks, a variety of methods have been used, including shock-capturing schemes such as weighted essentially non-oscillatory schemes, as well as the addition of artificial diffusivities to the governing equations. Centered finite difference schemes are often avoided near discontinuities due to the tendency for significant oscillations. However, such schemes have desirable conservation properties compared to many shock-capturing schemes. The objective of this work is to derive all necessary viscous/diffusion terms from first principles and then demonstrate the performance of these analytical terms within a centered differencing framework. The physical Euler equations are spatially-filtered with a Gaussian-like filter. Sub-filter scale (SFS) terms arise in the momentum and energy equations. Analytical closure is provided for each of them by leveraging the jump conditions for a shock. No SFS terms are present in the continuity or species equations. This approach is tested for several problems involving shocks in one and two dimensions. Implemented within a centered difference code, the SFS terms perform well for a range of flow conditions without introducing excessive diffusion.

Publication: Journal of Computational Physics Vol.: 477ISSN: 0021-9991

ID: CaltechAUTHORS:20230227-87934600.2

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Abstract: An analysis was conducted of the transpiration velocity of the streamwise periodic simulation of the turbulent flat plate boundary layer. As an often imposed quantity in numerical simulation, the transpiration velocity plays an important role in the shape of the wall-normal profile near the outer layer. Unlike other simulation frameworks which impose the transpiration velocity, the recently proposed framework [Ruan and Blanquart, Phys. Rev. Fluids 6, 024602 (2021)] relies on a single-scale rescaling of the wall-normal coordinate to perform streamwise periodic boundary layer simulations. The current manuscript highlights that any error in the transpiration velocity from these simulations is due to a difference in inner and outer layer growth rates. A new multiscale framework to compensate for these differing growth rates is proposed and verified but ultimately has negligible impact on the mean profiles and turbulent intensities. These remain in excellent agreement with previously published values. It is shown that any error in the mean continuity equation expresses itself primarily as an error in transpiration velocity, which decreases with Reynolds number. Overall, the error in the transpiration velocity can be used to quantify the error in single-scale, streamwise periodic simulations.

Publication: Physical Review Fluids Vol.: 6 No.: 11 ISSN: 2469-990X

ID: CaltechAUTHORS:20211130-211842779

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Abstract: We demonstrate a method for direct numerical simulations (DNS) of incompressible, flat-plate, zero pressure gradient, turbulent boundary layers, without the use of auxiliary simulations or fringe regions, in a streamwise periodic domain via the homogenized Navier-Stokes equations. This approach is inspired by Spalart's original (1987) method, but improves upon his drawbacks while simplifying the implementation. Most simulations of flat-plate boundary layers require long streamwise domains owing to the slow boundary layer growth and inflow generation techniques. Instead, we use anticipated self-similarity to solve the equations in a normalized coordinate system to allow for streamwise periodicity, similar to Spalart's original method. The resulting integral values, the skin friction coefficient and shape factor, H₁₂ and C_f, are within ± 1% and ± 3% of the empirical fits. The mean profiles show good agreement with spatially developing DNS and experimental results for a wide range of Reynolds numbers from Re_(δ∗) = 1460 to 5650. The method manages to reduce computational costs by an estimated one to two orders of magnitude.

Publication: Physical Review Fluids Vol.: 6 No.: 2 ISSN: 2469-990X

ID: CaltechAUTHORS:20210208-144010941

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Abstract: Implementing multicomponent diffusion models in numerical combustion studies is computationally expensive; to reduce cost, numerical simulations commonly use mixture-averaged diffusion treatments or simpler models. However, the accuracy and appropriateness of mixture-averaged diffusion has not been verified for three-dimensional, turbulent, premixed flames. In this study we evaluated the role of multicomponent mass diffusion in premixed, three-dimensional high Karlovitz-number hydrogen, n-heptane, and toluene flames, representing a range of fuel Lewis numbers. We also studied a premixed, unstable two-dimensional hydrogen flame due to the importance of diffusion effects in such cases. Our comparison of diffusion flux vectors revealed differences of 10–20% on average between the mixture-averaged and multicomponent diffusion models, and greater than 40% in regions of high flame curvature. Overall, however, the mixture-averaged model produces small differences in diffusion flux compared with global turbulent flame statistics. To evaluate the impact of these differences between the two models, we compared normalized turbulent flame speeds and conditional means of species mass fraction and source term. We found differences of 5–20% in the mean normalized turbulent flame speeds, which seem to correspond to differences of 5–10% in the peak fuel source terms. Our results motivate further study into whether the mixture-averaged diffusion model is always appropriate for DNS of premixed turbulent flames.

Publication: Combustion and Flame Vol.: 223ISSN: 0010-2180

ID: CaltechAUTHORS:20210112-144610773

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Abstract: Homogeneous shear turbulence (HST) is an idealized version of the shear turbulence observed in practical free shear flows, and can be simulated using simple computational domains. One of the numerically efficient configurations to simulate turbulent flows is to use triply periodic domains. However, owing to the mean streamwise velocity being nonhomogeneous, periodic boundary conditions cannot be used along one of the directions. Several studies included shear periodic boundary conditions in the cross-stream direction. However, in these simulations, the turbulence statistics grew exponentially with time, whereas the turbulence observed in free shear flows is statistically stationary. In Dhandapani et al. [Phys. Rev. Fluids 4, 084606 (2019)], the authors fixed this problem by focusing on the velocity fluctuations, performing HST simulations with only shear production and neglecting shear convection. The current study improves upon the previous simulations by including shear convection, by introducing an inflow/outflow in the cross-stream direction. To reduce the impact of the boundary conditions, an elongated domain is used. The simulation results show that the aspect ratio has very little effect on both isotropic and shear turbulence. When convection is included, the turbulence statistics still reach a statistically stationary state. The Reynolds shear stress and the anisotropy values agree very well with the results from experiments and simulations of mixing layers, planar jets, and round jets.

Publication: Physical Review Fluids Vol.: 5 No.: 12 ISSN: 2469-990X

ID: CaltechAUTHORS:20210114-143037936

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Abstract: We present a simple method to remove the stiffness associated with the chemical source terms in the fully compressible Navier-Stokes equations when the classical fourth order Runge-Kutta scheme is used.

Publication: Journal of Computational Physics Vol.: 414ISSN: 0021-9991

ID: CaltechAUTHORS:20200421-130353003

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Abstract: Thermo-acoustic instabilities remain problematic in the design of propulsion systems such as gas turbine engines, rocket motors, and ramjets. They arise from the constructive interaction of heat release rate and acoustic pressure oscillations, and can result in increased noise and mechanical fatigue. In the present work, we are concerned with the flame response to the thermodynamic fluctuations that accompany an incident acoustic wave. The objective is to investigate the flame dynamics under engine-relevant conditions using high-fidelity numerical simulations and detailed chemical kinetics. The focus is placed on the combustion of hydrogen and n-heptane, as they are both of practical interest and behave very differently when subjected to acoustic waves. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. We highlight the differences between results obtained using the fully compressible Navier-Stokes equations and the low Mach number approximation. The two simulation frameworks agree very well for acoustic wavelengths much larger than the flame thickness. However, they differ significantly at high frequencies. The gain erroneously reaches a plateau under the low Mach number approximation, while it decays to zero using the fully compressible framework. This difference is attributed to the spatial variations in the acoustic pressure, which are not captured by the low Mach number approximation.

Publication: Proceedings of the Combustion Institute Vol.: 38 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20200803-071751419

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Abstract: Understanding and quantifying the effects of flame stretch rate on the laminar flame speed and flame structure plays an important role from interpreting experimentally-measured laminar burning velocities to characterizing the impact of turbulence on premixed flames. Unfortunately, accounting for these effects often requires an unsteady reacting flow solver and may be computationally expensive. In this work, we propose a mathematical framework to perform simulations of stationary spherical flames. The objective is to maintain the flame at a constant radius (and hence a constant stretch rate) by performing a coordinate change. The governing equations in the new flame-attached frame of reference resemble the original equations for freely-propagating spherical flames. The only difference is the presence of additional source terms whose purpose is to drive the numerical solution to a steady state. These source terms involve one free parameter: the flame stretch rate, which may either be computed in real time or imposed by the user. This parameter controls ultimately the steady state flame radius and the steady state flame speed. That is why, at a given stretch rate, the results of the stationary spherical flame simulations match those of a freely-expanding spherical flame. As an illustration, the dependence of the laminar flame speed on the stretch rate is leveraged to extract Markstein lengths for hydrogen/air mixtures at different equivalence ratios, as well as for hydrocarbon/air mixtures (CH4 and C7H16). Numerical predictions are in good agreement with experimental measurements (within experimental uncertainties). Finally, the proposed methodology is implemented in the chemical kinetic software FlameMaster. The use of a dedicated steady-state solver with a non-uniform optimized mesh leads to significant reductions in the computational cost, highlighting that the proposed methodology is ideally suited for other chemical kinetic software such as Chemkin/Premix and Cantera.

Publication: Proceedings of the Combustion Institute Vol.: 38 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20200727-071315792

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Abstract: Establishing the mechanism for soot nucleation will require in situ experimental characterization of the identity and intermolecular interactions of the initial precursors, and electronic spectroscopy methods have the potential to do both. However, the optical response of polycyclic aromatic hydrocarbon (PAH) dimers and complexes differs significantly from that of the constituent monomers, and studies of soot precursor complexes have largely been limited to PAHs containing only six-membered aromatic rings. Hydrocarbons containing unsaturated five-membered rings are also present in high concentration in flames, and the photoresponse of complexes containing five-membered rings has not yet been examined. In this work, we elucidate the spectroscopic properties of small hydrocarbon complexes containing cyclopentadienyl groups or cyclopenta-fused groups, calculating ground- and excited-state binding energies, optimal excited-state geometries, repulsion energies, and fluorescence emission wavelengths. We show that excited-state distortion of cyclopentadienyl groups allows strong binding and low-energy fluorescence emission compared to similar-sized PAHs, and that a cyclopenta-fused group dramatically lowers the absorption and emission energies for acenaphthylene, dominating excited-state noncovalent interactions—findings that could shed light on the complex electronic properties of flames.

Publication: Combustion and Flame Vol.: 217ISSN: 0010-2180

ID: CaltechAUTHORS:20200420-152852324

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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: Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used to avoid these costs. However, to our knowledge, the accuracy and appropriateness of the mixture-averaged diffusion models has not been verified for three-dimensional turbulent premixed flames. In this study we propose a fast, efficient, low-memory algorithm and use that to evaluate the role of multicomponent mass diffusion in reacting-flow simulations. Direct numerical simulation of these flames is performed by implementing the Stefan–Maxwell equations in NGA. A semi-implicit algorithm decreases the computational expense of inverting the full multicomponent ordinary diffusion array while maintaining accuracy and fidelity. We first verify the method by performing one-dimensional simulations of premixed hydrogen flames and compare with matching cases in Cantera. We demonstrate the algorithm to be stable, and its performance scales approximately with the number of species squared. Then, as an initial study of multicomponent diffusion, we simulate premixed, three-dimensional turbulent hydrogen flames, neglecting secondary Soret and Dufour effects. Simulation conditions are carefully selected to match previously published results and ensure valid comparison. Our results show that using the mixture-averaged diffusion assumption leads to a 15% under-prediction of the normalized turbulent flame speed for a premixed hydrogen-air flame. This difference in the turbulent flame speed motivates further study into using the mixture-averaged diffusion assumption for DNS of moderate-to-high Karlovitz number flames.

Publication: Journal of Computational Physics Vol.: 406ISSN: 0021-9991

ID: CaltechAUTHORS:20191219-112735076

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Abstract: Numerical studies of passive scalars in three-dimensional (3D) periodic box turbulence have often used arbitrary scalar forcing schemes to sustain the variance. These existing methods represent certain flow configurations, but they have not been derived using specific velocity and scalar profiles. In this work, a forcing technique is devised to generate centerline scalar mixing of round jets in a triply periodic box. It 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. Direct numerical simulations at different Reλ have been performed with these source terms for unity Schmidt numbers. Scalar flux values and scaling exponents of 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. It may indicate that an appropriate relation between the velocity and scalar forcing schemes can help producing a proper scalar mixing environment.

Publication: Physical Review Fluids Vol.: 4 No.: 12 ISSN: 2469-990X

ID: CaltechAUTHORS:20200102-100023911

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Abstract: A numerically efficient configuration to simulate turbulent flows is to use triply periodic domains, with numerical forcing techniques to sustain turbulence. Previous homogeneous shear turbulence simulations considered only idealized homogeneous shear flows and not the statistically stationary shear turbulence observed in practical free shear flows. In contrast, the current study mathematically derives the complete forcing technique from the large scales of the turbulent free shear flows. Different statistically stationary free shear flows are considered in this study, namely, a nearly homogeneous shear turbulent flow, turbulent mixing layer, a turbulent planar jet, and a turbulent round jet. The simulations are performed on triply periodic, statistically homogeneous cubic domains in the vicinity of the shear layer in the self-similar region. An a priori analysis is performed to calculate the effects of the different forcing terms and to predict the expected turbulence quantities. The forcing technique is then used to perform direct numerical simulations at different Reynolds numbers. Numerical results for the different cases are discussed and compared with results from experiments and other simulations of free shear turbulent flows. Anisotropy is observed both in the components of velocity and vorticity, with stronger Reynolds number dependence in the anisotropy of vorticity. Energy spectra obtained from the present homogeneous shear turbulence agree well with the spectra from temporally evolving shear layers. The results also highlight the effects of the additional forcing terms that were neglected in previous studies and the role of shear convection and the associated splitting errors in the unbounded evolution of previous numerical simulations.

Publication: Physical Review Fluids Vol.: 4 No.: 8 ISSN: 2469-990X

ID: CaltechAUTHORS:20190828-092034904

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Abstract: PAH dimerization has been widely posited to play an important, even rate-determining role in soot nucleation, despite scanty experimental evidence of the existence of PAH dimers in flames. Laser-induced fluorescence (LIF) offers a promising in situ method of identifying PAH dimers, if dimer fluorescence can be distinguished from the fluorescence of the constituent monomers and other species present. Predicting transition energies for excited dimers (excimers) and excited complexes (exciplexes) represents a significant challenge for theory. Nonempirically tuned LC-BLYP functionals have been used to compute excited-state geometries and emission energies for a database of 81 inter- and intramolecular PAH excimers and exciplexes. Exciplex emission energies depend sensitively on the topology of the PAHs involved, but a linear relationship between the mean monomer bandgap and the computed exciplex emission means that dimer electronic properties can be predicted based on the properties of the constituent monomers. The range of fluorescence energies calculated for structures containing small to moderately-sized PAHs indicates that either noncovalent or aliphatically-linked complexes could generate the visible-range fluorescence energies observed in LIF experiments.

Publication: Physical Chemistry Chemical Physics Vol.: 21 No.: 20 ISSN: 1463-9076

ID: CaltechAUTHORS:20190510-105529462

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Abstract: Excimers play an important role in photochemical processes ranging from singlet fission to DNA damage, and the characteristic red-shift in fluorescence spectra associated with excimer formation can provide information about aggregate formation and the orientation of chromophores. When a mixture of chromophores is present, exciplex formation may lead to spectral characteristics distinct from those of either monomer or the corresponding excimers. To predict the effects of aggregation in a system containing a mixture of small acenes, binding energies and minimum-energy geometries have been calculated for three mixed S_1 exciplexes. Benchmark CASSCF/NEVPT2 multireference binding energies of 18.2, 27.7, and 49.3 kJ/mol are reported for the benzene-naphthalene, benzene-anthracene, and naphthalene-anthracene exciplexes, respectively. TDDFT calculations have been performed using a range of exchange-correlation functionals, showing that many functionals perform inconsistently, and the error in binding energy often depends on the character of the monomer excitation from which the exciplex state is derived. Moderate exciplex stabilization observed for the benzene-naphthalene and naphthalene-anthracene exciplexes results from a mixture of charge transfer and exciton delocalization.

Publication: Journal of Physical Chemistry A Vol.: 123 No.: 9 ISSN: 1089-5639

ID: CaltechAUTHORS:20190211-080713669

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Abstract: In multichromophore systems, characterization of electronic structure requires characterization of exciplexes, electron‐hole pairs delocalized over multiple molecules. Computing exciplex binding energy requires an accurate description of both the noncovalent interactions between the chromophores and their excited electronic states. The critical role of basis set selection for accurate description of noncovalent interactions is well known, but for some of the most accurate excited‐state methods, basis set dependence is incompletely understood. In this work, the impact of basis set size and diffuseness on CASSCF/NEVPT2 binding energies is determined for three systems in their lowest singlet excited states: the benzene excimer, the cis‐butadiene‐benzene exciplex, and the benzene‐naphthalene exciplex. We demonstrate that excellent CBS binding energies may be obtained using the moderately‐sized jun‐cc‐pV(D + d)Z and jun‐cc‐pV(T + d)Z basis sets and a simple N^(−3) model. Repeating this procedure with the N = 3, 4 basis sets from the most diffuse basis set family applied to each system yields a binding energy of 56.6 ± 1.2 kJ/mol for the benzene excimer and binding energies of 11.1 ± 0.5 kJ/mol and 19.2 ± 1.7 kJ/mol for the cis‐butadiene‐benzene exciplex and the benzene‐naphthalene exciplex, respectively.

Publication: International Journal of Quantum Chemistry Vol.: 119 No.: 5 ISSN: 0020-7608

ID: CaltechAUTHORS:20181105-081552037

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Abstract: Tabulated chemistry reduces the cost of modeling reacting flows by transporting fewer scalars. It also has the benefit of introducing fewer terms that must be closed for Reynolds-averaged Navier-Stokes and large eddy simulation modeling. In this study of premixed lean hydrogen–air flames, an extension to an existing tabulated chemistry model was developed by including differential diffusion and thermal diffusion of multiple species, using a mixture-averaged diffusion model. The transport equations for the tabulation variables (a progress variable and a mixture fraction-like variable) have been formulated, and curvature effects are intrinsic to the transport equations derived from first principles. The mathematical derivation is general, such that other fuel/air mixtures could be examined. The new tabulated chemistry model was then validated using a range of configurations, including flames with curvature, extinction, and hot spots. The model validation indicated excellent agreement with detailed chemistry simulations for lean premixed hydrogen–air mixtures. Conditional means of the progress variable source term were shown to agree well with detailed chemistry simulations of two-dimensional freely propagating flames and three-dimensional turbulent flames. Finally, progress variable source terms three times higher than one-dimensional flat flame results were identified and validated with detailed chemistry, and super-adiabatic hot spots were also predicted in the turbulent flame configuration.

Publication: Proceedings of the Combustion Institute Vol.: 37 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20180827-094621978

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Abstract: Thermo-acoustic instabilities are problematic in the design of continuous-combustion propulsion systems such as gas turbine engines, rocket motors, jet engine afterburners, and ramjets. Conceptually, the coupling between acoustics and flame dynamics can be divided into two categories: flame area fluctuations and changes in the local flame speed. The latter can be caused by the thermodynamic fluctuations that accompany an acoustic wave. This coupling is the focus of the present work. In this paper, we are concerned with the dynamics of laminar premixed flames involving large hydrocarbon species. Through high-fidelity numerical simulations, we investigate the flame response for a wide range of fuels and acoustic frequencies. The combustion of hydrogen and methane is considered for verification purposes and as baseline cases for comparison with two large hydrocarbon fuels, n-heptane and n-dodecane. We extract the phase and gain of the unsteady heat release response, which are directly related to the Rayleigh criterion and thus the stability of the system. For all fuels, we observe a local peak in the heat release gain. At high frequencies, we find that the fluctuations of the different species mass fractions decrease with the inverse of the acoustic frequency, leading to chemistry being “frozen” in the high-frequency limit. This allows us to predict the flame behavior directly from the steady-state solution.

Publication: Proceedings of the Combustion Institute Vol.: 37 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20181010-083802365

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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 forcing technique is devised to reproduce the centerline turbulent characteristics of round jets in a triply periodic box. It 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, which is intended to be used in a three-dimensional box to create turbulence. Four direct numerical simulations with different Re_λ have been performed with these forcing terms. The budget of the terms in the kinetic energy equation is very close to the experimental measurement on the centerline. The anisotropy, kinetic energy k, and dissipation rate ɛ of the simulations are also comparable to experimental values. Finally, the kinetic energy spectrum in the axial direction, ϕ(κ_1), is presented. With appropriate normalizations, the spectrum agrees well with the round jet spectrum on its centerline.

Publication: Physical Review Fluids Vol.: 3 No.: 8 ISSN: 2469-990X

ID: CaltechAUTHORS:20180829-095555389

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Abstract: This work details the development of a new, reduced thermal diffusion model. The proposed model derives from the thermal diffusion model of Chapman and Cowling (1970). In its derivation, a set of mixture-averaged like approximations are made, which results in the number of operations being reduced from O(n^2) to sub-linear, where n is the number of species in the chemical model. With these approximations, the new, reduced model thermal diffusion coefficients can be calculated independently for each species. The model is validated against multicomponent thermal diffusion cases using multiple fuel and diluent mixtures at various pressures, temperatures, and equivalence ratios. The resulting reduced model thermal diffusion fluxes agree well with the multicomponent values, with a multiplicative scaling factor identified using a least squares regression. Unstretched laminar flame speeds are compared using the multicomponent and newly developed models. Finally, an a posteriori comparison in a turbulent configuration shows excellent agreement of both the mean and fluctuations of the thermal diffusion coefficients.

Publication: Combustion and Flame Vol.: 191ISSN: 0010-2180

ID: CaltechAUTHORS:20180109-095122223

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Abstract: Oxygenated biofuels such as fatty acid methyl esters or ethanol are incorporated in larger and larger amounts into conventional hydrocarbon fuels for use in internal combustion and jet engines. The use of these alternative fuels, along with new engine technology, results in an increased production of toxic pollutants among which aldehydes are the most abundant. The present study focuses on the kinetic modeling of acetaldehyde pyrolysis and oxidation. Based on new ignition delay-time measurements obtained in shock tube and the data from the literature, a comprehensive validation database was assembled. Available kinetic parameters for the most important chemical reactions are reviewed and an updated reaction model is proposed. The new reaction model enables reproducing most of the trends observed experimentally and constitutes an overall improvement as compared to standard detailed chemical models including Aramco 2.0, CaltechMech, and JetSurf.

Publication: Fuel Vol.: 217ISSN: 0016-2361

ID: CaltechAUTHORS:20180404-101157691

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Abstract: Gas phase assocn. of polyarom. hydrocarbons (PAHs) is thought to play a key role in processes ranging from soot formation to cosmic dust growth. While small PAHs such as benzene and pyrene form relatively weakly bound van der Waals complexes in the ground state, significantly stronger binding has been obsd. in the first singlet excited state. Time-dependent d. functional theory (TDDFT) has proven an accurate and efficient method of calcg. excited state energies. However, the importance of static correlation in PAH systems means that multireference methods are often required for qual. accurate descriptions of excited states. In this work, benchmark binding energies are computed for the benzene excimer using a range of TDDFT hybrid and double hybrid functionals. Results are compared against multireference complete active space SCF (CASSCF) results with second-order n-electron valence state perturbation theory (NEVPT2) correction. Scaling relationships between dimer carbon atoms and binding energy are established using both TDDFT and NEVPT2 methods, allowing estn. of binding energy for large PAH excimers, for which multireference calcns. are not feasible. Complete potential energy surfaces are constructed for the benzene-naphthalene and the naphthalene-anthracene heterodimeric exciplexes at the double hybrid TDDFT level. The results allow a direct comparison of binding energy scaling and equil. geometry for homodimeric and heterodimeric complexes. They also provide a starting point for the statistical mech. anal. required for a complete understanding of PAH binding thermodn. and kinetics.

ID: CaltechAUTHORS:20170913-074933931

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Abstract: Accurate thermodynamic properties for species found in carbon–phenolic gas mixtures are essential in predicting material response and heating of carbon–phenolic heat shields of planetary entry vehicles. A review of available thermodynamic data for species found in mixtures of carbon–phenolic pyrolysis and ablation gases and atmospheres rich with C, H, O, and N such as those of Earth, Mars, Titan, and Venus, is performed. Over 1200 unique chemical species are identified from four widely used thermodynamic databases and a systematic procedure is described for combining these data into a comprehensive model. The detailed dataset is then compared with the Chemical Equilibrium with Applications thermodynamic database developed by NASA in order to quantify the differences in equilibrium thermodynamic properties obtained with the two databases. In addition, a consistent reduction methodology using the mixture thermodynamic properties as an objective function is developed to generate reduced species sets for a variety of temperature, pressure, and elemental composition spaces. It is found that 32 and 23 species are required to model carbon–phenolic pyrolysis gases mixed with air and CO_2, respectively, to maintain a maximum error in thermodynamic quantities below 10%.

Publication: Aerospace Science and Technology Vol.: 66ISSN: 1270-9638

ID: CaltechAUTHORS:20170628-154137549

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Abstract: The validity of the premixed flamelet equations and the dependence of the fuel burning rate on the parameters involved in these equations have been investigated using a large series of direct numerical simulations of turbulent premixed flames in the thin reaction zones (TRZ) and the distributed reaction zones (DRZ) regimes. Methane, toluene, n-heptane, and iso-octane fuels were considered over a wide range of unburnt conditions and turbulence characteristics. Flames with unity and non-unity Lewis numbers were investigated separately to isolate turbulence-chemistry interaction from differential diffusion effects. In both cases, the flamelet equations, which rely on the assumption of a thin reaction zone, are locally valid throughout the TRZ regime, more precisely up to a Karlovitz number at the reaction zone of 10 (based on the definition used in this paper). Consistent with this result, in the unity Lewis number limit, the fuel burning rate is strongly correlated with the dissipation rate of the progress variable, the only parameter in the flamelet equations. In the non-unity Lewis number case, the burning rate is a strong function of both the dissipation rate and the diffusion rate, both of which are parameters in the flamelet equations. In particular, the correlation with these parameters is significantly better than with curvature or tangential strain rate.

Publication: Combustion and Flame Vol.: 180ISSN: 0010-2180

ID: CaltechAUTHORS:20170313-082804893

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Abstract: The performance of different constraints for the rate-controlled constrained-equilibrium (RCCE) method is investigated in the context of modeling reacting flows characteristic of hypervelocity ground testing facilities and reentry conditions. Although the RCCE approach has been used widely in the past, its application in non-combustion-based reacting flows is rarely done; the flows being investigated in this work do not contain species that can easily be classified as reactants and/or products. The effectiveness of different constraints is investigated before running a full computational simulation, and new constraints not reported in the existing literature are introduced. A constraint based on the enthalpy of formation is shown to work well for the two gas models used for flows that involve both shocks and steady expansions.

Publication: Journal of Propulsion and Power Vol.: 33 No.: 3 ISSN: 0748-4658

ID: CaltechAUTHORS:20190211-103624005

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Abstract: Assumptions behind closure models for the filtered source term are studied a priori using results from DNS of turbulent n-heptane/air premixed flames at varying Karlovitz numbers. Simulations with both detailed chemistry and tabulated chemistry, as well as unity and non-unity Lewis numbers, are used to determine if finite-rate chemistry and differential diffusion effects affect the filtered chemical source terms. While the unfiltered source term shows large fluctuations, the filtered source terms from detailed chemistry and tabulated chemistry are in good agreement at sufficiently large filter widths (Δ ≳ l_F). Using the concept of optimal estimators, it is shown that a tabulation approach using the filtered progress variable and its variance can predict accurately the filtered chemical source terms. Finally, the filtered source terms from the DNS are compared to predictions from two commonly assumed sub-filter probability density function models. Both models show deviations from the filtered DNS source terms but predict accurately the mean turbulent flame speed. The results illustrate the potential of using simple tabulated chemistry approaches based on presumed PDFs for LES of premixed flames in the thin and distributed reaction zones regimes.

Publication: Combustion and Flame Vol.: 176ISSN: 0010-2180

ID: CaltechAUTHORS:20161212-104628077

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Abstract: The mixture-averaged thermal diffusion model originally proposed by Chapman and Cowling is validated using multiple flame configurations. Simulations using detailed hydrogen chemistry are done on one-, two-, and three-dimensional flames. The analysis spans flat and stretched, steady and unsteady, and laminar and turbulent flames. Quantitative and qualitative results using the thermal diffusion model compare very well with the more complex multicomponent diffusion model. Comparisons are made using flame speeds, surface areas, species profiles, and chemical source terms. Once validated, this model is applied to three-dimensional laminar and turbulent flames. For these cases, thermal diffusion causes an increase in the propagation speed of the flames as well as increased product chemical source terms in regions of high positive curvature. The results illustrate the necessity for including thermal diffusion, and the accuracy and computational efficiency of the mixture-averaged thermal diffusion model.

Publication: Combustion Theory and Modelling Vol.: 22 No.: 2 ISSN: 1364-7830

ID: CaltechAUTHORS:20171211-082509220

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Abstract: An experimental and numerical investigation of fuel and hydrodynamic effects is performed on piloted premixed jet flames. The investigation is carried out at a constant laminar flame speed, varying heat losses, jet Reynolds number, fuel molecular weight, and fuel chemical classification. Large Eddy Simulations are performed in an attempt to reproduce the behaviors observed experimentally. Simulations are compared against well-characterized boundary conditions, well-resolved two-dimensional velocity fields from particle image velocimetry, and line-of-sight CH⁎ profiles. Experimental results indicate that small amounts of heat losses may play a significant role on the jet reactivity as the flame heights scale with the heat loss from the jet. However, differences between flames with different fuels can still be seen in the absence of heat losses and these differences are magnified at higher Reynolds numbers. Particularly, methane flames are consistently taller and ethylene flames consistently shorter while other fuels present approximately the same flame height. LES reproduce the experimentally observed trends in global flame heights (effects of heat losses and Reynolds number) but some of the differences between fuels are not captured.

Publication: Proceedings of the Combustion Institute Vol.: 36 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20170407-120853660

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Abstract: The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence.

Publication: Physics of Fluids Vol.: 28 No.: 10 ISSN: 1070-6631

ID: CaltechAUTHORS:20161017-090914240

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Abstract: Direct numerical simulations of turbulent premixed flames at high Karlovitz numbers are performed using detailed chemistry. Different fuels, chemical mechanisms, and equivalence ratios are considered and their effects on turbulent flame speed, geometry of the reaction zone, and fuel burning rate are analyzed. Differential diffusion effects are systematically isolated by performing simulations with both non-unity and unity Lewis numbers. Heavy fuels with above unity Lewis numbers are considered. In the unity Lewis number limit, the n-heptane, iso-octane, toluene, and methane flames at a given reaction zone Karlovitz number present similar normalized turbulent flame speeds and fuel burning rates close to their respective laminar values. When differential diffusion effects are included, the turbulent flame speeds are lower than their unity Lewis number counterparts due to a reduction in the fuel burning rate. The turbulent reaction zone surface areas increase with the turbulence intensity but are not strongly affected by fuel, equivalence ratio, chemical mechanism, or differential diffusion. The geometry of the reaction zone is studied through the probability density functions of strain rate and curvature which are very similar when normalized by Kolmogorov scales at the reaction zone. The dependence of the chemical source terms on the scalar dissipation rate in the unity Lewis number case is shown and the distributions of scalar dissipation rate on the reaction surface are similar to those of passive scalars in homogeneous isotropic turbulence. The reduced burning rates in the presence of differential diffusion are discussed. The present results indicate that mean turbulent flame properties such as burning velocity and fuel consumption can be predicted with the knowledge of only a few global laminar flame properties. Once normalized by the corresponding laminar flame quantities, fuel and chemistry effects in high Karlovitz number premixed turbulent flames are mostly limited to differential diffusion.

Publication: Combustion and Flame Vol.: 167ISSN: 0010-2180

ID: CaltechAUTHORS:20160301-083406326

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Abstract: Experimental measurements on axisymmetric laminar premixed flames have been used extensively for chemical and soot model validation. Numerical simulations of these flames always rely on the assumption of one-dimensionality. However, the presumed one-dimensionality has not been justified in general, and may not be valid under all circumstances. In the current work, two-dimensional flow effects are investigated in four representative ethylene/air laminar premixed flames, which have been selected as validation targets for the International Sooting Flame workshop. These flames cover all typical experimental arrangements, namely stabilizing plate, steel plate with centered hole, and enclosed chamber. To assess the assumption of one-dimensionality, detailed numerical simulations with finite-rate chemistry are performed with the exact experimental set-ups. It is shown that flow entrainment and acceleration are significant for all four flames. Further, it is found that the flame centerlines cannot be approximated as one-dimensional, since the mass flow rates vary substantially along the centerlines. As a consequence, non-negligible differences are found between the soot profiles predicted in two-dimensional simulations and in simulations where one-dimensionality is assumed. Using data extracted from the two-dimensional simulations, a modified one-dimensional model is derived on the flame centerline to include two-dimensional effects. Results from the modified one-dimensional model are compared against detailed, two-dimensional simulation results and experimental measurements.

Publication: Combustion and Flame Vol.: 166ISSN: 0010-2180

ID: CaltechAUTHORS:20160426-081116400

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Abstract: An experimental investigation is conducted to analyze hot-surface ignition of n-hexane-air mixtures. The experimental setup, equipped with temperature diagnostics and schlieren imaging, utilizes a glow plug to initiate ignition in a flammable mixture. The hot-surface temperature at the point of ignition is measured for equivalence ratios ranging from 0.6 to 3 and chamber pressures varying from 25 to 100 kPa. The hot-surface temperature resulting in ignition is found to be weakly sensitive to equivalence ratio with a mean value of 980 K for mixtures with equivalence ratios between 0.75 and 3 at 100 kPa. Chamber pressure has a stronger influence with ignition temperature increasing to about 1140 K at 25 kPa. The experimental trends were reproduced in numerical simulations utilizing detailed chemistry of n-heptane as a surrogate for n-hexane given their similar ignition and flame propagation characteristics. The simulations further predict a two-stage ignition process resulting from an initial breakdown of the fuel with a small increase in temperature followed by a main ignition event accompanied by fuel depletion. Reaction rate analysis of the sequence of events leading to ignition conducted using a reduced order kinetic model suggests that the second-stage ignition event is caused primarily by the decomposition of hydrogen peroxide which occurs at temperatures above 900 K. The two-stage ignition process observed here is significantly different from that observed in previous studies due to the presence of convective and diffusive processes as well as the continuous increase in hot-surface temperature. These arguments are used to explain the insensitivity of ignition temperature to equivalence ratio, its decrease with increasing chamber pressure, and the location of the ignition kernel observed in experiments and simulations.

Publication: Combustion and Flame Vol.: 163ISSN: 0010-2180

ID: CaltechAUTHORS:20151019-143526927

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Abstract: To better understand the two-way coupling between turbulence and chemistry, the changes in turbulence characteristics through a premixed flame are investigated. Specifically, this study focuses on vorticity, ω, which is characteristic of the smallest length and time scales of turbulence, analyzing its behavior within and across high Karlovitz number (Ka) premixed flames. This is accomplished through a series of direct numerical simulations (DNS) of premixed n-heptane/air flames, modeled with a 35-species finite-rate chemical mechanism, whose conditions span a wide range of unburnt Karlovitz numbers and flame density ratios. The behavior of the terms in the enstrophy, ω^2 = ω ⋅ ω, transport equation is analyzed, and a scaling is proposed for each term. The resulting normalized enstrophy transport equation involves only a small set of parameters. Specifically, the theoretical analysis and DNS results support that, at high Karlovitz number, enstrophy transport obtains a balance of the viscous dissipation and production/vortex stretching terms. It is shown that, as a result, vorticity scales in the same manner as in homogeneous, isotropic turbulence within and across the flame, namely, scaling with the inverse of the Kolmogorov time scale, τ_η. As τ_η is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulentflames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration.

Publication: Physics of Fluids Vol.: 28 No.: 1 ISSN: 1070-6631

ID: CaltechAUTHORS:20160119-102220334

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Abstract: Accurate computation of molecular diffusion coefficients in chemically reacting flows can be an expensive procedure, and the use of constant non-unity Lewis numbers has been adopted often as a cheaper alternative. The goal of the current work is to explore the validity and the limitations of the constant non-unity Lewis number approach in the description of molecular mixing in laminar and turbulent flames. To carry out this analysis, three test cases have been 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 have been considered. The three flames are characterised 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 current 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.

Publication: Combustion Theory and Modelling Vol.: 20 No.: 4 ISSN: 1364-7830

ID: CaltechAUTHORS:20160620-103609370

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Abstract: Direct numerical simulations of premixed n-heptane/air flames at different Karlovitz numbers are performed using detailed chemistry. Differential diffusion effects are systematically isolated by performing simulations with both non-unity and unity Lewis numbers. Different unburnt temperatures and turbulence intensities are used and their effects on the flame structure and chemical source terms are investigated. As the unburnt gases are preheated, the viscosity ratio across the flame is reduced and the Karlovitz number at the reaction zone is increased. The increase in turbulence intensity suppresses differential diffusion effects on the flame structure (i.e. species dependence on temperature). However, differential diffusion effects on the chemical source terms are still noticeable even at the highest Karlovitz number simulated. Simulations with differential diffusion effects exhibit lower mean fuel consumption and heat release rates than their unity Lewis number counterparts. However, the difference is reduced as the reaction zone Karlovitz number is increased. Transition to distributed burning is characterized by a broadening of the reaction zone resulting from enhanced turbulent mixing. Local extinctions in the burning rate are observed only in non-unity Lewis number simulations and their probability decreases at high Karlovitz numbers. These results highlight the importance of using the reaction zone Karlovitz number to investigate the effect of turbulence on the chemical source terms and to compare flames at different unburnt temperatures.

Publication: Combustion and Flame Vol.: 162 No.: 9 ISSN: 0010-2180

ID: CaltechAUTHORS:20150622-141527006

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Abstract: A semi-implicit preconditioned iterative method is proposed for the time-integration of the stiff chemistry in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical kinetic mechanisms. Emphasis is placed on the simultaneous treatment of convection, diffusion, and chemistry, without using operator splitting techniques. The preconditioner corresponds to an approximation of the diagonal of the chemical Jacobian. Upon convergence of the sub-iterations, the fully-implicit, second-order time-accurate, Crank–Nicolson formulation is recovered. Performance of the proposed method is tested theoretically and numerically on one-dimensional laminar and three-dimensional high Karlovitz turbulent premixed n-heptane/air flames. The species lifetimes contained in the diagonal preconditioner are found to capture all critical small chemical timescales, such that the largest stable time step size for the simulation of the turbulent flame with the proposed method is limited by the convective CFL, rather than chemistry. The theoretical and numerical stability limits are in good agreement and are independent of the number of sub-iterations. The results indicate that the overall procedure is second-order accurate in time, free of lagging errors, and the cost per iteration is similar to that of an explicit time integration. The theoretical analysis is extended to a wide range of flames (premixed and non-premixed), unburnt conditions, fuels, and chemical mechanisms. In all cases, the proposed method is found (theoretically) to be stable and to provide good convergence rate for the sub-iterations up to a time step size larger than 1 μs. This makes the proposed method ideal for the simulation of turbulent flames.

Publication: Journal of Computational Physics Vol.: 295ISSN: 0021-9991

ID: CaltechAUTHORS:20150504-084647904

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Abstract: The objective of this work is to investigate the impact of spin contamination on the prediction of the enthalpies of formation of Polycyclic Aromatic Hydrocarbon (PAH) radicals and of the bond dissociation energies of their precursor molecule. These PAH radicals play a major role in the mass growth of soot precursors leading ultimately to the first soot particles. In this work, we highlights the errors due to spin contamination by comparing spin-unrestricted open-shell calculations (UHF, UMP2, and Quadratic CI singles and doubles [QCISD(T)]) with spin-restricted open-shell calculations (ROHF, ROMP2, and ROCCSD(T)). The results suggest that one should be very careful using any of the spin-unrestricted methods (even QCISD (T)) unless the 〈S^2〉 values are extremely close to the theoretical value. Following these observations, we propose a new set of best-estimates for the enthalpies of formation of these critical PAH radicals using spin-restricted open-shell ROMP2 and RCCSD(T) calculations.

Publication: International Journal of Quantum Chemistry Vol.: 115 No.: 12 ISSN: 0020-7608

ID: CaltechAUTHORS:20150326-131051398

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Abstract: This work proposes a new simulation methodology to study variable density turbulent buoyant flows. The mathematical framework, referred to as homogeneous buoyant turbulence, relies on a triply periodic domain and incorporates numerical forcing methods commonly used in simulation studies of homogeneous, isotropic flows. In order to separate the effects due to buoyancy from those due to large-scale gradients, the linear scalar forcing technique is used to maintain the scalar variance at a constant value. Two sources of kinetic energy production are considered in the momentum equation, namely shear via an isotropic forcing term and buoyancy via the gravity term. The simulation framework is designed such that the four dimensionless parameters of importance in buoyant mixing, namely the Reynolds, Richardson, Atwood, and Schmidt numbers, can be independently varied and controlled. The framework is used to interrogate fully non-buoyant, fully buoyant, and partially buoyant turbulent flows. The results show that the statistics of the scalar fields (mixture fraction and density) are not influenced by the energy production mechanism (shear vs. buoyancy). On the other hand, the velocity field exhibits anisotropy, namely a larger variance in the direction of gravity which is associated with a statistical dependence of the velocity component on the local fluid density.

Publication: Theoretical and Computational Fluid Dynamics Vol.: 29 No.: 3 ISSN: 0935-4964

ID: CaltechAUTHORS:20150518-131739902

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Abstract: A series of direct numerical simulations of a high Karlovitz number, n-C_7H_(16), turbulent premixed flames performed previously in Savard et al. (2014) are further analyzed in this paper. Two flames are considered: one with unity Lewis numbers to isolate the effect of turbulence on the flame, and one with non-unity Lewis numbers to study the influence of turbulence on differential diffusion. In this paper, the focus is put on the reaction zone and how it is affected by turbulence. First, the reaction zone is shown to be thin for both flames, yet large chemical source term fluctuations are observed. In particular, for the non-unity Lewis number flame, while being thin, the reaction zone is also broken. Second, differential diffusion is shown to have limited effect on the distributions of strain rate and curvature at the reaction zone. Due to the high level of turbulence, the flame behaves more like a material (i.e. passive) surface than a propagating surface. Third, the fuel consumption rate is found to be correlated (yet weakly) with strain rate in the unity Lewis number flame, whereas a stronger correlation with curvature is found in the non-unity Lewis number flame. All these results explain the apparent turbulent flame speeds. It is found that the contribution of the fluctuations in the fuel consumption rate averages away in the unity Lewis number flame. On the other hand, for the non-unity Lewis number flame, the non-linear correlation between fuel consumption rate and curvature has a strong impact on the turbulent flame speed.

Publication: Combustion and Flame Vol.: 162 No.: 5 ISSN: 0010-2180

ID: CaltechAUTHORS:20150204-093519569

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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: In this paper, Large Eddy Simulations (LES) have been performed on an ethylene/air piloted turbulent non-premixed sooting jet flame to quantify the importance of aromatic chemistry-turbulence interactions. Aromatic species are of primary importance since their concentrations control directly the soot nucleation rates. In the current work, the chemistry-turbulence interactions for benzene and naphthalene are taken into account by solving transport equations for their mass fractions. A recently developed relaxation model is used to provide closure for their chemical source terms. The effects of turbulent unsteadiness on soot yield and distribution are highlighted by comparing the LES results with a separate LES using tabulated chemistry for all species including the aromatic species. Results from both simulations are compared to experimental measurements. Overall, 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.

Publication: Proceedings of the Combustion Institute Vol.: 35 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20140804-083631192

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Abstract: In numerical simulations of turbulent combustion, accurate modeling of the fuel chemistry is a critical component of capturing the relevant physics. Various chemical models are currently being used including detailed chemistry, tabulated chemistry, one-step chemistry, and rate-controlled constrained-equilibrium. However, the differences between these models and their impacts on the fluid dynamics are not well understood. Towards that end, the interaction between a laminar premixed hydrogen-air flame and a two-dimensional monopole vortex is investigated through simulations using the four previously-mentioned chemistry models. In these simulations, the flame speed, viscosity, diffusivity, conductivity, heat capacity, density ratio, and initial vortex characteristics are virtually identical providing a comparison of the effects of each chemical model alone. The results with each model are compared by considering the evolution of the flame structure and the characteristics of the vortex. All four models predict very similar results for the interaction with a small, fast vortex. In the interaction with a large, slow vortex, results from one-step chemistry are different due to a different flame thickness. The large, fast vortex case showcases differences in the flame structure and larger discrepancies between the modeling approaches.

Publication: Proceedings of the Combustion Institute Vol.: 35 No.: 1 ISSN: 1540-7489

ID: CaltechAUTHORS:20140721-090952769

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Abstract: Results from a series of direct numerical simulations (DNS) of a high Karlovitz, slightly lean (ϕ=0.9ϕ=0.9), n-C_7H^(16)/air premixed turbulent flame are presented. The flame is statistically flat and is subjected to an inflow of homogeneous isotropic turbulence. A 35-species and 217-reaction mechanism (Bisetti et al., 2012) [17] is used to represent the chemistry. Two simulations have been performed: one with unity Lewis number to asses the effects of turbulence on the flame structure in the absence of differential diffusion, and the other with non-unity Lewis numbers to analyze how turbulence affects differential diffusion. The Karlovitz numbers are 280 and 220 respectively. The first simulation reveals that the flame is strongly affected by turbulence as enhanced mixing largely thickens the preheat zone. However, the turbulent flame structure (i.e. the correlation between species and temperature) is similar to that of a one-dimensional flat flame, suggesting that turbulence has limited effect on the flame in temperature space, in the absence of differential diffusion. In the second simulation, the flame structure is affected by turbulence, as differential diffusion effects are weakened. It is suggested that this result is attributed to the fact that turbulence drives the effective species Lewis numbers towards unity through an increase in effective species and thermal diffusivities. Finally, the reaction zones of both the unity and the non-unity Lewis number turbulent flames remain thin, and are locally broken (only to some extent for the unity Lewis number flame, and more strongly for non-unity).

Publication: Proceedings of the Combustion Institute Vol.: 35 No.: 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20140804-084542270

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Abstract: In order to address increasing greenhouse gas emissions, the future fossil fuel shortage and increasingly stringent pollutant emission regulations, a variety of biofuels are being progressively incorporated into conventional transportation fuels. Despite the beneficial impact of biofuels on most regulated pollutants, their combustion induces the increase of a variety of aldehydes that are being considered for specific regulations due to their high toxicity. One of the most hazardous aldehyde compounds is acrolein, C_2H_3CHO. Despite its high toxicity and increased formation during bioalcohol and biodiesel combustion, no experimental data are available for acrolein combustion. In the present study, we have investigated the ignition of acrolein–oxygen–argon mixtures behind reflected shock wave using three simultaneous emission diagnostics monitoring OH∗, CH∗ and CO_2∗. Experiments were performed over a range of conditions: Φ = 0.5–2; T_5 = 1178–1602 K; and P_5 = 173–416 kPa. A tentative detailed reaction model, which includes sub-mechanisms for the three measured excited species, was developed to describe the high-temperature chemical kinetics of acrolein oxidation. Reasonable agreement was found between the model prediction and experimental data.

Publication: Fuel Vol.: 135ISSN: 0016-2361

ID: CaltechAUTHORS:20140929-091641029

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Abstract: An improved bounded semi-Lagrangian scalar transport scheme based on cubic Hermite polynomial reconstruction is proposed in this paper. Boundedness of the scalar being transported is ensured by applying derivative limiting techniques. Single sub-cell extrema are allowed to exist as they are often physical, and help minimize numerical dissipation. This treatment is distinct from enforcing strict monotonicity as done by D.L. Williamson and P.J. Rasch [5], and allows better preservation of small scale structures in turbulent simulations. The proposed bounding algorithm, although a seemingly subtle difference from strict monotonicity enforcement, is shown to result in significant performance gain in laminar cases, and in three-dimensional turbulent mixing layers. The scheme satisfies several important properties, including boundedness, low numerical diffusion, and high accuracy. Performance gain in the turbulent case is assessed by comparing scalar energy and dissipation spectra produced by several bounded and unbounded schemes. The results indicate that the proposed scheme is capable of furnishing extremely accurate results, with less severe resolution requirements than all the other bounded schemes tested. Additional simulations in homogeneous isotropic turbulence, with scalar timestep size unconstrained by the CFL number, show good agreement with spectral scheme results available in the literature. Detailed analytical examination of gain and phase error characteristics of the original cubic Hermite polynomial is also included, and points to dissipation and dispersion characteristics comparable to, or better than, those of a fifth order upwind Eulerian scheme.

Publication: Journal of Computational Physics Vol.: 272ISSN: 0021-9991

ID: CaltechAUTHORS:20140626-095726693

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Abstract: Many velocity field forcing methods exist to simulate isotropic turbulence, but no in-depth analysis of the effects that these methods have on the generated turbulence has been performed. This work contains such a detailed study. It focuses on Lundgren’s linear and Alvelius’ spectral velocity forcing methods. Based on the constraints imposed on their associated forcing terms, these two are representative of the numerous forcing methods available in the literature. This study is conducted in the context of the Karman–Howarth equation, which, as a consequence of velocity forcing, has a source term appended to it. The expressions for the forcing method-specific Karman–Howarth source terms are derived, and their effect on key turbulent metrics, e.g. structure functions and spectra, is investigated. The behaviour of these source terms determines the state to which all turbulent metrics evolve, allowing for the differences noted between linearly and spectrally forced turbulent fields to be explained.

Publication: Journal of Turbulence Vol.: 15 No.: 7 ISSN: 1468-5248

ID: CaltechAUTHORS:20140612-090234324

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Abstract: The geometric orientation of the subfilter-scale scalar-flux vector is examined in homogeneous isotropic turbulence. Vector orientation is determined using the eigenframe of the resolved strain-rate tensor. The Schmidt number is kept sufficiently large so as to leave the velocity field, and hence the strain-rate tensor, unaltered by filtering in the viscous-convective subrange. Strong preferential alignment is observed for the case of Gaussian and box filters, whereas the sharp-spectral filter leads to close to a random orientation. The orientation angle obtained with the Gaussian and box filters is largely independent of the filter width and the Schmidt number. It is shown that the alignment direction observed numerically using these two filters is predicted very well by the tensor-diffusivity model. Moreover, preferred alignment of the scalar gradient vector in the eigenframe is shown to mitigate any probable issues of negative diffusivity in the tensor-diffusivity model. Consequentially, the model might not suffer from solution instability when used for large eddy simulations of scalar transport in homogeneous isotropic turbulence. Further a priori tests indicate poor alignment of the Smagorinsky and stretched vortex model predictions with the exact subfilter flux. Finally, strong filter dependence of subfilter scalar-flux orientation suggests that explicit filtering may be preferable to implicit filtering in large eddy simulations.

Publication: Physical Review E Vol.: 89 No.: 6 ISSN: 1539-3755

ID: CaltechAUTHORS:20140808-094738832

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Abstract: In this paper, the chemical response of different species to turbulent effects is investigated in the context of one-dimensional laminar non-premixed flamelets. Turbulent effects are modeled as abrupt changes in the scalar dissipation rate. One-dimensional unsteady flamelet calculations assuming unity-Lewis number for all species are performed for an ethylene/air configuration. From the time-evolution of the species mass fractions, it is found that transient effects are not substantial for radicals such as OH and H, and species such as CO; CO_2 and C_2H_2, consistent with their small characteristic chemical time scales. The steady state flamelet assumption for these species is well justified and their mass fractions can be pre-tabulated using the steady state flamelet solutions legibly. On the other hand, aromatic species are characterized by relatively slow chemistry, and substantial transient effects are observed for these species. The evolution of their mass fractions and chemical source terms are studied through a reaction flux analysis. Specifically for Polycyclic Aromatic Hydrocarbons (PAH), the chemical production terms are found to be linearly proportional to the mass fraction of smaller aromatic species, and the chemical consumption terms are found to be linearly proportional to their own mass fractions. Based on the unsteady flamelet results, the validity of various existing flamelet-based pre-tabulation methods is examined, and a new linear relaxation model is proposed for PAH. The proposed relaxation model is validated through the unsteady flamelet formulation, and results are compared against full chemistry calculations.

Publication: Combustion and Flame Vol.: 161 No.: 6 ISSN: 0010-2180

ID: CaltechAUTHORS:20140106-094049321

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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: An a priori model for the effective species Lewis numbers in premixed turbulent flames 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 (Aspden et al., 2011). The conditional mean profiles of various species mass fraction versus temperature are evaluated from the DNS and compared to 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 the Lewis numbers of the different species. A transition from “laminar” Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured. A model for those effective Lewis numbers with respect to the turbulent Reynolds number is developed. This model is derived from a Reynolds-averaged Navier–Stokes (RANS) formulation of the reactive scalar and temperature balance equations. The dependency of the effective Lewis numbers on the Karlovitz number instead of the Reynolds number is discussed in this paper. Unfortunately, given that the ratio of the integral length to the laminar flame thickness is fixed throughout this series of DNS, a change in the Karlovitz number is equivalent to a change in the Reynolds number. Incorporating these effective Lewis numbers in simulations of turbulent flames would have several impacts. First, the associated laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the turbulent premixed combustion regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used, and a dependency on the effective Lewis numbers has to be introduced. Finally, a turbulent flame speed model that takes into account these effective Lewis numbers is proposed.

Publication: Combustion and Flame Vol.: 161 No.: 6 ISSN: 0010-2180

ID: CaltechAUTHORS:20140127-092022793

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Abstract: When a level-set signed distance function is reinitialized in the vicinity of a contact line, there is a “blind spot” that prevents an accurate reconstruction of a signed distance function. The numerical method can create parasitic velocity currents near this region. If additional contact-line physics are included, the parasitic velocity currents would pollute the solution and alter the physical behavior. In this study, a modified reinitialization routine is proposed that combines the standard Hamilton–Jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot. Two test cases, an angled fluid wedge (zero curvature) and a circular fluid arc (constant curvature), are used to evaluate the numerical error induced by different methods. The proposed method has less numerically-induced interface distortion than other techniques examined. Furthermore, this routine can be easily extended to three dimensions. Drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method. A spreading fluid interface further shows that this method allows contact lines to merge naturally.

Publication: Journal of Computational Physics Vol.: 265ISSN: 0021-9991

ID: CaltechAUTHORS:20140403-135030798

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Abstract: The goal of this paper is to investigate the effects of curvature of mixture fraction iso-surfaces on the transport of species in diffusion flames. A general flamelet formulation is derived mathematically considering both curvature effects and differential diffusion effects. These theoretical results suggest that curvature does not play a role in the transport process irrespective of the flame curvature if species transport is described with a unity Lewis number. On the other hand, a curvature-induced term becomes explicit when differential diffusion effects are considered, and it acts as a convective term in mixture fraction space. It is found that this term needs to be taken into account when the radius of curvature is comparable or smaller than the local flame thickness. For the proper integration of the flamelet equations, the scalar dissipation rate and curvature dependences on mixture fraction are modeled by considering two basic curved one-dimensional flame configurations. The flamelet equations accounting for curvature effects are solved with various prescribed curvature values. Results indicate that the mass fraction profiles of species with very small or large Lewis numbers are shifted significantly in mixture fraction space by the inclusion of curvature. Differential diffusion effects are enhanced by negative curvature values and suppressed by positive curvature values. In cases where flame curvature is not uniform, the curvature-induced convective term generates gradients along mixture fraction iso-surfaces, which enhance tangential diffusion effects. Budget analysis is performed on an axisymmetric laminar coflow diffusion flame to highlight the importance of the curvature-induced convective term compared to other terms in the full flamelet equation. A comparison is made between full chemistry simulation results and those obtained using planar and curved flamelet-based chemistry tabulation methods.

Publication: Combustion and Flame Vol.: 161 No.: 5 ISSN: 0010-2180

ID: CaltechAUTHORS:20131204-102754620

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Abstract: Dense high speed non-compacted multiphase flows exist in variable phase turbines, explosions, and ejector nozzles, where the particle volume fraction is in the range 0.001<α_d<0.5. A canonical problem that can be used to study modeling issues related to these types of flows is a shock wave impacting a planar particle cloud. Thus far, prior work has modeled the flow using a 1-D volume-averaged point particle approach and developed momentum and energy coupling terms that reproduce accurately the trajectory of particles in the experiments. Although these early results are promising, it is appropriate to question whether all aspects of the experimental flow can be captured using a one-dimensional model that is traditionally only used for dilute flows. Thus the objective of this work is to set-up a two-dimensional configuration that captures qualitatively the multidimensional behavior of a real three-dimensional particle cloud, but can be used as an exact solution to compare with an equivalent volume-averaged model. The 2-D data is phase-averaged to reduce it to one dimension, and x–t diagrams are used to characterize the flow behavior. These results show the importance of the Reynolds stress term inside the particle cloud and in its turbulent wake. A one-dimensional (1-D) model is developed for direct comparison with the 2-D simulation. While the 1-D model characterizes the overall steady-state flow behavior well, it fails to capture aspects of the unsteady behavior inside and behind the particle cloud because it neglects important unclosed terms.

Publication: International Journal of Multiphase Flow Vol.: 61ISSN: 0301-9322

ID: CaltechAUTHORS:20140515-110845791

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Abstract: It is proposed that 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. This proposed configuration is termed the vertical expansion tunnel. 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 mass and thickness. An inviscid perfect-gas analysis and quasi-one-dimensional Euler computations are performed to find the available effective reservoir conditions (pressure and mass specific enthalpy) and useful test time in a vertical expansion tunnel for comparison to a conventional expansion tunnel and a reflected-shock tunnel. The maximum effective reservoir conditions of the vertical expansion tunnel are higher than the reflected-shock tunnel but lower than the expansion tunnel. The useful test time in the vertical expansion tunnel is slightly longer than the expansion tunnel but shorter than the reflected-shock tunnel. If some sacrifice of the effective reservoir conditions can be made, the vertical expansion tunnel could be used in hypervelocity ground testing without the problems associated with secondary diaphragm rupture.

Publication: AIAA Journal Vol.: 51 No.: 12 ISSN: 0001-1452

ID: CaltechAUTHORS:20140313-102812184

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Abstract: In experiments of hot surface ignition and subsequent flame propagation, a puffing flame instability is observed in mixtures that are stagnant and premixed prior to ignition. By varying the size of the hot surface, power input, and combustion vessel volume, it was determined that the instability is a function of the interaction of the flame, with the fluid flow induced by the combustion products rather than the initial plume established by the hot surface. Pressure ranges from 25 to 100 kPa and mixtures of n-hexane/air with equivalence ratios between ϕ = 0:58 and 3.0 at room temperature were investigated. Equivalence ratios between ϕ = 2:15 and 2.5 exhibited multiple flame and equivalence ratios above ϕ = 2:5 resulted in puffing flames at atmospheric pressure. The phenomenon is accurately reproduced in numerical simulations and a detailed flow field analysis revealed competition between the inflow velocity at the base of the flame and the flame propagation speed. The increasing inflow velocity, which exceeds the flame propagation speed, is ultimately responsible for creating a puff. The puff is then accelerated upward, allowing for the creation of the subsequent instabilities. The frequency of the puff is proportional to the gravitational acceleration and inversely proportional to the flame speed. A scaling relationship describes the dependence of the frequency on gravitational acceleration, hot surface diameter, and flame speed. This relation shows good agreement for rich n-hexane/air and lean hydrogen/air flames, as well as lean hexane/hydrogen/air mixtures.

Publication: Journal of Fluid Mechanics Vol.: 735ISSN: 0022-1120

ID: CaltechAUTHORS:20131204-164020799

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Abstract: A fluid dynamics video was created using data from a Direct Numerical Simulation of a premixed n-heptane flame at high Karlovitz number. The magnitude of vorticity and progress variable(a monotonically increasing variable through the flame) illustrate the turbulence-flame interaction.

Publication: arXiv
ID: CaltechAUTHORS:20191220-104545445

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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: As an alternative to spectral space velocity field forcing techniques commonly used in simulation studies of isotropic turbulence,Lundgren [Linearly forced isotropic turbulence,” in Annual Research Briefs (Center for Turbulence Research, Stanford, 2003), pp. 461–473] proposed and Rosales and Meneveau [“Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,” Phys. Fluids17, 095106 (2005)] validated a physical space forcing method termed “linear forcing.” Linear forcing has the advantages of being less memory intensive, less computationally expensive, and more easily extended to variable density simulations. However, this forcing method generates turbulent statistics that are highly oscillatory, requiring extended simulation run times to attain time-invariant properties. A slight modification of the forcing term is proposed, and it is shown to reduce this oscillatory nature without altering the turbulent physics.

Publication: Physics of Fluids Vol.: 25 No.: 10 ISSN: 1070-6631

ID: CaltechAUTHORS:20131202-090525084

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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: To realize the full potential of Direct Numerical Simulation in turbulent mixing studies, it is necessary to develop numerical schemes capable of sustaining the flow physics of turbulent scalar quantities. In this work, a new scalar field forcing technique, termed “linear scalar forcing,” is presented and evaluated for passive scalars. It is compared to both the well-known mean scalar gradient forcing technique and a low waveshell spectral forcing technique. The proposed forcing is designed to capture the physics of one-time scalar variance injection and the subsequent self-similar turbulent scalar field decay, whereas the mean scalar gradient forcing and low waveshell forcing techniques are representative of continuous scalar variance injection. The linear scalar forcing technique is examined over a range of Schmidt numbers, and the behavior of the proposed scalar forcing is analyzed using single and two-point statistics. The proposed scalar forcing technique is found to be perfectly isotropic, preserving accepted scalar field statistics (fluxes) and distributions (scalar quantity, dissipation rate). Additionally, it is found that the spectra resulting from the three scalar forcing techniques are comparable for unity Schmidt number conditions, but differences manifest at high Schmidt numbers. These disparities are reminiscent of those reported between scaling arguments suggested by theoretical predictions and experimental results for the viscous-convective subrange.

Publication: Physics of Fluids Vol.: 25 No.: 9 ISSN: 1070-6631

ID: CaltechAUTHORS:20131005-183833026

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Abstract: The intent of this paper is to predict the experimental sooting tendencies [Combust. Flame 148 (2007) 210–222] from a detailed chemical mechanism with relatively low computational cost, using a flamelet-based model. Towards that goal, direct numerical simulations using finite-rate chemistry are conducted on a methane–air confined axisymmetric co-flow diffusion flame to provide reference data. Soot transport model is excluded in these direct simulations for both simplicity and to be unbiased from the choice of soot model used. Sooting tendencies are estimated exclusively from the increment of polycyclic aromatic hydrocarbon (PAH) dimer production rate along the centerline when the flame is doped. Calculations using the conventional steady state diffusion flamelet model are performed and this model is shown to be inadequate in reproducing the correct species profiles on the centerline of the flame, where the sooting tendencies are defined. The main reason for the failure of the conventional flamelet model is due to the neglect of multidimensional convection and diffusion effects. In an effort to overcome these deficiencies, a new numerical framework based on modified flamelet equations is proposed. The flamelet equations are rederived for species mass fractions along the centerline of the co-flow diffusion flame considered. These equations take into account the effects of multidimensional diffusion and convection of species in mixture fraction space due to non-unity Lewis numbers. The modified flamelet equations take as input the temperature, convective velocity, and scalar dissipation rate profiles calculated from the direct simulation of the diffusion flame. The numerical sooting tendencies for both non-aromatic and aromatic test species are then calculated using the PAH dimer production rate generated from the flamelet solutions doped by the test species. These first numerically-computed sooting tendencies are derived from a detailed chemical kinetic mechanism and are in good agreement when compared to experimental values.

Publication: Combustion and Flame Vol.: 160 No.: 9 ISSN: 0010-2180

ID: CaltechAUTHORS:20130808-155417469

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Abstract: Mitigating the risk of explosion by hot-surface ignition of a flammable mixture has motivated experimental and numerical studies to characterize this phenomenon. The current numerical approach involves the solution of the low Mach-number Navier–Stokes equations coupled with detailed chemistry of n-heptane using a flamelet approach. Previous work with flamelets characterized by total enthalpy has allowed the inclusion of heat transfer effects (conduction and radiation) on ignition, flame propagation, and flame extinction. Unfortunately, total enthalpy and the progress variable (extent of reaction), typically used for the chemistry tabulation, are not independent. The current work details the development of a novel technique based on modeling enthalpy variations through the use of unburned gas temperature. A transport equation for the unburned gas temperature which forms a key component of this technique is derived from an energy balance for a reacting flow problem. After verifying the technique for 1-D freely propagating adiabatic flames, the improved model is used to study 2-D flame propagation in the presence of a thermal plume initiated by a hot-surface. A comparison of the simulation results with experimental data shows that the enthalpy based approach successfully captures finite-rate chemical kinetics in a thermally stratified mixture.

Publication: Combustion and Flame Vol.: 160 No.: 7 ISSN: 0010-2180

ID: CaltechAUTHORS:20130717-073851023

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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: In the present work, we investigate the possibility of performing velocity-resolved, scalar-filtered (VR-SF) numerical simulations of turbulent mixing of high Schmidt number scalars, by using a Large Eddy Simulation (LES)-type filter in the viscous-convective subrange. The only requirement for this technique is the large scale separation between the Kolmogorov and Batchelor length scales, which is a direct outcome of the high Schmidt number of the scalar. The present a priori analysis using high fidelity direct numerical simulation data leads to two main observations. First, the missing triadic interactions between (resolved) velocity and (filtered-out) scalar modes in the viscous-convective subrange do not affect directly the large scales. Second, the magnitude of the subgrid term is shown to be extremely small, which makes it particularly susceptible to numerical errors associated with the scalar transport scheme. A posteriori tests indicate that upwinded schemes, generally used for LES in complicated geometries, are sufficiently dissipative to overwhelm any contribution from the subgrid term. This renders the subgrid term superfluous, and as a result, VR-SF simulations run without subgrid scalar flux models are able to preserve large scale transport characteristics with remarkable accuracy.

Publication: Physics of Fluids Vol.: 25 No.: 5 ISSN: 1070-6631

ID: CaltechAUTHORS:20130718-101327879

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Abstract: Premixed flames are prone to develop thermo-diffusive instabilities when the diffusivity of the fuel is different from the rest of the mixture. Even when a uniform premixed composition is used, the local equivalence ratio across a flame front will not be constant. Therefore, a single quantity such as the progress variable is incapable of modeling accurately the combustion of non-unity Lewis number flames. In this work, a two-equation model is presented for the simulation of premixed laminar flames with non-unity Lewis number fuels. This model relies on the progress variable approach, which is suited for modeling premixed flames in which the fuel’s Lewis number is near unity. An additional transport equation for a mixture fraction is derived for non-unity Lewis numbers. The model is verified to be consistent with simple laminar unstretched premixed flames. Hydrogen- and propane–air mixtures are used to demonstrate the model’s ability to capture the respectively unstable and stable properties of each lean mixture. One dimensional spherical simulations reproduce the effects of flame stretch due to flow strain rate and flame curvature. Finally in two dimensions, the model captures the creation of cellular structures for negative Markstein length flames and the stable propagation of positive Markstein length flames.

Publication: Combustion and Flame Vol.: 160 No.: 2 ISSN: 0010-2180

ID: CaltechAUTHORS:20130222-111225830

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Abstract: Dense compressible multiphase flows exist in variable phase turbines, explosions, and fluidized beds, where the particle volume fraction is in the range 0.001 < α_d < 0.5. A simple model problem that can be used to study modeling issues related to these types of flows is a shock wave impacting a particle cloud. In order to characterize the initial shock-particle interactions when there is little particle movement, a two-dimensional (2-D) model problem is created where the particles are frozen in place. Qualitative comparison with experimental data indicates that the 2-D model captures the essential flow physics. Volume-averaging of the 2-D data is used to reduce the data to one dimension, and x-t diagrams are used to characterize the flow behavior. An equivalent one-dimensional (1-D) model problem is developed for direct comparison with the 2-D model. While the 1-D model characterizes the overall steady-state flow behavior well, it fails to capture aspects of the unsteady behavior. As might be expected, it is found that neglecting the unclosed fluctuation terms inherent in the volume-averaged equations is not appropriate for dense gas-particle flows.

ID: CaltechAUTHORS:20190712-112323497

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Abstract: An experimental and numerical study was performed to investigate and compare the behavior of a counter-rotating vortex pair and a single vortex in the vicinity of a wall. This analysis is motivated by the theoretical equivalence, in the inviscid limit, between these two configurations. A wind tunnel with two NACA0012 profiles mounted vertically with an optional splitter plate in the center and a stereoscopic particle image velocimetry system was used to experimentally study these interactions. Many significant differences were found between the two configurations, including the growth of the Crow instability in the two vortex configuration, but not in the one vortex/wall configuration. The numerical results re-enforced the experimental results, and emphasized 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.

Publication: Physics of Fluids Vol.: 24 No.: 7 ISSN: 1070-6631

ID: CaltechAUTHORS:20121011-083534771

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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: A Direct Numerical Simulation (DNS) of soot formation in an n-heptane/air turbulent nonpremixed flame has been performed to investigate unsteady strain effects on soot growth and transport. For the first time in a DNS of turbulent combustion, Polycyclic Aromatic Hydrocarbons (PAH) are included via a validated, reduced chemical mechanism. A novel statistical representation of soot aggregates based on the Hybrid Method of Moments is used [M.E. Mueller, G. Blanquart, H. Pitsch, Combust. Flame 156 (2009) 1143–1155], which allows for an accurate state-of-the-art description of soot number density, volume fraction, and morphology of the aggregates. In agreement with previous experimental studies in laminar flames, Damköhler number effects are found to be significant for PAH. Soot nucleation and growth from PAH are locally inhibited by high scalar dissipation rate, thus providing a possible explanation for the experimentally observed reduction of soot yields at increasing levels of mixing in turbulent sooting flames. Furthermore, our data indicate that soot growth models that rely on smaller hydrocarbon species such as acetylene as a proxy for large PAH molecules ignore or misrepresent the effects of turbulent mixing and hydrodynamic strain on soot formation due to differences in the species Damköhler number. Upon formation on the rich side of the flame, soot is displaced relative to curved mixture fraction iso-surfaces due to differential diffusion effects between soot and the gas-phase. Soot traveling towards the flame is oxidized, and aggregates displaced away from the flame grow primarily by condensation of PAH on the particle surface. In contrast to previous DNS studies based on simplified soot and chemistry models, surface reactions are found to contribute barely to the growth of soot, for nucleation and condensation processes occurring in the fuel stream are responsible for the most of soot mass generation. Furthermore, the morphology of the soot aggregates is found to depend on the location of soot in mixture fraction space. Aggregates having the largest primary particles populate the region closest to the location of peak soot growth. On the contrary, the aggregates with the largest number of primary particles are located much further into the fuel stream.

Publication: Combustion and Flame Vol.: 159 No.: 1 ISSN: 0010-2180

ID: CaltechAUTHORS:20120203-145922298

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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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Abstract: While the formation and growth of soot particles has received much attention, the subsequent destruction of the particles is less well understood. Soot particles are destroyed though two parallel processes: oxidation and fragmentation. Oxidation is the removal of mass from particles due to chemical reactions with molecular oxygen and hydroxyl radicals. Fragmentation is the break-up of large aggregates into smaller aggregates. Here, a new model for fragmentation inspired by previous experimental investigations is proposed and formulated within the Hybrid Method of Moments (HMOM). With the formulation, the rate of particle loss due to oxidation is closed, resolving a long-standing problem with the Method of Moments. Less important, secondary unclosed terms are introduced, and models for these terms are proposed. The oxidation and fragmentation models are validated using a set of laminar premixed methane flames and then applied to a series of laminar counterflow diffusion acetylene flames. The role of fragmentation is distinctly different in the two flame types. In the premixed flames, fragmentation only occurs in lean flames with a high oxygen concentration. In the diffusion flames, fragmentation is virtually absent, for soot passes through an OH radical layer and is completely oxidized before reaching high oxygen concentrations.

Publication: Proceedings of the Combustion Institute Vol.: 33 No.: 1 ISSN: 1540-7489

ID: CaltechAUTHORS:20110325-113611544

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Abstract: The intent of the current work is to present and further validate a new tri-variate model for the formation of soot particles, to apply this model in analyzing the effects of temperature on the formation and growth of soot, and to compare the findings with the present understanding derived from numerous experimental studies. In this novel model, a particle is represented as a fractal shaped aggregate and is described by three independent quantities: the volume, the surface area, and the number of hydrogenated sites (or active sites) on the surface. The introduction of this third variable allows for a better description of the surface reactivity at high temperatures. This approach is extended by a model for the total carbon-to-hydrogen (C/H) ratio of the particle. The model is validated first in high temperature premixed ethylene flames, premixed benzene flames, an acetylene counterflow diffusion flame, and toluene pyrolysis in shock-tubes. Then, the soot volume fraction is computed for a series of atmospheric laminar ethylene premixed flames with varying flame temperatures. The soot model is shown to reproduce the well known bell-shaped temperature dependence of soot volume fraction, which was found in many experiments. It is observed that nucleation is the largest contributor to soot volume fraction at low temperatures while growth by surface reactions is more important at higher temperatures. The surface reactivity and the volumetric carbon-to-hydrogen ratio (C/H) are also computed as a function of temperature. The surface reactivity is found to depend not only on the temperature but also on the particle size and the residence time in the flame. Finally, as observed experimentally, the C/H ratio is found to be essentially constant and close to unity for low temperature flames and increases with residence time in high temperature flames.

Publication: Combustion and Flame Vol.: 156 No.: 8 ISSN: 0010-2180

ID: CaltechAUTHORS:20091008-132108501

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Abstract: In this work, a new statistical model for soot formation and growth is developed and presented. The Hybrid Method of Moments (HMOM) seeks to combine the advantages of two moment methods, the Method of Moments with Interpolative Closure (MOMIC) and the Direct Quadrature Method of Moments (DQMOM), in an accurate and consistent formulation. MOMIC is numerically simple and easy to implement but is unable to account for bimodal soot Number Density Functions (NDF). DQMOM is accurate but is numerically ill-posed and difficult to implement. HMOM combines the best of both two methods to capture bimodal NDF while retaining ease of implementation and numerical robustness. The new hybrid method is shown to predict mean quantities nearly as accurately as DQMOM and high-fidelity Monte Carlo simulations. In addition, a model for combining particle coalescence with particle aggregation is presented and shown to accurately reproduce experimental measurements in a variety of sooting flames.

Publication: Combustion and Flame Vol.: 156 No.: 6 ISSN: 0010-2180

ID: CaltechAUTHORS:20091008-132108735

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Abstract: This article presents a chemical mechanism for the high temperature combustion of a wide range of hydrocarbon fuels ranging from methane to iso-octane. The emphasis is placed on developing an accurate model for the formation of soot precursors for realistic fuel surrogates for premixed and diffusion flames. Species like acetylene (C_2H_2), propyne (C_3H_4), propene (C_3H_6), and butadiene (C_4H_6) play a major role in the formation of soot as their decomposition leads to the production of radicals involved in the formation of Polycyclic Aromatic Hydrocarbons (PAH) and the further growth of soot particles. A chemical kinetic mechanism is developed to represent the combustion of these molecules and is validated against a series of experimental data sets including laminar burning velocities and ignition delay times. To correctly predict the formation of soot precursors from the combustion of engine relevant fuels, additional species should be considered. One normal alkane (n-heptane), one ramified alkane (iso-octane), and two aromatics (benzene and toluene) were chosen as chemical species representative of the components typically found in these fuels. A sub-mechanism for the combustion of these four species has been added, and the full mechanism has been further validated. Finally, the mechanism is supplemented with a sub-mechanism for the formation of larger PAH molecules up to cyclo[cd]pyrene. Laminar premixed and counterflow diffusion flames are simulated to assess the ability of the mechanism to predict the formation of soot precursors in flames. The final mechanism contains 149 species and 1651 reactions (forward and backward reactions counted separately). The mechanism is available with thermodynamic and transport properties as supplemental material.

Publication: Combustion and Flame Vol.: 156 No.: 3 ISSN: 0010-2180

ID: CaltechAUTHORS:20091008-132109092

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Abstract: In this work, a bivariate model of soot aggregation is formulated within the framework of the Method of Moments with Interpolative Closure (MOMIC). In the bivariate model, soot particles are represented by two independent variables: their volume and surface area. This joint formulation also allows for the blending of aggregation and coalescence with the two as limits. The new formulation is compared to the old formulation with the univariate model as well as both the Direct Quadrature Method of Moments (DQMOM) and Direct Simulation Monte Carlo (DSMC) for a laminar premixed ethylene flame. With the bivariate model, MOMIC is shown to predict volume fraction and number density very accurately and gives some insight into the properties of the aggregates.

Publication: Proceedings of the Combustion Institute Vol.: 32 No.: 1 ISSN: 1540-7489

ID: CaltechAUTHORS:20091008-132108905

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Abstract: The high order conservative finite difference scheme of Morinishi et al. [Y. Morinishi, O.V. Vasilyev, T. Ogi, Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations, J. Comput. Phys. 197 (2004) 686] is extended to simulate variable density flows in complex geometries with cylindrical or cartesian non-uniform meshes. The formulation discretely conserves mass, momentum, and kinetic energy in a periodic domain. In the presence of walls, boundary conditions that ensure primary conservation have been derived, while secondary conservation is shown to remain satisfactory. In the case of cylindrical coordinates, it is desirable to increase the order of accuracy of the convective term in the radial direction, where most gradients are often found. A straightforward centerline treatment is employed, leading to good accuracy as well as satisfactory robustness. A similar strategy is introduced to increase the order of accuracy of the viscous terms. The overall numerical scheme obtained is highly suitable for the simulation of reactive turbulent flows in realistic geometries, for it combines arbitrarily high order of accuracy, discrete conservation of mass, momentum, and energy with consistent boundary conditions. This numerical methodology is used to simulate a series of canonical turbulent flows ranging from isotropic turbulence to a variable density round jet. Both direct numerical simulation (DNS) and large eddy simulation (LES) results are presented. It is observed that higher order spatial accuracy can improve significantly the quality of the results. The error to cost ratio is analyzed in details for a few cases. The results suggest that high order schemes can be more computationally efficient than low order schemes.

Publication: Journal of Computational Physics Vol.: 227 No.: 15 ISSN: 0021-9991

ID: CaltechAUTHORS:20091008-132109270

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Abstract: The combustion of petroleum based fuels like kerosene, gasoline, or diesel leads to the formation of several kind of pollutants. Among them, soot particles are particularly bad for their severe consequences on human health. Over the past decades, strict regulations have been placed on car and aircraft engines in order to limit these particulate matter emissions. Designing low emission engines requires the use of predictive soot models which can be applied to the combustion of real fuels. Towards this goal, the present work addresses the formation of soot particles both from a chemical and statistical point of view. As a first step, a chemical model is developed to describe the formation of soot precursors from the combustion of several components typically found in surrogates, including n-heptane, iso-octane, benzene, and toluene. The same mechanism is also used to predict the formation of large Polycyclic Aromatic Hydrocarbons (PAH) up to cyclopenta[cd]pyrene (C_(18)H_(10)). Then, a new soot model which represents soot particles as fractal aggregates is used. In this model, a soot particle is described by three variables: its volume (V), its surface area (S), and the number of hydrogen sites on the surface (H). The Direct Quadrature Method of Moments (DQMOM) is used as a precise representation of the population of soot particles which includes small spherical particles and large aggregates. This model is shown to predict accurately the formation of soot in a wide range of flames including premixed and counter flow diffusion flames, low and high temperature flames and for a wide range of fuels from ethylene to iso-octane. Finally, this model predicts several aggregate properties like the primary particle diameter and gives insight into the reactivity of the soot surface.

ID: CaltechAUTHORS:20091009-110823693

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Abstract: In this article, we present a new database of thermodynamic properties for polycyclic aromatic hydrocarbons (PAH). These large aromatic species are formed in very rich premixed flames and in diffusion flames as part of the gas-phase chemistry. PAH are commonly assumed to be the intermediates leading to soot formation. Therefore, accurate prediction of their thermodynamic properties is required for modeling soot formation. The present database consists of 46 species ranging from benzene (C_6H_6) to coronene (C_(24)H_(12)) and includes all the species usually present in chemical mechanisms for soot formation. Geometric molecular structures are optimized at the B3LYP/6-31++G(d,p) level of theory. Heat capacity, entropy, and energy content are calculated from these optimized structures. Corrections for hindered rotor are applied on the basis of torsional potentials obtained from second-order Møller-Plesset perturbation (MP2) and Dunning's consistent basis sets (cc-pVDZ). Enthalpies of formation are calculated using the mixed G3MP2//B3 method. Finally, a group correction is applied to account for systematic errors in the G3MP2//B3 computations. The thermodynamic properties for all species are available in NASA polynomial form at the following address: http://www.stanford.edu/group/pitsch/.

Publication: Journal of Physical Chemistry A Vol.: 111 No.: 28 ISSN: 1089-5639

ID: CaltechAUTHORS:20091008-132109444

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Abstract: Preserving scalar boundedness is an important prerequisite to performing large-eddy simulations of turbulent reacting flows. A number of popular combustion models use a conserved-scalar, mixture-fraction to parameterize reactions that, by definition, is bound between zero and one. To avoid unphysical clipping, the numerical scheme solving the conserved-scalar transport equation must preserve these bounds, while minimizing the amount of numerical diffusivity. To this end, a flux correction method is presented and applied to the quadratic-upwind biased interpolative convective scheme that ensures preservation of the scalar’s physical bounds while retaining the low numerical diffusivity of the original quadratic-upwind biased interpolative convective scheme. It is demonstrated that this bounded quadratic-upwind biased interpolative convective scheme outperforms the third-order weighted essentially nonoscillatory scheme in maintaining spatial accuracy and reducing numerical dissipation errors both in generic test cases as well as direct numerical simulation of canonical flows.

Publication: AIAA Journal Vol.: 44 No.: 12 ISSN: 0001-1452

ID: CaltechAUTHORS:20091008-132109738

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Abstract: In this paper, a stochastic flamelet approach is used to model autoignition in an initially non-premixed medium in isotropic and decaying turbulence, using a one-step irreversible reaction. This configuration corresponds to the DNS data from Sreedhara and Lakshmisha [Proc. Combust. Inst. 29 (2002) 2069]. The system can be described by the flamelet equations for the temperature and fuel mass fraction, where the scalar dissipation rate appears as a stochastic parameter. In a turbulent flow, fluctuations of this scalar have a strong impact on autoignition. Assuming a log normal distribution, a stochastic differential equation (SDE) can be derived for the scalar dissipation rate. The decay rate of the mean dissipation rate is taken from the DNS. The DNS data suggest that the normalized variance is close to unity but depends upon the Reynolds number. The flamelet equations for the temperature and fuel mass fraction, and the stochastic differential equation are coupled and solved numerically. The effects of the turbulence are discussed, and the results are compared with the DNS database. The model reproduces the conditional mean temperature profiles and the ignition delay times with good accuracy.

Publication: Proceedings of the Combustion Institute Vol.: 30 No.: Part 2 ISSN: 1540-7489

ID: CaltechAUTHORS:20091008-132109941

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