Pitsch Group Publications

Blanquart, G., Pitsch, H., A Joint Volume-Surface-Hydrogen Multi-Variate Model for Soot Formation, in Combustion Generated Fine Carbonaceous Particles, Bockhorn, H., DAnna, A., Sarofim, A. F., Wang, H. (Ed.), pp. 439-466, Karlsruhe University Press, 2009.

PROCEEDINGS & REPORTS
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Wang, L., Pitsch, H. Prediction of Pollutant Emissions from Industrial Furnaces Using Large Eddy Simulation , 5th US Combustion Meeting, San Diego, CA, paper #B03, 2007. ( Full Text)

Ihme, M., Pitsch, H., Kaltenbacher, M. Prediction of combustion-generated noise in non-premixed turbulent flames using large-eddy simulation , 5th US Combustion Meeting, San Diego, CA, paper #B38, 2007. ( Full Text)

Blanquart, G., Pitsch, H. Thermochemical Properties of Polycyclic Aromatic Hydrocarbons (PAH) from G3MP2B3 Calculations , 5th US Combustion Meeting, San Diego, CA, paper #P45, 2007. ( Full Text)

Blanquart, G., Pitsch, H. Parameter free aggregation model for soot formation , 5th US Combustion Meeting, San Diego, CA, paper #F20, 2007. ( Full Text)

Knudsen, E., Pitsch, H. A Dynamic Model for the Turbulent Burning Velocity for Premixed Combustion LES , 5th US Combustion Meeting, San Diego, CA, paper #B30, 2007. ( Full Text)

Colket, M., Edwards, T., Williams, S., Cernansky, N. P., Miller, D. L., Egolfopoulos, F., Lindstedt, P., Seshadri, K., Dryer, F. L., Law, C. K., Friend, D., Lehnert, D. B., Pitsch, H., Sarofim, A., Smooke, M., Tsang, W. Development of an Experimental Database and Kinetic Models for Surrogate Jet Fuels , AIAA paper AIAA-2007-770, 2007. ( Full Text)

Pitz, W. J., Cernansky, N. P., Dryer, F. L., Egolfopoulos, F. N., Farrell, J. T., Friend, D. G., and Pitsch, H. Development of an Experimental Database and Chemical Kinetic Models for Surrogate Gasoline Fuels , SAE paper, SAE 2007-01-0175, 2007. ( Full Text)

Farrell, J. T., Cernansky, N. P., Dryer, F. L., Friend, D. G., Hergart, C. A., Law, C. K., McDavid, R. M., Mueller, C. J., Patel, A.K., and Pitsch, H. Development of an Experimental Database and Kinetic Models for Surrogate Diesel Fuels , SAE paper, SAE 2007-01-0201, 2007. ( Full Text)

Ihme, M., Bodony, D, Pitsch, H., Prediction of combustion-generated noise in non-premixed turbulent jet flames using large-eddy simulation , AIAA paper 2006-2614, presented at the 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), 8-10 May 2006, Cambridge, Massachusetts. ( Full Text)

J. J. Alonso, S. Hahn, F. Ham, M. Herrmann, G. Iaccarino. G. Kalitzin, P. LeGresley, K. Mattsson, G. Medic, P. Moin, H. Pitsch, J. Schluter, M. Svard, E. Van der Weide, D. You, X. Wu, CHIMPS: A High-Performance Scalable Module for Multi-Physics Simulations , AIAA paper 2006-5274, presented at the 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 9-12 July, Sacramento, California. ( Full Text)

Cook, D. J., Pitsch, H., Enthalpy-Based Flamelet Model for HCCI Applied to a Rapid Compression Machine, SAE Paper 2005-01-3735, 2005. ( Full Text)

Cook, D.J., Chen, J.H., Hawkes, E.R., Sankaran, R., Pitsch, H., Flamelet-Based Modeling of H2/Air Auto-Ignition with Thermal Inhomogeneities, Proc. Western States Section of Combust. Inst., Stanford University, October 17-18, 2005. ( Full Text)

Rai, V., Aryanpour, M., Dhanda, A., Walch, S., Pitsch, H., PEMFC Electrochemistry: Simulation Of Nonequilibrium Surface Chemistry On 3-Dimensional Geometries, presented at 207th Joint International Meeting of The Electrochemical Society- Quebec City, Canada, May 15 - May 20, 2005. ( Full Text)

Pepiot, P., Pitsch, H., Systematic Reduction of Large Chemical Mechanisms, 4th Joint Meeting of the U.S. Sections of the Combustion Institute, Philadelphia, PA, 2005. ( Full Text)

Pitsch, H., Ihme, M., An Unsteady/Flamelet Progress Variable Method for LES of Nonpremixed Turbulent Combustion, AIAA paper 2005-0557, presented at 43rd AIAA Aerospace Science Meeting and Exhibit, Jan 10 - Jan 13, 2005 ,Reno, NV. ( Full Text)

Ihme, M., Pitsch, H., LES of a Non-Premixed Flame Using an Extended Flamelet/Progress Variable Model, AIAA paper 2005-0558, presented at 43rd AIAA Aerospace Science Meeting and Exhibit, Jan 10 - Jan 13, 2005 ,Reno, NV. ( Full Text)

JOURNAL ABSTRACTS

Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers: Kim, S. H., Pitsch, H., Boyd, I. D. (back to top)

Accuracy of the lattice Boltzmann (LB) method for microscale flows with finite Knudsen numbers is investigated. We employ up to the eleventh-order Gauss- Hermite quadrature for the lattice velocities and diffuse-scattering boundary condition for fluid-wall interactions. Detailed comparisons with the direct sim- ulation Monte Carlo (DSMC) method and the linearized Boltzmann equation are made for planar Couette and Poiseuille flows. All higher-order LB meth- ods considered here give improved results as compared with the standard LB method. The accuracy of the LB hierarchy, however, does not monotonically increase with the order of the Gauss-Hermite quadrature. The results also show the sensitivity to a quadrature chosen, even when the Gauss-Hermite quadratures have the same order of formal accuracy. Among the schemes in- vestigated here, D2Q16 is the most efficient method and offers a quantitative prediction in the slip and transition regimes. The higher-order LB methods predict the Knudsen layer up to Kn = O(0.1). The Knudsen layer, however, rapidly disappears when the Knudsen number approaches unity due to a fi- nite number of the lattice velocities, while it is still present for Kn = O(1) in the Boltzmann equation. It is also found that the higher-order LB meth- ods adopted here do not capture the asymptotic behavior of the Boltzmann equation at large Knudsen numbers.

High order conservative finite difference scheme for variable density low Mach number turbulent flows: Desjardins, O., Blanquart, G., Balarac, G., Pitsch, H. (back to top)

The high order conservative finite difference scheme of Morinishi et al. [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 improves significantly the quality of the results in most of the cases.

Slip velocity and Knudsen layer in the lattice Boltzmann method for micro-scale flows: Kim, S. H., Pitsch, H., Boyd, I. D. (back to top)

We present mesoscopic fluid-wall interaction models for the lattice Boltzmann (LB) model simulations of micro-scale flows. The exact solution of the slip velocity for the LB equation with the Bhatnagar-Gross-Krook (BGK) collision operator is obtained for Poiseuille flow at finite Knudsen numbers. With a consistent definition of the Knudsen number, the slip coefficients of the LB equation with the standard D2Q9 scheme are found to be slightly larger than those of the Boltzmann equation with the same boundary condition, which makes the standard LB method remain quantitatively accurate only for small Knudsen numbers. By modifying the non- equilibrium energy flux or introducing the effective relaxation time, the LB method is shown to reproduce the slip phenomena up to second-order in the Knudsen number. For the standard LB method, the Knudsen layer is captured only with the modification of the relaxation dynamics such as in the effective relaxation time model.

Experimental Study and Structural Group Analysis for Soot Reduction Tendency of Oxygenated Fuels: Pepiot-Desjardins, P., Malhotra, R., Kirby, S. R., Boehman, A. L., Pitsch, H. (back to top)

Oxygenated additives are known to reduce soot formation in diesel engines. Numerous studies, both experimental and numerical, have reported that the reduction of particulate emissions depends on the molecular structure of the additives. To gain insight into the role of oxygen in soot reduction, a systematic study of a large number of oxygenates was conducted covering esters, ethers, alcohols, aldehydes, and ketones as well as a few mixed structures. As a surrogate for actual diesel engine emissions, the smoke point of an n-heptane-toluene mixture was measured, to which various amounts of the different oxygenates were added. A statistical analysis of this experimental database using a group contribution method was performed.The relative magnitudes of the different contributions to smoke point improvement, such as dilution effect and the type of the oxygen functional group in the additive, were estimated. Ketones and aldehydes were found to have the greatest impact on smoke point, followed by alcohols and ethers, then esters. Two additional sets of experiments available in the literature were analyzed using the same method. Although uncertainties are difficult to estimate accurately, similar trends were observed for these databases. Also, the present analysis provides an explanation for some seemingly contradictory observations found in the literature.

An efficient error propagation based reduction method for large chemical kinetic mechanisms: Pepiot-Desjardins, Pitsch, H. (back to top)

Production rates obtained from a detailed chemical mechanism are analyzed in order to quantify the coupling between the various species and reactions involved. These interactions can be represented by a directed relation graph. A geometric error propagation strategy applied to this graph accurately identifies the dependencies of specified targets and creates a set of increasingly simplified kinetic schemes containing only the chemical paths deemed the most important for the targets. An integrity check is performed concurrently with the reduction process to avoid truncated chemical paths and mass accumulation in intermediate species. The quality of a given skeletal model is assessed through the magnitude of the errors introduced in the targets predictions. The applied error evaluation is variable-dependent and unambiguous for unsteady problems. The technique yields overall monotonically increasing errors, and the smallest skeletal mechanism that satisfies a user-defined error tolerance over a selected domain of applicability is readily obtained. An additional module based on life-time analysis identifies a set of species that can be modeled accurately by quasi-steady state relations. An application of the reduction procedure is presented for auto-ignition using a large iso-octane mechanism. The whole process is automatic, fast, has moderate CPU and memory requirements and compares favorably to other existing techniques.

Scalar gradient and small-scale structure in turbulent premixed combustion: Kim, S. H., Pitsch, H. (back to top)

Scalar gradient and small-scale structure in turbulent premixed combustion are investigated with emphasis on flame thickening. A Lagrangian-type equation for the evolution of the scalar gradient following an iso-scalar surface is presented, which is useful in studying physical mechanisms for the scalar gradient evolution in premixed flames. The terms in the Lagrangian-type form of the scalar gradient equation are analyzed using direct numerical simulation (DNS) data for statistically 1-D planar flames with high intensity turbulence. Results show that the curvature plays an important role in the evolution of the scalar gradient in turbulent premixed flames. The tangential strain rate, which is the major term to steepen the scalar gradient, is shown to be negatively correlated with the curvature due to the relation between the dilatation and the displacement speed of iso-scalar surfaces. This represents the effects of heat release on the scalar gradient evolution. The alignment characteristics of the flame normal with the principal axis of the strain are also investigated in relation to the characteristics of the tangential strain rate. Variations of the curvature, weighted by the density and the diffusivity, along the normal to the iso-surfaces are found to be the major sink term in the scalar gradient equation and to have a negative correlation with the magnitude of the curvature. This provides evidence that smaller-scale wrinkling is more responsible for flame thickening. In the preheat zone, the tangential strain rate is balanced with the variation of the mass flux normal to the iso-surface, and the strength of the thickening process is determined by the curvature variation term. In the reaction zone, the evolution of the scalar gradient is determined by the balance of the tangential strain rate and the curvature variation term. It is also shown that the thickening process in the reaction zone is much weaker than that in the preheat zone. In one of the simulated flames, a sudden drop of the strength of flame thickening in the reaction zone is observed.

An Algorithm for Mass Matrix Calculation of Constrained Molecular Geometries: Aryanpour, M., Dhanda, A., Pitsch, H. (back to top)

Dynamic models for molecular systems require the determination of corresponding mass matrix. For constrained geometries, this computations is often not trivial, but needs special considerations. Here, assembling the mass matrix of constrained molecular structures is formulated as an optimization problem. Analytical expressions are derived for the solution of the di erent possible cases depending on the rank of the constraint matrix. Geometrical interpretations are further used to enhance the solution concept. As an application, we evaluate the mass matrix for a constrained molecule undergoing an electron-transfer reaction. The pre-exponential factor for this reaction is computed based on the harmonic model.

Watanabe, H., Kurose, R., Komori, S., Pitsch, H., , Comb. Flame, in press, 2007.

Effects of radiation on spray flame characteristics and soot formation: Watanabe, H., Kurose, R., Komori, S., Pitsch, H. (back to top)

Two-dimensional numerical simulations are applied to spray flames formed in a laminar counterflow, and the effects of radiation on spray flame characteristics and soot formation are studied. N-decane (C10H22) is used as the liquid spray fuel, and the droplet motion is calculated by the Lagrangian method. A single-step global reaction is employed for the combustion reaction model. A kinetically based soot model with flamelet model is used to predict soot formation. Radiation is taken into account using the discrete ordinate method. The results show that radiation strongly affects the spray flame behavior and soot formation. Without the radiation model, flame temperature and soot volume fraction are fatally over-estimated. The soot is formed in the diffusion flame regime and its radiation emission increases with the increase in the equivalence ratio of the droplet fuel. This trend is in good agreement with that of the luminous flame behavior observed in the experiments.

A Generalized Periodic Boundary Condition for Lattice Boltzmann Method Simulation of a Pressure Driven Flow in a Periodic Geometry: Kim, S. H., Pitsch, H. (back to top)

A new boundary closure scheme for the lattice Boltzmann method (LBM) is pro- posed for a fully developed, pressure driven flow in a periodic geometry. The new boundary condition is of higher accuracy than that of Zhang and Kwok [Phys. Rev. E 73, 047702 (2006)]. The accuracy of the generalized periodic boundary condition is analyzed for both incompressible and compressible flows. A body forcing approach, where a pressure gradient is replaced by an equivalent body force, is also analyzed for a flow in a complex geometry, and assessed using the generalized periodic boundary condition.

Generation of optimal artificial neural networks using a pattern search algorithm: Application to approximation of chemical systems: Ihme, M., Marsden, A. L., Pitsch, H. (back to top)

A pattern search optimization method is applied to the generation of optimal artificial neural networks (ANNs). Optimization is performed using a mixed variable extension to the generalized pattern search method. This method offers the advantage that categorical variables, such as neural transfer functions and nodal connectivities, can be used as parameters in optimization.When used together with a surrogate, the resulting algorithm is highly efficient for expensive objective functions. Results demonstrate the effectiveness of this method in optimizing an ANN for the number of neurons, the type of transfer function and the connectivity between neurons. The optimization method is applied to a chemistry approximation of practical relevance. In this application, temperature and a chemical source term are approximated as functions of two independent parameters using optimal ANNs. Comparison of the performance of optimal ANNs with conventional tabulation methods demonstrate equivalent accuracy by considerable savings in memory storage. The architecture of the optimal ANN for the approximation of the chemical source term consists of a fully-connected feed-forward network having four non-linear hidden layers and a total of 117 synaptic weights. An equivalent representation of the chemical source term using tabulation techniques would require a 500 * 500 grid point discretization of the parameter space.

An Efficient Semi-Implicit Compressible Solver for Large-Eddy Simulation: Moureau, V., Berat, C., Pitsch, H. (back to top)

In this paper, a pressure-based semi-implicit algorithm for low-Mach compressible flows is described. This type of solver is of great interest in combustion devices where the flow speed is small but where the unsteady heat release can be coupled to the acoustic modes and lead to instabilities. The fractional-step method used in this algorithm is based on a characteristic splitting, which clearly separates the acoustics from the advection. Because of this physical splitting, the algorithm is second-order in space and time for linear acoustics and for low-Mach advection without iterating the time step. Moreover, when kinetic-energy conserving schemes are used for the advection step, the algorithm discretely conserves the kinetic energy in the low-Mach limit. All these properties are illustrated on simple test cases and the algorithm is finally validated by performing the LES of the cold flow of an industrial burner.

Thermochemical Properties of Polycyclic Aromatic Hydrocarbons (PAH) from G3MP2B3 Calculations: Blanquart, G., Pitsch, H. (back to top)

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 ( 6 6 C H ) to coronene ( 24 12 C H ) 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 based on 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/groups/pitsch/.

Influence of parametric forcing on the nonequilibrium dynamics of wave patterns: Abarzhi, S. I., Desjardins, O., Nepomnyashchy, A., Pitsch, H. (back to top)

We investigate analytically and numerically the effect of inhomogeneities on the nonequilibrium dynamics of wave patterns in the framework of a complex Ginzburg-Landau equation (CGLE) with parametric, nonresonant forcing periodic in space and time. It is found that the forcing results in occurrence of traveling waves with different dispersion properties. In the limiting case of forcing with very large wavelength, the waves have essentially anharmonic spatial structure. We consider the influence of modulations on the development of an intermittent chaos and show that the parametric forcing may completely suppress the appearance of chaotic patterns. The relations between this and other pattern-forming systems are discussed. The results obtained are applied to describe the dynamics of thermal Rossby waves influenced by surface topography.

Flamelet-Based Modeling of H2/Air Auto-Ignition with Thermal Inhomogeneities: Cook, D. J., Pitsch, H., Chen, J. H., Hawkes, E. R. (back to top)

Homogeneous-Charge Compression Ignition (HCCI) engines have been shown to have higher thermal efficiencies and lower NOx and soot emissions than Spark Ignition engines. However, HCCI engines experience very large heat release rates which can lead too rapid an increase in pressure rise. One method of reducing the maximum heat release rate is to introduce thermal inhomogeneities, thereby spreading the heat release over several crank angle degrees. Direct Numerical Simulations (DNS) with complex H2 /Air chemistry by Hawkes et al. (2006) showed that both ignition fronts and deflagration-like fronts are present in systems with such inhomogeneities. Here, an enthalpy-based flamelet model is presented and applied to the four cases of varying initial temperature variance presented in Hawkes et al. (2006). This model uses a mean scalar dissipation rate to model the mixing between regions of higher and lower enthalpies. The predicted heat release rates agree well with the heat release rates of the four DNS cases. Although this model does not treat ignition fronts and deflagration-like fronts differently, here it is shown to be capable of capturing the combustion characteristics for both the case in which combustion occurs primarily in the form of spontaneous ignition fronts and for the case dominated by deflagration-type burning. The flamelet-based model shows considerably improved agreement with the DNS results over the popular multi-zone model, particularly, where both deflagrative and spontaneous ignition are occurring, that is, where diffusion is important.

A Consistent LES/Filtered-Density Function Formulation for the Simulation of Turbulent Flames with Detailed Chemistry: Raman, V., Pitsch, H. (back to top)

A hybrid large-eddy simulation/filtered-density function (LES-FDF) methodology is formulated for simulating variable density turbulent reactive flows. By using redundant mean field information from both solvers, a consis- tent numerical algorithm is proposed. Using this novel scheme, a partially premixed methane/hydrogen flame is simulated. To describe transport in composition space, a 16-species reduced chemistry mechanism is used along with the interaction-by-exchange with the mean (IEM) model. Two different flame configurations, namely, Sandia flames D and E are studied. Comparison of simulated radial profiles with experimental data show good agreement for both flames. The LES-FDF simulations accurately predict the increased extinction near the inlet and re-ignition further downstream. The conditional mean profiles show good agreement with experimental data for both flames.

A Ghost-Fluid Method for Large-Eddy Simulation of Premixed Combustion in Complex Geometries: Moureau, V., Minot, P., Berat, C., Pitsch, H. (back to top)

In this paper, a new Ghost--Fluid Method is described. It allows to compute efficiently turbulent premixed flames with a finite thickness in low-Mach flows. A level set algorithm is used to track accurately the flame and to define the overlapping region where the burned and unburned gases satisfy the jump conditions. These algorithms are combined to a fractional-step method to alleviate the acoustic CFL constraint. The full algorithm is verified for simple flame-vortex interactions and it is validated by computing a turbulent flame anchored by a triangular flame-holder. Finally, the algorithm is applied in the LES of an industrial lean-premixed swirl-burner.

An efficient dynamic Monte Carlo algorithm for time-dependent catalytic surface chemistry: Rai, V., Pitsch, H., Novikov, A. (back to top)

Several numerical algorithms for Dynamic Monte Carlo simulations of surface chemistry have been proposed in the past. The Variable Step Size Method (VSSM) is commonly used for systems where the rate coefficients are constant in time, owing to its good efficiency. If rate coefficients vary in time, the First Reaction Method (FRM) has been shown to be more efficient. However, the cost of this algorithm to execute a reaction step depends on the considered lattice size, which can make this method inefficient for systems involving surface phenomena on different scales. Here we propose a new general and efficient algorithm, the fast First Reaction Method (fFRM), which has the advantages of being applicable to systems with constant and time-varying rate coefficients, and of having a computational cost per reaction step that is independent of the lattice size. An additional feature of fFRM is that it is rejection-free, which means that once a reaction class is selected, a reaction of that type will be executed. A rejection-free variant of VSSM, called rVSSM, is also presented, which leads to an approximately 15% speed-up compared with the VSSM algorithm for the considered example.

Mixing characteristics and structure of a turbulent jet diffusion flame stablized on a bluff-body: Kim, S. H., Pitsch, H. (back to top)

Flow dynamics, scalar mixing, and pollutant formation in a turbulent jet diffusion flame stablized on a bluff-body are investigated using large-eddy simulation. The density weighted filtered equations for the flow and mixing fields are solved using dynamic models for the sub-filter quantities. Sub-filter combustion processes are modeled by the conditional filtering method. An integrated formulation that considers only axial variation of conditionally filtered quantities is presented. Results show that vortex shedding from the coflow stream and its interaction with the high speed main jet play an important role in the generation of high dissipation layers in the intense mixing region. The mechanisms that generate the high dissipation layers in the intense mixing region are identified. The relatively uniform composition of combustion products in the recirculation zone helps the flame stablization by maintaining low scalar dissipation rate and high temperature in the vicinity of the stoichiometric surfaces. The present integrated formulation is shown to reproduce these characteristics of the mixing field and to predict the flame structure and NO formation well. The weighted integral formulation of the conditional velocity allows the entrainment of the combustion products in the intense mixing region into the recirculation zone. The proper prediction of low conditional scalar dissipation in the recirculation zone is shown to be crucial for accurately describing the stabilization process. The decrease of NO at the end of the recirculation zone is reproduced due to the well-predicted mixing characteristics.

A low-complexity global optimization algorithm for temperature and pollution control in flames with complex chemistry: Debiane, L., Ivorra, B., Mohammadi, B., Nicoud, F., Poinsot, T., Ern, A., Pitsch, H. (back to top)

Controlling flame shapes and emissions is a major objective for all combustion engineers. Considering the complexity of reacting flows, novel optimization methods are required: this paper explores the application of control theory for partial differential equations to combustion. Both flame temperature and pollutant levels are optimized in a laminar Bunsen burner computed with complex chemistry using a recursive semi-deterministic global optimization algorithm. In order to keep the computational time low, the optimization procedure is coupled with mesh adaptation and incomplete gradient techniques.

Eulerian Transported-PDF Sub-filter Model for LES of Turbulent Combustion: Raman, V., Pitsch, H., Fox, R. O. (back to top)

(coming soon)

Computational study on the internal layer in a diffuser: X. Wu, J. U. Schlüter, P. Moin, H. Pitsch, G. Iaccarino, F. Ham (back to top)

The present internal layer exists in a region with stabilized positive skin friction downstream of a sharp reduction. The streamwise pressure gradient changes suddenly from slightly favorable to strongly adverse at the diffuser throat, and relaxes in a prolonged mildly adverse region corresponding to the skin friction plateau. Development of the internal layer into the outer region is slow, in contrast to the internal layers previously identified from certain external boundary layer flows where the sudden change in streamwise pressure gradient is from strongly adverse to mildly favorable. Signatures of the internal layer include inflectional point in the wall-normal profiles of streamwise turbulence intensity, and a well-defined logarithmic slope in mean streamwise velocity underneath a linear distribution extending to the core region of the diffuser. It is interesting to note that some of these characteristics bear certain resemblance to those existing in the C-type of Couette-Poiseuille turbulent flows. Frequency spectrum results indicate that application of strong adverse pressure gradient at the diffuser throat enhances the low-frequency content of streamwise turbulent fluctuations. Inside the internal layer the frequency energy spectra at different streamwise locations but with the same wall-normal coordinate nearly collapse. Two point correlations with streamwise, wall-normal and temporal separations were used to examine connections between fluctuations inside the internal layer and those in the core region of the diffuser where the mean streamwise velocity varies linearly with distance from the wall. Galilean decomposition of instantaneous velocity vectors reveals a string of well-defined spanwise vortices outside the internal layer.

Large-Eddy Simulation of Turbulent Combustion: Pitsch, H. (back to top)

Large-eddy simulation (LES) of turbulent combustion is a relatively new research field. Much research has been carried out over the past years, but to realize the full predictive potential of combustion LES, many fundamental questions still have to be addressed, and common practices of LES of non-reacting flows revisited. The focus of the present review is to highlight the fundamental differences between Reynolds averaged Navier Stokes and LES combustion models for non-premixed and premixed turbulent combustion, to identify some of the open questions and modeling issues for LES, and to provide future perspectives.

Convergent Iterative Constraint Variation Algorithm for Calculation of Electron-Transfer Transition States: Aryanpour, M., Rai, V., Pitsch, H. (back to top)

We present an efficient mathematical framework to determine the potential- dependent transition states of electron transfer reactions by quantum calcula- tions. This approach makes it more feasible to study heterogeneous electron transfer processes with the theory of local reaction center for electron transfer. It is shown that the new formulation regenerates previously published results obtained by the constrained variation method. Our solution algorithm replaces the constrained optimization problem defined in a multidimensional space by a single equation in terms of only one variable that is solved for in each iteration. This method leads to fast convergence, reliability, and robustness of the located transition states for more complex systems with a larger number of degrees of freedom especially for smooth energy surfaces.

A Consistent Level Set Formulation for Large-Eddy Simulation of Premixed Turbulent Combustion: Pitsch, H. (back to top)

A consistent formulation of the G-equation approach for LES is developed. The unfiltered G-equation is valid only at the instantaneous flame front location. Hence, in a filtering procedure applied to derive the appropriate LES equation, only the instantaneous unfiltered flame surface can be considered. A new filter kernel is provided, which averages along the flame surface. The filter kernel is used to derive the G-equation for the filtered flame front location. This equation has two unclosed terms, involving a flame front conditional averaged flow velocity, and a filtered propagation term. A model for the conditional velocity is derived, expressing this quantity in terms of the Favre-filtered flow velocity, which is typically known from a flow solver. This model leads to the appearance of a density ratio in the propagation term of the G-equation. LES of combustion in the thin reaction zones regime is discussed in the LES regime diagram. A new line is identified separating the thin reaction zones regime into two parts, where the broadended flame thickness is larger and smaller than the filter size, respectively. A model for the propagation term is provided. This leads to a term including the sub-filter turbulent burning velocity and an additional term proportional to the resolved flame front curvature. For the former, an algebraic model is provided from an equation for the sub-filter flame front wrinkling. The latter term depends on the inverse of the sub-filter Damk\"ohler number and disappears in the corrugated flamelets regime.
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Conditional Filtering Method for Large-Eddy Simulation of Turbulent Nonpremixed Combustion: Kim, S. H., Pitsch, H. (back to top)

The conditional filtering method is proposed as a subgrid scale combustion model for large eddy simulation (LES) of turbulent nonpremixed combustion. The novel method is based on conditional filtering of a reactive scalar field and an extension of conditional moment closure (CMC) for LES. Filtering conditioned on iso-surfaces of the mixture fraction is adopted to resolve small scale mixing and chemical reactions in nonpremixed combustion. The conditionally filtered equations are derived and the closure assumptions are discussed. A priori tests are performed using direct numerical simulation (DNS) data for reacting mixing layers. Results show that first-order closure of the reaction rate performs well when the filter width is less than half the integral length scale in the present cases. This shows that extinction processes are primarily governed by large scale flow structures. The accuracy of the first-order closure is not very sensitive to the level of local extinction since large scale fluctuations of reactive scalars on iso-surfaces of the mixture fraction are resolved. The integrated conditional filtering approach is introduced to reduce the computational cost and to resolve the low probability problem in the conditional filtering method. While the assumption of homogeneity in the integration direction is not as good as in the conditional average, the integrated formulation is shown to represent the extinction process caused by large scale fluctuations of the scalar dissipation rate quite well.

Development and Application of a Comprehensive Soot Model for Computational Diesel Engine Studies: S. Hong, M.S. Wooldridge, H.G. Im, D.N. Assanis, H. Pitsch (back to top)

A three-dimensional reacting flow modeling approach is presented for diesel engine studies that can be used for predictions of trends in soot emissions for a wide range of operating conditions. The modeling framework employs skeletal chemistry for n-heptane for ignition and combustion, and links acetylene chemistry to the soot nucleation process. The soot model is based on integration and modification of existing sub-models for soot nucleation, agglomeration, oxidation and surface growth. With the optimized modeling parameters, the simulations agree well with results of high-pressure shock tube studies of rich n-heptane mixtures, reproducing the trends for soot mass over a range of temperature and pressure conditions (T = 1550-2050 K, P = 20, 40 and 80 MPa). Engine simulation results for soot mass are in excellent agreement with diesel engine smoke number measurements over a range of injection timings (-11o ATDC - 2.4o ATDC) and two exhaust gas recirculation levels (16% and 26-27%). The model results demonstrate that correct description of the soot formation, as well as the soot transport processes, is critical to achieve reliable predictive capabilities in engine simulations.

Hybrid Large-Eddy Simulation/Lagrangian Filtered-Density-Function Approach for Simulating Turbulent Combustion: Raman, V., Pitsch, H., Fox, R. O. (back to top)

A consistent hybrid large-eddy simulation/filtered-density-function approach (LES-FDF) is formulated for variable-density low-Mach-number flows. The LES-FDF approach has been proposed as a suitable method for finite-rate-chemistry-based predictive modeling of turbulent reactive flows. Due to the large computational grid associated with LES, use of Lagrangian schemes is numerically expensive. In this work, a highly efficient parallel Lagrangian implementation is used for the simulation of a nonpremixed flame. This bluff-body-stabilized flame is characterized by complex flow fields that interact strongly with the combustion mechanism. A LES grid size of I million computational cells and roughly 15 million notional particles is used to simulate a time-accurate variable-density flow. The hybrid approach predicts the time-averaged velocity and root mean square (RMS) velocity components quite accurately. Species profiles including hydroxyl radical compare well with experimental data. Consistency and accuracy are established by comparing particle and Eulerian density, mixture fraction, and RMS mixture fraction fields. Scalar FDFs at select locations are shown to be well approximated by the presumed beta function used in typical combustion LES. Full Text

A Framework for Coupling Reynolds-Averaged with Large Eddy Simulations for Gas Turbine Applications: J. U. Schlüter, X. Wu, S. Kim, S. Shankaran, J. J. Alonso and H. Pitsch (back to top)

Full scale numerical prediction of the aero-thermal ow in gas turbine engines are currently limited by high computational costs. The approach presented here intends the use of different specialized ow solvers based on the Reynolds-averaged Navier-Stokes equations (RANS) as well as Large Eddy Simulations (LES) for different parts of the ow domain, running simultaneously and exchanging information at the interfaces. This study documents the development of the interface and proves its accuracy and efficiency with simple test-cases. Furthermore, its application to a turbomachinery application is demonstrated. Full Text

Large-Eddy Simulation of a Bluff-Body Stabilized Flame Using a Recursive-Refinement Procedure: V. Raman, H. Pitsch (back to top)

A Large-Eddy Simulation (LES) of a bluff-body stabilized flame has been carried out using a new strategy for LES grid generation. The recursively-refining (RR) grid strategy has been used to generate optimized clustering for variable density combustion simulations. A methane-hydrogenfuel based bluff-body stabilized experimental configuration has been simulated using state-of-theart LES algorithms and sub-filter models. The combustion chemistry is described using a precomputed, laminar flamelet model based look-up table. The GRI-2.11 mechanism is used to build the look-up table parameterized by mixture-fraction and scalar-dissipation rate. A beta-function is used for the sub-filter mixture-fraction filtered-density function (FDF). The simulations show good agreement with experimental data for the velocity field. Time-averaged profiles of major species and temperature are very well reproduced by the simulation. The mixture-fraction profiles show excellent agreement at all locations, which helps in understanding the validity of flamelet assumption for this flame. The results indicate that LES computations are able to quantitatively predict the flame structure quite accurately using the laminar-flamelet model. Simulations tend to corroborate experimental evidence that local extinction is not significant for this flame.
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Flamelet analysis of turbulent combustion: Bastiaans, R. J. M., Martin S. M., Pitsch, H., van Oijen, J. A., de Goey, L. P. H. (back to top)

Three-dimensional direct numerical simulations are performed of turbulent combustion of initially spherical flame kernels. The chemistry is described by a progress variable which is attached to a flamelet library. The influence of flame stretch and curvature on the local mass burning rate is studied and compared to an analytical model. It is found that there is a good agreement between the simulations and the model. Then approximations to the model are evaluated.
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Prediction of Local Extinction and Re-ignition Effects in Non-premixed Turbulent Combustion by a Flamelet/Progress Variable Approach: M. Ihme, C.M. Cha, H. Pitsch (back to top)

The flamelet/progress variable approach (FPVA) has been proposed by Pierce and Moin as a model for turbulent non-premixed combustion in large-eddy simulation. The filtered chemical source term in this model appears in unclosed form, and is modeled by a presumed probability density function (PDF) for the joint PDF of the mixture fraction Z and a flamelet parameter gimel. While the marginal PDF of Z can be reasonably approximated by a beta distribution, a model for the conditional PDF of the flamelet parameter needs to be developed. Further, the ability of FPVA to predict extinction and re-ignition has also not been assessed. In this paper, we address these aspects of the model using the DNS database of Sripakagorn et al. It is first shown that the steady flamelet assumption in the context of FPVA leads to good predictions even for high levels of local extinction. Three different models for the conditional PDF of the flamelet parameter are tested in an a priori sense. Results obtained using a delta function to model the conditional PDF of gimel lead to an overprediction of the mean temperature, even with only moderate extinction levels. It is shown that if the conditional PDF of gimel is modeled by a beta distribution conditioned on Z, then FPVA can predict extinction and re-ignition effects, and good agreement between the model and DNS data for the mean temperature is observed.

Modeling Auto-Ignition Under Diesel Engine Conditions Using a Stochastic Flamelet Approach: G. Blanquart, H. Pitsch (back to top)

A stochastic flamelet approach is developed to model auto-ignition in non-premixed turbulent environments. The scalar dissipation rate appears as an external stochastic parameter in the flamelet equations, representing the unsteady turbulent mixing process. To validate the model, it is applied in simulations of auto-ignition in an initially non-premixed medium in decaying isotropic turbulence using a one-step global reaction. Three different cases with varying Reynolds number have been considered, which correspond to the DNS data of Sreedhara & Lakshmisha (2002). Similar to the auto-ignition process in diesel engines, the initial scalar dissipation rate in the DNS is high enough to prevent auto-ignition, but decays strongly with time. The model predicts the conditional mean temperature profiles and the ignition delay times of the DNS data with good accuracy for all test cases. It is found that the scalar dissipation rate has a strong influence on auto-ignition, leading to largely increased ignition delay times. In addition, it has been found that the impact of fluctuations of the scalar dissipation rate is equally strong and substantially decreases auto-ignition delay times. Furthermore, these fluctuations result in a more gradual transition to a burning state. The reasons for these changes are investigated and the influence of model parameters is discussed.

Stochastic Mixing Model with Power Law Decay of Variance: S. Fedotov, M. Ihme, H. Pitsch (back to top)

A stochastic mixing model based on the law of large numbers is presented that describes the decay of the variance of a conserved scalar in decaying turbulence as a power law, sigma(c)(2) proportional to t(-alpha). A general Lagrangian mixing process is modeled by a stochastic difference equation where the mixing frequency and the ambient concentration are random processes. The mixing parameter X is introduced as a coefficient in the mixing frequency in order to account for initial length-scale ratio of the velocity and scalar field and other physical dependencies. We derive a nonlinear integral equation for the probability density function (pdf) of a conserved scalar that describes the relaxation of an arbitrary initial distribution to a delta-function. Numerical studies of this equation are conducted, and it is shown that X has a distinct influence on the decay rate of the scalar. Results obtained from the model for the evolution of the pdf are in a good agreement with direct numerical simulation DNS) data.

Anti-Aliasing Filters for Coupled LES-RANS Simulations: J. U. Schlüter, H. Pitsch (back to top)

The increasing complexity of engineering problems makes the coupling of multiple simulation codes attractive. In fluid mechanical applications, the physical range of flow phenomena that can be modeled can be extended significantly by coupling flow solvers based on the Reynolds-averaged Navier Stokes (RANS) approach and on Large-Eddy Simulations (LES). These separate flow solvers run simultaneously and exchange information at the interface. However, since the LES flow solver operates usually with a much smaller time-step, the LES data has to be sampled in order to provide data for the RANS flow solver. In the sampling process aliasing errors can occur. This study investigates possibilities in order to suppress aliasing errors while preserving the amplitude and phase of the long wave spectrum.

LES Outflow Conditions for Integrated LES/RANS Simulations: J. U. Schlüter, H. Pitsch, P. Moin (back to top)

The numerical ow prediction of highly complex ow systems, such as the aero-thermal ow through an entire aircraft gas turbine engine, require the application of multiple specialized ow solvers, which have to run simultaneously in order to capture unsteady multicomponent eects. The dierent mathematical approaches of dierent ow solvers, especially LES and RANS ow solvers, pose challenges in the denition of boundary conditions at the interfaces. Here, a method based on a virtual body force is proposed to impose Reynoldsaveraged velocity elds near the outlet of an LES ow domain in order to take ow eects downstream computed by a RANS ow solver into account. This method shows good results in a test case of a swirl ow, where the in uence of a ow contraction downstream of the LES domain is represented entirely by the Reynolds-averaged velocity eld at the outlet of the LES domain.

Extinction and Reignition in a Diffusion Flame: A Direct Numerical Simulation Study: P. Sripakagorn, S. Mitarai, G. Kosaly, H. Pitsch (back to top)

The goal of this study is to provide a window into the physics of extinction and reignition via three-dimensional simulations of non-premixed combustion in isotropic decaying turbulence using one-step global reaction and neglecting density variations. Initially non-premixed fields of fuel and oxidant are developing in a turbulent field. Due to straining, the scalar dissipation rate is initially increasing and its fluctuations create extinguished regions on the stoichiometric surface. Later in the process, the stoichiometric surface again becomes uniformly hot. Besides using Eulerian data, this research applies flame element tracking and investigates the time history of individual points (åflame elements¼) along the stoichiometric surface. The main focus of the study is the discussion of the different scenarios of reignition. This paper identifies three major scenarios: independent flamelet scenario, reignition via edge (triple) flame propagation, and reignition through engulfment by a hot neighbourhood. The results give insight into the role different scenarios play in the reignition process, reveal the physical processes associated with each scenario, and provide the relative frequency of reignition for each scenario.

Effects on Strain Rate on High-Pressure Nonpremixed N-Heptane Autoignition in Counterflow: S. Liu, J. C. Hewson, J. H. Chen, H. Pitsch (back to top)

The effect of steady strain on the transient autoignition of n-heptane at high pressures is studied numerically with detailed chemistry and transport in a counterflow configuration. Skeletal and reduced n-heptane mechanisms are developed and validated against experiments over a range of pressure and stoichiometries. Two configurations are investigated using the skeletal mechanism. First, the effect of strain rate on multistage n-heptane ignition is studied by imposing a uniform temperature for both the fuel and the oxidizer streams. Second, a temperature gradient between the fuel and the oxidizer streams is imposed. The global effect of strain on ignition is captured by a Damkohler number based on either the heat-release rate or the characteristic chain-branching rate. Results show that for low to moderate strain rates, both the low- and intermediate-temperature chemistries evolve in a manner comparable to that in homogeneous systems, including the negative temperature coefficient regime, but with somewhat slower evolution attributable to diffusive losses. At high strain rates diffusive losses inhibit ignition; for two-stage ignition, it is found that ignition is inhibited during the second, intermediate-temperature stage. The imposition of an overall temperature gradient further inhibits ignition because reaction zones for key branching reactions with large activation energies are narrowed. For a fixed oxidizer stream temperature that is not sufficiently high, a higher fuel temperature results in a shorter ignition delay provided that the heptyl radicals are mainly oxidized by low-temperature chemistry. As expected, an increase in pressure significantly increases reaction rates and reduces ignition delay time. However, with increasing pressure there is a shift toward single-stage low-temperature-dominated ignition which serves to delay ignition.

Large-Eddy Simulation Inflow Conditions for Coupling with Reynolds-Averaged Flow Solvers: J. U. Schlüter, H. Pitsch, P. Moin (back to top)

RANS-LES hybrid approaches have become increasingly popular. One way to construct a hybrid approach is to apply separate ow solvers to components of a complex system and to exchange information at the interfaces of the domains. For the LES ow solver, boundary conditions then have to be dened on the basis of the Reynolds-averaged ow statistics delivered by a RANS ow solver. This is a challenge, which also arises, for instance, when dening LES in ow conditions from experimental data. The problem for the coupled RANS-LES computations is further complicated by the fact that the mean ow statistics at the interface may vary in time and are unknown a priori, but only from the RANS solution. The present study denes a method to provide LES in ow conditions through auxiliary, a priori LES computations, where an LES in ow database is generated. The database is modied to account for the unsteadiness of the interface ow statistics.

Flamelet modeling of non-premixed turbulent combustion with local extinction and re-ignition: H. Pitsch, C. M. Cha, S. Fedotov (back to top)

Extinction and re-ignition in non-premixed turbulent combustion is investigated. A flamelet formulation accounting for transport along mixture fraction iso-surfaces is developed. Thereby a new transport term appears in the flamelet equations. It is assumed that this transport is only caused by changes of the local scalar dissipation rate. Space coordinates of the governing equations can then be replaced by the mixture fraction and the scalar dissipation rate. The dissipation rate of the scalar dissipation rate appears as a diffusion coefficient in the new term. This new parameter of the problem and is called the re-ignition parameter. The resulting equations are simplified and stochastic differential equations for the scalar dissipation rate and the re-ignition parameter are formulated. The system of equations is solved using Monte Carlo calculations. The results show that the newly appearing transport term acts by increasing the value of the scalar dissipation rate corresponding to the lower turning point of the S-shaped curve. In an a priori study, predictions using this model are compared with data from a DNS of non-premixed combustion in isotropic turbulence simulating extinction and re-ignition.

Improved Pollutant Predictions in Large-Eddy Simulations of Turbulent Non-Premixed Combustion by Considering Scalar Dissipation Rate Fluctuations: H. Pitsch (back to top)

In this study a new formulation of the unsteady flamelet model is derived to account for the locally resolved distribution of the scalar dissipation rate obtained from Large-Eddy Simulations (LES). Starting from the unsteady flamelet equations a transformation leads to an Eulerian Flamelet Model, in which the scalar dissipation rate appears as function of time, space, and mixture fraction. In previous work, we have shown that LES provides most of the fluctuations of the scalar dissipation rate. Therefore the present model can be solved within an LES using a local fluctuating scalar dissipation rate. The model is applied to the Sandia Flame D, which is a partially premixed, piloted jet diffusion flame. Previously, we have investigated this flame with an unsteady flamelet model, in which only conditionally averaged values for the scalar dissipation rate have been used. Compared to this simulation, accounting for scalar dissipation rate fluctuations leads to improved predictions of the flame structure. In particular, a region of heat release in the rich region of the flame, which is caused by the partial premixing of the fuel with air, does not occur if scalar dissipation rate fluctuations are considered, which is in agreement with the experimental data. This also leads to strongly improved predictions of the mass fractions of stable intermediate chemical species, such as CO and H2.

Large-Eddy Simulation of Premixed Turbulent Combustion Using a Level-Set Approach: H. Pitsch, L. Duchamp de Lageneste (back to top)

In the present study we have formulated the G-equation concept for LES of premixed turbulent combustion. The developed model for the sub-grid burning velocity is shown to correctly reflect Damk\"ohler's limits for large and small scale turbulence. From the discussion of the regime diagram for turbulent premixed combustion it is shown that given a particular configuration of flow parameters, changes in the LES filter width result in changes parallel to constant Karlovitz number lines. It is suggested for LES to choose the Karlovitz number as horizontal axis in the regime diagram. Then, changes in the filter width are represented by vertical lines. An important conclusion is that changes in the filter width cannot result in changing the combustion regime among the corrugated flamelets, thin reaction zones, and broken reaction zones regimes. This is a consistency requirement for the model, since the choice of the filter width cannot change the fundamental combustion mode. Changes from corrugated to wrinkled flamelets, or in general to a laminar regime, are possible. The latter transition for instance occurs, if the filter width becomes smaller than the Kolmogorov scale. In the application of the model to the numerical simulation of a turbulent Bunsen burner experiment, it is shown that the model results predict the mean flame front location, and thereby the turbulent burning velocity, and the influence of the heat release on the flow field in good agreement with experimental data.

Higher-Order Conditional Moment Closure Modelling of Local Extinction and Reignition in Turbulent Combustion: C. M. Cha, H. Pitsch (back to top)

Higher-order, conditional moment closure approaches to modelling local extinction and reignition in turbulent, nonpremixed combustion are investigated. A priori feasibility studies are done using direct numerical simulation experiments which exhibit varying degrees of local extinction. Results show that with moderate levels of extinction, the conditional probability density function (pdf) of the reduced temperature is unimodal, but skewed, and at least third-order terms in a series expansion of the nonlinear chemical source term conditional on the mixture fraction are required to predict the conditional means. With higher levels of local extinction, the conditional pdf shapes can be bimodal and third-order closure breaks-down. The success of a presumed beta pdf shape for conserved scalars is well known. A beta probability distribution for the conditional reactive scalar cannot describe either the unimodal or bimodal pdf shapes which result from the local extinction and reignition events. However, predictions of the conditional means are excellent with the beta pdf model incorporated into a conditional moment closure modelling framework. The cancellation of errors leading to the improved predictions over first-moment closure is described. The a priori modeling results show little sensitivity to the conditional variances.

Asymptotic Structure of Rich Methane Flames: K. Seshadri, X. S. Bai, H. Pitsch (back to top)

The asymptotic structure of unstrained, laminar, fuel-rich, premixed methane flame is analyzed using a reduced chemical-kinetic mechanism made up of three global steps. Analysis is carried out for values of equivalence ratio greater than 1.3. The flame structure is presumed to comprise three zones: an inert preheat zone, a thin reaction zone, and a post-flame zone. In contrast to previous asymptotic analyses of lean flames and moderately rich flames, where the reaction zone of these flamess was presumed to be made up of two layers, for rich flames analyzed here all chemical reaction are presumed to take place in one layer. The structure of the reaction zone of rich flames is obtained by integrating two second order ordinary differential equations, one giving the consumption of fuel and the other the consumption of oxygen. For values of equivalence ratio greater than 1.3, burning velocities obtained from the asymptotic analysis are found to agree reasonably well with those obtained using a chemical-kinetic mechanism made up of elementary reactions.

Modeling Extinction and Reignition in Turbulent Nonpremixed Combustion using a Doubly-conditional Moment Closure Approach: C. M. Cha, G. Kosaly, H. Pitsch (back to top)

The scalar dissipation rate is introduced as a second conditioning variable into the first-moment, singly-conditional moment closure model to describe extinction and reignition effects in turbulent, nonpremixed combustion. A priori testing of the combustion model using direct numerical simulation experiments exhibiting local extinction/reignition events is described. The singly-conditional moment closure model is either unable to describe the extinction seen in the numerical experiments or predicts global extinction when it does not occur. The new doubly-conditional moment closure approach is able to describe the extinction seen on average, but predicts the onset of reignition too early.

Scalar Mixing and Dissipation Rate in Large-Eddy Simulations of Non-Premixed Turbulent Combustion: H. Pitsch, H. Steiner (back to top)

Predictions of scalar mixing and the scalar dissipation rate from large-eddy simulations of a piloted non-premixed methane/air diffusion flame (Sandia flame D) using the Lagrangian Flamelet Model are presented. The results obtained for the unconditionally filtered scalar dissipation rate are qualitatively compared with general observations of scalar mixing from experiments in non-reactive and reactive jets. In agreement with experimental data it is found that provided the reaction zone has an inward direction, regions of high scalar dissipation rate are organized in layer-like structures, inwardly inclined to the mean flow and aligned with the instantaneous reaction zone. The analysis of single-point time records of the mixture fraction reveals ramp-like structures, which have also been observed in experiments and are believed to indicate large scale turbulent structures. The probability density function of the instantaneous resolved scalar dissipation rate at stoichiometric mixture evaluated at cross-sections normal the the nozzle axis is shown to be described accurately by a lognormal pdf with s = 1 A new model for the conditionally averaged scalar dissipation rate has been proposed and shown to account for local deviations from the simple mixing layer structure. The stabilizing effect of the pilot flame in the present configuration is also discussed. Finally, the influence of the resolved fluctuations of the scalar dissipation rate on the flame structure is investigated, revealing only a weak influence on temperature and nitric oxide predictions. However, the model requires further refinement for situations in which local extinction events become important.

Extinction and Autoignition of n-Heptane in Counterflow Configuration: R. Seiser, H. Pitsch, K. Seshadri, W. J. Pitz, H. J. Curran (back to top)

A study is performed to elucidate the mechanisms of extinction and autoignition of n-heptane in strained laminar flows under nonpremixed conditions. A previously developed detailed mechanism made up of 2540 reversible elementary reactions among 557 species is the starting point for the study. The detailed mechanism was previously used to calculate ignition delay times in homogeneous reactors, and concentration histories of a number of species in plug-flow and jet-stirred reactors. An intermediate mechanism made up of 1282 reversible elementary reactions among 282 species and a short mechanism made up of 770 reversible elementary reactions among 160 species are assembled from this detailed mechanism. Ignition delay times in an isochoric homogeneous reactor calculated using the intermediate and the short mechanism are found to agree well with those calculated using the detailed mechanism. The intermediate and the short mechanism are used to calculate extinction and autoignition of n-heptane in strained laminar flows. Steady laminar flow of two counterflowing streams toward a stagnation plane is considered. One stream made up of prevaporized n-heptane and nitrogen is injected from the fuel boundary and the other stream made up of air and nitrogen is injected from the oxidizer boundary. Critical conditions of extinction and autoignition given by the strain rate, temperature and concentrations of the reactants at the boundaries, are calculated. The results are found to agree well with experiments. Sensitivity analysis is carried out to evaluate the influence of various elementary reactions on autoignition. At all values of the strain rate investigated here, high temperature chemical processes are found to control autoignition. In general, the influence of low temperature chemistry is found to increase with decreasing strain. A key finding of the present study is that strain has more influence on low temperature chemistry than the temperature of the reactants.

Investigation of Scalar Dissipation Rate Fluctuations in Non-Premixed Turbulent Combustion Using a Stochastic Approach: H. Pitsch, S. Fedotov (back to top)

Turbulent fluctuations of the scalar dissipation rate are well known to have strong impact on ignition and extinction in non-premixed combustion. In the present study the influence of stochastic fluctuations of the scalar dissipation rate on the solution of the flamelet equations is investigated. By assuming a one-step irreversible reaction the system can be described by the solution of the temperature equation. By modeling the diffusion terms in the flamelet equation this can be written as a ordinary stochastic differential equation (SDE). In addition an SDE is derived for the scalar dissipation rate. From these two equations a Fokker-Planck equation can be obtained describing the joint probability of temperature and the scalar dissipation rate. The equation is analyzed and numerically integrated using a fourth order Runge-Kutta scheme. The influence of the main parameter, which are the Damk\"ohler number, the Zeldovich number, the heat release parameter, and the variance of the scalar dissipation rate fluctuation are discussed.

Unsteady Flamelet Modeling of Soot Formation in Turbulent Diffusion Flames: H. Pitsch, E. Riesmeier, N. Peters (back to top)

The unsteady flamelet model is applied in a numerical simulation of soot formation in a turbulent C2H4 jet diffusion flame. A kinetically based soot model is used, which relies on a detailed kinetic mechanism to describe the formation of small polycyclic aromatic hydrocarbons. To describe the formation, growth, and oxidation of soot particles, flamelet equations for the statistical moments of the particle size distribution are derived. Since the effective Lewis number of large particles tends to infinity, a formulation is given, which allows the investigation of the effect of different diffusion coefficients of the particles on the soot formation process. The results of the calculation are compared to experimental data, showing very good agreement for the temperature, which is shown to depend strongly on soot and gas radiation. The predicted soot volume fraction compares reasonably well with the measured data, if differential diffusion of the particles is considered. Calculations with unity particle Lewis numbers underestimate the experiments by an order of magnitude.

Unsteady Flamelet Modeling of Differential Diffusion in Turbulent Jet Diffusion Flames: H. Pitsch (back to top)

An unsteady flamelet model, which will be called the Lagrangian Flamelet Model, has been applied to a steady, turbulent CH4/H2/N2-air diffusion flame. The results have been shown to be in reasonable agreement with experimental data for axial velocity, mixture fraction, species mass fractions, and temperature. The application of three different chemical mechanisms leads to the promising conclusion that the state of the art mechanisms yield almost identical results. To explain the still remaining differences from the experimental data, the effects of differential diffusion are discussed. Three possible mechanisms leading to differential diffusion are proposed: Firstly, the occurrence of a laminar mixing layer in a region very close to the nozzle exit; secondly, the molecular diffusivity being of the same order of magnitude as the turbulent eddy diffusivity; thirdly, a typical length scale of the mixing layer thickness being smaller than the small turbulent eddies leading to a laminar sub-layer. By investigating the computational results for the considered configuration, the first mechanism has been concluded to be the only possibility. Further calculations have been performed, which account for differential diffusion by assuming the flow to be laminar very close to the nozzle and switching to unity Lewis numbers downstream of the potential core. The results lead to a significant improvement of the agreement to experimental data. It can be shown from the computational results and the experimental data that the differential diffusion effects arise from this laminar region. However, even though the Lewis numbers are assumed to be unity throughout the remaining part of the flow field these differential diffusion effects remain to a certain extent, even in the far downstream region, affecting for instance the centerline temperature by approximately 100 K. This demonstrates that differential diffusion can cause a strong history effect in turbulent jet diffusion flames.

Large-Eddy Simulation of a Turbulent Piloted Methane/Air Diffusion Flame (Sandia Flame D): H. Pitsch, H. Steiner (back to top)

The Lagrangian Flamelet Model is formulated as a combustion model for large-eddy simulations of turbulent jet diffusion flames. The model is applied in a large-eddy simulation of a piloted partially premixed methane/air diffusion flame (Sandia flame D). The results of the simulation are compared to experimental data of the mean and RMS of the axial velocity and the mixture fraction and the unconditional and conditional averages of temperature and various species mass fractions, including CO and NO. All quantities are in good agreement with the experiments. The results indicate in accordance with experimental findings that regions of high strain appear in layer like structures, which are directed inwards and tend to align with the reaction zone, where the turbulence is fully developed. The analysis of the conditional temperature and mass fractions reveals a strong influence of the partial premixing of the fuel.

3D Simulation of DI Diesel Combustion and Pollutant Formation Using a Two-Component Reference Fuel: H. Barths, H. Pitsch, N. Peters (back to top)

By separating the fluid dynamic calculation from that of the chemistry, the unsteady flamelet model allows the use of comprehensive chemical mechanisms, which include several hundred reactions. This is necessary to describe the different processes that occur in a DI Diesel engine such as autoignition, the burnout in the partially premixed phase, the transition to diffusive burning, and formation of pollutants like NOx and soot. The highly nonlinear reaction rates need not to be simplified, and the complete structure of the combustion process is preserved. Using the Representative Interactive Flamelet (RIF) model, the one-dimensional unsteady set of partial differential equations is solved online with the 3D CFD code. The flamelet solution is coupled to the flow and mixture field by several time dependent parameters (enthalpy, pressure, scalar dissipation rate). In return, the flamelet code yields the species concentrations, which are then used by the 3D CFD code to compute the temperature field and the density. The density is needed in the 3D CFD code for the solution of the turbulent flow and mixture field. Pollutant formation in a Volkswagen DI 1900 Diesel engine is investigated experimentally. The engine is fueled with Diesel and two reference fuels. One reference fuel is pure n-decane. The second is a two-component fuel consisting of 70% (liquid volume) n-decane and of 30% (liquid volume) alpha-methylnaphthalene (Idea-fuel). The experimental results show good agreement for the whole combustion cycle (ignition delay, maximum pressures, torque and pollutant formation) between the two-component reference fuel and Diesel. The simulations are performed for both reference fuels and are compared to the experimental data. Nine different flamelet calculations are performed for each simulation to account for the variability of the scalar dissipation rate, and its effect on ignition is discussed. Pollutant formation (NOx and soot) is predicted for both reference fuels. The contributions of the different reaction paths (thermal, prompt, nitrous, and reburn) to the NO formation are shown. Finally, the importance of the mixing process for the prediction of soot emissions is discussed.

Unsteady Flamelet Modeling of Turbulent Hydrogen/Air Diffusion Flames: H. Pitsch, M. Chen, N. Peters (back to top)

The unsteady flamelet model is applied in numerical simulations of a steady, turbulent, nitrogen diluted hydrogen/air diffusion flame. An unsteady flamelet is solved interactively with a CFD solver for the turbulent flow and the mixture fraction field. Transient effects occurring in steady jet diffusion flames are discussed in terms of the relevant time scales. It is shown that radiation can be neglected and that the flame structure is hardly influenced by transient effects for the present case. However, for predictions of slow processes like the formation of NO unsteady effects have to be considered. The results predicted by the model are in reasonable agreement to experimental data for temperature, major species mass fractions, OH, and NO mole fractions. On the contrary, the use of steady flamelet libraries yields good results for flame structure and even OH concentrations, but NO is overpredicted by an order of magnitude. However, reasonably well predicted NO concentrations can also be obtained by solving an unsteady flamelet as a post processing mode.

A Consistent Flamelet Formulation for Non-Premixed Combustion Considering Differential Diffusion Effects: H. Pitsch, N. Peters (back to top)

A flamelet formulation for non-premixed combustion that allows an exact description of differential diffusion has been developed. The main difference to previous formulations is the definition of a mixture fraction variable, which is not directly related to any combination of the reactive scalars, but defined from the solution of a conservation equation with an arbitrary diffusion coefficient and appropriate boundary conditions. Using this definition flamelet equations with the mixture fraction as the independent coordinate are derived without any assumptions about the Lewis numbers for chemical species. The formulation is shown to be exact if the scalar dissipation rate is prescribed as a function of the mixture fraction. Different approximations of the scalar dissipation rate that had been derived from analytic solutions for special cases are investigated by varying the diffusion coefficient of the mixture fraction transport equation. As examples, counterflow flames of hydrogen and n-heptane, which have much larger and much smaller diffusivities than oxygen and nitrogen, are considered. It is shown that the use of equal thermal and mixture fraction diffusivities yields a sufficiently well described flame structure and is therefore recommended for the definition of the mixture fraction diffusion coefficient. Finally, the possibility of using constant species Lewis numbers has been examined. It has been found that once an appropriate set of Lewis numbers is determined, good results are achieved over wide ranges of the parameters, such as scalar dissipation rate, pressure, and oxidizer temperature.

Asymptotic Analysis of the Structure of Moderately Rich Methane-Air Flames: K. Seshadri, X. S. Bai, H. Pitsch, N. Peters (back to top)

The asymptotic structure of laminar, moderately rich, premixed methane flames is analyzed using a reduced chemical-kinetic mechanism comprising four global reactions. This reduced mechanism is different from those employed in previous asymptotic analyses of stoichiometric and lean flames, because a steady-state approximation is not introduced for CH3. The aim of the present analysis is to develop an asymptotic model for rich flames, that can predict the rapid decrease of the burning velocity with increasing equivalence ratio. In the analysis, the flame structure is presumed to consist of three zones---a preheat zone with a normalized thickness of the order of unity, a thin reaction zone, and a postflame zone. The preheat zone is presumed to be chemically inert, and in the postflame zone the products are in chemical equilibrium and the temperature is equal to the adiabatic flame temperature, Tb. In the reaction zone the chemical reactions are presumed to take place in two layers: the inner layer and the oxidation layer. The rate constants of these reactions are evaluated at T0, which is the characteristic temperature at the inner layer. In the inner layer the dominant reactions taking place are those between the fuel and radicals, and between CH3 and the radicals. An important difference between the structure of the inner layer of rich flames and that of lean flames analyzed previously is the enhanced influence of the chain breaking reaction, CH3 + H + (M) --> CH4 + (M), in rich flames. Here M represents any third body. This reaction decreases the concentration of H radicals which in turn decreases the values of the burning velocity. In the oxidation layer of rich flames, the reactive-diffusive balance of O2 is considered. This differs from the structure of the oxidation layer of lean flames where the reactive-diffusive balance of H2 and CO was of primary interest. The burning velocities calculated using the results of the asymptotic analysis agree reasonably well with the burning velocities calculated numerically using chemical-kinetic mechanisms made up of elementary reactions. The values of the characteristic temperature at the inner layer T0 are found to increase with increasing values of the equivalence ratio and to approach Tb at phi=1.36. When T0 is very close to Tb, the asymptotic analysis developed here is not longer valid and an alternative asymptotic analysis must be developed for even larger equivalence ratios.

Reduced n-Heptane Mechanism for Nonpremixed Combustion with Emphasis on Pollutant Relevant Intermediate Species: M. Bollig, H. Pitsch, J. C. Hewson, K. Seshadri (back to top)

A chemical kinetic mechanism for nonpremixed combustion of n-heptane flames has been compiled and validated with experiments performed in a counterflow diffusion flame over a liquid pool. Using this mechanism and the principles of reduction by the introduction of steady-state assumptions for appropriate species, a seven-step reduced mechanism is derived. The oxidation of C1-species and the description of the hydrogen-oxygen system is similar to that of well-established reduced mechanisms for lower hydrocarbons. Additional steps are required to accurately describe the behavior of intermediate species; namely, propene, ethene, and acetylene are not in steady-state. Special attention is directed towards an accurate description of species relevant to pollutant formation. Excellent agreement between reduced and detailed chemistry is obtained for a wide range of conditions. The results serve to illustrate the major phenomena occuring in n-heptane diffusion flames and the manner in which these phenomena change with compression and mixing rate. The reduced mechanism provides a manageable approach to including elementary chemical kinetics in the computation of turbulent diffusion flames in the flamelet regime.

Numerical and Asymptotic Studies of the Structure of Premixed iso-Octane Flames: H. Pitsch, N. Peters, K. Seshadri (back to top)

Numerical calculations and rate-ratio asymptotic analysis are performed to obtain the structure and burning velocities of premixed iso-octane flames. The numerical calculations employ a detailed chemical-kinetic mechanism comprising 967 elementary reactions, a skeletal chemical-kinetic mechanism comprising 47 elementary reactions and a reduced chemical-kinetic mechanism made up of six overall reactions among nine species including the H radical. The values of burning velocities calculated numerically using the detailed, skeletal and reduced chemical-kinetic mechanisms are found to agree well with each other as well with previous measurements. The asymptotic structure of the flame is analyzed using a reduced chemical-kinetic mechanism comprising five overall reactions. This mechanism is deduced from the reduced chemical kinetic mechanism employed in the numerical calculations after introducing steady state approximation for the H radical. In the analysis the flame structure is presumed to consist of three zones - a pre-heat zone of thickness of order unity, a thin reaction zone and a post-flame zone. In the reaction zone the chemical reactions are presumed to take place in three layers - an inner layer, a C3H4-consumption layer and a H2-CO oxidation layer. Within the inner layer the fuel iso-octane is consumed in a thin sublayer and i-C4H8 is formed which subsequently reacts with radicals to form the intermediate hydrocarbon compound C3H4. This intermediate hydrocarbon is consumed in the C3H4-consumption layer. In the inner layer and the C3H4-consumption layer H2 and CO are formed. Most of the final products CO2 and H2O are formed in the H2-CO oxidation layer. In this layer H2 is presumed to be in steady state everywhere except in a thin sublayer called the H2-consumption layer. The burning velocities calculated using the results of the asymptotic analysis are found to agree reasonably well with those calculated numerically using the detailed, skeletal and reduced chemical-kinetic mechanisms and with previous measurements.

Detailed Kinetic Reaction Mechanism for Ignition and Oxidation of 1-Methylnaphthalene: H. Pitsch (back to top)

A detailed kinetic reaction mechanism capable of describing ignition and oxidation of 1-methylnaphthalene has been developed. This mechanism incorporates the removal of the methyl group, the oxidation of naphthalene and benzene, and the formation of PAHs. The kinetic rate data for two-ring species have been approximated by the corresponding one-ring data, since very few direct measurements are available. The model has been validated using species concentrations data obtained by gas chromatographic measurements in a turbulent flow reactor and ignition delay times from shock tube experiments, both from the recent literature. The predicted species concentrations are in reasonable agreement with the experimental data. Also, auto-ignition delay times are sufficiently well predicted. Applying reaction flux and sensitivity analysis, the main reaction paths are determined. (Image of mechanism)

Laminar Counterflow Mixing of Acetylene into Hot Combustion Products: H. Breitbach, J. Göttgens, F. Mauss, H. Pitsch, N. Peters (back to top)

In an axisymmetric counterflow configuration pure acetylene was blown against the hot post flame gases of a rich premixed acetylene-air flame stabilized on a sinter metal, thereby creating a broad pyrolysis zone. This one dimensional configuration has several interesting features for soot formation studies. There is the possibility to control the temperature, the oxygen leakage through the premixed flame and the residence time in the pyrolysis region independently by varying the stoichiometry and composition of the premixed flame and the velocity of the fuel counterflow. The thickness of the pyrolysis region, where the soot formation occurs, is large and thus experimentally well accessible and resolvable. Along the axis of symmetry, concentration profiles of various stable species up to C-4-hydrocarbons were measured by gas chromatography. Thermocouples were used for temperature measurements. The soot volume fraction was determined by a laserlight extinction method and Abel's inversion. The experimental results were compared with one-dimensional calculations using a kinetically based soot model. The reaction mechanism contains 62 species and about 400 reactions. The soot formation mechanism accounts for all possible coagulation processes between polyaromatic hydrocarbons (PAH) and soot particles, namely PAH-PAH coagulation leading to particle inception, PAH-particle coagulation, and particle-particle coagulation, for surface growth by C2H2 addition, and for oxidation. The results of the numerical simulation and the experiment show a good agreement for temperature and major species. The prediction for the maximum value of the soot volume fraction is quite good, but deviations in the measured and calculated profiles suggest an underestimated soot particle diffusion, indicating an overprediction of the particle sizes in the soot formation model.

PROCEEDINGS ABSTRACTS

Prediction of combustion-generated noise in non-premixed turbulent jet flames using large-eddy simulation : Ihme, M., Bodony, D, Pitsch, H. (back to top)

A model for the prediction of combustion-generated noise in non-premixed flames has been developed. This model is based on Lighthill's acoustic analogy and employs the flamelet/progress variable model to express the so-called excess density as function of the mixture fraction and the progress variable. The source terms appearing in this formulation have been analyzed and three sources have been identified as main contributors to the acoustic pressure observed at the far-field. The model has been applied in the numerical simulation of the acoustic pressure generated in a non-premixed turbulent open flame. For the prediction of the flow field a low Mach number large-eddy simulation has been performed. The relevant acoustic sources are extracted from the large-eddy simulation and are used for the prediction of the far-field pressure. Numerical results for the sound pressure level are in agreement with experimental data in the low frequency range but over-predict the measured spectra at higher frequencies.
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CHIMPS: A High-Performance Scalable Module for Multi-Physics Simulations: J. J. Alonso, S. Hahn, F. Ham, M. Herrmann, G. Iaccarino. G. Kalitzin, P. LeGresley, K. Mattsson, G. Medic, P. Moin, H. Pitsch, J. Schluter, M. Svard, E. Van der Weide, D. You, X. Wu (back to top)

As computational methods attempt to simulate ever more complex physical systems the need to couple independently-developed numerical models and solvers arises. This often results from the requirement to use different physical or numerical models for various portions of the domain of interest. In many situations it is also common to use different physical models that influence each other within the same domain of interest. The interaction between these models normally requires an exchange of information between the participating solvers. When the solvers that exchange information are distributed over a large number of processors in a parallel computer, the problem of exchanging information in an efficient and scalable fashion becomes complicated. This paper describes our efforts to develop a Coupler for High-Performance Integrated Multi-Physics Simulations library, CHIMPS, that can enable the exchange of information between solvers and that automates the search, interpolation and communication processes in order to allow the developer to focus on other matters of interest such as the appropriate strategies to couple the solvers in an accurate and stable fashion. Our basic approach, the underlying technology, the CHIMPS API, and a number of examples are presented. In addition, a series of appendices are included with actual sample code that can be used to become familiar with the CHIMPS library.
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Enthalpy-Based Flamelet Model for HCCI Applied to a Rapid Compression Machine: David J. Cook, H. Pitsch (back to top)

Homogeneous-Charge Compression Ignition (HCCI) engines have been shown to have higher thermal efficiencies and lower NOx and soot emissions than Spark Ignition engines. However, HCCI engines experience high levels of carbon monoxide (CO) and unburnt hydrocarbon (UHC) emissions. These pollutants are formed in regions of the cylinder where wall heat loss is significant. Improving CO and UHC emissions in HCCI engines requires a fundamental understanding of the heat loss, chemical kinetics, and transport between near wall regions and regions less affected by heat loss. In this study an enthalpy-based flamelet approach is introduced and applied to a Rapid Compression Machine operated under HCCI conditions. This approach directly models transport between regions of higher and lower enthalpies. Results are compared to experimental data from Murase and HanadaThe simulations correctly predict ignition timing trends as a function of initial mixture temperature. Additionally, the affect of modeled transport across enthalpies on ignition characteristics is quantified, and the magnitude of this transport term is compared to the chemical source term.

Flamelet-Based Modeling of H2/Air Auto-Ignition with Thermal Inhomogeneities: Cook, D.J., Chen, J.H., Hawkes, E.R., Sankaran, R., Pitsch, H. (back to top)

Homogeneous-Charge Compression Ignition (HCCI) engines have been shown to have higher thermal efficiencies and lower NO_x and soot emissions than Spark Ignition engines. However, HCCI engines experience very large heat release rates which can lead to the occurrence of damaging engine knock. One method of reducing the maximum heat release rate is to introduce thermal inhomogeneities, thereby spreading the heat release over several crank angle degrees. Direct Numerical Simulations (DNS) with complex H_2/Air chemistry by Hawkes et al. (2005) showed that both ignition fronts and deflagration-like fronts are present in systems with such inhomogeneities. Here, an enthalpy-based flamelet model is presented and applied to the four cases of varying initial temperature variance presented in Hawkes et al. (2005). This model uses a mean scalar dissipation rate to model the mixing between regions of higher and lower enthalpies. The predicted heat release rates agree well with the heat release rates of the four DNS cases. Although this model does not treat ignition fronts and deflagration-like fronts differently, here it is shown to be capable of capturing the combustion characteristics for both the case in which combustion occurs primarily in the form of spontaneous ignition fronts and for the case dominated by deflagration-type burning. The flamelet-based model shows considerably improved agreement with the DNS results over the popular multi-zone model, particularly, where both deflagrative and spontaneous ignition are occurring, that is, where diffusion is important.
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PEMFC Electrochemistry: Simulation Of Nonequilibrium Surface Chemistry On 3-Dimensional Geometries: V. Rai, M. Aryanpour, A. Dhanda, S. Walch, H. Pitsch (back to top)

The performance of polymer exchange membrane fuel cells is known to be strongly influenced by the electrochemical reactions occurring in the cathode catalyst layer. The dynamics of the elementary reaction steps in the oxygen reduction reaction on platinum based catalysts are investigated to provide a better understanding of the cathode overpotential. We present a new approach using Dynamic Monte Carlo (DMC) simulations for providing an accurate de- scription of the kinetics of ORR on real 3D nanoparticle geometries. Simula- tions of the ORR on model cubo-octahedral shaped nanoparticle are presented and are found to predict experimentally observed coverages of O-containing species with good accuracy.evelopment

LES of a Non-Premixed Flame Using an Extended Flamelet/Progress Variable Model: M. Ihme, H. Pitsch (back to top)

In previous a priori studies we have examined the flamelet/progress variable model proposed by Pierce and Moin and identified the most important areas for model improve- ments. The flamelet/progress variable approach is a conserved scalar based model for non-premixed combustion and uses a reactive scalar as an additional parameter in a table lookup. One of the main assumptions in this model is the use of a delta function as a presumed probability density function (PDF) for this reactive scalar. We have previously shown that the use of the beta function provides some improvement. Here, the statistically most-likely distribution is proposed as a presumed PDF for the flamelet parameter. This provides two advantages. First of all, the function depends on a chemical time-scale, and in addition, an arbitrary number of moments can be enforced. The model is applied to flames D and E of the Sandia piloted turbulent jet flame series and results are compared with experimental data.
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An Unsteady/Flamelet Progress Variable Method for LES of Nonpremixed Turbulent Combustion: M. Ihme, H. Pitsch (back to top)

An unsteady flamelet/progress variable model has been developed and formulated as an extension of the steady flamelet/progress variable model. For this model, a large number of unsteady laminar flamelet simulations is performed for various conditions, and solutions are recorded as function of time. From this, a flamelet library is generated, which provides the filtered quantities of all scalar values as function of the filtered mixture fraction, the mixture fraction sub-filter variance, the filtered reaction progress variable, and the filtered scalar dissipation rate. The model has been implemented in an LES code. Simulations have been performed for a confined swirl burner using the unsteady flamelet/progress variable model. The results are compared with experimental data for velocities and velocity fluctuations, temperature, CO2, and CO mole fractions. The results agree reasonably well with the experiments for all quantities. In particular, CO is predicted with good accuracy.
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Systematic Reduction of Large Chemical Mechanisms: Pepiot, P., Pitsch, H. (back to top)

The directed relation graph method with error propagation (DRGEP) is proposed as a new method for the systematic reduction of large chemical detailed mechanisms. The method is based on the directed relation graph (DRG) approach, but uses generalized coupling coefficients based on error propagations. A skeletal mechanism consisting of the lowest possible number of species and reactions, which reproduces selected targets such as species concentrations, ignition delay times or laminar burning velocities with a given accuracy, is automatically generated. The method has been successfully applied in the reduction of large mechanisms for n-heptane and primary reference fuel oxidation, achieving typical reduction ratios of 2.5 for the number of species and 5 for the number of reactions while keeping the errors on ignition delay time and main species concentrations below 10%. Compared with the DRG method, DRGEP provides significantly improved accuracy of the resulting reduced mechanism, if the same number of species is kept. Comparison with an existing manually reduced mechanism shows the potential of an additional automatic lumping procedure to obtain short skeletal mechanisms that can be directly used in more complex simulations.
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