Stephen B. Pope’s research while affiliated with Cornell University and other places

Large eddy simulation (LES)/ Probability Density Function (PDF) approaches are now well established and can be used for simulating challenging turbulent combustion configurations with strong turbulence chemistry interactions. Transported PDF methods are known to be computationally expensive compared to flamelet-like turbulent combustion models. The pre-partitioned adaptive chemistry (PPAC) methodology was developed to address this cost differential. PPAC entails an offline preprocessing stage, where a set of reduced models are generated starting from an initial database of representative compositions. At runtime, this set of reduced models are dynamically utilised during the reaction fractional step leading to computational savings. We have recently combined PPAC with in-situ adaptive tabulation (ISAT) to further reduce the computational cost. We have shown that the combined method reduced the average wall-clock time per time step of large-scale LES/particle PDF simulations of turbulent combustion by 39%. A key assumption in PPAC is that the initial database used in the offline stage is representative of the compositions encountered at runtime. In our previous study this assumption was trivially satisfied as the initial database consisted of compositions extracted from the turbulent combustion simulation itself. Consequently, a key open question remains as to whether such databases can be generated without having access to the turbulent combustion simulation. Towards answering this question, in the current work, we explore whether the compositions for forming such a database can be extracted from computationally-efficient low-dimensional simulations such as 1D counterflow flames and partially stirred reactors. We show that a database generated using compositions extracted from a partially stirred reactor configuration leads to performance comparable to the optimal case, wherein the database is comprised of compositions extracted directly from the LES/PDF simulation itself.

LES/PDF methods are known to provide accurate results for challenging turbulent combustion configurations with strong turbulence-chemistry interactions. These methods are generally applicable as they do not make any assumptions on the topology of the underlying flame structure. However, this added generality comes at an increased computational cost. To mitigate this added cost, the majority of the LES/PDF computations performed to date utilize reduced mechanisms. We recently presented a coupled pre-partitioned adaptive chemistry (PPAC) and tabulation (ISAT) methodology (Newale et al., Comb. Th. Mod., 2019), which retains the fidelity of the detailed mechanism, while keeping the computational cost affordable. This methodology was tested in a partially-stirred reactor configuration. In this work, we describe the developments required for a holistic integration of PPAC-ISAT with a LES/PDF framework. We examine the performance of this coupled methodology in two LES/PDF configurations of Sandia flame D. A smaller simulation domain is initially utilized to characterize the efficiency and accuracy of standalone PPAC and coupled PPAC-ISAT in detail. Then, the performance of PPAC-ISAT is examined in a full-scale LES/PDF simulation. We show that the coupled PPAC-ISAT LES/PDF captures the resolved mean and RMS profiles of temperature and major species mass fractions to within 2% and OH to within 5%, with a reduction in the average simulation wall clock time per time step of 39% over an ISAT implementation using the detailed mechanism.

The predictive numerical simulation of near-limit turbulent premixed combustion, in which the turbulent intensity is high and the fuel/air mixture is near the flammability limit, remains challenging. In this study, large-eddy simulation (LES)/filtered density function (FDF) simulations of a high-speed piloted premixed jet burner flame are performed to illustrate the importance of the resolved level of reactive scalars and micromixing modeling on predicting the overall combustion process. The simulations with increased resolved levels of reactive scalars yield notably improved predictions throughout the extinction–reignition region of this flame. The sources of grid sensitivity are thoroughly examined through the quantification of the resolved levels of the velocity and scalar fields, as well as the mixing-reaction budgets. Subgrid mixing is identified as the most prominent factor for grid sensitivity. The effects of mixing timescale modeling are investigated and quantified through a parametric study of the mixing rate parameter and the development of an augmented hybrid mixing timescale model in the LES context. As far as the mixing formulation is concerned, the Euclidean minimum spanning tree model shows a lower level of grid dependence than the interaction by exchange with the mean model due to the enforcement of localness in composition space.

Probability density function (PDF) methods are now well established and can be used to accurately simulate flames with strong turbulence chemistry interactions. A pre-partitioned adaptive chemistry (PPAC) methodology (Liang et al., Combustion and Flame, 2015) has been proposed recently for the efficient implementation of combustion chemistry in particle PDF methods. PPAC generates a library of reduced kinetic models in an offline preprocessing stage. At runtime, PDF particles are dynamically assigned one reduced model and its corresponding reduced representation, leading to a significant decrease in both storage requirements and CPU time required for the integration of chemical source terms. In this work, we augment PPAC by combining it with storage retrieval and dimension reduction techniques. Specifically, this work combines PPAC with in-situ adaptive tabulation (ISAT) and rate-constrained chemical equilibrium (RCCE). Implementations for PPAC-ISAT, PPAC-RCCE, and PPAC-RCCE-ISAT are described and their performance is examined for a partially stirred reactor (PaSR) test case. The combined PPAC-RCCE-ISAT methodology shows a significant improvement over the stand-alone PPAC methodology by reducing the number of redundant direct integrations of similar compositions and reducing the number of variables that need to be retained at runtime.

The LES/PDF methodology is applied to the Cambridge/Sandia turbulent stratified flame series. The methane chemistry is represented by the 16-species reduced ARM1 mechanism, and the in situ adaptive tabulation method is adopted to accelerate the chemistry calculations. Differential diffusion effects are taken into account. The simulations are performed for premixed (SwB1), and moderately and highly stratified (SwB5 and SwB9, respectively) cases under non-swirling conditions. The results from LES/PDF simulations are compared with the experimental measurements and with previous calculations. The calculated length of the recirculation zone, the mean and r.m.s. profiles of velocity, temperature, equivalence ratio and mass fractions of species are in very good agreement with the measurements. In the stratified cases, the CO profiles are underestimated within the recirculation zone, close to the bluff body. Scatter plots of species mole fractions and temperature are presented and compared with the experimental data. Conditional means of species mass fractions demonstrate overall good consistency with the measurements. A parametric study is then performed to examine the effect of differential diffusion and the effect of the parameter controlling the scalar mixing rate. It is found that differential diffusion has a negligible effect on the mean and r.m.s. results, whereas, the mixing rate parameter has a considerable effect on the flow structure. Finally, the effect of stratification is investigated and characterized by scatter plots of OH mass fraction and heat release rate (HRR) in the equivalence ratio space.

The LES/PDF methodology is applied to the Cambridge/Sandia turbulent stratified flame series. The methane chemistry is represented by the 16-species reduced ARM1 mechanism, and the in situ adaptive tabulation method is adopted to accelerate the chemistry calculations. Differential diffusion effects are taken into account. The simulations are performed for premixed (SwB1), and moderately and highly stratified (SwB5 and SwB9, respectively) cases under non-swirling conditions. The results from LES/PDF simulations are compared with the experimental measurements and with previous calculations. The calculated length of the recirculation zone, the mean and r.m.s. profiles of velocity, temperature, equivalence ratio and mass fractions of species are in very good agreement with the measurements. In the stratified cases, the CO profiles are underestimated within the recirculation zone, close to the bluff body. Scatter plots of species mole fractions and temperature are presented and compared with the experimental data. Conditional means of species mass fractions demonstrate overall good consistency with the measurements. A parametric study is then performed to examine the effect of differential diffusion and the effect of the parameter controlling the scalar mixing rate. It is found that differential diffusion has a negligible effect on the mean and r.m.s. results, whereas, the mixing rate parameter has a considerable effect on the flow structure. Finally, the effect of stratification is investigated and characterized by scatter plots of OH mass fraction and heat release rate (HRR) in the equivalence ratio space.

A large-eddy simulation (LES)/probability density function (PDF) method is developed for simulations of turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modeled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation (ISAT) method [1, 2] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilize a block struc-tured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [3] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelized using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate cou-* pling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D and a turbulent premixed/stratified flames under non-swirling and swirling conditions from the Cambridge turbulent stratified flame series [4]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.

The filtered density function (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.