Mehdi B. Nik

Scalar Filtered Density Function for Large Eddy Simulation of a Bunsen Burner

The scalar filtered density function methodology is employed for large eddy simulation of a turbulent stoichiometric premixed methane-air flame. The scalar filtered density function accounts for the subgrid-scale chemical reaction by considering the mass-weighted probability density function of the subgrid-scale scalar quantities. A transport equation is derived for the scalar filtered density function in which the effects of chemical reactions appear in closed form. The subgrid-scale mixing is modeled via the linear mean square estimation model, and the convective fluxes are modeled via a subgrid-scale viscosity. The modeled scalar filtered density function transport equation is solved by a hybrid finite difference and Monte Carlo scheme. A novel irregular Monte Carlo portioning procedure is developed that facilitates efficient simulations with realistic flow parameters. Combustion chemistry is modeled via five-step, nine-species reduced chemical kinetics. Simulated results are assessed by comparisons against laboratory data. Good agreements are observed, capturing several important features of the flame as observed experimentally.

An Irregularly Portioned Lagrangian Monte Carlo Method for Turbulent Flow Simulation

A novel computational methodology, termed “Irregularly Portioned Lagrangian Monte Carlo” (IPLMC) is developed for large eddy simulation (LES) of turbulent flows. This methodology is intended for use in the filtered density function (FDF) formulation and is particularly suitable for simulation of chemically reacting flows on massively parallel platforms. The IPLMC facilitates efficient simulations, and thus allows reliable prediction of complex turbulent flames. Sample results are presented of LES of both premixed and non-premixed flames via this method, and the results are assessed via comparison with laboratory data.

A priori assessment of the subgrid scale viscous/scalar dissipation closures in compressible turbulence

An appraisal is made of several subgrid scale (SGS) viscous/scalar dissipation closures via a priori analysis of direct numerical simulation data in a temporally evolving compressible mixing layer. The effects of the filter width, the compressibility level and the Schmidt number are studied for several models. Based on the scaling of SGS kinetic energy, a new formulation for SGS viscous dissipation is proposed. This yields the best overall prediction of the SGS viscous dissipation within the inertial subrange. An SGS scalar dissipation model based on the proportionality of the turbulent time scale with the scalar mixing time scale also performs the best for the filter widths in the inertial subrange. Two dynamic methods are implemented for the determination of the model coefficients. The one based on the global equilibrium of dissipation and production is shown to be more satisfactory than the conventional dynamic model.

Progress in Large Eddy Simulation of High Speed Turbulent Mixing and Reaction

The filtered density function (FDF) method is being extended for subgrid scale (SGS) closure as required in large eddy simulation (LES) of high speed turbulent reacting flows. The primary advantage of FDF is that the effects of SGS chemical reactions appear in a closed form. The suitable means of invoking FDF in high speed flows is via consideration of the SGS statistics of the energy, the pressure, the velocity and the scalar fields. This formulation is under way in which modeled stochastic differential equations are being developed to account for the SGS transport of all of these fields. The simplest subset of this model considers the SGS transport of the scalar field. Results are presented of our latest LES of scalar mixing in a high speed shear flow via this method. M odeling and simulation of high speed turbulent reacting flows have been the subject of widespread investigations for several decades now. The state of the practice in simulations of such flows typically solves the Reynolds averaged Navier-Stokes (RANS) equations, expanded to include scalars’ transport. Closure is usually through two-equation turbulence models in conjunction with Boussinesq and gradient-diffusion assumption. Chemical reaction source terms are usually formulated using the law of mass action, and the effects of turbulence fluctuations on reaction rates are either completely ignored or modeled via eddy break up and/or assumed probability density function (PDF) methods. This first generation model has been incorporated in majority of CFD codes worldwide. This technology, however, is severely limited in many respects and the shortcomings are well documented in literature. The physics of high speed combustion is rich with many complexities. From the modeling standpoint, some of the primary issues are the development of accurate descriptors for turbulence, chemistry, compressibility, and turbulence-chemistry interactions. The phenomenon of mixing at both micro- and macro-scales and its role and capability (or lack thereof) to provide a suitable environment for combustion and the subsequent effects of combustion on hydrodynamics, are at the heart of hypersonic physics. From the computational viewpoint, novel strategies are needed to allow affordable simulation of complex flows with state-of-the art physical models. The power of parallel scientific computing now allows inclusion of more complex physical phenomena which in turn translate into greatly improved predictive capabilities. It is now widely accepted that the optimum means of capturing the detailed, unsteady physics of turbulent combustion is via large eddy simulation (LES). 1, 2 The primary issue associated with LES is accurate modeling of the subgrid scale (SGS) quantities. The filtered density function (FDF) methodology 1, 3 has proven particularly effective for this closure. The FDF is the counterpart of the probability density function (PDF) methodology in RANS. 3, 4 The idea of using the PDF method for LES was first suggested by Givi. 5 But it was the formal definition of FDF by Pope 6 which provided the mathematical foundation of LES/FDF. Within the past several years, significant progress has been made in developments and applications of the FDF. In its simplest form, the “assumed” FDF method was suggested by Madnia et al., 7, 8 where all of the drawbacks of this simple approach were highlighted. Similar to PDF methods, there are different ways by which transport of the FDF can be considered. These differ in the flow variables which are being considered, and whether the method is applicable to constant density or variable density flows. The marginal scalar FDF (SFDF) was developed by Colucci et al. 9 This work demonstrated, for the first time, that solution of

Interactive Exploration of Stress Tensors Used in Computational Turbulent Combustion

Simulation and modeling of turbulent flow, and of turbulent reacting flow in particular, involves solving for and analyzing time-dependent and spatially dense tensor quantities, such as turbulent stress tensors. The interactive visual exploration of these tensor quantities can effectively steer the computational modeling of combustion systems. In this chapter, we discuss the challenges in dense symmetric-tensor visualization applied to turbulent combustion calculation, and analyze the feasibility of using several established tensor visualization techniques in the context of exploring space-time relationships in computationally-simulated combustion tensor data. To tackle the pervasive problems of occlusion and clutter, we propose a solution combining techniques from information and scientific visualization. Specifically, the proposed solution combines a detailed 3D inspection view based on volume rendering with glyph-based representations—used as 2D probes—while leveraging interactive filtering and flow salience cues to clarify the structure of the tensor datasets. Side-by-side views of multiple timesteps facilitate the analysis of time-space relationships. The resulting prototype enables an analysis style based on the overview first, zoom and filter, then details on demand paradigm originally proposed in information visualization. The result is a visual analysis tool to be utilized in debugging, benchmarking, and verification of models and solutions in turbulent combustion. We demonstrate this analysis tool on three example configurations and report feedback from combustion researchers.

A clustering method for identifying regions of interest in turbulent combustion tensor fields

Production of electricity and propulsion systems involve turbulent combustion. Computational modeling of turbulent combustion can improve the efficiency of these processes. However, large tensor datasets are the result of such simulations; these datasets are difficult to visualize and analyze. In this work we present an unsupervised statistical approach for the segmentation, visualization and potentially the tracking of regions of interest in large tensor data. The approach employs a machine learning clustering algorithm to locate and identify areas of interest based on specified parameters such as strain tensor value. Evaluation on two combustion datasets shows this approach can assist in the visual analysis of the combustion tensor field.