Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches

In large-eddy simulation (LES) of turbulent dispersed flows, modelling and numerical inaccuracies are incurred because LES provides only an approximation of the filtered velocity. Interpolation errors can also occur (on coarse-grained domains, for instance). These inaccuracies affect the estimation of the forces acting on particles, obtained when the filtered fluid velocity is supplied to the Lagrangian equation of particle motion, and accumulate in time. As a result, particle trajectories in LES fields progressively diverge from particle trajectories in DNS fields, which can be considered as the exact numerical reference: the flow fields seen by the particles become less and less correlated, and the forces acting on particles are evaluated at increasingly different locations. In this paper, we review models and strategies that have been proposed in the Eulerian\u2013Lagrangian framework to correct the above-mentioned sources of inaccuracy on particle dynamics and to improve the prediction of particle dispersion in turbulent dispersed flows

Progress Toward Affordable High Fidelity Combustion Simulations Using Filtered Density Functions for Hypersonic Flows in Complex Geometries

Significant progress has been made in the development of subgrid scale (SGS) closures based on a filtered density function (FDF) for large eddy simulations (LES) of turbulent reacting flows. The FDF is the counterpart of the probability density function (PDF) method, which has proven effective in Reynolds averaged simulations (RAS). However, while systematic progress is being made advancing the FDF models for relatively simple flows and lab-scale flames, the application of these methods in complex geometries and high speed, wall-bounded flows with shocks remains a challenge. The key difficulties are the significant computational cost associated with solving the FDF transport equation and numerically stiff finite rate chemistry. For LES/FDF methods to make a more significant impact in practical applications a pragmatic approach must be taken that significantly reduces the computational cost while maintaining high modeling fidelity. An example of one such ongoing effort is at the NASA Langley Research Center, where the first generation FDF models, namely the scalar filtered mass density function (SFMDF) are being implemented into VULCAN, a production-quality RAS and LES solver widely used for design of high speed propulsion flowpaths. This effort leverages internal and external collaborations to reduce the overall computational cost of high fidelity simulations in VULCAN by: implementing high order methods that allow reduction in the total number of computational cells without loss in accuracy; implementing first generation of high fidelity scalar PDF/FDF models applicable to high-speed compressible flows; coupling RAS/PDF and LES/FDF into a hybrid framework to efficiently and accurately model the effects of combustion in the vicinity of the walls; developing efficient Lagrangian particle tracking algorithms to support robust solutions of the FDF equations for high speed flows; and utilizing finite rate chemistry parametrization, such as flamelet models, to reduce the number of transported reactive species and remove numerical stiffness. This paper briefly introduces the SFMDF model (highlighting key benefits and challenges), and discusses particle tracking for flows with shocks, the hybrid coupled RAS/PDF and LES/FDF model, flamelet generated manifolds (FGM) model, and the Irregularly Portioned Lagrangian Monte Carlo Finite Difference (IPLMCFD) methodology for scalable simulation of high-speed reacting compressible flows

Modelling of the evolution of a droplet cloud in a turbulent flow

The effects of droplet inertia and turbulent mixing on the droplet number density distribution in a turbulent flow field are studied. A formulation of the turbulent convective diffusion equation for the droplet number density, based on the modified Fully Lagrangian Approach, is proposed. The Fully Lagrangian Approach for the dispersed phase is extended to account for the Hessian of transformation from Eulerian to Lagrangian variables. Droplets with moderate inertia are assumed to be transported and dispersed by large scale structures of a filtered field in the Large Eddy Simulation (LES) framework. Turbulent fluctuations, not visible in the filtered solution for the droplet velocity field, induce an additional diffusion mass flux and hence additional dispersion of the droplets. The Lagrangian formulation of the transport equation for the droplet number density and the modified Fully Lagrangian Approach (FLA) make it possible to resolve the flow regions with intersecting droplet trajectories in the filtered flow field. Thus, we can cope successfully with the problems of multivalued filtered droplet velocity regions and caustic formation. The spatial derivatives for the droplet number density are calculated by projecting the FLA solution on the Eulerian mesh, resulting in a hybrid Lagrangian–Eulerian approach to the problem. The main approximations for the method are supported by the calculation of droplet mixing in an unsteady one-dimensional flow field formed by large-scale oscillations with an imposed small-scale modulation. The results of the calculations for droplet mixing in decaying homogeneous and isotropic turbulence are validated by the results of Direct Numerical Simulations (DNS) for several values of the Stokes number

A volume-filtered description of compressible particle-laden flows

In this work, we present a rigorous derivation of the volume-filtered viscous compressible Navier–Stokes equations for disperse two-phase flows. Compared to incompressible flows, many new unclosed terms appear. These terms are quantified via a posteriori filtering of two-dimensional direct simulations of shock-particle interactions. We demonstrate that the pseudo-turbulent kinetic energy (PTKE) systematically acts to reduce the local gas-phase pressure and consequently increase the local Mach number. Its magnitude varies with volume fraction and filter size, which can be characterized using a Knudsen number based on the filter size and inter-particle spacing. A transport equation for PTKE is derived and closure models are proposed to accurately capture its evolution. The resulting set of volume-filtered equations are implemented within a high-order Eulerian–Lagrangian framework. An interphase coupling strategy consistent with the volume filtered formulation is employed to ensure grid convergence. Finally PTKE obtained from the volume-filtered Eulerian–Lagrangian simulations are compared to a series of two- and three-dimensional direct simulations of shocks passing through stationary particles

Computational models for the simulation of turbulent poly-dispersed flows: Large Eddy Simulation and Quadrature-Based Moment Method

This work focuses on the development of efficient computational tools for the simulation of turbulent multiphase polydispersed flows. In terms of methodologies we focus here on the use of Large Eddy Simulation (LES) and Quadrature-Based Methods of Moments (QBMM). In terms of applications the work is finalised, in order to be applied in the future, to particle production processes (precipitation and crystallisation in particular). An important part of the work concerns the study of the flow field in a Confined Impinging Jets Reactor (CIJR), frequently used in particle production processes. The first part is limited to the comparison and analysis of micro Particle Image Velocimetry (μPIV) experiments, carried out in a previous work, and Direct Numerical Simulation (DNS), carried out in this thesis. In particular the effects of boundary and operating conditions are studied and the numerical simulations are used to understand the experimental predictions and demonstrate the importance of unavoidable fluctuations in the experimental inlets. This represents a preparatory work for the LES modelling of the CIJR. Before investigating the accuracy of LES predictions for this particular application, the model and the implementation are studied in a more general context, represented by a well-known test case such as the periodic turbulent channel flow: the LES model implementation in TransAT, the code used in this work, is compared with DNS data and with predictions of other codes. LES simulations for the CIJR, provided with the proper boundary conditions obtained by the previous DNS/μPIV study, are then performed and compared with experiments, validating the model in a more realistic test case. Since particle precipitation and crystallization often result in complex interactions between particles and the continuous phase, in the second part of the work particular attention has been paid in the modelling of the momentum transfer and the resulting velocity of the particles (relative to the fluid). In particular the possibility of describing poly-disperse fluid-solid systems with QBMM together with LES and Equilibrium Eulerian Model (EEM) is assessed. The study is performed by comparing our predictions with DNS Lagrangian data in the turbulent channel flow previously described, seeded with particles corresponding to a realistic Particle Size Distribution (PSD). The last part of the work deals with particle collisions, extending QBMM to the investigation of non-equilibrium flows governed by the Boltzmann Equation with a hard-sphere collision kernel. The evolution of the particle velocity distribution is predicted and compared with other methods for kinetic equations such as Lattice Boltzmann Method (LBM), Discrete Velocity Method (DVM) and Grad’s Moment Method (GM). The overall results of this thesis can be extended to a broad range of other applications of single-phase, dispersed multiphase and non-equilibrium flows

Large eddy simulations of a confined rectangular jet

Turbulent flows have the ability to transport momentum and mix species at a higher rate than molecular diffusion alone, which is critical in reacting flows. Of importance to this research is the mixing of liquid-phase high Schmidt number flows for applications in the chemical process industry. Computational fluid dynamics (CFD) has the potential to be used as a tool to improve reactor designs and examine the mixing characteristics but requires extensive validation of the computational models. This research presents detailed analysis and validation of a nonreacting turbulent flow for a confined rectangular jet with a co-flowing fluid using CFD. Large eddy simulations (LES) for the incompressible Filtered Navier-Stokes equations are performed on a partially staggered finite difference grid. A second-order central difference scheme and sixth-order compact scheme are employed for the spatial derivatives. A third-order low storage Runge-Kutta method is used for the temporal derivatives. To reduce computational memory and time requirements, message passing interface (MPI) is implemented and an efficient parallel linear equation solver (Aztec) is utilized for solving the elliptical pressure Poisson equation. Solutions for the momentum and non-reacting scalar transport are obtained for a Reynolds number of 20,000 based on the average velocity at inlet and hydraulic diameter. Validation is performed for the LES by comparing one-point and two-point statistics with particle image velocimetry data for the velocity field and planar laser induced fluorescence measurements for the scalar concentration. Such detailed validation with experiments is performed for the very first time. The effect of different parameters such as grid resolution, numerical schemes and subgrid models on the numerical solution are studied. For the scalar transport, numerical schemes that preserve boundedness are tested and implemented. Overall, the LES compared very well with the experiments and recommendations are made to extend the LES work toward reacting flows

Turbulence: Numerical Analysis, Modelling and Simulation

The problem of accurate and reliable simulation of turbulent flows is a central and intractable challenge that crosses disciplinary boundaries. As the needs for accuracy increase and the applications expand beyond flows where extensive data is available for calibration, the importance of a sound mathematical foundation that addresses the needs of practical computing increases. This Special Issue is directed at this crossroads of rigorous numerical analysis, the physics of turbulence and the practical needs of turbulent flow simulations. It seeks papers providing a broad understanding of the status of the problem considered and open problems that comprise further steps

Enhancement of engine simulation using LES turbulence modeling and advanced numerical schemes

The goal of this study is to develop advanced numerical models and algorithms to improve the accuracy of engine spray combustion simulation. This study developed a large eddy simulation (LES) turbulence model and adaptive mesh refinement (AMR) algorithms to enhance the accuracy and computational efficiency of engine simulation. The LES approach for turbulence modeling is advantageous over the traditional Reynolds Averaged Navier Stokes (RANS) approach due to its capability to obtain more detailed flow information by resolving large-scale structures which are strongly geometry dependent. The current LES approach used a one-equation, non-viscosity, dynamic structure model for the sub-grid stress tensor and also used a gradient method for the sub-grid scalar fluxes. The LES implementation was validated by comparing the predicted spray penetrations and structures in a non-evaporating diesel spray. The present LES model, when coupled with spray breakup and detailed chemistry models, were able to predict the overall cylinder pressure history, heat release rate data, and the trends of NOx and soot emissions with respect to different injection timings and EGR levels in a heavy-duty diesel engine. Results also indicated that the LES model could predict the unsteadiness of in-cylinder flows and have the potential to provide more detailed flow structures compared to the RANS model. AMR algorithms were also developed to improve transient engine spray simulation. It is known that inadequate spatial resolution can cause inaccuracy in spray simulation using the stochastic Lagrangian particle approach due to the over-estimated diffusion and inappropriate liquid-gas phase coupling. Dynamic local mesh refinement, adaptive to fuel spray and vapor gradients, was developed to increase the grid resolution in the spray region. AMR was parallelized using the MPI library and various strategies were also adopted in order to improve the computational efficiency, including timestep control, reduction in search of the neighboring cells on the processor boundaries, and re-initialization of data at each adaptation. The AMR implementation was validated by comparing the predicted spray penetrations and structures. It was found that a coarse mesh using AMR could produce the same results as those using a uniformly fine mesh with substantially reduced computer time. The parallel performance using AMR varied depending on the geometry and simulation conditions. In general, the computations without valve motion or using a fine mesh could obtain better parallel performance than those with valve motion or using a coarse mesh

Studying Turbulence Using Numerical Simulation Databases

The Seventh Summer Program of the Center for Turbulence Research took place in the four-week period, July 5 to July 31, 1998. This was the largest CTR Summer Program to date, involving thirty-six participants from the U. S. and nine other countries. Thirty-one Stanford and NASA-Ames staff members facilitated and contributed to most of the Summer projects. A new feature, and perhaps a preview of the future programs, was that many of the projects were executed on non-NASA computers. These included supercomputers located in Europe as well as those operated by the Departments of Defense and Energy in the United States. In addition, several simulation programs developed by the visiting participants at their home institutions were used. Another new feature was the prevalence of lap-top personal computers which were used by several participants to carry out some of the work that in the past were performed on desk-top workstations. We expect these trends to continue as computing power is enhanced and as more researchers (many of whom CTR alumni) use numerical simulations to study turbulent flows. CTR's main role continues to be in providing a forum for the study of turbulence for engineering analysis and in facilitating intellectual exchange among the leading researchers in the field. Once again the combustion group was the largest. Turbulent combustion has enjoyed remarkable progress in using simulations to address increasingly complex and practically more relevant questions. The combustion group's studies included such challenging topics as fuel evaporation, soot chemistry, and thermonuclear reactions. The latter study was one of three projects related to the Department of Energy's ASCI Program (www.llnl.gov/asci); the other two (rocket propulsion and fire safety) were carried out in the turbulence modeling group. The flow control and acoustics group demonstrated a successful application of the so-called evolution algorithms which actually led to a previously unknown forcing strategy for jets yielding increased spreading rate. A very efficient algorithm for flow in complex geometries with moving boundaries based on the immersed boundary forcing technique was tested with very encouraging results. Also a new strategy for the destruction of aircraft trailing vortices was introduced and tested. The Reynolds Averaged Modeling (RANS) group demonstrated that the elliptic relaxation concept for RANS calculations is also applicable to transonic flows with shocks; however, prediction of laminar/turbulent transition remains an important pacing item. A large fraction of the LES effort was devoted to the development and testing of a new algorithmic procedure (as opposed to phenomenological model) for subgrid scale modeling based on regularized de-filtering of the flow variables. This appears to be a very promising approach, and a significant effort is currently underway to assess its robustness in high Reynolds number flows and in conjunction with numerical methods for complex flows. As part of the Summer Program two review tutorials were given on Turbulent structures in hydrocarbon pool fires (Sheldon Tieszen), and Turbulent combustion modeling: from RANS to LES via DNS (Luc Vervisch); and two seminars entitled Assessment of turbulence models for engineering applications (Paul Durbin) and Subgrid-scale modeling for non-premixed, turbulent reacting flows (James Riley) were presented. A number of colleagues from universities, government agencies, and industry attended the final presentations of the participants on July 31 and participated in the discussions. There are twenty-six papers in this volume grouped in five areas. Each group is preceded with an overview by its coordinator