Large Eddy Simulation Scheme Research Articles

Bridging Large Eddy Simulation and Reduced-Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives

Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical stabilization or closure models in order to account for the effect of the discarded modes. The literature on ROM closures and stabilizations is large and growing fast. In this paper, instead of reviewing all the ROM closures and stabilizations, we took a more modest step and focused on one particular type of ROM closure and stabilization that is inspired by large eddy simulation (LES), a classical strategy in computational fluid dynamics (CFD). These ROMs, which we call LES-ROMs, are extremely easy to implement, very efficient, and accurate. Indeed, LES-ROMs are modular and generally require minimal modifications to standard (“legacy”) ROM formulations. Furthermore, the computational overhead of these modifications is minimal. Finally, carefully tuned LES-ROMs can accurately capture the average physical quantities of interest in challenging convection-dominated flows in science and engineering applications. LES-ROMs are constructed by leveraging spatial filtering, which is the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. It also “bridges” two distinct research fields (LES and ROMs) that have been disconnected until now. This paper is a review of LES-ROMs, with a particular focus on the LES concepts and models that enable the construction of LES-inspired ROMs and the bridging of LES and reduced-order modeling. This paper starts with a description of a versatile LES strategy called evolve–filter–relax (EFR) that has been successfully used as a full-order method for both incompressible and compressible convection-dominated flows. We present evidence of this success. We then show how the EFR strategy, and spatial filtering in general, can be leveraged to construct LES-ROMs (e.g., EFR-ROM). Several applications of LES-ROMs to the numerical simulation of incompressible and compressible convection-dominated flows are presented. Finally, we draw conclusions and outline several research directions and open questions in LES-ROM development. While we do not claim this review to be comprehensive, we certainly hope it serves as a brief and friendly introduction to this exciting research area, which we believe has a lot of potential in the practical numerical simulation of convection-dominated flows in science, engineering, and medicine.

SIMULATING SPRAY DYNAMICS WITH A FINITE ELEMENT METHOD FOR INTERNAL COMBUSTION ENGINES USING LARGE EDDY SIMULATIONS

Spray dynamics in an internal combustion engine is comprised of complex phenomena while interacting with unsteady turbulence. Physics requires detailed modeling of the dynamics for spray and carrier gases to accurately predict a spray's fate. Large eddy simulation (LES) turbulence modeling approaches are capable predictors of the turbulent processes and of dynamically modeling sub-grid scales, therefore enabling calculation of model coefficients for the smallest resolved scale. Dynamic LES methods are also well suited for unsteady flows associated with spray injection and engine fluid dynamics. In this study, for the first time, a dynamic Verman LES scheme employed in a stabilized a finite element (FE) framework is used to model the spray process with emphasis on injected fuels for simulating internal combustion engines. Spray modeling often comprises a coupled Eulerian-Lagrangian approach to capture the droplet/particle dynamics, where the droplets are modeled in the Lagrangian frame, interacting with the gas. The momentum and heat exchange between the fluid gases and the evaporating and atomizing spray droplets are modeled in a two-way coupling system as described in this paper. Direct injected liquid is modeled in this paper as a spherical ligament of fuel and ligament breakup to atomization use our version of the Kelvin Helmholtz break-up scheme. Discussed are models and methods of the whole system in some detail. The method for simulation of the fluid's momentum, heat transfer, and turbulence are discussed as is the system to evaluate droplet or ligament properties. Validation or results of the modeling are presented on test cases as determined by the Engine Combustion Network, base cases G along with some benchmarking cases. We demonstrate in the paper by using the FE method combined with the Verman LES model, and our version of the Kelvin Helmholtz-Rayleigh Taylor spray break-up model combined with two-way coupling is quite capable of modeling sprays, having distinct and significant advantages over the more traditional finite volume discretization framework using similar spray modeling methods.

Meshless Large-Eddy Simulation of Propeller–Wing Interactions with Reformulated Vortex Particle Method

The vortex particle method (VPM) has gained popularity in recent years due to a growing need to predict complex aerodynamic interactions during the preliminary design of electric multirotor aircraft. However, VPM is known to be numerically unstable when vortical structures break down close to the turbulent regime. In recent work, the VPM has been reformulated as a large-eddy simulation (LES) in a scheme that is both meshless and numerically stable without increasing its computational cost. In this study, we build upon this meshless LES scheme to create a solver for interactional aerodynamics. Propeller blades are introduced through an actuator line model following well-established practices for LES. A novel, vorticity-based actuator surface model (ASM) is developed for wings, which is suitable for propeller–wing interactions when a wake impinges on the surface of a wing. This ASM imposes the no-flow-through condition at the airfoil centerline by calculating the circulation that meets this condition and by immersing the associated vorticity in the LES following a pressure-like distribution. Extensive validation of propeller–wing interactions is presented by simulating a tailplane with tip-mounted propellers and a blown wing with propellers mounted midspan.

Stable Vortex Particle Method Formulation for Meshless Large-Eddy Simulation

A novel formulation of the vortex particle method (VPM) is developed for large-eddy simulation (LES) in a meshless scheme that is numerically stable. A new set of VPM governing equations are derived from the LES-filtered Navier–Stokes equations. The new equations reinforce the conservation of angular momentum by resizing vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures, where the predominant cascade mechanism is vortex stretching. The mean and fluctuating components of turbulent flow and Reynolds stresses are validated through the simulation of a turbulent round jet. The computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100 times faster than a mesh-based LES with similar fidelity. The implementation of our meshless LES scheme is released as open-source software, called FLOWVPM.

Toward the use of LES for industrial complex geometries. Part I: automatic mesh definition

With the constant increase of computational power for the past years, Computational Fluid Dynamics (CFD) has become an essential part of the design in complex industrial processes. In this context, among the scale resolving numerical methods, Large-Eddy Simulation (LES) has become a valuable tool for the simulation of complex unsteady flows. To generalise the industrial use of LES, two main limitations are identified. First, the generation of a proper mesh can be a difficult task, which often relies on user-experience. Secondly, the ‘time-to-solution’ associated with the LES approach can be prohibitive in an industrial context. In this work, these two challenges are addressed in two parts. In this Part I, an automatic procedure for mesh definition is proposed, whereas the Part II is devoted to numerical technique to reduce the LES ‘time-to-solution’. The main goal of these works is then to develop an accurate LES strategy at an optimised computational cost. Concerning the mesh definition, because LES is based on separation between resolved and modelled subgrid-scales, the quality of the computed solution is then directly linked to the quality of the mesh. However, the definition of an adequate mesh is still an issue when LES is used to predict the flow in an industrial complex geometry without a priori knowledge of the flow dynamics. This first part presents a user-independent approach for both the generation of an initial mesh and the convergence of the mesh in the LES framework. An automatic mesh convergence strategy is proposed to ensure LES accuracy. This strategy is built to guarantee a mesh-independent mean field kinetic energy budget. The mean field kinetic energy is indeed expected to be mesh independent since only turbulent scales should be unresolved in LES. The approach is validated on canonical cases, a turbulent round jet and a turbulent pipe flow. Finally, the PRECCINSTA swirl burner is considered as a representative case of complex geometry. First, an algorithm for the generation of an unstructured mesh from a STL file is proposed to generate a coarse initial mesh, before applying the mesh convergence procedure. The overall strategy including automatic first mesh generation and its automatic adaptation paves the way to use LES approach as a decision support tool for various applications, provided that the ‘time-to-solution’ is compatible with the applications constraint. A second paper, referred as Part II, is devoted to the reduction of this time.

Applications of Large-eddy Simulation Method for Flow Prediction of Internal Combustion Engines

Due to the rapid development in the field of computer science, the computational power has increased exponentially. Computers these days have become convenient tools for all industries, including car manufacturing industry. Car manufacturers use computers to simulate the conditions under which car components are working in order to see the performance. Large Eddy Simulation (LES) is a kind of computational fluid dynamic method to examine the states and morphologies of fluid like fuels within different car components. LES has been extensively used in predicting the internal flow of the internal combustion engines. This paper summarizes the related applications of the improved version of LES, error predicting scheme for LES and the effectiveness of similar simulating method in the performance prediction of engines. The mechanisms, advantages, drawbacks, improvement, and application of LES and related methodologies are concluded, providing a helpful summarization for other researchers who want to obtain a general knowledge on LES and wish to contribute on fluid simulation.

An analytically reduced chemistry scheme for large eddy simulation of lithium-ion battery fires

The recent evolution of Lithium-Ion cells toward increasing energy-to-weight ratios makes them prone to critical events such as Thermal Runaway. Flammable and toxic gases are suddenly produced from the decomposition of internal components. To avoid an uncontrolled opening of the cell casing, the gases are vented out, which can potentially lead to fire. In this paper, six gaseous mixtures sampled experimentally, based on four different cathode materials are first compared for commonly observed 0D and 1D combustion processes. A single Analytically Reduced Chemistry scheme is derived for the six mixtures to lower computational cost and allow 3D high fidelity simulations. In comparison to the root detailed scheme, the reduced scheme offers low errors and an average speed up of 5.5 when computing targeted 1D flames, making it suitable for a 3D reactive Large Eddy Simulation of a burning so called “18650”-type cell. Such 3D simulations show a true potential to study simple safety design choices prior to any experimental investigation, reducing development costs. Under the same venting conditions, the number of venting holes is predicted to play a crucial role on flame intrinsic behavior.

Aerodynamic stability of typical sea-crossing bridge with streamlined box girder under wave-interfered complex wind fields

Tropical cyclones landing on the coast are usually associated with both strong winds and waves, posing a major threat to sea-crossing bridges. Strong waves riding on the elevated storm surge squeeze the narrow gap between the sea surface and bottom of the bridge deck, thus complicating the wind field and leading to different bridge nonlinear flutter responses as compared with the steady flow field. In this study, to evaluate the bridge safety under such circumstances, wind tunnel test was carried out for a typical sea-crossing bridge with streamlined box girder based on a developed dynamic response test system for simulating the coupling effect of wind, wave, and current on bridges, where the clearance, underneath the bridge deck, and wave speed can be systematically adjusted to investigate the wind field characteristics and bridge nonlinear flutter response. Numerical simulation with the LES (large eddy simulation) scheme was employed to successfully visualize the wind field around the bridge and the mechanism of the nonlinear flutter response was analyzed in detail. The results of this preliminary investigation show that: (a) In the wind tunnel tests, when the wave crest passes under the bridge, the acceleration effect due to the narrow gap can lead to an increase for the nonlinear flutter amplitude of the bridge, which threatens the structural safety; (b) The measured wind speed at the bridge site exhibits strong turbulence intensity and non-Gaussian distribution tendency; and (c) Based on the numerical simulation, the airflow between the wave crest and the main structure features a large vertical velocity component, leading to a large AOA (angle of attack) value of the incoming flow. Meanwhile, the air pressure around the girder is unevenly distributed, thus unavoidably weakening the aerodynamic stability of the bridge.

High-order gas-kinetic scheme for large eddy simulation of turbulent channel flows

In this study, the high-order gas kinetic scheme (GKS) is employed for explicit large eddy simulation (hereafter referred to simply as “LES”) and implicit large eddy simulation (iLES) of turbulent channel flows. The main objective is to compare the performance of iLES and LES in the high-order finite volume framework, and study which is most suitable for turbulence simulation. The prediction abilities of different explicit LES models and iLES method on various statistics and flow structures are compared. Most results from both iLES and explicit LES are very close to those of direct numerical simulation. Moreover, iLES is generally superior to explicit LES in predicting several important flow properties, including the mean velocity profiles, Reynolds stress, and Q-criterion iso-surfaces. This superior performance of iLES may arise that the numerical dissipation of the high-order scheme is enough to replace the subgrid dissipation needed in large eddy simulation of turbulence. If the explicit LES model is further adopted, the dissipation will increase, so the results degrade. The overall satisfactory results show that the high-order GKS can provide appropriate numerical dissipation and is suitable for iLES of turbulence.

Backflow stabilization by deconvolution-based large eddy simulation modeling

In the numerical simulations of incompressible fluids, the occurrence of incoming flows through outlet boundaries where Neumann conditions are prescribed may introduce the numerical instability known as the backflow instability. This backflow instability is related to the nonlinear convective term and is often challenging the numerical simulation of the blood flow in large vessels. In fact, the alternation of systole and diastole induces backflows at the outlets, which are usually Neumann boundaries since the lack of velocity data requires the prescription of traction/pressure conditions. The Reynolds numbers that trigger the backflow instability are generally moderate (in the range of a few hundreds and above).In this work, we prove that a particular Large Eddy Simulation (LES) model implicitly stabilizes the backflow instability. This LES model uses deconvolution filters and is the basis of the so-called Evolve-Filter-Relax scheme recently introduced by Layton, Rebholz and their collaborators as an effective alternative to Direct Numerical Simulations for the moderate or large Reynolds number flow. With a judicious selection of the parameters of this LES scheme, it is possible to suppress the term that triggers the numerical backflow instability, so to obtain reliable and efficient numerical simulations. This is particularly attractive in computational clinical studies, where many cases need to be studied in a relatively short time.We provide a rigorous proof of our statement and numerical evidence that corroborates the theory on both idealized and realistic cases. For the latter, we consider a patient-specific aortic aneurysm geometry. Aortic simulations feature Reynolds numbers and flow regimes that particularly benefit from this serendipity (aka ‘two-birds-one-stone’) circumstance, where a LES modeling is stabilizing a numerical artifact.

Improving Lake-Breeze Simulation with WRF Nested LES and Lake Model over a Large Shallow Lake

AbstractThe Weather Research and Forecasting (WRF) Model is used in large-eddy simulation (LES) mode to investigate a lake-breeze case occurring on 12 June 2012 over the Lake Taihu region of China. Observational data from 15 locations, wind profiler radar, and the Moderate Resolution Imaging Spectroradiometer (MODIS) are used to evaluate the WRF nested-LES performance in simulating lake breezes. Results indicate that the simulated temporal and spatial variations of the lake breeze by WRF nested LES are consistent with observations. The simulations with high-resolution grid spacing and the LES scheme have a high correlation coefficient and low mean bias when evaluated against 2-m temperature, 10-m wind, and horizontal and vertical lake-breeze circulations. The atmospheric boundary layer (ABL) remains stable over the lake throughout the lake-breeze event, and the stability becomes even stronger as the lake breeze reaches its mature stage. The improved ABL simulation with LES at a grid spacing of 150 m indicates that the non-LES planetary boundary layer parameterization scheme does not adequately represent subgrid-scale turbulent motions. Running WRF fully coupled to a lake model improves lake-surface temperature and consequently the lake-breeze simulations. Allowing for additional model spinup results in a positive impact on lake-surface temperature prediction but is a heavy computational burden. Refinement of a water-property parameter used in the Community Land Model, version 4.5, within WRF and constraining the lake-surface temperature with observational data would further improve lake-breeze representation.

On the use of kinetic energy preserving DG-schemes for large eddy simulation

Recently, element based high order methods such as Discontinuous Galerkin (DG) methods and the closely related flux reconstruction (FR) schemes have become popular for compressible large eddy simulation (LES). Element based high order methods with Riemann solver based interface numerical flux functions offer an interesting dispersion dissipation behavior for multi-scale problems: dispersion errors are very low for a broad range of scales, while dissipation errors are very low for well resolved scales and are very high for scales close to the Nyquist cutoff. In some sense, the inherent numerical dissipation caused by the interface Riemann solver acts as a filter of high frequency solution components. This observation motivates the trend that element based high order methods with Riemann solvers are used without an explicit LES model added. Only the high frequency type inherent dissipation caused by the Riemann solver at the element interfaces is used to account for the missing sub-grid scale dissipation. Due to under-resolution of vortical dominated structures typical for LES type setups, element based high order methods suffer from stability issues caused by aliasing errors of the non-linear flux terms. A very common strategy to fight these aliasing issues (and instabilities) is so-called polynomial de-aliasing, where interpolation is exchanged with projection based on an increased number of quadrature points. In this paper, we start with this common no-model or implicit LES (iLES) DG approach with polynomial de-aliasing and Riemann solver dissipation and review its capabilities and limitations. We find that the strategy gives excellent results, but only when the resolution is such, that about 40% of the dissipation is resolved. For more realistic, coarser resolutions used in classical LES e.g. of industrial applications, the iLES DG strategy becomes quite inaccurate. We show that there is no obvious fix to this strategy, as adding for instance a sub-grid-scale models on top doesn't change much or in worst case decreases the fidelity even more. Finally, the core of this work is a novel LES strategy based on split form DG methods that are kinetic energy preserving. The scheme offers excellent stability with full control over the amount and shape of the added artificial dissipation. This premise is the main idea of the work and we will assess the LES capabilities of the novel split form DG approach when applied to shock-free, moderate Mach number turbulence. We will demonstrate that the novel DG LES strategy offers similar accuracy as the iLES methodology for well resolved cases, but strongly increases fidelity in case of more realistic coarse resolutions.

Initial conditions and modeling for simulations of shock driven turbulent material mixing

Abstract We focus on the simulation of shock-driven material mixing driven by flow instabilities and initial conditions (IC). Beyond complex multi-scale resolution issues of shocks and variable density turbulence, me must address the equally difficult problem of predicting flow transition promoted by energy deposited at the material interfacial layer during the shock interface interactions. Transition involves unsteady large-scale coherent-structure dynamics capturable by a large eddy simulation (LES) strategy, but not by an unsteady Reynolds-Averaged Navier–Stokes (URANS) approach based on developed equilibrium turbulence assumptions and single-point-closure modeling. On the engineering end of computations, such URANS with reduced 1D/2D dimensionality and coarser grids, tend to be preferred for faster turnaround in full-scale configurations. With suitable initialization around each transition – e.g., reshock, URANS can be used to simulate the subsequent near-equilibrium weakly turbulent flow. We demonstrate 3D state-of-the-art URANS performance in one such flow regime, in the context of a sequential LES/URANS hybrid simulation strategy. We first simulate canonical shock-tube (AWE and CEA) experiments with an implicit LES (ILES) strategy. We report new validation studies benchmarking ILES with the available turbulence velocity and mixing data from the CEA laboratory studies. In turn, the ILES generated flow data is then used to initialize and as reference to assess the 3D URANS. We find that by prescribing (ILES generated) physics-based 3D IC and allowing for 3D convection with just enough resolution, the computed dissipation in 3D URANS blends effectively with the modeled dissipation to yield significantly improved statistical predictions.

All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence

ABSTRACTAs a type of shock-capturing scheme, the traditional Roe scheme fails in large eddy simulation (LES) because it cannot reproduce important turbulent characteristics, such as the famous k−5/3 spectral law, as a consequence of the large numerical dissipation. In this work, the Roe scheme is divided into five parts, namely, ξ, δUp, δpp, δUu, and δpu, which denote basic upwind dissipation, pressure difference-driven modification of interface fluxes, pressure difference-driven modification of pressure, velocity difference-driven modification of interface fluxes, and velocity difference-driven modification of pressure, respectively. Then, the role of each part in the LES of homogeneous decaying turbulence with a low Mach number is investigated. Results show that the parts δUu, δpp, and δUp have little effect on LES. Such minimal effect is integral to computational stability, especially for δUp. The large numerical dissipation is due to ξ and δpu, each of which features a larger dissipation than the sub-grid scale model. On the basis of these conditions, an improved all-speed Roe scheme for LES is proposed. This scheme can provide satisfactory LES results even for coarse grid resolutions with usually adopted second-order reconstructions for the finite volume method.

Towards robust unstructured turbomachinery large eddy simulation

Industrial legacy codes usually have had long pedigrees within companies, and are deeply embedded into design processes. As the affordability and availability of computing power has increased, these codes have found themselves pushed into service as large eddy simulation solvers. The approximate Riemann solver of Roe, which is frequently used as the core method in such legacy codes, is shown to need much user care when adopted as the discretisation scheme for large eddy simulation. A kinetic energy preserving (KEP) scheme—which retains the same advantageous stencil and communications halo as the original Roe scheme—is instead implemented and tested. The adaptations of code required to switch between the two schemes were found to be extremely straightforward. As the KEP scheme intrinsically bounds the growth of the kinetic energy, it is significantly more stable than the classical non-dissipative schemes. This means that the expensive smoothing terms of the Roe scheme are not always necessary. Instead, an explicit subgrid scale turbulence model can be sensibly applied. As such, a range of mixed linear–non-linear turbulence models are tested. The performance of the KEP scheme is then tested against that of the Roe for canonical flows and engine-realistic turbine blade cutback trailing edge cases. The new KEP scheme is found to perform better than the original in all cases. A range of mesh topologies: hexahedral; prismatic; and tetrahedral; are also tested with both schemes, and the KEP scheme is again found to perform significantly better on all mesh types for these flows.

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

In this work we study the performance of some variational multiscale models (VMS) in the large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by different subgrid scale approximations which include either static or dynamic subscales, linear or nonlinear multiscale splitting, and different choices of the subscale space. After a brief review of these models, we discuss some implementation aspects particularly relevant to the simulation of turbulent flows, namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used. We analyze the energy conservation (and numerical dissipation) of the alternative VMS formulations, which is numerically evaluated. In the numerical study, we have considered three well known problems: the decay of homogeneous isotropic turbulence, the Taylor–Green vortex problem and the turbulent flow in a channel. We compare the results obtained using different VMS models, paying special attention to the effect of using orthogonal subscale spaces. The VMS results are also compared against classical LES scheme based on filtering and the dynamic Smagorinsky closure. Altogether, our results show the tremendous potential of VMS for the numerical simulation of turbulence. Further, we study the sensitivity of VMS to the algorithmic constants and analyze the behavior in the small time step limit. We have also carried out a computational cost comparison of the different formulations. Out of these experiments, we can state that the numerical results obtained with the different VMS formulations (as far as they converge) are quite similar. However, some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different. The dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness.

Study on Wind Load Characteristics of a Super Tall Building Based on Numerical Simulation

This paper present some selected numerical results of a typical super-tall building based on a new Large Eddy Simulation scheme. The spatial correlation of local wind forces were presented and discussed in detail. The probabilistic characteristics of fluctuating wind loads were evaluated. Furthermore, the along-wind and across-wind spectral characteristics were studied and compared with the von Karman spectrum. The output of this study is expected to be of considerable interest and practical use to professionals and researchers involved in the design of super-tall buildings.

A novel principal component analysis-based acceleration scheme for LES–ODT: An a priori study

A parameterization of the composition space based on principal component analysis (PCA) is proposed to represent the transport equations with the one-dimensional turbulence (ODT) solutions of a hybrid large-eddy simulation (LES) and ODT scheme. The 1D ODT solutions are embedded in the 3D LES domain and solve for thermo-chemical scalars; while, the LES governing equations solve for the flow. An a priori validation of the proposed approach is implemented based on stand-alone ODT solutions of the Sandia Flame F, which is characterized by different regimes of combustion starting with pilot stabilization, to extinction and reignition and self-stabilized combustion. The PCA analysis is carried out with a full set of the thermo-chemical scalars’ vector as well as a subset of this vector. The subset is made up primarily of major species and temperature. The results show that the different regimes are reproduced using only three principal components for the thermo-chemical scalars based on the full and a subset of the thermo-chemical scalars’ vector. Reproduction of the source term of the principal components represents a challenge, because of the inherent non-linearity of reaction rates’ expressions. It is found that using the subset of the thermo-chemical scalars’ vector both minor species and the first three principal components source terms are reasonably well predicted.

A semi‐implicit scheme for large Eddy simulation of piston engine flow and combustion

SUMMARYA semi‐implicit scheme is presented for large eddy simulation of turbulent reactive flow and combustion in reciprocating piston engines. First, the governing equations in a deforming coordinate system are formulated to accommodate the moving piston. The numerical scheme is made up of a fourth‐order central difference for the diffusion terms in the transport equations and a fifth‐order weighted essentially nonoscillatory (WENO) scheme for the convective terms. A second‐ order Adams–Bashforth scheme is used for time integration. For higher density ratios, it is combined with a predictor–corrector scheme. The numerical scheme is explicit for time integration of the transport equations, except for the continuity equation which is used together with the momentum equation to determine the pressure field and velocity field by using a Poisson equation for the pressure correction field. The scheme is aimed at the simulation of low Mach number flows typically found in piston engines. An efficient multigrid method that can handle high grid aspect ratio is presented for solving the pressure correction equation. The numerical scheme is evaluated on two test engines, a laboratory four‐stroke engine with rectangular‐shaped engine geometry where detailed velocity measurements are available, and a modified truck engine with practical cylinder geometry where lean ethanol/air mixture is combusted under a homogeneous charge compression ignition (HCCI) condition. Copyright © 2012 John Wiley & Sons, Ltd.

Projection method with self‐adaptive time steps for LES of ignition and extinction in non‐premixed jet flames

AbstractIn this paper, a modified projection method is combined with a self‐adaptive time step procedure to develop numerical scheme for large eddy simulation (LES) of low Ma number turbulent reactive flows. The projection method introduced by Chorin is modified in this study to satisfy the simulation requirement of low Ma number reactive flow. The time step in this computation is automatically determined according to the time scales of both chemical reaction and turbulent fluctuations. This enables the simulation to capture detailed flow structures with less computational time. Numerical simulation of methane–air jet flames is carried out as an example to validate the developed numerical scheme. The mechanism of a simplified 4‐step chemical kinetics is applied for the methane–air reaction. The dynamic model is adopted for the turbulent motion of sub‐grid scale (SGS). The dynamic similarity model is used as the SGS model for the reaction rate. The LES results satisfactorily depict the ignition process of the turbulent jet flames and illustrate lucid and detailed coherent structures of the fully developed turbulent reactive jet flow. The LES results also exhibit the mechanism and characteristics of local extinction. The method developed in this study provides an effective way to capture more flow details with less computational time. In addition the method also helps one to investigate the mechanism of ignition and local extinction in jet flames. Copyright © 2008 John Wiley & Sons, Ltd.