A parallel, finite-volume algorithm for large-eddy simulation of turbulent flows

A parallel, finite-volume algorithm has been developed for large-eddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear least-square reconstruction, trilinear finite-element interpolation, Roe flux-difference splitting (FDS), and second-order MacCormack time marching. A systematic and consistent means of evaluating the surface and volume integrals of the control volume is described. Parallel implementation is done using the message-passing programming model. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. For the first time, a finite volume method with Roe FDS was used for LES of turbulent flow in a square duct, and the effects of grid resolution, upwind numerical dissipation, and subgrid-scale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe FDS adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 3–5% of the standard Roe FDS dissipation is needed.     

Application of Compact Schemes to Large Eddy Simulation of Turbulent Jets

We present 3-D large eddy simulation (LES) results for a turbulent Mach 0.9 isothermal round jet at a Reynolds number of 100,000 (based on jet nozzle exit conditions and nozzle diameter). Our LES code is part of a Computational Aeroacoustics (CAA) methodology that couples surface integral acoustics techniques such as Kirchhoff's method and the Ffowcs Williams– Hawkings method with LES for the far field noise estimation of turbulent jets. The LES code employs high-order accurate compact differencing together with implicit spatial filtering and state-of-the-art non-reflecting boundary conditions. A localized dynamic Smagorinsky subgrid-scale (SGS) model is used for representing the effects of the unresolved scales on the resolved scales. A computational grid consisting of 12 million points was used in the present simulation. Mean flow results obtained in our simulation are found to be in very good agreement with the available experimental data of jets at similar flow conditions. Furthermore, the near field data provided by the LES is coupled with the Ffowcs Williams–Hawkings method to compute the far field noise. Far field aeroacoustics results are also presented and comparisons are made with experimental measurements of jets at similar flow conditions. The aeroacoustics results are encouraging and suggest further investigation of the effects of inflow conditions on the jet acoustic field.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

LES of bubble dynamics in wake flows

The results of large eddy simulations (LES) of turbulent bubbly wake flows are presented. The LES technique was applied together with the Lagrangian particle dynamics method and a random flow generation (RFG) technique to the cases of a two-phase bubbly mixing layer and the high-Reynolds number bubbly ship-wake flows. The validation was performed on the experimental data for the bubbly mixing layer. Instantaneous distributions and probability density functions of bubbles in the wake were obtained using a joint LES/RFG approach. Separate estimates of bubble decay due to dissolution and buoyancy effects were obtained. The analysis of bubble agglomeration effects was done on the basis of experimental data for a turbulent vortex to satisfy one-way coupling that is used in this study.     

The variational multiscale method for laminar and turbulent flow

Summary  The present article reviews the variational multiscale method as a framework for the development of computational methods for the simulation of laminar and turbulent flows, with the emphasis placed on incompressible flows. Starting with a variational formulation of the Navier-Stokes equations, a separation of the scales of the flow problem into two and three different scale groups, respectively, is shown. The approaches resulting from these two different separations are interpreted against the background of two traditional concepts for the numerical simulation of turbulent flows, namely direct numerical simulation (DNS) and large eddy simulation (LES). It is then focused on a three-scale separation, which explicitly distinguishes large resolved scales, small resolved scales, and unresolved scales. In view of turbulent flow simulations as a LES, the variational multiscale method with three separated scale groups is refered to as a “variational multiscale LES”. The two distinguishing features of the variational multiscale LES in comparison to the traditional LES are the replacement of the traditional filter by a variational projection and the restriction of the effect of the unresolved scales to the smaller of the resolved scales. Existing solution strategies for the variational multiscale LES are presented and categorized for various numerical methods. The main focus is on the finite element method (FEM) and the finite volume method (FVM). The inclusion of the effect of the unresolved scales within the multiscale environment via constant-coefficient and dynamic subgrid-scale modeling based on the subgrid viscosity concept is also addressed. Selected numerical examples, a laminar and two turbulent flow situations, illustrate the suitability of the variational multiscale method for the numerical simulation of both states of flow. This article concludes with a view on potential future research directions for the variational multiscale method with respect to problems of fluid mechanics.     

The computation of massively separated flows using compressible vorticity confinement methods

Vorticity confinement methods have been shown to be very effective in the computation of flows involving the convection of thin vortical layers. These are the only Eulerian methods whereby simulations of these layers remain very thin and persist long distances without significant dissipation. Initially developed by Steinhoff and co-workers for incompressible flow, these methods have been used successfully to predict complex flows, particularly involving helicopter rotors. Recently, the method has been extended to a compressible finite-volume form, which will enable the methods to be used for a much broader class of problems. In this paper, we examine the ability of the compressible vortex confinement methodology to handle an important class of vortex-dominated flows involving massive separation from bluff bodies. We evaluate the effectiveness of the method by comparisons with experimental data and available state-of-the-art computations. An important conclusion of the present work is that vortex confinement applied to massively separated flows, without modeling the viscous terms and on an essentially inviscid grid, can result in a reasonable approximation to turbulent separated flows. The computed flow structures and velocity profiles were in good agreement with time-averaged values of the data and with LES simulations even though the confinement approach utilized more than a factor of 50 fewer cells in the computation (20,000 compare to more the 1 million). The success of the method for these classes of flows may be attributed to the accurate calculation of the rotational inviscid flow which dominates the convection of the large-scale flow structures.     

Globally conservative high-order filters for large-eddy simulation and computational aero-acoustics

In computational aero-acoustics, large-eddy simulations (LES) or direct numerical simulations (DNS) are often employed for flow computations in the source region. As part of the numerical implementation or required modeling, explicit spatial filters are frequently employed. For instance, in LES spatial filters are employed in the formulation of various subgrid-scale (SGS) models such as the dynamic model or the variational multi-scale (VMS) Smagorinsky model; both in LES or DNS, spatial high-pass filters are often used to remove undesired grid-to-grid oscillations. Though these type of spatial filters adhere to local accuracy requirements, in practice, they often destroy global conservation properties in the presence of non-periodic boundaries conditions. This leads to the incorrect prediction of the flow properties near hard boundaries, such as walls. In the current work, we present globally conservative high-order accurate filters, which combine traditional filters at the internal points with one-sided conservative filters near the wall boundary. We test these filters to remove grid-to-grid oscillations both in a channel-flow case and in 2D cavity flow. We find that the use of a non-conservative filter leads to erroneous predictions of the skin friction in channel flows up to 30%. In the cavity-flow simulations, the use of non-conservative filters to remove grid-to-grid oscillations leads to important shifts in the Strouhal number of the dominant mode, and a change of the flow pattern inside the cavity. In all cases, the use of conservative high-order filter formulations to remove grid-to-grid oscillations lead to very satisfactory results. Finally, in our channel-flow test case, we also illustrate the importance of using conservative filters for the formulation of the VMS Smagorinsky model.     

Recent Developments in Variational Multiscale Methods for Large-Eddy Simulation of Turbulent Flow

The variational multiscale method is reviewed as a framework for developing computational methods for large-eddy simulation of turbulent flow. In contrast to other articles reviewing this topic, which focused on large-eddy simulation of turbulent incompressible flow, this study covers further aspects of numerically simulating turbulent flow as well as applications beyond incompressible single-phase flow. The various concepts for subgrid-scale modeling within the variational multiscale method for large-eddy simulation proposed by researchers in this field to date are illustrated. These conceptions comprise (i) implicit large-eddy simulation, represented by residual-based and stabilized methods, (ii) functional subgrid-scale modeling via small-scale subgrid-viscosity models and (iii) structural subgrid-scale modeling via the introduction of multifractal subgrid scales. An overview on exemplary numerical test cases to which the reviewed methods have been applied in the past years is provided, including explicit computational results obtained from turbulent channel flow. Wall-layer modeling, passive and active scalar transport as well as developments for large-eddy simulation of turbulent two-phase flow and combustion are discussed to complete this exposition.     

Study of jet precession, recirculation and vortex breakdown in turbulent swirling jets using LES

Large eddy simulations (LES) are used to investigate turbulent isothermal swirling flows with a strong emphasis on vortex breakdown, recirculation and instability behaviour. The Sydney swirl burner configuration is used for all simulated test cases from low to high swirl and Reynolds numbers. The governing equations for continuity and momentum are solved on a structured Cartesian grid, and a Smagorinsky eddy viscosity model with the localised dynamic procedure is used as the sub-grid scale turbulence model. The LES successfully predicts both the upstream first recirculation zone generated by the bluff body and the downstream vortex breakdown bubble. The frequency spectrum indicates the presence of low frequency oscillations and the existence of a central jet precession as observed in experiments. The LES calculations well captured the distinct precession frequencies. The results also highlight the precession mode of instability in the center jet and the oscillations of the central jet precession, which forms a precessing vortex core. The study further highlights the predictive capabilities of LES on unsteady oscillations of turbulent swirling flow fields and provides a good framework for complex instability investigations.     

Aerodynamic noise simulation of the flow past an airfoil trailing-edge using a hybrid zonal RANS-LES

This paper document the evaluation of a zonal RANS-LES approach for the prediction of broadband and tonal noise generated by the flow past an airfoil trailing edge at a high Reynolds number. A multi-domain decomposition is considered, where the acoustic sources are resolved with a LES sub-domain embedded in the RANS domain. At the RANS-LES interface, a stochastic vortex method is used to generate synthetic turbulent perturbations. The simulations are performed with the general-purpose unstructured control-volume code FLUENT. The far-field noise is calculated using the aeroacoustic analogy of Ffowcs-Williams and Hawkings. The results of the simulation are compared with available acoustic and mean velocity measurements. The investigation demonstrates the ability of this approach to predict the aerodynamic and aeroacoustic properties of the flow. Two simulations are performed in order to address the sensitivity of the results to the perturbation model. The comparison clearly indicates the critical influence of the model.     

An investigation of turbulent open channel flow with heat transfer by large eddy simulation

Large eddy simulation of fully developed turbulent open channel flow with heat transfer is performed. The three-dimensional filtered Navier-Stokes and energy equations are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. Two typical temperature boundary conditions, i.e., constant temperature and constant heat flux being maintained at the free surface, respectively, are used. The objective of this study is to explore the behavior of heat transfer in the turbulent open channel flow for different temperature boundary conditions and to examine the reliability of the LES technique for predicting turbulent heat transfer at the free surface, in particular, for high Prandtl number. Calculated parameters are chosen as the Prandtl number (Pr) from 1 up to 100, the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel depth. Some typical quantities, including the mean velocity, temperature and their fluctuations, heat transfer coefficients, turbulent heat fluxes, and flow structures based on the velocity, vorticity and temperature fluctuations, are analyzed.     

A zonal RANS-LES method to determine the flow over a high-lift configuration

High Reynolds number flows are particularly challenging problems for large-eddy simulations (LES) since small-scale structures in thin and often transitional boundary layers are to be resolved. The range of the turbulent scales is enormous, especially when high-lift configuration flows are considered. For this reason, the prediction of high Reynolds number flow over the entire airfoil using LES requires huge computer resources. To remedy this problem a zonal RANS-LES method for the flow over an airfoil in high-lift configuration at Re_c=1.0×10⁶ is presented. In a first step, a 2D RANS solution is sought, from which boundary conditions are formulated for an embedded LES domain, which comprises the flap and a sub-part of the main airfoil. The turbulent fluctuations in the boundary layers at the inflow region of the LES domain are generated by controlled forcing terms, which use the turbulent shear stress profiles obtained from the RANS solution. The comparison with an LES solution for the full domain and with experimental data shows likewise results for the velocity profiles and wall pressure distributions. The zonal RANS-LES method reduces the computational effort of a full domain LES by approx. 50%.     

Flow over periodic hills - Numerical and experimental study in a wide range of Reynolds numbers

The paper presents a detailed analysis of the flow over smoothly contoured constrictions in a plane channel. This configuration represents a generic case of a flow separating from a curved surface with well-defined flow conditions which makes it especially suited as benchmark case for computing separated flows. The hills constrict the channel by about one third of its height and are spaced at a distance of 9 hill heights. This setup follows the investigation of Fröhlich et al. [Fröhlich J, Mellen CP, Rodi W, Temmerman L, Leschziner MA. Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J Fluid Mech 2005;526:19-66] and complements it by numerical and experimental data over a wide range of Reynolds numbers. We present results predicted by direct numerical simulations (DNS) and highly resolved large-eddy simulations (LES) achieved by two completely independent codes. Furthermore, these numerical results are supported by new experimental data from PIV measurements. The configuration in the numerical study uses periodic boundary conditions in streamwise and spanwise direction. In the experimental setup periodicity is achieved by an array of 10 hills in streamwise direction and a large spanwise extent of the channel. The assumption of periodicity in the experiment is checked by the pressure drop between consecutive hill tops and PIV measurements. The focus of this study is twofold: (i) Numerical and experimental data are presented which can be referred to as reference data for this widely used standard test case. Physical peculiarities and new findings of the case under consideration are described and confirmed independently by different codes and experimental data. Mean velocity and pressure distributions, Reynolds stresses, anisotropy-invariant maps, and instantaneous quantities are shown. (ii) Extending previous studies the flow over periodic hills is investigated in the wide range of Reynolds numbers covering 100?Re?10,595. Starting at very low Re the evolution and existence of physical phenomena such as a tiny recirculation region at the hill crest are documented. The limit to steady laminar flow as well as the transition to a fully turbulent flow stage are presented. For 700?Re?10,595 turbulent statistics are analyzed in detail. Carefully, undertaken DNS and LES predictions as well as cross-checking between different numerical and experimental results build the framework for physical investigations on the flow behavior. New interesting features of the flow were found.     

Analysis of the energy budget in turbulent channel flow using orthogonal wavelets

The spatial and scale statistics of turbulence kinetic energy are examined in turbulent channel flow at Re_τ = 300 using the orthonormal wavelet transform. The behaviour of the production, viscous and transfer terms is examined in terms of their variation with both space and scale. All terms are numerically large at wavenumbers at which a −5/3 slope is apparent in the velocity spectra, and they all exhibit significant spatial variability as evidenced by large flatnesses which increase with decreasing scale size. The flatness of terms involving transfer are particularly large. Attention focusses primarily on the sublayer and local-equilibrium regions: in the former, scale-to-scale flux is large and negative and consistent with conventional “backscatter” in Fourier space. In the linear sublayer, the flux is positive, consistent with Couette-like vortex stretching. The present work paves the way for close scrutiny of those components of the subgrid-scale stress that contribute most to the subgrid energy flux in large-eddy simulation of near-wall turbulent flows.     

An investigation of pulsating turbulent open channel flow by large eddy simulation

Pulsating turbulent open channel flow is investigated by use of large eddy simulation (LES) technique coupled with a dynamic subgrid-scale (SGS) model for turbulent SGS stress. The three-dimensional filtered Navier-Stokes equation is numerically solved by a fractional-step method. The objective of this study is to deal with the behaviors of pulsating turbulent open channel flow, in particular turbulence characteristics in the free surface-influenced layer, and to examine the reliability of the LES approach for predicting the pulsating turbulent flow with a free surface. In this study, the frequency of driving pressure gradient ranges low, medium and high value. The mean and phase-averaged statistical turbulence quantities, the resolved turbulent kinetic energy and Reynolds stresses budgets, and the flow structures are obtained and analyzed. With the increase of the driving frequency, the depth of the surface-influenced layer increases and the turbulent Stokes length near the bottom wall decreases. Different turbulence characteristics between the accelerating and decelerating phases are interpreted comprehensively. Turbulence intensities reveal that turbulent flow has a strong anisotropy in the free surface-influenced layer, in particular in the decelerating phases during the pulsating cycle. The budget terms of the resolved turbulent kinetic energy, the vertical and spanwise Reynolds stresses in the free surface region are analyzed. The flow structures clearly exhibit that bursting processes near the bottom wall are ejected toward the surface and the most surface renewal events are closely correlated with the bursting processes. These processes are strengthened during the decelerating period since strong turbulence intensities are generated.     

Numerical investigation of cyclic variations in gasoline engines using a hybrid URANS/LES modeling approach

Cycle to cycle variations are an important aspect in the development and optimization process of internal combustion engines. In this study the feasibility of using a detached eddy simulation (DES) SST model, which is a hybrid URANS/LES model, to predict cycle to cycle variations is investigated. In the near wall region or in regions where the grid resolution is not sufficiently fine to resolve smaller structures, the two-equation RANS shear-stress transport (SST) model is used. In the other regions with higher grid resolution an LES model is applied. First, the numerical requirements associated with the hybrid URANS/LES and the employed solver are studied in detail. The numerical dissipation of the spatial scheme and the choice of the temporal scheme including the step size are evaluated. In addition, the accuracy of the solver for moving meshes, which are required for engine calculations, is assessed. The modeling constant linking the grid size to the DES filter length scale is determined by calculating a decaying homogeneous isotropic turbulence test case for different grid resolutions. The final applications of the model are two different engine cases with increasing complexity. The first case is the statistically stationary flow through an engine intake port. The time resolved flow structure predicted by the DES SST model is analyzed and the resulting time-averaged velocity fields are compared to experimental data at different locations. The second application is a motored multi-cycle simulation of a series production engine. The instantaneous flow development during the intake and compression stroke of one single cycle is studied and the ensemble-averaged and the instantaneous velocity fields as well as the resolved velocity fluctuations are compared to optical measurements. Special emphasis is placed on the cyclic differences of the velocity fluctuations at the time of ignition in the vicinity of the spark plug and the expected influence on the combustion process.     

Large-eddy simulation of turbulent flow in a stirred tank driven by a Rushton turbine

Large-eddy simulation (LES) of mixing process in a baffled tank was presented. The impeller rotation was modeled using the sliding mesh technique. In this study the CFD code was used for simulation of a standard vessel agitated by a 6-blade Rushton turbine and results were evaluated in terms of the predicted flow field, power number, mean velocity components, mixing time, turbulent kinetic energy and turbulent dissipation rate using published experimental data. Subsequently, the effects of varying injection position of the passive scalar have been investigated. The results show that LES is a reliable tool to investigate the unsteady behavior of the turbulent flow in stirred tank.     

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.     

LES of synthetic jets in boundary layer with laminar separation caused by adverse pressure gradient

In the development of synthetic jet actuators (SJAs) for active flow control, numerical simulation has played an important role. In controlling the boundary layer flow separation, an integrated numerical model which includes both the baseline flow and the SJA is still in its initial stage of development. This paper reports preliminary results of simulating the interaction between a synthetic jet and a laminar separation bubble caused by adverse pressure gradient in a boundary layer. The computational domain was three-dimensional and Large-eddy simulation (LES) was adopted. The initial and boundary conditions were defined using or referring to our wind tunnel experimental results. Prior to numerically simulating the interaction between the synthetic jets and the baseline flow, a numerical model for simulating the separation bubble was developed and verified. In the numerical model including the SJA, the synthetic jet velocity at the exit of the SJA was defined as an input. The numerical model was further verified by comparing the simulation with experimental results. Based on reasonable agreement between the numerical and experimental results, simulations were carried out to investigate the dependency of flow control using synthetic jets on the forcing frequency, focused on the lower frequency range of the Tollmien-Schlichting (T-S) instability, and on the forcing amplitude which was represented by the maximum jet velocity at the exit of the SJA. Supporting the hypothesis based on the experiment, LES results showed that the forcing frequency had stronger influence on SJA’s effective elimination of the separation bubble than the forcing amplitude did.     

Large eddy simulation of complex flow fields

The large eddy simulation (LES) technique can provide detailed information about time-dependent and three-dimensional turbulent flow fields at high Reynolds number. The application of LES to practical problems and in the basic study of turbulence require investigation. More studies are needed on the boundary conditions and on the subgrid-scale (SGS) model in order to make LES practical. In this paper, the laws of the wall (two-layer model or Spalding's law) are applied as a special approach to the solid boundary in LES. This wall boundary condition is adapted to plane channel flow and the suitability of this method is tested. Further, improvements of the SGS model in which the Smagorinsky model coefficient C_S is not constant are attempted. Recently, Yoshizawa [Phys. Fluids A1(7), 1293 (1989)] derived the form of the variable C_S from a statistical analysis. Here, we optimize this new model in both the decay of isotropic turbulence and plane channel flow simultaneously.