Wall-modeled Large Eddy Simulation Research Articles

Wall-modeled large eddy simulation of 90° bent pipe flows with/without particles: A comparative study

Wall-modeled large eddy simulation (WMLES) has been proven to be a cost-effective approach capable of resolving turbulence up to certain resolutions. Among the simplest wall models used are the equilibrium wall models, assuming the pressure gradient and convective terms balance out in the momentum equations. There is a lack of studies to assess the performance of these standard wall models in internal turbulent flows including separation regions with/without particles. Regarding this research gap, we have conducted WMLES of incompressible turbulent flows, to the authors’ knowledge, for the first time, in 90° bent pipes with and without particles using an algebraic equilibrium wall model (Spalding’s function). A pipe flow simulation was conducted to confirm the simulation setup and assess the sensitivity with respect to the modeling parameters. In each case, comparisons are made with experiment or direct numerical simulation (DNS), and depending on the case, with other existing simulation methods in the literature: WMLES, standard (wall-resolving) LES, and Reynolds stress model (RSM) for Reynolds-averaged Navier-Stokes (RANS) simulations. Despite the controversy on the performance of equilibrium wall models in nonequilibrium flows, our results show acceptable accuracy of this type of wall models. Specifically in the bent pipe flow with particles, WMLES succeeded in predicting particle deposition efficiency at Stokes numbers greater than 0.5, but obtained less accurate results for smaller Stokes numbers. The WMLES errors were, however, on par with those of the standard LES employed with a tenfold higher grid cell count. Improved results would be expected if combined with auxiliary mechanisms such as stochastic models.

A wall model for large-eddy simulation of highly compressible flows based on a new scaling of the law of the wall

Wall modelling in large-eddy simulation (LES) is of high importance to allow scale resolving simulations of industrial applications. Numerous models were developed and validated for incompressible flows, including a simple quasi-analytical model based on Reichardt's formula that approximates the law of the wall. In this paper, a scaling is proposed to generalize this wall model to highly compressible flows. First, the results of wall-resolved LES (wrLES) of adiabatic compressible turbulent channel flows at $Re_\tau = 1000$ and at centreline Mach numbers of $M_c= 0.76$ and $1.5$ are presented. Then, three potential scalings of the incompressible wall model are proposed, and their a priori performance is evaluated : (i) the Howarth–Stewartson scaling, (ii) an improved Van Driest scaling and (iii) a new scaling obtained from a blending of those two. The results of wall-modelled LES (wmLES) of compressible channel flows using these three models are compared with the reference wrLES data, showing the superior accuracy of the hybrid scaling. The consistency of the new wall model at low Mach numbers is also verified by comparing the results of a wmLES at $M_c= 0.25$ with those of reference incompressible DNS data at $Re_\tau = 1000$ and $5200$ . Finally, the proposed wall model is also applied to a turbulent channel flow at $M_c=1.5$ and $Re_\tau =5200$ .

Advanced Modeling of Flow and Heat Transfer in Rotating Disk Cavities Using Open-Source Computational Fluid Dynamics

Abstract Code_Saturne, an open-source computational fluid dynamics (CFD) code, has been applied to a range of problems related to turbomachinery internal air systems. These include a closed rotor–stator disk cavity, a co-rotating disk cavity with radial outflow and a co-rotating disk cavity with axial throughflow. Unsteady Reynolds-averaged Navier–Stokes (RANS) simulations and large eddy simulations (LES) are compared with experimental data and previous direct numerical simulation and LES results. The results demonstrate Code_Saturne's capabilities for predicting flow and heat transfer inside rotating disk cavities. The Boussinesq approximation was implemented for modeling centrifugally buoyant flow and heat transfer in the rotating cavity with axial throughflow. This is validated using recent experimental data and CFD results. Good agreement is found between LES and RANS modeling in some cases, but for the axial throughflow cases, advantages of LES compared to URANS are significant for a high Reynolds number condition. The wall-modeled large eddy simulation (WMLES) method is recommended for balancing computational accuracy and cost in engineering applications.

Continuous Eddy Simulation vs. Resolution-Imposing Simulation Methods for Turbulent Flows

The usual concept of simulation methods for turbulent flows is to impose a certain (partial) flow resolution. This concept becomes problematic away from limit regimes of no or an almost complete flow resolution: discrepancies between the imposed and actual flow resolution may imply an unreliable model behavior and high computational cost to compensate for simulation deficiencies. An exact mathematical approach based on variational analysis provides a solution to these problems. Minimal error continuous eddy simulation (CES) designed in this way enables simulations in which the model actively responds to variations in flow resolution by increasing or decreasing its contribution to the simulation as required. This paper presents the first application of CES methods to a moderately complex, relatively high Reynolds number turbulent flow simulation: the NASA wall-mounted hump flow. It is shown that CES performs equally well or better than almost resolving simulation methods at a little fraction of computational cost. Significant computational cost and performance advantages are reported in comparison to popular partially resolving simulation methods including detached eddy simulation and wall-modeled large eddy simulation. Characteristic features of the asymptotic flow structure are identified on the basis of CES simulations.

Using graph neural networks for wall modeling in compressible anisothermal flows

Abstract Compressible anisothermal flows, which are commonly found in industrial settings such as combustion chambers and heat exchangers, are characterized by significant variations in density, viscosity, and heat conductivity with temperature. These variations lead to a strong interaction between the temperature and velocity fields that impacts the near-wall profiles of both quantities. Wall-modeled large-eddy simulations (LESs) rely on a wall model to provide a boundary condition, for example, the shear stress and the heat flux that accurately represents this interaction despite the use of coarse cells near the wall, and thereby achieve a good balance between computational cost and accuracy. In this article, the use of graph neural networks for wall modeling in LES is assessed for compressible anisothermal flow. Graph neural networks are a type of machine learning model that can learn from data and operate directly on complex unstructured meshes. Previous work has shown the effectiveness of graph neural network wall modeling for isothermal incompressible flows. This article develops the graph neural network architecture and training to extend their applicability to compressible anisothermal flows. The model is trained and tested a priori using a database of both incompressible isothermal and compressible anisothermal flows. The model is finally tested a posteriori for the wall-modeled LES of a channel flow and a turbine blade, both of which were not seen during training.

Generalized wall-modeled large eddy simulation model for industrial applications

In this work, a generalized wall-modeled large eddy simulation model (GWMLES) is presented. An extended formulation of the classical WMLES approach is proposed that also enables the modeling of the entire log-layer by using a Reynolds-averaged Navier–Stokes (RANS) model. GWMLES is validated against direct numerical simulations, large eddy simulations (LES), WMLES, hybrid RANS/LES, unsteady RANS (URANS), and experimental data of test cases featuring industrial flows. It is demonstrated that GWMLES does not share the main shortcoming of current WMLES models. When the entire log-layer is solved with a RANS model, GWMLES gives a level of accuracy similar to recent LES results, as well as computational cost savings that are proportional to the Reynolds number in wall-bounded flows. The model shows superior performance than URANS even when the resolved portion of the energy spectrum is reduced. Motivated by the different time scales of the flow and RANS variables, it requires approximately 30% lower computational costs than the detached eddy simulation family models in the turbulent flows considered. These features represent significant advancements in the simulation of wall-bounded flows at high Reynolds numbers, particularly in industrial applications.

Key ingredients for wall-modeled LES with the Lattice Boltzmann method: Systematic comparison of collision schemes, SGS models, and wall functions on simulation accuracy and efficiency for turbulent channel flow

Key ingredients for wall-modeled LES with the Lattice Boltzmann method: Systematic comparison of collision schemes, SGS models, and wall functions on simulation accuracy and efficiency for turbulent channel flow

A wall-modeled hybrid RANS/LES model for flow around circular cylinder with coherent structures in subcritical Reynolds number regions

In the present paper, a hybrid RANS/LES model with the wall-modelled LES capability (called WM-HRL model) is developed to perform the high-fidelity CFD simulation investigation for complex flow phenomena around a bluff body with coherent structure in subcritical Reynolds number region. The proposed method can achieve a fast and seamless transition from RANS to LES through a filter parameter <i>r</i><sub>k</sub> which is only related to the space resolution capability of the local grid system for various turbulent scales. Furthermore, the boundary positions of the transition region from RANS to LES, as well as the resolving capabilities for the turbulent kinetic energy in the three regions, i.e. RANS, LES and transition region, can be preset by two guide index parameters <i>nr</i><sub>k1-Q</sub> and <i>nr</i><sub>k2-Q</sub>. Through a series of numerical simulations of the flow around a circular cylinder at Reynolds number <i>Re</i> = 3900, the combination conditions are obtained for such two guide index parameters <i>nr</i><sub>k1-Q</sub> and <i>nr</i><sub>k2-Q</sub> that have the capability of high-fidelity resolving and capturing temporally- and spatially-developing coherent structures for such complex three-dimensional flows around such a circular cylinder. The results demonstrate that the new WM-HRL model is capable of accurately resolving and capturing the fine spectral structures of the small-scale Kelvin-Helmholtz instability in the shear layer for flow around such a circular cylinder. Furthermore, under a consistent grid system, through different combinations of these two guide index parameters <i>r</i><sub>k1</sub> and <i>r</i><sub>k2</sub>, the fine structuresof the recirculation zones with two different lengths and the U-shaped and V-shaped distribution of the average stream-wise velocity in the cylinder near the wake can also be obtained.

Numerical analysis of turbulent fluctuations around an axisymmetric body of revolution based on wall-modeled large eddy simulations

Numerical analysis of turbulent fluctuations around an axisymmetric body of revolution based on wall-modeled large eddy simulations

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layer with Spatially Varying Pressure Gradients

Wall-modeled large-eddy simulations of turbulent boundary layers subjected to spatially varying streamwise pressure gradients are conducted to assess the predictive performance of three wall models: ordinary differential equation equilibrium, integral nonequilibrium, and partial differential equation (PDE) nonequilibrium models. The test case is based on experiments conducted by Volino (Journal of Fluid Mechanics, Vol. 897, Aug. 2020, p. A2), where the flow is subjected successively to zero pressure gradient (ZPG), favorable pressure gradient (FPG), recovery ZPG, and adverse pressure gradient (APG) regions. Skin friction is overpredicted in FPG by all the wall models. For equilibrium and integral models, this overprediction is attributed to the strong deviation of mean velocity profiles within FPG from the log law, used explicitly in the equilibrium and implicitly in the integral model. The overprediction is more pronounced for the PDE model, which is attributed to dynamic correction of wall-model eddy viscosity for resolved stresses and a lack of correction for pressure gradient. Potential remedies to mitigate this problem are proposed. Grid refinement improves wall-stress predictions in both FPG and APG but only affects the outer profiles in APG, revealing that accurate wall-flux modeling is more critical for APG. Anisotropic grid analysis shows streamwise grid refinement to be more crucial than spanwise for the convergence of skin-friction, outer velocity, and Reynolds stress profiles.

A multi-time-scale wall model for large-eddy simulations and applications to non-equilibrium channel flows

The recent Lagrangian relaxation towards equilibrium (LaRTE) approach (Fowleret al.,J. Fluid Mech., vol. 934, 2022, A44) is a wall model for large-eddy simulations (LES) that isolates quasi-equilibrium wall-stress dynamics from non-equilibrium responses to time-varying LES inputs. Non-equilibrium physics can then be modelled separately, such as the laminar Stokes layers that form in the viscous region and generate rapid wall-stress responses to fast changes in the pressure gradient. To capture additional wall-stress contributions due to near-wall turbulent eddies, a model term motivated by the attached eddy hypothesis is proposed. The total modelled wall stress thus includes contributions from various processes operating at different time scales (i.e. the LaRTE quasi-equilibrium plus laminar and turbulent non-equilibrium wall stresses) and is called the multi-time-scale (MTS) wall model. It is applied in LES of turbulent channel flow subject to a wide range of unsteady conditions from quasi-equilibrium to non-equilibrium. Flows considered include pulsating and linearly accelerating channel flow for several forcing frequencies and acceleration rates, respectively. We also revisit the sudden spanwise pressure gradient flow (considered in Fowleret al.,J. Fluid Mech., vol. 934, 2022, A44) to review how the newly introduced model features affect this flow. Results obtained with the MTS wall model show good agreement with direct numerical simulation data over a vast range of conditions in these various non-equilibrium channel flows. To further understand the MTS model, we also describe and test the instantaneous-equilibrium limit of the MTS wall model. In this limit, good wall-stress predictions are obtained with reduced model complexity but providing less complete information about the wall-stress physics.

A Hybrid Large Eddy Simulation Algorithm Based on the Implicit Domain Decomposition

The resolution of small near-wall eddies encountered in high-Reynolds number flows using large eddy simulation (LES) requires very fine meshes that may be computationally prohibitive. As a result, the use of wall-modeled LES as an alternative is becoming more popular. In this paper, the near-wall domain decomposition (NDD) approach that was originally developed for Reynolds-averaged Navier–Stokes simulations (RANSs) is extended to the hybrid RANS/LES zonal decomposition. The algorithm is implemented in two stages. First, the solution is computed everywhere with LES on a coarse grid using a new non-local slip boundary condition for the instantaneous velocity at the wall. The solution is then recomputed in the near-wall region with RANS. The slip boundary conditions used in the first stage guarantee that the composite solution is smooth at the inner/outer region interface. Another advantage of the model is that the turbulent viscosity in the inner region is computed based on the corresponding RANS velocity. This shows improvement over those hybrid models that have only one velocity field in the whole domain obtained from LES. The model is realized in the open source code OpenFOAM with different approximations of turbulent viscosity and is applied to the planar channel flow at frictional Reynolds numbers of Reτ=950, 2000, and 4200. Mean streamwise velocity and Reynolds stress intensities are predicted reasonably well in comparison to the solutions obtained with unresolved LES and available DNS benchmarks. No additional forcing at the interface is required, while the log–layer mismatch is essentially reduced in all cases.

Wall-modeled large-eddy simulation of turbulent non-Newtonian power-law fluid flows

For high-fidelity predictions of turbulent flows in complex practical engineering problems, the Wall-Modeled (WM) Large-Eddy Simulation (LES) has aroused great interest. In the present study, we prove that the conventional Wall-Stress Models (WSMs) developed for WMLES of Newtonian fluids fail to predict the shear-thinning-induced drag reduction in power-law fluids. Therefore, we propose novel algebraic, integrated, and Ordinary-Differential-Equation (ODE) WSMs, for the first time, for WMLES of power-law Non-Newtonian (NN) fluids and assess their performance against reference Wall-Resolved (WR) LES solutions. In addition, the effects of the key model parameters, including the WSM type, sampling height, sampling cell, and axial grid resolution are explored, and it is revealed that turbulent NN flow predictions have a much higher sensitivity to the choice of WSM, compared to their Newtonian counterparts. It is manifested that, in contrast to WRLES, accurate modeling of the mean apparent and subgrid-scale NN viscosities in the Non-Newtonian ODE (NNODE) model can improve the predictions considerably. Therefore, closures with lower uncertainties on coarse WMLES grids are sought for these terms. Finally, the best performance for the present test cases is obtained via the integrated NN WSM, sampling at the lower edge of the log layer within the third off-the-wall grid cell. Nevertheless, the new NNODE WSM can have an advantage in the presence of non-equilibrium effects in more complex problems.

A wall-modelled large eddy simulation approach based on large scale parallel computing for post stall flow over an iced airfoil

Safety evaluation for ice accretion is one of the most important jobs for the airworthiness certification of commercial aircraft. Ice accretion would induce strong performance degradation of lifting surfaces by modifying the geometry of the leading edge and the state of boundary layers, and inducing premature flow separation. In this paper, a wall-modelled large eddy simulation (WMLES) approach combined with high performance computing is presented and evaluated for numerical simulation of post stall flow at Mach number 0.12 and Reynolds number 3.5 million over an iced airfoil with angle of attack 6 degrees for business jet, which is known as the GL305/944 airfoil with horn ice. Both RANS and an improved DDES (IDDES) based on SST model are also completed to validate the results. The results are compared with the experimental data in details that includes total forces, velocity profile, averaged velocity field, RMS of pulsating velocity, et al. It is concluded that the WMLES approach presented here can greatly improve the numerical accuracy for post stall flow with large separation; Basically, WMLES can relatively accurately predict the total forces, the pressure rooftop length and the pressure recovery, and the shear layer instability induced by the horn ice.The relative error of lift coefficient for WMLES is only 0.47%, which is far less than RANS with -26.7%.

Multi-GPU-based real-time large-eddy simulations for urban microclimate

This study presents an innovative real-time urban microclimate simulation strategy using a large-eddy simulation (LES) solver deployed on a multi-GPU architecture. The present LES solver is developed using a monolithic projection-based method with staggered time discretization, ensuring efficient computation and a high CFL number. It is hosted on a multi-GPU platform using CUDA Fortran and CUDA-aware MPI, which enhances its performance. To capture the complexity of urban geometries, we utilized a building-resolved, wall-modeled LES augmented by an immersed boundary method. First, we validated the results in an isolated building by comparing them with wind tunnel profiles. Next, we evaluated the developed LES solver using an idealized street array. A set of evaluation metrics, namely FAC2 and hit rate, was employed to determine the optimal grid configuration that produces physically valid results. Moreover, we proposed a real-time indicator that provides insight into the interplay among grid resolution, simulation domain size, and the number of GPUs. This facilitates feasibility assessments for real-time simulations. The performance of the LES solver was further tested using real urban geometry, conducting simulations over an area of 10.49 km2 in Seoul, with a grid resolution of 4 m. The simulation results efficiently highlighted variations in wind patterns with altitude, demonstrating its potential to provide useful wind information for pedestrian-level wind comfort assessment and urban air mobility.

On the coupling between wall-modeled LES and immersed boundary method towards applicative compressible flow simulations

The current work presents an innovative numerical technique for high-Reynolds/high-Mach number compressible flow simulations in complex configurations. In particular, the research combines a novel wall-modeled large-eddy simulation technique with a sharp-interface immersed boundary method in the framework of high-order numerical schemes. The proposed approach enables the best from wall modeling and the immersed boundary. The first is concerned with accurately dealing with wall flows while avoiding direct control of near-wall resolution; the second is related to efficiently treating arbitrarily complex geometries in Cartesian grids. In particular, the paper extends a well-established wall model already presented by the research group to arbitrarily-shaped bounds. The method yields a minimally invasive technique that switches between wall-resolved and wall-modeled large-eddy simulations according to the local near-wall resolution. Thus, easily fitting aerodynamic simulation needs. After discussing the numerical procedure, the paper provides several benchmarks to demonstrate the validity of the proposed approach. In particular, literature-available direct numerical datasets are mined to compare acquired outcomes. The results’ accuracy is found to be remarkable from low-Mach-channel and -pipe flow configurations up highly-compressible flows concerning the spatial deployment of the boundary layer over a flat plate and the shock-wave/boundary-layer interaction over a compression ramp. Thus, the proposed method appears to be a promising framework for dealing with engineering-relevant flow simulations along with the efficient path of Cartesian meshes combined with massively parallel GPU-accelerated architectures.

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.

Large eddy simulations of pilot-stage equivalence ratio effects on combustion instabilities in a coaxial staged model combustor

In this paper, the effects of pilot-stage equivalence ratio on combustion instabilities in a coaxial staged model combustor are investigated using the Wall-Modeled Large Eddy Simulation. The global equivalence ratio is maintained constant, and the Stratification Ratio of the first main-stage and the second main-stage is set to 1; the dynamic mode decomposition and system identification methods are employed to analyze the flame dynamics, velocity, heat release rate modes, and flame transfer function (FTF) of the model combustor under different pilot-stage equivalence ratios. The results show that when the pilot-stage equivalence ratio is 0.6, the oscillation amplitude of heat release rate (HRR) exceeds 7.5% of the global average HRR, and the velocity oscillation and the global HRR oscillation in the combustor are coupled. As the pilot-stage equivalence ratio increases to 0.8, the oscillation amplitude of HRR decreases to 2.5%, and the oscillation of velocity and global HRR in the combustor are decoupled. Furthermore, the maximum value of FTF decreases from 3.5 to below 1 with the increase in the pilot-stage equivalence ratio.

Parametric dependence and elementary modelling for compressor disc cavity heat transfer

A wall-modelled large-eddy simulation (WMLES) method previously validated against laboratory experiments is applied to a real engine disc cavity geometry with surface and air temperatures representative of maximum power conditions. An appropriate set of independent nondimensional parameters describing the problem is defined and the sensitivities to these parameters are investigated by independently varying each parameter in the WMLES. Effects of a change in disc temperature distribution and a reduction in radius of the downstream disc are also investigated. The flow and heat transfer mechanisms predicted are very similar to those found for the research rig configuration although rotating cavity flow structures with two or more lobes are found for the engine geometry rather than the single-lobed structures shown in previous work. The simulations are compared with an elementary model giving further insight into scaling of the flow and heat transfer with operating conditions. The model assumes a well-mixed core flow in the cavity with constant rothalpy, relates shroud heat transfer to that of natural convection under gravity for high Rayleigh number, and relates disc heat transfer to conduction across unsteady Ekman layers. An energy balance for the cavity is used to obtain an effective mass flow exchange rate between the axial throughflow and the disc cavity to the disc and shroud heat transfer and core temperature. The model is considered to give a useful basis for engineering calculations involving correlation and extrapolation of WMLES and experimental results.

Near-wall numerical coherent structures and turbulence generation in wall-modelled large-eddy simulation

Near-wall turbulence structures and generation in the wall-modelled large-eddy simulation (WMLES) are revealed. To elucidate the turbulence structures driving a near-wall turbulence generation in the WMLES, flat-plate turbulent boundary-layer flows calculated by the WMLES and direct numerical simulation (DNS) are closely investigated. A conditional-averaging technique is applied to the instantaneous flow fields and the near-wall statistical structures of the ejection and sweep pairs, which produce the turbulence, are revealed to exist even in the WMLES although the structures are non-physically elongated compared with those obtained by the DNS. Since the near-wall turbulence structures in the WMLES are revealed not to be disordered, but to be coherent structures with low- and high-speed fluids alternating in the spanwise direction, it is suggested that the near-wall turbulence generation in the WMLES is explained by the numerically elongated coherent structures. Furthermore, the Reynolds number effects of wall-bounded turbulent flows, i.e. the appearance of the outer peak in the energy spectrum of the streamwise velocity fluctuations at increasing Reynolds numbers, is found not to be reproduced by the WMLES, and the origin of the outer peak is discussed in association with the inner–outer-layer interactions. The near-wall turbulence structures in the WMLES could depend heavily on the computational grids and the numerical methods. Therefore, additional cases varying the grid resolutions and the numerical methods (numerical schemes and sub-grid-scale models) are also conducted to confirm the consistency of the present conclusions.