Wall-modeled Large Eddy Simulation Research Articles

Effects of roughness on non-equilibrium turbulent boundary layers

The effects of roughness were considered as part of a NATO Advanced Vehicle Technology effort titled ‘Non-Equilibrium Turbulent Boundary Layers at High Reynolds Numbers’ (NATO AVT-349). This paper comments on the current state of understanding of the flow physics and modelling efforts to predict rough-wall boundary layer behaviour. Outer layer similarity to smooth wall flows and Reynolds number effects are discussed for zero, favourable, and adverse pressure gradients based on the results of experiments and numerical simulations. Various types of modelling are considered including Reynolds averaged Navier-Stokes (RANS) models with different roughness and turbulence models, wall-modelled large eddy simulations (WMLES), and resolvent models. Current needs and gaps in present understanding are discussed along with recommendations for future experiments and computations.

Numerical prediction of mean flow and acoustic field of a supersonic impinging jet

The three-dimensional turbulent mean flow and acoustic field of a supersonic jet impinging on a solid plate is studied computationally using the general purpose CFD code Ansys Fluent. A pressure-based coupled solver formulation with the second order weighted central-upwind spatial discretization is applied to compute transient solutions. Cold and hot jet thermal conditions are considered. Mean flow characteristics are investigated by a steady-state modeling approach. Acoustic radiation of impingement tones is simulated using a transient time-domain formulation. The effects of turbulence in steady-state are modeled by the SST k-ω turbulence model. The Wall-Modeled Large-Eddy Simulation (WMLES) model is applied to compute transient solutions. The near-wall mesh on the impingement plate is fine enough to resolve the viscosity-affected near-wall region all the way to the laminar sublayer. Nozzle-to-plate distance is parameterized in the model for automatic re-generation of the mesh and results. Steady-state predictions of hover lift loss and mean jet velocity distributions are compared with experimental data, and favorable agreement is reported. The transient solution reproduces the mechanism of impingement tone generation by the interaction of large scale vortical structures with the impingement plate. The acoustic near-field is directly resolved by Computational Aeroacoustics (CAA) to accurately propagate impingement tone waves to near-field microphone locations. Calculated impingement tone frequencies and sound pressure levels agree with experimental values.

Embedded large eddy simulation of boundary layer transition behind a micro-ramp

Boundary layer transition induced by surface roughness elements plays an important role in aerodynamic and aero-thermodynamic design of subsonic/supersonic/hypersonic vehicles. However, the effect of three-dimensional isolated roughness element in the process of promoting/suppressing boundary layer transition is far from being fully understood, particularly in the incompressible laminar flow. In the present study, the laminar-to-turbulent transition induced by a three-dimensional isolated micro-ramp element immersed in an incompressible laminar boundary layer is investigated numerically. The embedded large eddy simulation (ELES) combining the intermittency transition model and the wall-modeled large eddy simulation (WMLES) S − Ω model is employed for the first time. Numerical results on the time-averaged/instantaneous flow field and the statistical flow fluctuations are analysed and validated thoroughly by the existing experimental measurements. It is found that the interaction of the secondary and the tertiary streamwise vortices causes a high level of wall shear and an inflectional velocity distribution in the near-wall region. An additional eddy system that develops nonlinearly from the unstable inflectional flow may trigger the boundary layer transition. The present study validates that the ELES combined with the WMLES S − Ω model is an efficient simulation tool for industrial wall-bounded flows allowing effective compromise between flexibility, cost, and accuracy.

Wall-modeled large eddy simulation of a tandem wing configuration in transonic flow

In this study, the interaction between a turbulent wake and the boundary layer of a horizontal tail plane (HTP) in the transonic flow regime is investigated. The setup considered corresponds to a generic tandem wing configuration with an OAT15A airfoil as the main wing and a National Advisory Committee for Aeronautics (NACA) 64A-110 as an HTP. Due to the transonic flow, the suction side of the OAT15A exhibits buffet. The numerical approach consists of a two-stage procedure in which a detached eddy simulation (DES) provides unsteady inflow conditions for a subsequent zonal high-fidelity large eddy simulation (LES) performed for the HTP region only; the turbulent boundary layer is modeled using scale-resolved wall-modeled LES (WMLES). The study mainly pursues two objectives: first, to discuss the influence of wake turbulence on the flow characteristics of the NACA airfoil; and second, to evaluate the capability of WMLES as a low-cost but high-resolution numerical approach in challenging flow conditions. Essentially, the study confirms the expected result that the outer part of the HTP's boundary layer is dominated by the wake of the main wing. Mainly based on a discussion of turbulence spectra, the study further demonstrates the advantage of WMLES over DES, proving that WMLES is able to capture the effects of wake turbulence on boundary layer dynamics, and thus validates the WMLES approach as a cost-effective, high-resolution turbulence modeling approach. On a superordinate level, the study further sketches a possible way on how a flow problem with such a strongly unsteady behavior could be systematically evaluated.

Centralized Gradient-Based Reconstruction for Wall Modelled Large Eddy Simulations of Hypersonic Boundary Layer Transition

In this study, we introduce a robust central Gradient-Based Reconstruction (GBR) scheme for the compressible Navier-Stokes equations. The method leverages transformation to characteristic space, allowing selective treatment of waves from the compressible Euler equations. By averaging left- and right-biased state interpolations, a central scheme is achieved for all but the acoustic waves, which require upwinding for stability. Distinct differences were observed between transformations using either primitive or conservative variables. We evaluated the method's robustness and superiority using benchmark problems, including the two-dimensional shock entropy problem, two-dimensional viscous shock tube, and three-dimensional inviscid Taylor-Green vortex. Subsequently, we assessed the method in the context of Wall Modelled Large Eddy Simulations (WMLES), where coarse grids are used to reduce computational cost but also introduce substantial numerical dissipation. Using WMLES, we simulated oblique shock impingement on a Mach 6 disturbed boundary layer and a Mach 7.7 flow over a 15∘ compression ramp. Our findings reveal that: 1) transformation to characteristic space using conservative variables leads to more accurate results; 2) minimizing numerical dissipation through centralized interpolation is crucial. In the compression ramp case, boundary layer separation was shifted slightly upstream, and there was an over-prediction of wall heating, likely attributable to the equilibrium-assuming wall model. Overall, this work showcases the method's potential in accurately capturing complex flow dynamics with reduced numerical dissipation.

Tip-leakage-flow excited unsteadiness and associated control

Tip leakage flow in turbomachinery inherently generates intense unsteady features, named self-excited unsteadiness, which significantly affects the operating stability, aerodynamic efficiency, and noise but has not been well understood. A zonalized large eddy simulation is employed for a linear cascade, with wall-modeled large eddy simulation active only in the tip region. The simulation is well validated with advantages demonstrated for effectively reducing the computational cost while maintaining an equivalent prediction accuracy in the region of interest. The time-averaged and spatial-spectral characteristics of tip leakage vortex (TLV) structures are systematically discussed. The self-excited unsteady processes of TLV include the tip gap separation, the tip leakage and jet-mainstream interaction, the primary tip leakage vortex (PTLV) wandering motion, and the induced separation near end wall. The Spectral Proper Orthogonal Decomposition (SPOD) is used to examine the dominant frequencies and their coherent structures. It is found that these unsteady features change from a single high frequency to multiple lower frequencies due to the PTLV breakdown. The SPOD and correlation analyses reveal that the self-excited unsteadiness originates initially from unsteady vortex separation in the tip gap and is then fed by the interactions between the tip leakage jet and mainstream. The associated unsteady fluctuations are convected along the tip leakage jet trajectory, causing the wandering motion of PTLV core. Based on the revealed unsteadiness sources, a micro-offset tip design is proposed and shown to be an effective solution to reducing the tip flow unsteadiness. This work improves the understanding of tip-leakage-flow dynamics and informs the control of the associated unsteady fluid oscillation and noise.

Direct-Noise of an Ultrahigh-Bypass-Ratio Turbofan: Periodic-Sector vs Full-Annulas Large-Eddy Simulations

The tonal and broadband noise of an ultrahigh-bypass-ratio fan stage, which has been developed at École Centrale de Lyon, is studied using large-eddy simulations (LES). Wall-modeled LES of a periodic sector and a 360-deg full fan stage have been performed at approach conditions, which is a relevant operating point for aircraft noise certifications. The fan noise is directly obtained from the fully compressible LES, using a well-refined unstructured mesh, and compared with state-of-the-art analytical models. The impact of the periodic boundary conditions, which are often used for high-fidelity simulations of turbofan engines, is assessed. The results from the 360-deg and periodic-sector LES are compared from aerodynamic and acoustic perspectives, including an analysis of the mean and turbulent flow quantities and sound-pressure spectra. Aerodynamic parameters show similar results for both configurations. However, the fan blade loading is slightly reduced in the 360-deg- LES near the blade tip. Acoustically, lower sound power levels at the intake and exhaust sections of the fan stage are obtained in the 360-deg LES, when compared to the periodic sector LES, particularly at low and middle frequencies. This can be associated with lower coherence levels in the fan wakes and smaller spanwise correlation lengths at the trailing edge of the blades. The modal content of the acoustic field has also been analyzed in detail and shows that the periodic sector LES cannot correctly simulate the modal content of the fan noise.

A detached-eddy simulation study on assessing the impact of extreme wind conditions on load and wake characteristics of a horizontal-axis wind turbine

This study utilizes improved delayed detached-eddy simulation (IDDES) to investigate the impact of extreme wind conditions on a horizontal-axis wind turbine, as specified by the IEC-61400 standard. The employed IDDES has a hybrid formulation, where SST K-ω is used to model the turbulence in the boundary layers and large-eddy simulation (LES) is used to resolve turbulence in separated flow regions and the wake area. It also allows for switching to a wall-modeled LES approach, depending on the incoming turbulence content. The research focuses on extreme operating gust (EOG), extreme horizontal shear (EHS), and extreme vertical shear (EVS) conditions at two Tip Speed Ratios (TSR). The loadings and wake characteristics are compared to uniform inlet velocity results to highlight the effects of extreme winds. The novelty of this research lies in its comprehensive investigation of wake behavior under extreme wind conditions, providing valuable insights for improving wind farm layout design and reliability in challenging operational environments. The analysis shows that the impact of the TSR on wind turbine loadings during EOG, EVS, and EHS events is significant. During EOG events for a turbine operating at low TSR, the thrust force and bending moment reach 2.38 and 2.57 times their respective values in uniform inflow conditions, while at the optimal TSR, the thrust force and bending moment increase by only 25%. In all extreme wind cases, there is an escalation in turbulence within the wake, and wake meandering is observed in the EHS and EVS cases.

Wall-Modeled Large-Eddy Simulation of Transonic Buffet over NASA-CRM Using FFVHC-ACE

This study investigates the capability of wall-modeled large-eddy simulation (WMLES) in predicting the transonic buffet phenomenon over three-dimensional aircraft configurations at high Reynolds numbers. The WMLES is conducted using the Cartesian-grid-based flow solver FrontFlow/Violet Hierarchical Cartesian for Aeronautics Based on Compressible-Flow Equations (FFVHC-ACE). To extend the capability of FFVHC-ACE to transonic flow simulations with shock waves, a hybrid kinetic energy and entropy preserving/upwind scheme is implemented in FFVHC-ACE. To validate the employed simulation framework, the flow around the NASA Common Research Model in the near-cruise condition is simulated. In this case, the surface pressure distributions and force coefficients are reasonably predicted and show the trend of grid convergence. Furthermore, the WMLES at the buffet conditions reproduces the wavy structures of the shock wave (i.e., buffet cells) propagating outboard. The obtained propagation speed of the buffet cells and surface pressure spectra show reasonable agreement with the wind tunnel experiments.

Large eddy simulations of turbulent pipe flows at moderate Reynolds numbers

Wall-bounded turbulence is relevant for many engineering and natural science applications, yet there are still aspects of its underlying physics that are not fully understood, particularly at high Reynolds numbers. In this study, we investigate fully developed turbulent pipe flows at moderate-to-high friction velocity Reynolds numbers (361≤Reτ≤2000), corresponding to bulk velocity-based Reynolds numbers of 11 700≤Reb≤82 500, using wall-modeled large eddy simulations (LES) in OpenFOAM. A grid convergence study is performed for Reτ=361, followed by an investigation of the accuracy of various subgrid-scale stress models for the same Reynolds number. Results show that the wall-adapting local eddy (WALE) model performs well compared to experiments and direct numerical simulations, while one-equation eddy-viscosity model and Smagorinsky are too dissipative. LES utilizing WALE is then performed for four different Reynolds numbers with gradually refined grids, revealing excellent agreement with DNS data in the outer region. However, a significant deviation from DNS data is observed in the sub-viscous layer region, indicating the need for further mesh refinement in the wall-normal direction to accurately capture the smallest-scale motions' behavior. Additional mesh sensitivity analysis uncovered that, as the Reτ value rises, it becomes crucial for a grid to adhere to the condition of Δx+≤20−25 and Δz+≤10 in order to precisely capture substantial large and small-scale fluctuations. Overall, the WALE model enables accurate numerical simulations of high-Reynolds number, wall-bounded flows at a fraction of the computational cost required for temporal and spatial resolution of the inner layer.

Toward the Usage of Deep Learning Surrogate Models in Ground Vehicle Aerodynamics

This study introduces a deep learning surrogate model designed to predict the evolution of the mean pressure coefficient on the back face of a Windsor body across a range of yaw angles from 2.5∘ to 10∘. Utilizing a variational autoencoder (VAE), the model effectively compresses snapshots of back pressure taken at yaw angles of 2.5∘, 5∘, and 10∘ into two latent vectors. These snapshots are derived from wall-modeled large eddy simulations (WMLESs) conducted at a Reynolds number of ReL=2.9×106. The frequencies that dominate the latent vectors correspond closely with those observed in both the drag’s temporal evolution and the dynamic mode decomposition. The projection of the mean pressure coefficient to the latent space yields an increasing linear evolution of the two latent variables with the yaw angle. The mean pressure coefficient distribution at a yaw angle of 7.5∘ is predicted with a mean error of e¯=3.13% when compared to the WMLESs results after obtaining the values of the latent space with linear interpolation.

Continuous Eddy Simulation (CES) of Transonic Shock-Induced Flow Separation

Reynolds-averaged Navier–Stokes (RANS), large eddy simulation (LES), and hybrid RANS-LES, first of all wall-modeled LES (WMLES) and detached eddy simulation (DES) methods, are regularly applied for wall-bounded turbulent flow simulations. Their characteristic advantages and disadvantages are well known: significant challenges arise from simulation performance, computational cost, and functionality issues. This paper describes the application of a new simulation approach: continuous eddy simulation (CES). CES is based on exact mathematics, and it is a minimal error method. Its functionality is different from currently applied simulation concepts. Knowledge of the actual amount of flow resolution enables the model to properly adjust to simulations by increasing or decreasing its contribution. The flow considered is a high Reynolds number complex flow, the Bachalo–Johnson axisymmetric transonic bump flow, which is often applied to evaluate the performance of turbulence models. A thorough analysis of simulation performance, computational cost, and functionality features of the CES model applied is presented in comparison with corresponding features of RANS, DES, WMLES, and wall-resolved LES (WRLES). We conclude that CES performs better than RANS, DES, WMLES, and even WRLES at a little fraction of computational cost applied for the latter methods. CES is independent of usual functionality requirements of other methods, which offers relevant additional advantages.

Grid Convergence Properties of Wall-Modeled Large Eddy Simulations in the Asymptotic Regime

Abstract This study explores the grid convergence properties of wall-modeled large eddy simulation (WMLES) solutions as the large eddy simulation (LES) grid approaches the direct numerical simulation (DNS) grid. This aspect of WMLES is fundamental but has not been previously investigated or documented. We investigate two types of grid refinements: one where the LES/wall-model matching location is fixed at an off-wall grid point, and another where the matching location is fixed at a specific distance from the wall. In both cases, we refine the LES grid simultaneously in all three Cartesian directions, with grid resolution ranging from typical LES resolution to typical DNS resolution. Our focus is on examining the mean flow and turbulent kinetic energy (TKE) as the grid refines. While the turbulence statistics consistently converge toward the DNS solution, we observe nonmonotonic convergence in the mean flow statistics. We show that improving the grid resolution does not necessarily enhance the accuracy of the mean flow predictions. Specifically, we identify a negative log layer mismatch when the LES/wall-model matching location lies below the logarithmic layer, regardless of grid resolution and matching location. Finally, we demonstrate that the nonmonotonic convergence of the mean flow can lead to misleading conclusions from grid convergence studies of WMLES.

Effect of Rim Seal Geometry on Rotationally-Driven Ingestion

Abstract This study investigates turbine rim seal geometry effects within the rotationally-driven ingestion regime. Computations were performed with a wall-resolved unsteady Reynolds-averaged Navier–Stokes (URANS) model and a large-eddy simulation (LES) model including near-wall boundary layer modeling, that is, wall-modeled LES (WMLES). Use of simplified rim sealing models is proposed as an efficient method of ranking seal designs and investigating sensitivity to seal geometry. Four rim seal configurations, two chute seals, an axial seal and a radial seal which are representative of those used in gas turbines and in previous research were investigated. Furthermore, hybrid seals combining geometric characteristics from both the chute and radial seal were considered. Significant sensitivities of sealing performance to turbulence modeling are identified, but URANS and WMLES show similar trends in ranking of seal performance, and these are consistent with previous experimental work. The addition of an outer radial clearance section to a chute seal is effective in reducing ingestion levels.

Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow

In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such investigations have been conducted for attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows with separation are notably sparse. To bridge this gap, our study focuses on the flow over a two-dimensional Gaussian-shaped bump at a moderately high Reynolds number, which involves smooth-body separation of a turbulent boundary layer under pressure-gradient and surface-curvature effects. In the simulations, the no-slip condition at the wall is replaced by three different forms of boundary condition based on the thin boundary layer equations and the mean wall-shear stress from high-fidelity numerical simulation to avoid the additional complexity of modeling the wall-shear stress. Various statistics, including the mean separation bubble size, mean velocity profile, and dissipation from SGS model, are compared and analyzed. The results reveal that capturing the separation bubble strongly depends on the choice of SGS model. While simulations approach grid convergence with resolutions nearing those of wall-resolved LES meshes, above this limit, the LES predictions exhibit intricate sensitivities to mesh resolution. Furthermore, both wall boundary conditions and the anisotropy of mesh cells exert discernible impacts on the turbulent flow predictions, yet the magnitudes of these impacts vary based on the specific SGS model chosen for the simulation.

On robust boundary treatments for wall‐modeled LES with high‐order discontinuous finite element methods

SummaryTo robustly and accurately simulate wall‐bounded turbulent flows at high Reynolds numbers, we propose suitable boundary treatments for wall‐modeled large‐eddy simulation (WMLES) coupled with a high‐order flux reconstruction (FR) method. First, we show the need to impose an auxiliary boundary condition on auxiliary variables (solution gradients) that are commonly introduced in high‐order discontinuous finite element methods (DFEMs). Auxiliary boundary conditions are introduced in WMLES, where the grid resolution is too coarse to resolve the inner layer of a turbulent boundary layer. Another boundary treatment to further enhance stability with under‐resolved grids, is the use of a modal filter only in the wall‐normal direction of wall‐adjacent cells to remove the oscillations. A grid convergence study of turbulent channel flow with a high Reynolds number () shows that the present WMLES framework accurately predicts velocity profiles, Reynolds shear stress, and skin friction coefficients at the grid resolutions recommended in the literature. It was confirmed that a small amount of filtering is sufficient to stabilize computation, with negligible influence on prediction accuracy. In addition, non‐equilibrium periodic hill flow with a curved wall, including flow separation, reattachment, and acceleration at a high Reynolds number (), is reported. Considering stability and the prediction accuracy, we recommend a loose auxiliary wall boundary conditions with a less steep velocity gradient for WMLES using high‐order DFEMs.

Wall-modeled large eddy simulation in the immersed boundary-lattice Boltzmann method

This work presents the wall-modeled large eddy simulation (WMLES) in the immersed boundary-lattice Boltzmann method (IB-LBM). Here, the wall model with both diffusive- and sharp-interface immersed boundary methods (IBMs) is incorporated into the IB-LBM to handle the turbulent boundary layer in high Reynolds number turbulent flows. To maintain the numerical stability, two collision models, i.e., multiple-relaxation-time (MRT) and recursive regularized (RR), are implemented. The performance of these models in the WMLES is examined and compared in the simulation of internal and external flows by considering four benchmarks, i.e., turbulent flow in a channel, flow around a hull of submarine, flow around an Ahmed car model, and flow around a circular cylinder. It is found that a diffusive-interface IBM with wall model is capable to achieve excellent results for the simulation of external flows around bluff objects but fails in the simulation of internal flows of underestimating the wall shear stress due to its extra dissipation. The sharp-interface IBM with the wall model predicts the internal flow very well but fails in some simulations of external flow around bluff bodies due to the failure in the separation flow modeling. It is also found that the MRT-LBM is less dissipative than the RR-LBM, but it generates spurious nonphysical noise in the turbulent flows and tends to be unstable at high Reynolds numbers. Therefore, the diffusive-interface IBM with the wall model is more suitable for the external turbulent flow modeling, while its sharp-interface counterpart is more suitable for the internal turbulent flow modeling. The RR-LBM outperforms the MRT-LBM for the better stability and less nonphysical noise.

Rotor aeroacoustic response to an axisymmetric turbulent boundary layer

The acoustic response of a five-bladed rotor to an axisymmetric turbulent boundary layer at the tail end of a body of revolution (BOR) is investigated numerically to elucidate the physical sources of acoustics, particularly the role of coherent structures in sound generation. The BOR is at a length-based Reynolds number of $1.9 \times 10^6$ and free-stream Mach number of 0.059. Two rotor advance ratios, $1.44$ and $1.13$ , are considered. The turbulent boundary layer on the nose and midsection of the BOR is computed using wall-modelled large-eddy simulation, whereas that in the acoustically important tail-cone section is wall-resolved. The radiated acoustic field is calculated using the Ffowcs Williams–Hawkings equation. The computed flow statistics and sound pressure spectra agree well with the experimental measurements at Virginia Tech. In addition to broadband turbulence-ingestion noise, spectral humps near multiples of the blade-passing frequency and accompanying valleys are captured. They are shown to be caused by correlated blade unsteady-loading dipole sources and their constructive and destructive interference as a result of successive blades cutting through the same coherent structures. The latter undergo rapid growth in the decelerating tail-cone boundary layer before their interaction with the rotor. The acoustic radiation is dominated by the outer region of the blade owing to a combination of larger blade chord-length, inflow turbulence intensity and blade speed. The numerical results also correctly predict the effect of the rotor advance ratio on the acoustic field. A mixed free-stream/convection Mach-number scaling successfully collapses the sound pressure spectra at the two advance ratios.

Calibrating sub-grid scale models for high-order wall-modeled large eddy simulation

AbstractHigh-order methods have demonstrated orders of magnitude reduction in computational cost for large eddy simulation (LES) over low-order methods in the past decade. Most such simulations are wall-resolved implicit LES (ILES) without an explicit sub-grid scale (SGS) model. The use of high-order ILES for severely under-resolved LES such as wall-modeled LES (WMLES) often runs into robustness and accuracy issues due to the low dissipation embedded in these methods. In the present study, we investigate the performance of several popular SGS models, the static Smagorinsky model, the wall-adapting local eddy-viscosity (WALE) model and the Vreman model, to improve the robustness and accuracy of under-resolved LES using high-order methods. The models are implemented in the high-order unstructured grid LES solver called hpMusic based on the discontinuous flux reconstruction method. The length scales in these SGS models are calibrated using the direct numerical simulation (DNS) database for the turbulent channel flow problem. The Vreman model has been found to produce the most accurate and consistent results with a proper choice of the length scale for WMLES.

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.