Wall-modeled Large Eddy Simulation Research Articles

A wall model for external laminar boundary layer flows applied to the Wall-Modeled LES framework

Wall-Modeled Large Eddy Simulation (WMLES) is a prominent technique for obtaining high-fidelity solutions of turbulent, high Reynolds number flows, with reasonably acceptable computational costs. However, for external flows, the very thin laminar boundary layer developing near the body leading edge imposes quite restrictive mesh resolution requirements, leading to prohibitively high computational costs for practical Reynolds numbers. We propose a wall-modeling approach for the laminar portion of the boundary layer in order to alleviate these costs by reducing the aforementioned mesh resolution requirements. The wall model is based on local self-similar solutions of the boundary layer, and is implemented in the same context of wall-stress models in the WMLES approach. A thorough assessment of the proposed wall model is performed in terms of the distribution of both pressure and skin friction coefficients along the surface, for a fully laminar flow around a NACA 0012 airfoil geometry, with a chord Reynolds number of Rec=5×103 and Mach number of M∞=0.5. Simulations are carried out to evaluate the effects of the wall model height on the solution. The influence of mesh refinement and mesh element distributions along the surface are also analyzed and discussed. The results obtained in the simulations using the proposed wall model are in good agreement with the reference solution, demonstrating the suitability of the model for external laminar flows.

HLPW-4: Wall-Modeled Large-Eddy Simulation and Lattice–Boltzmann Technology Focus Group Workshop Summary

A summary of the nine submissions to the Wall-Modeled Large-Eddy Simulation and Lattice–Boltzmann (WMLESLB) Technical Focus Group (TFG) at the 4th High lift Prediction Workshop is provided. The focus of this TFG was to assess the current capabilities of WMLES and LB methods on a complex high-lift configuration across a wide range of angles of attack. Analysis of the submitted data suggests that >250 M spatial degrees of freedom are needed to accurately predict pitching moments at high angles of attack due to large pressure gradients present on the outboard slat and main element for α>17° (corrected for free-air). While some scatter is reported in pitching moment coefficient at the low-angles of attack (α<11°), excellent agreement is observed between submissions near the CL,max state. Objective superiority of WMLES methods over Reynolds-averaged Navier–Stokes (RANS) can be seen in terms of lack of excess outboard separation; a majority of the WMLES and LB submissions predict wedge-shaped separation patterns consistent with the experimental oil flow. The in-tunnel simulations show excellent agreement with the experiment in terms of a) integrated loads, b) surface flow-topology, and c) mechanism for the onset of inboard stall. Further evidence is provided to demonstrate both qualitative and quantitative superiority of the WMLES submissions over RANS.

URANOS: A GPU accelerated Navier-Stokes solver for compressible wall-bounded flows

URANOS, a massively parallel GPU-accelerated compressible flow solver for high-fidelity modeling of compressible wall flows, is presented. URANOS is based on modern high-fidelity and high-resolution discretization strategies for time-accurate compressible flow predictions. The solver provides six different convective scheme implementations, a cutting-edge method for viscous terms treatment, and three different frameworks for turbulence modeling (DNS, LES, and innovative WMLES), while utilizing a high-order finite-difference approach, ranging from second to sixth order spatial accuracy. This paper details all of these numerical models and implementation issues. Computationally, URANOS combines multiple three-dimensional MPI parallelization strategies with the open standard, OpenACC, for machine wide, on node, and on GPU parallelism, tailoring the software to match the state-of-the-art HPC computing facilities. Special attention is given to the GPU porting and data management, detailing the solver scaling properties and performance for multi-node/-GPU systems on three distinct architectures. In these experiments the different MPI strategies are compared for both GPU-aware MPI/GPU (Host-based MPI) and results are provided proving, consistently, that the GPU-aware MPI outperforms the GPU (Host-based MPI) approach. Furthermore, the GPU version is compared to the CPU only demonstrating over three times speed-up for a node-to-node comparison, even at large scales, with an efficiency of about 80% while using 1024 GPUs. Finally, the manuscript presents several validation benchmarks, from simple academic comparisons to turbulent channel and boundary layer configurations. URANOS is compared with the best DNS data available in the literature across various Mach numbers, ranging from almost incompressible conditions to hypersonic regimes, illustrating the solver's capability in treating a wide range of complex wall-flows problems using DNS, wall-resolved, and wall-modeled LES approaches. Thus, using OpenACC as a paradigm, URANOS provides a straightforward and efficient platform that can efficiently exploit the most modern GPU-accelerated computing architectures in a totally open-source and non-vendor-specific way. The solver represents a framework where the CFD community can explore the limits of modeling, test new models/methods all across a broad range of Mach and Reynolds numbers flows. The solver is released under a BSD license. Program summaryProgram title: Unsteady Robust All-around Navier-StOkes Solver (URANOS)CPC Library link to program files:https://doi.org/10.17632/pw5hshn9k6.1Developer's repository link:https://gitlab.com/fralusa/uranos_gpuLicensing provisions: BSD License 2.0Programming language: Fortran 90, OpenACC, MPINature of problem: Solving the compressible Navier-Stokes system of equations in a three-dimensional Cartesian framework from low to high Mach and Reynolds numbers conditions.Solution method: Convective terms are treated with several high-order high-resolution shock-capturing schemes (WENO/TENO) in hybrid and non-hybrid versions. The system dynamics is advanced in time with a three-stage, third-order total variation diminishing Runge-Kutta method. Three-dimensional MPI parallelization is implemented in several optimized arrangements and coupling OpenACC directives in a genuinely multi-GPU logic.

Large-Eddy Simulation of Compound Channels with Staged Floodplains: Flow Interactions and Turbulent Structures

Numerous sources of overtopping and flood events suggest different cross-sectional land characteristics of the river and urban river water systems. Multiple stages of floodplains in compound channels are viable in urban areas to facilitate bank slope stability and a higher discharge capacity for different flow rates. The complexity of the contiguous floodplains’ compound channel flows manifold with the interactive geometry and roughness of the surrounding floodplains. In the present study, a large-eddy simulation study is undertaken to investigate the turbulent structure of open channels with multiple-stage floodplains. The validation uses experimental data collected at individual contiguous multiple-stage floodplains for three depth ratios from shallow to deep flow regimes. The wall-modelled large eddy simulations were validated with the depth-averaged velocity, primary velocity and secondary currents. Furthermore, the impact of the multiple-stage floodplains on the instantaneous flow fields and large-scale vortical structures is predicted herein. It was found that vortical structures affect the distribution of the momentum exchange over multiple-stage floodplains.

Investigation of Flow-Induced Instabilities in a Francis Turbine Operating in Non-Cavitating and Cavitating Part-Load Conditions

The integration of intermittent renewable energy resources to the grid system requires that hydro turbines regularly operate at part-load conditions. Reliable operation of hydro turbines at these conditions is typically limited by the formation of a Rotating Vortex Rope (RVR) in the draft tube. In this paper, we investigate the formation of this vortex using the scale-resolving methods SST-SAS, wall-modeled LES (WMLES), and zonal WMLES. The numerical results are first validated against the available experimental data, and then analyzed to explain the effect of using different scale-resolving methods in detail. It is revealed that although all methods can capture the main features of the RVRs, the WMLES method provides the best quantitative agreement between the simulation results and experiment. Furthermore, cavitating simulations are performed using WMLES method to study the effect of cavitation on the flow in the turbine. These effects of cavitation are shown to be highly dependent on the amount of vapor in the RVR. If the amount of vapor is small, cavitation induces broadband high-frequency fluctuations in the pressure and forces exerted on the turbine. As the amount of cavitation increases, these fluctuations tend to have a distinct dominant frequency which is different from the frequency of the RVR.

A wall stress model to predict high-Reynolds number flow over rough walls

Wall-modeled large eddy simulation of turbulent channel flow with rough walls was performed for Reynolds numbers of Reτr=615–2080. The eddy viscosity parameter in a wall stress model was modified to include the effects of wall roughness. Symmetric and asymmetric channel flows were studied for transitionally and fully rough states with ks+=62 and 112, respectively. The wall shear stress was estimated based on the velocity field within the wall layer using the total shear stress term. For the wall layer, the matching point was located well above the height of the virtual roughness elements. The numerical predictions for the mean velocity profile and Reynolds stresses compared well with the experimental data. The prediction for the mean velocity shift due to roughness agreed with the experimental measurements and empirical correlations. For the asymmetric channel flows with roughness on only one wall, the numerical simulations correctly reproduced the displacement of the mean flow away from the rough wall. Overall, the proposed wall-model allows for the prediction of the effects of wall roughness without resolving the geometry of the roughness elements on the wall. This is consistent with the goal of performing large eddy simulations of wall-bounded flows at high-Reynolds numbers with minimal resolution of the wall region, which results in a much reduced computational cost.

Numerical Investigation of Prediction on the NASA High-Lift Common Research Model

An assessment of a hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation (HRLES) approach for prediction is presented for the NASA High-Lift Common Research Model (CRM-HL). Both free-air and wind tunnel configurations of the CRM-HL are investigated, and the results are compared to the QinetiQ wind tunnel experiments and two other numerical approaches: RANS and wall-modeled LES (WMLES). For the free-air configuration, HRLES is shown to address some of the known shortcomings with RANS and prevent inboard and outboard flow separation particularly in the region of and poststall. To achieve these improvements over RANS, LES-appropriate grids and numerical discretizations are required. It was also found that, when applying HRLES to a RANS best practice grid and numerics, the HRLES method significantly underperformed RANS. For the in-tunnel configuration, HRLES showed good agreement with the loads, surface pressure, and oil-flow photographs obtained in the experiment. HRLES was able to improve upon the RANS simulations, which showed a sharp loss of lift at the two highest angles of attack due to large-scale inboard and outboard separation on the wing, by correctly predicting the corner flow separation and showing remarkably close agreement in the flow topologies with the experiment.

Residual estimation for grid modification in wall-modeled large eddy simulation using unstructured high-order methods

The accuracy and computational cost of a large eddy simulation are highly dependent on the computational grid. Building optimal grids manually from a priori knowledge is not feasible in most practical use cases; instead, solution-adaptive strategies can provide a robust and cost-efficient method to generate a grid with the desired accuracy. We adapt the residual estimation algorithm developed by Toosi and Larsson (2020) for Discontinuous Galerkin Spectral Elements Methods (DGSEM) to guide the grid-adaptation process. The core of the method is the computation of the estimated modeling residual using the polynomial basis functions used in DGSEM, and the averaging of the estimated residual over each element. The final method is assessed in multiple channel flow test cases and for the transonic flow over an airfoil, in both cases making use of mortar interfaces between elements with hanging nodes. The method is found to be robust and reliable, and to provide solutions on grids with significantly fewer elements at comparable accuracy compared to when using human-generated grids.

Numerical simulation of turbulent, plane parallel Couette–Poiseuille flow

We present numerical simulation and mean-flow modelling of statistically stationary plane Couette–Poiseuille flow in a parameter space $(Re,\theta )$ with $Re=\sqrt {Re_c^2+Re_M^2}$ and $\theta =\arctan (Re_M/Re_c)$ , where $Re_c,Re_M$ are independent Reynolds numbers based on the plate speed $U_c$ and the volume flow rate per unit span, respectively. The database comprises direct numerical simulations (DNS) at $Re=4000,6000$ , wall-resolved large-eddy simulations at $Re = 10\,000, 20\,000$ , and some wall-modelled large-eddy simulations (WMLES) up to $Re=10^{10}$ . Attention is focused on the transition (from Couette-type to Poiseuille-type flow), defined as where the mean skin-friction Reynolds number on the bottom wall $Re_{\tau,b}$ changes sign at $\theta =\theta _c(Re)$ . The mean flow in the $(Re,\theta )$ plane is modelled with combinations of patched classical log-wake profiles. Several model versions with different structures are constructed in both the Couette-type and Poiseuille-type flow regions. Model calculations of $Re_{\tau,b}(Re,\theta )$ , $Re_{\tau,t}(Re,\theta )$ (the skin-friction Reynolds number on the top wall) and $\theta _c$ show general agreement with both DNS and large-eddy simulations. Both model and simulation indicate that, as $\theta$ is increased at fixed $Re$ , $Re_{\tau,t}$ passes through a peak at approximately $\theta = 45^{\circ }$ , while $Re_{\tau,b}$ increases monotonically. Near the bottom wall, the flow laminarizes as $\theta$ passes through $\theta _c$ and then re-transitions to turbulence. As $Re$ increases, $\theta _c$ increases monotonically. The transition from Couette-type to Poiseuille-type flow is accompanied by the rapid attenuation of streamwise rolls observed in pure Couette flow. A subclass of flows with $Re_{\tau,b}=0$ is investigated. Combined WMLES with modelling for these flows enables exploration of the $Re\to \infty$ limit, giving $\theta _c \to 45^\circ$ as $Re\to \infty$ .

A unified understanding of scale-resolving simulations and near-wall modelling of turbulent flows using optimal finite-element projections

The main objective of this work is to develop a unified framework that can be used as a lens to quantitatively assess and augment a wide range of coarse-grained models of turbulence, namely large eddy simulations (LES), hybrid Reynolds-averaged/LES methods and wall-modelled (WM)LES. Taking a turbulent channel flow as an example, optimality is assessed in the wall-resolved limit, the hybrid RANS–LES limit and the WMLES limit, via projections at different resolutions suitable for these approaches. These optimal a priori estimates are shown to have similar characteristics to existing a posteriori solutions reported in the literature. Consistent accuracy metrics are developed for scale-resolving methods using the optimal solution as a reference, and evaluations are performed. We further characterise the slip velocity in WMLES in terms of the near-wall under-resolution and develop a universal scaling relationship. Insights from the a priori tests are used to augment existing slip-based wall models. Various a posteriori tests reveal superior performance over the dynamic slip wall model. Guidance for the development of improved slip-wall models is provided, including a target for the dynamic procedure.

Numerical Investigation of Wall-Cooling Effect on Aero-Optical Distortions for Hypersonic Boundary Layer

Compressible wall-modeled large-eddy simulations of Mach 8 turbulent boundary-layer flows over a flat plate were carried out for the conditions of the hypersonic wind tunnel at Sandia National Laboratories. The simulations provide new insight into the effect of wall cooling on the aero-optical path distortions for hypersonic turbulent boundary-layer flows. Four different wall-to-recovery temperature ratios, 0.3, 0.48, 0.71, and 0.89, are considered. Despite the much lower grid resolution, the mean velocity, temperature, and resolved Reynolds stress profiles from the simulation for a temperature ratio of 0.48 are in good agreement with those from a reference direct numerical simulation. The normalized root-mean-square optical path difference obtained from the present simulations is compared with that from reference direct numerical simulations, Sandia experiments, as well as predictions obtained with a semi-analytical model by Notre Dame University. The present analysis focuses on the effect of wall cooling on the wall-normal density correlations, on key underlying assumptions of the aforementioned model such as the strong Reynolds analogy, and on the elevation angle effect on the optical path difference. Wall cooling is found to increase the velocity fluctuations and decrease the density fluctuations, resulting in an overall reduction of the normalized optical path distortion. Compared to the simulations, the basic strong Reynolds analogy overpredicts the temperature fluctuations for cooled walls. Also different from the strong Reynolds analogy, the velocity and temperature fluctuations are not perfectly anticorrelated. Finally, as the wall temperature is raised, the density correlation length, away from the wall but inside the boundary layer, increases significantly for beam paths tilted in the downstream direction.

WMLES of flows around small-scale propellers - estimating aerodynamic performance and wake visualization

Wall-modeled large-eddy simulation (WMLES) is an advanced mathematical model for turbulent flows which solves for the low-pass filtered numerical solution. A subgrid-scale (SGS) model is used to account for the effects of unresolved small-scale turbulent structures on the resolved scales (i.e. for the dissipation of the smaller scales), while the flow behavior near the walls is modeled by wall functions (thus reducing the requirements for mesh fineness/ quality). This paper investigates the possibilities of applying WMLES in the estimation of aerodynamic performance of small-scale propellers, as well as in the analysis of the wake forming downstream. Induced flows around two propellers designed for unmanned air vehicles (approximately 25 cm and 75 cm in diameter) in hover are considered unsteady and turbulent (incompressible or compressible, respectively). Difficulties in computing such flows mainly originate from the relatively low values of Reynolds numbers (several tens to several hundreds of thousands) when transition and other flow phenomena may be present. The choice of the employed numerical model is substantiated by comparisons of resulting numerical with available experimental data. Whereas global quantities, such as thrust and power (coefficients), can be predicted with satisfactory accuracy (up-to several percents), distinguishing the predominant flow features remains challenging (and requires additional computational effort). Here, wakes forming aft of the propeller rotors are visualized and analyzed. These two benchmark examples provide useful guidelines for further numerical and experimental studies of small-scale propellers.

Turbulence-induced electrical discharges in charged particle-laden Martian boundary layers

Martian dust storms in the planetary boundary layer share many qualitative similarities to terrestrial sandstorms. Both of these turbulence-driven, particle-laden boundary layer flows are known to generate electric fields due to the transport of differentially charged particles; this charge separation can be strong enough to lead to dielectric breakdown in the form of sparks or lightning. Using wall-modelled large-eddy simulations supplemented with conservation of equations for the charged particle transport, representative simulations of neutrally stable Martian and terrestrial particle-laden boundary layer flows are compared. The simulations, albeit canonical in nature, provide evidence to support previous observations of the less frequent occurrence of lightning on Mars but a higher occurrence of localised electric discharge events due to the much lower breakdown potential. The rarefied Martian atmosphere impedes charged particle transport, resulting in a weaker electric field than the equivalent terrestrial sandstorm. The lower drag force in the rarefied Martian atmosphere means that the electrostatic force plays a more significant role in the particle transport, which results in a self-regulation of the electric field. The strongest Martian dust storms show evidence of significant breakdown events and these discharge events only occur very close to the ground despite the very large boundary layer on Mars.

Wall-Modeled and Hybrid Large-Eddy Simulations of the Flow over Roughness Strips

The flow over alternating roughness strips oriented normally to the mean stream is studied using wall-modeled large-eddy simulations (WMLES) and improved delayed detached-eddy simulations (IDDES) (a hybrid method solving the Reynolds-averaged Navier–Stokes (RANS) equations near the wall and switching to large-eddy simulations (LES) in the core of the flow). The calculations are performed in an open-channel configuration. Various approaches are used to account for roughness by either modifying the wall boundary condition for WMLES or the model itself for IDDES or by adding a drag forcing term to the momentum equations. By comparing the numerical results with the experimental data, both methods with both roughness modifications are shown to reproduce the non-equilibrium effects, but noticeable differences are observed. The WMLES, although affected by the underlying equilibrium assumption, predicts the return to equilibrium of the skin friction in good agreement with the experiments. The velocity predicted by the IDDES does not have memory of the upstream conditions and recovers to the equilibrium conditions faster. Memory of the upstream conditions appears to be a critical factor for the accurate computational modeling of this flow.

Wall-Modeled Large-Eddy Simulation with Second-Order-Accurate Upwind Scheme

In aircraft aerodynamic design, it is essential for certification by analysis to estimate aircraft aerodynamic characteristics with high fidelity across the full flight envelope using computational fluid dynamics. Improving accuracy of the simulation of unsteady flows such as transonic buffet is one of the problems. Wall-modeled large-eddy simulation (WMLES) is expected to improve the accuracy. In this study, three quantitative requirements for the matching points, where LES feeds the wall model with flow variables, are proposed to ensure the accuracy of the WMLES with a second-order-accurate upwind scheme that is often used for engineering codes. These requirements are related to 1) matching point height, 2) the number of cells below the matching point, and 3) grid resolution at the matching point. The proposed requirements are assessed on a flat-plate turbulent boundary layer and a shock/turbulent boundary-layer interaction flow. As a result, it is clarified that all of the requirements are necessary to ensure the accuracy in terms of mean velocity, Reynolds stresses, and skin friction.

The interaction of longitudinal vortex pairs with a turbulent boundary layer

In this study, we demonstrate an efficient approach to investigating the interaction of vortex pairs on a turbulent boundary layer. Our aim is to assess how vortex characteristics impact the downstream flow. Wall-modelled large eddy simulations are used together with an inlet defined by a Batchelor vortex model superimposed on a turbulent boundary layer profile, generated using synthetic turbulence and a precursor Reynolds-averaged Navier–Stokes calculation. This set-up allows for the efficient testing of multiple configurations whilst providing adequate resolution of outer boundary layer and the vortex–vortex interactions. After validating the methodology, we report a set of simulations for both co- and counter-rotating vortex pairs at different separations and asymmetric strengths. The separation distance between the vortices was found to have a significant effect upon the merging of the vortices. Asymmetric strength vortex pairs, analogous to vortex generators in yaw, demonstrate performance independent of flow direction for small angles. Detailed analysis of this flow provides insight into turbulence generation mechanisms and Reynolds stress anisotropy – valuable reference data for the development of lower-order models. Skin-friction enhancement is shown to be more effective for counter-rotating vortex pairs than co-rotating pairs of the same strength and spacing. Additionally, a wider spacing between the initial vortex positions results in a faster rise in the skin-friction coefficient.

Large Eddy Simulation of Compound Open Channel Flows with Floodplain Vegetation

Floodplain vegetation is of great importance in velocity distribution and turbulent coherent structure within compound open channel flows. As the large eddy simulation (LES) technique can provide detailed instantaneous flow dynamics and coherent turbulent structure predictions, it is of great importance to perform LES simulations of compound open channel flows with floodplain vegetation. In the present study, a wall-modeled large eddy simulation (WMLES) method was employed to simulate the compound open channel flows with floodplain vegetation. The vegetation-induced resistance effect was modeled with the drag force method. The WMLES model, incorporating the drag force method, was verified against flume measurements and an analytical solution of vegetated open channel flows. Numerical simulations were conducted with a depth ratio of 0.5 and four different floodplain vegetation densities (frk = 0, 0.28 m−1, 1.13 m−1 and 2.26 m−1). The main flow velocity, secondary flow, bed shear stress and vortex coherent structure, based on the Q criterion, were obtained and analyzed. Based on the numerical results, the influences of floodplain vegetation density on the flow field and turbulent structure of compound open channel flows were summarized and discussed. Compared to the case without floodplain vegetation, the streamwise velocity in the main channel increased by 10.8%, 19.9% and 24.4% with the frk = 0.28 m−1, 1.13 m−1 and 2.26 m−1, respectively. The results also indicated that, when the floodplain vegetation density increased, the following occurred: the velocity increased in the main channel, while the velocity decreased in the floodplain; the transverse momentum exchange was enhanced; and the strip structures were more concentrated near the junction area of compound open channel flows.

Wall-Modeled Large Eddy Simulation and Detached Eddy Simulation of Wall-Mounted Separated Flow via OpenFOAM

Considering grid requirements of high Reynolds flow, wall-modeled large eddy simulation (WMLES) and detached eddy simulation (DES) have become the main methods to deal with near-wall turbulence. However, the flow separation phenomenon is a challenge. Three typical separated flows, including flow over a cylinder at ReD = 3900 based on the cylinder diameter, flow over a wall-mounted hump at Rec = 9.36 × 105 based on the hump length, and transonic flow over an axisymmetric bump with shock-induced separation at Rec = 2.763 × 106 based on the bump length, are used to verify WMLES, shear stress transport k-ω DES (SST-DES), and Spalart–Allmaras DES (SA-DES) methods in OpenFOAM. The three flows are increasingly challenging, namely laminar boundary layer separation, turbulent boundary layer separation, and turbulent boundary layer separation under shock interference. The results show that WMLES, SST-DES, and SA-DES methods in OpenFOAM can easily predict the separation position and wake characteristics in the flow around the cylinder, but they rely on the grid scale and turbulent inflow to accurately simulate the latter two flows. The grid requirements of Larsson et al. (δ/Δx,δ/Δy,δ/Δz≈(12,50,20)) are the basis for simulating turbulent boundary layers upstream of flow separation. A finer mesh (δ/Δx,δ/Δy,δ/Δz≈(40,75,40)) is required to accurately predict the separation and reattachment. The WMLES method is more sensitive to grid scales than the SA-DES method and fails to obtain flow separation under a coarser grid, while SST-DES method can only describe the vortices generated by the separating shear layer, but not within the turbulent boundary layer, and overestimates the separation-reattachment zone based on the grid system in this paper.

Artificial neural network-based wall-modeled large-eddy simulations of turbulent channel and separated boundary layer flows

Wall-models in a large-eddy simulation (LES) are essential to alleviate the large near-wall resolution requirements for high-Reynolds-number turbulent flow simulations. Among the existing wall-models for a LES, an equilibrium wall-stress model has the highest computational efficiency. Because this model has limitations, such as a lack of non-equilibrium effects and the assumption of a particular law of the wall in the mean velocity, we propose artificial neural network-based wall-stress models (AWMs). The input variables for the AWMs are extracted from the decomposition of the skin-friction coefficient proposed by Fukagata et al. [1], and the AWMs are shown to be able to predict the wall-shear stress in complex flows accurately. The performance of the AWMs is tested for two types of flows, a fully developed turbulent channel flow and a separated turbulent boundary layer flow. A direct comparison of the turbulence statistics with those obtained by previous wall-models (i.e., a log-law-based wall-stress model and a non-equilibrium wall-stress model) shows that better predictions are achieved using the AWMs for both flows, even with untrained Reynolds numbers. When using a coarse grid along the wall-normal direction in wall-modeled LESs (WMLESs) with the AWMs, an upward shift of the mean velocity profile (positive log-layer mismatch, LLM) compared to direct numerical simulation data is found, consistent with previous studies. However, this LLM problem can be overcome by imposing a filtered wall-normal velocity at the wall that is dynamically determined based on the continuity equation and the Taylor series expansion within wall-adjacent cells.

Simulation of a round supersonic combustor using wall-modeled large eddy simulation and partially-stirred reactor models

Simulations are presented for a generic, round supersonic combustor. Turbulence is modeled in the combustor using a wall-modeled large eddy simulation approach. Combustion is modeled using a small quasi-global mechanism and a more detailed skeletal mechanism. Both mechanisms are used in conjunction with two variations of the partially-stirred reactor model for sub-grid turbulence chemistry interactions. Sensitivity of the solutions to grid resolution is investigated. It is found that in order to achieve reasonable grid convergence in the mean wall pressure, the model constant that appears in the partially-stirred reactor model must be a function of both the chemistry mechanism and the grid resolution. Most of the combinations of mechanism and turbulent combustion model tested can be tuned in order to predict the location of the pre-combustion shock train and the peak mean pressure in the combustor. It is found that while the different models are able to reproduce the mean wall pressure, there are significant differences in the mean temperature and heat release rate fields. The sensitivity of the different combinations of mechanisms and partially-stirred reactor formulation is quantified and some combinations are found to be more prone to blowout. Two of the tuned models were tested across several fuel equivalence ratios with a single value of the partially-stirred reactor model constant. One model produced reasonable predictions of shock location and peak mean pressure for each equivalence ratio. The second model captured the global trends in the mean wall pressure, but was unable to quantitatively predict the shock location and peak mean pressure for all equivalence ratios tested.