Wall-modeled Large Eddy Simulation Research Articles

Wall-modeled LES of shock-wave/boundary layer interaction

The present paper discusses the physical reliability of turbulence modeling in an adverse pressure gradient wall flow setup at moderate/high Reynolds number by comparing wall-modeled and wall-resolved LES with DNS and experimental data. A canonical configuration of shock-wave/boundary-layer interaction is used to illustrate the wall modeling behavior. In particular, a standard equilibrium-based wall-modeling approach, combined with an innovative strategy to keep active the no-slip velocity and adiabatic/isothermal temperature constraints at the wall, is adopted. The method, in particular, does not rule out flow separations from the description of the near-wall dynamics and automatically reverts to a wall-resolved LES approach if the spatial resolution allows it. The paper demonstrates how the proposed wall modeling strategy accurately describes the incoming and recovering boundary layers. On the other hand, the recirculation region appears oversized compared to wall-resolved LES and the experimental references. However, bubble shape and morphology are always well described, almost independently from the adopted resolution, well-fitting the experimental results. Thus, the present methodology seems a promising strategy to deal with high Reynolds and Mach number flow with adverse pressure gradient conditions.

Effect of convective schemes in wall-resolved and wall-modeled LES of compressible wall turbulence

The current study discusses how numerical schemes and discretization approaches affect wall-resolved and wall-modeled LES outcomes. A turbulent boundary layer setup over a flat plate in both super- and hypersonic conditions is used to illustrate the effect of different numerical discretization strategies. In particular, six convective methods are examined, as well as various degrees of hybridization between shock-capturing and centered approaches: The former introducing non-negligible numerical viscosity, the latter being virtually dissipation-free. The analysis reveals that injected numerical viscosity due to upwinding procedures considerably alters wall dynamics for both wall-resolved and especially wall-modeled arrangements. In particular, if low-order or pure shock-capturing schemes are used, wall modeling fails in heading the system dynamics due to a strong modulation of main turbulent features. Conversely, realistic turbulence patterns are recovered if hybrid and/or high-order shock-capturing methods are employed. Thus, the paper establishes criteria for selecting a suitable numerical setup in wall-modeled LES, providing suggestions for grid resolution levels and convective scheme selection/hybridization. An overview perspective concerning numerical diffusion coupling with turbulent stresses in wall-resolved and wall-modeled LES is also provided.

Analysis of a higher-order vorticity confinement scheme in flux correction form

This article presents a detailed comparison of the classical source-term formulation of higher-order Vorticity Confinement with a flux-correction version, through an application to a series of well-documented cases. Both formulations and their numerical implementation are presented first. Then the methods are applied to the simple case of the long-time advection of an inviscid and isentropic vortex. A shock-vortex interaction case is also computed to demonstrate the compatibility of the method with the shock-capturing properties of the baseline scheme. Both methods are finally applied to a ZDES mode 3 (Wall-Modelled LES) simulation of a zero-pressure-gradient flat-plate turbulent boundary layer, showing a better preservation of smaller-scale vortical structures with respect to standard higher-order numerical schemes. Furthermore, the flux-correction form of Vorticity Confinement significantly improves the prediction of skin friction with respect to both the baseline scheme and the classical source-term formulation, thus showing that the flux-correction form of confinement is essential for a reliable prediction of this quantity.

Computational hydroacoustic analysis of the BB2 submarine using the advective Ffowcs Williams and Hawkings equation with Wall-Modeled LES

In the present work we perform the numerical characterization of the hydrodynamic and the hydroacoustic field of a notional submarine geometry (the BB2 submarine). Starting from a model-scale CFD simulation, the full scale acoustic signature of the submarine is derived. We use large eddy simulation with a wall-layer model and perform laboratory-scale numerical experiments at a value of Reynolds number equal to 1.2×106. The conditions are those of a wind-tunnel test. The study is carried out focusing on the submarine in its own basic configuration without propeller to highlight the acoustic properties of the hull by itself and to replicate the silent advancing running (where all the non-essential source of noise are shut down and the speed is minimum to minimize the propeller noise). In this configuration, the wake is the main source of noise. The computational hydroacoustic analysis is based on the Ffowcs-Williams and Hawkings equation, here considered in advective form, which is the most suitable form for wind-tunnel-like problems. The results show that the acoustic spectrum is broadband in the far field and the SPL evaluated in the near field contains the signature of coherent structures associated to the presence of the sail and appendages.

Evaluation of wind loads on high-rise buildings at various angles of attack by wall-modeled large-eddy simulation

This study is to validate the accuracy of large-eddy simulation (LES) of wind pressures and loads on high-rise buildings at various angles of attack based on approaching flow simulation framework with synthetized inflow turbulence. The wake flow field and pressure distribution on building surfaces are quite different at different angles of attack due to sensitivity of flow phenomena (separation, vortex, wake effects, etc.). To better capture such complex flow features around the building, local octree mesh refinement is proposed as an efficient meshing strategy to improve the simulation of wind loads statistics with acceptable additional computational cost. Its accuracy is demonstrated by comparing the simulation results from progressive levels of mesh refinement with experimental data. It is shown that octree mesh refinement can improve the prediction of skewness and kurtosis of wind pressures, which are important for the prediction of peak pressures. Moment-based Hermite model approach is introduced for better assessment of probability distribution of peak pressures from short duration of simulation samples.

Analysis of Space-Time Correlations to Support the Development of Wall-Modeled LES

Analysis of Space-Time Correlations to Support the Development of Wall-Modeled LES

An immersed boundary method for wall-modeled large-eddy simulation of turbulent high-Mach-number flows

The excessive computational resource requirements for direct numerical simulation (DNS) and wall-resolved large eddy simulation (LES) make these methods intractable for simulations concerning turbulent flows over complex, real-world geometries. Wall-modeled LES (WMLES) approaches seek to reduce this cost by applying wall-layer models to the inner-most region of turbulent boundary layers. Immersed boundary methods (IBMs) have grown in popularity over the past few decades since the mesh can be automatically generated for any complex geometry - a potentially major advancement for common industrial CFD simulations. However, immersed boundary approaches suffer from reduced numerical accuracy and, possibly, stability at the wall, primarily attributable to irregular discretization of boundary operators. This is a problem that is especially significant for WMLES of high Mach number flows, where numerical schemes have the conflicting requirements to be both stable at high wavenumbers and non-dissipative. This presentation introduces a coupled IBM-WMLES approach that is tailored to the simulation of high-speed turbulent flows. The basis of this method is to carefully address numerical dissipation and stability away from and close to the wall. This is achieved by using a hybrid central-upwind flux reconstruction scheme and careful application of smooth boundary conditions. The presented test cases evaluate the current scheme for a wide range of physical flow phenomena, and include a turbulent channel for basic validation, a hypersonic transitional boundary layer to investigate high-speed zero-pressure-gradient flows, a hypersonic shock wave boundary layer interaction to investigate adverse pressure gradients, separation, and turbulent heating, and a hypersonic compression ramp which is significantly challenging as it combines all of the features from the aforementioned high-speed flow problems.

A non-equilibrium slip wall model for large-eddy simulation with an immersed boundary method

A non-equilibrium wall model for large-eddy simulation with the immersed boundary (IB) method is proposed to reduce the required number of grid points in simulating wall-bounded turbulence. The proposed wall model is presented as an appropriate slip velocity on the wall. The slip velocity is constructed by integrating the simplified turbulent boundary layer (TBL) equation along the wall-normal direction, which enhances the integral momentum balance near the wall on a coarse grid. The effect of pressure gradient on the near wall flow is taken into account by retaining the pressure gradient term in the simplified TBL equation. The proposed model is implemented in the form of a direct-forcing IB method with moving-least-square reconstruction near the wall. The benchmarks of plane channel turbulence and the flows over a backward-facing step are used for validation. The proposed model improves the wall stresses and velocity profiles in the region where the pressure gradient dominates the near wall flows.

Scale-resolving simulations of the flow in the Francis-99 turbine at part-load condition

In this paper, we investigate the formation of the Rotating Vortex Rope (RVR) using scale-resolving methods, SAS and Wall-Modeled LES (WMLES). We compare the results from these simulation methods with the experimental data of the Francis-99 workshop. This comparison shows that the general features of the RVR can be captured with both methods. However, using WMLES methods would lead to a better quantitative agreement between the velocity profiles in the draft tube in the simulation and the experiment. The reasons for this better agreement are discussed in detail. A comparison of the pressure fluctuations in the draft tube captured in the simulations and the experiment is also presented. This comparison shows that all simulations under-predict the Root Mean Square (RMS) of these pressure fluctuations, although the RMS values predicted by the WMLES simulation are closer to the experimental values.

High Order Wall-Modeled Large-Eddy Simulation on Mixed Unstructured Meshes

In the present study, an algebraic equilibrium wall model previously developed for hexahedral elements is extended to handle mixed meshes including prismatic, tetrahedral, and pyramidal elements in the context of a discontinuous high-order method. This extension is needed for complex geometries, for which high-order mixed elements (e.g., tetrahedral and pyramidal elements) are often necessary near solid walls to avoid meshing challenges. Various design decisions are discussed to achieve the best performance on massively parallel CPU/GPU architectures for a production-level high-order large-eddy simulation solver based on the flux reconstruction/correction procedure via reconstruction method, hpMusic. The extension to other elements is first evaluated using a benchmark channel flow problem at various Reynolds numbers. After that, flow over the NASA high-lift Common Research Model (CRM-HL) from the 4th AIAA High-lift Prediction Workshop is computed to further test the new implementation. Computational results at the third- and fourth-order accuracies are compared with experimental data.

Wall-modeled large-eddy simulation of noise generated by turbulence around an appended axisymmetric body of revolution

Wall-modeled large-eddy simulation of noise generated by turbulence around an appended axisymmetric body of revolution

Evidence that uniform momentum zones originate from roughness sublayer structure interactions in fully rough channel turbulence

Fully rough wall-sheared turbulence is composed of an inner and outer layer, the former occupied by sinuous structures sustained by the well-known autonomous inner cycle, the latter occupied by inclined parcels of momentum deviations relative to the average. The outer-layer structures are also known as uniform momentum zones (UMZs), where the presence of successive UMZs manifests instantaneously with a distinct ‘staircase’ pattern in streamwise velocity. Direct numerical simulation (DNS) of fully rough channel turbulence was recently used to interpret UMZs as wakes originating from antecedent bluff-body-like interactions within the inner layer (Anderson & Salesky, J. Fluid Mech., vol. 906, 2020, A8). Wake-scaling arguments agreed precisely with instantaneous results from DNS. Foremost among these results was evidence that the instantaneous wall-normal gradient of streamwise velocity exhibited scaling of ${\sim }x_3^{-1/2}$ , where $x_3$ is wall-normal location; this is in contrast to logarithmic scaling, which requires the wall-normal gradient of streamwise velocity to scale as ${\sim }x_3^{-1}$ . Herein, wake-scaling arguments have been advanced and compared against results from wall-modelled large-eddy simulation (LES). New results from the ‘bottom up’ wake-scaling arguments agree with LES results, such that the shear associated with the instantaneous staircase-like streamwise velocity follows a clear trend. We have leveraged conditional sampling during LES – predicated upon instantaneous low-frequency, high-magnitude surface stress values known to correspond to large-scale inertial-layer coherence – to further assess the predictive value of the wake-scaling arguments. Model results compare favourably.

Quasi-wall-resolved large eddy simulation of transitional flow in a transonic compressor rotor

The large eddy simulation (LES) method is a high-resolution and promising approach for the accurate turbulence analysis of axial-flow compressors. However, the validity of LES method in the analysis of the laminar-turbulent transition in the high-speed compressor is unknown or not fully exploited, and the flow physics associated with the interaction between the transition and the shock-induced boundary layer separation remains unclear. In the present work, a concept of quasi-wall-resolved LES (QWRLES) method is developed, in which the near-wall grid resolution lies between that of wall-resolved LES (WRLES) and wall-modeled LES (WMLES) but the height of the first layer of near-wall grid cell is within 10 in wall units to permit a direct calculation of wall-shear stress via the Newtonian constitutive relation. The prediction accuracy of QWRLES is first verified in the channel-flow and transonic bump-flow problems. Then, the simulation of the transonic compressor NASA Rotor 37 is carried out to validate the QWRLES method and to explore the transition mechanism. Reasonable agreement between the calculated and measured aerodynamic performance is achieved. The simulation results show that the transition occurs in a bypass mode on the blade suction surface and near the shroud- and hub-endwalls. The shock-boundary layer interaction, the strong shear in the tip-leakage region and the pitchwise shear of the rotating hub are responsible for the transition in the above three regions, respectively. The simulation results show high resolution of the LES method for the transitional and turbulent flows in axial-flow compressors.

Large Eddy Simulation of HAWT and VAWT performances in the vicinity of a building

This work compares the performances of a Horizontal Axis Wind Turbine (HAWT) and a Vertical Axis Wind Turbine (VAWT) using Wall modeled Large Eddy Simulation (WMLES) coupled with an actuator line method. The wind turbines are located in the vicinity of a real size industrial building. Both wind turbines are sized to produce the same power at their respective optimum Tip Speed Ratio for a same incident wind speed. Two relevant incident wind directions (SW and SSW) are investigated, the influence of the building on the performance of the two wind turbines is also analysed. The results obtained show that the HAWT has a better overall performance compared to the VAWT. Overspeeds are observed for both directions analysed, due to the presence of the building which locally increases the flow velocity. However, these overspeeds remain low due to the low height of the building. The change of wind direction only slightly impacts the HAWT production, while the VAWT production remains insensitive. However, the presence of the building improves the global production of both wind turbines. Qualitatively, this change of wind direction induces a deviation in the wake of both turbines, which is greater for a SW direction.

A wall-modeled approach accounting for wave stress in Large Eddy Simulations of offshore wind farms

In the context of offshore wind farms, accurate predictions of surface fluxes in the marine atmospheric boundary layer are critical for Large Eddy Simulations (LES) of airflow over waves. The effect of the waves on the airflow is often modeled by prescribing the roughness length in the framework of Monin-Obukhov similarity theory. However, such approaches lack generalizability over different wave conditions due to reliance on model coefficients tuned to specific datasets. Wave phase-resolving simulations on the other hand have higher accuracy but also a higher computational cost. In this work, a sea surface-based hydrodynamic drag model is applied to model the pressure-based surface drag felt by the wind due to the waves. An offshore wind farm configuration is simulated using a wall-modeled LES, with the effect of the waves represented using the wave-drag model and the wind turbines represented by an actuator disk model. The approach is validated with data from high fidelity wave-resolving Large Eddy Simulations. The effect of the waves and the farm configuration on the mean velocity profiles power production, and kinetic energy budget are quantified.

Aeroacoustic prediction based on large-eddy simulation and the Ffowcs Williams\u2013Hawkings equation

A hybrid noise computation method is presented in this paper. Large-eddy simulation with wall-model equation is proposed to compute the flow field. With a stress-balanced wall-model equation, the near-wall computation cost of large eddy simulation was effectively reduced. The instantaneous flow variables obtained by the large-eddy simulation were used to compute the noise source terms of the Ffowcs Williams–Hawkings equation. The present method was investigated with two test cases: a single cylinder at Re = 10,000 and a rod-airfoil at Re = 480,000. The flow quantities and aeroacoustic characteristics were compared with the reference data. The mean velocity profiles and spectra of the flow fluctuations were consistent with data from the literature. When compared with the reference data, the noise computation error was less than 3 dB. The computation results demonstrate the present wall-modeled large eddy simulation is efficient for the noise computation of complex vortex shedding flows.

Adaptive Determination of the Optimal Exchange Location in Wall-Modeled Large-Eddy Simulation

Wall-modeled large-eddy simulation introduces a modeling interface (or exchange location) separating the wall-modeled layer from the rest of the domain. The current state-of-the-art is to rely on user expertise when choosing where to place this modeling interface, whether this choice is tied to the grid or not. This paper presents a postprocessing algorithm that determines the exchange location systematically. The algorithm is based on a model for the error in the predicted wall shear stress and a model for the computational cost, and then finds the exchange location that minimizes a combination of the two. The algorithm is tested both a priori and a posteriori using an equilibrium wall model for the flow over a wall-mounted hump, a boundary layer in an adverse pressure gradient, and a shock/boundary-layer interaction. The algorithm produces exchange locations that mostly agree with what an experienced user would suggest, with thinner wall-modeled layers in nonequilibrium flow regions and thicker wall-modeled layers where the boundary layer is closer to equilibrium. This suggests that the algorithm should be useful in simulations of realistic and highly complex geometries.

A new single formula for the law of the wall and its application to wall-modeled large-eddy simulation

In this work, a new single formula is proposed for the law of the wall, which is dubbed as the LOG–EXP (logarithmic–exponential) formula, for predicting the mean velocity profile in different regions near the wall. When deriving the LOG–EXP formula, a correction term instead of a damping function is introduced to model the difference between the mixing-length eddy viscosity model and the actual Reynolds shear stress for the near-wall effect. The formula is tested using the direct numerical simulation (DNS) data of turbulent channel flows, the experimental data of the boundary layer flow over a flat plate, and the circular pipe flow for different Reynolds numbers. The formula is then employed as the wall model in wall-modeled large-eddy simulation (WMLES) and tested using the turbulent channel flow at three different Reynolds numbers. An overall good performance of the LOG–EXP formula is observed for all the considered cases. When refining the grid, no significant improvements are observed for the Reynolds stresses, as there are several factors, e.g., the grid employed, and the subgrid-scale model, affecting the predictive capability of WMLES. Further work is needed to quantify their effects and improve the WMLES predictions on a fine grid but not fine enough for a wall-resolved large-eddy simulation.

Wall-Modeled Large Eddy Simulation of High Speed Flows

The use of wall-modeled large-eddy simulation (WMLES) is explored in the context of compressible flows with a focus on cold-wall boundary layers and flows with shock-induced separation. It is observed that for cold-wall flows, a “mixed” scaling for the length scale appearing in the eddy viscosity formulation outperforms the classical semilocal scaling for obtaining predictions of heat flux and skin friction. A few shock/boundary-layer interaction (SBLI) cases are examined in some detail, and model modifications are proposed to overcome identified deficiencies. It is shown that using WMLES the low-frequency characteristics of SBLI at high Reynolds number can be quantitatively captured. A dynamically switched version of the equilibrium model is proposed; this shows promise for relatively inexpensive simulations at these conditions.

Numerical investigation of convection heat transfer characteristics in sloshing corium pools

The convection flow and heat transfer actuated by internal decay heat and the sloshing of vessels are the primary problems in the study of thermal behaviors in volumetrically heated reactor corium pools under ocean conditions. The wall-modeled large eddy simulation (WMLES) method, volume of fluid model, and phase-change model combined with dynamic mesh technology, were used to develop a three-dimensional flow and heat transfer process simulation model of the sloshing corium pool. In addition, the heat conduction behavior in the crust and vessel wall, as well as the pressure-vessel-wall integrity evaluation was considered. The predicted internal heat transfer characteristics (the temperature distribution, the wall heat flux, and the shell thickness) in the corium pool and the evolution feature of the free surface height near the wall were in good agreement with the LIVE-L4 test results and sloshing experimental data, respectively. Furthermore, the coupled heat transfer phenomenon of the melt and vessel was simulated. The simulation results indicated that the time required to reach stable heat transfer was shortened, the structure of thermal stratification was transformed, and the heat flux along the inner surface of the vessel wall of the shell was improved at the resonance state. The comparisons of local Nusselt (Nu) number at the near-wall between static and sloshing corium pool conditions showed that heat transfer characteristics were significantly influenced by sloshing (T = 2.5 s, A = 0.07 rad) motion, and the Nu number of forced convection fraction had a strong correlation with the local Reynolds number in sloshing corium pools. Conclusively, the transient heat flux distribution of the sloshing melting pool differed from that of the static corium pool, increasing the molten range, and molten peak depth of the pressure-vessel-wall.