Wall-modeled Large Eddy Simulation Research Articles

Prediction of Flow Separation and Side-loads in Rocket Nozzle Using Large-eddy Simulation

The design process is a critical issue in order to improve rocket engine performance. Indeed, the prediction of the aerodynamic forces acting on the nozzle, in particular the off-axis loads, is challenging even for modern methods. In this study, the flow of an exit Mach number Truncated Ideal Contour (TIC) nozzle is numerically investigated by means of Large-Eddy Simulation (LES), using the unstructured compressible AVBP solver developed by CERFACS. The study focuses on an over-expanded regime characterised by a Free-Shock Separation (FSS). To obtain an accurate prediction of the flow, an Adaptive Mesh Refinement (AMR) methodology is used. Results show that wall-modelled LES combined with AMR allows to accurately capture the jet flow dynamics while at the same time reducing the CPU time of LES: both the location of the mean separation point along with the pressure fluctuations inside the nozzle are well captured. In particular, the two peaks of the pressure Power Spectral Density contributing to the side-loads mechanism are correctly predicted compared to experiment.

Physics and modeling of trailing-edge stall phenomena for wall-modeled large-eddy simulation

Predictability of trailing-edge stall phenomena using wall-modeled large-eddy simulations (LES) is investigated with a wall-resolved LES database. An analysis based on the momentum integral relation shows that the skin friction accumulation effect near the leading edge to the mid chord dominates boundary layer development, and thus, affects flow separation prediction near the trailing edge. The results indicate that accurate wall modeling near the leading edge to the mid chord is essential for predicting stall phenomena, but not necessarily required near and downstream of the separation.

Numerical Simulation of Supersonic Separated Flow over Inclined Backward-Facing Step Using RANS and LES Methods

A description of two methods for simulation of the flow around complex test configurations is considered. One method implements a well-known approach to solving the Reynolds-averaged Navier-Stokes equations with a closing differential turbulence model. Another method is based on scale-resolving wall-modelled LES approach (WMLES). The classical problem of the flow around the inclined backward-facing step with the generation of expansion waves, intensive shock waves and separated flow zones is considered. A comparison of computational and experimental data is done. The physics of the flow is described. The accuracy of the both approaches is evaluated.

Numerical Investigation of the Unsteady Flow Past an Iced Multi-Element Airfoil

Unsteady flow characteristics are investigated using wall-modeled large-eddy simulation for a 30P30N three-element airfoil with streamwise ice and horn ice accreted at its slat leading edge, respectively. The ice accretions cause massive flow separation above the slat, which results in a surface pressure plateau on the slat and further unloads the downstream wing elements. The above mentioned two ice shapes lead to lift decreases of 10.66 and 16.45% and drag increases of 44.58 and 59.42%, respectively. Ice-induced vortices first roll up due to Kelvin–Helmholtz instability above the slat with ice accretions, and the subsequent vortex pairing halves their characteristic motion frequency. The developed vortices, composed of multiscale structures, dominate the slat upper surface and are convected through the main element to aggravate the flow separation over the flap. Moreover, extremely strong acoustic resonance occurs in the iced slat cove, and its tonal frequencies are consistent with theoretical model predictions. These intense tones are believed to result from the elevated pressure fluctuations along the cavity free shear layer, which are in turn related to the propagation of the ice-induced pressure fluctuations from above the slat because their most dominant frequencies identified by proper orthogonal decomposition are nearly equal to the resonant frequencies.

Localizing effect of Langmuir circulations on small-scale turbulence in shallow water

Wall-resolved and wall-modelled large-eddy simulations are performed to study the localizing effect of Langmuir cells (LCs) on small-scale background turbulence in shallow water. The total velocity fluctuations are decomposed into an LC content extracted by streamwise averaging and a background turbulence part. Based on the large-scale motions of LCs, the spanwise domain is divided into three regions dominated by the upwelling, spanwise and downwelling flows of LCs, respectively. The localized Reynolds stresses in different spanwise regions are compared to show the localizing effects of the LCs on the background turbulence quantitatively, where (or ), (or ) and (or ) represent the streamwise, vertical and spanwise components of the background turbulence velocity, respectively, and denotes time and streamwise averaging. It is shown that the magnitudes of the localized Reynolds stresses in different spanwise regions vary significantly. The transport equations of the localized Reynolds stresses are then analysed to investigate the mechanisms underlying the localizing effects. It is discovered that the difference in the energy production correlated to the shear of the LC content among different regions is the key factor that leads to the localization of background turbulence. In addition, the energy production correlated to the shear of the mean flow, the energy redistribution due to the pressure–strain correlation, and the interaction between the localized Reynolds stresses and the shear of the Stokes drift also play important roles. Based on the results obtained from the analysis of the transport equations, predictive models are proposed for the localizing effects, which assess the spatial dependence of the Boussinesq model for background turbulence in coastal Langmuir turbulence. These models show good scaling performance of near the water bottom and of , and in the central region of the water column under various flow conditions with different values of the Reynolds number, turbulent Langmuir number and wavenumber.

Active flow control for external aerodynamics: from micro air vehicles to a full aircraft in stall

We investigate the aerodynamic performance of active flow control of airfoils and wings using synthetic jets with zero net-mass flow. The study is conducted via wall-resolved and wall-modeled large-eddy simulation using two independent CFD solvers: Alya, a finite-element-based solver; and charLES, a finite-volume-based solver. Our approach is first validated in a NACA4412, for which numerical and experimental results are already available in the literature. The performance of synthetic jets is evaluated for two flow configurations: a SD7003 airfoil at moderate Reynolds number with laminar separation bubble, which is representative of Micro Air Vehicles, and the high-lift configuration of the JAXA Standard Model at realistic Reynolds numbers for landing. In both cases, our predictions indicate that, at high angles of attack, the control successfully eliminates the laminar/turbulent recirculations located downstream the actuator, which increases the aerodynamic performance. Our efforts illustrate the technology-readiness of large-eddy simulation in the design of control strategies for real-world external aerodynamic applications.

Flux Reconstruction Implementation of an Algebraic Wall Model for Large-Eddy Simulation

In the present study, an algebraic equilibrium wall model is implemented and tested for a large-eddy simulation (LES) solver based on the flux reconstruction (FR) method. One of the objectives of the present paper is to verify the main results of Frère et al. (“Application of Wall Models to Discontinuous Galerkin LES,” Physics of Fluids, Vol. 29, No. 8, 2017, Paper 085111) under the FR framework. In addition, the influence of the mesh growth ratio in the wall-normal direction and the mesh resolutions in the wall-parallel directions are investigated, as well as the size of the first element in the wall-normal direction. In the present wall model, the wall shear stress is computed according to the wall tangential velocity at the interface between the first and second cells from the wall. The stress is then used to update the solution unknowns. Various strategies are evaluated using a turbulent channel flow at a high Reynolds number. A comparison between a wall-modeled LES and implicit LES (ILES) without a wall model on a coarse mesh shows that the wall-modeled approach produces better results than the ILES. The wall model is then evaluated with the two-dimensional periodic hill problem to assess its capability of capturing flow separation and reattachment. The equilibrium wall model fails to capture turbulent flow separation and reattachment, indicating the need for nonequilibrium wall models for such problems.

A comparative study on the large-scale-resolving capability of wall-modeled large-eddy simulation

Wall-modeled large-eddy simulation (WMLES) could be a useful predictive tool in high-Reynolds-number wall-bounded turbulent flows that are ubiquitous in nature and engineering, but its capability to resolve large-scale energy-containing outer motions has yet to be assessed comprehensively. In this study, moderately high-Reynolds-number turbulent channel flows up to Reτ ≈ 5200 are simulated by WMLES with various subgrid-scale (SGS) models and wall models in comparison with direct-numerical simulation data. The main objective is to assess the predictive capability of WMLES in the context of the turbulence kinetic energy spectrum in the outer region. Four classical eddy-viscosity-type SGS models are compared, i.e., the Smagorinsky model, the Lagrangian dynamic model, the Lagrangian scale-dependent (LASD) model, and the Vreman model. It is shown that the performance of the LASD model is superior to others in predicting one-point statistics as well as kinetic energy spectra. Three types of wall models are involved, i.e., the equilibrium wall model, the slip-wall model, and the integral wall model. We find that the wall model does not significantly affect prediction of turbulence fluctuations in the outer region. Although near-wall turbulent motions are not fully resolved in WMLES, we clearly show that the spectral characteristics of large-scale energy-containing turbulent motions in the outer region can reasonably be predicted with appropriate models. We also provide a preliminary discussion on the effects of domain setup and grid resolution. The difference in the spectral energy distribution between full- and half-channel flows is also reported.

Shock-Induced Flow Separation in an Overexpanded Supersonic Planar Nozzle

Shock-induced flow separation in an overexpanded supersonic planar nozzle is investigated numerically by means of three-dimensional wall-modeled large-eddy simulations (LES). The objective of this study is to identify the origin of the low-frequency shock oscillations (LFO) and the associated side-loads generation in planar nozzles. The computational results are compared with the experimental data for validation. The promise of the near-wall LES modeling approach, adopted in this study, is supported by its satisfactory performance in correctly predicting the shock-induced flow separation and offering a major advantage of being 30–40 times faster than the wall-resolved LES counterpart, allowing thereby the capture of very–low-frequency shock oscillations with much better statistics convergence. The simulations bring clear evidence of the existence of broadband and energetically significant LFO in the vicinity of the separated shock, whose forward and backward movements are mainly driven by changes in the downstream flow conditions. The complex interactions between the backflow, the separation bubbles, and the large-scale turbulent structures developing in the shear-layer region strongly influence the shock unsteadiness, which in turn drives the LFO. A scenario of the LFO, confirming conclusions from earlier studies, is described in this work.

Validation of Wall-Modeled LES Based on Lattice Boltzmann Method with Turbulent Channel Flow

Validation of Wall-Modeled LES Based on Lattice Boltzmann Method with Turbulent Channel Flow

Wavelet-Based Adaptive Unsteady Reynolds-Averaged Navier–Stokes Simulations of Wall-Bounded Compressible Turbulent Flows

A wavelet-based adaptive approach, called wavelet-based adaptive unsteady Reynolds-averaged Navier–Stokes (WA-URANS), is proposed to solve the URANS equations for the computation of wall-bounded internal and external compressible turbulent flows. The new approach uses anisotropic wavelet-based mesh refinement, and its effectiveness is demonstrated for flow simulations with two different turbulence models, namely, the Spalart–Allmaras and models for a variety of two- and three-dimensional flow configurations with arbitrary geometries, different speed regimes, and various boundary conditions. Supersonic plane channel flow, a weakly compressible channel flow with periodic hill constrictions, a subsonic zero-pressure-gradient flat-plate boundary-layer flow, the separated flow over NASA wall-mounted hump, the Bachalo–Johnson flow (axisymmetric transonic bump flow), and a flow past a circular cylinder at a subcritical Reynolds number are tested as benchmark flows. The effectiveness and efficiency of the new wavelet-based approach are demonstrated by comparing the results of the WA-URANS simulations with literature data. This comprehensive validation of the WA-URANS approach encourages its application to practical problems of industrial interest, and demonstrates the feasibility of extending this approach to wavelet-based wall-modeled large-eddy simulation (LES) and hybrid URANS/LES. Finally, the current study serves as a baseline for the development of a unified hierarchical framework for eddy-resolving turbulence modeling, capable of performing computations of different fidelity, ranging from adaptive direct numerical simulations to adaptive URANS computations.

Wall-Modeled Large-Eddy Simulations of a Multistage High-Pressure Compressor

This study aims at evaluating the feasibility and the accuracy of a Wall-Modeled Large Eddy Simulation of an actual aeronautical multistage axial high-pressure compressor. The computational domain is composed of 37 blades and a geometrically complex recirculating cavity. The numerical method TurboAVBP is able to handle such a technical challenge thanks to its unstructured and massively parallel approach as well as dedicated rotor-stator interface treatments. The influence of grid resolution, from less than 100 millions to more than 1 billion of cells, is particularly evaluated. The intermediate grid correctly predicts the global aerodynamic performances up to the lowest mass flow rate regime. In comparing with time-resolved measurements, the finest grid is shown to accurately predict flow within rotors, especially in their tip regions that are critical for performances and stability of the whole compressor.

Wall-modeled large-eddy simulations of spanwise rotating turbulent channels—Comparing a physics-based approach and a data-based approach

We develop wall modeling capabilities for large-eddy simulations (LESs) of channel flow subjected to spanwise rotation. The developed models are used for flows at various Reynolds numbers and rotation numbers, with different grid resolutions and in differently sized computational domains. We compare a physics-based approach and a data-based machine learning approach. When pursuing a data-based approach, we use the available direct numerical simulation data as our training data. We highlight the difference between LES wall modeling, where one writes all flow quantities in a coordinate defined by the wall-normal direction and the near-wall flow direction, and Reynolds-averaged Navier-Stokes modeling, where one writes flow quantities in tensor forms. Pursuing a physics-based approach, we account for system rotation by reformulating the eddy viscosity in the wall model. Employing the reformulated eddy viscosity, the wall model is able to predict the mean flow correctly. Pursuing a data-based approach, we train a fully connected feed-forward neural network (FNN). The FNN is informed about our knowledge (although limited) on the mean flow. We then use the trained FNNs as wall models in wall modeled LES (WMLES) and show that it predicts the mean flow correctly. While it is not the focus of this study, special attention is paid to the problem of log-layer mismatch, which is common in WMLES. Our study shows that log-layer mismatch, or rather, linear-layer mismatch in WMLES of spanwise rotating channels, is not present at high rotation numbers, even when the wall-model/LES matching location is at the first grid point.

Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

In wall-bounded turbulent flows, the wall-normal gradient in turbulence intensity causes inertial particles to move preferentially toward the wall, leading to elevated concentration levels in the viscous sublayer. At first glance, wall-modelled large-eddy simulations may seem ill suited for accurately simulating this behaviour, given that the sharp gradients and coherent structures in the viscous sublayer and buffer region are unresolved in this approach. In this paper, a detailed inspection of conservation equations describing the influence of turbophoresis and near-wall structures on particle concentration profiles reveals a more nuanced view depending on the friction Stokes number. The dynamics of low and moderate Stokes number particles indeed depends strongly on the complex spatio-temporal details of streaks, ejections, and sweeps in the near-wall region. This significantly impacts the near-wall particle concentration through a biased sampling effect which provides a net force away from the wall on the particle ensemble caused by the tendency of inertial particles to accumulate in low-speed ejection regions. At higher Stokes numbers, however, this biased sampling is of minimal importance, and the particle concentration becomes inversely proportional to the wall-normal particle velocity variance at a given distance from the wall. As a result, wall-modelled large-eddy simulations can predict concentration profiles with more accuracy in the high Stokes number regime than low Stokes numbers simply by modifying the interpolation scheme for particles between the first grid point and the boundary. However, accurate representation of low and moderate Stokes number particles depends critically on information not present in standard wall-modelled large-eddy simulations.

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model which explains the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1,000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressure-strain correlation which ultimately inhibits the generation of Reynolds stress. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium, three-dimensional flows.

Prediction of the impact of support structures on the aerodynamic performance of large wind farms

An extended theoretical model based on a two-scale coupled momentum balance method is proposed to estimate aerodynamic effects of wind turbine towers on the performance of both ideal (infinitely large) and more realistic (large but finite-size) wind farms. A key implication of the extended model is that a normalized support-structure drag, AS/A×CD*, where A and AS are the rotor swept area and support-structure frontal projected area, respectively, and CD* is an effective support-structure drag coefficient, may play an important role in the design of future large wind farms. For the infinitely large case, the theoretical model shows that the optimal turbine spacing should increase with the value of AS/A×CD*, whereas for the large finite case, this also depends on an additional parameter describing the response characteristics of the atmospheric boundary layer to the total farm drag. To validate the theoretical model for the infinitely large case, Wall-Modeled Large-Eddy Simulations of a periodic array of actuator disks with and without support structures are conducted. The results show a reasonably good agreement (within 10% in the prediction of power) with the theoretical model.

Advanced simulations of turbulent boundary layers under pressure-gradient conditions

A high-Reynolds-number turbulent boundary layer experiencing pressure gradients is simulated with Reynolds-averaged Navier-Stokes (RANS) and hybrid RANS/LES (Large Eddy Simulation) advanced turbulence modeling approaches, namely, two eddy viscosity models, two Reynolds Stress models (RSMs), and Zonal Detached Eddy Simulation (ZDES) mode 3 which corresponds to a wall-modeled LES approach. Such a study is the first of its kind to the authors’ best knowledge. The test-case considered is the experimental work of Cuvier et al. [“Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology,” J. Turbul. 18, 929–972 (2017)]. Some modifications of the top wall geometry have been proposed to take into account the blockage effect of the boundary layers developing over the wind tunnel side walls so that statistically two-dimensional simulations are possible. Comparisons have shown that there are some difficulties in properly predicting the mean skin friction and the Reynolds stresses in the adverse-pressure-gradient region for the ZDES and RSMs. The mean velocity profiles in this region are, however, poorly reproduced by all models. The atypical profiles experimentally observed at the beginning of the favorable-pressure-gradient region are well reproduced by RSMs, one eddy viscosity model, and ZDES for the mean velocity; however, only ZDES is able to satisfactorily predict the Reynolds stresses at this station. A spectral analysis of streamwise velocity fluctuations and Reynolds shear stress by means of ZDES has allowed us to identify external energetic turbulent structures at y ≈ 0.5δ and of size λx ≈ 3δ which are probably responsible for these atypical profiles. The present numerical test-case may constitute a development base for turbulence modeling under pressure gradient effects.

Large eddy simulation of pseudo shock structure in a convergent–long divergent duct

In this paper, the Pseudo shock structure in a convergent–long divergent duct is investigated using large eddy simulation on the basis of Smagorinsky–Lilly,​ Wall-Adapting Local Eddy-Viscosity and Algebraic Wall-Modeled LES subgrid models. The first objective of the study is to apply different subgrid models to predict the structure of Lambda form shocks system, while the ultimate aim is to obtain further control of the shock behavior. To achieve these goals, the dynamic grid adaption and hybrid initialization techniques are applied under the 3D investigation to reduce numerical errors and computational costs. The results are compared to the existing experimental data and it is found that the WMLES subgrid model results in more accurate predictions when compared to the other subgrid models. Subsequently, the influences of the divergent section length with the constant ratio of the outlet to throat area and, the effects of discontinuity of the wall temperature on the flow physics are investigated. The results indicate that the structure of compressible flow in the duct is affected by varying these parameters. This is then further discussed to provide a deeper physical understanding of the mechanism of Pseudo shock motion.

Modification to Improved Delayed Detached-Eddy Simulation Regarding the Log-Layer Mismatch

The wall-modeled large-eddy simulation branch of the widely used improved delayed detached-eddy simulation (IDDES) method is supposed to resolve the problems of log-layer mismatch and underprediction of skin friction, as claimed by the authors of the IDDES (Shur, M. L., Spalart, P. R., Strelets, M. K., and Travin, A. K., "A Hybrid RANS-LES Model with Delayed DES and Wall-Modeled LES Capabilities," International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 1638–1649). But, some researchers did meet these problems when using the IDDES. Aiming at finding out the reason and seeking a remedy, an analysis of the IDDES is carried out that focuses on the relation between the wall-parallel grid size and the length scale of the energetic turbulent structures at the Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) interface, and it reveals that the flaw of the IDDES arises from the fact that, in the IDDES approach, the energetic, large-scale, and stress-carrying turbulent structures in the vicinity of the RANS/LES interface are essentially impossible to well resolve by the LES mode. On the basis of the analysis, a modification to the IDDES is proposed by moving the RANS/LES interface further away from the wall so that, at the RANS/LES interface, the wall-parallel grid size is sufficient to resolve the turbulent structures. The modification is simple in form but has clear physical meaning. Through a series of sensitivity tests, it can be concluded that the modified IDDES does resolve the problems of log-layer mismatch and underprediction of skin friction, and it is applicable to low-, moderate-, and high-Reynolds-number flat plate boundary-layer flows without exception.

Wall-Modeled Large Eddy Simulation of the Flow Through PWR Fuel Assemblies at ReH = 66 000—Validation on CALIFS Experimental Setup

The EDF aims to identify what causes fuel assembly vibrations in pressurized water reactors. The present work focuses on the validation of pressure fluctuations along the central rod of a 5 × 5 configuration for wall-modeled large eddy simulations. New experiments, called CALIFS, have been carried out by the Atomic Energy Commission (CEA) on a 5 × 5 mixing vane grid (MVG) in the framework of the Fuel Assembly EDF/CEA/FRAMATOME tripartite project. In addition to pressure drop and velocity measurements using particle image velocimetry, pressure measurements have been performed along the central rod. The computational domain is representative of a span of the experimental mock-up composed of a 5 × 5 rod bundle equipped with a split-type MVG. The hydraulic Reynolds number is equal to 66 000 and periodic boundary conditions are imposed in the streamwise direction. The mesh is fully hexahedral and conformal. Computations give very satisfactory results for the pressure drop, the mean velocity, and the Reynolds stresses at different locations. The root-mean-square of the pressure along the central rod is also compared to experimental data at different heights. The behavior is in very good agreement up to five hydraulic diameters downstream of the MVG.