Wall-modeled Large Eddy Simulation Research Articles

Large Eddy Simulation of Film Cooling Over a Flat Plate in Supersonic Flow

Abstract In the present work, large eddy simulation (LES) was performed to access the film cooling performance in the supersonic flow over a flat plate with a perpendicular slot injection configuration. The study was carried out for three mainstream Mach No.; Mα = 1.2, 2.67, and 3.3 and three coolant stream Mach No.: 0.05, 0.1, and 0.15. In supersonic flow, temperature rise inside the boundary layer is a major issue considering it causes high rates of heat transfer to the coolant film. To select a suitable LES sub-grid scale (SGS) model, LES results obtained from the present study using the LES SGS models such as Smagorinky-Lilly, wall adapted local eddy viscosity (WALE), and wall-modeled LES (WMLES) models were compared with DNS results of Keller and Kloker. The parametric study showed that the higher mainstream Mach No. caused increased wall temperature and reduced effectiveness. The film cooling effectiveness appeared to reduce almost by 10% when the mainstream Mach No. is increased from 1.2 to 2.67; however, no apparent difference was observed in effectiveness between the mainstream Mach No. 2.67 and 3.3. It was found that doubling and tripling the coolant stream Mach No. from 0.05 to 0.1 and 0.15, the length of potential core region also doubled and tripled, respectively, from 4 X/S to 8 X/S and 13 X/S and hence significant improvement in the film cooling effectiveness was observed.

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layers with Mean-Flow Three-Dimensionality

We examine the performance of wall-modeled large-eddy simulation (WMLES) to predict turbulent boundary layers (TBLs) with mean-flow three-dimensionality. The analysis is performed for an ordinary-differential-equation-based equilibrium wall model due to its widespread use and ease of implementation. Two test cases are considered for this purpose: a spatially developing TBL in a square duct with a 30 deg bend, and the flow behind a wall-mounted skewed bump with a three-dimensional separation bubble. In the duct simulation, WMLES is capable of predicting mean-velocity profiles and crossflow angles in the outer region of the flow to within 1–5% error using 10 points per boundary-layer thickness. The largest disagreement (20% error) is observed in the crossflow angles in the bend region, where three-dimensional effects are the most significant. In the skewed bump simulation, it is shown that the present equilibrium wall model with a grid resolution of about 40 points across the three-dimensional separation region predicts mean-velocity profiles and separation location to within 1–3% error. The bubble size and vortex structures in the bump wake are also correctly represented. It is demonstrated that WMLES is capable of achieving accurate results in the separated region and its vicinity, provided that the strong shear layer generated at the apex of the bump is well resolved.

Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation

We revisit the grid-point requirement estimates in Choi and Moin [“Grid-point requirements for large eddy simulation: Chapman’s estimates revisited,” Phys. Fluids 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer. We show that by allowing the local grid spacing to scale with the local Kolmogorov length scale, the grid-point requirement for DNS of a spatially developing turbulent boundary layer is N∼ReLx2.05 rather than N∼ReLx2.64, as suggested by Choi and Moin, where N is the number of grid points and Lx is the length of the plate. In addition to the grid-point requirement, we estimate the time-step requirement for DNS and LES. We show that for a code that treats the convective term explicitly, the time steps required to get converged statistics are Nt∼ReLx/Rex06/7 for wall-modeled LES and Nt∼ReLx/Rex01/7 for wall-resolved LES and DNS (with different prefactors), where Rex0 is the inlet Reynolds number. The grid-point and time-step requirement estimates allow us to estimate the overall cost of DNS and LES. According to the present estimates, the costs of DNS, wall-resolved LES, and wall-modeled LES scale as ReLx2.91, ReLx2.72, and ReLx1.14, respectively.

A Bayesian approach to the mean flow in a channel with small but arbitrarily directional system rotation

The logarithmic law of the wall loses part of its predictive power in flows with system rotation. Previous work on the topic of mean flow scaling has mostly focused on flows with streamwise, spanwise, or wall-normal system rotation. The main objective of this work is to establish the mean flow scaling for wall-bounded flows with small but arbitrarily directional system rotation. Our approach is as follows. First, we apply dimensional analysis to the Reynolds-averaged momentum equation. We show that when a boundary-layer flow is subjected to small system rotation, the constant stress layer survives, and the mean flow U+ is a universal function of y+, Ωx+, Ωy+, and Ωz+, where U is the mean flow, y is the distance from the wall, Ωi is the system rotation speed in the ith direction (in the locally defined coordinate), and the superscript + denotes normalization by the local wall units. Second, we survey the three-dimensional parameter space of Ωx,y,z+ and determine U+(y+,Ωx+,Ωy+,Ωz+) for small Ω+. Here, we conduct direct numerical simulation (DNS) of a Reτ = 180 channel at various rotation conditions. This approach is conventionally considered as “brutal force.” However, as we will show in this work, the Bayesian approach allows us to very efficiently sample the parameter space. Four independent surveys are conducted with 146 DNSs, and the resulting Bayesian surrogate agrees well with our DNSs. Finally, we upscale to high Reynolds numbers via wall-modeled large-eddy simulation. In general, the present framework provides a path for surrogate modeling in a high-dimensional parameter space at high Reynolds numbers when sampling in a designated parameter space is possible at only a few conditions and at a low Reynolds number.

Development of a Wall Modeled LES for Turbulence with Temperature Dependent Viscosity

Development of a Wall Modeled LES for Turbulence with Temperature Dependent Viscosity

Mathematical formulation for the analysis of the periodic convergence during co-processing routines in long-run, scale-resolving simulations of turbomachinery

Scale-resolving simulations, like LES modelling, are recent CFD techniques to analyse numerically unsteady flows and turbulence in turbomachinery. Despite their high computational costs, they provide an unsteady, time-resolved solution of the flow with embedded turbulent scales that requires an additional statistical description. This paper provides the mathematical formulation required to compute and assure its periodic convergence, updating the phase-averaged values and the residual on the run, so the amount of data to be stored is extremely reduced. The formulation, applied over a numerical database of a wall-modelled LES simulation of the rotor-stator interaction in a low-speed axial fan using a 3D linear cascade model, reveals that primary flow variables converge faster than turbulent structures due to inherent instabilities of the coherent flow vortices. This work forms part of the concept of co-processing, where some post-processing routines are resolved during the iterative process of CFD simulations to save computational costs.

Mathematical formulation for the analysis of the periodic convergence during co-processing routines in long-run, scale-resolving simulations of turbomachinery

Scale-resolving simulations, like LES modelling, are recent CFD techniques to analyse numerically unsteady flows and turbulence in turbomachinery. Despite their high computational costs, they provide an unsteady, time-resolved solution of the flow with embedded turbulent scales that requires an additional statistical description. This paper provides the mathematical formulation required to compute and assure its periodic convergence, updating the phase-averaged values and the residual on the run, so the amount of data to be stored is extremely reduced. The formulation, applied over a numerical database of a wall-modelled LES simulation of the rotor-stator interaction in a low-speed axial fan using a 3D linear cascade model, reveals that primary flow variables converge faster than turbulent structures due to inherent instabilities of the coherent flow vortices. This work forms part of the concept of co-processing, where some post-processing routines are resolved during the iterative process of CFD simulations to save computational costs.

Large-Eddy Simulation with Modeled Wall Stress for Complex Aerodynamics and Stall Prediction

The aerodynamics of aircraft high-lift devices at near-stall conditions is particularly difficult to predict numerically. The computational requirements for accurate wall-resolved large-eddy simulations are currently prohibitive, whereas Reynolds-averaged Navier–Stokes (RANS) models are generally reliable only for low angles of attack with fully attached boundary layers. Methods such as detached-eddy simulation resolve unsteadiness of the outer boundary layer and can predict separation, but they rely upon a thick RANS layer and highly stretched cells that damp the resolved turbulent fluctuations near the wall. An alternative approach, adopted here, is to extend the LES down to the wall, employing a relatively large near-wall normal grid spacing and avoiding grid stretching and high aspect ratios near the wall. A boundary condition then applies the correct wall shear stress as provided by a semiempirical wall model. An adaptive formulation of this wall-modeled large-eddy simulation is presented here and validated using realistic test cases. Validation using a channel flow case at a range of Reynolds numbers demonstrates accurate results with a seamless transition between fully resolved () and wall resolved (). Predictions of the MD-30P/30N airfoil using a modest grid with give excellent agreement with experiments and correctly predict . Finally, the method is demonstrated for the NASA High-Lift Common Research Model providing surface pressure coefficients and velocity profiles. The predictions using a 50-million-cell mesh (for a full aircraft half-model) are in good agreement with considerably finer-grid RANS solutions. The presented method has considerable potential because it can produce accurate solutions to challenging engineering problems involving separation with modest grid and computational requirements while being robust to variations in near-wall grid spacing.

Shock-induced heating and transition to turbulence in a hypersonic boundary layer

Abstract

On the generation of turbulent inflow for hybrid RANS/LES jet flow simulations

The present work is devoted to the assessment of a low-noise turbulence generation methodology used to produce boundary layer with three-dimensional resolved turbulence at the exit of a jet nozzle to reproduce experimental conditions. The method relies on the use of roughness elements introduced in the computational domain with Immersed Boundary Conditions and ZDES mode 3 (Wall Modelled LES branch of ZDES). The simulation of a round jet at M = 0.9 and Reynold number 106 with turbulence generation is compared to a simulation with no resolved turbulence in the nozzle boundary layer using ZDES mode 2. The behaviour of the boundary layer downstream of the roughness elements inside the nozzle is scrutinized using two grids. The turbulence generation method combined with ZDES mode 3 produces satisfying levels of resolved turbulence at the nozzle exit. The early stages of the shear layer development are modified by the ZDES mode 3 simulations providing an initially turbulent shear layer. On the other hand, the ZDES mode 2 simulations, with a turbulent mean exit velocity profile but no resolved turbulence, display a short area of strong shear layer instabilities leading to the quick development of three-dimensional turbulence in the mixing layer. The present results give insights on the level of turbulent modelling of the nozzle boundary layer needed depending on the purposes of the jet flow simulations considered.

Turbulent flow and heat flux analysis from validated large eddy simulations of flow past a heated cylinder in the near wake region

We conduct non-isothermal large eddy simulations (LESs) of flow past a heated cylinder (Re = 3900) to investigate flow physics throughout the wake region and develop a foundation upon which future heat flux wall models can be built (both for wall-modeled LES and other lower fidelity models) for mathematical closure of the energy equation. A rigorous validation of the mesh is made under isothermal conditions with results showing a closer match to experimental data than any other LES studies to date. The insights gained into the mesh design and approach are discussed. Simulation of non-isothermal flow is performed on the validated mesh for temperature differences between the cylinder surface and the freestream of 25 K and 300 K. The mesh design and realistic (temperature-dependent) thermodynamic property variations play key roles in predicting delayed separation, larger re-circulation zones, and enhanced turbulence intensity for the higher temperature difference case. The effect of both temperature differences on the flow is analyzed, and a new scaling of the flow domain is proposed to gain further insight into non-isothermal flow physics. Key scaling variables, friction temperature and friction velocity, are able to reduce nearly all of the temperature dependence of first and second order flow statistics, including turbulent heat fluxes. This leads to the finding that the turbulent heat flux in the wake region scales with the wall heat flux irrespective of the temperature difference in the flow.

Simulation of approaching boundary layer flow and wind loads on high-rise buildings by wall-modeled LES

This study presents a simulation framework of approaching boundary layer flow with appropriate characteristics by large-eddy simulation (LES), which is critically important for predictions of wind pressures and loads on buildings and other structures. The framework is consisted of spectral representation (synthesis) approach for inflow turbulence field generation and adjusting strategies to achieve appropriate approaching flow characteristics. The adjusting strategies include implementation of wall-stress model based on the equilibrium law of wall and adjusting of inflow turbulence parameters. The wall-stress model facilitates modeling of the effects of ground roughness without explicitly resolving the geometric roughness elements, also bypassing the prohibitive near-wall grid resolution requirement. The adjusting of inflow turbulence parameters, including correlation coefficient of inflow longitudinal and vertical fluctuating velocity components and amplification factor of inflow vertical fluctuation level, is proposed based on Reynolds stress budget to shorten the buffer region and to mitigate the decay of longitudinal turbulence intensity profile. To verify the proposed framework, the approaching flow corresponding to a wind tunnel test is firstly simulated and a comprehensive parametric study is conducted. With the adequately simulated turbulence field, the wind pressures and integrated loads on a high-rise building model are then simulated and compared with the wind tunnel test results. The results demonstrate effectiveness of the proposed wall-modeled LES framework for approaching flow simulation and wind loads assessment.

A mesh adaptation strategy for complex wall-modeled turbomachinery LES

A mesh adaptation methodology for wall-modeled turbomachinery Large Eddy Simulation (LES) is proposed, simultaneously taking into account two quantities of interest: the average kinetic energy dissipation rate and the normalized wall distance y+. This strategy is first tested on a highly loaded transonic blade with separated flow, and is compared to wall-resolved LES results, as well as experimental data. The adaptation methodology allows to predict fairly well the boundary layer transition on the suction side and the recirculation bubble of the pressure side. The method is then tested on a real turbofan stage for which it is shown that the general operating point of the computation converges toward the experimental one. Furthermore, comparison of turbulence predictions with hot-wire anemometry show good agreement as soon as a first adaptation is performed, which confirms the efficiency of the proposed adaptation method.

Development of an algebraic wall heat transfer model for LES in IC engines using DNS data

This paper presents a novel algebraic wall-modeled large-eddy simulation (WMLES) approach for wall heat transfer (WHT) in internal combustion engines (ICE) using recent high-fidelity simulation data from two real ICE and a flame-wall interaction (FWI) setup. The model formulation is based on intuitive arguments rather than simplified forms of near-wall governing equations. Input information from the two wall-normal wall-adjacent nodes is used, facilitating the interpretation of the local state of the thermal boundary layer (TBL). With filtered direct numerical simulation (DNS) data (i.e. a ‘perfect’ LES), model performance is evaluated locally at different near-wall resolutions. The proposed model is compared to a widely used wall function (WF) approach and to a data-driven model.

Spinning behavior of flow-acoustic resonant fields inside a cavity: Vortex-shedding modes and diametral acoustic modes

The spinning behavior of flow-acoustic resonant fields inside an axisymmetric cavity configuration was numerically investigated in four flow conditions containing different resonances between vortex-shedding modes and diametral acoustic modes. Zonal large-eddy simulations (ZLESs) were conducted to determine the aeroacoustic and aerodynamic fields simultaneously. In the ZLESs, a shear stress transport turbulence model was used to model the relatively steady flow field inside the inlet and outlet sections. Simultaneously, the wall-modeled LES formulation was used in the cavity section to resolve the highly complex flow-acoustic resonant fields. The ZLES results were well validated by the experimental results in the literature in terms of the frequency, amplitude, and spatial features of the acoustic pressure pulsations. Subsequently, the spinning behavior and mechanism of the excited diametral acoustic modes and the resonant vortex-shedding modes were comprehensively illustrated. The results showed that the excited diametral acoustic mode span anticlockwise along the cavity circumference, resulting in intense acoustic-pressure fluctuations several times greater than at the inlet dynamic-pressure head, together with longitudinal pressure propagations. Using proper orthogonal decomposition analysis, the spinning mechanism was found to be closely related to the interaction between the α-mode and the β-mode, which had fixed temporal and spatial phase lags. Thereafter, the first vortex-shedding mode gave rise to a strong spinning motion of the resonant flow field, while the second vortex-shedding mode created a slight spinning motion. The corresponding phase-dependent flow fields at consecutive planes along the cavity circumference revealed the spatiotemporal evolution of the velocity variations, surface streamlines, and vorticity variations of the shedding vortices. Large-scale helical vortex tubes were formed within the cavity volume due to the strong spinning behavior.

Characterization of pressure fluctuations within a controlled-diffusion blade boundary layer using the equilibrium wall-modelled LES

In this study, the generation of airfoil trailing edge broadband noise that arises from the interaction of turbulent boundary layer with the airfoil trailing edge is investigated. The primary objectives of this work are: (i) to apply a wall-modelled large-eddy simulation (WMLES) approach to predict the flow of air passing a controlled-diffusion blade, and (ii) to study the blade broadband noise that is generated from the interaction of a turbulent boundary layer with a lifting surface trailing edge. This study is carried out for two values of the Mach number, {{rm Ma}}_{infty } = 0.3 and 0.5, two values of the chord Reynolds number, {{rm Re}}=8.30 times 10^5 and 2.29 times 10^6, and two angles of attack, AoA =4^circ and 5^circ. To examine the influence of the grid resolution on aerodynamic and aeroacoustic quantities, we compare our results with experimental data available in the literature. We also compare our results with two in-house numerical solutions generated from two wall-resolved LES (WRLES) calculations, one of which has a DNS-like resolution. We show that WMLES accurately predicts the mean pressure coefficient distribution, velocity statistics (including the mean velocity), and the traces of Reynolds tensor components. Furthermore, we observe that the instantaneous flow structures computed by the WMLES resemble those found in the reference WMLES database, except near the leading edge region. Some of the differences observed in these structures are associated with tripping and the transition to a turbulence mechanism near the leading edge, which are significantly affected by the grid resolution. The aeroacoustic noise calculations indicate that the power spectral density profiles obtained using the WMLES compare well with the experimental data.

RETRACTED: A novel rough-wall model for large eddy simulation of high-Reynolds-number flow

This study develops a novel rough-wall model for large eddy simulation (LES) based on recent work on wall-modelled LES. This approach is capable of solving for the basic flow character over a rough wall at high Reynolds numbers without resolving the details of the roughness elements. The wall-modelled LES approach on a smooth wall is proven to be sufficiently precise to predict the velocity profile and wall shear stress. The average roughness shear stress can be combined with the smooth-wall shear stress in the inner-layer wall model by defining a roughness shear stress ratio α. The instantaneous shear stresses caused by the roughness elements are calculated by the pressure projection and elevation fields. The total shear stress is fed back to the outer-layer LES mesh as a new boundary condition. The results of the wall-modelled LES correspond well with the experimental data. The comparison between the simulation and experiment reveals that the wall-modelled LES approach presented in this research is capable of predicting the flow in a rough-wall boundary layer without resolving the detailed roughness element geometries.

Assessment of the SST-IDDES with a shear-layer-adapted subgrid length scale for attached and separated flows

A shear-layer-adapted subgrid length scale is applied to the improved delayed detached eddy simulation using the shear stress transport background model (SST-IDDES). The aim is to assess the combination of the wall-modeled LES (WMLES) branch of the SST-IDDES with the new length scale in computing attached flows, as well as to assess the effect of the new length scale when it is applied to the SST-IDDES for mitigating the “grey area” issue through initiating a dramatic drop of eddy viscosity in the initial region of a free shear layer. The assessment is conducted through simulations of a turbulent boundary layer, a fully developed channel flow, a near-sonic turbulent jet and a backward-facing step flow. The results provide strong evidence for the conclusion that the SST-IDDES combined with the new length scale performs the same as the original SST-IDDES when its WMLES branch is applied to compute the resolved parts of an attached flow, and the combination helps mitigate the “grey area” issue of the SST-IDDES and accurately represent the K-H instability in the initial region of a free shear layer. In addition, the superiority is particularly remarkable for the simulations with coarse grids.

Analysis of shock-wave unsteadiness in conical supersonic nozzles

Large Eddy Simulations (LES) of an over-expanded conical nozzle are performed to study the complex interaction between the turbulent boundary layer, the internal shock wave and the separated mixing layer. Both wall-modeled (WM) and wall-resolved (WR) LES strategies are employed to investigate the three-dimensional unsteady aspect of shock-wave boundary-layer interaction (SWBLI). First, a comparison of flow behavior in a conical nozzle against an equivalent planar nozzle is made. It was found that whilst both configurations may share common flow features such as large-scale turbulent structures and shock-wave patterns, they show contrasts on the symmetry of the flow and the shock dynamics. In particular, the latter was found to have a shorter excursion length in conical nozzle compared to the planar one. The strong adverse pressure gradient tends to reduce the amplitude of the shock movements in conical flows. Additionally, the dynamic mode decomposition (DMD) analysis showed the existence of two unsteady modes; the non-helical modes which are low-frequency based, appearing mainly in the streamwise forces and the helical modes which are high frequency dominated modes and are largely responsible for the side side-loads generation.

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.