Implementation and Validation of an Algebraic Wall Model for LES in Nek5000

Approximate Near-Wall Treatments Based on Zonal and Hybrid RANS-LES Methods for LES at High Reynolds Numbers

In this paper the development and a partially verification of an anisotropic modification of linear and nonlineare models of turbulence is presented. This modification departs from the observation that there are some regions of fluid domains in which the Reynolds stresses do not depend on the magnitude of the mean flow gradients. The model is based on the hypothesis that actions of fluctuating motion on mean motion are almost exclusively due to large turbulent eddies, and that the latter contain the same kinetic energy of the small eddies of mean flow. The contribution of large turbulent eddies to the Reynolds stresses is then modelled by a linear combination of an isotropic term and an anisotropic term. The latter is obtained by multiplying a quote of the turbulent kinetic energy by a normalised redistribution tensor. The performances of the model are tested calculating the Reynolds stresses in a fully developed turbulent channel flow, and simulating the separated turbulent flow over a backward-facing step, and a fully developed turbulent flow in a squared duct. The results show that the modified models improve the prediction of the normal Reynolds stresses in a bidimensional channel and of the reattachment point in a backward-facing step. On the other hand, these models do not supply any improvement of the secondary flow in a squared duct. INTRODUCTION Algebraic two-equation models of turbulence for Reynolds averaged Navier-Stokes equations are still, today, among the most widely used in the field of engineering design. The two major alternative to such models are the second-order closure models and large-eddy simulations (LES). The weak points of the first approach are high computational cost, due to the five more equations to be solved, and wall-bounded turbulent flows. On the other hand, LES requires much more computational time than second-order closure models, and improved models for the smallscale and the wall region are needed. For these reasons these two approaches have not become yet a useful engineering tool. The aim of this work is to develop an anisotropic modification for linear and nonlinear turbulence model which improves the prediction of normal Reynolds stresses, without increasing the number of differential equations to be solved. More precisely, the objective is to simulate the contribution to the anisotropy of the turbulent stresses observable in areas characterised by low mean velocity gradients. This phenomenon, which can be noted, for example, in experimental data of the turbulent channel flow in figure 5, is not actually described by standard, explicit algebraic models. The starting point of this model consists in the substitution of turbulent kinetic energy by an appropriate vectorial magnitude which provides information about the anistropy of the turbulent stresses. The quantity is identified by the field of velocity of the small eddies of mean motion. The kinetic energy of these small eddies is obtained by assuming that these t Dr, Center of Studies and Activities for Space (CISAS). Dr, Department of Mechanical Engineering. ' Professor, Department of Mechanical Engineering. Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1 American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. have the same kinetic energy content of the large turbulent eddies: the two fields of motion are said to be similar. It has been demonstrated that the field of motion of large turbulent eddies, or coherent structures^ can be obtained directly from measurements of instantaneous velocity once the quota of turbulent kinetic energy has been defined. The models obtained provides improvements in the predictions of normal Reynolds stresses present in the turbulent flow of a bidimensional channel; as for the separated turbulent flow in a backward-facing step appreciable improved results of mean flow and of normal Reynolds stresses have been attained compared to standard algebraic models. On the other side, as it will be shown in the following paragraphs, the model of the turbulent kinetic energy redistribution tensor does not supply any improvement in the case of the fully developed turbulent flow in a squared duct. ANISOTROPIC MODIFICATION OF THE REYNOLDS STRESSES Let us consider a field of turbulent motion of a viscous, homogenous and incompressible fluid; the instantaneous velocity v and the instantaneous pressure p can be set out as follows in a mean and fluctuating parts: v = v -f v' p-p + p (1) The evolution of the velocities and mean pressures can be described completely by the well-known Reynolds equations:

A library for wall-modelled large-eddy simulation based on OpenFOAM technology

Most of the flow problems encountered in practical engineering are wall-bounded turbulent flows at high Reynolds numbers. Wall-modeled large eddy simulation (WMLES) is one of the most viable approaches for predicting these realistic flows. Immersed boundary (IB) approach is an efficient computational technique to solve flow problems involving complex and/or moving geometries. This work extends a sharp-interface IB method, named the local domain-free discretion (DFD), to WMLES of compressible flows at high Reynolds numbers. An equilibrium wall model based on solving the simplified compressible turbulent boundary layer equations is utilized to alleviate the requirement of high near-wall mesh resolution. In conjunction with the approximate boundary conditions prescribed by the modeled wall shear stress and wall heat flux, the tangential velocity and temperature at an exterior dependent node are evaluated. Then, the closure of the discrete form of governing equations at an interior node in the immediate vicinity of the immersed wall is accomplished. A simple non-equilibrium correction of the wall shear stress provided by the equilibrium wall model is introduced explicitly. The WMLES/DFD method is applied to a supersonic zero-pressure-gradient turbulent boundary layer flow, a shock wave/flat-plate boundary layer interaction, a supersonic compression ramp flow and high-speed turbulent Couette flows with various thermal boundary conditions. The influence of grid resolution is investigated in the simulation of zero-pressure-gradient turbulent boundary layer flow. By comparing the computed results with the referenced experimental data and/or numerical results, the accuracy and ability of the WMLES/DFD method to simulate compressible turbulent flows are verified.

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.

We present an assessment and enhancement of the hybrid two-level large-eddy simulation method (A.G. Gungor and S. Menon, A new two-scale model for large eddy simulation of wall-bounded flows, Prog. Aerosp. Sci. 46 (2010), pp. 28–45), a multi-scale formulation for simulation of high Reynolds number wall-bounded turbulent flows. The assessment of the method is performed by examining role of static and dynamic blending functions used to perform hybridisation of two-level simulation (K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows, J. Comput. Phys. 220 (2006), pp. 290–311; K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows. Part 2: Non-homogeneous flows, J. Comput. Phys. 222 (2007), pp. 673–701) and large-eddy simulation methods. The sensitivity of first- and second-order turbulence statistics to the type of blending functions is investigated by simulating a fully developed turbulent flow in a channel at a friction Reynolds number Reτ = 395 and comparing the results with those obtained using a direct numerical simulation. The first-order statistics do not show any significant differences for different blending functions, but the second-order statistics show some minor differences. The dynamic evaluation of the hybrid region and the blending function is necessary for non-equilibrium and complex flows where use of a static blending function can lead to inaccurate results. We propose two criteria for the dynamic evaluation; first evaluates extent of the hybrid region based on the subgrid turbulent kinetic energy and the second estimates the blending function based on a characteristic length scale. The computational efficiency of the method is enhanced by incorporating a hybrid programming paradigm where a standard domain decomposition by the message-passing-interface library is combined with the open multi-processing based parallelisation. A further enhancement of the method is achieved by incorporating a closure model for the unclosed hybrid terms in the governing equations, which appear due to hybridisation of two-level- and large-eddy-simulation methods. The model is based on an order of magnitude approximation and a preliminary assessment of the model shows improvement of turbulence statistics when used to simulate turbulent flow in a periodic channel. The assessment and improvements to the multi-scale method make it more suitable for simulation of practical wall-bounded turbulent flows at higher Reynolds number than a conventional large-eddy simulation. This is demonstrated by simulating two representative cases; turbulent flow at high Reynolds number in a periodic channel and flow over a bump placed on the lower surface of a channel, where a relatively coarser computational grid is found to be sufficient for reasonably accurate results.

Most of nature and industry flows are turbulence. There are three kinds of numerical simulation methods for turbulent flows (Lesieur 1990; Pope 2000; Sagaut 2000, 2006): direct numerical simulation (DNS), Reynolds-averaged Navier-Stokes equations (RANS) and large eddy simulation (LES). DNS is a straightforward way to simulate turbulent flows. Full Navier-Stokes equations are discretized and solved numerically without any model, empirical parameter or approximation. Theoretically speaking, results of DNS exactly reflect the real flow and the whole range of turbulence scales are computed. With DNS, people can compute and visualize any quantity of interest, including some that are too difficult or impossible to be measured by experiments. But as we all know the computation cost is very high. For high Reynolds number flow, even modern computer technology can not satisfy the computation requirement. In RANS, the flow quantities are decomposed into two parts: the average or mean term and the fluctuating term by applying Reynolds averaging. The effect of the fluctuating quantities on the mean flow quantities is described by the so called Reynolds stress tensor, which is must be modelled in terms of the mean velocities. Typical models can be grouped loosely into three categories: algebraic models, one-equation models and two-equation models. RANS is simple and robust. It is widely used in engineering problem. The general limitation of RANS is the fact that the model must represent a very wide range of scales. While the small scales tend to be universal, and depend on viscosity, the larger scales depend largely on flow condition and boundaries. So there is no one universal model for all flows. For different flows, the model must be modified to obtain good results. Another issue is that usually a time averaging is adopted in RANS. So RANS has difficult to handle unsteady flows. In LES, a filter is applied to separate the large scales from small scales. Then only the large, energy carrying scales (or called resolved scales) of turbulence are computed exactly by solving the governing equations. While the small, fluctuating scales are modelled, which is also called subgrid scales (SGS). Compared to RANS, LES has several advantages: 1) LES can capture the large scales directly which are the main energy container of turbulence and response for the momentum and energy transfer. 2) The dissipation of turbulence energy is believed to be done by small scales. Since small scales are thought to be homogenous,

Large eddy simulation was applied for flow of Re=2000 in a stenosed pipe in order to undertake a thorough investigation of the wall shear stress (WSS) in turbulent flow. A decomposition of the WSS into time averaged and fluctuating components is proposed. It was concluded that a scale resolving technique is required to completely describe the WSS pattern in a subject specific vessel model, since the poststenotic region was dominated by large axial and circumferential fluctuations. Three poststenotic regions of different WSS characteristics were identified. The recirculation zone was subject to a time averaged WSS in the retrograde direction and large fluctuations. After reattachment there was an antegrade shear and smaller fluctuations than in the recirculation zone. At the reattachment the fluctuations were the largest, but no direction dominated over time. Due to symmetry the circumferential time average was always zero. Thus, in a blood vessel, the axial fluctuations would affect endothelial cells in a stretched state, whereas the circumferential fluctuations would act in a relaxed direction.

A hybrid immersed boundary/wall-model approach for large-eddy simulation of high-Reynolds-number turbulent flows

Large eddy simulation of the flow around an inclined prolate spheroid

Data-driven wall modeling for turbulent separated flows

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.

Accurate prediction of the wall shear stress in rod bundles with the spectral element method at high Reynolds numbers

Approximate near-wall treatments based on zonal and hybrid RANS–LES methods for LES at high Reynolds numbers

A mixed subgrid-scale (SGS) model based on coherent structures and temporal approximate deconvolution (MCT) is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation (LES) of turbulent drag-reducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence (FHIT) with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation (DNS) results. Compared with the LES results using the temporal approximate deconvolution model (TADM) for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number. For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.