求解复杂湍流的非线性涡黏性系数模型和代数应力模型

非线性涡黏性系数模型和代数应力模型联系了线性涡黏性系数湍流模型和完整的微分 雷诺应力模型.随着它们受到日益关注,其形式也越来越多样化.本篇综述的目的是对这些模 型加以总结并比较它们之间的共同点及不同之处,指出它们与完整微分雷诺应力模型之间的 关系,以及相对于线性涡黏性系数模型而言它们在预报流场上所具有的优势.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

On the construction of manufactured solutions for one and two‐equation eddy‐viscosity models

This paper presents manufactured solutions (MSs) for some well‐known eddy‐viscosity turbulence models, viz. the Spalart & Allmaras one‐equation model and the TNT and BSL versions of the two‐equation k–ω model. The manufactured flow solutions apply to two‐dimensional, steady, wall‐bounded, incompressible, turbulent flows. The two velocity components and the pressure are identical for all MSs, but various alternatives are considered for specifying the eddy‐viscosity and other turbulence quantities in the turbulence models. The results obtained for the proposed MSs with a second‐order accurate numerical method show that the MSs for turbulence quantities must be constructed carefully to avoid instabilities in the numerical solutions. This behaviour is model dependent: the performance of the Spalart & Allmaras and k–ω models is significantly affected by the type of MS. In one of the MSs tested, even the two versions of the k–ω model exhibit significant differences in the convergence properties. Copyright © 2006 John Wiley & Sons, Ltd.     

Computation of strongly swirling confined flows with cubic eddy‐viscosity turbulence models

An investigation on the predictive performance of four cubic eddy‐viscosity turbulence models for two strongly swirling confined flows is presented. Comparisons of the prediction with the experiments show clearly the superiority of cubic models over the linear k–εmodel. The linear k–εmodel does not contain any mechanism to describe the stabilizing effects of swirling motion and as a consequence it performs poorly. Cubic models return a lower level of Reynolds stresses and the combined forced‐free vortex profiles of tangential velocity close to the measurements in response to the interaction between swirl‐induced curvature and stresses. However, a fully developed rotating pipe flow is too simple to contain enough flow physics, so the calibration of cubic terms is still a topic of investigation. It is shown that explicit algebraic stress models require fewer calibrations and contain more flow physics. Copyright © 2003 John Wiley & Sons, Ltd.     

Turbulent flows in channels with injection. results of large eddy simulation and the two-equation turbulence model

Turbulent flows in channels with intense distributed injection are modeled using the large eddy method and the two-equation k-? turbulence model. The calculations are carried out for different velocities of injection from the channel walls. For a channel with one-sided injection the results of large eddy simulation are in good agreement with the measured data, whereas the calculations in accordance with the k-? model give a less convex cross-sectional velocity profile and an appreciable error in determining the surface friction coefficient on the impermeable wall and also have certain other shortcomings. In the case of two-sided injection, the results of the calculations by the large eddy method and the k-? model are in good agreement with one another and the data of physical experiments.     

Effect of the Turbulent Energy Gradient and the Presence of a Wall on the Turbulent Process of Momentum Transport

A mathematical model of turbulent transport processes is modified to make allowance for the turbulent energy gradient and the presence of walls. The modification consists in making the variance tensor in the Gaussian probability density distribution for the initial mole velocities anisotropic for nonzero turbulent energy gradient and a ratio of the turbulence scale to the distance from the wall of the order of unity. Formulas for the variance tensor components are derived and the empirical coefficients of these formulas are determined. The expression for the dimensionless turbulent friction stress is compared with experimental data for three boundary-layer-type flows, namely, in the wake of a cylinder, in the boundary layer on a flat plate, and in a channel with parallel walls.     

Large eddy simulation in a fully developed turbulent flow in a channel and comparison of subgrid eddy viscosity models

The accuracy and computational efficiency are compared for a number of models of subgrid eddy viscosity (Smagorinsky model, renormalization group model, and dynamic and one-parameter models). Space-filtered Navier-Stokes equations are solved numerically by the control-volume approach on a nonuniform grid with the use of high-resolution schemes in time and space. The numerical data are compared with the results of a physical experiment and direct numerical simulation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 31–42, May–June, 2006.     

Cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density

An investigation on the predictive performance of cubic eddy‐viscosity turbulence models for strongly swirling confined flows with variable density is presented. Comparisons of the prediction with the experiments show some improvements of cubic models over the linear k–ε model. The linear k–ε model does not contain any mechanism to represent the interaction of swirl and density variation and as a consequence it performs poorly. With appropriate modelling, two‐equation cubic turbulence models can capture the subcritical nature of the flow, represent the azimuthal velocity profiles of combined forced‐free vortex motion, and predict the combined effects of swirl and density variation fairly well. However, the calibration of model coefficients is still a topic of investigation. Further amendments are also needed for the equations of k and ε to take into account the effects of swirl and density gradients correctly. Copyright © 2004 John Wiley & Sons, Ltd.     

Compound Wall Treatment for RANS Computation of Complex Turbulent Flows and Heat Transfer

We present a generalised treatment of the wall boundary conditions for RANS computation of turbulent flows and heat transfer. The method blends the integration up to the wall (ItW) with the generalised wall functions (GWF) that include non-equilibrium effects. Wall boundary condition can thus be defined irrespective of whether the wall-nearest grid point lies within the viscous sublayer, in the buffer zone, or in the fully turbulent region. The computations with fine and coarse meshes of a steady and pulsating flow in a plane channel, in flow behind a backward-facing step and in a round impinging jet using the proposed compound wall treatment (CWT) are all in satisfactory agreement with the available experiments and DNS data. The method is recommended for computations of industrial flows in complex domains where it is difficult to generate a computational grid that will satisfy a priori either the ItW or WF prerequisites.     

Short-and resonant-range interactions between scales in turbulence and their applications

Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the shortrange viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation ( LES ) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.     

Large Eddy and Reynolds-Averaged Navier - Stokes Simulations of Turbulent Flow Over an Airfoil

A Large Eddy Simulation (LES) of turbulent flow over an airfoil near stall is performed. Results of the LES are compared with those of Reynolds-Averaged Navier-Stokes (RANS) simulations using two well-known turbulence models, namely the Baldwin-Lomax model and the Spalart-Allmaras model. The subgrid scale model used for the LES is the filtered structure function model. All simulations are performed using the same structured multi-block code. In order to reduce the CPU time, an implicit time stepping method is used for the LES. The purpose of this study is to show the possibilities and limitations of LES of complex flows associated with aeronautical applications using state of the art simulation techniques. Typical flow features are captured by the LES such as the adverse-pressure gradient and flow retardation. Visualization of instantaneous flow fields shows the typical streaky structures in the near-wall region.     

LES Study of Turbulent Boundary Layer Over a Smooth and a Rough 2D Hill Model

Large eddy simulation (LES) is carried out to investigate the turbulent boundary-layer flows over a hill-shaped model with a steep or relatively moderate slope at moderately high Reynolds numbers (Re = O(10³)) defined by the hill height and the velocity at the hill height. The study focuses on the effects of surface roughness and curvature. For Sub-grid Scale (SGS) modeling of LES, both the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) are applied. The behavior of the separated shear layer and the vortex motion are affected by the oncoming turbulence, such that the shear layer comes close to the ground surface, or the size of a separation region becomes small because of the earlier instability of the separated shear layer. Appropriate measures are required to generate the inflow turbulence. The methods of Lund et al. (J. Comput. Phys., 140:233–258, 1998) and Nozawa and Tamura (J. Wind Eng. Ind. Aerodyn., 90:1151–1162, 2002; The 4th European and African Conference on Wind Engineering, 1–6, 2005) are employed to simulate the smooth- and rough-wall turbulent boundary layers in order to generate time-sequential data of inflow turbulence. This paper discusses the unsteady phenomena of the wake flows over the smooth and rough 2D hill-shaped obstacles and aims to clarify the roughness effects on the flow patterns and the turbulence statistics distorted by the hill. Numerical validation is conducted by comparing the simulation results with wind tunnel experiment data for the same hill shape at almost the same Re. The applicability of DSM and DMM are discussed, focusing on the recirculation region behind a steep hill.     

A Two-Time-Scale Model for Turbulent Mixing Flows Induced by Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

A two-time-scale closure model for compressible flows previously developed is extended to turbulent Rayleigh-Taylor and Richtmyer-Meshkov driven flows where mixing coexists with mean pressure gradients. Two model coefficients are calibrated with the help of Canuto-Goldman's model. For several Rayleigh-Taylor configurations, it is shown that the characteristic lengths scale as t ² while the kinetic energies and spectral transfers behave as t ² and t, respectively. The computed phenomenological coefficients of Youngs' scaling law are compared with experimental data ones. Comparisons with Youngs' three-dimensional numerical simulation (The Physics of Fluids A 3 (1991) 1312) are also performed. Finally three shock tube experiments, where the Richtmyer-Meshkov instability initiates the mixing, are simulated. The mixing thickness evolution is well reproduced while the turbulence levels seem to be overestimated with such first order models. The capability of the two-time-sale model to recover available data for different turbulent flows allows us to conclude to a more universal behavior in comparison with single-time-scale models. This revised version was published online in July 2006 with corrections to the Cover Date.     

Continuation methods applied to the 2D Navier–Stokes equations at high Reynolds numbers

Nonlinearities arise in aerodynamic flows as a function of various parameters, such as angle of attack, Mach number and Reynolds number. These nonlinearities can cause the change from steady to unsteady flow or give rise to static hysteresis. Understanding these nonlinearities is important for safety validation and performance enhancement of modern aircraft. A continuation method has been developed to study nonlinear steady state solutions with respect to changes in parameters for two‐dimensional compressible turbulent flows at high Reynolds numbers. This is the first time that such flows have been analysed with this approach. Continuation methods allow the stable and unstable solutions to be traced as flow parameters are changed. Continuation has been carried out on two‐dimensional aerofoils for several parameters: angle of attack, Mach number, Reynolds number, aerofoil thickness and turbulent inflow as well as levels of dissipation applied to the models. A range of results are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

A ‘poor man's Navier–Stokes equation’: derivation and numerical experiments—the 2‐D case

We present a systematic derivation of a discrete dynamical system directly from the two‐dimensional incompressible Navier–Stokes equations via a Galerkin procedure and provide a detailed numerical investigation (covering more than 107 cases) of the characteristic behaviours exhibited by the discrete mapping for specified combinations of the four bifurcation parameters. We show that this simple 2‐D algebraic map, which consists of a bilinearly coupled pair of logistic maps, can produce essentially any (temporal) behaviour observed either experimentally or computationally in incompressible Navier–Stokes flows as the bifurcation parameters are varied in pairs over their ranges of stable behaviours. We conclude from this that such discrete dynamical systems deserve consideration as sources of temporal fluctuations in synthetic‐velocity forms of subgrid‐scale models for large‐eddy simulation. Copyright © 2004 John Wiley & Sons, Ltd.     

Unified turbulence models for LES and RANS,FDF and PDF simulations

A review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function (FDF) or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier–Stokes (RANS) methods. It is then shown that such unified stochastic and deterministic turbulence models can be constructed by explaining the dependence of the characteristic time scale of velocity fluctuations on the scale considered. The unified stochastic model obtained generalizes usually applied FDF and PDF models. The unified deterministic turbulence model that is implied by the stochastic model recovers and extends well-known linear and nonlinear LES and RANS models for the subgrid-scale and Reynolds stress tensor.      

Comparative study of implicit and subgrid‐scale model large‐eddy simulation techniques for low‐Reynolds number airfoil applications

A computational study of a high‐fidelity, implicit large‐eddy simulation (ILES) technique with and without the use of the dynamic Smagorinsky subgrid‐scale (SGS) model is conducted to examine the contributions of the SGS model on solutions of transitional flow over the SD7003 airfoil section. ILES without an SGS model has been shown in the past to produce comparable and sometimes favorable results to traditional SGS‐based large‐eddy simulation (LES) when applied to canonical turbulent flows. This paper evaluates the necessity of the SGS model for low‐Reynolds number airfoil applications to affirm the use of ILES without SGS‐modeling for a broader class of problems such as those pertaining to micro air vehicles and low‐pressure turbines. It is determined that the addition of the dynamic Smagorinsky model does not significantly affect the time‐mean flow or statistical quantities measured around the airfoil section for the spatial resolutions and Reynolds numbers examined in this study. Additionally, the robustness and reduced computational cost of ILES without the SGS model demonstrates the attractiveness of ILES as an alternative to traditional LES. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Large eddy simulation (2D) of spatially developing mixing layer using vortex‐in‐cell for flow field and filtered probability density function for scalar field

A large eddy simulation based on filtered vorticity transport equation has been coupled with filtered probability density function transport equation for scalar field, to predict the velocity and passive scalar fields. The filtered vorticity transport has been formulated using diffusion‐velocity method and then solved using the vortex method. The methodology has been tested on a spatially growing mixing layer using the two‐dimensional vortex‐in‐cell method in conjunction with both Smagorinsky and dynamic eddy viscosity subgrid scale models for an anisotropic flow. The transport equation for filtered probability density function is solved using the Lagrangian Monte‐Carlo method. The unresolved subgrid scale convective term in filtered density function transport is modelled using the gradient diffusion model. The unresolved subgrid scale mixing term is modelled using the modified Curl model. The effects of subgrid scale models on the vorticity contours, mean streamwise velocity profiles, root‐mean‐square velocity and vorticity fluctuations profiles and negative cross‐stream correlations are discussed. Also the characteristics of the passive scalar, i.e. mean concentration profiles, root‐mean‐square concentration fluctuations profiles and filtered probability density function are presented and compared with previous experimental and numerical works. The sensitivity of the results to the Schmidt number, constant in mixing frequency and inflow boundary conditions are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 2: The discrete problem and numerical experiments

In this second part, we analyse the associated discrete problem arising from a conforming finite element method formulation of the mathematical model presented in the first part. Thus, existence and uniqueness of the discrete solution when using small enough data are stated following the same strategy used in the continuous case, with a Cea's type error estimate established as the main result. Some numerical experiments, steady and unsteady, are performed, which allow us to validate the previous mathematical model and its discrete approximation. Copyright © 2007 John Wiley & Sons, Ltd.