An Exact Riemann Solver for Multicomponent Turbulent Flow

The main objective of this paper is to provide some adequate way to compute the non-conservative hyperbolic system which describes a multicomponent turbulent flow. The model is written for an isentropic gas. The exact solution of the Riemann Problem (RP) associated to the hyperbolic system is exhibited. It is composed of constant states separated by rarefaction waves, or shock waves and a contact discontinuity.

The selection of the admissible part of the shock curve is obtained using an entropy criterion. This entropy is the total energy of the system. Thanks to the latter, one may compute the exact solution of the Riemann problem, assuming genuinely non linear fields contain sufficiently weak shocks.     

Direct Numerical Simulation of Transitional Turbulent Flow in a Closed Rotor-Stator Cavity

The transitional turbulent regime in confined flow between a rotating and a stationary disc is studied using direct numerical simulation. Besides its fundamental importance as a three-dimensional prototype flow, such flows frequently arise in many industrial devices, especially in turbomachinary applications. The present contribution extends the DNS simulation into the turbulent flow regime, to a rotational Reynolds number Re =3 × 10⁵. An annular rotor-stator cavity of radial extension ΔR and height H, is considered with L = 4.72(L = ΔR/H) and Rm = 2.33 (Rm = (R ₁+ R ₀)/ΔR). The direct numerical simulation is performed by integrating the time-dependent Navier–Stokes equations until a statistically steady state is reached. A three-dimensional spectral method is used with the aim of providing both very accurate instantaneous fields and reliable statistical data. The instantaneous quantities are analysed in order to enhance our knowledge of the physics of turbulent rotating flows. Also, the results have been averaged so as to provide target turbulence data for any subsequent modelling attempts at reproducing the flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

离心泵叶轮内宾汉流体湍流流场的数值计算

考虑宾汉流体本构关系特点,建立了任意曲线坐标系（ζ,η）下宾汉流体湍流流动的基本方程,应用压力加权校正算法,实现了速度场和压力场的关联,采用交错网格技术,解决了非物理压力振荡问题,在此基础上,对离心泵叶轮内回转面上宾汉流体湍流流动进行了数值模拟,并分析探讨了离心泵叶轮内宾汉流体湍流流动机理。     

Numerical Simulation of a Turbulent Flow in a Channel with Surface Mounted Cubes

In this paper we report on a fourth-order, spectro-consistent simulation of a complex turbulent flow. A spatial discretization of a convection-diffusion equation is termed spectro-consistent if the spectral properties of the convective and diffusive operators are preserved, i.e. convection skew-symmetric; diffusion symmetric positive definite. We consider a fully developed flow in a channel, where a matrix of cubes is placed at a wall of the channel. The Reynolds number (based on the channel width and the mean bulk velocity) is equal to Re = 13,000. The three-dimensional flow around the surface mounted cubes has served at a test case at the 6th ERCOFTAC/IAHR/COST workshop on refined flow modeling (Delft, June 1997). Here, mean velocity profiles as well as Reynolds stresses at various locations in the channel have been computed without using any turbulence models. The results agree well with the available experimental data.     

Spray Penetration in a Turbulent Flow

Analytical expressions for mass concentration of liquid fuel in a spray are derived taking into account the effects of gas turbulence, and assuming that the influence of droplets on gas is small (intitial stage of spray development). Beyond a certain distance the spray is expected to be fully dispersed. This distance is identified with the maximum spray penetration. Then the influence of turbulence on the spray stopping distance is discussed and the rms spray penetration is computed from a trajectory (Lagrangian) approach. Finally, the problem of spray penetration is investigated in a homogeneous two-phase flow regime taking into account the dispersion of spray away from its axis. It is predicted that for realistic values of spray parameters the spray penetration at large distances from the nozzle is expected to be proportional to t ^2/3 (in the case when this dispersion is not taken into account this distance is proportional to t ^1/2). The t ^2/3 law is supported by experimental observations for a high pressure injector. This revised version was published online in July 2006 with corrections to the Cover Date.     

离心风机子午通道内湍流场数值模拟

由进风口－叶轮－无叶扩压器－蜗壳等部件组成的离心风机通道内流分析是非常复杂的，目前还只能是分别计算各部件内的流场，但必须考虑部件间的相互影响。本文采用轴对称Ｎ－Ｓ方程，根据三维叶轮通道计算给出的叶片力分布，求解了考虑叶片力的进风口－叶轮－无叶扩压器组成的子午通道问题，所得结果可用来给出三维叶轮通道计算的进口条件，并可用于优化设计进风口及叶轮前、后盘形状。该方法已得到实践检验。     

The Use of DNS to Define Stress Producing Events for Turbulent Flow over a Smooth Wall

Over the past 15 years direct numerical simulations (DNS) of turbulent flow and particle image velocimetry (PIV) have provided the opportunity to obtain information about a turbulent velocity field simultaneously at a large number of locations. This paper gives a personal viewpoint of how these techniques are providing new insights about the Reynolds stress producing structures in turbulence generated by flow over a smooth boundary. This revised version was published online in August 2006 with corrections to the Cover Date.     

蜗壳内紊流流场的有限元法计算

用有限元法计算径流式叶轮机械蜗壳的紊流时均流场.有关紊流模型采用K-ε两方程模型,用关于压力p的罚函数方法求解.所得结果可供分析蜗壳流场用.文中方法也可用于计算其他形状的二维通道流动.     

Turbulent flow past a transverse cavity with inclined side walls. 1. Flow structure

The process of vortex formation in a cavity with inclined walls, which has a moderate aspect ratio, is experimentally studied, and the distribution of pressure coefficients is measured. The angle of inclination of the side walls ϕ is varied from 30 to 90°. It is found that the flow in the cavity becomes unstable in the range of inclination angles ϕ = 60–70°. Flow reconstruction occurs, which substantially alters the surface-temperature and static-pressure distributions. Large changes in these characteristics and their nonuniform distributions for these angles are observed across the cavity on its frontal wall and on the bottom. For small angles (ϕ = 30 and 45°), the pressure on the rear wall drastically increases, which leads to a small increase in pressure averaged over the entire cavity surface. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 68–76, September–October, 2006.     

Response of a Thin Cylindrical Shell Excited by a Turbulent Internal Flow

This paper presents results obtained within the scope of a collaboration between the “Laboratoire de Mécanique et d'Acoustique” (Marseille, France), the “Laboratoire de Mécanique des Fluides et d'Acoustique” of the Ecole Centrale (Lyon, France) and the “Laboratoire de Vibrations et d'Acoustique” of the Institut National des Sciences Appliquées (Lyon, France). The main aspect of this collaboration is to establish a comparison between a measured and a model vibro-acoustics response of a thin cylindrical pipe excited by a turbulent internal flow. After a brief review of the literature, a model of the response of the shell, based on a matched asymptotic expansion, is given. Some numerical results are also given. The spectral density of the acceleration of the shell is compared with experimental results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dissipation matrix and artificial heat conduction for Godunov‐type schemes of compressible fluid flows

This paper aims to reassess the Riemann solver for compressible fluid flows in Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov‐type schemes in the sense that associated dissipation matrix has zero determinant if an exact or approximate Riemann solver is used to construct numerical fluxes in the Lagrangian frame. This fact connects to some numerical defects such as the wall‐heating phenomenon and start‐up errors. To cure these numerical defects, a traditional numerical viscosity is added, as well as the artificial heat conduction is introduced via a simple passage of the Lax–Friedrichs type discretization of internal energy. Copyright © 2016 John Wiley & Sons, Ltd.     

DNS of the Turbulent Channel Flow of a Dilute Polymer Solution

A direct numerical simulation of the turbulent channel flow of a dilute polymer solution has been performed in order to compare its turbulence statistics with those obtained in a Newtonian channel flow. The viscoelastic flow has been simulated by solving the whole set of continuity, momentum and constitutive equations for the six independent components of the extra-stress tensor induced by polymer addition. The Finitely Extensible Nonlinear Elastic dumbbell model was adopted in order to simulate a non-linear modulus of elasticity and a finite extendibility of the polymer macromolecules. Simulations were carried out under the narrow channel assumption at a Reynolds number of 169 based on the channel half height and on the friction velocity; they showed a significant reduction in drag, dependent on the influence of the elastic properties of the chains. A qualitative comparison with experiments at a higher Reynolds number has shown that the model here adopted is capable of reproducing all the main features of the polymer solution flow. Analysis of the turbulence statistics suggests that a dilute polymer solution can affect the intensity of the streamwise vortices, leading to an increase in the spacing between low speed streaks and eventually to a turbulent shear stress reduction.     

分块隐式有限差分法计算弯管紊流

本文利用贴体坐标系中分块隐式有限差分法计算矩形截面90°弯管中不可压恒定紊流.在计算中,雷诺方程的数值离散采用混合差分格式,局部联立求解雷诺方程和连续方程而得到速度压力解.在全流场的迭求解过程中采用对称联立Gauss—Seidel法.利用标准K-ε紊流模型模拟紊流.计算结果与有关试验进行了对比.     

DNS of Mixing and Reaction of Two Species in a Turbulent Channel Flow: A Validation of the Conditional Moment Closure

We consider the chemical reaction in a turbulent flow for the case that the time scale of turbulence and the time scale of the reaction are comparable. This process is complicated by the fact that the reaction takes place intermittently at those locations where the species are adequately mixed. This is known as spatial segregation. Several turbulence models have been proposed to take the effect of spatial segregation into account. Examples are the probability density function (PDF) and the conditional moment closure (CMC) models. The main advantage of these models is that they are able to parameterize the effects of turbulent mixing on the chemical reaction rate. As a price several new unknown terms appear in these models for which closure hypothesis must be supplied. Examples are the conditional dissipation 〈 χ ∣ φ 〉, the conditional diffusion 〈 κ ∇² φ ∣ u, φ 〉 and the conditional velocity 〈 u ∣ φ 〉. In the present study we investigate these unknown terms that appear in the PDF and CMC model by means of a direct numerical simulation (DNS) of a fully developed turbulent flow in a channel geometry. We present the results of two simulations in which a scalar is released from a continuous line source. In the first we consider turbulent mixing without chemical reaction and in the second we add a binary reaction. The results of our simulations agree very well with experimental data for the quantities on which information is available. Several closure hypotheses that have been proposed in the literature, are considered and validated with help of our simulation results. This revised version was published online in July 2006 with corrections to the Cover Date.     

桥梁颤振气动导数在均匀流与紊流作用下的统一辨识理论研究

桥梁断面颤振气动导数的准确识别是桥梁空气动力稳定性研究的基础,一直是桥梁风工程研究领域的前沿课题。基于工况模态分析理论,本文首先导出了紊流条件下桥梁颤振气动导数辨识的完整方法;其次,将上述数据处理方式运用到由均匀流条件引起的自由衰减振动中,得出与紊流情况类似的结果。本文提出的方法能够用同样的辨识原理、同一个数据处理程序统一地对紊流和均匀流下的桥梁气动导数进行辨识;最后,利用数值仿真算例验证上述理论。     

各向同性湍流内颗粒碰撞率的直接模拟研究

对 Re_{\lambda } 约为51均匀各向同性湍流内 St_{k}(=\tau_{p}/\tau_{k}) 为 0 ~10.0 的 有限惯性颗粒的碰撞行为进行了直接数值模拟，以研究湍流对有限惯性 颗粒碰撞的影响. 结果表明，具有一定惯性颗粒的湍流碰撞率完全不同于零惯性的轻颗粒 (St_{k}=0) 和可忽略湍流作用的重颗粒 (St{k} \to \infty) , 其变化趋势极其复杂： 在Stk为 0~1.0 之间，颗粒的碰撞率随 St 的增加而近乎线性地剧烈增长，在 Stk≈1.0 3.0(对应的StE=τp/Te≈0.5)附近，颗粒碰撞率出现两个峰值，在Stk>3.0以后，颗粒的碰撞率随惯性增 大而逐渐趋向于重颗粒极限；在峰值处，有限惯性颗粒的平均碰撞率的峰值较轻颗粒增强了 30倍左右. 为进一步分析湍流作用下颗粒碰撞率的影响因素，分别使用可能发生碰撞 的颗粒对的径向分布函数和径向相对速度来量化颗粒的局部富集效应和湍流掺混效应，表明 St_{k} \approx 1.0 时局部富集效应最为强烈，使得颗粒的碰撞率出现第1个峰值； 湍流掺混效应则随着颗粒Stk的增大而渐近增大；局部富集和湍流掺混联合作用的结果， 使得颗粒碰撞率在 St_{k} \approx 3.0 附近出现另一个峰值.     

The Asymptotic Finite-dimensional Character of a Spectrally-hyperviscous Model of 3D Turbulent Flow

We obtain attractor and inertial-manifold results for a class of 3D turbulent flow models on a periodic spatial domain in which hyperviscous terms are added spectrally to the standard incompressible Navier–Stokes equations (NSE). Let P _m be the projection onto the first m eigenspaces of A =−Δ, let μ and α be positive constants with α ≥3/2, and let Q _m =I − P _m , then we add to the NSE operators μ A _φ in a general family such that A _φ≥Q _m A ^α in the sense of quadratic forms. The models are motivated by characteristics of spectral eddy-viscosity (SEV) and spectral vanishing viscosity (SVV) models. A distinguished class of our models adds extra hyperviscosity terms only to high wavenumbers past a cutoff λ _m0 where m ₀ ≤ m, so that for large enough m ₀ the inertial-range wavenumbers see only standard NSE viscosity. We first obtain estimates on the Hausdorff and fractal dimensions of the attractor (respectively and ). For a constant K _α on the order of unity we show if μ ≥ ν that and if μ ≤ ν that where ν is the standard viscosity coefficient, l ₀ = λ₁^−1/2 represents characteristic macroscopic length, and is the Kolmogorov length scale, i.e. where is Kolmogorov’s mean rate of dissipation of energy in turbulent flow. All bracketed constants and K _α are dimensionless and scale-invariant. The estimate grows in m due to the term λ _m /λ₁ but at a rate lower than m ^3/5, and the estimate grows in μ as the relative size of ν to μ. The exponent on is significantly less than the Landau–Lifschitz predicted value of 3. If we impose the condition , the estimates become for μ ≥ ν and for μ ≤ ν. This result holds independently of α, with K _α and c _α independent of m. In an SVV example μ ≥ ν, and for μ ≤ ν aspects of SEV theory and observation suggest setting for 1/c within α orders of magnitude of unity, giving the estimate where c _α is within an order of magnitude of unity. These choices give straight-up or nearly straight-up agreement with the Landau–Lifschitz predictions for the number of degrees of freedom in 3D turbulent flow with m so large that (e.g. in the distinguished-class case for m ₀ large enough) we would expect our solutions to be very good if not virtually indistinguishable approximants to standard NSE solutions. We would expect lower choices of λ _m (e.g. with a > 1) to still give good NSE approximation with lower powers on l ₀/l _ε, showing the potential of the model to reduce the number of degrees of freedom needed in practical simulations. For the choice , motivated by the Chapman–Enskog expansion in the case m = 0, the condition becomes , giving agreement with Landau–Lifschitz for smaller values of λ _m then as above but still large enough to suggest good NSE approximation. Our final results establish the existence of a inertial manifold for reasonably wide classes of the above models using the Foias/Sell/Temam theory. The first of these results obtains such an of dimension N > m for the general class of operators A _φ if α > 5/2. The special class of A _φ such that P _m A _φ = 0 and Q _m A _φ ≥ Q _m A ^α has a unique spectral-gap property which we can use whenever α ≥ 3/2 to show that we have an inertial manifold of dimension m if m is large enough. As a corollary, for most of the cases of the operators A _φ in the distinguished-class case that we expect will be typically used in practice we also obtain an , now of dimension m ₀ for m ₀ large enough, though under conditions requiring generally larger m ₀ than the m in the special class. In both cases, for large enough m (respectively m ₀), we have an inertial manifold for a system in which the inertial range essentially behaves according to standard NSE physics, and in particular trajectories on are controlled by essentially NSE dynamics.      

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.     

Some Features of a Turbulent Separated Flow and Heat Transfer Behind a Step and a Rib. 2. Heat Transfer in a Separated Flow

Results of an experimental study of heat transfer in a separated flow behind a step and a rib are presented. The influence of the obstacle height (H = 6–30 mm) on heat and mass transfer and the structure of the thermal boundary layer is studied. The features of heat transfer in recirculation and relaxation zones of the separated flow are analyzed, and the effect of separation on intensification and suppression of turbulent heat transfer is determined.     

高速列车紊态外流场的数值模拟研究

高速列车是近地运行的细长、庞大物体,它的空气绕流问题有其特殊性,本文以不可压缩粘性流体的Navier-Stokes方程和k-ε两方程紊流模型为基础,采用有限元方法求解了高速列车三维紊态外流场,针对有限元法应用于流场计算时常出现的问题,采用分离式解法,非对称矩阵一维变带宽压缩存储及带宽极小化等方法,最大限度地降低计算存储量;并采用罚函数法,集中质量矩阵,缩减积分法,带参数迭代法以及 引入松弛因子等技术,提出了一套用有限元法计算非线性问题的求解方法,提高了收敛速度的计算严谨,计算方法和计算结果对列车空气动力学的深入研究有一定的帮助。