新型可压缩尺度在跨声速流动中的应用

基于von Karman长度尺度和新型Reynolds应力本构关系对k-ε湍流模型重构,将k方程封闭,采用代数形式对湍流耗散项进行模化.在KDO（kinetic dependent only）模型的基础上,引入可压缩von Karman长度尺度,得到一种适用于复杂可压缩流动的新型湍流模型CKDO（compressible kinetic dependent only）,在CKDO模型中没有任何经验系数,仅有两个来自边界层精细化标定的可调参数.对RAE2822翼型、轴对称圆筒管道凸起流动、ONERA-M6机翼跨声速流动等算例进行数值计算,结果显示CKDO湍流模型对上述算例流场的压力系数模拟结果与实验值吻合较好,表明CKDO模型能够对跨声速流场进行较为准确的模拟.      

Explicit algebraic Reynolds stress model for compressible flow turbulence

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a new ARSM model is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for ARSM for compressible flow can hardly be obtained due to dilatation terms. We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.     

A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence

We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals − 1.      

The mean-field method in the problem of acoustic wave propagation in a turbulent atmosphere

We analyze the problem of acoustic-wave propagation in a turbulent atmosphere using the mean-field method. The equation for the sound pressure is written with accuracy up to terms that are linear with respect to the Mach number of the turbulent air flow. An expression for the attenuation constant of the mean field is obtained. For the turbulence model described by the von Kármán correlation function of fluctuations, the attenuation coefficient of the mean field is numerically studied in detail. It is shown that under typical conditions of the near-ground atmospheric layer, the predominant contribution to scattering of acoustic waves is given by the turbulent motion of the air masses. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 413–424, May 2008.     

On spectral relaxation method approach for steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating, viscous dissipation and suction/injection

In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations.     

Vortex patterns in quasi-two-dimensional flows of a viscous rotating fluid

A modified von Kármán problem that describes steady vortex flow in a rotating thin viscous fluid layer is solved. An analysis of the effect of bottom friction on the behavior of cyclonic and anticyclonic vortices at arbitrary values of the Rossby number is presented. Several anticyclonic flow patterns are examined. An approximate analytical solution obtained for steady flows is compared with numerical computations of a time-dependent problem. Experimental results on cyclonic and anticyclonic vortices in multiple-vortex quasi-turbulent flow are presented, and their interpretation based on the solution of the model problem is given.     

Extension of the Launder,Reece and Rodi model on compressible homogeneous shear flow

This article describes the second order closure progress that was made to calculate compressible homogeneous shear flow with significant compressibility. Several DNS results show that compressibility has an important effect on the pressure-strain correlation. The term recognized as the principal responsible for the change in the magnitude of Reynolds-stress anisotropies. Thus, the pressure-strain incompressible models do not correctly predict compressible turbulence at high-speed shear flow. A method of including compressibility effects in the pressure-strain correlation is the subject of the present study. The concept of the growth rate of turbulent kinetic energy can be used to construct a compressible correction to the Launder, Reece and Rodi model for the pressure-strain correlation. This correction concerns essentially the C ₁,C ₃ and C ₄ coefficients which become in a compressible turbulence situation a function of the turbulent Mach number. The application of the new model shows good agreement with DNS results of Sarkar for cases A ₁, A ₂ and A ₃. These cases correspond to a moderate mean shear rate, so that nonlinear effects are important. This revised version was published online in July 2005 with corrections to some characters in the abstract.     

Controlling the Bénard-von Kármán instability in the wake of a cylinder by driving the pressure at the front stagnation point

We report an experimental method for inhibiting vortex shedding generated by the Bénard von Kármán instability (BvK) in the wake of a cylinder. We show that monitoring the pressure at the front stagnation point of a circular cylinder can completely suppress the Bénard-von Kármán instability for Reynolds numbers in the range 48.5<Re<150. We then study some properties of the BvK instability in the presence of suction at the front stagnation point and mention that this method can be used to generate well-controlled localized vortical structures in the form of vortex pairs. Received 2 August 1999     

Ludwig Prandtl’s envisage: elimination of von Kármán vortex street with boundary-layer suction

Journal of Visualization - The present study is a revisit to Ludwig Prandtl’s elimination of von Kármán vortex street behind a circular cylinder by using steady suction in the...     

可压缩混合层流场光学效应分析与实验研究

利用量级分析和风洞实验研究了末制导光学外冷窗口典型流动(可压缩混合层流动)气动光学效应的规律性.理论分析主要针对视线误差(boresight error, BSE)与混合层流场特征参数之间的关系进行了讨论. 研究结果表明: 在可压缩混合层中影响时均BSE的特征参数主要有 对流马赫数、雷诺数、自由流与混合层界面剪切应力、自由流速度比和密度比等因素; 采用细光束穿越混合层流场的风洞试验结果主要证实了时均BSE与对流马赫数之间的关系. 关键词： 气动光学效应 可压缩混合层 对流马赫数     

可压缩混合层光学传输效应理论分析与实验研究

利用量级分析和风洞实验研究了可压缩混合层流动第二发展阶段气动光学效应的规律性.理论分析主要针对二维大尺度结构存在时视线误差(boresight error,BSE)与混合层流场及其特征参数之间的关系进行了讨论.研究结果表明:在混合层发展的第二阶段,时均BSE与对流马赫数呈现出复杂的非线性关系;同时还发现流场中的湍动能和混合层界面处的雷诺应力分布也是影响时均BSE的重要因素;采用细光束穿越混合层流场的风洞试验结果主要证实了时均BSE与对流马赫数之间的非线性关系.     

Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

有厚度平板尾缘可压缩剪切层中的涡结构数值模拟

采用一个新型Fu Ma高精度UCD5 SCD6紧致差分算法,通过直接求解二维Navier Stokes方程,成功实现了有厚度平板尾缘可压缩剪切层中涡结构的数值模拟,并考查了平板厚度对其的影响.计算对流马赫数M_c=0.3,平板厚度分别为1,2,3,4个参考长度.结果表明,增加平板厚度可促使平板尾缘可压缩剪切层中的涡提前卷起,有利于两股气流混合.     

Statistical symmetries and its impact on new decay modes and integral invariants of decaying turbulence

Classical decay laws of isotropic turbulence usually derived from the von Kármán–Howarth equation are essentially based on two paradigms. First, scaling symmetries of space and time, both tracing back to the Navier–Stokes equations in the limit of large Reynolds numbers (or r?η), give rise to a temporal power-law decay for the turbulent kinetic energy and at the same time an algebraic growth of the integral length scale at an exponent that is uniquely coupled to the latter energy decay. Second, global invariants such as Birkhoff or Loitsianskii integrals determine the exponent of both power laws. We presently show that this class of decay laws may be considerably extended considering the entire set of multi-point correlation equations that admit a much wider class of symmetries. It was recently shown that these new symmetries are of paramount importance, e.g. in deriving the logarithmic law of the wall being an analytic solution of the multi-point equations. For the present case, it is particularly an additional scaling group, which we call statistical scaling group, that gives rise to two additional families of ‘canonical’ decay laws including those with an exponential characteristic for both the kinetic energy and the integral length scale. Finally, a second rather generic group admitted by all linear differential equations corresponding to the superposition principle induces an infinite set of scaling laws of rather complex form that may match rather generic initial conditions. All scaling laws are analyzed in the light of the above-mentioned integral invariants that have been further extended in the present contribution to an exponential-type invariant.     

Simulations of turbulent asymptotic suction boundary layers

A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. Three Reynolds numbers (defined as ratio of free-stream and suction velocity) of Re = 333, 400 and 500 and a variety of domain sizes were considered in temporal simulations in order to investigate the turbulence statistics, the importance of the computational domain size, the arising flow structures as well as temporal development length required to achieve the asymptotic state. The effect of these two important parameters was assessed in terms of their influence on integral quantities, mean velocity, Reynolds stresses, higher order statistics, amplitude modulation and spectral maps. While the near-wall region up to the buffer region appears to scale irrespective of Re and domain size, the parameters of the logarithmic law (i.e. von Kármán and additive coefficient) decrease with increasing Re, while the wake strength decreases with increasing spanwise domain size and vanishes entirely once the spanwise domain size exceeds approximately two boundary-layer thicknesses irrespective of Re. The wake strength also reduces with increasing simulation time. The asymptotic state of the TASBL is characterised by surprisingly large friction Reynolds numbers and inherits features of wall turbulence at numerically high Re. Compared to a turbulent boundary layer (TBL) or a channel flow without suction, the components of the Reynolds-stress tensor are overall reduced, but exhibit a logarithmic increase with decreasing suction rates, i.e. increasing Re. At the same time, the anisotropy is increased compared to canonical wall-bounded flows without suction. The reduced amplitudes in turbulence quantities are discussed in light of the amplitude modulation due to the weakened larger outer structures. The inner peak in the spectral maps is shifted to higher wavelength and the strength of the outer peak is much less than for TBLs. An additional spatial simulation was performed, in order to relate the simulation results to wind tunnel experiments, which – in accordance with the results from the temporal simulation – indicate that a truly TASBL is practically impossible to realise in a wind tunnel. Our unique data set agrees qualitatively with existing literature results for both numerical and experimental studies, and at the same time sheds light on the fact why the asymptotic state could not be established in a wind tunnel experiment, viz. because experimental studies resemble our simulation results from too small simulation boxes or insufficient development times.     

Kinematic dynamo simulations of von Kármán flows: application to the VKS experiment

The VKS experiment has evidenced dynamo action in a highly turbulent liquid sodium von Kármán flow [R. Monchaux et al., Phys. Rev. Lett. 98, 044502 (2007)]. However, the existence and the onset of a dynamo happen to depend on the experimental configuration. Performing kinematic dynamo simulations on real flows, we study the influence of the configuration on dynamo action, namely the sense of rotation and the presence of an annulus in the shear layer plane. The 3 components of the mean velocity fields are measured in a water prototype for different VKS configurations through Stereoscopic Particle Imaging Velocimetry. Experimental data are then processed in order to use them in a periodic cylindrical kinematic code. Even if the kinematic predicted mode appears to be different from the experimental saturated one, the results concerning the existence of a dynamo and the thresholds are in qualitative agreement, showing the importance of the flow characteristics.     

The Zero-Mach Limit of Compressible Flows

We prove that compressible Navier-Stokes flows in two and three space dimensions converge to incompressible Navier-Stokes flows in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the external force, the initial velocity, or the time interval. We assume instead that the incompressible flow exists and is reasonably smooth on a given time interval, and prove that compressible flows with compatible initial data converge uniformly on that time interval. Our analysis shows that the essential mechanism in this process is a hyperbolic effect which becomes stronger with smaller Mach number and which ultimately drives the density to a constant. Received: 10 June 1997 / Accepted: 15 July 1997     

Linear and non-linear features of the Taylor–Green dynamo

The Taylor–Green flow is a model flow sharing many properties with the von Kármán flow, in which experimental turbulent dynamo action has recently been achieved. We present here recent numerical results on the Taylor–Green dynamo instability, both in the linear and non-linear regime. Various properties are considered, such as the influence of turbulence, the energy transfer between different scales, the spatial structure of the neutral mode, the nature of the bifurcation and the saturation mechanisms. We also discuss the role of the velocity fluctuations on the dynamo onset. To cite this article: Y. Ponty et al., C. R. Physique 9 (2008).     

Nonlinear free vibration of a microscale beam based on modified couple stress theory

This paper presents a nonlinear free vibration analysis of the microbeams based on the modified couple stress Euler–Bernoulli beam theory and von Kármán geometrically nonlinear theory. The governing differential equations are established in variational form from Hamilton principle, with a material length scale parameter to interpret the size effect. These partial differential equations are reduced to corresponding ordinary ones by eliminating the time variable with the Kantorovich method following an assumed harmonic time mode. The resulting equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the size-dependent characteristic relations of nonlinear vibration frequency vs. central amplitude of the microbeams are obtained successfully. The comparisons with available published results show that the current approach and algorithm are of good practicability. A parametric study is conducted involving the dependency of the frequency on the length scale parameter along with Poisson ratio, which shows that the nonlinear vibration frequency predicted by the current model is higher than that by the classical one.     

Nonlocal plate model for nonlinear bending of single-layer graphene sheets subjected to transverse loads in thermal environments

This paper investigates the nonlinear bending behavior of a single-layer rectangular graphene sheet subjected to a transverse uniform load in thermal environments. The single-layer graphene sheet (SLGS) is modeled as a nonlocal orthotropic plate which contains small scale effect. Geometric nonlinearity in the von Kármán sense is adopted. The thermal effects are included and the material properties are assumed to be size dependent and temperature dependent, and are obtained from molecular dynamics (MD) simulations. The small scale parameter e ₀ a is estimated by matching the deflections of graphene sheets observed from the MD simulation results with the numerical results obtained from the nonlocal plate model. The numerical results show that the temperature change as well as the aspect ratio has a significant effect on the nonlinear bending behavior of SLGSs. The results reveal that the small scale parameter reduces the static large deflections of SLGSs, and the small scale effect also plays an important role in the nonlinear bending of SLGSs.