常数速度梯度时均匀湍流的二元速度关联函数

在湍流脉动速度比较小的条件下,本文得到了富氏变换过后脉动速度方程的解.它所代表的涡旋,在平均速度梯度为小量时,化为具有常数平均速度梯度的、组成后期均匀各向同性湍流场的涡旋和组成后期各向异性湍流场的涡旋.利用不同时刻的这种涡旋解,组成定常的有常数平均速度梯度的湍流场,这个湍流场可以近似地表达槽流和管流近中心区域的湍流场.我们求得了这种湍流场的二元速度关联函数,包括纵向的关联系数f(γ/λ)和横向的关联系数g(γ/λ).并且和均匀各向同性湍流实验中的前期和后期的f(γ/λ)和g(γ/λ)进行了比较.并且弄清楚了速度梯度对关联系数f(γ/λ)所产生的影响,最后还得到了雷诺应力和涡旋粘性系数的表达式.     

壁面加热湍流耗散率标度指数测量的实验研究

对中等雷诺数下壁面常温和壁面加热的平板湍流边界层中速度和温度粗粒化的耗散率结构函数标度指数进行了实验测量.用热线风速仪测量了风洞中壁面常温和加热的平板湍流边界层中不同法向位置的流向速度分量和温度的时间序列信号,研究了由于湍流边界层近壁区域相干结构的存在而导致的非各向同性、非均匀性对湍流耗散率结构函数标度指数的影响,研究发现,中等雷诺数下壁面加热的边界条件和剪切湍流的平均速度梯度对速度和温度耗散率结构函数的标度指数没有影响,均匀各向同性湍流的耗散率结构函数标度指数的层次结构模型对壁面加热平板湍流边界层的速度和温度耗散率结构函数的标度指数也是适用的.     

Langevin equation of a fluid particle in wall-induced turbulence

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-induced turbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer). The analysis is based on the asymptotic behavior at a large Reynolds number. We use the Lagrangian Kolmogorov theory, recently derived asymptotic expressions for the spatial distribution of turbulent energy dissipation, and also newly derived reciprocity relations analogous to the Onsager relations supplemented with recent measurement results. The long-time limit of the derived Langevin equation yields the diffusion equation for admixture dispersion in wall-induced turbulence.     

壁湍流多尺度湍涡结构推广的自相似标度律

在水槽中测量了中等雷诺数下平板湍流边界层中的瞬时流向速度的时间序列,验证了Benzi提出的推广的自相似标度律,用子波变换将壁湍流脉动速度分解为多尺度湍涡结构的速度,研究了每一个尺度的湍涡速度结构函数的推广的自相似标度律。主要结论如下:湍流的统计性质是自相似的,这不仅适用于充分发展湍流,而且适用于中等雷诺数和低雷诺数湍流,而且具有相同的标度指数;推广的自相似标度律的适用的尺度范围远远大于惯性子区的范围,可以一直延伸至耗散区的尺度范围;推广的自相似标度律不仅适用于均匀各向同性湍流,也适用于剪切湍流如边界层湍流。     

Spectral characteristics of atmospheric turbulence model

In this paper, KdV-Burgers equation can be regarded as the normal equation of atmospheric turbulence in the stable boundary layer. On the basis of the travelling wave analytic solution of KdV-Burgers equation, the turbulent spectrum is obtained. We observe that the behavior of the spectra is consistent with actual turbulent spectra of stable atmospheric boundary layer.     

High-order accurate bicompact schemes for solving the multidimensional inhomogeneous transport equation and their efficient parallel implementation

The method of lines is used to obtain semidiscrete equations for a bicompact scheme in operator form for the inhomogeneous linear transport equation in two and three dimensions. In each spatial direction, the scheme has a two-point stencil, on which the spatial derivatives are approximated to fourth-order accuracy due to expanding the list of unknown grid functions. This order of accuracy is preserved on an arbitrary nonuniform grid. The equations of the method of lines are integrated in time using diagonally implicit multistage Runge–Kutta methods of the third up fifth orders of accuracy. Test computations on refined meshes are presented. It is shown that the high-order accurate bicompact schemes can be efficiently parallelized on multicore and multiprocessor computers.     

Effects of plane strain on inhomogeneous turbulence

The influence of the mean plane strain on the turbulence transportation is investigated by large eddy simulation (LES) in the shearless turbulence mixing layer. It is found that the mean strains enhance the turbulent fluctuations in the mixing region. Compression in the inhomogeneous direction can greatly increase the transport of turbulent kinetic energy by triple correlation terms, while stretching in the inhomogeneous direction decreases the turbulence transportation. The gradient diffusion models for turbulent transportation are evaluated and it is found that the intermittency consideration can improve the prediction ability of the gradient-type models for the triple correlation terms. Project supported by the Sino-French Laboratory in Beijing and the National Natural Science Foundation of China (Grant No. 19572041).     

Wavefronts in a Relativistic Two-Phase Turbulent Flow

The simplest model of isotropic relativistic turbulence consists of the relativistic two-phase fluid equations augmented by an equation for the turbulent energy.     

运动壁面槽道流动的直接数值模拟

采用谱方法,在曲线坐标系下对不可压缩Newton流体的N-S方程进行求解,采用定义在物理空间中的流动物理量以避免使用协变、逆变形式的控制方程．在计算空间采用Fourier-Chebyshev谱方法进行空间离散,时间推进采用高精度时间分裂法．为了减小时间分裂带来的误差,采用了高精度的压力边界条件．与其他求解协变、逆变形式控制方程的谱方法相比,该方法在保持谱精度的同时减小了计算量．首先通过静止波形壁面和行波壁面槽道湍流的直接数值模拟,对该数值方法进行了验证;其次,作为初步应用,利用该方法研究了槽道湍流中周期振动凹坑所产生的流动结构．     

基于改进位移模式的二维有限元线法超收敛算法

提出了基于改进位移模式的二维有限元线法超收敛算法．利用单元内部需满足平衡方程的条件,推导了超收敛计算的解析公式的显式,即将高阶有限元线法解的位移模式用常规有限元线法解的位移模式表示．用常规有限元线法解的位移模式与高阶有限元线法解的位移模式之和构造新的位移模式,基于线性形函数,采用变分形式推导了有限元线法求解的修正的常微分方程组．该算法在前和后处理同时使用超收敛计算公式,在原有试函数的基础上,增加了高阶试函数．使得单元内平衡方程的残差减少,从而达到提高精度的目标．对于二维Poisson方程问题,给出了有代表性的算例,结点和单元内的位移、导数的收敛精度得到了极大的提高．     

颗粒的有限尺寸对颗粒在均匀各向同性湍流中扩散的影响

本文指出固体颗粒对流体湍流运动的响应有不同的机理,颗粒受大涡的粘性拖动,但受小涡的随机碰撞.基于这种原理,本文计算了有限尺寸的固体颗粒在均匀各向同性湍流中的扩散.结果显示存在着二种相互抵消的效应:颗粒的惯性使颗粒长期扩散系数上升,而颗粒尺寸使颗粒的长期扩散系数下降.     

Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM

Understanding transition and turbulence in the flow of shear-thinning non-Newtonian fluids remains substantially unresolved and additional research is required to develop better computational methods for wall-bounded turbulent flows of these fluids. Previous DNS studies of shear-thinning fluids mainly use purpose-built codes and simple geometries such as pipes and channels. However in practical application, the geometry of mixing vessels, pumps and other process equipment is far more complex, and more flexible computational methods are required. In this paper a general-purpose DNS approach for shear-thinning fluids is undertaken using the OpenFOAM CFD library. DNS of turbulent Newtonian and non-Newtonian flow in a pipe flow are conducted and the accuracy and efficiency of OpenFOAM are assessed against a validated high-order spectral element-Fourier DNS code – Semtex. The results show that OpenFOAM predicts the flow of shear-thinning fluids to be a little more transitional than the predictions from Semtex, with lower radial and azimuthal turbulence intensities and higher axial intensity. Despite this, the first and second order turbulence statistics differ by at most 16%, and usually much less. An assessment of the parallel scaling of OpenFOAM indicates that OpenFOAM scales very well for the CPUs from 8 to 512, but the intranode scalability is poor for less than 8CPUs. The present work shows that OpenFOAM can be used for DNS of shear-thinning fluids in the simple case of pipe flow, and suggests that more complex flows, where flow separation is often important, are likely to be simulated with accuracies that are acceptably good for engineering application.     

On the stability of explicit finite difference methods for advection–diffusion equations

In this article we study the stability of explicit finite difference discretization of advection–diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability of the system of ordinary differential equations that is obtained by discretizing the ADE in space and then extends to fully discretized methods in combination with explicit Runge–Kutta methods. In particular, we prove that all stable semi-discretization of the ADE leads to a conditionally stable fully discretized method as long as the time-integrator is at least first-order accurate, whereas high-order spatial discretization of the advection equation cannot yield a stable method if the temporal order is too low. In the second half of the article, the analysis and the stability results are extended to a partially dissipative wave system, which serves as a model for common practice in many fluid mechanics applications that incorporate a viscous stress in the momentum equation but no heat dissipation in the energy equation. Finally, the major theoretical predictions are verified by numerical examples.     

复合多层介质在可变温度和集中荷载作用下的位移和应力

研究了多层介质中的热弹性位移和应力.多层介质具有不同厚度,各层又具有不同的弹性性质,最上层表面上作用热荷载和集中荷载.假设各层分别是均匀、各向同性弹性材料,各层相关的位移分量是轴对称的,对称轴为各层表面的垂线.因此,各层应力函数满足无体力的单一方程.利用积分变换法求解了该方程,对由任意多个层数构造的多层介质,给出了其相应层数基础热弹性位移和应力的解析表达式.并对3层介质和4层介质时的数值结果进行了比较.     

2D numerical simulation of submerged hydraulic jumps

Hydraulic jumps are usually used to dissipate energy in hydraulic engineering. In this paper, the turbulent submerged hydraulic jumps are simulated by solving the unsteady Reynolds averaged Navier–Stokes equations along with the continuity equation and the standard k–? equations for turbulence modeling. The Lagrangian moving grid method is employed for the simulation of the free surface. In the developed model, kinematic free-surface boundary condition is solved simultaneously with the momentum and continuity equations, so that the water elevation can be obtained along with velocity and pressure fields as part of the solution. Computational results are presented for Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. Comparisons with experimental measurements show that numerical model can simulate the velocity field, variation of free surface, maximum velocity, Reynolds shear and normal stresses at various stations with reasonable accuracy.     

Structure of a Linear Array of Uniform Vortices

The shape and properties of an infinite steady linear array of uniform vortices are calculated. A nonlinear singular integrodifferential equation is obtained for the shapes, which is solved numerically by Newton's method and Euler continuation to give a one parameter family of shapes as size over separation is varied. The kinematic properties and energy of the array are obtained. It is found that there exists an array of maximum area, for given separation, which also possesses minimum energy in accordance with a general argument of Kelvin. A simple model based on elliptical vortices is constructed, which reproduces the qualitative kinematic properties and is quantitatively quite accurate. Continuation of the numerical solution past the array of maximum area leads to a limit of finite, lens shaped, touching vortices. This array is also shown to be limit of a finite amplitude bifurcation of a vortex sheet of finite thickness. The stability of the array to two dimensional subharmonic and superharmonic disturbances is considered. General arguments, based on ideas of Kelvin, are given to show that the array is stable to superharmonic disturbances if the area is less than the maximum and otherwise unstable, and that it is always unstable to subharmonic disturbances, of which the pairing instability is a special case. It is verified by direct calculation in an Appendix that hollow vortices, whose shapes can be determined analytically in closed form, are unstable to the pairing instability whatever their size. Some speculations are made about the possible relevance of the results to the observed properties of organized structures in the turbulent mixing layer.     

Statistics of numerically generated turbulence

This paper considers numerically generated turbulence obtained by integrating the complete time-dependent three-dimensional Navier-Stokes equations. The simulated unidirectional turbulent flow, bounded by two parallel planes, is strongly inhomogeneous in the direction normal to the planes but homogeneous in the parallel directions. The resulting flow field, which is considered a numerical realization of fully developed turbulent channel flow, contains detailed information on spatial coherent flow structures as well as on the time-dependency and statistics of the three-dimensional velocity and pressure fields. Focussing here on the statistics of the numerically generated turbulence, second-moments and higher-moments are presented and compared with the most recent PTV and LDV laboratory measurements. It is concluded that direct numerical simulations are an invaluable approach to turbulence which complements field studies and laboratory investigations. Numerical experiments are now becoming a principal source of detailed and reliable information, which play a key role in the deepening of our understanding of turbulent flow phenomena.     

Direct numerical simulation of transition and turbulence in compressible mixing layer

The three-dimensional compressible Navier-Stokes equations are approximated by a fifth order upwind compact and a sixth order symmetrical compact difference relations combined with three-stage Ronge-Kutta method. The computed results are presented for convective Mach numberMc = 0.8 andRe = 200 with initial data which have equal and opposite oblique waves. From the computed results we can see the variation of coherent structures with time integration and full process of instability, formation of A -vortices, double horseshoe vortices and mushroom structures. The large structures break into small and smaller vortex structures. Finally, the movement of small structure becomes dominant, and flow field turns into turbulence. It is noted that production of small vortex structures is combined with turning of symmetrical structures to unsymmetrical ones. It is shown in the present computation that the flow field turns into turbulence directly from initial instability and there is not vortex pairing in process of transition. It means that for large convective Mach number the transition mechanism for compressible mixing layer differs from that in incompressible mixing layer.     

Direct numerical method for an inverse problem of a parabolic partial differential equation

A coefficient inverse problem of the one-dimensional parabolic equation is solved by a high-order compact finite difference method in this paper. The problem of recovering a time-dependent coefficient in a parabolic partial differential equation has attracted considerable attention recently. While many theoretical results regarding the existence and uniqueness of the solution are obtained, the development of efficient and accurate numerical methods is still far from satisfactory. In this paper a fourth-order efficient numerical method is proposed to calculate the function u(x,t) and the unknown coefficient a(t) in a parabolic partial differential equation. Several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method.     

High-order filtered scheme for front propagation problems

In this work we develop a specific application of the scheme proposed and analyzed in [1] to front propagation problems. The approach is based on the level-set method which leads in the isotropic case to a classical evolutive first order Hamilton- Jacobi equation.We will apply to this equation high-order “filtered schemes”, for these schemes the strong monotonicity property will not be satisfied. However, a weak ?-monotonicity property applies and this is enough to obtain a convergence result and a precise error estimate. In the last section we will present several examples where we solve front propagation problems by filtered scheme in two and three dimensions showing the accuracy of our method.