HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。     

2D vortex interaction in a non-uniform flow

In a two-dimensional incompressible fluid, we study the interaction of two like-signed Rankine vortices embedded in a steady shear/strain flow. The numerical results of vortex evolutions are compared with the analytical results for point vortices. We show the existence of vortex equilibria, and of merger for initial distances larger than those without external flow. The evolutions depend on the initial orientation of the vortices in the external flow.     

Instantaneous structure and statistical feature of unsteady flow in a channel obstructed by a square rod

A two-dimensional numerical computation has been made for an unsteady flow in a channel obstructed by an inserted square rod. The results of the computation made for the flow with a parabolic inlet velocity profile at a specific value of channel Reynolds number are analyzed in detail. The obtained results reveal that momentum transfer is enhanced due to the apparent shear stress resulting from the nonzero value of cross-correlation between the streamwise and normal components of fluctuating velocity, , just as in turbulent shear flows, although the studied flow is quite different from turbulent flows in the sense that it is highly periodical and therefore free from randomness. This periodicity leads to a quick recovery of the velocity defect in some region of the wake of the rod. Special attention is paid to the time variation of flow structure. The crisscross motion of the Karman vortex previously found to occur is discussed again, and how it appears is explained in terms of the interaction between the Karman vortex and the disturbed wall shear layer. In the discussion of this relationship, wavering motion of the separation vorticity layers formed on both sides of the rod and the periodic formation of an isolated vortex island from the lifted tip of the wall vorticity layer are analyzed. The vortex island is found to play an important role not only for the occurrence of the crisscross motion of Karman vortex but also for the generation of the nonzero value of .     

Turbulent flow around a wall-mounted cube: A direct numerical simulation

An immersed-boundary method was employed to perform a direct numerical simulation (DNS) of flow around a wall-mounted cube in a fully developed turbulent channel for a Reynolds number Re = 5610, based on the bulk velocity and the channel height. Instantaneous results of the DNS of a plain channel flow were used as a fully developed inflow condition for the main channel. The results confirm the unsteadiness of the considered flow caused by the unstable interaction of a horseshoe vortex formed in front of the cube and on both its sides with an arch-type vortex behind the cube. The time-averaged data of the turbulence mean-square intensities, Reynolds shear stresses, kinetic energy and dissipation rate are presented. The negative turbulence production is predicted in the region in front of the cube where the main horseshoe vortex originates.     

The effect of a single vortex generator jet on the characteristics of a turbulent boundary layer

A flat plate experiment was performed in a water tunnel to determine the effects of a vortex generator jet on the characteristics of a turbulent boundary layer at various wall normal locations. The results show that the characteristic distributions of the turbulent fluctuation quantities are nearly unaffected by the induced vortex structures neither in the steady nor in the dynamic blowing case. The shear layer interaction between the turbulent main flow and the jet flow produces less turbulent fluctuations than it is expected from a turbulent free jet flow. Thus, the mixing process of this flow control strategy is based only on a large-scale momentum transport superimposed by the turbulent fluctuation quantities. This allows a separation of scales for physical interpretation and numerical simulations.     

One Singularly Perturbed Problem of Turbulent Gas Dynamics

The problem of the interaction of a Prandtl–Mayer wave with a shear layer is solved using the small parameter method for the case where the flow vorticity in the shear layer is small. A direct expansion is constructed and its inadequacy at large distances from the vortex layer is proved. The strained coordinate method is used to obtain a uniformly adequate expansion. It is shown that for certain velocity distributions in the shear layer, the characteristics in the reflected simple wave resulting from the interaction intersect each other and a shock arises in the flow. There coordinates of the shock origin and the function describing the shock shape are obtained.     

Mixing Characteristics in a Supersonic Combustor with Gaseous Fuel Injection Upstream of a Cavity Flameholder

Non-reacting experiments and numerical simulations have been performed to investigate the mixing characteristics in a supersonic combustor with gaseous fuel injection upstream of a flameholding cavity in a supersonic vitiated air flow with stream Mach number 1.7. Using helium as simulated fuel, the acetone vapor is adulterated into the fuel jet. The fuel distribution in spanwise and streamwise direction is imaged by the planar laser-induced fluorescence (PLIF) measurement. According to the similarity of experimental observations with different cavities, the typical L/D = 7 cavity with aft wall angle 45° is chosen and the flowfield with the injection is calculated by Large Eddy Simulation. Experimental and numerical results have shown that most of the fuel flow away upon the open cavity with the lifting counter-rotating vortex structures induced by the transverse jet. Only a small portion of the fuel is convected into the cavity shear layer by the vortex interaction of the jet with cavity shear layer, and then transported into the cavity due to the cavity shear layer motion and the interaction of the shear layer with the cavity trailing edge.     

Wave/vortex decompositions in stably stratified flows

The slowly evolving vortex part of stably stratified flows, both homogeneous and of shear-layer type, is extracted using a diagnostic decomposition of the velocity field based upon the potential vorticity. Comparisons with a decomposition theoretically valid for the linear regime are also made. For the homogeneous flows considered here, the vortex part apparently strongly interacts with the wave field, whatever the decomposition in use. A numerical wave filtering process is applied to simulate the flow dynamics driven by the vortex part only. The resulting vortex flow is the same for each decomposition. In the shear layers, by contrast, only the decomposition based upon the potential vorticity is able to extract the vortex part of the flow, whether the shear layer is moderately or strongly stratified. We propose an argument to account for the fact that a highly energetic vortex part is more likely to be found in a strongly stratified shear layer.This work has been supported by EDF (Direction des Etudes et Recherches, Laboratoire National d'Hydraulique) under Contract No. 2J6773.     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

用扰动涡方法模拟叶轮机内动静叶的相互作用

发展了一种研究叶轮机内动、静叶间的相互作用的新方法———扰动涡方法，它利用全三维的定常解为基础解，并由此给出非定常扰动场的初始解．为计算叶片对扰动场的响应过程，采用拉格朗日方法追踪扰动涡团的对流流动过程，用确定性涡方法来描述流体的粘性扩散过程．发展了代数湍流模型（Ｂａｌｄｗｉｎ Ｌｏｍａｘ湍流模型）在尾迹中的应用方法，克服了其它数值方法中无法准确捕捉尾迹中心线的运动轨迹，以及计算出的边界层外的湍流涡粘性系数偏大的缺陷．利用该方法计算轴流叶轮机内由于动、静叶间的相互作用而引起的非定常流动过程，与实验的对照表明，模拟结果与实验数据吻合得相当好，从而说明本文发展的方法是可信的，为更直观地描述尾迹等非定常因素的流动及叶轮机内的掺混问题提供依据．     

剪切流动中声、涡弱非线性作用与声控流动机理

对非均匀流（特别是平行剪切流）中声、涡运动模式的划分及其相互作用进行了弱非线性分析，着重研究了一阶声、涡作用产生二阶涡的情况，计算了二阶生成涡相对于一阶涡的时均放大倍数。从这一角度分析了声学控制流动问题，指出与声波发生作用的涡的性质以及涡频率与声频率之间的关系，并定性地讨论了声压阈值问题。     

Weakly non-linear analysis on identification of vortex sound & heat and their interactions in shear flow

The identification of vortex, sound and heat motions and the interactions among them are discussed by means of velocity vector split and perturbation method in this paper. Especially the shear flow is considered. All the obtained weakly non-linear equations have clear physics concept. Basing on the analysis, the interaction between first order sound and vortex and the creation of the second order vortex are studied and some experiment phenomena of airfoil flow control by sound are explained.Project supported by the Doctoral Program Foundation of China     

Reynolds stress modelling of rectangular open‐channel flow

A Reynolds stress model for the numerical simulation of uniform 3D turbulent open‐channel flows is described. The finite volume method is used for the numerical solution of the flow equations and transport equations of the Reynolds stress components. The overall solution strategy is the SIMPLER algorithm, and the power‐law scheme is used to discretize the convection and diffusion terms in the governing equations. The developed model is applied to a flow at a Reynolds number of 77000 in a rectangular channel with a width to depth ratio of 2. The simulated mean flow and turbulence structures are compared with measured and computed data from the literature. The computed flow vectors in the plane normal to the streamwise direction show a small vortex, called inner secondary currents, located at the juncture of the sidewall and the free surface as well as the free surface and bottom vortices. This small vortex causes a significant increase in the wall shear stress in the vicinity of the free surface. A budget analysis of the streamwise vorticity is carried out. It is found that both production terms by anisotropy of Reynolds normal stress and by Reynolds shear stress contribute to the generation of secondary currents. Copyright © 2006 John Wiley & Sons, Ltd.     

Vortex shedding from a square cylinder in presence of a moving wall

A numerical study on the flow past a square cylinder placed parallel to a wall, which is moving at the speed of the far field has been made. Flow has been investigated in the laminar Reynolds number (based on the cylinder length) range. We have studied the flow field for different values of the cylinder to wall separation length. The governing unsteady Navier–Stokes equations are discretized through the finite volume method on a staggered grid system. A SIMPLE type of algorithm has been used to compute the discretized equations iteratively. A shear layer of negative vortex generates along the surface of the wall, which influences the vortex shedding behind the cylinder. The flow‐field is distinct from the flow in presence of a stationary wall. An alternate vortex shedding occurs for all values of gap height in the unsteady regime of the flow. The strong positive vortex pushes the negative vortex upwards in the wake. The gap flow in the undersurface of the cylinder is strong and the velocity profile overshoots. The cylinder experiences a downward force for certain values of the Reynolds number and gap height. The drag and lift are higher at lower values of the Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd.     

Characteristics of unsteady type IV shock/shock interaction

Characteristics of the unsteady type IV shock/shock interaction of hypersonic blunt body flows are investigated by solving the Navier–Stokes equations with high-order numerical methods. The intrinsic relations of flow structures to shear, compression, and heating processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous surface-heating peak is caused by the fluid in the “hot spot” generated by an oscillating and deforming jet bow shock (JBS) just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer interaction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the interaction of the JBS and the shear layers formed by a supersonic impinging jet, and then the interaction of the freestream bow shocks and the compression waves results in entropy and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of the flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.     

Vortices in time-periodic shear flow

Vortices emerging in geophysical turbulence may experience deformations due to the non-uniform ambient flow induced by neighbouring vortices. At first approximation this ambient flow is modeled by a linear shear flow. It is well known from previous studies that the vortex may be (partially) destructed through removal of weak vorticity at the vortex edge—a process referred to as ‘stripping’. While most previous studies considered a stationary external shear flow, we have examined the behaviour of the vortex embedded in a linear shear flow whose strength changes harmonically in time. Aspects of the vortex dynamics and the (chaotic) transport of tracers have been studied by both laboratory experiments and numerical simulations based on a simple kinematical model.     

Numerical simulation of Taylor Couette flow of Bingham fluids

The Bingham fluid flow between two concentric cylinders is studied using numerical simulation. The cylinders are assumed to rotate independently, and with an imposed axial sliding. The flow field is decomposed with linearity arguments of the base circular Couette shear flow and corresponding deviation field. The numerical methods are based on the expression of the deviation field in terms of complete sets of orthogonal functions and Chebyshev series. The Galerkin projection method is used with the pressure term being eliminated. The Adams Bashforth scheme is adopted for time marching. The results show that the vortices are squeezed toward the inner cylinder due to the effect of yield stress. When the outer cylinder is held stationary, the yield stress plays a role in weakening the vortex flow. However, for the co-rotation situation, the vortex flow is initially strengthened with an increase of yield stress, and then weakened as the yield stress is raised large enough. The annular unyielded regions emerge and stick to the outer cylinder. In case of Taylor Couette flow with an imposed axial sliding, a spiral vortex flow is visible with spiral unyielded region being obtained.     

Numerical simulation of flow around a square cylinder in uniform-shear flow

This paper presents results obtained from a numerical simulation of a two-dimensional (2-D) incompressible linear shear flow over a square cylinder. Numerical simulations are performed, using the lattice Boltzmann method, in the ranges of 50⩽Re⩽200 and 0⩽K⩽0.5, where Re and K are the Reynolds number and the shear rate, respectively. The effect of the shear rate on the frequency of vortex shedding from the cylinder, and the lift and drag forces exerted on the cylinder are quantified together with the flow patterns around the cylinder. The present results show that vortex structure behind the cylinder is strongly dependant on both the shear rate and Reynolds number. When Re=50, a small K can disturb the steady state and cause an alternative vortex shedding with uneven intensity. In contrast, a large value of K will suppress the vortex shedding from the cylinder. When Re>50, the differences in the strength and size of vortices shed from the upper and lower sides of the cylinder become more pronounced as K increases. Vortex shedding disappears when K is larger than a critical value, which depends on Re. The flow patterns around the cylinder for different Re tend towards self-similarity with increasing K. The lift and drag forces exerted on the cylinder, in general, decrease with increasing K. Unlike a shear flow past a circular cylinder, the vortex shedding frequency past a square cylinder decreases with increasing the shear rate. A significant reduction of the drag force occurs in the range 0.15<K<0.3.     

自由剪切湍流中颗粒-拟序结构相互作用研究进展

从实验和数值模拟两方面评述了颗粒-湍流拟序结构相互作用的近期研究进展.关于Stokes数不同对颗粒行为和拟序结构影响的试验研究,从单点激光多普勒测量到粒子图像全场测速,并与流场显示定性方法结合,揭示了不同Stokes数范围颗粒-拟序结构相互作用的规律.基于涡方法、直接数值模拟和大涡模拟等的模拟研究,进一步揭示颗粒-拟序结构的相互耦合作用和外界激励的调制作用等规律,同时推动了算法的发展.      

Optical Analysis and Qualitative Discrimination of Vortex-Flame Interaction in a Plane Premixed Shear Layer

To obtain practical schemes of vortex–flame interactions, a series of organized eddies formed in the plane premixed shear layer is investigated, instead of a single vortex ring or a single vortex tube. The plane premixed shear layer is first formed between two parallel uniform propane–air mixture streams. For getting clear qualitative pictures of vortex–flame interactions in the plane premixed shear layer, two extreme ignition points are assigned; one is assigned at the center of an organized eddy where the vortex motion plays an important role, the other at the midpoint between two adjacent organized eddies where the rolling-up motion prevails. A premixed flame is initiated by an electric discharge at one of the two assigned points and propagates either in the large scale organized eddy or along the interface between two uniform mixture streams. Propagation and deformation processes of the flame are observed using the simultaneously two-directional and high-speed Schlieren photography. The tangential velocity of organized eddy and the equivalence ratio of premixed shear flow are varied as two main parameters. The outline of propagating flame after the midpoint ignition is numerically analyzed by superposing the flame propagation having a constant burning velocity on the vortex flow field simulated with the discrete vortex method. The results obtained show that there exists another type of vortex–flame interaction in the plane shear layer in addition to the vortex bursting, and that it is caused by the rolling-up motion particular to the coherent structure in the plane shear layer and is simply named the vortex boosting. It is qualitatively concluded therefore that, in the ordinary turbulent premixed flames formed in the plane premixed shear layer, these two fundamental vortex-flame interactions get tangled with each other to augment the propagation velocity. An empirical expression which qualitatively takes into account of the effects of both vortex and chemical properties is finally proposed.