激波自管口出射后绕射与反射流场的数值计算

激波自激波管口出射后感生的波系图案,以及由它感生的超压场,可简化为二维非定常激波的绕射、反射问题.这个气体动力学方程组是非线性的,其解会随着时间自行产生间断.即使其初始值为连续函数,其解也可能出现间断.这就引起了困难.本文采用欧拉坐标、人工粘性、有限差分法来求解.为写出管口的边条件,首先找出一维管道气体流动的分析解,由此算出管口处的速度、压力、密度随时间变化的曲线.计算结果同实验做了比较,二者是一致的.我们曾对激波自管口出射后的绕射,激波在地面上的斜反射,激波与垂直挡板迎面相撞后的正反射,激波的爬坡过程,以及管口涡环的形成和发展的波系图案等用纹影法做了观测,同时对管口外由波系所感生的超压场分布做了测量.本文对激波自管口出射后绕射与反射流场做了数值计算.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

矩形凹槽管道中激波传播的数值研究

基于二维Euler方程,结合五阶加权基本无振荡(weighted essentially nonoscillatory,WENO)格式以及自适应网格加密(adaptive mesh refinement,AMR)技术对入射激波在矩形凹槽管道内传播过程进行了数值模拟。数值结果清晰地显示了入射激波传播过程中与多个矩形凹槽作用以及在凹槽内变化的整个过程,且与已有的实验结果吻合较好。另外,结果还揭示了入射激波与单个凹槽作用时,会发生绕射产生膨胀波,还会发生碰撞从而诱导反射激波。膨胀波会导致入射激波压力降低,而反射激波则导致其升高,但膨胀波的影响占主导作用,因而入射激波波阵面强度出现振荡下降。     

绕射激波和反射激波作用下N_2/SF_6界面R-M不稳定性实验研究

利用高速纹影测试实验研究低马赫数入射激波绕圆柱体后冲击N2/SF6平面界面,以及来自固壁的反射激波再冲击过程的(Richmyer--Meshkov,R--M)不稳定性特征.与平面激波作用不同的是,绕射后的激波会在界面处生成局部扰动.实验结果显示,入射激波作用下界面宽度增长缓慢,而反射激波再冲击后,局部扰动会产生大的"尖钉"和"气泡"结构;以及反射激波与边界层相互作用产生壁面涡,它们会加剧湍流混合区的增长;实验中反射激波过后混合区增长率不十分依赖于波前状态,增长规律同Mikaelian模型较吻合;来自尾部固壁的反射稀疏波会再次加剧湍流混合区的增长.     

EXPERIMENTALLY STUDY OF THE RICHTMYER-MESHKOV INSTABILITY AT N2/SF6 FLAT INTERFACES BY DIFFRACTED INCIDENT SHOCK WAVES AND RESHOCK

利用高速纹影测试实验研究低马赫数入射激波绕圆柱体后冲击N₂/SF₆平面界面,以及来自固壁的反射激波再冲击过程的（Richmyer-Meshkov,R-M）不稳定性特征.与平面激波作用不同的是,绕射后的激波会在界面处生成局部扰动.实验结果显示,入射激波作用下界面宽度增长缓慢,而反射激波再冲击后,局部扰动会产生大的“尖钉”和“气泡”结构;以及反射激波与边界层相互作用产生壁面涡,它们会加剧湍流混合区的增长;实验中反射激波过后混合区增长率不十分依赖于波前状态,增长规律同Mikaelian模型较吻合;来自尾部固壁的反射稀疏波会再次加剧湍流混合区的增长.     

由激波诱导产生的二维圆柱上的非定常阻力

激波管是一种具有结构简单、参数可调范围大和使用方便等特点的气体动力学试验装置。因此,它在跨声速和超声速流的实验研究中得以广泛地应用。但由于激波管中气流的持续时间很短(通常为毫秒量级),所以在激波管中直接测量试验模型上的压力分布等气动参数将是十分困难的。本文利用马赫-曾德干涉仪在激波管中拍摄出激波在二维圆柱上的绕射和反射时的干涉图,直接给出了整个流场的密度分布。再由波后气流满足等熵关系式,可以计算得到流场的压力分布和非定常阻力的大小。     

马赫反射研究进展

前言平面激波在刚壁的反射问题,30多年来一直是一个在理论上和实验上进行研究的课题[1～60]。人们注意到用激波管进行激波绕射楔角的实验可以得到如图1所示的四种反射图案[10,28—34,40,443:(1)入射激波i在楔角为α的楔面A点上反射出一道激波r,Von Neumann(1943)[24]称它为规则反射(RR);(2)反射点A离开楔面,成为i,r与Mach杆m的三波交点,即单Mach反射(SMR);(3)三波点附近的r阵面出现扭      

可燃气体中激波与障碍物作用在下游形成爆轰波的数值研究

对平面激波和单个矩形障碍物作用的过程进行了数值模拟,研究了反射产生的上行爆轰波在下游可燃气体中形成爆轰波的过程。数值结果表明,下游爆轰波形成过程主要有2种模式:爆轰波直接绕射和绕射波在上壁面反射,这和已有的实验结果是一致的。通过研究下游爆轰波的形成过程受入射激波马赫数、混合气体的压力和管道尺度的影响,分析了上游爆轰波向下游传播的波动力学过程,讨论了2种形成过程的作用规律和控制因素,阐明了下游爆轰波的形成规律。     

爆轰波通过扩张喷管的双曝光全息实验和数值研究

结合实验和数值模拟方法,对以脉冲爆轰发动机为背景的爆轰波通过扩张喷管的流动进行了系列研究。实验采用双曝光全息干涉方法对爆轰波绕射流场进行测量,得到了比传统的纹影法更清晰和可定量化的照片。发展了基于非结构四边形网格自适应有限体积程序,结合基元化学反应模型对扩张喷管中爆轰化学反应流场进行了数值模拟,模拟结果与实验照片吻合较好。实验和数值模拟结果表明,爆轰波绕射具有许多和激波绕射不同的流场特征,其中包括二次起爆现象、化学反应面与前导激波相脱离而引起的复杂流场等,同时初始压力和扩张角度变化也对爆轰波绕射过程产生较大影响,初始压力越低,化学反应区和前导激波分离现象越明显,且前导激波的曲率越大。     

可压缩流向涡与反向运动激波相互作用的实验

对可压缩流向涡与反向运动激波相互作用的现象进行了实验研究．实验在９４ｍｍ×９４ｍｍ的方截面激波管中进行．在实验段上游安装了一个有限翼展平直机翼．当入射激波通过机翼后，波后２区气流在模型翼尖诱导出一条流向涡．入射激波在激波管端壁反射后，形成的反射激波在观察窗处和流向涡发生作用．实验中拍摄了激波与流向涡作用全过程的纹影照片，观察到了一些和定常激波与旋涡相互作用不同的现象，并与数值计算结果进行了初步比较     

Unsteady interaction of shock wave diffracting around a circular cylinder in air

The reflection and diffraction of a planar shock wave around a circular cylinder are a typical problem of the complex nonlinear shock wave phenomena in literature. It has long been studied experimentally, analytically as well as numerically. Takayama in 1987 obtained clear experimental pictures of isopycnics in shock tube under the condition that the impinging shock wave propagates as far as 3 diameters away from the cylinder. To know more completely the whole unsteady process, it is desirable to get experimental results in a region which is more than 10 diameters away from the cylinder. This is what has been done in this paper by using the pulsed laser holographic interferometry for several shock Mach numbers of the impinging shock. Results for several moments are shown, giving more knowledge about the whole unsteady flow field. This is useful for a reliable and complete understanding of the changing force acting on the cylinder, and provides interesting data to check the performance of many recently developed high resolution numerical methods for unsteady shock wave calculation. The project suported partially by National Natural Science Foundation of China     

Study of unsteady flow past bodies behind shock waves

Several theoretical and experimental studies have been devoted to the problem of the nonstationary action of the stream behind a shock wave on bodies of varied shape. In particular, in [1], the pressure and density are calculated for flow about bodies of the more typical shapes in the initial stage of the process. The basic relations which accompany the interaction of shock waves are considered in [2, 3]. The analysis of the phenomena of diffraction of shock waves on the sphere, cylinder, and cone is presented in [4]. Problems of unsteady flow about a wing are examined in [5, 6]. A detailed review of the foreign studies on unsteady flow is given in [7]. Of great practical interest is the question of the time for flow formation and the magnitudes of the unsteady loads during this period. Experimental investigations have been made recently [8, 9] in which some criteria are presented for estimating the bow shock formation time for supersonic flow about the sphere and cylinder with flat blunting. However the question of the formation time of the stationary pressure on the body surface is not referred to in these studies and no relationship is shown between the transient position of the reflected wave and the corresponding unsteady pressure on the surface. Moreover, in [8] the dimensionless time criterion is determined very approximately, independently of the Mach number of the shock wave. The present study was undertaken with the object of determining the basic criteria which characterize unsteady flow about bodies behind a plane shock wave which has time-independent parameters, and clarification of the shock wave reflected from the body and the pressure on the surface of the body during the transient period. The most typical body shapes were studied: 1) a cylinder with flat face aligned with the stream; 2) a spherically-blunted cylinder; and 3) a cylinder transverse to the stream. The experiments were conducted in a conventional shock tube using the single-diaphragm scheme. The measurements of the pressure on the models and the velocity of the incident shock wave were made using the technique analogous to that of [10, 11]. A highspeed movie camera was used to record the pattern of the wave diffraction on the body. The Mach number of the incident shock wave varied in the range from M=1.5 to M≈6.0, which corresponded to a range of Mach numbers M_∞ of the stream behind the shock wave from 0.6 to 2.1. The calculations of the required gas dynamic parameters for high temperatures were made with account for equilibrium dissociation of the air on the basis of the data of [10, 12, 13]. The magnitude of the relative maximal shock wave standoff Δ at the stagnation point obtained in the present experiments was compared with the values of Δ from other studies. In the case of the flat-blunted cylinder it was in good agreement with the results of [8–14], and in the case of the spherically-blunted cylinder and the transverse cylinder it was in agreement with the results of [15].     

3D Steady and Unsteady Bifurcations in a Shock-wave/Laminar Boundary Layer Interaction: A Numerical Study

The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging a laminar boundary layer developing on a plate plane. More precisely, this paper shows that some unsteadiness, in particular the low frequency unsteadiness, originate in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer and not necessarily to the coherent structures resulting from the turbulent character of the boundary layer crossing the shock wave. Numerical computations of a shock-wave/laminar boundary-layer interaction (SWBLI) have been compared with a classical test case (Degrez test case) and both two-dimensional and three-dimensional (3D) unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high order AUSM+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. Finally, discussions and assumptions are made about the origin of the 3D low frequency unsteadiness.     

A comparison of four recent numerical schemes giving high resolution of shock wave and concentrated vortex

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Three dimensional shock wave/boundary layer interactions

An investigation into a three-dimensional, curved shock wave interacting with a three-dimensional, curved boundary layer on a slender body is presented. Three different nose profiles mounted on a cylindrical body were tested in a supersonic wind tunnel and numerically simulated by solving the Navier–Stokes equations. The conical and hemispherical nose profiles tested were found to generate shock waves of sufficient strength to separate the boundary layer on the cylinder, while the shock wave generated by the ogival profile did not separate the boundary layer. For the separated flow, separation was found to occur predominantly on the windward side of the cylinder with the lee-side remaining shielded from the direct impact of the incident shock wave. A thickening of the boundary layer on the lee-side of all the profiles was observed, and in the conical and hemispherical cases this leads to the re-formation of the incident shock wave some distance away from the surface of the cylinder. A complex reflection pattern off the shock wave/boundary layer interaction (SWBLI) was also identified for the separated flow cases. For comparative purposes, an inviscid simulation was performed using the hemispherical profile. Significant differences between the viscous and inviscid results were noted including the absence of a boundary layer leading to a simplified shock wave reflection pattern forming. The behaviour of the incident shock wave on the lee-side of the cylinder was also affected with the shock wave amalgamating on the surface of the cylinder instead of away from the surface as per the viscous case. Test data from the wind tunnel identified two separation lines present on the cylindrical surface of the hemispherical SWBLI generator. The pair of lines were not explicitly evident in the original CFD simulations run, but were later identified in a high-resolution simulation.     

Aspects of self-similar diffraction gas flows and their numerical simulation

A large number of papers has been devoted to the investigation of the interaction of a plane shock wave with bodies of various geometric shapes, and they have been generalized and classified for a stationary body in [1, 2]. Separate results of experimental and theoretical investigations of the interaction of a shock wave with a wedge, cone, sphere, and cylinder moving with supersonic velocities are contained in [3–9]. Analysis of the available results shows that the features of the unsteady gas flows formed in this case largely depend on the nature of the boundary-value problem that arises for the system of differential gas dynamic equations. The question of the wave structure of the unsteady gas flow and the accuracy of the obtained solution is central to the numerical investigation of the present class of problems. The most characteristic types of unsteady self-similar gas flows that arise on the interaction of a plane shock wave with bodies of a wedge or convex corner type are calculated on the basis of an explicit numerical continuous calculation method of the second order of accuracy. The accuracy of the numerical solutions is discussed on the basis of a comparison with the experimental data. The case of the interaction of a shock wave with the rarefaction wave that arises in a supersonic flow past a convex corner is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 146–152, July–August, 1986.     

On the flow behaviour of confined finite-length wavy cylinders

Confined aspect-ratio of 6 wavy cylinders with a mean blockage-ratio of 0.5 were studied using time-resolved particle-image velocimetry at a sub-critical Reynolds number of 2700. Wavelengths and wave amplitudes of 2–4 and 0.1–0.3 mean diameters respectively were investigated. Results show that vortices are generally shed from the wavy cylinder and channel walls regularly, reminiscent of the unsteady symmetric flow configuration in confined non-wavy cylinders. Furthermore, vortex formation lengths for confined wavy cylinders are generally shorter than their unconfined counterparts, though their variations with respect to geometrical changes remain consistent with unconfined flow conditions. Gross cross-stream flow behaviour does not differ significantly between confined and unconfined wavy cylinders, indicating that finite-length effects are independent of the present confinement. Confined wavy cylinder wake regions are more sensitive towards geometrical changes and a combination of small wavelength and large wave amplitude leads to significant suppression of coherent cylinder and wall vortex-shedding. This is supported by phase-averaged flow reconstructions derived from Proper Orthogonal Decomposition analysis. Lastly, larger wave amplitudes lead to redistributions of dominant flow energy further downstream and to higher mode numbers, which suggests a causal link to the formation of stronger and more coherent streamwise vortices.     

Oscillatory behavior of supersonic impinging jet flows

Oscillatory flows of a choked underexpanded supersonic impinging jet issuing from a convergent nozzle have been computed using the axisymmetric unsteady Navier--Stokes system. This paper focuses on the oscillatory flow features associated with the variation of the nozzle-to-plate distance and nozzle pressure ratio. Frequencies of the surface pressure oscillation and flow structural changes from computational results have been analyzed. Staging behavior of the oscillation frequency has been observed for both cases of nozzle-to-plate distance variation and pressure ratio variation. However, the staging behavior for each case exhibits different features. These two distinct staging behaviors of the oscillation frequency are found to correlate well if the frequency and the distance are normalized by the length of the shock cell. It is further found that the staging behavior is strongly correlated with the change of the pressure wave pattern in the jet shear layer, but not with the shock cell structure. Communicated by K. Takayama PACS 02.60.Cb; 47.40.−x; 47.40.Nm; 47.35.+I; 47.15.−x     

A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems. Received May 25, 1995 / Accepted September 11, 1995