激波主导流动下壁板的热气动弹性稳定性理论分析

针对激波主导流动下弹性壁板的热气动弹性稳定性分析问题,建立了基于当地活塞流理论的分析模型,并用数值仿真方法来验证其正确性. 首先基于Hamilton原理和Von-Karman大变形理论,建立壁板的热气动弹性运动方程,其中假设壁板受热后温度均匀分布,激波前后区域的气动力模型采用当地一阶活塞流理论;利用Galerkin方法将具有连续参数系统的偏微分颤振方程离散为有限个自由度的常微分方程;基于李雅普诺夫间接法将非线性颤振方程组在平衡位置处进行线化,再用Routh-Hurwits判据来判断线性系统的稳定性,从而来推论出非线性颤振系统的气动弹性稳定性. 在时域中采用龙格--库塔法对非线性颤振方程进行数值积分,得到壁板非线性颤振响应的时间历程,与理论分析结果进行对比. 研究结果表明,壁板受到斜激波冲击时,更容易发生颤振失稳,并且激波强度越大,极限环幅值和频率越大;激波主导流场中的壁板失稳边界不同于传统单纯超声速气流中壁板颤振的失稳边界;只有在斜激波前后不同的动压值都满足颤振稳定性边界的条件下,壁板才可能保持其气动弹性稳定性.      

Starting of an axisymmetric convergent-divergent nozzle in a hypersonic flow

The starting of an axisymmetric convergent-divergent nozzle, with the result that supersonic flow is formed within almost the entire channel, is modeled, as applied to the hypersonic aerodynamic setup of the Institute of Mechanics of Moscow State University. A successful starting is realized when the nozzle is thrown in a uniform supersonic air flow at a fairly high Mach number. The steady flow structure is studied. It is numerically shown that in the convergent section of the channel there arises an oblique shock wave whose interaction with the nozzle axis leads to the formation of a reflected shock and a curvilinear Mach disk with a region of unsteady subsonic flow in the vicinity of the throat. The mathematical model is based on the two-dimensional Euler equations for axisymmetric gas flows.     

Passage of a subsonic flow around V-shaped wings

In view of the problems involved in the design of hypersonic aircraft great interest has arisen in recent years as to the behavior of wings in fast supersonic flows. Two main approaches have been used: a study of hypersonic flow around traditional wings, and a search for new configurations with optimum aerodynamic properties. Aerodynamic [1, 2], heat-transfer [3], and stability investigations (for V-shaped wings in super- and hypersonic flows) belong to the latter category. Before attaining supersonic flight the aircraft has to overcome the range of subsonic velocities. In this connection it is important to study flow around V-shaped wings at M < 1. Little research has been devoted to flow around such configurations at subsonic velocities, principal attention having been directed at the study of rapid flow around aircraft configurations with V-shaped wings or tails. The results of analytical and numerical calculations allowing for the interference of transient aerodynamic forces acting on a V-shaped and mutiple-fin tail group in combination with the fuselage were presented in [4, 5]. An experimental study of V-shaped wings as regards the influence of the wing dihedral angle on the aerodynamic characteristics of a model aircraft was presented in [6, 7].Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 4, pp. 102–106, July–August, 1975.     

基于非结构网格的TTGC有限元格式的实现及在超声速流动中的应用

基于非结构网格系统,实现了时空三阶精度的TTGC有限元格式,并在三阶TTGC格式上发展了基于人工粘性的激波捕捉技术。在非结构网格下,采用这种方法对若干典型的超声速流动问题(SOD激波管、马赫数为3的前台阶流动以及马赫数为8的高超声速圆柱流动)进行了验证计算。结果表明,TTGC格式分辨率高,在粗糙网格下能够准确的模拟超声速流场中的激波、接触间断等复杂流动现象,并且能有效的控制间断附近的数值色散现象。与传统的有限体积方法相比,本文实现的TTGC有限元格式在模拟超声速流动问题方面具有格式精度高、数值耗散小等优点。     

Thermodynamic properties of equilibrium air by an exact two-equation model for Euler and Navier–Stokes CFD algorithms

This paper details an exact two-equation procedure to generate pressure, temperature and mass and mole fractions as well as their thermodynamic and Jacobian partial derivatives for five-species neutral equilibrium air. Applicable for arbitrary forms of equilibrium constants and especially designed for explicit and implicit CFD algorithms, the procedure algebraically reduces to two equations the six-equation thermodynamic system comprising the equations for internal energy, law of mass action and conservation of species mass and ratio of oxygen and nitrogen nuclei. This exact algebraic reduction explicitly expresses four mass fractions in terms of nitric oxide mass fraction and temperature, which are then determined through a rapidly converging numerical solution of the internal energy and nitric oxide mass action equations. The procedure then exactly determines the partial derivatives of pressure, temperature and mass fractions analytically. The mathematical formulation also introduces a convenient system non-dimensionalization that makes the procedure uniformly applicable to flows ranging from shock tube flows with zero initial velocity to aerothermodynamic flows with supersonic/hypersonic freestream Mach numbers. Over a wide range of density and internal energy the predicted distributions of mole fractions for the model five species agree with independent published results, while pressure and temperature as well as their partial derivatives remain continuous, smooth and physically meaningful. © 1997 John Wiley & Sons, Ltd.     

Hypersonic flow of nonequilibrium air over blunt bodies

A numerical method is described for computing nonequilibrium three-dimensional supersonic flow of a gas in the shock layer over the forward surface of blunt bodies with discontinuities of shape. The basic idea is to divide the original system of differential equations into two subsystems, which are solved in succession: first for the gasdynamic variables, the velocity components and the pressure, and then for the relaxation parameters and the enthalpy. To calculate the velocity components and the pressure we use the iterative marching method [1, 2] in the form given in [3]. The relaxation equations and the enthalpy equation are integrated numerically along the stream lines. A discussion is given of the effect of nonequilibrium of physical and chemical reactions on the distribution of parameters in the inviscid shock layer and on the aerodynamic coefficients of blunt bodies in hypersonic air flow. The unsteady aerodynamic coefficients are calculated by the curved body method [4]. The computational algorithm takes the form of a program in “ALGOL-60” for the BéSM-6 computer.     

TVD格式在超音速喷管三维粘性流动求解中的应用

详细给出了任意三维曲线坐标系中Ｎｏｖｉｅｒ－Ｓｔｏｋｅｓ方程的对流项ＴＶＤ格式的构造过程，建立了数值求解三维粘性流动的计算方法，应用该方法对三维超音速喷管中有激波及无激波情况下的两种工况的层流流场进行了数值求解，并与实验做了对比。结果表明本文建立的计算方法具有较高的精度，同时也证明ＴＶＤ格式具有分辩率高，稳定收敛等优点，为进一步开展叶栅流场及紊流的研究打下了基础。     

Simulation of supersonic flows on the basis of splitting algorithms

For the numerical simulation of aerodynamics problems, the Euler and Navier — Stokes equations written in integral form are used to construct an implicit finite-volume predictor-corrector scheme. At the predictor stage, the splitting of equations into physical processes and spatial directions is introduced, which makes it possible to reduce the solution of the original system to the solution of individual equations on fractional steps by the scalar sweep method and ensure the stability of the algorithm as a whole. The paper also describes the supersonic gas flows in a narrowing channel with regular and non-regular reflection of the compression shock from the symmetry plane and the numerical substantiation of the existence of pulsating flow with a supersonic flow past a cylinder with a needle.     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

高超声速飞行复现风洞理论与方法

针对高超声速飞行伴随的热化学反应流动,本文回顾了郭永怀先生的科研理念和学科布局,综述了他亲手成立的高温气动团队在高超声速飞行风洞实验模拟理论与方法方面的研究进展.高温气体的迅速产生与迅速应用是一种理想的风洞运行方法,而激波管就是这样一种实验装备.论文首先介绍了激波管技术的基本理论与方程,指出将其用于高超声速流动实验模拟时所具有的独特优势.然后讨论了应用激波风洞复现需要的高超声速飞行状态的可行性、基本方程和需要解决的关键问题.针对这些关键问题,进一步介绍了如何应用爆轰现象研发激波风洞驱动技术的理论,并给出了基于爆轰驱动方法的技术发展和工程应用验证.最后,论文介绍了爆轰驱动激波风洞的界面匹配条件,该条件奠定了长实验时间激波风洞运行基础,是其他驱动方法尝试解决而没能完全解决的难题.高温气动团队关于高超声速飞行复现风洞的理论与技术研究,实现了郭永怀先生的战略规划,成就了国际领先的高超声速热化学反应流动研究平台.      

AN APPROXIMATE MODEL OF UNSTEADY AERODYNAMICS FOR HYPERSONIC PROBLEMS AT HIGH ALTITUDE

针对高空高马赫数飞行环境和强黏性干扰的物理特性, 在当地流活塞理论的基础上引入有效外形修正, 发展了黏性修正当地流活塞理论, 结合定常N-S方程解给出了高空高马赫数下针对该方法的有效外形的判据, 并通过数值算例对该判据进行了验证.通过对典型尖头薄翼和典型钝头翼的一系列二维非定常算例, 将该方法与一阶活塞理论、基于欧拉(Euler)方程的当地流活塞理论和非定常N-S方程数值解进行了对比. 结果显示在高度为40~70 km、马赫数为10~20范围内, 通过该方法计算得到的非定常气动力与非定常N-S方程数值解吻合较好, 明显优于活塞理论和基于Euler方程的当地流活塞理论.该方法克服了传统的活塞理论和当地流活塞理论不能用于高空高马赫数这类强黏性效应情况的弊端, 在较宽的马赫数、攻角、飞行高度范围内都有良好的适用性, 同时其计算效率远高于非定常N-S方程.     

Study on the numerical schemes for hypersonic flow simulation

Hypersonic flow is full of complex physical and chemical processes, hence its investigation needs careful analysis of existing schemes and choosing a suitable scheme or designing a brand new scheme. The present study deals with two numerical schemes Harten, Lax, and van Leer with Contact (HLLC) and advection upstream splitting method (AUSM) to effectively simulate hypersonic flow fields, and accurately predict shock waves with minimal diffusion. In present computations, hypersonic flows have been modeled as a system of hyperbolic equations with one additional equation for non-equilibrium energy and relaxing source terms. Real gas effects, which appear typically in hypersonic flows, have been simulated through energy relaxation method. HLLC and AUSM methods are modified to incorporate the conservation laws for non-equilibrium energy. Numerical implementation have shown that non-equilibrium energy convect with mass, and hence has no bearing on the basic numerical scheme. The numerical simulation carried out shows good comparison with experimental data available in literature. Both numerical schemes have shown identical results at equilibrium. Present study has demonstrated that real gas effects in hypersonic flows can be modeled through energy relaxation method along with either AUSM or HLLC numerical scheme.     

A calculating method of shock wave oscillating frequency due to turbulent shear layer fluctuations in supersonic flow

One of the more severe fluctuating pressure environments encountered in supersonic orhypersonic flows is the shock wave oscillation driven by interaction of a shock wave withboundary layer.The high intensity oscillating shock wave may induce structure resonanceof a high speed vehicle.The research for the shock oscillation used to adopt empirical orsemiempirical methods because the phenomenon is very complex.In this paper atheoretical solution on shock oscillating frequency due to turbulent shear layer fluctuationshas been obtained from basic conservation equations.Moreover,we have attained theregularity of the frequency of oscillating shock varying with incoming flow Mach numbersM_∞and turning angleθ.The calculating results indicate excellent agreement withmeasurements.This paper has supplied a valuable analytical method to study aeroelasticproblems produced by shock wave oscillation.     

Some unique features of supersonic unsteady gas flow around bodies

We consider unsteady supersonic gas flow about bodies for small Strouhal numbers. The amplitude of the angles of attack is assumed arbitrary under the condition that the bow shock remains attached, and the flow behind the shock is supersonic. A criterion is formulated which permits the comparison of the damping characteristic for small and large amplitudes of the disturbed motion. A comparison is made, using the wedge as an example, of the damping characteristics calculated by various theories, and the hypersonic similarity law is verified. Simple asymptotic equations are presented for the rotary derivatives of the thin wedge in a hypersonic gas stream.     

On the accuracy and efficiency of CFD methods in real gas hypersonics

A study of viscous and inviscid hypersonic flows using generalized upwind methods is presented. A new family of hybrid flux-splitting methods is examined for hypersonic flows. The hybrid method is constructed by the superposition of the flux-vector-splitting (FVS) method and second-order artificial dissipation in the regions of strong shock waves. The conservative variables on the cell faces are calculated by an upwind extrapolation scheme to third-order accuracy. A second-order-accurate scheme is used for the discretization of the viscous terms. The solution of the system of equations is achieved by an implicit unfactored method. In order to reduce the computational time, a local adaptive mesh solution (LAMS) method is proposed. The LAMS method combines the mesh-sequencing technique and local solution of the equations. The local solution of either the Euler or the NAVIER-STOKES equations is applied for the region of the flow field where numerical disturbances die out slowly. Validation of the Euler and NAVIER-STOKES codes is obtained for hypersonic flows around blunt bodies. Real gas effects are introduced via a generalized equation of state.     

Viscous hypersonic flows for various aerophysical models

The results of mathematical simulation of hypersonic air flow past a sphere with allowance for chemical nonequilibrium and ionization are presented. The calculated data are obtained on the basis of a numerical solution of the Navier-Stokes equations and the hypersonic viscous shock layer equations. The equilibrium radiation temperature of the body surface, the pressure, and the shock wave detachment are compared for these models. The combined effect of molecular transport and the catalytic properties of the body surface on the aerodynamic heating is analyzed. The results of the effect of certain models of the thermochemical disequilibrium of the gas on the temperature of the body surface are also analyzed along a heat-stressed interval of the reentry trajectory of an aerospace vehicle.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 151–161, July–August, 1996.     

Revised model coefficients for vibrational relaxation in a nitrogen–oxygen gas mixture

A numerical investigation of thermal non-equilibrium flows requires species specific relaxation rates, which are often calculated using the Landau–Teller model. This model requires the determination of collision specific relaxation times, which can be computed using Millikan and White’s empirical formula. The coefficients used in this formula for each specific collision pair form a set of coefficients, which are assessed here. The focus of the investigation lies on their performance in hypersonic low-temperature (300–2,500?K) flows that occur at shock-tunnel nozzle exits or in supersonic combustion ramjets (scramjets) before combustion. Two experimental validation cases are chosen; a shock-tunnel nozzle and a sharp cone in hypersonic cross-flow experiment. A comparison of the experimentally measured vibrational temperatures at the nozzle exit against numerical data shows large discrepancies for two commonly used coefficient sets. A revised set of coefficients is proposed that greatly improves the agreement between the numerical and experimental results. Furthermore, the numerically generated shock shape over the sharp cone using the revised set of coefficients correlates well with the experimental measurements.     

Numerical simulation of a pulsating flow arising over an axisymmetric spiked blunt body at Mach 2.21 and Mach 6.00

The present paper reports a numerical simulation of the supersonic/hypersonic unsteady flow over a spiked blunt body. Axisymmetric compressible Navier-Stokes equations are solved using a high-resolution unfactored implicit upwind Roe's scheme and a time-accurate pseudo-time method is employed for advancing in time. Unsteady flows arising at Mach 2.21 and Mach 6.00 around a spiked cylinder are simulated and the computational results are compared with measurements. The simulated results are used to increase understanding of the mechanisms of the flow. Received 28 September 1999 / Accepted 26 July 2000     

Parametric study on supersonic flutter of angle-ply laminated plates using shear deformable finite element method

The influence of fiber orientation,flow yaw angle and length-to-thickness ratio on flutter characteristics of angle-ply laminated plates in supersonic flow is studied by finite element approach.The structural model is established using the Reissner-Mindlin theory in which the transverse shear deformation is considered.The aerodynamic pressure is evaluated by the quasi-steady first-order piston theory.The equations of motion are formulated based on the principle of virtual work.With the harmonic motion assumption,the flutter boundary is determined by solving a series of complex eigenvalue problems.Numerical study shows that (1) The flutter dynamic pressure and the coalescence of flutter modes depend on fiber orientation,flow yaw angle and length-to-thickness ratio;(2) The laminated plate with all fibers aligned with the flow direction gives the highest flutter dynamic pressure,but a slight yawing of the flow from the fiber orientation results in a sharp decrease of the flutter dynamic pressure;(3) The angle-ply laminated plate with fiber orientation angle equal to flow yaw angle gives high flutter dynamic pressure,but not the maximum flutter dynamic pressure;(4) With the decrease of length-to-thickness ratio,an adverse effect due to mode transition on the flutter dynamic pressure is found.     

Implementation of high‐order compact finite‐difference method to parabolized Navier–Stokes schemes

The numerical solution to the parabolized Navier–Stokes (PNS) and globally iterated PNS (IPNS) equations for accurate computation of hypersonic axisymmetric flowfields is obtained by using the fourth‐order compact finite‐difference method. The PNS and IPNS equations in the general curvilinear coordinates are solved by using the implicit finite‐difference algorithm of Beam and Warming type with a high‐order compact accuracy. A shock‐fitting procedure is utilized in both compact PNS and IPNS schemes to obtain accurate solutions in the vicinity of the shock. The main advantage of the present formulation is that the basic flow variables and their first and second derivatives are simultaneously computed with the fourth‐order accuracy. The computations are carried out for a benchmark case: hypersonic axisymmetric flow over a blunt cone at Mach 8. A sensitivity study is performed for the basic flowfield, including profiles and their derivatives obtained from the fourth‐order compact PNS and IPNS solutions, and the effects of grid size and numerical dissipation term used are discussed. The present results for the flowfield variables and also their derivatives are compared with those of other basic flow models to demonstrate the accuracy and efficiency of the proposed method. The present work represents the first known application of a high‐order compact finite‐difference method to the PNS schemes, which are computationally more efficient than Navier–Stokes solutions. Copyright © 2008 John Wiley & Sons, Ltd.