Global Shock Waves¶for the Supersonic Flow Past a Perturbed Cone

We prove the global existence of a shock wave for the stationary supersonic gas flow past an infinite curved and symmetric cone. The flow is governed by the potential equation, as well as the boundary conditions on the shock and the surface of the body. It is shown that the solution to this problem exists globally in the whole space with a pointed shock attached at the tip of the cone and tends to a self-similar solution under some suitable conditions. Our analysis is based on a global uniform weighted energy estimate for the linearized problem. Combining this with the local existence result of Chen–Li [1] we establish the global existence and decay rate of the solution to the nonlinear problem. Received: 1 August 2001 / Accepted: 14 January 2002     

Effect of nose shape on the shock standoff distance at nearsonic flows

This paper describes a numerical solution of the bow shock shape ahead of some blunt and sharp axisymmetric noses containing sphere, blunt cone, and sharp cone at steady transonic flow in the Mach number range of 1.01 to 1.2. For validating the results, one sphere and three blunt cones are modeled, and their shock standoff distance is compared with other experimental and numerical studies. The flow over other noses with similar geometric parameters is then solved and compared with each other. In this study, the Reynolds-averaged Navier—Stokes equations are solved using the Spalart—Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for some blunt and sharp noses at low supersonic free flight speed. The shock standoff distance is determined from the Mach number curve on the symmetry line. The present numerical simulations reach down to M8=1.01 a range where it is almost very difficult to set in experimental studies. The shock wave locations were found to agree well with previous numerical and experimental studies. Our results are closer to the experimental results compared to other numerical studies. In addition, the results for shock standoff distances over paraboloids in these speed ranges have not been previously published as far as we know.     

平面定常超音速绕流问题的新的数值解法

用特征线法解平面定常超音速绕流问题虽然有效,但当激波很弱、几乎与特征线平行时则很难处理。用有限差分法计算此问题也比较复杂。本文把作者在文章中^[1]提出的新的数值解法,发展并应用到平面定常超音速绕流的问题。仍然采用了许为厚教授提出的新拉格朗日变量^[2],这使边界条件的提法大为简化。此新的数值解法按变量指标之和,一排排地往下计算,方法简单,可以处理各种形状物体的超音速绕流。本文对向上弯曲的抛物形固壁绕流向题的实例进行了具体计算。算出了激波的形状。当激波没有形成以前,相应的普朗特一迈耶气流是有准确分析解的,把数值解与准确解进行了l比较结果是满意的。     

基于BOS的超声速流场瞬态密度场的可视化

瞬态密度场的可视化对于超声速流场复杂流动机理研究有着重要的参考价值.设计了基于脉冲激光照明的瞬态密度场可视化系统,针对非对称尖锥模型在Ф=120 mm激波风洞开展了双方向密度场可视化应用研究,获得了Ma=6条件下激波流场清晰的瞬态和长曝光背景纹影图像.研究表明,瞬态背景纹影图像曝光时间为10 ns,能够有效"冻结"超声...     

Vorticity on the Surface of an Axially Symmetric Body behind a Detached Shock Wave

Doklady Physics - The vorticity on the surface of an axially symmetric body streamlined by a steady unswirling homogeneous ideal gas supersonic flow with a detached shock wave has been studied. The...     

Influence of the adiabatic index on switching between different types of shock wave reflection in a steady supersonic gas flow

A comprehensive pattern of different types of shock wave reflection in a steady supersonic gas flow is analytically constructed with regard to a new wave configuration found by the authors-negative-angle irregular reflection. A double Mach reflection with a negative reflection angle in a steady supersonic gas flow is numerically obtained for the first time.     

超声速气膜冷却中激波抑制的研究

针对激波破坏超声速气膜冷却的机理,本文提出了一种壁面开孔的结构,数值研究结果表明：一方面,壁面开孔的结构能使激波作用的区域壁面附近的压力分布较均匀,从而使近壁区的马赫数分布比不开孔的壁面要高,有利于超声速气膜冷却。同时在激波的作用下,冷却气体可以通过开孔壁面的孔进入槽道内,而在槽内的下游再从孔里流出,保护下游的壁面,这...     

Nonlinear Stability of a Self-Similar 3-Dimensional¶Gas Flow

We show that the 3-dimensional supersonic gas flow past an infinite cone is nonlinear staple upon the perturbation of the obstacle. The perturbed flow exists globally in space and tends to the self-similar flow downstream. There is a thin layer of concentration of vorticities and entropy variation. Our analysis is based on an approximation scheme using local self-similar solutions as building blocks. This enables us to obtain global estimates of the nonlinear interactions of waves needed for the stability analysis. Received: 23 November 1998 / Accepted: 26 January 1999     

钝锥绕流流动稳定性分析与转捩预报

研究了超音速钝锥绕流的稳定性和转捩点预报的数值计算方法,首先采用Euler方程求解钝锥绕流基本流场,用所得到的物面压力分布作为粘性边界层的外缘压力分布,给出了基本流场的初值;然后应用反迭代法与边界层渐近匹配的方法求解了钝锥边界层的稳定性方程,得到了钝锥边界层转捩数据.该方法可提高计算精度,节约计算时间.     

Experimental investigation of magnetohydrodynamic action on a heat flux toward the surface of a model

Experimental data for magnetohydrodynamic (MHD) action on a supersonic nitrogen flow about an axisymmetric model are presented. The experiments were carried out in the Big Shock Tube (Ioffe Physical-Technical Institute), at the end of which a test section equipped with a supersonic nozzle was mounted. A test conic model coupled with a cylinder is attached to the output cross section of the nozzle. A magnetic field is produced by a solenoid placed on the cylindrical part of the model through which a pulsed current due to an external voltage source discharging passes. Electrodes on the conic part of the model initiate a gas discharge, which rotates about the axis of the model in the solenoidal magnetic field. The influence of the magnetic field on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface is investigated. Schlieren patterns of the flow about the model, photographic scans of the discharge glow, and heat flux measurements are taken. It is found that the magnetic field has an effect on the gasdynamic pattern of the flow near the model and on the heat flux toward its surface. The dependence of MHD effects on the external voltage polarity is also revealed.     

The characteristics of surface arc plasma and its control effect on supersonic flow

The characteristic of surface arc plasma included millisecond and microsecond actuation in supersonic flow is investigated both experimentally and numerically. In the experiment, the discharge characteristic of surface arc plasma in quiescent air and supersonic flow is recorded. The stable oblique shock could be observed with millisecond actuation. And the unstable compressive wave could be also observed with microsecond actuation. In the numerical investigation, plasma actuation is defined as a source term with input power density from discharge V–I characteristic, which is expected to better describe the influence of heating process. The numerical results are coincident with experimental results. In order to confirm the capability of surface arc plasma actuation to control supersonic flow, experimental investigations on control shock induced by ramp and separation of boundary layer induced by impinging shock are performed. All the results demonstrate the control effect of surface arc plasma actuation onto supersonic flow.     

Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixtures

Unstructured adaptive grid flow simulation is applied to the calculation of high-speed compressible flows of inert and reactive gas mixtures. In the present case, the flowfield is simulated using the 2-D Euler equations, which are discretized in a cell-centered finite volume procedure on unstructured triangular meshes. Interface fluxes are calculated by a Liou flux vector splitting scheme which has been adapted to an unstructured grid context by the authors. Physicochemical properties are functions of the local mixture composition, temperature, and pressure, which are computed using the CHEMKIN-II subroutines. Computational results are presented for the case of premixed hydrogen–air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave fronts. A parametric analysis of the influence of the adaptation parameters on the computed solution is performed.     

一类高压比新概念风扇转子激波结构探索

为适应未来超声速巡航飞机动力系统的要求,作为一种可能的解决方案,本文对于一类来流为轴向超声速、出口为相对亚声速的高压比新概念风扇开展了研究,主要采用三维定常粘性数值方法对转子通道内部激波结构进行了初步探讨,根据流场分布构造了转子三维激波结构,为此类风扇气动设计提供了一定的依据。     

三维高超声速无粘定常绕流的数值模拟

本文采用一种简单有效的通量分裂结合一种二阶TVD格式的数值通量的方法,提出一种隐式的迎风有限体积格式,并利用这种格式,从气体动力学非定常Euler方程组出发,数值模拟了三维不对称物体的高超声速无粘定常绕流。数值结果表明此格式具有分辨率较高和收敛速度较快的优点。     

Visualization of shock-vortex interaction radiating acoustic waves

Unsteady compressible flow fields past a wedge and a cone, evolved by propagation and interaction of shock waves, slip lines, and vortices, are studied by shadowgraphs and holographic interferograms taken during the shock tube experiment. The supplementary numerical calculation also presented time-accurate solution of the shock wave physics which was essential to recognize the similarity and dissimilarity between the wedge and the conical flows. The decelerated shock detained by the vortex interacts with the small vortexlets along the slip layer, producing diverging acoustics: this phenomenon is more distinct in the case of wedge flow for a given shock Mach number. The decelerated shock penetrated through the vortex core constitutes a transmitted shock, which eventually merges with the diaphragm shock that bridges the vortex pair/vortex ring. This phenomenon became remarkably salient in the case of conical flow.     

Formation of transverse waves in oblique detonations

The structure of oblique detonation waves stabilized on a hypersonic wedge in mixtures characterized by a large activation energy is investigated via steady method of characteristics (MoC) calculations and unsteady computational flowfield simulations. The steady MoC solutions show that, after the transition from shock-induced combustion to an overdriven oblique detonation, the shock and reaction complex exhibit a spatial oscillation. The degree of overdrive required to suppress this oscillation was found to be nearly equal to the overdrive required to force a one-dimensional piston-driven detonation to be stable, demonstrating the equivalence of two-dimensional steady oblique detonations and one-dimensional unsteady detonations. Full unsteady computational simulations of the flowfield using an adaptive refinement scheme showed that these spatial oscillations are transient in nature, evolving in time into transverse waves on the leading shock front. The formation of left-running transverse waves (facing upstream) precedes the formation of right-running transverse waves (facing downstream). Both sets of waves are convected downstream away from the wedge in the supersonic flow behind the leading oblique front, such that the mechanism of instability must continuously generate new transverse waves from an initially uniform flow. Together, these waves define a cellular structure that is qualitatively similar to a normal propagating detonation.     

Control of spray spot in cold spray technology. Part 1. Gas dynamic aspects

This paper presents a study of supersonic jets formed by approaches that are new for cold spray technique: the main flow is swirled, the nozzles with permeable profiles and with exit slots on the supersonic section are engineered. The flow swirling achieved in the nozzle prechamber retains downstream to substrate surface. The system of vortices created within the permeable nozzles changes the shock wave features of the overexpanded jet and the geometry of the bow shock wave ahead of the substrate surface. These new features of flow may affect particle motion and particlesubstrate interaction under the conditions of cold spray process; this offers tools for obtaining the necessary shape of a spray spot.     

Visualization of unsteady shock oscillations in the High-enthalpy flow field around double cones

The presence of an adverse pressure gradient, shock/shock interaction and shock wave/boundary layer interaction often induces flow separation around bodies. However, the effect of dissociated flow on separated flow characteristics, especially at hypersonic speeds, is still not clear, and considerable differences are observed between experiments and numerical simulations. In this investigation, the unsteady separated flow features around double cones are visualized in the Shock Wave Research Center (SWRC) free-piston driven shock tunnel at a nominal Mach Number of 6.99 using multiple optical techniques. The time resolved shock structure oscillations in the flow field around double cones (first cone, semi-apex angle = 25°; second cone, semi-apex angles=50°, 65°, 68° and 70°) have been visualized using a high-speed image converter camera (IMACON) at a nominal stagnation enthalpy of 4.8 MJ/kg. In addition, flow visualization studies around the double cone is also carried out using Schlieren and double exposure holographic interferometry in order to precisely locate the separation point and measure the separation length. The presence of a triple shock structure in front of the second cone and a non-linear unsteady shock structure oscillation in the flow field are the significant results from visualization studies on the 25° /65°, 25° /68° and 25°/70° double cones. On the other hand, the flow field around 25° /50° is relatively steady and Type V shock/shock interaction is observed. Illustrative numerical simulation studies are carried out by solving N-S equations to complement the experiments. The simulated flow features around a double cone agree well qualitatively with experiments.     

Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Non-equilibrium rarefied flows are encountered frequently in supersonic flight at high altitudes, vacuum technology and in microscale devices. Prediction of the onset of non-equilibrium is important for accurate numerical simulation of such flows. We formulate and apply the discrete version of Boltzmann’s H-theorem for analysis of non-equilibrium onset and accuracy of numerical modeling of rarefied gas flows. The numerical modeling approach is based on the deterministic solution of kinetic model equations. The numerical solution approach comprises the discrete velocity method in the velocity space and the finite volume method in the physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter and a third-order WENO schemes. The use of entropy considerations in rarefied flow simulations is illustrated for the normal shock, the Riemann and the two-dimensional shock tube problems. The entropy generation rate based on kinetic theory is shown to be a powerful indicator of the onset of non-equilibrium, accuracy of numerical solution as well as the compatibility of boundary conditions for both steady and unsteady problems.     

On the influence of a single roughness element on the flow in supersonic boundary layer on a blunted cone

The work presents the results of numerical modeling of a supersonic flow around a blunted cone with an isolated cylindrical roughness on the forebody surface in the three-dimensional formulation. The roughness element is shown to distort the mean flow and to give rise to small-amplitude disturbances with distinguished spectral peaks in the boundary layer.