Numerical simulation of blast flow fields induced by a high-speed projectile

Numerical investigations on the launch process of a projectile in a nearly realistic situation have been performed in this article. The Arbitrary Lagrangian–Eulerian (ALE) of Euler equations is solved by the AUSMDV scheme and the dynamic chimera grid technique are used for describing the moving of the projectile. Based on our numerical results, the muzzle blast flow field of the transient launch process of a projectile at a relative high Mach number of 3.0 has been visualized numerically, and the prominent characteristics including the propagation of first and second blast waves, the generation of bow shock wave and moving of the projectile, etc. have been discussed in detail.      

Diaphragm rupture. Impingement by a conically-nosed, ram-accelerator projectile

The effect of diaphragm rupture by a conically-nosed projectile on the gasdynamics related to ram accelerator operation was experimentally and numerically studied. The experiments were conducted using a 25-mm-bore ram accelerator. Either air or nitrogen was used as the test gas. Using a high-speed image converter camera, it was observed that during the process of the diaphragm rupture a region with strong radiation developed between the diaphragm and the approaching projectile/sabot. This radiating region corresponds to the shock-heated gas which is originated from a precursory shock wave driven by the accelerating projectile/sabot. The flow around the projectile upon entering the test section by rupturing the diaphragm was visualized by holographic interferometry. During the diaphragm rupture, the system of oblique shock waves around the conical nose of the projectile was seen undisturbed on the downstream side of the diaphragm. Under the same condition as the experiment, numerical simulation was conducted using GRP (Generalized Riemann Problem) scheme which was extended to the computation of compressible flow fields bounded by moving surfaces. Two diaphragm rupture models were examined: (1) the diaphragm deformed by wrapping tightly around the moving projectile; (2) the diaphragm was ruptured instantly at the moment the projectile touched the diaphragm. Comparing these models with the experimentally visualized flow, the former was found to express the diaphragm rupture process much better than the latter. Received 9 February 1998 / Accepted 9 September 1998     

Transient shock wave flows in tubes with a sudden change in cross section

This paper describes propagation of shock waves within circular cross-section shock tubes with a sudden area change in cross section. A dispersion-controlled scheme was used to solve the Euler equations assuming axisymmetric flows. For experimental visualizations an aspheric cylindrical test section was designed to keep collimated incident light rays parallel once they were reflected or refracted on the inner and outer surfaces of the test section. For effective comparisons with experimental results, equivalent numerical interferograms were constructed to demonstrate effectiveness of the numerical method and verify the observed shock-wave phenomena. The numerical method was used to calculate three further cases with variations of the initial shock-wave Mach number and the flow geometry to clarify the role of these parameters. Complex transient shock-wave phenomena, such as shock-wave reflection, shock/vortex interaction and shock-wave focusing were observed in these cases, and interpreted with shock wave theory. In addition, the research clearly shows that combination of CFD with experiments is effective to highlight physical phenomena in axisymmetric flows. Received 15 June 1996 / Accepted 20 December 1996     

Flow effects resulting from relative motion between shocks and supersonic bodies

The effect relative motion between a shock and supersonic flow has on the Mach number of flow behind a planar shock is considered. It is shown that for multiple moving reference frames, such as that encountered in a shock-wave/moving-body interaction the choice of reference frame can result in a Mach number that can either increase or decrease across the shock. This depends on the relative velocities of the reference frames and under certain conditions can remain unchanged for a given shock of finite strength. Euler simulations run at the various computationally predicted transitions have numerically confirmed the idealised analysis presented here.Received: 14 October 2002, Revised: 21 February 2003, Accepted: 29 July 2003, Published online: 12 November 2003     

Focusing shock waves generated by an accelerating projectile

Unsteady flow fields past a projectile either in parabolic motion or in accelerated motion are investigated numerically, with special attention to shock wave focusing phenomena induced by the motions. The two-dimensional Euler equations are solved by a moving-cell, MUSCL TVD finite-volume method with Steger-Warming flux-vector splitting. The pattern of shock wave focusing induced by the projectile is found to be similar to that of shock waves reflected from a concave wall observed in a laboratory experiment using a shock tube. Effects of projectile shapes and trajectories on focusing are also examined.     

高速弹丸诱导斜爆轰激波结构实验研究

斜爆轰推进系统在高超声速推进领域具有广阔的应用前景,其释热迅速、比冲高、燃烧室结构简单的优点吸引研究人员的持续关注.然而,斜爆轰的地面试验同时涉及到高速试验环境模拟、燃料与氧化剂混合、高温燃烧流场结构测量等技术难点,当前国内外系统的试验研究仍然十分有限,难以支撑斜爆轰发动机的研制.为了研究自持传播的斜爆轰激波结构与波面流动特性,基于爆轰驱动二级轻气炮开展了高速弹丸诱导斜爆轰实验研究,使用直径30 mm球头圆柱形弹丸发射进入充满氢/氧可燃混合气体的实验舱中以起爆斜爆轰波,并采用两种阴影技术对实验流动结构进行测量.实验中在不同速度、不同充气压力下观察到三种弹丸诱导激波结构,即激波诱导燃烧、弹丸起爆爆轰波和相对弹丸驻定的斜爆轰波,实验舱充气压力下降则会造成爆轰横波尺度增加与波面流动失稳.实验中,斜爆轰激波角与理论分析结果吻合较好,弹丸气动不稳定带来较大的弹丸攻角会对激波角测量带来一定偏差.通过对斜爆轰波波面法向传播速度的测量发现,随着远离弹丸,斜爆轰传播速度由弹丸飞行速度衰减至接近实验气体CJ速度,弹丸速度的降低会加速斜爆轰波传播速度的衰减.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Comparisons of TVD schemes for turbulent transonic projectile aerodynamics computations with a two-equation model of turbulence

The development of a computer program to solve the axisymmetric full Navier--Stokes equations with k-ε two-equation model of turbulence using various total variation diminishing (TVD) schemes is the primary interest of this study. The computations are performed for the turbulent, transonic, viscous flow over a projectile with/without supporting sting at zero angle of attack. The predicted results, as well as the convergence characteristics, by various TVD schemes are compared with each other. The results show that the TVD schemes of higher-order accuracy do have influence on the regions of high gradients such as shock, base corner and base flow. However, the schemes of third-order accuracy do not necessarily improve the agreement with measured data (which is not available on the base) than that of second-order accuracy, but surely generate apparent different result of base flow. The supporting sting on the projectile base will complicate the base flow and the existence of the sting will slightly shift the shock location and slightly change the flow field after the shock. More iteration steps are needed to get the converged results in the computation for the projectile with sting.     

基于ALE方程的动网格膛口流场数值研究

基于ALE(Arbitrary Lagrangian-Eulerian Equation)方程的有限体积法,采用高精度Roe方法及结构化动网格,利用嵌入网格技术及动边界条件,对弹丸由膛内高压气体推动射出到完全飞高初始流场的整个过程进行了数值模拟.根据数值结果绘制了膛口流场密度和压力分布的时序图,形象地再现了膛口流场中初始激波、弓形激波及膛口冲击波,以及接触闻断、漩涡和剪切层等的动力学发展过程.结果基本反映了膛口流场的典型变化特征,为进一步研究真实膛口流场(如带化学反应、湍流等)奠定了基础.     

Shock-wave-initiated lifting of particles from a cavity

The dynamics of particles of the disperse phase in a turbulent gas flow in planar shock waves sliding along a solid surface with a trapezoid cavity is examined numerically. Lifting of particles from the cavity walls is calculated in the approximation of a rarefied gas suspension. It is shown that the intensity of the transient shock wave and the initial positions of particles have a significant effect on the particle-lifting properties. The height of particle lifting is found to nonmonotonically depend on the initial streamwise coordinate and shock-wave Mach number. It is shown that zones of aggregation and subtraction of particles may be formed at the cavity bottom. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 24–34, January–February, 2007.     

Dynamics of oblique detonations in ram accelerators

Time-accurate numerical simulations are used to study the dynamic development of oblique detonations on accelerating projectiles in ram accelerators. These simulations show that the oblique detonation can be stabilized on the projectile. The high pressure generated behind the detonation can result in accelerations up to 10⁶G and propel the projectile to velocities higher than 4.0 km/s. The detonation structure on the projectile is sensitive to the projectile geometry. A small change in the projectile shape is sufficient to alter the overall detonation structure and significantly affect the pressure distribution on the projectile. In order to maximize the thrust, an appropriate projectile shape has to be chosen to generate the detonation structure just behind the widest part of the projectile body. The projectile acceleration also has strong effects on the flow field and the detonation structure. During the acceleration, the location of the oblique detonation moves upstream from one reflected shock to another. However, one the detonation is stabilized behind the upstream shock, it remains at the new location until the transition to the next upstream shock occurs. In the simulations, the Non-Inertial-Source (NIS) technique was used to accurately represent of the projectile acceleration. Also, the Virtual-Cell-Embedding (VCE) method was employed to efficiently treat the complex projectile geometry on cartesian grids.     

Numerical investigations on dynamic process of muzzle flow

The integrative process of a quiescent projectile accelerated by high-pressure gas to shoot out at a supersonic speed and beyond the range of a precursor flow field was simulated numerically. The calculation was based on ALE equations and a second-order precision Roe method that adopted chimera grids and a dynamic mesh. From the predicted results, the coupling and interaction among the precursor flow field, propellant gas flow field and high-speed projectile were discussed in detail. The shock-vortex interaction, shockwave reflection, shock-projectile interaction with shock diffraction, and shock focus were clearly demonstrated to explain the effect on the acceleration of the projectile.     

Submerged shocks in conical gas flows in the presence of a mach shock-wave configuration

The results of a numerical study of a new type of singularities in the Mach shock-wave structure realized in supersonic nonsymmetric conical flows over V-wings with a bow shock attached to the leading edges are presented. Within the framework of the ideal gas model we study the changes in the shock system on transition, with increase in the sweep angle, from the region of nonsymmetric Mach interaction of the shocks attached to the leading edges of the wing to the region of special flow patterns, where on the windward cantilever surface a rarefaction flow is realized rather than a flow with an internal shock. It is shown, in particular, that in the region with special wing flow patterns a Mach system of shocks with a submerged shock proceeding from the branch point above the windward cantilever may exist.     

Numerical simulation of flow during compression of cylindrical samples by a glancing detonation wave

The parameters of shock waves created in cylindrical samples of various materials during detonation of explosive charges surrounding them have been determined experimentally [1–3]. It was established that in a number of materials the reflection of a conical shock wave from the symmetry axis of a sample leads to the formation of a Mach triple shock-wave configuration which gives rise to a complex flow pattern in the region beyond the shock waves. Analytic study of irregular reflection is a complex problem. Solutions obtained under various assumptions about the nature of the flow are presented in papers reviewed in [4]. In the present paper, axisymmetric flow of detonation products (DP) and sample material in the region adjacent to the detonation front is determined from the solution of a two-dimensional, time-dependent problem in gasdynamics by the finite-difference method [5].     

一种弹体入水冲击波阴影成像可视化系统及其试验研究

扩大成像视野对于开展充水容器中弹体入水冲击波传播及弥散方面的可视化研究具有重要的实际意义。阴影成像技术适用于大视野实验,且对流场冲击波和扰动的可视化研究具有简单性和通用性,其中直接阴影成像最为简单,但可靠点光源的缺乏是阻碍其发展应用的瓶颈。因此基于国产短弧氙灯管,自制了短弧氙灯点光源,根据阴影成像原理,设计出一种弹体入水冲击波阴影成像可视化系统,详细介绍了其组成和运行原理。利用该系统对高速弹体入水进行了试验研究,获得了弹体入水冲击波的阴影成像和冲击波信号的压力时程曲线,通过阴影成像和冲击波信号相结合分析了弹体入水冲击波的传播特性,并进行了理论验证。结果表明:该弹体入水冲击波阴影成像可视化系统具有可靠性和设计的合理性。弹体高速入水后,初始冲击波的强度最大,随着冲击波的传播,冲击波强度逐渐降低,水中冲击波的传播速度不断降低,球形冲击波的半径逐渐增大。     

Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.     

Transonic shock oscillations on NACA0012 aerofoil

The mechanism of the origin of shock oscillations on NACA0012 aerofoils is investigated using a moving grid thin layer Navier Stokes code. The method used to understand the mechanism is to initiate the shock oscillations on an aerofoil by moving the aerofoil from a regime of steady transonic flow into a regime of periodic flow by a change in airflow incidence. The results indicate that the shock induced bubble plays a leading role in the origin of shock oscillations and the trailing edge has an affect on its amplitude. Received 1 April 1997 / Accepted 1 December 1997     

The effect of an unsteady drag force on the structure of a non-equilibrium region behind a shock wave in a gas-particle mixture

For numerical analysis of shock wave propagation in gas-particle mixtures, drag coefficients of a sphere in steady flows are generally used. However, it is shown both experimentally and numerically that a shock loaded solid sphere experiences unsteady drag forces. The paper describes a model of unsteady drag force and its effect on the structure of the non-equilibrium region behind a shock front traveling in a dusty gas. The results are compared with those obtained by using a steady drag coefficient and are discussed. It is demonstrated that the large drag force at the early stage of the interaction between shock-wave induced flow and a solid particle affects the flow structure that is obtained with a steady drag force.      

Performance Improvement of a Supercritical Airfoil by a Multi-point Optimized Shock Control Channel

A shock control channel (SCC) is a flow control method introduced here to control the shock wave/boundarylayer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. An SCC transfers an appropriate amount of mass and momentum from downstream of the shock wave location to its upstream to decrease the pressure gradient across the shock wave and as a result the shock-wave strength is reduced. Here, a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of the SCC. This flow control method is implemented on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of the SCC. The solver is validated against experimental works studying effect of cavities in transonic airfoils. It is shown that the application of an SCC improves the average aerodynamic efficiency in a range of off-design conditions by 13.2% in comparison with the original airfoil. The SCC is shown to be an effective tool also for higher angle of attack at transonic flows. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.