Shock wave standoff distance for a sphere slightly above Mach one

This paper describes a numerical simulation of bow shock formation ahead of a sphere at steady supersonic flow in the Mach number range of 1.025–1.20. Turbulent viscous flow results are presented using the Spalart–Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for a spherical projectile at slightly supersonic free flight speeds. Results are compared to experimental data, including double exposure holographic interferograms obtained from a 40 mm polycarbonate sphere launched by a light gas gun. The shock standoff distance was determined from the interferograms. The present numerical simulations were found to agree with previously published data, and reached down to M = 1.025—a range where almost no previously published data exists. The computed flow structure and shock wave locations agree well with recently obtained free-flight interferograms.     

Structure of the heating layer ahead of the front of a strong intensely emitting shock wave

The problem of the structure and brightness of strong shock waves arises in the investigation of such phenomena as the motion of large meteoroids in the atmosphere, optical and electrical discharges, the development of strong explosions, and other similar processes and in the creation of powerful radiation sources based on them. This problem also has a general physics interest. As the propagation velocity of a strong shock wave increases the gas temperature behind its front and the role of emission grow. Part of the radiation emitted by the gas heated and compressed in a shock wave is absorbed ahead of the front, forming the so-called heating layer. The quasisteady structure of a strong intensely emitting shock wave was studied in [1, 2]. In this case a diffusional approximation and the assumption of a gray gas were used to describe the radiation transfer. They introduced the concept of a wave of critical amplitude, when the maximum temperature T_- in the heating layer reaches the temperature T_a determined on the basis of the conservation laws, i.e., from the usual shock adiabat; it is shown that behind a compression shock moving through an already heated gas there is a temperature peak in which the maximum temperature T₊ exceeds T_a. The problem of the quasisteady structure of an emitting shock wave in air of normal density was solved numerically in [3]. The angular distribution of the radiation was approximately taken into account — it was assigned by a simple cosinusoidal law. The spectral effects were taken into account in a multigroup approximation. They introduced 38 spectral intervals, which is insufficient to describe a radiation spectrum with allowance for the numerous lines and absorption bands.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1978.     

Visualization of burning flow around a ram accelerator projectile by coaxial simultaneous shadow/direct photography

Experimental investigations with flow visualization of a ram accelerator are reported. The ram accelerator at Hiroshima University uses a tube with a rectangular cross section and a two-dimensional projectile. Observation windows installed on the flat wall of the rectangular tube enable visualization of the flow field around the projectile. In addition to the instantaneous shadow photography method conventionally used for visualization, a direct photography method has been introduced. This direct photography can detect the precise position and brightness of combustion that cannot be observed by shadowgraph. The experiments were conducted at various projectile velocities in the thermally choked mode. The propellant mixture is stoichiometric methane-oxygen diluted by carbon dioxide. It is observed that a tiny flamelet, assumed to be the remains of the starting process, adheres to the projectile forebody, however, visible light emission could not be detected there by direct photography. The brightest emission from combustion is observed around the rear of the projectile, and strong emission is found in the boundary layer on the surface of the projectile afterbody and at the center of the tube behind the projectile. It is also found that the gas mixture is burned over a shorter distance when the projectile moves more slowly.     

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     

The numerical and experimental simulation of hypervelocity flow around the HYFLEX vehicle forebody

Numerical and experimental techniques are used to model the flow and pressure distribution around the forebody of the HYFLEX hypersonic flight vehicle. We compare numerical simulation results with modified Newtonian theory and flight data to determine the accuracy of the computational fluid dynamics (CFD) technique used. The numerical simulations closely match the trends in flight data, and show that real gas effects have a small but significant influence on the nose pressure distribution. We also present pressure results from a scale-model tested in a shock tunnel, and compare them with simulation results. For the shock tunnel experiment, the model was placed such that part of the upper surface was in a region of the test flow where nonuniformities were significant, and it was shown that the numerical simulation could adequately capture these experimental flow features. The binary scaling parameter (describing the similarity in species dissociation between flight and model) was used to design the scale-model tests in the shock tunnel, and its effectiveness is discussed. We find that matching the flight Mach number in the shock tunnel experiment is not critical for reproducing flight pressure data, so long as flight velocity is matched, and binary scaling is maintained. Received 11 June 1998 / Accepted 1 September 1998     

Thermal de-cohesion model for time of craze failure in cohesive zone

The cohesive parameter corresponding to craze failure time is predicted for thermoplastics material. A craze failure separation criterion is proposed for a cohesive zone subjected to a melt layer formed and thickened by adiabatic deformation heat from a craze drawing. The numerical simulation of cohesive zone separation is based on non-linear thermal conduction and convection in the craze region and bulk region around the active layer, associated with a mechanical craze fibrils drawing in an uniaxial direction. The craze failure time is predicted with the assumption of the constant craze thickening rate and cohesive stress for a pipe-grade polyethylene. The numerically computed model reveals the inverse power law decay of the craze failure time, t_f, with increasing in craze thickening rate, v_c, (almost, t_f∝V_c⁻¹) for the thermoplastics. The full notch impact test experimental results are consistent with the analysis prediction. It is concluded that the craze failure time can be theoretically predicted using the numerical modeling.     

高速双锥绕流中热化学与输运模型影响研究

激波与边界层之间相互作用是高超声速飞行中的常见现象,对飞行器气动性能与飞行安全至关重要.对于高焓来流,流场中通常存在复杂的物理化学现象,此时准确模拟流场中激波边界层相互作用的难度大,相关物理化学建模仍有待进一步考察和研究.本文针对最近文献中纯净空气高超声速双锥绕流实验开展数值研究,分别研究了不同热化学模型与输运模型对壁面压力与热流的影响.热力学模型包括完全气体、热力学平衡和非平衡模型,化学模型包括冻结和非平衡化学模型,输运模型包括经典的Wilke/Blottner/Eucken模型与更加复杂的Gupta/SCEBD模型,以及考虑壁面催化/非催化影响的模型.计算了6个不同算例,涵盖了低焓至高焓来流等不同工况.壁面压力与热流的数值计算结果与实验结果符合较好;对于低焓来流,计算结果主要受到分子内能分布的影响,输运模型对计算结果的影响不大;对于高焓来流,一方面计算结果受到化学反应与壁面催化的影响较大,另一方面不同输运模型对计算结果的影响也更加明显.      

球形颗粒遮弹层对高速侵彻弹体的作用机理

在钻地弹威慑之下,重要目标工事外覆盖遮弹层是常见加固和防护手段。硬质球形颗粒（以下简称颗粒）是常见的遮弹层组成结构。本文中将研究高速侵彻弹体与颗粒作用机理,分析遮弹效率的控制因素。首先,基于动态空腔膨胀理论,计及靶的自由面效应和颗粒强度差异,建立了靶对弹体侵彻阻力的表征模型。然后,采用弹靶分离计算方法,模拟并分析了斜侵彻含球形颗粒有限大高强混凝土时弹体的运动与变形,研究颗粒的强度、位置及尺寸对来袭弹侵彻行为的影响规律。结果表明,颗粒的遮弹作用主要取决于与其作用时弹体的姿态,其随颗粒位置变化无明显规律;颗粒强度越高,遮弹效果越好;颗粒半径从1倍到10倍弹径变化时,颗粒对弹体的作用机理从弹道偏转为主转变为弹道偏转与侵彻阻力增加两者耦合。因此,为达到良好的遮弹效果,单层球形颗粒密排遮弹层的颗粒半径建议在5倍弹体直径之上;若采用较小颗粒制作遮弹层,建议采用多层错排方式,且遮弹层厚度须在10倍弹径之上。     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

Jet interaction at supersonic cross flow conditions

The thrust produced by lateral jet systems has been successfully used for several years to control the flight trajectory, i.e., the maneuverability of spacecraft in the high atmosphere and in orbit. Recently this technology has also been applied to projectiles and rockets flying in the low atmosphere from sea level up to more than 10 km. At ISL, investigations have been performed with a 90 mm caliber full-scale projectile in order to study a special side jet controlling system at flight speeds of about 1500 m/s, i.e., Mach number at altitudes of 1.5 and 7.5 km. The High Energy ISL Shock Tunnel facility is used as a ground testing facility in which the flow around the projectile is studied at fully duplicated flight conditions. In the test facility the projectile is fixed inside the test chamber and the atmospheric air is set in motion flowing around the projectile test model. The air flow is generated in the ISL Shock Tunnel STB which is equipped for this purpose with a divergent square nozzle with an exit side length of 184 mm. A lateral gas jet is produced by combusting a solid propellant in a combustion chamber, placed inside the projectile. The powder gases are blown out laterally via a nozzle, creating a complex flow field by the interaction of the lateral jet with the external cross flow. Differential interferometry is used to visualize the behavior of the external flow field distorted by the lateral jet outflow. Numerical simulations have been performed based on steady state computations using the conservation equations of mass, momentum and energy. This was done to theoretically predict the development of the flow field around the projectile under the influence of the side jet. As final result the lateral force acting on the projectile is given as force and moment amplification factors, K_F and K_M respectively.Received: 7 May 2002, Accepted: 12 March 2003, Published online: 16 May 2003An abridged version of this paper was presented at the 23rd Int. Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001     

Dust entrainment in a shock-induced,turbulent air flow

Dust from a layer on the floor of a shock tube is entrained by the air flow behind the unsteady shock wave. The development of the dust mass concentration profiles is measured by means of an optical extinction method. The concentration profiles which can be described by an exponential law approach a stationary limit consistent with the results of pneumatic transport theory. A theoretical model simulating the dust entrainment by a diffusion process is evaluated numerically and compared with the experimental results.     

Aerodynamic calibration of TCM2 facility and study of a bow shock layer by emission and laser spectroscopy

Flow properties in the TCM2 free piston shock tube/tunnel are determined by time-resolved pressure and heat flux measurements in numerous points of the shock tube and the nozzle, and in the free flow for two stagnation enthalpy conditions (3.5 and 11 MJ/kg). These measurements demonstrate the homogeneity of the flow during more than 1 ms. The cleanness of the useful test time is shown with time-resolved emission measurements at critical wavelengths. NO fluorescence profiles are established with local and planar laser-induced fluorescence in the shock layer around a cylindrical model. It allows to determine the shock stand-off distance for both enthalpy conditions. The problems of quenching and amplified spontaneous emission are considered. The importance of atomic oxygen and atomic nitrogen densities as well as temperature effects is also shown. Evaluation of the temperatures behind the shock front through spectroscopic data agrees with calculations. The proof of the presence of vibrationally excited NO ahead of the shock layer is given. Received 14 March 2000 / Accepted 18 June 2001     

The puzzle of whip cracking – uncovered by a correlation of whip-tip kinematics with shock wave emission

During whip cracking the whip-tip reaches a supersonic velocity for a period of about 1.2 ms, thereby emitting a head wave with a parabolic-shaped geometry. A detailed study of this mechanism which encompasses the motion analysis of the whip-tip as well as the determination of the local origin of the shock emission requires a sophisticated recording technique. A pre-trigger framing high-speed video camera system was used which was triggered by an acoustical sensor and synchronized with a pulsed copper-vapour laser. The phenomena were visualized by the direct shadowgraph method and recorded cinematographically as digital images at a frame rate of 9 kHz using a CCD-matrix with pixels. The resulting series of frames allowed, for the first time, (i) a reconstruction of the whip-tip trajectory, (ii) a determination of the tuft velocity and acceleration, (iii) a correlation of whip-tip kinematics with shock wave emission, and (iv) a motion analysis of the turning and unfolding mechanism of the tuft. The tuft at the whip-tip was accelerated within a distance of about 45 cm from a Mach number of to a maximum of , thereby reaching a maximum acceleration of 50,000 g. The shock is emitted at the moment when the cracker, arriving at the turning point of the lash, is rapidly turned around. After emission of the shock wav within a short distance of only 20 cm. Received 3 March 1997 / Accepted 21 July 1997     

杆式弹对厚壁壳体装药冲击起爆机制模拟分析

为研究高速杆式弹冲击厚壁壳体装药的起爆机制,运用冲击物理显式欧拉型动力学SPEED软件,开展了不同弹径和弹长的钨合金杆式弹与厚壁壳体Comp-B装药相互作用过程的数值模拟,采用升降法获得弹体起爆装药临界着速及装药起爆位置变化。研究结果表明:弹体起爆装药临界着速随弹径增大而显著降低,随弹长增大呈先降低后平缓变化的规律;弹体以临界着速起爆装药时,存在2种装药起爆机制,即弹体贯穿壳体后的宏观剪切起爆和未贯穿壳体的低速冲击起爆,且其机制随弹体着速在临界着速以上继续提高会发生转变,最终均会转变为高速冲击起爆机制;装药起爆位置均发生在炸药壳体交界面后一定距离处,相同机制下此距离随弹体着速提高而减小。     

Soil Behavior at the Interface with a Rigid Projectile During Penetration

The motion and state of soil at the interface with a penetrating rigid projectile is studied by numerical solution of the problem of a cylindrical projectile which expands and at the same time moves translationally along its axis in soil. The soil behavior is described using the model of a compressible elastoplastic medium with transition to a plastic state depending on the pressure in it. It is shown that a thin layer of soil at the interface with the projectile nose should be set in motion and move together with the projectile without sliding. An analysis is performed of the validity of using the dry friction law to determine the shear stresses on the projectile surface during penetration. The heat release in the soil layer at the interface due to internal friction and its possible effect on the penetration are estimated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 116–127, November–December, 2005.     

Disturbance evolution in the leading-edge region of a blunt flat plate in supersonic flow

The spatio-temporal dynamics of small disturbances in viscous supersonic flow over a blunt flat plate at freestream Mach number M_∞=2.5 is numerically simulated using a spectral approximation to the Navier–Stokes equations. The unsteady solutions are computed by imposing weak acoustic waves onto the steady base flow. In addition, the unsteady response of the flow to velocity perturbations introduced by local suction and blowing through a slot in the body surface is investigated. The results indicate distinct disturbance/shock-wave interactions in the subsonic region around the leading edge for both types of forcing. While the disturbance amplitudes on the wall retain a constant level for the acoustic perturbation, those generated by local suction and blowing experience a strong decay downstream of the slot. Furthermore, the results prove the importance of the shock in the distribution of perturbations, which have their origin in the leading-edge region. These disturbance waves may enter the boundary layer further downstream to excite instability modes.     

Research on the skirt tail explosively formed projectile stable shaping technology

The effect of the arc-cone liner configuration parameters on explosively formed projectile (EFP) flight stability is studied experimentally. The effect of the liner edge structure on the EFP formation is computed numerically. The results show that an EFP formed by a liner whose thickness is 0.046 times the charge caliber has improved flight stability and can perforate a steel armor 0.5 times the charge caliber thick in the case of large stand-off distances. A good tail skirt EFP can be formed by choosing appropriate parameters: the liner-to-charge diameter ratio in the interval 0.96–0.98, the liner edge thickness equal to 0.0020–0.0025 times the charge caliber, and the liner edge chamfer of 45–50°.     

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.     

Effect of Partial Closure of the Channel on the Pressure Pulse in a Shock Wave Emerging from a Duct

The temporal-spatial development of the flow pattern behind a shock wave emerging from open-ended and half-closed ducts at M₀=1.15 to 3.0 Mach number is investigated both experimentally and numerically and the action of the diffracted wave on a barrier placed at different distances from the duct exit is studied. Flow toeplerograms are obtained and the pressure on the barrier is measured. The distinctive features of the interaction between the shock wave and a barrier mounted perpendicular to the duct axis are established. It is found that partial closing of the duct results in a decrease in the barrier pressure in the case of a strong shock (M₀ > 2.2) and leads to a pressure decrease when a weak shock is diffracted (M₀=1.1 to 1.7). A dependence characterizing the dynamic action of the shock wave on the barrier and specifying the threshold value of a combination of the shock Mach number and the distance from the barrier determining whether the pressure pulse on the barrier increases or decreases, is obtained.     

A comprehensive PIV measurement campaign on a fully equipped helicopter model

The flow field around a helicopter is characterised by its inherent complexity including effects of fluid?Cstructure interference, shock?Cboundary layer interaction, and dynamic stall. Since the advancement of computational fluid dynamics and computing capabilities has led to an increasing demand for experimental validation data, a comprehensive wind tunnel test campaign of a fully equipped and motorised generic medium transport helicopter was conducted in the framework of the GOAHEAD project. Different model configurations (with or without main/tail rotor blades) and several flight conditions were investigated. In this paper, the results of the three-component velocity field measurements around the model are surveyed. The effect of the interaction between the main rotor wake and the fuselage for cruise/tail shake flight conditions was analysed based on the flow characteristics downstream from the rotor hub and the rear fuselage hatch. The results indicated a sensible increment of the intensity of the vortex shedding from the lower part of the fuselage and a strong interaction between the blade vortex filaments and the wakes shed by the rotor hub and by the engine exhaust areas. The pitch-up phenomenon was addressed, detecting the blade tip vortices impacting on the horizontal tail plane. For high-speed forward flight, the shock wave formation on the advancing blade was detected, measuring the location on the blade chord and the intensity. Furthermore, dynamic stall on the retreating main rotor blade in high-speed forward flight was observed at r/R?=?0.5 and 0.6. The analysis of the substructures forming the dynamic stall vortex revealed an unexpected spatial concentration suggesting a rotational stabilisation of large-scale structures on the blade.