Computation of wave interference and relaxation of particles after passing of a shock wave

Interaction of a shock wave with a system of motionless or relaxing particles is numerically simulated. Regimes of the gas flow around these particles are described, and the influence of the initial parameters of the examined phenomenon on the flow pattern is analyzed. The drag coefficient of particles is calculated as a function of the Mach number behind the shock wave at a fixed Reynolds number. The dynamics of heat exchange for particles of different sizes (10 μm–1 mm) is determined, and the laws of thermal relaxation after passing of a shock wave over the system of particles are found. The times of thermal and velocity relaxation of particles are estimated as functions of the Reynolds number, and the predicted relaxation time is compared with the corresponding empirical dependences.     

Dynamics of irregularly shaped bodies in a flow behind a shock waveLa dynamique des corps de forme irrégulière dans un écoulement derrière une onde de choc

For the first time, the multi-frame shadow visualization technique coupled with a laser stroboscopic source of light has been used to obtain data on the dynamics of irregularly shaped bodies in the flow behind shock wave. A procedure for determining body acceleration from body trajectory is proposed, which, together with the diagnostic technique used, represents a kind of contactless aerodynamic balance. Drag data for spheres and irregularly shaped bodies in the flow behind shock wave with Mach number of 0.5 to 1.5 and Reynolds number of 10⁵ are reported. To cite this article: V.M. Boiko, S.V. Poplavski, C. R. Mecanique 332 (2004).     

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the prac-ticability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disinte-grates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17%occurs with a triangular shape, while the max-imum increase in aerodynamic efficiency (lift-to-drag ratio) of around 10%happens with a rectangular shape at an angle of attack of 2.26?.     

Investigation of the acceleration of aluminum particles behind a shock wave using instantaneous Laser Doppler Velocimetry

The acceleration of aluminum particles with a 5μm diameter in the flow field behind an incident shock wave was investigated experimentally in a 10-m long and 70 mm inner diameter shock tube. By means of instantaneous Laser Doppler Velocimetry (LDV) the velocity of the particles was observed directly. The light scattered by the moving particles is Doppler shifted and sent to the laser Doppler velocimeter. The velocimeter essentially consists of a phase-stabilized Michelson interferometer used as a sensitive spectrometer. An electro-optical circuit ensures the phase stabilization that results in a voltage signal independent of the scattered light intensity and proportional to the mean velocity of the particles at the measurement point. Because of the very short response time (1μs) of the LDV system used here, the latter gives a continuous real-time signal of the particle acceleration. To avoid particle oxidation the particles were accelerated by a high-speed nitrogen gas flow. From the measured velocity the dimensionless drag coefficient was calculated. The drag coefficient is related to the fluid dynamic force exerted by the gas on the particles. The experimental data were compared to theoretical models from the literature. A significant deviation between the model and the experimental data was observed. This deviation is supposed to be induced by the shock wave, which hits the particles and breaks them into pieces of a smaller diameter. Further experiments will be carried out in the future to check the size distribution of the particles after the shock has gone past them.      

激波驱动的气固两相流的动态压力测量

利用水平圆柱形激波管对激波驱动的可压缩性气固两相流进行了试验研究.利用压电式压力传感器、电荷放大器、示波器及计算机组成的压力信号测试系统, 对激波与颗粒作用前后的气相参数进行测量及分析. 试验中测得了激波在管中的传播速度, 波后气流的压力, 反射激波、透射激波的压力和速度等. 分别考察颗粒、装载比、驱动气源以及入射激波马赫数等因素的差异对气相参数的影响.试验结果表明: 激波与颗粒群相互作用时, 会产生反射激波和透射激波,其强度与驱动气源、颗粒大小、颗粒装载比等参数有关;激波衰减率随着装载比、马赫数的增大而减小. 研究指出,在颗粒群被激波加速的初始阶段, 颗粒间的弹性碰撞起着重要的作用.      

Hypersonic flow past a plane magnetic dipole with parallel orientation of the magnetic moment and free-stream velocity vectors for moderate magnetic Reynolds numbers

The two-dimensional problem of hypersonic flow past a cylindrical body with a plane magnetic dipole in the presence of an external magnetic field is considered. The magnetic moment of the dipole is parallel to the free-stream velocity. The flow parameters correspond to a velocity of 7000 m/s at an altitude of approximately 65 km in the Earth’s atmosphere. The system of MHD equations (the Euler equations with volume MHD momentumand energy sources and the magnetic induction equation) was solved using the stabilization method. The calculations were carried out for two magnetic Reynolds numbers: (Re_m)₁ = 0.18 (corresponds to the parameters of the equilibrium ionized plasma in the shock layer) and (Re_m)₂ = 1.8 (the plasma conductivity increases by a factor of 10). The solutions obtained are analyzed, the effect of Re_m on the flow characteristics, namely, the shock wave stand-off from the body, the configuration of the vortex structures, and the aerodynamic and ponderomotive components of the body drag, is determined.     

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 m and on the order of 10¹² particles/m³, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.     

逆向喷流流场模态分析及减阻特性研究

逆向喷流减阻的基本原理是利用逆向高速喷流与飞行器绕流的相互作用，使飞行器周围的流场结构发生变化，致使飞行器的气动特性发生改变，从而改善飞行器的气动性能。利用数值模拟方法对轴对称球头、截锥的逆向喷流流场开展了研究，考虑了高温非平衡化学反应对流场的影响。模拟了球头和截锥在不同总压比时流场不同的模态：长穿透流模态（LPM）和短穿透流模态（SPM），得到了不同模态下钝体表面压力、气动力系数和不同模态之间转换的瞬态效应．简单分析了喷流在减阻方面的应用，给出了几个喷口参数与减阻效率之间的关系，提出了喷流减阻工程应用时应考虑的主要因素。     

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.      

Interaction of a shock with a sphere suspended in a vertical shock tube

Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M _s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.Received: 31 March 2003, Accepted: 7 July 2003, Published online: 2 September 2003     

The influence of acceleration and deceleration on shock wave movement on and around aerofoils in transonic flight

This paper examines the shock wave dynamics of a biconvex aerofoil in transonic flight during acceleration and retardation. The aerofoil has a cord length of 1 m and air at infinity is at 101.325 kPa and 300 K. Using Fluent as the CFD software, constant velocity (steady state) simulations were conducted at transonic Mach numbers. The aerofoil was then accelerated at 1041m/s² (106 g), starting at Mach 0.1, and decelerated at −1041m/s², starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were found in the transonic region between the steady and the unsteady aerodynamic forces. Analysis of the flow field in this region showed that acceleration-dependent variations in the position of the shock wave on the surfaces of the aerofoil were the main reason for this. As very high accelerations were used in order to emphasize differences, which do not have many practical applications, simulations using accelerations lower than 9 g were also conducted in order to confirm the results. The acceleration-dependent behaviour of other shock waves around the aerofoil, such as the bow shock in front of the aerofoil and the trailing wave were also examined. The trailing wave followed behind the aerofoil changing position with different accelerations at the same Mach number.      

Optimal airfoil shapes for low Reynolds number flows

Flow over NACA 0012 airfoil is studied at α = 4^° and 12^° for Re?500. It is seen that the flow is very sensitive to Re. A continuous adjoint based method is formulated and implemented for the design of airfoils at low Reynolds numbers. The airfoil shape is parametrized with a non‐uniform rational B‐splines (NURBS). Optimization studies are carried out using different objective functions namely: (1) minimize drag, (2) maximize lift, (3) maximize lift to drag ratio, (4) minimize drag and maximize lift and (5) minimize drag at constant lift. The effect of Reynolds number and definition of the objective function on the optimization process is investigated. Very interesting shapes are discovered at low Re. It is found that, for the range of Re studied, none of the objective functions considered show a clear preference with respect to the maximum lift that can be achieved. The five objective functions result in fairly diverse geometries. With the addition of an inverse constraint on the volume of the airfoil the range of optimal shapes, produced by different objective functions, is smaller. The non‐monotonic behavior of the objective functions with respect to the design variables is demonstrated. The effect of the number of design parameters on the optimal shapes is studied. As expected, richer design space leads to geometries with better aerodynamic properties. This study demonstrates the need to consider several objective functions to achieve an optimal design when an algorithm that seeks local optima is used. Copyright © 2008 John Wiley & Sons, Ltd.     

Supersonic low-concentration dusty-gas flow past a plane cylinder in the presence of an oblique shock wave interacting with the bow shock

The motion of an inertial dispersed admixture near a plane cylinder immersed in a steady-state hypersonic dusty flow in the presence of an oblique shock wave interacting with the bow shock is considered. It is assumed that the free-stream particle mass concentration is small and the particles do not affect the carrier flow. The III and IV shock wave interaction regimes are considered. The gas flow parameters in the shock layer are calculated from the numerical solution of the full Navier-Stokes equations for the perfect gas. A TVD second-order finite-difference scheme constructed on the basis of a finite volume method is used. For calculating the dispersed-phase parameters, including the concentration, the full Lagrangian method is used. On a wide range of variation of the particle inertia parameters, the patterns of the particle trajectories, velocity, concentration, and temperature in the shock layer are studied. The possibility of aerodynamic focusing of the particles behind the shock wave intersection point and the formation of narrow beams with a high particle concentration is revealed. These beams impinge on the cylinder surface and result in a sharp increase in the local heat fluxes. The maximal possible increase in the heat fluxes caused by the particles colliding with the cylinder surface is estimated for the flows with and without the incident oblique shock wave.     

Effect of Localization of Pulsed Energy Addition on the Wave Drag of an Airfoil in a Transonic Flow

The possibility of controlling the aerodynamic characteristics of airfoils with the help of local pulsed-periodic energy addition into the flow near the airfoil contour at transonic flight regimes is considered. By means of the numerical solution of two-dimensional unsteady equations of gas dynamics, changes in the flow structure and wave drag of a symmetric airfoil due to changes in localization and shape of energy-addition zones are examined. It is shown that the considered method of controlling airfoil characteristics in transonic flow regimes is rather promising. For a zero angle of attack, the greatest decrease in wave drag is obtained with energy addition at the trailing edge of the airfoil.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 60–67, September–October, 2005.     

探测器对超音速刚性盘-缝-带型降落伞系统的影响

研究了流体初始马赫数为 2.0 时, 探测器的存在与否对刚性盘-缝-带型降落伞系统气动减速性能以及流场流体结构特性的影响. 对于非定常可压缩流体的数值模拟, 流场采用了三层块结构自适应网格加密技术, 配合混合形式的TCD (tuned center difference)和WENO (weighted essentially non-oscillatory)计算格式以及基于拉伸涡亚格子模型的大涡模拟方法来处理超音速流中的激波以及大尺度湍流旋涡结构等. 结果表明: 无探测器时, 降落伞系统的流场结构稳定, 扰动较小; 有探测器存在时, 探测器后端的湍流尾迹和伞衣内部逆向运动溢出的流体与伞衣前端的弓形激波周期性的相互作用, 使得激波位置发生前移、激波倾角变小, 伞衣内部流场难以达到平衡稳定状态. 这加剧了降落伞系统的气动阻力振荡脉动变化, 降低了降落伞系统气动阻力系数, 同时也使得降落伞系统流场尾迹结构更加复杂.      

Supersonic drag of three-dimensional bodies with a star-shaped cross section and its calculation

The effect on the aerodynamic drag of the real properties of the gas in the shock layer around pyramidal star-shaped bodies (the viscosity, the displacement thickness of the boundary layer, its separation under the influence of the inner shocks) is considered. It is shown that the models for calculating the total drag of star-shaped bodies which do not take into account the displacement thickness of the boundary layer are applicable only at low supersonic free-stream velocities (M < 3). A model of the boundary layer displacement thickness is proposed and tested over a broad range of variation of the parameters that determine the geometry of the pyramidal bodies for high supersonic or hypersonic speeds. A comparison with the experimental data shows that the calculation procedure adequately reflects the results of experiments on the aerodynamic drag of star-shaped bodies in cases in which the inner shocks in the shock layer do not lead to boundary layer separation and can be used in optimization problems.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 57–69, January–February, 1993.     

Analytical Solution for Isothermal Flow in a Shock Tube Containing Rigid Granular Material

Analytical solution of shock wave propagation in pure gas in a shock tube is usually addressed in gas dynamics. However, such a solution for granular media is complex due to the inclusion of parameters relating to particles configuration within the medium, which affect the balance equations. In this article, an analytical solution for isothermal shock wave propagation in an isotropic homogenous rigid granular material is presented, and a closed-form solution is obtained for the case of weak shock waves. Fluid mass and momentum equations are first written in wave and (mathematical) non-conservation forms. Afterwards by redefining the sound speed of the gas flowing inside the pores, an analytical solution is obtained using the classical method of characteristics, followed by Taylor’s series expansion based on the assumption of weak flow which finally led to explicit functions for velocity, density and pressure. The solution enables plotting gas velocity, density and pressure variations in the porous medium, which is of high interest in the design of granular shock isolators.     

Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas

Similarity solutions are obtained for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential cylindrical shock wave propagating in a rotational axisymmetric dusty gas, which has variable azimuthal and axial fluid velocities. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to obey exponential laws. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. To obtain some essential features of the shock propagation, small solid particles are considered as a pseudo-fluid; it is assumed that the equilibrium flow conditions are maintained in the flow field, and that the viscous stresses and heat conduction in the mixture are negligible. Solutions are obtained for the cases when the flow between the shock and the piston is either isothermal or adiabatic, by taking into account the components of the vorticity vector. It is found that the assumption of zero temperature gradient results in a profound change in the density distribution as compared to that for the adiabatic case. The effects of the variation of the mass concentration of solid particles in the mixture \(K_p\) , and the ratio of the density of solid particles to the initial density of the gas \(G_a\) are investigated. A comparison between the solutions for the isothermal and adiabatic cases is also made.     

Reaching High Temperatures by Compressing a Vapor Bubble

The process of compression of a vapor bubble under the action of an instantaneously applied pressure is considered. The effect of initial parameters on compression dynamics is analyzed. Conditions of emergence of a shock wave inside the bubble are considered. It is shown that the temperature in the bubble is lower than 10⁴ K under uniform compression.