Interaction of a shock wave with a particle cloud of finite size

We present the results of the numerical modelling of the interaction of a shock wave with a cloud of finite size particles. The computations were carried out within the framework of continuum/discrete model with the use of the techniques of digital diagnostics and pattern recognition. The shock wave and vortex formation behind the cloud of particles as well as the formation of a dense layer in the cloud have been revealed. For this reason, the use of a cloud of particles for relaxing the shock wave may prove to be inefficient.     

Attenuation of a shock wave passing through a cloud of water droplets

The mitigation of a planar shock wave caused by a cloud of calibrated water droplets was studied both experimentally and numerically. Experiments were carried out, with different shock wave Mach numbers ranging from 1.1 to 1.8, in a vertical shock tube coupled with a droplet generator which produced a well-characterized cloud of droplets of 120, 250 and 500 μm in diameter. By exploiting such an experimental set-up, we successfully measured the attenuation of a normal shock wave when passing through the water droplet cloud. This series of experiments allowed to identify the main parameters of this investigation and a clear dependence between the attenuation of the shock wave and terms governing the regimes of droplet breakup has been found. On the other hand, to support this experimental approach, 1D unsteady calculations were performed in similar configurations. Although the mathematical model based on an Eulerian/Eulerian approach was actually incomplete, the first comparisons between the experiments and the simulations were rather interesting and pointed out the need to improve the physical model, by taking into account the fragmentation and the vaporization of the droplets submitted to the shock wave as well as the size distribution of the water spray.     

Criterion of formation of a shock wave reflected from a cloud of particles

The problem of the formation of a “collective” shock wave reflected from a cloud of particles, which was previously observed in experiment, is considered. A criterion of formation of a reflected shock wave is obtained based on the numerical and analytical solutions of the problem. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 44–51, May–June, 1998.     

Interaction of a shock wave with a cloud of particles of finite dimensions

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 26–37, March–April, 1994.     

铝颗粒激波点火机制初探

通过对铝颗粒在激波后的高温热气流中由于温度升高产生的热应力进行分析计算 ,对铝颗粒的激波点火机制进行初步探讨。计算结果表明在激波后的气流中 ,铝颗粒的温度只要升高 70C左右 ,铝颗粒的氧化层就会产生裂纹。当铝颗粒的铝完全熔化后 ,如果这时气流对颗粒的作用使得已经产生裂纹的氧化层进一步破裂并失去对铝的保护 ,铝颗粒将被点火 ;但如果此时气流对铝颗粒的作用未能使氧化层失去保护作用 ,铝颗粒的温度需达到或接近三氧化二铝的熔点时才能被点火。     

A multiphase shock tube for shock wave interactions with dense particle fields

Currently there is a substantial lack of data for interactions of shock waves with particle fields having volume fractions residing between the dilute and granular regimes. To close this gap, a novel multiphase shock tube has been constructed to drive a planar shock wave into a dense gas–solid field of particles. A nearly spatially isotropic field of particles is generated in the test section by a gravity-fed method that results in a spanwise curtain of spherical 100-micron particles having a volume fraction of about 20%. Interactions with incident shock Mach numbers of 1.66, 1.92, and 2.02 are reported. High-speed schlieren imaging simultaneous with high-frequency wall pressure measurements are used to reveal the complex wave structure associated with the interaction. Following incident shock impingement, transmitted and reflected shocks are observed, which lead to differences in particle drag across the streamwise dimension of the curtain. Shortly thereafter, the particle field begins to propagate downstream and spread. For all three Mach numbers tested, the energy and momentum fluxes in the induced flow far downstream are reduced about 30–40% by the presence of the particle field.     

Lifting of dust particles behind a reflected shock wave sliding above a particle layer

The paper presents results of mathematical simulation of particle lifting behind a shock wave reflected from the face wall and sliding above the particle layer. It is shown that particle lifting occurs in a vortex initiated in the gas when the shock wave is reflected from the wall.     

On investigation of particle dispersion by a POD approach

The aim of this communication is to show the ability of POD to compute the instantaneous flow velocity when applying the Lagrangian technique to predict particle dispersion. The instantaneous flow velocity at the particle's location is obtained by solving a low-order dynamical model, deduced by a Galerkin projection of the Navier-Stokes equations onto each POD eigenfunction and it is coupled with the particle's equation of motion. This technique is applied to particle dispersion in a three-dimensional lid driven cavity. It yields a substantial decrease in computing time in comparison with LES computation and it enables treating different cases of particle dispersion Published in Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 133–142, January 2008.     

Shape of a shock wave diffracted by a rounded corner

The diffraction of shock waves by rounded corners has been studied experimentally. Some features introduced by the rounding of the corner in the profile of the diffracted shock wave are found. The velocity of the wall part of the diffracted shock wave in the flat section after the rounding is determined. The unsteady motion of a shock wave along a cylindrical surface is considered.     

Analysis of shock wave reflection from fixed and moving boundaries using a stabilized particle method

In the present paper, the efficiency of an enhanced formulation of the stabilized corrective smoothed particle method （CSPM） for simulation of shock wave propagation and reflection from fixed and moving solid boundaries in compressible fluids is investigated. The Lagrangian nature and its accuracy for imposing the boundary conditions are the two main reasons for adoption of CSPM. The governing equations are further modified for imposition of moving solid boundary conditions. In addition to the traditional artificial viscosity, which can remove numerically induced abnormal jumps in the field values, a velocity field smoothing technique is introduced as an efficient method for stabilizing the solution. The method has been implemented for one- and two-dimensional shock wave propagation and reflection from fixed and moving boundaries and the results have been compared with other available solutions. The method has also been adopted for simulation of shock wave propagation and reflection from infinite and finite solid boundaries.     

Unsteady drag on a sphere by shock wave loading

The dynamic drag coefficient of a sphere by shock wave loading is investigated numerically and experimentally. The diameter of the sphere is varied from 8 m to 80 mm in numerical simulation. The axisymmetric Navier-Stokes equations are solved on a fine grid, and the grid convergence of the drag coefficient is achieved. The numerical result is validated by comparing the experimental data of a 80 mm sphere, measured by the accelerometer in a vertical shock tube. It is found that the sphere experiences in the early interaction one order higher drag than in the steady state. A transient negative drag, mainly resulting from the focusing of shock wave on the rear side of the sphere, is observed only for high Reynolds number flows, and the drag becomes positive because of increased skin friction for low Reynolds number flows.Received: 10 March 2004, Accepted: 24 May 2004, Published online: 20 August 2004[/PUBLISHED]M. Sun: Send offprints requests to     

激波与可运动颗粒群相互作用反射与透射机理实验研究

对水平圆柱形激波管内可压缩性气体与颗粒群的相互作用进行了实验研究与理论分析。利用由压力传感器、信号放大器、示波器和计算机组成的压力测量系统对激波与颗粒群作用时的动态压力进行了测量。发现激波管内发生的是一个复杂的过程,包括激波与颗粒群作用时伴随了激波和膨胀波的反射与透射现象、激波和膨胀波与接触面的干涉、以及激波从激波管端壁的反射等现象。当颗粒装载比α=1时,透射激波被直径为6mm的颗粒群衍射并且有膨胀波紧随其后,因此由透射激波引起的第一个压力峰急剧下降。颗粒装载比和颗粒直径影响透射激波的衍射和衰减。     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

Vorticity produced by shock wave diffraction

Numerical simulations with a monotonicity preserving flow solver have been performed to study shock diffraction phenomena and shock wave generated vorticity. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme, which has been shown to have an excellent predictive capability for various compressible flows with both strong and weak shocks. An adaptive unstructured methodology based on adapting to high density and entropy gradients was used in conjunction with a conservative shock-capturing scheme to adequately resolve strong and weak flowfield gradients. The chief interest was the formation of vorticity arising from shock wave propagation over a sharp corner and the high accuracy and resolution of the interacting compressible wave features. Numerical simulations were compared with previous experimental results and exhibited remarkably good agreement in terms of compressible wave propagation, as well as vorticity development and transport. The computations also allowed insight into the fundamental fluid dynamics, specifically shock diffraction, vortex convection and shock-vortex interactions.     

Instability theory of shock wave in a shock tube

The instability theory of shock wave in a shock tube including the effects of tube wall and contact surface is studied. The experimental data of unstable shock wave coincide with one of instability criteria derived in the present paper.