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.     

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.     

Parameter formation behind the reflected wave in a shock tube with a nozzle

The reflection of a shock wave from the inlet of a nozzle of very simple geometry is analyzed on the basis of calculations carried out in the two-dimensional formulation. The nozzle throat is a sharp-edged slit in the end face of the tube leading to an expanding duct with straight generators. In this formulation the results of the investigation are quite general, since they depend on a minimum number of the determining parameters varied in the calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–159, July–August, 1987.The authors wish to thank G. N. Nikolaev and I. M. Naboko for useful discussion of their results.     

Shock wave interaction with a cloud of particles

The present paper is devoted to experimental and theoretical investigation of the shock wave (SW) propagation in a mixture of gas and solid particles in the presence of explicit boundaries of the two-phase region (cloud of particles). The effect of the qualitative change in the supersonic flow behind the SW in a cloud of particles within the range of the volume concentration of the disperse phase 0.1-3% is experimentally shown and theoretically grounded. Received 15 April 1996 / Accepted 3 June 1996     

Formation of a jet and vortices behind a shock wave reflected from a concave body

A jet and vortices have been observed when a plane shock wave reflects from a concave body in a shock tube. If the cavity is deep enough then two reflected shocks appear near its edges. Air, carbon tetrafluoride (CF) and dichlorodifluoromethane (CClF) were chosen as test gases. The flow was visualized with the aid of a conventional shadow technique. Pressure measurements at the body surface were also obtained. Numerical studies have been conducted using a two-dimensional inviscid model. There is a good qualitative agreement between the experimental and numerical results. Received 8 February 1996 / Accepted 30 June 1997     

Dense particle cloud dispersion by a shock wave

A dense particle flow is generated by the interaction of a shock wave with an initially stationary packed granular bed. High-speed particle dispersion research is motivated by the energy release enhancement of explosives containing solid particles. The initial packed granular bed is produced by compressing loose powder into a wafer with a particle volume fraction of $\phi _\mathrm{p} = 0.48$ . The wafer is positioned inside the shock tube, uniformly filling the entire cross-section. This results in a clean experiment where no flow obstructing support structures are present. Through high-speed shadowgraph imaging and pressure measurements along the length of the channel, detailed information about the particle shock interaction was obtained. Due to the limited strength of the incident shock wave, no transmitted shock wave is produced. The initial solid-like response of the particle wafer acceleration forms a series of compression waves that eventually coalesce to form a shock wave. Breakup is initiated along the periphery of the wafer as the result of shear that forms due to the fixed boundary condition. Particle breakup is initiated by local failure sites that result in the formation of particle jets that extend ahead of the accelerating, largely intact, wafer core. In a circular tube, the failure sites are uniformly distributed along the wafer circumference. In a square channel, the failure sites, and the subsequent particle jets, initially form at the corners due to the enhanced shear. The wafer breakup subsequently spreads to the edges forming a highly non-uniform particle cloud.     

The interaction of a shock wave with the boundary layer in a reflected shock tunnel

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.     

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     

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.     

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.     

Effect of surface gas condensation on the velocity of a reflected shock wave

The time-dependent one-dimensional problem of the normal reflection of a shock wave propagating at constant velocity in a gas (vapor) at rest from the plane surface of its condensed phase under steady-state condensation-evaporation conditions on the interphase plane is considered within the framework of the kinetic equation for a monatomic gas with a model collision operator (S-model). The solution is obtained using a conservative second-order finite-difference method. Attention is concentrated on the steady-state regime of the condensation process. The effect of the condensation (evaporation) coefficient on the velocity of the reflected shock wave is studied.     

Temperature measurement of reflected shock wave by using chemical indicator

This report describes a new method for measuring the temperature of the gas behind the reflected shock wave in shock tube, corresponding to the reservoir temperature of a shock tunnel, based on the chemical reaction of small amount of CF₄ premixed in the test gas. The final product C₂F₄ is used as the temperature indicator, which is sampled and detected by a gas chromatography in the experiment. The detected concentration of C₂F₄ is correlated to the temperature of the reflected shock wave with the initial pressureP ₁ and test time τ as parameters in the temperature range 3 300 K<T<5 600 K, pressure range 5 kPa<P ₁<12 kPa and τ≅0.4 ms. The project supported by the China Aerodynamics Project for Basic Researches (J13.5.2 ZK04)     

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.     

Wake formation when shock wave is shed from the edge of a plate

The formation of a laminar wake in the flow behind a shock wave when the latter is shed from the trailing edge of a semi-infinite plate is investigated in this paper. It is shown that the flow on the plate and in the wake turns out to be self-similar, dependent on two dimensionless combinations of variables, and the flow on the plate, including the trailing edge, remains steady in a coordinate system coupled to the shock wave (the fact of the flow self-similarity in the wake was first noted in [1]). An analytic solution of the problem of the wake in the neighborhood of the trailing edge is obtained, from which it follows that, in contrast to [2], there is no line of singularities in the nonstationary boundary-layer equations in the flow domain. This fact is also verified by the analysis of the flow in the neighborhood of a line of tagged particles leaving the trailing edge simultaneously with the shock wave. Hence the problem under consideration is solved by the traditional numerical methods using conditions in the initial section (which is taken to be the section in the neighborhood of the trailing edge), on the wake axis, and at an infinite distance away. Approximate formulas are obtained for the longitudinal velocity profiles in the whole range of shock-wave intensities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 59–66, July–August, 1978.