Shock Waves in Gas-Particle Mixtures

Shock waves in a dusty gas are analyzed numerically by taking into account a continuous distribution of particle sizes. A distribution function for the particle radii is introduced in order to describe the continuous particle sizes. The equations for the gas and the particles are solved by the Runge-Kutta-Gill method, where the integrations in these equations are calculated with Simpson's formula. It is made clear that the effects on the flow, or the flow structure, behind a shock front of the distribution function are very important. Also, the usual approximation for single sizes of particles will lead to poor results in many practical problems

Gas-particle Flows Over a Wavy Wall

This paper describes a theoretical investigation into the perturbation problem of gas-particle two-phase flows over a wavy wall. It is assumed that the gas is inviscid except for its interaction with the particles, and no phase change takes place. The flow region is split into two sub-regions, an inner region near the wavy wall, where particle-free regions appear, and an outer region above the inner region. The inner and the outer expansions are matched with each other in some overlapping domain. The inner problem is solved numerically, and the outer problem is solved analytically. Main attention is paid to the flow structure near the wavy wall, and also the drag of the wavy wall

Change of Oscillation Modes of Circular Underexpanded Jet by Impingement on a Small Plate

The frequency characteristics of the discrete tones generated by the impingement of a circular underexpanded jet on a small circular plate were studied experimentally. When the plate was moved along the jet axis at fixed pressure ratios, it was found that the frequencies could basically be divided into two groups. These groups belong to the categories of the impinging tones and the screech tones. Furthermore, it was observed that three types of frequency changes of the screech tones, (sawtooth, stepwise and intermittent ones), are realized periodically with the increasing nozzle-to-plate distance. Therefore, it is considered that the frequency change of the screech tone by the insertion of a small plate into the jet is associated with the self-sustained oscillation of the circular underexpanded free jet. The most interesting phenomenon discovered is the stepwise change of the frequencies of discrete tones. The pressure ratio range of the stepwise change of the frequencies overlaps that for the helical oscillation mode of the free jet and that for the radiation of the strong hole tone

Discrete tones generated by the impingement of a high-speed jet on a circular cylinder

Experimental measurements were made of the frequencies of discrete tones emanating from high subsonic and choked underexpanded jets of air issuing from a circular nozzle and impinging on a slender circular cylinder placed normal to the jet axis. In the experiments, a few types of discrete tones were observed. It is proved that the frequencies of the discrete tones can be calculated by using a feedback model proposed by Powell, and Ho and Nosseir. Schlieren photographs of the flow field along with the near-sound field were taken for various nozzle-to-cylinder distances and various pressure ratios. Close investigation of these schlieren photographs has shown that for the subsonic jet, one strong sound wave is emitted near the cylinder and two large ring vortices are produced near the nozzle exit during one cycle of the feedback loop. These two large ring vortices merge together in a later stage of the loop. For the choked underexpanded jet, one strong sound wave is emitted and one large ring vortex is produced during one cycle of the feedback loop. In this case, a merging of the successive large ring vortices has not occurred

Structure of Shock Waves in Bubbly Liquid

In this paper, steady and unsteady shock waves in a bubbly liquid are treated numerically. A new system of model equations describing the bubbly flow is applied and the detailed flow structure behind a shock front is investigated in detail. It is proved that the velocity difference between the liquid and the gas phases induced by a stationary shock wave is of order α1/2, wher α is the void fraction of the gas-phase. Radial oscillation of bubbles tends to produce a oscillatory profile of the translational velocity of the bubbles near the wave fronts. Numerical simulation shows that oscillatory behaviour of the mixture pressure is significantly suppressed by the translational motion of bubbles and that the whole shock structure is remarkably affected by the velocity difference between the phases especially in the case of weak shocks. It is confirmed that the stationary shock wave is realized as an asymptotic solution for a shock tube problem with uniform conditions in the low pressure and high pressure chambers

Bubbly Flows through a Convergent-Divergent Nozzle

Characteristics of bubbly flow with a small void fraction through a vertical, two-dimensional, converging-diverging nozzle are investigated experimentally and numerically. Emphasis is placed on the mechanism for large velocity slip near the nozzle throat, where the pressure gradient is very large. Bubble velocities are measured by taking double-exposure photographs with stroboscopic light sources having a flash duration of a few μ sec. The pressure distribution of the mixture along the nozzle axis is measured by semiconductor pressure transducers. The local liquid velocity is determined through continuity equations of gas and liquid in conjunction with the measured data of pressure distribution and experimental conditions at the nozzle inlet and exit. The power spectrum density of the pressure fluctuations is measured to investigate some instabilty of the bubbly flow, which is believed to be inherent to the velocity slip. It is proved that the numerical results using Wijngaarden's model equations agree well with the experiments. The characteristics of flow instability are explained according to the theoretical predictions of Morioka et al

Theoretical Analysis of Supersonic Gas-Particle Two-Phase Flow and Its Application to Relatively Complicated Flow Fields

This paper describes supersonic flows of a gas-particle two-phase mixture in considerably complicated situations. For the flow field of gas-particle mixtures such that the gas-phase and the particle-phase interact with each other, the model is constructed by incorporating the particle-trajectory method into the system of gas-phase equations in the two-fluid model. First, the one-phase and two-phase flows of round underexpanded jets exhausted from a sonic nozzle are investigated in detail. The one-phase results are compared with the experimental ones in order to confirm whether the present scheme is reliable or otherwise. For the two-phase results, the particles with the same velocity and temperature as those of the gas-phase are injected at the nozzle exit plane, and the effect of the presence of the particles on the flow field is examined by comparing these two-phase results with the one-phase ones. Second, the results of the numerical experiments in which underexpanded sonic round jets impinge on a flat plate normal to the jet axis are presented and analyzed for both the one-phase and two-phase cases. For the one-phase flow, periodic unstable oscillations have been found to give fairly good agreement with the experimental results. Third, supersonic gas-particle two-phase flows around a sphere are simulated in view of the numerical experiments. The instability in the particle motion near the stagnation region in the shock layer is discussed in detail. A few new findings are also described throughout the present paper

Theoretical Model of Two-Phase Flow in a Nozzle and Its Application to Numerical Experiments for Mist Flow

A numerical analysis of subsonic as well as supersonic nozzle flows of gas-particle mixtures is described. The theoretical model modified here is applied to the case where a gas-particle mixture is composed of air and water-particles in relation to the mist nozzle flow utilized for the secondary cooling zone of a continuously cast slab. For the subsonic nozzle flow, all of the flow properties are calculated on the basis of a given nozzle geometry with a parallel region. Next, for the supersonic nozzle, the so-called specified pressure method is applied to evaluate the behaviour of the gas-particle mixture in the flow field, as wel as to design the converging-diverging nozzle configuration according to the desired pressure profile. The results so obtained are examined and discussed from a numerical point of view

Numerical and Experimental Studies on Choked Underexpanded Jets

Axisymmetric underexpanded supersonic jets are investigated numerically and experimentally. A time-dependent technique of solution is applied to solve the Euler equations for a compressible ideal gas. The characteristics of the Mach disk obtained by the numerical calculations are compared with the experiments, and a good agreement is obtained. It is shown that the numerical results are very sensitive to the choice of the boundary conditions imposed on the artificially introduced numerical boundaries. The boundary condition giving the best results is found to be the ambient gas condition. It is shown that the global jet structure with a nearly regular shock pattern, wich is stable and steady itself, is destabilized by the vortex rings (Kelvin-Helmholtz roll-up) on the jet boundary. These vortices produce shocks inside the jet, which are convected downstream with the eddies. This strongly suggests that a time-independent or a time-converged solution cannot be expected without making a suitable time-averaging of the time-dependent solutions