Specific gasdynamical features of spontaneous condensation in an unsteady rarefaction wave

On the basis of numerical modeling, the formation of an unsteady shock wave induced by a condensation shock in a rarefaction wave moving in the high-pressure channel of a shock tube filled with moist air is demonstrated. It is shown that in a fairly long channel a periodic structure consisting of an alternating sequence of condensation shocks and the shock waves they generate may be formed. This structure is a linear unsteady analog of the self-oscillation regime of type IV in the classification [1] for condensing medium flows in the subsonic section of a Laval nozzle. The specific features detected are important for planning and interpreting experiments aimed at investigating spontaneous condensation using a “condensation shock tube”.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

Decay of a plane shock wave in a two-parameter medium with arbitrary equation of state

Special curves, called shock polars, are frequently used to determine the state of the gas behind an oblique shock wave from known parameters of the oncoming flow. For a perfect gas, these curves have been constructed and investigated in detail [1]. However, for the solution of problems associated with gas flow at high velocities and high temperatures it is necessary to use models of gases with complicated equations of state. It is therefore of interest to study the properties of oblique shocks in such media. In the present paper, a study is made of the form of the shock polars for two-parameter media with arbitrary equation of state, these satisfying the conditions of Cemplen's theorem. Some properties of oblique shocks in such media that are new compared with a perfect gas are established. On the basis of the obtained results, the existence of triple configurations in steady supersonic flows obtained by the decay of plane shock waves is considered. It is shown that D'yakov-unstable discontinuities decompose into an oblique shock and a centered rarefaction wave, while spontaneously radiating discontinuities decompose into two shocks or into a shock and a rarefaction wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1982.     

The Riemann Solution for the Injection of Steam and Nitrogen in a Porous Medium

We solve the model for the flow of nitrogen, vapor, and water in a porous medium, neglecting compressibility, heat conductivity, and capillary effects. Our choice of injection conditions is determined by the application to clean up polluted sites. We study all mathematical structures, such as rarefaction, shock waves, and their bifurcations; we also develop a systematic method to find fundamental solutions for thermal compositional flows in porous media. In addition, we unexpectedly find a rarefaction evaporation wave which has not been previously reported in any other study.     

Direct Shocks in a Vibrationally Nonequilibrium Gas

Direct shocks in flows of a high-temperature diatomic gas with rotational and vibrational degrees of freedom are considered. Gas-dynamic parameters and populations of molecular vibrational levels behind a shock are studied for the case of disturbance of vibrational equilibrium in an incident flow.     

Dynamics of vapor bubbles

The nonlinear problem of the thermal, mass, and dynamic interaction of a single vapor bubble with the surrounding liquid is discussed. This problem has ramifications in research on flows of vapor-liquid mixtures with a bubble-matrix structure, in particular, the propagation of shock waves in such media. Results are given from a numerical solution of the problem of the radial motion imparted to a bubble by a sudden change of pressure in the liquid; this problem corresponds, in particular, to the behavior of bubbles behind a shock front when the latter enters a bubble curtain.     

Derivation of a linear theory for nonequilibrium and equilibrium flows

Conventional linear theory of nonequilibrium and equilibrium gas flows yields correct results only for very small deviations of the stream parameters from the unperturbed values. Moreover, if in linearization we take the coordinates in planar flow as independent variables, then the flow past concave and convex corners is described in exactly the same fashion. In this case the characteristic emanating from the corner is (depending on the type of corner) a compression or rarefaction shock. In the case of a break in the wall of an axisymmetric channel the shock intensity approaches infinity with approach to the centerline, which indicates a deficiency of this type of linear theory. In the following we use a modification which eliminates the deficiencies noted above. This involves conversion to new independent and dependent variables such that the coefficients of the exact equations being linearized become weakly varying functions of the unknown parameters, the linearized boundary conditions coincide with the exact conditions at all or part of the boundaries, and the rarefaction shocks become rarefaction wave bundles of finite width. The last condition is achieved as a result of the fact that, in accordance with the Lighthill method of deformable coordinates [1], we take as one of the independent variables a quantity which maintains a constant value on each characteristic of the bundle of characteristics emanating from the break point [for equilibrium flows the semicharacteristic (or characteristic) independent variables were used in deriving the linear theory, for example, in [2–4]]. The study was based on the example of two-dimensional stationary nonequilibrium flow of an inviscid and nonheatconducting gas. In this case we find that boththelinear equations at a finite distance from the walls and the boundary conditions for determining the potential and nonequilibrium parameters outside the rarefaction wave bundles coincide with the equations and the conditions of conventional linear theory [5], while the relations associating the values of the parameters on the closing characteristics of each bundle (outside the bundles the same value of the characteristic variable corresponds to these characteristics) at some distance from the axis or from some reflecting surface are identical to the conditions on the rarefaction shocks. This fact makes it possible to use several results of conventional linear theory.     

Numerical simulation of compressible two-phase flow using a diffuse interface method

In this article, a high-resolution diffuse interface method is investigated for simulation of compressible two-phase gas–gas and gas–liquid flows, both in the presence of shock wave and in flows with strong rarefaction waves similar to cavitations. A Godunov method and HLLC Riemann solver is used for discretization of the Kapila five-equation model and a modified Schmidt equation of state (EOS) is used to simulate the cavitation regions. This method is applied successfully to some one- and two-dimensional compressible two-phase flows with interface conditions that contain shock wave and cavitations. The numerical results obtained in this attempt exhibit very good agreement with experimental results, as well as previous numerical results presented by other researchers based on other numerical methods. In particular, the algorithm can capture the complex flow features of transient shocks, such as the material discontinuities and interfacial instabilities, without any oscillation and additional diffusion. Numerical examples show that the results of the method presented here compare well with other sophisticated modeling methods like adaptive mesh refinement (AMR) and local mesh refinement (LMR) for one- and two-dimensional problems.     

Influence of shear layers on the structure of shocks formed by rectangular and parabolic blockages placed in a subsonic flow-field

Flow blockages are used to promote the transition of a flame to a detonation. The structure of shock waves formed with different configurations of blockages was experimentally determined for subsonic incoming flow. High speed subsonic flows could develop ahead of a turbulent flame and the interaction of such flows with blockages could lead to the formation of interacting shock waves, slipstreams, and expansion waves. A blow-down test setup was designed to study the interacting shock pattern formed with different configurations of blockages. The flow was found to accelerate to low supersonic velocities during its passage over the blockages. The shock structure downstream of the blockages was found to depend on the shape, size, and number of blockages as well as the spacing between them. While a parabolic-shaped blockage provided shocks of maximum strength, large blockage ratio values did not permit the formation of shocks. The shear layer, formed in the flow downstream of the blockages, reflected the expansion fan as shock waves and was found to be a major feature influencing the formation of the interacting structure of oblique shocks. The structure and strength of the shock waves are analyzed using hodograms. The formation of the interacting family of shock waves using different configurations of blockages and the spacings between them are discussed.     

Interaction Between a Slow Magnetohydrodynamic Shock Wave and a Tangential Discontinuity

The self-similar problem of the oblique interaction between a slow MHD shock wave and a tangential discontinuity is solved within the framework of the ideal magnetohydrodynamic model. The constraints on the initial parameters necessary for the existence of a regular solution are found. Various feasible wave flow patterns are found in the steady-state coordinate system moving with the line of intersection of the discontinuities. As distinct from the problems of interaction between fast shock waves and other discontinuities, when the incident shock wave is slow the state ahead of it cannot be given and must to be determined in the process of solving the problem. As an example, a flow in which the slow shock wave incident on the tangential discontinuity is generated by an ideally conducting wedge located in the flow is considered. The basic features of the developing flows are determined.     

Modeling transonic weakly underexpanded turbulent jets

The results of the calculations of model and actual turbulent jet flows with shock waves at low supersonic Mach numbers are presented. The gasdynamic flow features characterizing shock reflection from a mixing layer are analyzed. A possible version of the modified model for the turbulent viscosity is proposed; the model makes it possible to improve the prediction of the shock (rarefaction wave) intensity distribution along jet flows.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Interference of oblique shock waves of one family in a hypersonic flow

A study is made of the irregular regime of interaction of two shock waves of the same direction when a hypersonic gas stream flows past bodies of complicated shape. It is shown that the rarefaction waves formed in the flow field significantly weaken the shock wave that approaches the body. This effect is confirmed by the results of an experiment and numerical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–138, September–October, 1982.     

NND schemes and numerical simulation of axial symmetric free jet flows

Through a study on one-dimensional Navier-Stokes equations, it was found that the spurious oscillations occuring near shock waves with finite difference equations are related to the dispersion term in the corresponding modified differential equations. If the sign of dispersion coefficient is properly adjusted so that the sign changes across shock waves, the undesirable oscillations can be totally suppressed. Based on this finding, the non-oscillatory, containing no free parameters and dissipative shheme (NND scheme) is developed. This scheme is one of “TVD”. The axisymmetric free jet flows are simulated numerically using this scheme. The results obtained by the present scheme are compared with the experimental picture. It is shown that the agreement is very good, and that this scheme has advantages of high resolution for capturing shocks and contact discontinuities. Project supported by National Science Foundation of China     

Vapor condensation behind a shock wave propagating through a large molecular-mass medium

Measurements of film condensation were made behind the incident shock wave propagating through a vapor-liquid two-phase medium. Major objective of the study is to identify condensing heat transfer rates of the vapor to the shock-tube side wall as well as to learn the condensing main flow field. Ethanol and E-10 (a heavy liquid named Afluid by the manufacturer) were extensively used as working fluid. Steady accumulation of the condensing vapor was confirmed on the wall surface, as similarly seen in the end-wall experiment conducted elsewhere. A most significant result is that "dual-step" shock pressurization was observed in E-10. The first pressure rise is a normal one created by an incident shock front, whereas the second pressure rise is taken place by some large disturbance in the main flow. The reason for this is not certain yet, but is speculated to be a long relaxation time or inefficient compressibility of the fluid. The visualized shock front and its vicinity of E-10 is completely different from those of normal gases. Received May 31, 1994 / Accepted April 20, 1995     

Four-Component Gas/Oil Displacements in One Dimension: Part I: Global Triangular Structure

This paper presents an analysis of the mathematical structure of three-component and four-component gas displacements. The structure of one-dimensional flows in which components partition between two phases is governed by the geometry of a set of equilibrium tie lines. We demonstrate that for systems of four components, the governing mass conservation laws for the displacement can be represented by an eigenvalue system whose coefficient matrix has a global triangular structure, which is defined in the paper, for only specific types of phase behavior. We show that four-component systems exhibit global triangular structure if and only if (1) tie lines meet at one edge of the quaternary phase diagram or (2) if tie lines lie in planes. For such systems, shock and rarefaction surfaces coincide and are planes. We prove that systems are of category (2) if equilibrium ratios (K-values) are independent of mixture composition. In particular, for such systems shock and rarefaction curves will coincide. We also show that for systems with variable K-values, the rarefaction surfaces are almost planar in a precise sense, which is described in the paper. Therefore, systems with variable K-values may be well approximated by assuming shock and rarefaction surfaces do coincide. For these special systems the construction of solutions for one-dimensional, two-phase flow with phase behavior simplifies considerably. In Part II, we describe an application of these ideas to systems in which K-values are constant.     

Lift-to-drag ratio at supersonic speeds

Wave lift-to-drag ratio is analyzed ignoring friction and using flows behind oblique shock waves and rarefaction waves. It is shown that the lift-to-drag ratio of an infinite oblique plate can surpass considerably that of triangular plates with subsonic, sonic, or supersonic edges. The simplest finite-span oblique wing is a wing with characteristic edges. However, when the normal-to-the-edge flow velocity component behind a shock reaches the speed of sound, the wing contracts into an edge, and other means must be used to exclude the end effect. Several possible variants are indicated. A straight wedge with side plates is the optimal shape for a lifting body with fixed volume, lift, length, and width. Under the same conditions, the cross-section of a pyramidal body formed by stream planes behind one or two plane shocks has practically no effect on the lift-to-drag ratio, while the region of high lift-to-drag ratio is much narrower than for a wedge. If a pyramid fails to provide the required lift-to-drag ratio, it is necessary to turn to forms that better fill the given area. Redistribution of lift between body and wing permits an improvement in the lift-to-drag ratio.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–141, September–October, 1993.     

Imploding conical shock waves

The behaviour of conical shock waves imploding axisymmetrically was first studied numerically by Hornung (J Fluid Mech 409:1–12, 2000) and this prompted a limited experimental investigation into these complex flow patterns by Skews et al. (Shock Waves 11:323–326, 2002). Modification of the simulation boundary conditions, resulting in the loss of self-similarity, was necessary to image the flow experimentally. The current tests examine the temporal evolution of these flows utilising a converging conical gap of fixed width fed by a shock wave impinging at its entrance, supported by CFD simulations. The effects of gap thickness, angle and incident shock strength were investigated. The wave initially diffracts around the outer lip of the gap shedding a vortex which, for strong incident shock cases, can contain embedded shocks. The converging shock at exit reflects on the axis of symmetry with the reflected wave propagating outwards resulting in a triple point developing on the incident wave together with the associated shear layer. This axisymmetric shear layer rolls up into a mushroom-shaped toroidal vortex ring and forward-facing jet. For strong shocks, this deforms the Mach disk to the extent of forming a second triple point with the primary shock exhibiting a double bulge. Separate features resembling the Richtmeyer–Meshkov and Kelvin–Helmholtz instabilities were noted in some tests. Aside from the incident wave curvature, the reflection patterns demonstrated correspond well with the V- and DV-types identified by Hornung although type S was not clearly seen, possibly due to the occlusion of the reflection region by the outer diffraction vortex at these early times. Some additional computational work explicitly exploring the limits of the parameter space for such systems has demonstrated the existence of a possible further reflection type, called vN-type, which is similar to the von Neumann reflection for plane waves. It is recommended that the parameter space be more thoroughly explored experimentally.