Ordinary Gasdynamics Research Articles

Solution of Riemann problem for dusty gas flow

A direct approach is used to solve the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady planar flow of an isentropic, inviscid compressible fluid in the presence of dust particles. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed for a dusty gas. The generalised Riemann invariants are used to find the solution between rarefaction wave and the contact discontinuity and also inside rarefaction fan. Unlike the ordinary gasdynamic case, the solution inside the rarefaction waves in dusty gas cannot be obtained directly and explicitly; indeed, it requires an extra iteration procedure. Although the case of dusty gas is more complex than the ordinary gas dynamics case, all the parallel results for compressive waves remain identical. We also compare/contrast the nature of the solution in an ordinary gasdynamics and the dusty gas flow case.

High-Order Numerical Method for Magnetohydrodynamic Control of Shock-Induced Separation

Magnetic fields significantly affect the flow of ionized gases and may be exploited for the control of separation, transition, and turbulence. The wave structure of ionized gas high-speed flows under the influence of magnetic fields is more involved than the waves of ordinary gas dynamics and high-resolution is required to accurately compute the complex wave interactions of such flows with discontinuities. Numerical solutions of the nonlinear ideal and viscous magnetohydrodynamic equations are obtained with a high-order-accurate shock-capturing scheme. The numerical method is tested for flows containing strong magnetohydrodynamic discontinuities and smooth flow features to ensure that it maintains high-order accuracy for the smooth parts of the flow, it preserves numerical stability, and eliminates nonphysical features that result from the violation of the divergence-free condition for the magnetic field. Problems with exact solutions, such as the convection of smooth waves caused by magnetic fields, are also solved numerically to validate the method. The numerical method is applied to simulate separation control at the interaction region of an oblique shock with a laminar boundary layer under the influence of magnetic fields.

Formation and evolution of density singularities in hydrodynamics of inelastic gases

We use hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a finite-time density blowup, where the gas pressure remains finite. The density blowup signals the formation of close-packed clusters. The blowup dynamics is universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass pointlike singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.

Existence of gasdynamic subshocks in Hall magnetohydrodynamics

We report the existence of oblique gasdynamic subshocks in Hall‐MHD. These gasdynamic subshocks propagate at a finite angle θ with respect to the local magnetic field and are embedded in a rotating magnetic field. Across these subshocks, the plasma density, velocity and pressure satisfy the Rankine‐Hugoniet (R‐H) jump conditions in ordinary gasdynamics. In addition, there is no jump in magnetic field across the subshocks. The existence of these gasdynamic subshocks require a finite viscosity, the rotation of magnetic field, and the presence of Hall term in the generalized Ohm's law. These gasdynamic subshocks can be formed in the transition regions of rotational discontinuities (RDs) and intermediate shocks.

On steady field‐aligned double‐adiabatic flow

The four general double‐adiabatic invariants governing ideal MHD flow in a narrow flux tube are summarized and are put in a form suitable for calculation of flow in tubes of nonconstant cross‐ sectional area. Results for converging‐diverging (Laval‐type) flux tubes are developed and compared to single‐adiabatic results which are identical to those for ordinary gasdynamic flow. As in such flows, a transition from subsonic to supersonic double‐adiabatic flow requires the presence of a minimum in the flux tube area, i.e., a maximum in the field strength. With increasing subsonic values of the parallel Mach number, M∥ = ν(ρ/3p∥)1/2, as the plasma moves toward the field maximum where M∥ = 1, the density, ρ, in double‐adiabatic flow initially increases rather than decreases, behavior that is the exact opposite of that in ordinary gasdynamics. A density maximum occurs at the subsonic value M∥ = (1 ‐ p⊥/3p∥)1/2; for larger M∥ values, the density then decreases monotonically as in ordinary gasdynamics. The two pressures, p∥ and p⊥, behave in qualitatively the same way as ρ. A fifth invariant, valid for general two‐dimensional (∂/∂z ≡ 0; Vz ≠ 0; Bz ≠ 0) single‐ or double‐adiabatic field‐aligned flow, is derived. Such two‐dimensional flows over slender obstacles are then analyzed by use of linear theory. It is found that in certain parameter regimes the governing equation for the vector potential is elliptic and can be reduced to Laplace's equation by simple stretching of one coordinate. In other regimes the equation is hyperbolic, indicating the presence of standing wave patterns. The relevance of these results to flow over magnetopause undulations, including flux transfer events, is discussed briefly; actual quantitative applications will be presented in a subsequent paper (D. W. Walthour et al., submitted, 1992).

On the debris phenomenon with laser-sputtered polymers

The sputtering of polymer films with 248 or 308 nm laser pulses causes two groups of particles to be emitted. Light particles are emitted more rapidly and escape to form a shock wave. Heavy particles are emitted more slowly and under some conditions are impeded by the light ones, expand sideways, and leave debris on the target surface. Debris formation can be understood from ordinary gas dynamics where it is equivalent to recondensation beyond the bombarded spot. This is shown by numerical solution of the flow equations.

Thermal-layer effect in a magnetically active plasma

For the first time computer simulation theoretically demonstrates the feasibility of forming a large-scale continuously growing precursor when a shock wave interacts with an extended density perturbation ("thermal-layer" effect) in the case of magneto~asdynamic flows. A criterion is obtained for the formation of an unsteady~precursor. The flow pattern in a field parallel to the line of intersection of the shock wavefront and the precursor is shown to be analogous to that from ordinary gasdynamics in many ways.

The configuration of slow‐mode shocks

Interest in slow‐mode shocks in space physics applications has increased in recent years. These shocks, which can arise from the steepening of linear slow‐mode magnetohydrodynamic waves, might form ahead of objects moving through a magnetized, highly conducting gas at speeds greater than the slow‐mode speed. In particular, slow shocks are the only shocks possible for speeds between those of the slow and fast modes. This appears to be the speed range, for example, of many and perhaps most coronal mass ejections. Despite the interest in and detection of slow‐mode shocks in the heliosphere, there appear to date to be no calculations of flows involving slow shocks. Basic properties like shock configuration and standoff distance are therefore unknown, although several authors have pointed out that slow shocks should extend upstream of the obstacle giving rise to the shock. This paper presents a simple method for computing slow shock flows in an infinitely conducting plasma, based on the solution of a free boundary problem for the shock configuration that matches a post shock potential flow to a uniform preshock flow. Such potential‐flow methods have been used in ordinary gasdynamics to obtain crude approximations to blunt‐body flows containing shocks; arguments given here suggest that the potential‐flow approximation should be more accurate in the case of slow MHD shocks. The method is applied to shocks arising from flow about spherical and paraboloidal obstacles. A parametric study of shock formation as a function of sonic and Alfvén Mach numbers shows standoff distance increasing as either Mach number decreases. Streamlines and shock configurations for several slow shock flows are also presented.

Proposal of a new method of solution of the unsteady non-linear eddington–vogt–sweet circulation

Abstract We propose a new method of solution of the unsteady non-linear Eddington-Vogt-Sweet circulation. We do not use eddy viscosity, in contrast to Tassoul and Tassoul (1982a), and we take the turbulent flow in the radiative region of a rotating main sequence star as an unsteady laminar flow. Analogous to the situation in ordinary gasdynamics (Kawamura and Kuwahara, 1984), results based on our laminar type model of a turbulent flow in a rotating star will complement a series of results by Tassoul and Tassoul for the inner rotation of a star. By employing our method, the following results are obtained. (1) We derive a non-linear partial differential equation of the perturbation as the basic equation of the main bulk of flow in the radiative region. (2) We show that the boundary layer at the interface between the convective and the radiative regions is of the Ekman type. We show ways to resolve the singularity of the meridional velcoity on the interface and give boundary conditions for the main bulk of t...

Converging magnetogasdynamic cylindrical shock waves in a uniform atmosphere

A self-similar solution to the problem of the implosion of a cylindrical shock wave in the presence of a magnetic field has been investigated. A strong shock wave in a cylindrically-symmetric flow travels to the axis of symmetry through a gas of uniform initial density ρ0 and zero-pressure. A comparative study has been made between the results obtained in ordinary gasdynamics and magnetogasdynamics with transverse and axial components of the magnetic field. The value of similarity exponent α has been assigned from that found in the paper of Whitham (1958).

Similarity solutions for explosions in radiating stars with time-dependent energy and idealized magnetic field

A stellar model in which density in the undisturbed conducting-gas medium is assumed to obey a power law is considered. Similarity solutions for central explosion in radiating stars have been obtained under the assumption of isothermal-shock conditions. For the existence of self-similar character, we have assumed that both radiation pressure and energy are negligible. The results of numerical calculations for different models are illustrated through graphs. Moreover, a comparative study has been made between the results in ordinary gasdynamics and those obtained in magnetogasdynamics.

Strong-plane shock waves in optically-thin atmospheres in magnetogasdynamics

In this paper, similarity solutions for the propagation of strong-plane shock waves in optically-thin grey atmospheres are obtained in the presence of a magnetic field. Density and magnetic field are constant in the undisturbed gaseous medium in front of the shock. Planck's diffusion approximation has been taken into account in this problem and a comparative study has been made between the results of ordinary gasdynamics and magnetogasdynamics.

Inviscid Flow of Radiation Dusty Gas Dynamics

The effects of radiation pressure and radiation energy on the flow of anideal radiating dusty gas at very high temperature has been studied. The most important parameter is the ratio of radiation pressure to the pressure of the mixture (gas+dust), the radiation pressure number R sub/p. Even though some basic phenomena for this present case are similar to those of ordinary gas dynamics, many new phenomena occur. The maximum possible velocity of a dusty gas from a given stagnation condition depends on the concentration of the dust particles. The jump of temperature across a normal shock is proportional to the square root of the shock Mach number.

An explosion model in magne to gasdynamics

By taking into account the interaction with magnetic field, in an axially symmetric inhomogeneous medium and assuming Gaussian density profile in radial direction instead of the cusped exponential law, a point explosion has been investigated by generalising the method suggested by Laumbach and Probstein (1969). The shock envelope becomes increasingly elongated along the axis of rotation, until it finally breaks through into the intergalactic space before it can spread considerably in equatorial directions as in ordinary gasdynamics. A comparison has been made between our results and those obtained in ordinary gasdynamics.

Transonic nozzle flows of dispersive compressible fluids

The transonic equation is derived for several dispersive compressible fluids. A similar transformation by Tomotika–Tamada is still applicable and provides nozzle flow solutions. When the coefficient of the dispersion term is positive, the choked flow with a shock wave in the divergent section in ordinary gasdynamics is replaced by the flow with a wavetrain and an appreciable change in the flow rate. There is a critical state of maximum mass flow as in ordinary gasdynamics. For negative coefficients of the dispersion term, the features of the low supersonic flow resemble that of the high subsonic flow for positive coefficients. The detailed calculation shows that the weak dispersion and the two-dimensional structure play an important role in the nozzle flow near the critical state.

Steady Two-Dimensional Jet-Flow of a Dispersive Compressible Fluid

A steady, two-dimensional jet-flow of a dispersive compressible fluid issuing a medium at rest is considered on the basis of the linearized theory. The explicit solution is presented by using the Fourier transform technique and by solving the associated dual integral equations. The supersonic jet-flow shows almost periodic oscillation and exponential damping, while the regular subsonic jet-flow is permitted only for uniform stream with constant cross-section. Both solutions are reasonably connected at the critical upstream condition and they are also reduced to the solutions in ordinary gasdynamics as the dispersion vanishes.

Artificial mechanism of heat conduction for the discussion of magnetogasdynamic shocks

The artificial mechanism of heat conduction introduced bySachdev andPrasad into ordinary gasdynamics has been extended to the case of magnetogasdynamics. This requires an additional field equation, alters the momentum and energy equations and at the same time needs satisfaction of the conditions adopted bySachdev andPrasad. Although the stability conditions of the difference and differential equations are slightly disturbed, they remain almost the same. We observe that in place of ordinary medium if we take magnetised medium into consideration, the same order of artificial heat conduction can smear out the shock discontinuity easily but on account of the magnetic field, the shock region is divided into two subregions.

Self-similar magnetogasdynamic flows accompanied by detonation and combustion waves

Magnetogasdynamic (MGD) flows with detonation waves and combustion fronts have attracted more and more attention in recent years. Intensive heat supply assures such a significant increase in the temperature and pressure behind the heat liberation fronts that the gaseous combustion products become conductive so that the flow map in the electric and magnetic fields can vary substantially as compared with ordinary gasdynamics. In the case of finite gas conductivity, when the magnetic Reynolds numbers Rm are low, the asymptotic laws of detonation wave propagation which either go over into the Chapman-Jouguet (CJ) mode (in a number of cases at a finite distance from the initiation source) or remain overcompressed, have been studied [1]. Stationary flow modes behind detonation waves have been investigated in [2] and the problem of the detonation wave originating at the closed end of the tube emerging in the stationary mode in crossed homogeneous magnetic and electric fields has been examined. Results are presented in this paper of an investigation of one-dimensional self-similar flows caused by piston motion in a hot gas mixture in which a detonation wave or combustion front is propagated. The motion is realized in external electric and magnetic fields which exert a substantial effect on the flow of the conductive combustion products. Domains of application of the governing parameters in which the various flow modes are realized are found by using a qualitative and numerical analysis. The results obtained are used to solve problems about the hypersonic gas flow around a thin wedge in an axial magnetic field.

Propagation of Disturbance through a Gas Plug Enclosed by Liquid in a Pipe

The disturbance propagating thorough a single gas plug bounded by liquid on both sides in a pipe is considered on the basis of the linearized theory in ordinary gasdynamics. The temporal and spatial features of the propagation in such a two-phase system are discussed analytically and numerically. It is explicitly shown that there are two characteristic times of the propagation and that the transmission through a plug is promoted with the strength of a disturbance. A similar discussion can be applied to a liquid plug bounded by gas on both sides.

Propagation of a Disturbance through a Separated Gas-Liquid System

The disturbance propagating through a simple separated gas-liquid system is considered on the basis of the linearized theory in the ordinary gasdynamics. The two-dimensional and unsteady field is analyzed by using the Laplace-Fourier transform technique, and the asymptotic solution expanded in powers of the ratio of the gas density to the liquid density is discussed. It is shown that the initial disturbance is subjected to a change in shape in the course of time and that the propagation aspect differs depending on the type of the disturbance. The separated gas-liquid system has a dispersion property.