Exact Solution for Isothermal Flow behind a Shock Wave in a Self-Gravitating Gas of Variable Density in an Azimuthal Mag
- PDF / 495,655 Bytes
- 8 Pages / 594 x 792 pts Page_size
- 73 Downloads / 177 Views
Journal of Engineering Physics and Thermophysics, Vol. 93, No. 5, September, 2020
EXACT SOLUTION FOR ISOTHERMAL FLOW BEHIND A SHOCK WAVE IN A SELF-GRAVITATING GAS OF VARIABLE DENSITY IN AN AZIMUTHAL MAGNETIC FIELD G. Nath,a Mrityunjoy Dutta,b and S. Chaurasiac
UDC 533.951
Similarity solution for the propagation of a spherical shock wave in a self-gravitating perfect gas with an azimuthal magnetic field in the case of isothermal flow is investigated. The density and azimuthal magnetic field strength in the ambient medium are assumed to vary and obey power laws. An exact similarity solution obtained using the McVittie method in the case of isothermal flow is reported for the first time. The obtained solutions show that the radial fluid velocity, density, pressure, magnetic field strength, and the mass tend to zero as the point of symmetry is approached. The effects of the changes in the values of the adiabatic exponent γ and the exponent w in the variation of an initial density are considered in detail. It is shown that the magnetic field strength and mass increase with γ, whereas an increase in w exerts the reverse effect on these flow variables. Keywords: shock waves, similarity solution, gravitation, perfect gas, magnetogasdynamics, exact solution. Introduction. Shock waves are produced due to a sudden release of a large amount of energy by sources, as in a nuclear explosion, rupture of a pressurized vessel, and chemical detonation. The study of shock waves is an important field of research for the safety assessments and predictions of disasters due to explosions. Shock waves are characterized by a supersonic shock front followed by an exponential-type decay of the physical gas properties [1]. The explanation and analysis of the internal motion in stars is one of the basic problems in astrophysics. According to observational data, the unsteady motion of a large gas mass followed by a sudden energy release results in flare-ups in the novae and supernovae. Parker [2] and Zel'dovich and Raizer [3] concluded that the hydrodynamic blast wave theory can successfully describe a large domain of phenomena, among which is expansion of the solar corona. Using similarity method, they presented a number of numerical solutions for the idealized adiabatic "solar wind" model. These solutions correspond to the flow driven by a spherical piston in the power-law motion for the surface which is the contact discontinuity enveloping the fresh flare corona in the centre core. Behavior of a gaseous mass may be discussed qualitatively with the help of the equations of motion and equilibrium where the gravitational forces are taken into account. Numerical solutions for self-similar adiabatic flows in a self-gravitating gas were obtained independently by Sedov [4] and Carrus et al. [5]. Purohit [6] and Singh and Vishwakarma [7] considered homothermal flows behind a spherical shock wave in a self-gravitating gas, using similarity method. A shock wave propagating through a medium of variable density was studied by Sedov [4], Sakurai [8], R
Data Loading...
