Author/Authors :
Narsimhulu, D Department of Mathematics - Birla Institute of Technology and Science Pilani - Hyderabad Campus, Shameerpet, Hyderabad,Telangana, India , Ramu, A Department of Mathematics - Birla Institute of Technology and Science Pilani - Hyderabad Campus, Shameerpet, Hyderabad,Telangana, India , Kumar Satpathi, D Department of Mathematics - Birla Institute of Technology and Science Pilani - Hyderabad Campus, Shameerpet, Hyderabad,Telangana, India
Abstract :
A theoretical model for strong converging cylindrical and spherical shock waves in non-ideal gas
characterized by the equation of state (EOS) of the Mie-Gruneisen type is investigated. The governing
equations of unsteady one dimensional compressible flow including monochromatic radiation in Eulerian
hydrodynamics are considered. These equations are reduced to a system of ordinary differential equations
(ODEs) using similarity transformations. Shock is assumed to be strong and propagating into a medium
according to a power law. In the present work, two different equations of state (EOS) of Mie-Gruneisen type
have been considered and the cylindrical and spherical cases are worked out in detail. The complete set of
governing equations is formulated as finite difference problem and solved numerically using MATLAB. The
numerical technique applied in this paper provides a global solution to the problem for the flow variables, the
similarity exponent for different Gruneisen parameters. It is observed that increase in measure of shock
strength
has effect on the shock front. The velocity and pressure behind the shock front increases
quickly in the presence of the monochromatic radiation and decreases gradually. A comparison between the
results obtained for non-ideal and perfect gas in the presence of monochromatic radiation has been illustrated
graphically.
Keywords :
Numerical solution , Mie-Gruneisen EOS , Rankine-Hugoniot jump relations , Finite difference methods , Radiation hydrodynamics , Shock waves