On the jet collision: General model and reduction to the Mie-Grüneisen state equation

Abstract

We study the stationary direct supersonic collision of jets of condensed materials. We determine the basic flow characteristics: the maximum values of pressure, temperature, and densities on outgoing shock wave fronts and at the wave stagnation and penetration points. To this end, just as in the Lavrentiev problem about the jet collision in the framework of an incompressible fluid model, it suffices to consider the flow only along the central streamline, i.e., the symmetry axis. We consider the general caloric (incomplete) equation of state and, to close the thermodynamic construction and determine the temperature dependence on the state parameters, supplement them with thermodynamic identities. We also consider the conditions on discontinuities, the Bernoulli integrals, i.e., the conservation laws, to relate the states behind the wave front and the stagnation point, and the continuity conditions at this point. Just as in the collision problem for jets of incompressible fluid, we neglect the strength, viscosity, and heat conduction. As a result, we construct a mathematical model, i.e., a system of 12 integro-algebraic equations, and propose a semi-inverse solution method, in which the system splits into separate equations. In the special case of the Mie-Grüneisen state equation, the system becomes much simpler. We perform computations and construct the dependence of maximal pressures and temperatures on the impact velocity in the range 1–20 km/s for many pairs of materials of the colliding jets. We also compare the results with the solution obtained according to the incompressible fluid model.