Numerical Simulation of a High-Speed Impact of Metal Plates Using a Three-Fluid Model

Abstract

The process of wave formation at the contact boundary of colliding metal plates is a fundamental basis of explosive welding technology. In this case, the metals are in a pseudo-liquid state at the initial stages of the process, and from a mathematical point of view, a wave formation process can be described by compressible multiphase models. The work is devoted to the development of a three-fluid mathematical model based on the Baer–Nunziato system of equations and a corresponding numerical algorithm based on the HLL and HLLC methods, stiff pressure, and velocity relaxation procedures for simulation of the high-speed impact of metal plates in a one-dimensional statement. The problem of collision of a lead plate at a speed of 500 m/s with a resting steel plate was simulated using the developed model and algorithm. The problem statement corresponded to full-scale experiments, with lead, steel, and ambient air as three phases. The arrival times of shock waves at the free boundaries of the plates and rarefaction waves at the contact boundary of the plates, as well as the acceleration of the contact boundary after the passage of rarefaction waves through it, were estimated. For the case of a 3-mm-thick steel plate and a 2-mm-thick lead plate, the simulated time of the rarefaction wave arrival at the contact boundary constituted 1.05 μs, and it was in good agreement with the experimental value 1.1 μs. The developed numerical approach can be extended to the multidimensional case for modeling the instability of the contact boundary and wave formation in the oblique collision of plates in the Eulerian formalism.