Numerical simulation of momentum transfer from a shock wave to a bubbly medium

Abstract

Based on the system of equations of two phase compressible viscous flow, we performed a two dimensional numerical simulation of momentum transfer by a shock wave propagating from a gas to a con tinuous aqueous medium or an aqueous medium with air bubbles. When a shock wave impinges on a contin uous aqueous medium, the incompressible liquid is set in motion by gas overpressure after the reflection of the shock wave from the gas-liquid interface; however, when a shock wave impinges on a bubbly aqueous medium, the compressible liquid is set in motion due to the penetration of a shock wave into it. Parametric calculations have shown that momentum transfer from a shock wave to a bubbly fluid can be accompanied by dynamic effects, which ensure that the momentum transferred to the bubbly liquid for some time by far exceeds the momentum transferred to a continuous liquid, all other things being equal. These dynamic effects can be used to develop energy efficient hydrojet propulsion units.

Momentum transfer from a shock wave to a bubbly liquid

“…The experimental values of the SW velocity were obtained from pressure oscil lograms. For comparison, the relevant dependences of the SW velocity on α 10 calculated by the method described in [5][6][7] are also displayed.…”

“…To do this, the scene always included a scaling segment of known length. Figure 3 compares the measured and calculated (by the method described in [5][6][7]) dependences of the velocity of the contact surface and the velocity of air bubbles in the water on the initial volumetric gas con tents for SWs of different intensity.…”

“…A detailed description of the mathematical model and numerical procedure for solving the problem of the interaction of a shock wave with a bubbly liquid is given in [5][6][7]. The mathematical model is based on two dimensional differential equations of two phase flow obtained within the concept of interpenetrating continua [8], more specifically, the equations of con servation of mass, momentum, and energy of the phases with additional closure relations describing the dynamic of the interaction of the phases.…”

“…Using the Zel'dovich cycle in liquid fuel rocket engines and air breathing jet engines has been widely discussed (see, e.g., review [3]), whereas the use of this cycle in hydrojet engines has been discussed only in our papers [4][5][6][7]. According to [4][5][6][7], a pulse detona tion hydrojet engine consists of a water duct and detona tion wave generator operating on a given fuel mixture. The most important problem in the implementation of the Zel'dovich cycle in hydrojet engines is to ensure an efficient transfer of the momentum from the shock wave (SW) coming out from the generator into the water duct to the aquatic medium.…”

Pulse-Detonation Hydrojet

“…In our patent [4] and articles [1][2][3] we suggested to replace conventional screw propellers used in boats and ships by a pulse-detonation hydrojet. Such a propulsion device is composed of a pulse-detonation tube inserted in a properly shaped water guide submerged in water.…”