Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

Abstract

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

Grid-Characteristic Method for Calculation of Discontinuous Non-Steady Flows of a Multicomponent Reacting Gas in Channels

“…When solving many applied problems, numerically examining unsteady flows of multicomponent gas mixture with physicochemical transformations is required. In this case, in the flow field, there may be zones of rapid changes in the flow parameters or their gradients; they may include shock waves, contact discontinuities (strong discontinuities), and boundary characteristics of expansion wave fans (weak discontinuities) [1][2][3][4][5][6][7][8]. Moreover, the works [1][2][3][4][5][6][7] describe methods in which shock waves and contact discontinuities are clearly distinguished.…”

“…In this case, in the flow field, there may be zones of rapid changes in the flow parameters or their gradients; they may include shock waves, contact discontinuities (strong discontinuities), and boundary characteristics of expansion wave fans (weak discontinuities) [1][2][3][4][5][6][7][8]. Moreover, the works [1][2][3][4][5][6][7] describe methods in which shock waves and contact discontinuities are clearly distinguished. Work [8] is a typical representative of a large number of works, in which reacting flows with shock waves and contact discontinuities are simulated using the shock-capturing method with the condensation of grid lines in areas with a large gradient of parameters.…”

“…Methods with explicit isolation of discontinuity surfaces, unlike the shock-capturing method [1][2][3][4][5][6], allow one to construct adaptive difference grids consisting of both fixed and mobile nodes that can move along the paths of the indicated strong and weak discontinuities, gas trajectories, moving boundaries, etc. This approach provides high-precision results on relatively coarse grids.…”

An Approximate Analytical Model of a Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock

“…In this regard, it is necessary to generalize the approximate analytical models [11][12][13], which have proven themselves well for the flows of a perfect non-reacting gas, to the case of a change in the chemical composition and pulsed energy release on emerging shocks. In [19][20][21], the classical shock-wave relations are generalized to the case of a change in the chemical composition and the impulse energy efflux within the framework of Chapman-Jouguet stationary detonation theory. In particular, "detonation" polars have been constructed instead of classical shock polars [19][20][21]; generalized criteria for regular or Mach shock reflection transition were derived, and their shift compared to the flow without energy supply and change in chemical composition was analyzed.…”

“…In [19][20][21], the classical shock-wave relations are generalized to the case of a change in the chemical composition and the impulse energy efflux within the framework of Chapman-Jouguet stationary detonation theory. In particular, "detonation" polars have been constructed instead of classical shock polars [19][20][21]; generalized criteria for regular or Mach shock reflection transition were derived, and their shift compared to the flow without energy supply and change in chemical composition was analyzed.…”