Numerical simulation of fuel combustion in stationary detonation wave in variable cross-section channel with supersonic flow at the inlet and outlet


Аuthors

Gidaspov V. Y.*, Kononov D. S.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: gidaspov@mai.ru
**e-mail: dr.kononoff@yandex.r

Abstract

The authors studied the case of (H2 + 0.5O2 + 1.881N2) hydrogen-air mixture combustion in the stationary detonation wave. Analysis of possible flow patterns with stationary detonation wave was performed in chemically equilibrium quasi-single dimensional problem statement according to the technique [8] for a channel in the form of two successively arranged Laval nozzles. In case [8], solution depends exclusively on the radii ratio in the current, initial and minimum channel cross-sections. Passage modelling of a chemically non-equilibrium flow rate through the speed of sound was being realized employing “adjustment of fire” method (algorithm for a singular point passing) [10] using equilibrium solution as an initial approximation. This algorithm allows obtaining a quasi-one-dimensional non-equilibrium stationary solution with a detonation wave in the longitudinal x-coordinate of the l with the given mixture and basic thermodynamic parameters by varying setting coordinate of the detonation wave. Positions of detonation wave are close enough in both equilibrium and non-equilibrium cases. The range of mixture with detonation wave flow rates can be predicted with equilibrium analysis. As in the equilibrium case, three possible solutions with detonation waves in non-equilibrium flow exist in the loop.

Only one solution with detonation wave in the expanding section is stable. This fact was proved by Godunov’s method. The presented quasi-one-dimensional formulation of the problem can be employed for the initial analysis of flows. At the same time, the indisputable advantage of this technique is the high speed of calculations.

Keywords:

numerical modeling, variable cross-section channels, quasi-one-dimensional stationary flow model, direct problem of nozzle theory, non-equilibrium chemical transformations

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