Mathematical modeling of a rotating detonation wave in a hydrogen-oxygen mixture

Abstract

A two-dimensional unsteady mathematical model of spin detonation in an annular cylindrical ramjet-type combustor is formulated. The wave dynamics in the combustor filled by a hydrogen-oxygen mixture is studied numerically.

Continuous spin detonation of hydrogen-oxygen mixtures. 1. Annular cylindrical combustors

“…The flow occurred in an annular space of the combustor with the boundaries Γ 1 (end face of the combustor with injectors for injecting the combustible mixture) and Γ 2 (open end of the combustor with exhaustion of combustion products). The mathematical formulation of a two-dimensional unsteady problem on a rotating detonation wave in a rocket-type annular cylindrical combustor and the method for the numerical solution of this problem were described in [4]. For comparisons with experiments, numerical simulations were performed for the same geometric sizes of the combustors as those used in the tests described above.…”

“…Using the prescribed thermodynamic properties of the gas mixture and normalizing, as in [4], the sought functions, coordinates, and time (p/p 0 , ρ/ρ 0 , T /T 0 , μ/μ 0 , u/u 0 , v/u 0 , x/l, y/l, and t/t 0 ) in the equations and boundary conditions to the pressure p 0 , density ρ 0 , temperature T 0 , molecular weight μ 0 , velocity of sound u 0 = p 0 /ρ 0 , distance between the neighboring TDWs l, and time t 0 = l/u 0 , we find that the solution of the problem of continuous spin detonation depends on the following governing parameters: three dimensionless parameters in the injection system (stagnation pressure of the mixture p m /p 0 , stagnation temperature of the mixture T m /T 0 , and ratio of the total cross-sectional area of injector orifices to the total cross-sectional area of the combustor entrance S * /S c ) and four scales (total length of the combustor L, length of the cylindrical part of the combustor L c , ratio of the cross-sectional areas of the combustor exit and entrance S exit /S c , and perimeter l). The numerical study was performed for a stoichiometric mixture 2H 2 + O 2 with the following values of scaling constants: T 0 = 300 K, p 0 = 1.013·10 5 Pa, μ 0 = 12 kg/kmole, ρ 0 = p 0 m 0 /RT 0 = 0.487 kg/m 3 , and u 0 = p 0 /ρ 0 = 456 m/sec.…”

“…With the use of this "illumination" technique [3], it seemed reasonable to make an attempt to register continuous spin detonation in H 2 -O 2 gas mixtures as well. Moreover, the physicomathematical model of continuous spin detonation predicted [4] a periodic solution with TDWs for a stoichiometric hydrogen-oxygen mixture.…”

“…The objectives of the present activities were to study the regime of continuous detonation burning of a hydrogen-oxygen mixture in an annular cylindrical combustor and to verify the mathematical model developed in [4]; based on experimental data and the model of continuous spin detonation, to study the properties of transverse detonation waves and the flow structure with variations in the combustor geometry, conditions of fuel injection, and counterpressure of the medium; to calculate the specific impulse for the detonation regime and estimate the degree of its efficiency.…”

Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

“…Due to the three-dimensional structure of rotating detonation waves, experimental observations are limited to the visualization of detonations and in addition, a great number of previous numerical investigations are two-dimensional, therefore the flow pattern of the RDE is not yet fully understood [11][12][13][14].…”