Combustion stability in an annular gas combustor.

Abstract

The conditions for either stable or oscillatory combustion are determined analytically for a burning mixture of ideal gases in an annular combustion zone. The mixture, flowing steadily in the axial direction, is perturbed by a small-amplitude, tangentially propagating pressure disturbance. The rate of energy release is described by an Arrhenius function. The stability of the system is governed by an amplif cation coefficient that reflects the effects due to the rate of energy release and the convective transport of energy. The stability criterion is employed to evaluate the effects of changes in the system parameters on the combustion stability. A critical value of the Arrhenius exponent is determined which exists at a line demarcating regions of stable and oscillatory combustion; it is a function of the flowfield variables, the specific-heat ratio, and the reaction rate frequency factor. A partial, qualitative verification of the stability trends predicted by the analysis is provided by the known stability behavior of premixed gases burned in cylindrical and annular combustors.Mach number m = mean molecular weight n = wave number for tangential mode of oscillation p -static pressure p i} p. 2 = amplitude constants r = mean radius of annulus, radial coordinate R -gas constant R u -universal gas constant t = time T = static temperature v = velocity vector v$j v z = tangential and axial velocity components, respectively Xij Xj = mass fractions of components i and j z = axial coordinate & = na/r Sij 5 2 = constant phase angles e = activation energy 0 = angular coordinate p = density <r = mean collision diameter oj = angular frequency (~) = steady-state variable ( )' = perturbed variable ( ) = mean value D/Dt = substantial derivative V = del operator

Unsteady Combustion in Gaseous Propellant Rocket Motors

“…All perturbation quantities were taken to be of order Mach number and proportional to e , As will be demonstrated in this report this is not quite correct for the case of low mean flow Mach number and led Merk to the incorrect conclusion that the only pressure sensitive energy source of importance in the heat release-pressure oscillation coupling is the fluctuation in flame area. Nevertheless, the theoretical analyses of Merk As was noted earlier, the development of the gas rocket as a viable research tool for the determination of the influence of gas phase processes (within the combustion chamber) on the phenomenon of unstable combustion occurred independently at Purdue University's (57-71) Jet Propulsion Center, the University of Tokyo (72)(73)(74)(75)(76) and at the Guggenheim Laboratories at Princeton (26)(27)(28)(29)(30)(31)(32). These researches have been motivated by interest in the practical problems of nonsteady combustion in liquid propellant rocket motors.…”