Study of the Effects of Unsteady Heat Release in Combustion Instability

Arnau Pons, Purdue University

Abstract

Rocket combustors and other high-performance chemical propulsion systems are prone to combustion instability. Recent simulations of rocket combustors using detailed chemical kinetics show that the constant pressure assumption used in classical treatments may be suspect due to high rates of heat release. This study is a exploration on the effects of these extraordinary rates of heat addition on the local pressure field, and interactions between the heat release and an acoustic field. The full problem is decomposed into simpler unit problems focused on the particular interactions of physical phenomena involved in combustion instability. The overall strategy consists of analyzing fundamental problems with simplified scenarios and then build up the complexity by adding more phenomena to the analysis. Seven unit problems are proposed in this study. nit problems are proposed in this study. The first unit problem consists of the pressure response to an unsteady heat release source in an unconfined one-dimensional domain. An analytical model based on the acoustic wave equation with planar symmetry and an unsteady heat source is derived and then compared against results from highly-resolved numerical simulations. Two different heat release profiles, one a Gaussian spatial distribution with a step temporal profile, and the other a Gaussian spatial distribution with a Gaussian temporal distribution, are used to model the heat source. The analytical solutions predict two different regimes in the pressure response depending on the Helmholtz number, which is defined as the ratio of the acoustic time over the duration of the heat release pulse. A critical Helmholtz number is found to dictate the pressure response regime. For compact cases, in the subcritical regime, the amplitude of the pressure pulse remains constant in space. For noncompact cases, above the critical Helmholtz number, the pressure pulse reaches a maximum at the center of the heat source, and then decays in space converging to a lower far field amplitude. At the limits of very small and very large Helmholtz numbers, the heat release response tends to be a constant pressure process and a constant volume process, respectively. The parameters of the study are chosen to be representative of the extreme conditions in a rocket combustor. The analytical models for both heat source profiles closely match the simulations with a slight overprediction. The differences observed in the analytical solutions are due to neglecting mean flow property variations and the absence of loss mechanisms. The numerical simulations also reveal the presence of nonlinear effects such as weak shocks that cannot be captured by the linear acoustic wave equation The second unit problem extends the analysis of the pressure response of an unsteady heat release source to an unconfined three-dimensional domain. An analytical model based on the spherical acoustic wave equation with an unsteady heat source is derived and then compared against results from highly-resolved three-dimensional numerical simulations. Two different heat release profiles, a three-dimensional Gaussian spherical distribution with either a step or a Gaussian temporal distribution, are used to model the heat source. Two different regimes in the pressure response depending on the Helmholtz number are found. This analysis also reveals that whereas for the one-dimensional case the pressure amplitude is constant over the distance, for the three-dimensional case it decays with the radial distance from the heat source.

Degree

Ph.D.

Advisors

Anderson, Purdue University.

Subject Area

Acoustics

COinS