Volume-to-surface reduction of vorticoacoustic stability integrals

Abstract

It is generally accepted that incorporation of unsteady rotational sources and sinks into the acoustic energy balance equation leads to a more precise assessment of acoustic instability in rocket chambers. The process involves the calculation of 10 acoustic growth rate terms that arise in the context of an oscillating flow in an idealized rocket chamber; the chamber is modelled as an injection-driven enclosure with coupling along its porous walls between acoustical and vortical waves. In this study, we convert the 10 stability integrals from volume to surface form. The surface integrals are then verified using numerical comparisons for three baseline cases that span a practical range of solid rocket motors. The surface integrals are further reduced and presented in a strictly acoustical form that is directly amenable to implementation in the standard stability prediction program. This code devotes itself to the assessment of acoustic energy in rocket motors. The reduction to surface form facilitates the evaluation of individual stability growth rates as each becomes a function of quantities that are distributed along the chamber's boundaries. By obviating the need to compute the rotational field (which is the most difficult to capture, especially in complex geometry), the evaluation of acoustic stability integrals is simplified for motors with variable grain configuration.