Some rotational corrections to the acoustic energy equation in injection-driven enclosures

Abstract

This article presents rotational corrections to the energy stability equation in injection-driven porous enclosures used to simulate solid rocket motors. The evaluation of stability growth rate factors is carried out both numerically and asymptotically. Analytical expressions for the energy stability factors are obtained over a spectrum of physical parameters encompassing solid rocket motor operation. For all representative motors under investigation, the analytical estimates are shown to exhibit negligible errors compared to their numerical values. Both numerics and asymptotics converge in predicting less stable systems than projected by purely irrotational stability theory. The differences can be ascribed to the dismissal of time-dependent rotational coupling in some past formulations. The current study unravels the details of six additional growth rate corrections not accounted for previously. These include the rotational flow, inviscid vortical, viscous, pseudoacoustical, pseudorotational, and unsteady nozzle growth rate factors. The fourth and fifth terms are due to acoustical and vortical interactions with the often neglected pseudopressure. The sixth is due to the energy associated with the unsteady rotational flow exiting the porous enclosure. This study enables us to explain the influence of distinct flow variables on stability. Based on asymptotic approximations for individual growth rates, explicit criteria are presented in the form of critical Mach numbers, penetration numbers, or motor lengths that must not be exceeded in prevention of system instability. The net rotational corrections have been recently appended to the widely used Standard Stability Prediction code.

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

“…This may be owed to its association with several studies involving hydrodynamic instability [23][24][25][26][27][28], acoustic instability [29][30][31][32][33][34][35], wave propagation [36][37][38][39], particle-mean flow interactions [40], and rocket performance measurements [41][42][43]. The Taylor-Culick solution was originally verified to be an adequate representation of the expected flowfield in SRMs both numerically by Sabnis et al [44] and experimentally by Dunlap et al [45,46], thereby confirming its character in a nonreactive chamber environment.…”

Analytical Models for Hybrid Rockets

“…Attempts at predicting these instabilities have invariably pointed to the importance of providing accurate assessments of rocket core flow detail [30][31][32][33][34]. Attempts at predicting these instabilities have invariably pointed to the importance of providing accurate assessments of rocket core flow detail [30][31][32][33][34].…”

Combustion Instability Involving Vortex Shedding in Hybrid Rocket Motors

“…It is worthwhile to note that the coupling between the acoustic waves and the boundary driven vorticity is here neglected while this may play a role in some combustion systems as evidenced in Ref. [10,11,12]. Considering that the vortex size is much smaller than the acoustic wavelength and the longitudinal dimension of the combustion chamber, and that the combustion time is much smaller that the vortex convection, it is assumed that burning is localized in space and time.…”