Simulation of Axial Combustion Instability Development and Suppression in Solid Rocket Motors

Abstract

In the design of solid-propellant rocket motors, the ability to understand and predict the expected behaviour of a given motor under unsteady conditions is important. Research towards predicting, quantifying, and ultimately suppressing undesirable strong transient axial combustion instability symptoms necessitates a comprehensive numerical model for internal ballistic simulation under dynamic flow and combustion conditions. An updated numerical model incorporating recent developments in predicting negative and positive erosive burning, and transient, frequency-dependent combustion response, in conjunction with pressuredependent and acceleration-dependent burning, is applied to the investigation of instabilityrelated behaviour in a small cylindrical-grain motor. Pertinent key factors, like the initial pressure disturbance magnitude and the propellant's net surface heat release, are evaluated with respect to their influence on the production of instability symptoms. Two traditional suppression techniques, axial transitions in grain geometry and inert particle loading, are in turn evaluated with respect to suppressing these axial instability symptoms. NOMENCLATURE INTRODUCTIONOver the last fifty years or so, there has been a number of research efforts directed towards understanding the physical mechanisms, or at least the surrounding factors, behind the appearance of symptoms associated with nonlinear axial combustion instability [1-2] in solid rocket motors (SRMs). Traditionally, these symptoms are a sustained axial pressure wave presence in the combustion chamber, sometimes accompanied by a substantial rise in the base chamber pressure [dc shift]. The motivation for these past and present studies was and is of course to bring this better understanding to bear in more precisely suppressing, if not eliminating, these symptoms. Studies of nonlinear axial combustion instability have ranged from numerous experimental test firing series on the one hand [3], and linear/nonlinear acoustic theory modelling on the other [2,[4][5][6]. Largely, the acoustic analysis produces frequency-based standing wave solutions for a given chamber geometry, but typically without some useful quantitative information. On occasion, researchers have employed a numerical modelling approach, to work towards a more comprehensive quantitative understanding of the physics involved [7][8]. The numerical model would typically produce a travelling wave solution to a limit pressure wave amplitude and a corresponding small or larger dc shift in chamber pressure, a time-based result evolving from an initial pulse disturbance introduced into the chamber flow. Available computational power and associated result turnaround times commonly forced some simplifications in the given numerical model. A comprehensive numerical model for simulation of nonlinear dynamic flow and combustion conditions is ultimately essential in the quest for the ability to predict and quantify axial combustion instability symptoms in SRMs. An effective model combines the ef...

Scale Effects on Solid Rocket Combustion Instability Behaviour

“…Figure 5 illustrates a segment of a simulated reference motor firing's head-end pressure-time profile, showing a sustained axial wave system after the initial 2-atm pulse disturbance is introduced. In this case (and for subsequent runs, in order to narrow the scope of the present paper), the effect of acceleration [5] on the combustion process has been nullified. The sustained pressure wave is not shock-fronted [5], and one can note the apparent absence of an appreciable dc shift (rise in base chamber pressure).…”

“…The effects of such factors as turbulence can be included through one or more additional equations that employ the information from the bulk flow properties arising from the solution of the above one-dimensional equations of motion. The principal differential equations themselves can be solved via a higher-order random-choice method (RCM) approach [3][4][5]9]. Given that the current investigation will not be incorporating particles within the flow (particle loading mass fraction a p ≈ 0%), for brevity, the particle-phase differential equations of motion are not presented here; the reader is referred to [8].…”

“…While some solid propellants can also exhibit a strong sensitivity to normal acceleration as relates to burning [5], this component will be left out of the present study, for brevity. The pressure-based burning component may be found through de St. Robert's empirical law:…”

“…On the numerical prediction side, as various component models evolve, say for transient burning rate or structural vibration, their incorporation into an overall internal ballistics simulation program allows for new motor firing simulations to take place, which in turn allows for updated comparisons to available experimental firing data, and a better understanding of the influence of various factors. Examples of pulsed motor firing simulations completed previously, at interim stages of earlier simulation model development, may be found in [3][4][5].…”

Numerical Evaluation of the Use of Aluminum Particles for Enhancing Solid Rocket Motor Combustion Stability

“…In the present investigation, an updated numerical model developed from previous SRM studies [7][8][9][10][11] is used in the prediction of the unsteady instability-related behaviour in a reference small cylindrical-grain motor. In conjunction, the internal ballistic simulation model will allow for an evaluation of the corresponding effectiveness of placing reactive spherical aluminum particles in the central chamber flow as a means of suppressing instability symptoms.…”