Sean R. Fischbach

Nonlinear Rocket Motor Stability Prediction: Limit Amplitude, Triggering, and Mean Pressure Shift

High-amplitude pressure oscillations in solid propellant rocket motor combustion chambers display nonlinear effects including: 1) limit cycle behavior in which the fluctuations may dwell for a considerable period of time near their peak amplitude, 2) elevated mean chamber pressure (DC shift), and 3) a triggering amplitude above which pulsing will cause an apparently stable system to transition to violent oscillations. Along with the obvious undesirable vibrations, these features constitute the most damaging impact of combustion instability on system reliability and structural integrity. The physical mechanisms behind these phenomena and their relationship to motor geometry and physical parameters must, therefore, be fully understood if instability is to be avoided in the design process, or if effective corrective measures must be devised during system development. Predictive algorithms now in use have limited ability to characterize the actual time evolution of the oscillations, and they do not supply the motor designer with information regarding peak amplitudes or the associated critical triggering amplitudes. A pivotal missing element is the ability to predict the mean pressure shift; clearly, the designer requires information regarding the maximum chamber pressure that might be experienced during motor operation. In this paper, a comprehensive nonlinear combustion instability model is described that supplies vital information. The central role played by steep-fronted waves is emphasized. The resulting algorithm provides both detailed physical models of nonlinear instability phenomena and the critically needed predictive capability. In particular, the true origin of the DC shift is revealed.

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

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 unstead...

Acoustic streaming in simplified liquid rocket engines with transverse mode oscillations

This study considers a simplified model of a liquid rocket engine in which uniform injection is imposed at the faceplate. The corresponding cylindrical chamber has a small length-to-diameter ratio with respect to solid and hybrid rockets. Given their low chamber aspect ratios, liquid thrust engines are known to experience severe tangential and radial oscillation modes more often than longitudinal ones. In order to model this behavior, tangential and radial waves are superimposed onto a basic mean-flow model that consists of a steady, uniform axial velocity throughout the chamber. Using perturbation tools, both potential and viscous flow equations are then linearized in the pressure wave amplitude and solved to the second order. The effects of the headwall Mach number are leveraged as well. While the potential flow analysis does not predict any acoustic streaming effects, the viscous solution carried out to the second order gives rise to steady secondary flow patterns near the headwall. These axisymmetric,...

Volume-to-Surface Transformations of Rocket Stability Integrals

This study reports a critical development in the widely used combustion stability algorithm used by propulsion industries as a predictive tool for the design of large combustors. It has been recently demonstrated that, by incorporating unsteady rotational sources and sinks in the acoustic energy assessment, a more precise formulation of the acoustic instability in rocket motors can be achieved. The new algorithm, when applied to the linear stability formulation, leads to ten growth rate terms. In this article, we convert these ten stability corrections from volumetric to surface integral form. We further convert them to an acoustic form that is directly amenable to implementation in the Standard Stability Prediction code. The reduction to surface form greatly facilitates the evaluation of individual stability growth rates as they become function of quantities distributed along the chamber’s control surface. This will preclude the need to carry out a rotational flow analysis inside the motor. Only surface quantities will be needed and these will be converted to acoustic form whenever possible using the no slip condition or other applicable response functions. Effectively, all needed information will be obtainable directly from the acoustic field. By precluding the need to evaluate the rotational field (which can be highly uncertain in arbitrary geometry), the evaluation of acoustic stability integrals is made possible in practical motors with variable grain perforation. In this article the conversion process is carefully detailed. The analysis entails acquiring and applying several vortico-acoustic and vector identities, the most notable of which being the Gaussian divergence theorem.