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

Abstract

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.

Non-normality and nonlinearity in thermoacoustic instabilities

“…[11][12][13][14][15] An important conclusion of these studies is that systems that have linear heat release rate and nonlinear gas dynamics from first to third order do not exhibit subcritical bifurcations. 16 As well as in the above references, nonlinear heat release has been examined by Refs.…”

Large eddy simulations and experiments of nonlinear flow interactions in hybrid rocket combustion

“…Flandro et al [5] also have demonstrated a predictive algorithm for DCshift based on the comprehensive nonlinear combustion instability models. Their analysis includes very complicated nonlinear models such as steep-fronted, shock pressure waves, e¨ects of irrotational §ow interactions, combustion coupling effects, and pressure coupling with the oscillatory §ow ¦eld.…”

Integrated Vehicle Health Management for Solid Rocket Motors

“…local burning-through of the rocket case; (iii) propellant cracking; (iv) overpressure and breakage of the case induced by nozzle blocking or bore choking. The combustion instabilities were studied in detail in the classical papers of (Culick & Yang, 1992;Culick, 1996) and (Flandro et al, 2004). Bore choking phenomenon due to radial deformation of the propellant grain near booster joint segments was studied numerically in (Dick et al, 2005;Isaac & Iverson, 2003;Wang et al, 2005) and observed in primary construction of the Titan IV (see the report, Wilson at al., 1992).…”

“…The FD&P system can be developed using the fact that many fault modes of the SRMs have unique dynamical features in the time-traces of gas pressure, accelerometer data, and dynamics of nozzle gimbal angle. Indeed, analysis shows that many fault modes leading to SRMs failures, including combustion instabilities (Culick,1974;Culick & Yang, 1992;Culick,1996;Flandro et al, 2004), bore choking (Dick et al, 2005;Isaac & Iverson, 2003;Wang et al, 2005), propellant cracking, nozzle blocking, and case breach (Rogers, 1986), have unique dynamical features in the time-traces of pressure and thrust. Ideally, the corresponding expert knowledge could be incorporated into on-board FD&P within a general Bayesian inferential framework allowing for faster and more reliable identification of the off-nominal regimes of SRMs operation in real time.…”