On the nonsteady flowfield in solid rocket motors

Glick, Robert L.; Renie, J.

doi:10.2514/6.1984-1475

Cited by 6 publications

(4 citation statements)

References 5 publications

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“…Considerable progress has been made in the last decade in understanding both the precise source of the vorticity and the resulting changes in the oscillatory flow. Analytical, 42,[47][48][49][50][51][52][53][54][55] numerical, [56][57][58][59][60][61] and experimental investigations [62][63][64] have demonstrated that rotational flow effects play an important role in the unsteady gas motions in solid rocket motors. Much effort has been directed to constructing the required corrections to the acoustic model.…”

Section: B Rotational Flow Effectsmentioning

confidence: 99%

Nonlinear rocket motor stability prediction: Limit amplitude, triggering, and mean pressure shift

2007

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High-amplitude pressure oscillations in solid propellant rocket motor combustion chambers display nonlinear effects including: ͑1͒ limit cycle behavior in which the fluctuations may dwell for a considerable period of time near their peak amplitude, ͑2͒ elevated mean chamber pressure ͑DC shift͒, and ͑3͒ 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 origin of the DC shift is revealed.

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Section: B Rotational Flow Effectsmentioning

confidence: 99%

Nonlinear rocket motor stability prediction: Limit amplitude, triggering, and mean pressure shift

2007

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“…Considerable progress has been made in the last decade in understanding both the precise source of the vorticity and the resulting changes in the oscillatory flow. Analytical, 48,[53][54][55][56][57][58][59][60] numerical, [61][62][63][64][65][66] and experimental investigations [67][68][69][70] have demonstrated that rotational flow effects play an important role in the unsteady gas motions in solid rocket motors. Much effort has been directed to constructing the required corrections to the acoustic model.…”

Section: B Rotational Flow Effectsmentioning

confidence: 99%

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

Flandro

Fischbach

Majdalani

et al. 2004

40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit

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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.

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“…The equation for the acoustic component (u ") is, to first order: du du" > dx (4) ff d_ dy (6) p>V"l <p> < (7) h <v>p" (5) du" v>~^-= dy d<u> )~a…”

Section: A Order Of Magnitude Analysis 19mentioning

confidence: 99%

“…Although the more general (~) averaging is used in the above notation, the only mean velocity component retained is i>, which is nearly equal to < v > in this study because of the approximately isothermal and isobaric conditions assumed. The pressure along the duct, p = <p > +p "(*»0» is specified by the one-dimensional standing wave solution p " = (7) where II ma is the maximum relative acoustic pressure amplitude and u ma = n ma # 0 /7. All calculations to be presented were performed at the velocity antinode of the first longitudinal mode.…”

Section: B Computational Analysismentioning

confidence: 99%

Turbularization of an acoustic boundary layer on a transpiring surface

Beddini

Roberts

1988

AIAA Journal

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Turbularization of an acoustic boundary layer (Stokes layer) on impermeable and permeable surfaces is analytically considered. The theoretical approach utilizes a second-order closure model of turbulence. Both an approximate, closed-form solution and a more comprehensive finite-difference solution of the time-dependent, parabolic, one-dimensional governing equations are obtained. For simple acoustic boundary layers on impermeable surfaces, both the approximate solution and the numerical results for the critical acoustic Mach number required for turbulent transition are qualitatively confirmed by experiment. The calculations for acoustic boundary layers with transpiration (injection) indicate a substantial reduction of the acoustic Mach number required for transition, up to a limiting injection velocity that is frequency dependent. The results may provide a mechanism for flow-related combustion instability in practical systems, particularly solid propellant rockets, since turbularization of the near-surface combustion zone could result at relatively low-acoustic Mach numbers. Nomenclaturea = sonic speed c p = specific heat at constant pressure / = frequency, Hz h = specific sensible enthalpy k = thermal conductivity k s = equivalent sand roughness height p = static pressure ___ q = turbulence intensity, (u ri u • ) I/2 q m = maximum value of q R = inner radius of a cylindrical duct Re c = axial-flow Reynolds number, p c ii c d/jji c Re s = injection Reynolds number, p s v s d/jJi s Re t = turbulence Reynolds number, pqA/p R u = universal gas constant t -time T = static temperature Uj = velocity vector (u, v, w) Xj = coordinate vector (x,r,z) x 0 = axial distance at which computational initial conditions are specified y = distance from surface 4> -characteristic length scale A = turbulence macrolength scale //, = viscosity v -kinematic viscosity p = density a =k/c o v = r = turbulence shear stress < > = time mean of variable Superscripts -= average of variable over turbulent fluctuations = turbulent fluctuating value of variable " = acoustic fluctuating value of variable

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On the nonsteady flowfield in solid rocket motors

Cited by 6 publications

References 5 publications

Nonlinear rocket motor stability prediction: Limit amplitude, triggering, and mean pressure shift

Nonlinear rocket motor stability prediction: Limit amplitude, triggering, and mean pressure shift

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

Turbularization of an acoustic boundary layer on a transpiring surface

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