Numerical study of the unsteady flow in a simulated solid rocket motor

Smith, Thomas M.; Roach, Robert L.; Flandro, Gary A.

doi:10.2514/6.1993-112

Cited by 13 publications

(9 citation statements)

References 9 publications

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“…Similar results were obtained by Smith et al [17]. In both cases the acoustic disturbances are generated by imposed pressure variations along an axial location rather than from a prescribed time-dependent mass addition on the sidewall.…”

Section: Introductionsupporting

confidence: 85%

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

Hegab

2009

Computers & Fluids

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Section: Introductionsupporting

confidence: 85%

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

Hegab

2009

Computers & Fluids

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“…Both results demonstrate that for sufficiently large wall injection rates unsteady vorticity need not be confined to thin viscous acoustic boundary layers adjacent to the injecting wall, like those observed in the numerical studies of Baum and Levine 13 and Baum 14 and in the acoustic boundarylayer analysis of Flandro. 5 Flandro and Roach 15 and Smith et al 16 describe numerical simulations of the Brown et al 1 ' 2 experiments. Significant radial gradients in the axial velocity are seen about halfway out toward the centerline.…”

Section: Introductionmentioning

confidence: 98%

Unsteady vorticity generation and evolution in a model of a solid rocket motor

Kirkkopru

Kassoy

Zhao

1996

Journal of Propulsion and Power

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The cylindrical, axisymmetric Navier-Stokes equations are solved numerically to study the generation and evolution of vorticity in an injection-induced transient shear flow. An initially steady internal flowfield driven by constant sidewall injection is disturbed by positive transient sidewall injection, which simulates the unsteady mass input from propellant burning variations. The disturbance amplitude is as large as that of the steady sidewall injection to ensure that nonlinear effects influence the vorticity field evolution. Initial value solutions show that relatively intense vorticity is generated at the sidewall and eventually fills the cylinder with a rotational flow. Although the pressure response is essentially that found in acoustic stability theory, the axial and radial velocity components contain large local radial velocity gradients that cannot be predicted from acoustic theory alone.

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“…Traditionally, in combustion stability predictions, the oscillatory velocity is assumed to be irrotational and inviscid with an associated quasisteady boundary layer that is con ned to a thin viscous region near the transpiring surface. Computational predictions of the velocity eld by Roach et al, 4 and Vuillot and Avalon, 5 and Vuillot, 6 and cold-ow tests by Brown et al, 10 have shown that the rotational region in such ows, sometimes referred to as the acoustic boundary layer, is actually distributed over a signi cant portion of the chamber radius. Recent analytical and numerical predictions of the transient evolution of the velocity eld prescribed by harmonic endwall 11 and sidewall 12 disturbances have also indicated the important role played by the rotational component of the time-dependent velocity.…”

mentioning

confidence: 97%

Multiple-Scales Solution to the Acoustic Boundary Layer in Solid Rocket Motors

Majdalani

Moorhem

1997

Journal of Propulsion and Power

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The acoustic boundary-layer structure is investigated in a cylindrical tube where steady sidewall injection is imposed upon an oscillatory ow. Culick's steady, rotational, and inviscid solution is assumed for the mean ow. The time-dependent velocity is obtained by superimposing the acoustic (compressible, inviscid, irrotational) and the vortical (incompressible, viscous, rotational) velocity vectors. A multiplescales perturbation technique that utilizes proper scaling coordinates is applied to the axial momentum equation by retaining the viscous terms and ignoring the axial convection of vorticity. A closed-form expression for the time-dependent axial velocity is derived that agrees well with the corresponding numerical solution, cold-ow experimental data, and Flandro's near-wall analytic expression. A similarity parameter that controls the thickness of the rotational region is identi ed. The role of the Strouhal number in controlling the wavelength of rotational waves is established. An accurate assessment of the amplitude and phase relation between unsteady velocity and pressure components is obtained. Increasing viscosity is found to reduce the depth of penetration of the rotational region. Nomenclature a 0 = mean chamber speed of sound, m/s f = oscillation mode frequency, Hz k = dimensionless wave number or frequency, vR/a 0 L = internal tube length M b = blowing Mach number, V b/ a 0 P 0 = mean chamber pressure p = dimensionless pressure, p*/P 0 R = effective radius, volume/half of porous area, m Re = Reynolds number based on sound speed, a 0 R/n Re a = acoustic Reynolds number, k/d 2 = vR 2 /n = 2 2 R /d s r = dimensionless radial position, r*/R r 1 = radial scale, magni ed or compressed S p = penetration number, = 3 2 2 2 2 3 2 2 2 1 2 1St = Strouhal number, k/M b = vR/Vb t = dimensionless time, t*a 0/ R =t/k U = Culick's steady ow velocity vector, (U r , U z ) U r = Culick's steady radial velocity, 2r 2 1 sin u u = dimensionless velocity, u*/a0 u 9 z = acoustic velocity, sin(kz)exp(ikt) V b = injection velocity at the porous boundary, m/s Y = penetration control parameter, S p

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Numerical study of the unsteady flow in a simulated solid rocket motor

Cited by 13 publications

References 9 publications

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

Unsteady vorticity generation and evolution in a model of a solid rocket motor

Multiple-Scales Solution to the Acoustic Boundary Layer in Solid Rocket Motors

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