The generation and evolution of unsteady vorticity in a model of a solid rocket engine chamber

Zhao, Qingyun; Kassoy, D. R.

doi:10.2514/6.1994-779

Cited by 13 publications

(35 citation statements)

References 15 publications

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“…The observed axial variation in the radial temperature distribution is explained in terms of the acoustic-injected fluid interaction derived in the asymptotic analyses of Staab et al [9], Rempe et al [10] and Zhao et al [11,12]. Related ideas are used to show why the axial distribution of the temperature, temperature gradient, and vorticity is sensitive to the wave numbers of the axial variation of the injection velocity.…”

Section: Introductionmentioning

confidence: 93%

“…(1), Zhao et al [11] found the solution for the steady flow variables with axial variation injection velocity for the limit M ? 0 and d 2 /Re ?…”

Section: Steady Flowmentioning

confidence: 99%

“…The number and spacing of the grid points used defines the accuracy and resolution of the local variations of flow variables in the axial and transverse directions. In each case, the distribution is chosen to meet scaling needs suggested in the asymptotic analysis by Zhao et al [11]. The accuracy criterion for explicit schemes, introduced by Courant-Friedrichs-Lewy CFL (1969) and employed by MacCormack [21] to determine the size of the time step for calculations of Navier-Stokes equations, is satisfied at all interior mesh points.…”

Section: The Computational Approachmentioning

confidence: 99%

“…Secondly, several investigators developed a competitive linear theory to demonstrate that accurate descriptions of internal flow dynamics frequently require the presence of co-existing rotational and irrotational velocity fields (see for example, Flandro [13], Majdalani and Van Moorhem [14,15]). Finally, systematic nonlinear asymptotic modeling, valid for larger amplitude disturbances, shows formally that the basic velocity and pressure fields are decoupled from thermal processes (see for example, Staab et al [9], Zhao et al [11,12]). It follows that velocity and vorticity dynamics can be assessed without concern for temperature effects.…”

Section: Introductionmentioning

confidence: 98%

“…Staab et al [9], Rempe et al [10] and Zhao et al [11,12] employ asymptotic methods to demonstrate that unsteady addition of mass from the lateral boundaries of a cylinder is the immediate source of acoustic disturbances that propagate in the low axial Mach number (M), high Reynolds number (Re) mean flow. Their analytical results are used to prove that an inviscid and non-conducting interaction between the acoustic transients and the fluid injected from the sidewall causes transverse axial velocity gradients (vorticity) and transverse temperature gradients (heat transfer) to appear on the sidewalls.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Introductionmentioning

confidence: 93%

“…(1), Zhao et al [11] found the solution for the steady flow variables with axial variation injection velocity for the limit M ? 0 and d 2 /Re ?…”

Section: Steady Flowmentioning

confidence: 99%

Section: The Computational Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Acoustically generated vorticity in an internal flow

et al. 2000

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A mathematical model is formulated to describe the initiation and evolution of intense unsteady vorticity in a low Mach number (M), weakly viscous internal flow sustained by mass addition through the sidewall of a long, narrow cylinder. An O(M) axial acoustic velocity disturbance, generated by a prescribed harmonic transient endwall velocity, interacts with the basically inviscid rotational steady injected flow to generate time-dependent vorticity at the sidewall. The steady radial velocity component convects the vorticity into the flow. The axial velocity associated with the vorticity field varies across the cylinder radius and in particular has an instantaneous oscillatory spatial distribution with a characteristic wavelength O(M) smaller than the radius. Weak viscous effects cause the vorticity to diffuse on the small radial length scale as it is convected from the wall toward the axis. The magnitude of the transient vorticity field is larger by O(M−1) than that in the steady flow.An initial-boundary-value formulation is employed to find nonlinear unsteady solutions when a pressure node exists at the downstream exit of the cylinder. The complete velocity consists of a superposition of the steady flow, an acoustic (irrotational) field and the rotational component, all of the same magnitude.

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Three-dimensional flow in a cylinder with sidewall mass addition

Staab

Kassoy

2002

Physics of Fluids

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Three-dimensional, time-dependent, nonlinear flow dynamics within a cylinder with sidewall mass injection are investigated. A nonaxisymmetric transient injection velocity, prescribed along the sidewall boundary of a long, narrow, half-open cylinder, induces a low Mach number, high Reynolds number flow. The injection drives nearly planar axial acoustic disturbances, which interact with the injected fluid to produce the azimuthal component of vorticity on the sidewall in an inviscid manner. A smaller, but important azimuthally dependent transient disturbance, driven by the nonaxisymmetric injection disturbance leads to the axial component of vorticity on the cylinder sidewall. Both components of vorticity are shown to convect toward the center of the cylinder, diffuse radially, and convect downstream. Other results show that the axial component of vorticity produced along the sidewall is largest near the maximum of a mass source distribution in the azimuthal dimension. The amplitude of the axial vorticity component decreases significantly away from the injection surface and at other azimuthal locations. The analysis of these flow processes is based on the full three-dimensional Navier–Stokes equations. A formal multiple-scale asymptotic analysis, based on the behavior of the axial Mach number M→0, is used to derive reduced equations. It is shown that the primary rotational flow response is described by a nonlinear, convection-diffusion equation.

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The generation and evolution of unsteady vorticity in a model of a solid rocket engine chamber

Cited by 13 publications

References 15 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

Acoustically generated vorticity in an internal flow

Three-dimensional flow in a cylinder with sidewall mass addition

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