Convergence of Two Internal Mean Flow Solutions for Spinning Rocket Motors

Cecil, Orie M.; Majdalani, Joseph

doi:10.2514/1.j058620

Cited by 5 publications

References 31 publications

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On the compressible biglobal stability of the mean flow motion in porous tubes

Majdalani

kumar

Akiki³

2021

Physics of Fluids

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In this work, a compressible biglobal stability approach is used to investigate the growth characteristics of hydrodynamic and vorticoacoustic waves in porous tubes with uniform wall injection. The retention of compressibility effects enables us to construct a physics-based formulation that is capable of predicting both hydrodynamic and vorticoacoustic wave motions simultaneously with no need for mode decomposition. At first, we show that, in the absence of a mean flow, the stability framework reproduces traditional Helmholtz frequencies and modal shapes. This confirms the embedment of the wave equation within the compressible Navier–Stokes framework. We then proceed to simulate the idealized motion in solid rocket motors, often modeled as porous tubes, where a mean flow expression is available. Specifically, using the compressible Taylor–Culick profile as a base flow, our solver produces a comprehensive frequency spectrum that returns both hydrodynamic and vorticoacoustic modes in one swoop with the added benefit of pinpointing the flow-induced longitudinal, radial, and mixed frequencies at user-prescribed tangential modes. Moreover, we find that increasing the flow Mach number leads to a slight reduction in the vorticoacoustic frequencies relative to their strictly acoustic counterparts. Similar results are obtained while increasing the Reynolds number and aspect ratio, thus affirming the origin of frequency shifts often observed in motor firings. Finally, the vorticoacoustic velocity fluctuations are shown to resemble those obtained asymptotically. Particularly, their depths of penetration appear to be controlled by the penetration number, a dimensionless parameter that combines the effects of sidewall injection, oscillatory frequency, viscosity, and chamber radius.

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On the compressible biglobal stability of the mean flow motion in porous tubes

Majdalani

kumar

Akiki³

2021

Physics of Fluids

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Solid rocket motor internal ballistics using an enhanced surface-vorticity panel technique

et al. 2021

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This work explores the use of surface-mesh flow solvers to model solid rocket internal ballistics with arbitrary grain geometry. Specifically, a surface-vorticity approach, originally intended for external flow applications, is adapted for internal flow analysis using boundary conditions that are suitable for solid rocket motors. In this study, an enhanced panel code is shown to be capable of resolving internal rocket flowfields with a striking level of fidelity and with such a degree of computational efficiency to make it valuable in the conceptual and preliminary design of rocket motors. In this process, the vortex paneling approach embodied within FlightStream® is refined using boundary conditions appropriate for solid rocket rotational flows. The simulation results are then compared to existing analytical solutions for cylindrical and planar chamber configurations exhibiting small taper angles and uniform headwall injection. For a more realistic validation case, the space shuttle's reusable solid rocket motor (RSRM) is examined. Guided by the analytical models, simple rotational and compressibility corrections are incorporated into the solver, and the results are subsequently compared to two other computational models and experimental measurements gathered from qualification motors. For the basic configurations, our results are shown to agree well with theoretical predictions. For the RSRM case, the corrected solution agrees well with the validation data in the first half of the motor; however, it becomes less robust in the aft region unless a recirculation zone boundary patch is applied; the latter approximates the added vorticity introduced by intersegmental gaps and the submerged nozzle effects.

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On steady rotational high speed flows: The swirling compressible Trkalian profile with headwall injection

Cecil,

Little,

Majdalani

2023

Physics of Fluids

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This work considers a uniquely configured swirling motion that develops inside a porous tube due to sidewall injection. The bulk fluid motion is modeled as a steady inviscid Trkalian flow field with a swirl-velocity component that increases linearly along the axis of the chamber. The underlying procedure consists of solving the compressible Bragg–Hawthorne equation using a Rayleigh–Janzen expansion that produces a closed-form approximation for the stream function. Based on the latter, most remaining flow attributes may be readily inferred. Results are then compared to their counterparts obtained using a strictly incompressible Trkalian motion. They are also benchmarked against available compressible solutions in an effort to characterize the dilatational effects caused by flow acceleration in long chambers or chambers with sufficiently large sidewall injection. In addition to the stream function, the velocity, pressure, temperature, and density are evaluated over a range of physical parameters. Finally, the distortions affecting the velocity profiles are characterized and shown to result in a blunter motion near the center and a steeper curvature near the sidewall as a consequence of high-speed flow. In comparison with a non-swirling complex-lamellar solution, we find the Trkalian motion to be generally faster and therefore capable of reaching sonic conditions in a shorter distance from the headwall.

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Convergence of Two Internal Mean Flow Solutions for Spinning Rocket Motors

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Cited by 5 publications

References 31 publications

On the compressible biglobal stability of the mean flow motion in porous tubes

On the compressible biglobal stability of the mean flow motion in porous tubes

Solid rocket motor internal ballistics using an enhanced surface-vorticity panel technique

On steady rotational high speed flows: The swirling compressible Trkalian profile with headwall injection

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