Analytical Models for Hybrid Rockets

doi:10.2514/5.9781600866876.0207.0246

Cited by 6 publications

References 74 publications

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On the compressible Hart-McClure and Sellars mean flow motions

2012

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We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flow assuming uniform injection of a calorically perfect gas in a porous, right-cylindrical chamber. This equation is expanded to order M 4 w using a Rayleigh-Janzen sequence in powers of M 2 w , where M w is the wall Mach number. At leading order, we readily recover the original Hart-McClure profile and, at M 2 w , a closed-form representation of the compressible correction. By way of confirmation, the same solution is reconstructed using a novel application of the vorticity-streamfunction technique. In view of the favorable convergence properties of the Rayleigh-Janzen expansion, the resulting approximation can be relied upon from the headwall down to the sonic point and slightly beyond in a long porous tube or nozzleless chamber. As a windfall, the compressible Sellars motion that arises in the reverse flow problem driven by wall suction is deduced. Based on the simple closed-form expressions that prescribe this motion, the principal flow attributes are quantified parametrically and compared to existing incompressible and one-dimensional theories. In this effort, the local Mach number and pressure are calculated and shown to provide an improved formulation when gauged against one-dimensional theory. Our results are also compared to the two-dimensional axisymmetric solution obtained by Majdalani ["On steady rotational high speed flows: The compressible Taylor-Culick profile," Proc. R. Soc. London, Ser. A 463, 131-162 (2007)]. After rescaling the axial coordinate by the critical length L s , a parametrically-free form is obtained that is essentially independent of the Mach number. This behavior is verified analytically, thus confirming Majdalani's geometric similarity with respect to the critical distance. A secondary verification by computational fluid dynamics is also undertaken. When compared to existing rotational models, the compressible Hart-McClure plug-flow requires, as it should, a slightly longer distance to reach the speed of sound at the centerline. With this model, however, not only the centerline but the entire cross-section becomes fully choked.

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On the compressible Hart-McClure and Sellars mean flow motions

2012

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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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Energy Steepened States of the Taylor-Culick Profile

Majdalani¹,

Saad²

2007

43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference &Amp;amp; Exhibit

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Analytical Models for Hybrid Rockets

Cited by 6 publications

References 74 publications

On the compressible Hart-McClure and Sellars mean flow motions

On the compressible Hart-McClure and Sellars mean flow motions

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

Energy Steepened States of the Taylor-Culick Profile

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