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Research Papers: Fundamental Issues and Canonical Flows

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

[+] Author and Article Information
Joseph Majdalani

Mechanical, Aerospace and Biomedical Engineering Department, University of Tennessee Space Institute, Tullahoma, TN 37388maji@utsi.edu

Michel Akiki

Mechanical, Aerospace and Biomedical Engineering Department, University of Tennessee Space Institute, Tullahoma, TN 37388

J. Fluids Eng 132(10), 101202 (Oct 12, 2010) (7 pages) doi:10.1115/1.4002397 History: Received May 02, 2009; Revised August 16, 2010; Published October 12, 2010; Online October 12, 2010

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 4

Rotational streamlines shown for two increasing head end injection parameters. The inset in part (c) corresponds to a magnified section of part (b) illustrating the normal sidewall injection feature.

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Figure 5

Description of (a) axial and (b) radial velocities in addition to (c) vorticity and (d) pressure drop at the chamber’s head end. Both axial velocity and vorticity are shown at a fixed axial position.

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Figure 6

Description of (a) the main characteristic function F along with the corresponding (b) axial and (c) radial velocities. Broken lines depict the flow where ε=0.02, 0.1 and 0.2 whereas solid lines correspond to the inviscid flow field.

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Figure 7

Comparison between the present solution and those obtained by Yuan and Finkelstein (33) and Terrill and Thomas (34)

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Figure 3

Sketch of the rotational full-length hybrid model depicting mass addition along both sidewall and endwall boundaries. Here the oxidizer injection at the head end corresponds to a sinusoidal profile.

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Figure 2

Decreasing fuel concentration zones above solid surface during hybrid grain pyrolysis

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Figure 1

Schematic of the circular-port hybrid rocket

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