The mean gaseous motion in solid rocket motors has been traditionally described using an inviscid solution in a porous tube of fixed radius and uniform wall injection. This model, usually referred to as the Taylor–Culick profile, consists of a rotational solution that captures the bulk gaseous motion in a frictionless rocket chamber. In practice, however, the port radius increases as the propellant burns, thus leading to time-dependent effects on the mean flow. This work considers the related problem in the context of viscous motion in a porous tube and allows the radius to be time dependent. By implementing a similarity transformation in space and time, the incompressible Navier–Stokes equations are first reduced to a nonlinear fourth-order ordinary differential equation with four boundary conditions. This equation is then solved both numerically and asymptotically, using the injection Reynolds number and the dimensionless wall regression ratio as primary and secondary perturbation parameters. In this manner, closed-form analytical solutions are obtained for both large and small Reynolds number with small-to-moderate . The resulting approximations are then compared with the numerical solution obtained for an equivalent third-order ordinary differential equation in which both shooting and the irregular limit that affects the fourth-order formulation are circumvented. This code is found to be capable of producing the stable solutions for this problem over a wide range of Reynolds numbers and wall regression ratios.
Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls
AIAA Journal ; 55 , 11 ; 3868-3880
01.11.2017
Aufsatz (Konferenz) , Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
ERRATUM - Higher Mean-Flow Approximation for a Solid Rocket Motor with Radially Regressing Walls
Online Contents | 2009
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