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 Re and the dimensionless wall regression ratio α 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 α. 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.


    Access

    Access via TIB

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls


    Contributors:

    Published in:

    Publication date :

    2017




    Type of media :

    Article (Journal)


    Type of material :

    Print


    Language :

    English



    Classification :

    BKL:    55.50 Luftfahrzeugtechnik / 55.60 Raumfahrttechnik / 55.60 / 50.93 / 55.50 / 50.93 Weltraumforschung
    Local classification TIB:    770/7040