Convergence of Two Internal Mean Flow Solutions for Spinning Rocket Motors

Abstract

In this work, two mathematical procedures are used to derive the incompressible mean flow profile in a simulated solid rocket motor that is modeled as a spinning right-cylindrical porous tube. The first approach starts with the Navier–Stokes equations and leads to a large wall-injection Reynolds number approximation. The second begins with the inviscid Bragg–Hawthorne equation, where the variation of the stagnation head is taken to reproduce the classical Taylor–Culick flow approximation for nonspinning rockets. To permit swirl to develop, the injected fluid is introduced with a finite angular momentum that is prescribed by the spinning rate of the motor. The core singularity that naturally evolves in the inviscid formulation is overcome through the use of viscous matched-asymptotic expansions. The closed-form expressions emerging from both techniques are then compared and verified using finite volume simulations of the unabridged Navier–Stokes equations. Results from all three approaches are found to be in substantial agreement over a wide range of Reynolds numbers, thus helping to validate the asymptotic treatment of the core boundary-layer analysis pursued in this and similar studies. Additional flow features, such as the vorticity and pressure, are also described and compared to the nonspinning motor case.