THE EFFECT OF COMBUSTION GAS FLOW ON THE ROTATIONAL DYNAMICS OF A SPINNING SOLID FUEL ROCKET (THRUST DAMPING)

The flow of combustion gases exerts a moment on a spinning solid fuel rocket. If the details of the internal combustion gas flow are known, accurate moment calculations may be obtained by means of a computationally expensive numerical volume integral. This internal gas flow model, however, is seldom available and represents a formidable problem in its own right. An alternative method developed here describes the moment induced by the combustion gas flow in terms of the angular momentum flux through a control volume. For steady flow, the resulting theory provides equations which accurately describe both the lateral and axial components of the induced moment and do not involve the internal gas flow. The moment induced by the steady flow can be computed with no knowledge of the flow details within the combustion chamber. Computation of the lateral steady moment (jet damping) requires only the mass flow rates at the burning surface and at the nozzle exit. The axial steady moment requires, in addition, one component of the combustion gas velocity at the nozzle exit.; Approximate equations describing the lateral moment induced by the steady combustion gas flow have been available for over 40 years. These classical jet damping equations can be significantly in error when applied to the solid fuel motor geometries commonly in use today. Utilizing the theory described above, modern jet damping equations are derived which are accurate for a variety of realistic combustion chamber shapes and rocket geometries.; For completeness, the moment induced by the unsteady flow is derived utilizing the angular momentum flux method. Much of the advantage of the method is lost, however, since internal flow details and a volume integral are required.; General rigid body dynamic models are developed for both the steady and unsteady moment cases, followed by an example simulation of a STAR 48 rocket motor and vehicle dynamics.