Internal ballistics modeling of high performance SRMs with coupled nozzle erosion characterization

The accurate prediction of the internal ballistics of high performance solid rocket motors represents a very challenging task, especially during motor design and development. A study is conducted with the purpose to enhance the prediction capabilities of the overall internal ballistics of full-scale SRMs, from ignition transient to motor burn-out. The presented approach is based on an unsteady quasi-one dimensional model of the internal flow field conditions of solid rocket motors, SPINBALL, coupled with a three-dimensional grain burning surface evolution model of the propellant surface and a full and predictive characterization of the nozzle throat erosion. The latter is made through an “a priori” characterization of the dependence upon pressure of the nozzle throat erosion rate, performed with an axi-symmetric Navier-Stokes solution of nozzle flow field, accounting for heterogeneous chemical reactions at the nozzle surface. The validation of the proposed approach is made for two different SRMs of the new European launcher VEGA: Zefiro 23 and Zefiro 9A, second and third solid stage. Results of the internal ballistics simulations indicate that a very good agreement with experimental data can be obtained using the same “a priori” standard hump curve for finocyl grain propellant and the same scale factor, within the classical range used in the open literature. A semi-empirical correlation for nozzle throat erosion is also proposed, exploiting the characterization of the nozzle throat erosion obtained for Zefiro 23 and Zefiro 9A. It is based on the main functional dependences of the phenomena, in a diffusion limited regime, upon pressure and presence of the main oxidizing species in the flowfield (as result of BATES experimental activities), modified in order to account also for nozzle scale and shape. The proposed functional correlation is promising, since it is found to fit the complete characterization, given by the full nozzle ablation model and hence, to be predictive for the nozzle erosion phenomena of the analyzed SRMs.