Numerical simulations of slag accumulation in the aft end of the Titan solid rocket motor upgrade (SRMU) are described. These quasisteady, two-phase flow solutions at 0-, 30-, 55-, 80-, 110-, and 125-s burnback geometries involve a gas phase and an A1 2 O 3 liquid phase of a single droplet size, where four droplet sizes (10, 35, 60, and 100 fim) have been considered. The two-phase flow calculations are inviscid and rotational (Euler equations), with full momentum and energy coupling between the phases. Both phases are treated with an Eulerian approach. The stability of the AI 2 O 3 droplets with respect to breakup is shown not to affect our predictions. The capture rate as a function of time is determined from the solutions at the five burn times, which is then integrated over the total burn time to determine the total slag captured. It is found that slag capture starts at time zero and continues throughout the firing. Using a droplet size distribution from a recent experimental study produces a total slag accumulation of 2265 kg, which is in good agreement with the static test results. Also, predictions of the slag pool depth as a function of time show good agreement with real-time radiography measurements. Small changes in propellant grain design, such as the use of a short-lived inhibitor in the submerged nozzle region, only provide a small reduction in the total slag captured during the burn. Slag accumulation is unaffected by the g levels typical of an SRMU flight.
Nomenclature= total energy per unit volume for the gas, p/(y -1) 4-(i)p(u 2 4-v 2 ) e k = total energy per unit volume for the liquid droplet phase F, F k = flux variables defined by Eqs. (1) and (8) G, G k = flux variables defined by Eqs. (1) and (8) g = body force acceleration, in the z direction //, H k = source terms defined by Eqs. (1) and (8) K = propellant burn rate constant n = propellant burn rate exponent Pr = Prandtl number p = gas pressure /? ret = reference pressure Psurface = propellant surface pressure r = radial coordinate t = time T = gas temperature T k = liquid droplet temperature U, U k = conserved dependent variables defined by Eqs.(1) and (8) w, v = velocity components in the r, z directions u k , v k = liquid droplet velocity components in the r, z directions u n -velocity normal to the surface We = Weber number z = axial coordinate a = heat transfer coefficient of the liquid droplet y = gas specific heat ratio ju, = gas viscosity Presented as Paper 94-3287 at the AIAA/ASME/SAE/ASEE 30th
