The cylindrical solid propellant grain of the Solid Propellant Rocket Engine (Fig.1) is tested for the withstanding to high temperature. The hot air flows through the inner channel (grain port). The outer cylindrical surface of the grain is completely insulated. The tips of the grain are maintained at the constant temperatures T1 and T2 (Fig.2). Spontaneous steady-state chemical exothermic and endothermic reactions proceed inside the grain which could be treated as a sources and sinks of energy (q) in 2 symmetrical points “A”, and 2 symmetrical points “B” as shown on the Diagram. Each point “A” generates the amount of heat of 350000 w/m3. At the same time each point “B” consumes the energy of 100000 w/m3.
1. Compute the steady-state temperature distribution in the grain cross section assuming the unit depth (neglect the cylindrical shape), using Gauss-Seidel method or method of matrix inversion. Converging criterion for nodal temperatures is: epsilon = 0.5 Degrees. Since grain is symmetrical consider a half of the grain.
2. Reduce the grid by factor 2, and determine again the corresponding nodal temperatures.
3. Determine the ability of the solid grain to withstand high temperatures if the temperature of the solid propellant decomposition is 950 K.
