Stability and Accuracy of Power-series Method Applied to Transpiration Cooling Problems

Abstract

ABSTRACT The power-series method, i.e., a finite analytic approach based on power-series expansion, was applied to transpiration cooling problems, and the stability and accuracy of the method were evaluated. Stability analysis using von Neumann's method showed that the power-series method was stable for transpiration-cooling problems on the condition that Δx ≥ gΔt, where g is a mass flow rate parameter. The solutions obtained with the power-series method for typical problems were compared with those obtained with the fully implicit finite-difference method. The comparisons revealed that the power-series method yielded more accurate solutions for problems with Robin and Neumann boundary conditions, but less accurate solutions for problems with Robin and Dirichlet boundary conditions. For problems with Robin and Robin boundary conditions, the accuracy of the power-series method depended on the value of the mass flow rate parameter g.