Solution for Aircraft Anti-Icing System Simulation by a Modified Perturbation Method

Abstract

A solution of the surface temperature and the runback water mass flow rate distributions along the body contour for an electrothermal or a hot-air anti-icing system of an aircraft, when water droplets impinge on the surface, is obtained by a modified perturbation method. In the method, a small dimensionless parameter a that represents the ratio of the external convective heat transfer rate from the airfoil surface to the internal heating rate is used. Because of the high nonlinearity in the energy equation, obtaining a convergent solution by normal use of the perturbation method is virtually impossible. To improve the convergence properties of the solution, the calculation procedure is modified. The main idea behind the modification is splitting of the nonlinear term into linear and nonlinear terms and introducing a new variable e, by which a in each linear term is replaced. These modifications of the perturbation method help reduce the contribution of the nonlinear term, which drastically improves the convergence characteristics of the solution. The solutions agree well with the results obtained by the Runge-Kutta method and experimental and numerical results found in literature.