Newton method on axisymmetric transonic flow and linearized 3D flow prediction

Abstract

An axisymmetric transonic viscous flow analysis and design method has been developed by applying stream-surface based Newton method. This method incorporates a linearized three-dimensional flow prediction capability, using linear perturbations of the axisymmetric solution. Euler equations are coupled with axisymmetric integral boundary equations with two-dimensional closure and transition models. Stream-surface based finite volume formulations allow efficiency and useful design features. An actuator disk is used to model the fan disk inside a powered nacelle. A stream-surface grid generation scheme using a panel method has been developed to provide an adequate initial grid. Comparisons are made to analytic solutions and wind tunnel experiments of nacelles, resulting in good agreements. The algorithm shows fast convergence, typically within 10 iterations. NOMENCLATURE AI, AI conservation cell vectors B~, B conservation cell vectors CD, Cf dissipation, friction coefficients CT shear stress coefficient enthalpy shape, kinematic shape factors cell indices iteration level perturbed residuals Mach number grid location, amplification factor conservation cell vector h H, Hk i,j k Lh,Lv M n,n N p q pressure streamwise speed 'Research Specialist, AIAA Member f Associate Professor, AIAA Fellow Copyright ©1998 American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Q vector of variables R vector of equations 5 conservation cell vector Ue boundary layer edge speed M Mach number Re Reynolds number T coupling terms from swirl velocity u, v boundary layer velocity components y radius 7 ratio of specific heats 6*, 6 displacement, momentum thickness TT, TT~ pressure on conservation cell surfaces p density T shear stress £, T] boudary layer coordinates Subscripts ( ) i ,2 cell indices ()e boundary layer edge ( ) h , v horizontal, vertical set ()t stagnation