8 - Differential Methods with Algebraic Turbulence Models

Abstract

Differential methods are based on the solution of the boundary-layer equations in their partial-differential equation form. They vary depending on the numerical method used to solve the equations, and the turbulence model employed to model the Reynolds stresses. There are several numerical methods for solving the boundary-layer equations in differential form. The Crank–Nicolson and Keller's box methods are the most convenient ones. A modification of the two-dimensional eddy-viscosity distribution for thick axisymmetric boundary layers improves the calculations. The solution of the boundary-layer equations for laminar and turbulent external flows with prescribed velocity distribution is sometimes referred to as the standard problem or direct problem. The boundary-layer equations are not singular at separation, if the external velocity or pressure is computed as part of the solution. This procedure is known as the inverse problem and has been extensively used for airfoil flows. In general, two procedures have been pursued. Unlike for single element and wing-flap configurations, stall can occur without flow separation on the body and may be caused due to a sudden increase of the wake thickness. This reduces the circulation on the entire configuration.