Numerical Solutions of Turbulent Models for Flow over a Flat Plate with Angle of Attack

摘要

Numerical solutions of the two-dimensional boundary layer equations were developed as applied to flow over a flat plate at various angles of attack. Three methods of approach were examined. An integral solution was constructed for laminar and turbulent flow, as well as finite difference solutions for zeroth- and first-order turbulence models. The models also account for buoyancy effects. A three part mixing length model was employed in the zeroth-order model, and an additional turbulent kinetic energy equation was utilized for the first-order model. The computational method utilized Patankar-Spalding coordinates and differs from other methods in that no matching procedure is required for the inner and outer flow regions. The Falkner-Skan velocity profile is applied as an edge boundary condition while variable wall temperature conditions can be imposed. The effects of freestream velocity and angle of attack on skin friction and heat transfer were established, and the velocity and temperature fields were determined. Results of the zeroth-order solution are in excellent agreement with the Colburn equation and several other data sources. These solutions provide correlations in terms of Nusselt number and skin friction coefficient versus local Reynolds number which can be used for estimating heat transfer and wind loadings on a flat plate. Results generated are especially useful in predicting the performance of solar system designs. (ERA citation 10:027286)