Three-Dimensional and Unsteady Boundary- Layer Computations

Abstract

From an engineering point of view, several methods are relatively successful in calculating two-dimensional, incompressible, steady turbulent boundary layers on a smooth surface, although considerable work (both computation­ ally and experimentally) needs to be done for flows with separation. The most advanced calculation methods reproduce a few characteristics of the flow. In practice, the features of interest are the skin friction, the displacement thickness, (occasionally) the mean velocity profiles, and (rarely) the turbulent kinetic energy or the Reynolds stresses. This situation could be considered to be satisfactory; however, improvements are needed, and it should be recognized that the practical calculation methods include few physical inputs. Thus, their extensions to new problems require careful studies and extensive comparisons with experimental data. This is certainly the case for three-dimensional and unsteady boundary layers, which are discussed in this review. Indeed, these flows introduce a third dimension and therefore new parameters. In order to focus the discussion on a more precise objective, we examine here both the three-dimensional boundary layers that develop, for example, either on a wing or on a fuselage of an aircraft and the unsteady boundary layers that develop under the influence of an imposed unsteadiness (oscillating flow, for example). In both cases, the flow is assumed incompressible. Three main problems are discussed. The first is related to the numerical aspects. This includes the numerical scheme for use in solving the equations, the choice and construction of a coordinate system (especially for the three-