Surface Curvature Effects on Three-Dimensional Blunt-Body Boundary Layers

Abstract

THE governing equations for laminar, transitional and/or turbulent, incompressible, three-dimensional boundary layers are solved numerically. The equations are developed in an orthogonal surface coordinate system and include surface curvature effects. Surface heat- and mass-transfer effects on the boundary-layer flowfield have also been included. The coordinates are generated numerically, whereas the inviscid flow is obtained from a general potential flow procedure. The only restrictions on body geometry are that it possess a blunt nose and a plane of symmetry. The boundary-layer equations, after being transformed into similarity type variables, are solved using the Krause implicit finite-difference scheme. Various test cases are presented to demonstrate the accuracy of the resulting computer program. Contents Theoretical Model Second-order boundary-layer theory including the effects of longitudinal and transverse curvature is quite well developed for the two-dimensional or axisymmetric case for both compressible and incompressible flow.1'2 These effects become important in situations where the boundary-layer thickness is small compared to a characteristic body length but may be of the same order of magnitude as the local longitudinal or transverse radius of curvature. Such situations can arise near stagnation points, near pointed noses or tails, and over very slender bodies of revolution. The current work develops a second-order theory for the three-dimensional incompressible boundary-layer flows. The geometries considered in the current work are arbitrary blunt-nosed bodies having a plane of symmetry. Pressure distributions about these shapes are obtained from either the axisymmetric or three-dimensional Douglas-Neumann codes.3-4 The coordinate system used for the boundary-layer calculations is the one developed recently by Blottner and Ellis.5 To remove the stagnation point singularity, this coordinate system uses the inviscid stagnation point as its origin. The details of the coordinate system are shown in Fig. 1. The coordinate system and its associated metric coefficients are generated numerically from either analytic or discrete data of the form r = r(x,(f)).