Computation of three-dimensional boundary layers on fuselages

Abstract

A new approach is developed to construct boundary-layer coordinates, and to handle metric properties, transformations, and so forth on realistic configurations. The approach, which employs tensorial concepts, is discussed in its major steps. Results of boundary-laye r computations on a helicopter body, a car body, and on a supersonic fighter nose found with the integral method of COUSTEIX are then used to show the potential of the approach. Special attention is given to the interpretation of the boundary-layer results with regard to possible separation patterns. The results may be used in order to model separated flow. ETHODS for the computation of laminar or turbulent three-dimensional boundary layers have been available for several years. Comparisons of integral and finite- difference methods, as well as applications to test cases organized for instance by the EUROVISC-Working Party on Three-Dimensional Shear Layers,1'2 have established an acceptable level of confidence for applications in design aerodynamics. Boundary-layer computations on simple wing geometries are made routinely today. The computation of boundary layers on general configurations, especially fuselage con- figurations, has been hampered because of the problems connected with the creation of boundary-laye r coordinates on the surfaces of such configurations. Recently, means have been developed for the definition of general, nonorthogonal, curvilinear boundary-layer coordinates,3'4 so that boundary- layer theory can now be applied in design aerodynamics to flows on rather complicated shapes. In the present paper a brief description is given of some of the concepts obtained in Ref. 3 with regard to boundary-layer problems on fuselages. Results of boundary-laye r studies on a helicopter fuselage, a car body, and on a supersonic fighter nose are discussed in order to show the value of the approach. Because three-dimensional boundary-layer separation is difficult to detect in computations, some ad hoc criteria are applied: \T - minimum criterion,5 convergence of skin- friction lines, and bulging of boundary-laye r thickness and displacement-thickness contours.6 Special attention is given to the interpretation of the boundary-layer results with regard to possible separation patterns, which may be used in order to model separated flow. The above separation criteria, together with topological laws and details of the skin-friction distribution, allow one in many cases to sketch the skin- friction line topology beyond the region where boundary- layer results were found; that is, the separation region. The boundary-layer method used for the studies is the integral method of COUSTEIX 7 in the form of COUSTEIX- AUPOIX. In this method a mixing length model is used together with similarity solutions to find families of both main-flow and cross-flow profiles. The continuity equation is applied as an entrainment equation. The surface is assumed to be insulated. The method is formulated for arbitrary boundary-layer coordinates and can be applied to flows with