Kalle Kaups

A general method for calculating three-dimensional laminar and turbulent boundary layers on ship hulls

Abstract : This report describes the progress made during the past year towards the development of a general method for computing three-dimensional incompressible laminar and turbulent boundary layers on ship hulls. The method employs an implicit two-point finite-difference method and an algebraic eddy-viscosity formulation. During the past year the efforts concentrated on the choice of an appropriate coordinate system; the calculation of the geometric parameters of this coordinate system; the numerical solution of the governing equation of the orthogonal curvilinear system; and obtaining preliminary results for simple ship forms. Further studies are in progress and will be reported in a forthcoming report.

Separation and Reattachment near the Leading Edge of a Thin Wing

An interactive boundary-layer procedure based on a quasi-three-dimensional approximation is used to calculate separation and reattachment near the leading-edge of a thin wing. Results for a given sweep angle show that, as in two-dimensional flows, reverse flow solutions exist only for a limited range of angles of attack above the critical angle at which the non-interactive boundary layer separates. The solutions for the upper branch behave in the same manner as those predicted by the triple-deck theory for marginal separation in two-dimensional flows. The existence of solutions for the lower branch remains to be investigated.

A method for removing the coordinate singularity on bodies with blunt rounded noses at incidence

Abstract A general method for calculating the boundary-layer development in the stagnation region of bodies with blunt rounded noses at incidence and with planes of symmetry is investigated. The three-dimensional equations are expressed in a nonorthogonal body-oriented coordinate system and appropriate transformations are devised for the line of symmetry equations to remove the singularity appearing in the metric coefficients and geodesic curvatures. A novel procedure based on a quasi-three-dimensional form of the equations and the characteristic box scheme is used to compute the initial conditions on a coordinate line off the line of symmetry. Sample calculations are reported on the line of symmetry for three shapes which include one typical of those found on ships with bulbous bows. Results are also presented for the nose region of a prolate spheroid at incidence and the solutions are compared with the previous solutions of Cebeci, Khattab and Stewartson. The results demonstrate that the method, with its essential transformations and solution procedures, represents the boundary-layer development accurately and can be used for axisymmetric and nonaxisymmetric bodies with blunt rounded noses.

Interactive boundary-layer calculations of a transonic wing flow

Results obtained from iterative solutions of inviscid and boundary-layer equations are presented and compared with experimental values. The calculated results were obtained with an Euler code and a transonic potential code in order to furnish solutions for the inviscid flow; they were interacted with solutions of two-dimensional boundary-layer equations having a strip-theory approximation. Euler code results are found to be in better agreement with the experimental data than with the full potential code, especially in the presence of shock waves, (with the sole exception of the near-tip region).