Differential Prediction Method for Three-Dimensional Laminar and Turbulent Boundary Layers of Rotating Propeller Blades

摘要

A general mathematical formulation is given for the three dimensional boundary-layer flow on a rotating propeller blade. The basic equations are presented in a nonorthogonal coordinate system which rotates with the blade. Finite difference methods are used to develop a computer code for solving the laminar and turbulent boundary-layer equations. The Reynolds stress tensor is modeled by an algebraic eddy-viscosity formulation. In general, the equations are solved numerically using the standard Keller box method. However, regions of flow reversal across the boundary-layer are computed by the characteristics box method. A companion geometry computer code, developed to model propeller geometry characteristics, and an existing inviscid flow code for computing propeller blade pressures are combined with the boundary-layer computer code to form an efficient computation scheme. For a given potential-flow solution, a typical boundary-layer solution of 690 grid points requires 64 seconds CPU time on a CYBER 176 computer. Computed results are presented for several propeller blade geometries. The rotating segment solution compares well with analytical and experimental data. Predictions for a model propeller also compare favorably with experimental data and illustrate that two-dimensional theory may provide adequate predictions for applications where crossflow effects are not important. Geometry effects of warp and skew are shown to be small for the boundary-layer predictions on three model propellers.