Analysis and simulation of new approximation equations for boundary-layer flow on curved surfaces

An accurate and computationally efficent simulation of viscous flow fields exhibiting streamline curvature effects is important for the basic understanding and optimal design of a variety of mechanical systems. Examples include flow part airfoils, marine crafts, and automobiles or flow in diffusors and curved ducts. In this paper a new set of second-order boundary-layer equations is derived for steady incompressible two-dimensional or axisymmetric flow in regions where the streamlines stay approximately parallel to the curved surface. The performances of the new approximation equations and commonly used second-order boundary-layer equations are evaluated in two case studies. First, in a well-defined computer experiment, results from the two different sets of approximation equations are compared with a solution of the full Navier—Stokes equations for laminar flow past a representative body with longitudinal curvature. Then, turbulent flow versions of the new and traditionally used second-order boundary-layer equations are compared with experimental data sets for a representative axisymmetric body with strong longitudinal and transverse curvatures.