Arclength numerical continuation in free-boundary flow

作者：Cruceanu Stefan Gicu; Rapeanu Eleonora; Carabineanu Adrian^*

来源：Applied Mathematics and Computation, 2014, 230: 138-153.

DOI：10.1016/j.amc.2013.12.080

• Wake
• Integral equation
• Nonlinear solvers
• Bifurcation diagram
• Wind turbine

Using Helmholtz%26apos;s wake model, we reduce the study of the free boundary flow past an obstacle consisting of an arc of circle to the investigation of a Hammerstein nonlinear integral equation depending on a real parameter lambda. The papers dedicated to this problem investigated the case lambda %26gt; 0 which corresponds to a convex obstacle with respect to the incoming fluid. Herein, we apply for the first time in the literature the arclength continuation method for the case lambda %26lt; 0 corresponding to a concave arc of a circle. For lambda %26gt; 0 the existence and the uniqueness of the solution was demonstrated, but for lambda %26lt; 0, depending on its value compared to the one of a turning point, the integral equation has either no solution or two distinct solutions corresponding to two different obstacles. We numerically calculate the free lines, the velocity field and the stream lines. A diagram of the drag coefficient versus the arc measure for both convex and concave obstacles suggests us to draw some conclusions concerning the optimization of the blades of a vertical axis (Savonius) wind turbine.

• 出版日期2014-3-1