Shape Optimization of an abrupt contraction using numerical streamlining

This research was conducted to find a reliable technique to shape an abrupt contraction for minimizing the energy loss. The method may find broader applications in design of variety of transitional cross-sections in hydraulic structures. The streamlines in a 2-D contraction were calculated through solving the potential flow equations in rectangular and curvilinear coordinates. The natural cubic spline equations were applied to approximate the shape of streamlines. The streamlines close to the solid boundary, usually those that represent 5 and 95 percent of the discharge, were repeatedly mapped onto the solid boundary in a trial and error procedure until a negligible difference between two consecutive shapes was achieved. This procedure was applied through a code developed in C++, namely Streamlining Program Code or SPC. The initial and final shapes were used to validate SPC by the help of a robust CFD software, OpenFOAM. In a 2-D contraction with contraction ratio of 5, entrance velocity of 1 m/s and outlet pressure of atmosphere (P = 0 pa), the maximum spatial difference between the stream lines found by the code and OpenFOAM was limited to 2.74% that occurred in the entrance of the contraction. Finally, according to the validation, the streamlining technique and the code could successfully applied to shape optimization of hydraulic structures.