Shape Optimization of an abrupt contraction using numerical streamlining

Document Type: Research Paper

Authors

Department of Civil Engineering, Shahrood University of Technology, Shahrood, Iran

Abstract

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.

Keywords


  1. J. H. Herlock and J. D. Denton, "A review of some early design practice using computational fluid dynamics and a current perspective," Journal of Turbomachinery, vol. 127, pp. 5-13, January 2005.
  2. E. Lund, H. Moller and L. A. Jakobsen, "Shape design optimization of stationary fluid-structure interaction problems with larg displacements and turbulence," Structural and Multidisciplinary Optimization, vol. 25, pp. 283-392, 2003.
  3. R. Amirante, L. A. Catalano, A. Dadone and V. S. E. Daloiso, "Design optimization of the intake of a small-scale turbojet engine," Computer Modeling in Engineering and Sciences, vol. 18, pp. 17-30, 2007.
  4. L. M. Ferro, L. M. Gato and A. F. Falcao, "Design and experimental validation of the inlet guide vane system of a mini hydraulic bulb-turbine," Renewable Energy, vol. 35, pp. 1920-1928, 2009.
  5. J. Takachi Tomita and J. R. Barbosa, "The use and comparison of avialabe design tools for a 3-stage axial-flow compressor: meanline, streamline curvature and cfd," in 20th International congress of mechanical engineering, Gramado, 2009.
  6. V. Prasad, V. K. Gahlot and P. Krishnamachar, "CFD approach for design optimization and validation for axial flow hydraulic turbine," Indian Journal of Engineering and Material Sciences, vol. 16, pp. 229-236, August 2009.
  7. V. Sharma and O. PrakashShukla, "Design and development of clamping and ejection systems for mould used on gravity die casting machine," International Journal of Engineering and Technology, vol. 2, no. 10, pp. 890-897, 2013.
  8. L. Junhong and T. Junliang, "Streamlining of bridge piers as scour countermeasures: optimization of cross section," in Transport Research Board 94th Annual Meeting, Washington, 2015.
  9. K. P. Kundu and I. M. Cohen, Fluid mechanics, 4th ed., Burlington, Massachusetts: Academic Press, 2010.
  10. K. K. Hoffmann and S. T. Chiang, Computaional fluid dynamics, 4th ed., vol. 1, Wichita, Kansas: Engineering Education System, 2000.
  11. J. d. Anderson, Computational fluid dynamics; the basics with applications, 1st ed., New York: McGraw-Hill Education, 1995.