Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (5): 645-662.doi: https://doi.org/10.1007/s10483-011-1446-6

• Articles • 上一篇    下一篇

Turbulent flow in converging nozzles, part one:boundary layer solution

 R. MADDAHIAN, B. FARHANIEH, B. FIROOZABADI   

  1. Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology, P. O. Box 11365-9567, Tehran, Iran
  • 收稿日期:2010-06-11 修回日期:2011-02-21 出版日期:2011-04-27 发布日期:2011-05-01

Turbulent flow in converging nozzles, part one:boundary layer solution

 R. MADDAHIAN, B. FARHANIEH, B. FIROOZABADI   

  1. Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology, P. O. Box 11365-9567, Tehran, Iran
  • Received:2010-06-11 Revised:2011-02-21 Online:2011-04-27 Published:2011-05-01

摘要: The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.

Abstract: The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.

中图分类号: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals