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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (6): 679-686.doi: https://doi.org/10.1007/s10483-012-1579-7

• Articles •     Next Articles

Applications of parabolized stability equation for predicting transition position in boundary layers

Jia LI, Ji-sheng LUO   

  1. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China
  • Received:2011-07-20 Revised:2012-03-19 Online:2012-06-10 Published:2012-06-10
  • Contact: Ji-sheng LUO E-mail:jsluo@tju.edu.cn
  • Supported by:

    Project supported by the National Basic Research Program of China (No. 2009CB724103)

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Abstract: The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional (2D) wave and two three-dimensional (3D) waves. The parabolized stability equation (PSE) is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation.

2010 MSC Number: 

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