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Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method

Published online by Cambridge University Press:  03 June 2015

Hua-Shu Dou  and
Boo Cheong Khoo
Hua-Shu Dou*
Affiliation:
Temasek Laboratories, National University of Singapore, 10 Kent Ridge Crescent, Singapore 117411, Singapore
Boo Cheong Khoo*
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore
*
Corresponding author. URL: http://serve.me.nus.edu.sg/khoobc/ Email: [email protected]Email: [email protected]
Email: [email protected]
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Abstract

The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function K (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function K for plane Couette flow is derived. The result indicates that K reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain. The critical value of K at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).

Keywords

47.20.-k47.15.Fe47.20.Ft47.20.Gv47.27.CnFlow instabilityturbulent transitionplane Couette flowenergy gradientenergy losscritical condition
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 2 , April 2011 , pp. 165 - 180
Copyright
Copyright © Global-Science Press 2011

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