A short remark on Chien's variational principle of maximum power losses for viscous fluids

作者：Liu, H. Y.; Si, Na; He, Ji-Huan^*

来源：International Journal of Numerical Methods for Heat and Fluid Flow, 2016, 26(3-4): 694-697.

DOI：10.1108/HFF-09-2015-0368

• Variational theory
• Navier-Stokes equation
• Semi-inverse method
• Viscous flow

Purpose - The purpose of this paper is to point out a paradox in variational theory for viscous flows. Chien (1984) claimed that a variational principle of maximum power loses for viscous fluids was established, however, it violated the well-known Helmholtz's principle.
Design/methodology/approach - Restricted variables are introduced in the derivation, the first order and the second order of variation of the restricted variables are zero.
Findings - An approximate variational principle of minimum power loses is established, which agrees with the Helmholtz's principle, and the paradox is solved.
Research limitations/implications - This paper focusses on incompressible viscose flows, and the theory can be extended to compressible one and other viscose flows. It is still difficult to obtain a variational formulation for Navier-Stokes equations.
Practical implications - The variational principle of minimum power loses can be directly used for numerical methods and analytical analysis.
Originality/value - It is proved that Chien's variational principle is a minimum principle.

• 出版日期2016
• 单位中原工学院; 苏州大学