Energy dissipation analysis based on velocity gradient tensor decomposition

A velocity gradient tensor decomposition method based on a normal frame is introduced in this paper. The velocity gradient tensor is decomposed into a compression-stretching tensor, pure rotation tensor, and pure shear tensor. The analysis shows that both the strain rate tensor and vorticity tensor in Helmholtz velocity decomposition contain shear tensor components, and the total pure shear tensor is the combination of shear components in the two tensors. Based on this decomposition and the physical meaning of each tensor term, the energy dissipation of the channel flow with or without a pressure gradient and a turbine passage flow are analyzed. The results show that the energy dissipation is caused by shear deformation and expansion and contraction deformation of the motion fluid, and pure rotation does not cause energy dissipation. In particular, the pure shear is the primary factor of energy dissipation. Shear accounts for 99.9% of energy dissipation in the fully developed turbulence of zero-pressure gradient channel flow, 99% of the energy dissipation in the separated boundary layer flow is caused by the pure shear, and 81% of the energy dissipation in the turbine stage flow is caused by pure shear.