Field synergy principle for compressible laminar flow and the application for drag reduction in microchannel

Considering the density variation of compressible fluid, the field synergy principle for compressible laminar flow is presented based on the incompressible flow field synergy principle. The flow resistance is related to the synergy of velocity field and density logarithmic gradient field. Based on the principle of minimum mechanical energy dissipation, the compressible laminar flow field synergy equation is derived. The field synergy principle is verified by an example of the microchannel with expansion cross section, and the structure is optimized. The results indicate that the viscous dissipation value in the entire flow domain of the optimized structure can be reduced by 13.5%, and the angle between the velocity vector and the gradient field of logarithm of density increases. In fluid flows, it will reduce the fluid flow drag to decrease the synergy angle between the velocity vector and the gradient field of logarithm of density.