Direct Numerical Simulation Of Spatial Smooth Pipe Flow Transition

The present work is carried out by direct numerical simulation (DNS), the non-linear Navier-Stokes equation is formulated in terms of spectral method with fringe method. The objective of present work is to explore the spatial and temporal evolution of pipe flow with the disturbance imposed on the pipe wall in the form of periodic suction and blowing (PSB). The Reynolds number of the flow is 3000. The circumferential wave number of PSB disturbance is 1. The frequency of disturbance is 0.5. The width of disturbance is . Based on these parameters, the present work studies the transition of pipe flow with the different amplitude of PSB disturbance. The present work simulates the whole time-space process of the transition from laminar to turbulence and secondary transition phenomenon in pipe flow for the first time. The main structure in pipe flow transition is hair-pin vortex; the evolution of hair-pin vortex is related with the transition of pipe flow. Furthermore, hair-pin vortex is closely related with high-shear layer structure and spike structure in the pipe flow.When the PSB amplitude is weak, a series of hair-pin vortex will be formed. The formation, diffusion, breakup of the front edge of hair-pin vortex and the break of the head of hair-pin vortex lead to the first instability and form the slug structure. The slug structure does not get the persistent disturbance that comes from upstream and cannot hold its position by itself, so it travels to downstream. When increase the amplitude of the weak PSB disturbance, slug structure is formed in pipe flow firstly, this is the first transition. While slug structure is leaving from computing domain, the successive disturbance develop in downstream direction, the legs of hair-pin vortex approach the wall continuously and induce vortex structures near the wall. The evolution of this near-wall vortex structures brings the secondary transition to turbulence in the pipe flow. The by-pass transition appears in the pipe flow under the influence of strong PSB disturbance. The main structure in by-pass transition caused by strong PSB is hair-pin vortex. The head of hair-pin vortex rise to the center of the pipe and horse-shoe vortex is formed. Then the horse-shoe vortex detaches from hair-pin vortex and form isolated ring-like vortex. The detachment of ring-like vortex from hair-pin vortex induces the breakdown of the head of hair-pin vortex. Then the broken small vortex structures move towards the wall. When the legs of hair-pin vortex move to downstream and extend in azimuth direction, they cause the formation of the vortex structure near the wall. This near-wall vortex structure develops to downstream quickly. Finally there are many kinds of vortexes in pipe flow from the center to the wall, and the flow loses its stability. The new hair-pin vortex is formed continuous with PSB disturbance, the breakup of hair-pin vortex makes the instability position of the strong by-pass transition is immobile and near the upstream of flow.