Conservation-Law Approach for Transition in Pipe Flows

The laminar to turbulent transition in a pipe flow is studied from the viewpoint of momentum conservation. The transition is presumed to happen downstream of the laminar flow development. The inflow conditions to the transition region are presumed not to change at the moment of transition. The exit pressure is presumed not to change either. In the present model, the turbulent transition is a function of the ratio of the pipe length to its diameter, and becomes larger as the pipe length ratio increases. The natural transition Reynolds number calculated shows reasonable agreement with previous experimental results. The critical transition Reynolds number calculated is 1,752, and is close to the critical number of 1,760 measured previously. The distribution of difference in pressure drop between the laminar and turbulent flows corresponds to the reported location of the puffs and slugs in the Reynolds number under forced transition.