The model of laminar pulsatile flow in tubes in rolling motion

The laminar pulsatile flow in tubes in rolling motion is investigated theoretically. The theoretical model of laminar flow in rolling motion is developed and the velocity correlation is also derived. The effect of rolling motion on velocity and frictional resistance factor is analyzed. The rolling motion mainly affects on the laminar flow by the tangential force. The centrifugal force does not affect on the flow. The tangential force affects on the flow in axial direction, its radial effect is very weak and could be omitted. There are two critical rolling points in rolling motion. After the first critical rolling point, the flowing velocity next to the wall reverses. Moreover, the flow rate at the tube cross-section becomes negative after the second critical rolling point. The buoyancy force is only one part of the effects that affects on the average velocity of a natural circulation system in rolling motion. The effect of Womersley number on the velocity is significant, which can not only affect on the average velocity but also on the oscillating period and velocity amplitude. The rolling motion does not affect on the average frictional resistance of laminar pulsatile flow. If the rolling motion is very serious, the flow is at a transitional or turbulent flow state, in this case the effect of rolling motion on the average frictional resistance is considerable.