Determining the Critical Condition for Flow Transition in a   Full-Developed Annulus Flow
  Axial flow in an annulus between two concentric cylinders is commonly seen in various flow devices used in chemical processing industries and petroleum science and engineering. The flow state in the annulus strongly influences the performance of fluid transportation in the devices. Therefore, the determination of flow state which is laminar flow or turbulent flow is an important task to predict the performance of the flow devices. In previous works, we have proposed an energy gradient method for studying the flow instability and turbulent transition. In this method, it is shown that the flow instability and turbulent transition in wall bounded shear flows depend on the relative magnitude of the gradient of the total mechanical energy in transverse direction and the rate of loss of the total mechanical energy along the streamwise direction for a given imposed disturbance. For pipe and plane Poiseuille flows, it has been demonstrated that the transition to turbulence for these wall bounded parallel flows occurs at a consistent value of the energy gradient parameter (Kmax). In present study, the critical condition for turbulent transition in annulus flow is calculated with the energy gradient method for various radius ratios. The critical flow rate and critical Reynolds number are given for various radius ratios. Then, the analytical results are compared with the experiments in the literature. Finally, the implication of the result is discussed in terms of the drag reduction and mixing as well as heat transfer in practical industrial applications of various fluid delivery devices. 
Hua-Shu Dou, Boo Cheong Khoo, and Her Mann Tsai