Instability of Taylor–Couette flow between concentric rotating cylinders

Abstract

The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. This theory has been strictly derived in our previous works.In our previous studies, the energy gradient theory was demonstrated to be applicable for wallbounded parallel flows. It was found that the critical value of the energy gradient parameter K max at subcritical transition is about 370-389 for wall-bounded parallel flows (which include plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which no turbulence occurs.In this paper, the detailed derivation for the calculation of the energy gradient parameter in the flow between concentric rotating cylinders is provided. The theoretical results for the critical condition of primary instability obtained are in very good agreement with the experiments found in literature. The mechanism of spiral turbulence generation for counter-rotation of two cylinders is also explained using the energy gradient theory. The energy gradient theory can also serve to relate the condition of transition in Taylor-Couette flow to that in plane Couette flow. The latter reasonably becomes the limiting case of the former when the radii of cylinders tend to infinity. It is our contention that the energy gradient theory is possibly universal for analysis of flow instability and turbulent transition, and is valid for both pressure and shear driven flows in both parallel and rotating flow configurations.

Theory and Prediction of Turbulent Transition

“…The results from energy gradient theory have been compared with the available experimental data for Taylor-Couette flow between concentric rotating cylinders, and excellent agreement has been obtained [32]. Here, some examples are given in Fig.8 and Fig.9.…”

“…For obtaining a correlation of c K with the curvature of streamlines, much experimental data are needed. For primary instability of the base laminar flow occurring in Taylor-Couette flow, this correlation has been available [32].…”

“…(9), kinetic energy plus pressure energy while gravitational energy is neglected) [32]. The mechanism of energy loss enhancing flow stability has been studied for both plane Couette flow and Taylor-Couette flow in [22].…”

Instability Analysis of the Talyor-Couette Flow

“…Here, we use the Linear Classical theory to study the Instability of the Taylor-Couette flow. The Energy Gradient theory is also used to study the Instability of the Taylor-Couette flow [2][3]. The Non-linear theory is also used to analysis the T-C flow but it is complicated and time consuming methods.…”

A Numerical Study of Natural Convection Heat Transfer in Fin Ribbed Radiator

“…Although some optimum fin arrays design can obtain a satisfying heat transfer rate which resulted from flow instability, the physical mechanism of flow instability of natural convection is still not fully understood. Recently, Dou et al [16][17][18][19][20][21][22][23][24] suggested an energy gradient method which can reasonably reveal the physical mechanism of flow instability. Dou and Phan-Thien [16] described the rules of fluid material stability from the viewpoint of energy field.…”