Dynamic Study Of The Flow Between Rotating Conical Cylinders

The flow between two concentric rotating cylinders is calledTaylor-Couette flow. The formation of Taylor vortex and the transition oflaminar flow to turbulence is an important research subject of Taylor-Couetteflow. Although many scholars have investigated the formation of Taylor vortexand the transition of laminar flow to turbulence for conical cylinders flow byexperimental observation or numerical simulation, most of them didn’t makeany theoretical accurate estimation.In this paper, the form of Navier-Stokes equations are rewritten in cylindercoordinates, non-dimensional analysis is carried out by selecting proper scales,the dimensionless form of Navier-Stokes equations of conical cylinders flow isobtained for two cases: only the inner cone rotates, both the inner cone and theouter one rotate. The corresponding Reynolds numbers for two cases are given,which not only simplify Navier-Stokes equations, but also reduce thedimension of the problem. Gap width, radius and angular velocity of the innercone and the outer cone are united to one parameter: Reynolds number. TheReynolds number is full used to our theoretical and numerical study.Further we consider the conical cylinders flow for the case when the innercone rotates together with the end plate at the top, the effect of the end plate atthe top is investigated by theoretical analysis and numerical simulation fordifferent Reynolds number. The theoretical estimate of the critical Reynoldsnumber for the appearance of the first vortex is given, which coincides withnumerical simulation. We also compare the stationary end plate at the top withthe rotating one and consider the effect of gap size by counting the number ofTaylor vortex for different gap sizes.The last part of this paper is the numerical simulation comparison betweentwo cases: the inner cone rotates and the outer one is at rest; the outer conerotates and the inner one is at rest. The distributions of pressure, velocity andshear stress show that the more unstable case is the inner cone rotates and the outer one is at rest.