Gas-Dynamic Processes in a Rotating Cylinder in the Presence of Axial Temperature Gradients

A three-dimensional flow of a viscous heat-conducting gas in a rapidly rotating straight circular cylinder in the presence of axial temperature gradients is studied. At the initial stage, gas-dynamic and thermal boundary layers on a rotating extended disk are considered. When taking into account the temperature change in density, the Dorodnitsyn transformation is used, which makes it possible to reduce the solution of the problem to the integration of a system of ordinary differential equations. Taking into account inertial effects, an approximate analytical solution of the problem is obtained in the case of small values of the Prandtl number, when the thermal boundary layer thickness exceeds the thickness of the hydrodynamic layer. The result of the calculation for an extended disk is used to estimate the intensity of the axial circulation flow in a rotating cylinder of finite dimensions. The influence of the intensity of temperature perturbation on the radial profile of circulation in a rotor is studied.