Computational approach to the turbulent boundary layer of a rotating porous cylinder with strong suction based on an algebraic turbulence model

Abstract

Many important technical systems operate according to the principles of momentum transfer, heat transfer and mass transfer near the surface of a cylinder rotating in a confined space. Numerical study of the Taylor–Couette flow with an imposed inward radial throughflow in the rotating inner cylinder demonstrates the possibility of flow stabilization to prevent large-scale vortices up to high rotation rates. The fluid is involved in rotation by the inner rotating cylinder only in a thin layer (boundary layer) near the cylinder surface with strong radial throughflow. Turbulence in the boundary layer may occur before the centrifugal instability, and there is a way to control the thickness of the layer as well as shear intensity and turbulence intensity near the surface of the rotating cylinder. The present work develops a compact and robust approach for the turbulent boundary layer calculation on the surface of a rotating cylinder based on an algebraic turbulence model. The generalized Cebeci–Smith model was supplemented with Richardson number-based corrections to address the centrifugal force action. It also generalized the correction used for accounting for wall suction. Analytical corrections and empirical coefficients of the model were tuned to reflect the coupled influence of the specific flow conditions. The approach, comprehensively verified in the preliminary research, was adapted to the desired geometric configuration and checked. The modified algebraic turbulent model was incorporated into an iterative calculation method developed especially for the case of axisymmetric boundary layers. The results of the algebraic turbulence model with different combinations of rotational speed and suction velocity agree well with the simulation results of the Reynolds stress turbulent model. The method proposed provides efficient practical engineering calculations and can be applied up to approaching the centrifugal instability in the boundary layer.

Keywords

• boundary layer
• numerical simulation
• rotating cylinder
• turbulence model
• wall suction