THEORETICAL STUDY OF A THREE-DIMENSIONAL TURBULENT BOUNDARY LAYER OVER A ROTATING CONE OR DISK

Abstract

In this study, we investigated turbulent boundary layer flow due to a rotating cone or disk. A comprehensive theoretical analysis was performed and the results for several physical quantities of significant interest are presented. The problem was modeled such that both cone and disk cases could be achieved under the same formulation. In most situations, comparisons were made with the experimental results available in the literature. A primary objective of this study was to present reliable results of a rotating cone or disk with respect to several physical quantities of significant interest in order to facilitate future studies. The results were obtained at 45° and 60° angles in the cone case and at a 90° angle in the disk case. The Keller-box method was applied to numerically solve the Reynolds-averaged Navier-Stokes equations. The mixing-length turbulent model was implemented to incorporate the turbulence effects. The validity of this method was first confirmed by comparing the obtained solution for the disk case with the existing literature produced by different researchers. Circumferential and radial velocity distributions and polar plots in the cone and disk cases are presented for Reynolds numbers up to Re<i><sub>r</sub></i> = 1 × 10<sup>6</sup>. However, the circumferential and radial skin-friction coefficients, combined friction coefficient, moment coefficient, boundary layer thickness, displacement thickness, velocity shape factor, flow rate, and flow swirl angle are provided up to Re<i><sub>r</sub></i> = 1 × 10<sup>8</sup>. We also noted that the asymptotic nature of velocities can be achieved by setting the value of grid parameter <i>K</i>.