Numerical Study of Sphere Drag Coefficient in Turbulent Flow at Low Reynolds Number

Abstract

The drag coefficient of a sphere immersed in turbulent air flow in the Reynolds number (Re = U _∞ d/ν _∞) range up to 250 and turbulence intensity (u _∞′/U _∞) up to 60% is computed numerically. Reynolds-averaged Navier-Stokes equations (RANS) are solved in Cartesian coordinates by using a blocked-off technique. To our knowledge, the present work is the first to employ the blocked-off technique for flow over a sphere. Closure for the turbulence stress term is accomplished by testing four different turbulence closure models. The main findings of the present investigation are that the laminar numerical data compare well with numerical and experimental published work. However, different turbulence closure models produce different trends in the range of Reynolds number up to Re = 100, and this difference is demarcated by the nonagreement between the turbulent predictions and the “standard” drag coefficient results. However, the results obtained using Menter's SST turbulence model show fair agreement with the well-known sphere “standard” drag over the range of test conditions explored here. Thus, the present results confirm recently published findings, which suggest that the free-stream turbulence intensity does not have a significant effect on the sphere mean drag.

Financial support for this research was provided by the Canadian Natural Sciences and Engineering Research Council (NSERC) and the University of Manitoba. The authors gratefully acknowledge valuable discussions with R. S. Azad, professor emeritus of mechanical engineering at the University of Manitoba.