Prediction of Vortex Shedding with Heat Transfer

Abstract

ABSTRACT The article reports on the prediction of the flow field around, and the heat transfer rates from, smooth circular cylinders in cross flow. Both laminar and turbulent flow conditions are considered, the latter in the subcritical regime (3 × 104 ≤ Re ≤ 9 × 104). The principal feature of the predicted flows is the development of a von Karman vortex street leading to periodic variations in the lift and drag coefficients and the Nusselt number. It is demonstrated that the demands placed on obtaining solutions that are reasonably free of numerical errors are especially severe in these flows. When the flows are turbulent, it also becomes necessary to account explicitly for the interactions between the organized mean-flow periodicity and the random turbulence motions. An extension to an eddy-viscosity turbulence closure to allow for the direct input of kinetic energy into the turbulence at the vortex-shedding frequency is shown to produce significant improvements in the predictions of the thermal field. Specifically, and in sharp contrast with the weak fluctuations produced by the standard model, the new formulation captures fluctuations in Nusselt number that amount to 60% of the mean value. To our knowledge, this is the first study to report on the prediction of heat transfer rates in turbulent flows with periodic vortex shedding.