Numerical modelling of confined flow past a cylinder of square cross‐section at various orientations

Abstract

AbstractResults are presented for the unsteady, two‐dimensional flow and heat transfer due to a square obstruction of diameter d located asymmetrically between the parallel sliding walls of a channel with length‐to‐height ratio W/H = 6·44. Analysis is based on the numerical solution of spatially and temporally second‐order accurate finite difference approximations of the transport equations expressed in curvilinear co‐ordinates. Laminar, constant property flow is assumed for obstruction configurations in which the blockage ratio is d/H = 0·192, the nearest‐wall distances are g/d = 0·2, 0·5 and 1, the orientation angles are α=0°, 10° and 20° and the Reynolds numbers are Re=100, 500, and 1000. Preparatory testing of the numerical procedure was performed for a variety of documented flows to verify its physiconumerical accuracy and obtain estimates of the residual grid‐dependent uncertainties in the variables calculated. Heat transfer, drag and lift coefficients and Strouhal numbers for the present flow were finally calculated to within 4%–7% of their grid‐dependent values using non‐uniformly spaced grids consisting of (x=99, y=55) nodes. Above a critical value of the Reynolds number, which depends on the geometrical parameters, the flow is characterized by alternate vortex shedding from the obstruction top and bottom surfaces. Streamline, vorticity and particle streakline plots provide qualitative impressions of the unsteady vortical flow. Especially noteworthy are the extremes in the lift coefficient which ranges from large positive values for an obstruction with g/d=0·2 and α=10° to negative values for one with g/d=0·5 and α=0°. Both the drag and lift coefficients as well as the Strouhal number exhibit non‐monotonic variations with respect to the parameters explored. Asymmetries in the obstruction location and orientation account for relatively large vortex‐induced periodic variations in heat transfer, especially along the wall nearest the obstruction. Notable differences are also predicted for the heat transfer coefficients of the individual obstruction surfaces as a function of the orientation angle.