On pressure invariance, wake width and drag prediction of a bluff body in confined flow

Abstract

In the present investigation, the form drag on a bluff body in confined flow is studied. From the observation of invariance in pressure distribution between a disk and a flat plate normal to free upstream in unconfined flow, a linear relation linking the drag to the base pressure is derived when the potential-flow model by Parkinson & Jandali (J. Fluid Mech., vol. 40, 1970, p. 577) is incorporated. A theoretical wake width deduced from well-documented experimental data for a disk is proposed such that the wake Strouhal number is independent of inclination. This width, when combined with the momentum equation and solved simultaneously with the aforementioned linear equation, leads to realistic predictions of the drag and the base pressure. The method is consistent when applied to a cone of arbitrary vertex angle, a circular cylinder at subcritical Reynolds numbers and a sphere at subcritical as well as supercritical Reynolds numbers. The case of the inclined disk is also discussed. As the pressure distribution is invariant under wall constraint, analytical expressions for the effect of confinement on the loading of bluff bodies are derived and found to provide the correct trend of experimental data.