The orientational dependence correction for pressure drag ratio of prolate spheroids at finite Reynolds numbers

The pressure drag ratio, which is defined as the contribution of the pressure drag to the total drag, is essential in analyzing the variation law of total drag and the relationship between force and vorticity. However, only the expression of the pressure drag ratio for spheroids at Stokes flow regime is available. This study aims to quantify the pressure drag ratio for prolate spheroids at finite Reynolds numbers. The correction is extended by considering the influence of convection on the pressure drag ratio. By spanning a parameter space defined by the Reynolds number, aspect ratio, and angle of attack, 804 numerical results are available for the regression of the correlation. The flow field analysis revealed that both an increase in the windward-side area and enhanced viscous effects elevate the pressure drag coefficient. While the windward-side area depends on the aspect ratio and angle of attack, viscous effects are governed by the Reynolds number. It is found that the pressure drag ratio does not follow the existing sine-squared relation with the angle of attack at finite Reynolds numbers when the pressure drag is the dominant component in the total drag. Therefore, a new model for the pressure drag ratio is proposed, considering the coupled effects of the Reynolds number, aspect ratio, and angle of attack on the orientational dependence. The proposed model accounts for the influence of convection on the pressure drag ratio using the orientational dependence correction, and the validity of the model is restricted to the analyzed parameter space.