A general and accurate correlation for the drag on spherocylinders

Abstract

The dimensionless hydrodynamic force and torque or drag, lift and torque coefficients exerted on spherocylinders placed in uniform flows depend on three dimensionless parameters: the aspect ratio β, the incident angle θ, and the flow Reynolds number Re. An accurate Direct Numerical Simulation (DNS) method is developed and more than one thousand simulations are performed to generate numerical data on the drag of spherocylinders in the aspect ratio range 1≤β≤6, incident angle range 0∘≤θ≤90∘, and Reynolds number range 0.1 ≤ Re ≤ 300. A systematic analysis of the data shows the correct dependence of the drag coefficient on β, θ and Re as well as the general trends of the drag coefficient. It also generates an accurate engineering correlation with an average error of around 2%, when compared to the more than one thousand DNS numerical results. The results also show – and analysis explains – other salient features of the drag on spherocylinders, in particular the exponent for the function sinθ, and a local minimum of the drag coefficient, which is due to the interplay between the friction and the form (pressure) parts of the drag.