Drag, lift, and torque coefficients for various geometrical configurations of elliptic cylinder under Stokes to laminar flow regimes

Abstract

In this study, the drag, lift, and torque coefficients are derived as a function of the axis ratio ( AR) and angle of attack ( AOA) for elliptic cylinders with simple and straightforward correlations in flow regimes ranging from Stokes to laminar flow. An immersed boundary method, based on an implicit direct forcing scheme to impose a more accurate no-slip condition for viscous flow, is utilized to compute the hydrodynamic forces on the elliptic cylinder. Numerical simulations are performed for two-dimensional flow around an elliptic cylinder. The ARs and AOAs of the elliptic cylinder are within 0.3–1.0 and 0°–90°, respectively. A critical Reynolds number ( Re crt) map is obtained, indicating a transition between steady and unsteady flows as a function of the AR and AOA. Based on Re crt for the circular cylinder, it is observed that a more prolonged elliptic cylinder delays Re crt to a higher Re value at low AOAs but causes an unsteady transition at a lower Re value when the AOA exceeds ∼30°. The correlations are selected as simple functions, such as power laws and trigonometric functions, based on the hydrodynamic force behaviors according to variations in the AR, AOA, and Re. The prediction accuracy of the proposed correlations assessed in terms of mean relative errors is ∼1.5%, 8.9%, and 11.2% for drag, lift, and torque, respectively. This comparison demonstrates that the proposed correlations are suitable for accurately predicting hydrodynamic forces in Stokes to laminar flow regimes, even when using simple basic forms.