A Generalized Model for Predicting the Drag Coefficient of Arbitrary Bluff Shaped Bodies at High Reynolds Numbers

TL;DR

This paper introduces a generalized, shape-independent model for predicting the drag coefficient of bluff bodies at high Reynolds numbers, validated against historical and various modern geometries, with a new power-based formulation included.

Contribution

The paper develops a shape- and orientation-independent model for high Reynolds number drag coefficients of bluff bodies, incorporating a novel correlation with boundary layer frictional drag and a power-based alternative.

Findings

Model accurately predicts drag coefficients for diverse bluff bodies.

The rate of change of drag with Reynolds number is shape-independent.

The power-based model effectively estimates asymptotic form drag.

Abstract

We propose an accurate model for the drag coefficient of arbitrary bluff bodies that is valid for high Reynolds numbers ($Re$). The model is based on the drag coefficient model derived for the case of a sphere:, $C_D = a_1 +{\frac{K a_2}{Re}} +{a_3\log(Re)+ a_4\log^2(Re) + a_5\log^4(Re)}$ (El Hasadi and Padding, Chemical Engineering Science, Vol. 265, 2023). The coefficients $a_2$, $a_3$, $a_4$, and $a_5$ do not depend on the object's shape or its orientation with respect to the flow, and $K$ is the Stokes drag correction factor, which for the case of the sphere, is equal to 1.0. The shape and orientation effects are included in the value of $a_1$ for the high Reynolds number flow regime. Interestingly, we found a strong correlation between the value of the $a_1$ coefficient and the frictional drag derived from boundary layer theory. One of the main findings of this investigation is that the rate of change of the drag coefficient with respect to the Reynolds number in the inertial flow regime is independent of the shape of the body or its orientation. Our model successfully predicts, with acceptable accuracy, the historical data of Wieselsberger (Technical Report, 1922) for the case of an infinite cylinder. Additionally, the model predicts the drag coefficient of other bluff body geometries such as oblate and prolate spheroids, spherocylinders, cubes, normal flat plates and irregular non-spherical particles\@. Additionally, we present a power-based model for the drag coefficient: \( C_D = a_{p_1} + \frac{24K}{Re} + \frac{4.119}{\sqrt{Re}} \). In this model, the term \( a_{p_1} \) represents the asymptotic form drag in the subcritical flow regime for different bluff body geometries\@.