How Surface Roughness and

Angular Velocity Affect Cl

By Jon Kjar and Jeffrey Carruth

Introduction

A common study in fluids is that of lift and drag. For spheres, we learned that the rotation of the sphere affects its lift and drag coefficients. This occurrence is commonly known as the Magnus Effect. The following video explains what the Magnus Effect is:

Magnus Effect

Research

After doing some research, we found out that surface roughness also plays a part when determining the coefficient of lift, as described by our textbook:

“Although the drag coefficient is fairly independent of the rate of rotation, the lift coefficient is strongly dependent on it. In addition, both Cl and Cd are dependent on the roughness of the surface.”

-Munson, Fundamentals of Fluid Mechanics

Previous Research

The current research shown in the graph is for a smooth sphere. This correlates the coefficient of lift with a non-dimensional number involving the angular velocity.

The Question:

But what about for spheres of different roughnesses?

CFD setup

We used a Star CCM+ model of a rotating sphere to get some answers.

Re = 60,000

Results

By varying the surface roughness and angular velocity of the sphere, we obtained the following results:

As can be seen, there appears to beonly minor differences in the coefficient of lift.

Matlab GUI

With the results, we made a Matlab GUI that fitted a curve to the points and allows the user to enter a roughness and angular velocity to find out the coefficient of lift!

You can find this calculator in Matlab’s file exchange.Search: Surface Roughness, Angular Velocity, or Coefficient of Lift.