Computations of the drag coefficients for low-Reynolds-number flow past rings

The variation in the drag coefficient for low-Reynolds-number flow past rings orientated normal to the direction of flow is investigated numerically. An aspect ratio parameter is used for a ring, which describes at its limits a sphere and a circular cylinder. This enables a continuous range of bodies between a sphere and a circular cylinder to be studied. The computed drag coefficients for the flow past rings at the minimum and maximum aspect ratio limits are compared with the measured and computed drag coefficients reported for the sphere and the circular cylinder. Some interesting features of the behaviour of the drag coefficients with variation of Reynolds number and aspect ratio emerge from the study. These include the decrease in the aspect ratio at which the minimum drag coefficient occurs as the Reynolds number is increased, from $\hbox{\it Ar} \,{\approx}\, 5$ at $\hbox{\it Re} \,{=}\, 1$ to $\hbox{\it Ar} \,{\approx}\, 1$ at $\hbox{\it Re} \,{=}\, 200$ . In addition, a substantial decrease in the pressure component of the drag coefficient is observed after the onset of three-dimensional flow while the viscous contribution is similar to that for flow with imposed axisymmetry. Typically, the sudden reduction in drag caused by transition to Mode A shedding is 6%, which is consistent with the behaviour for flow past a circular cylinder. Power-law fits to the drag coefficient for $\hbox{\it Re} \,{\lesssim}\, 100$ are provided, which are accurate within approximately 2%.