Channels, Fall 2020

Channels • 2 020 • Volume 5 • Number 1 Page 5 Fig. 4 Cross section of elliptical (a) Model A and (b) Model B for N=19 The characteristic length for flow over an ellipse is the major axis. To maintain the same Reynolds number of 6 ∗ 10 4 between the elliptical and circular models, the wind speed over the elliptical models was reduced from 23.3 m/s to 17.3 m/s. B. Experimental Results and Analysis The first experimental study on elliptical cylinders examined the depth of the grooves. The groove depth was varied from 1.02 mm to 4.06 mm. The maximum drag reduction occurred at a groove depth of 2.03 mm. This depth yielded a drag reduction of 53% from the smooth elliptical cylinder. This data is recorded in Table II and in Fig 5. For the error, the average standard deviation of the coefficient of drag was 0.0560 for the groove depth study and is also displayed in Fig. 5. TABLE II E XPERIMENTAL G ROOVE D EPTH S TUDY Groove Depth (mm) Coefficient of Drag 0 0.4879 0.51 0.4222 1.02 0.2879 2.03 0.2293 3.05 0.2707 4.06 0.4379 The second study varied the number of grooves for Model B while maintaining the groove depth constant at 1.02 mm. The elliptical cylinder with 21 and 23 grooves both showed significant drag reduction compared to the smooth model of 36%. The coefficient of drag, in the groove study, yielded a greater average standard deviation during testing with a value of 0.0586. The data for the groove number study can be seen in Table III and Fig. 6. Both parameters resulted in drag reduction, but the depth of grooves had a greater effect on reducing the coefficient of drag. This trend seen in elliptical cylinders parallels Song’s suggestion in [1] that groove depth most significantly impacts the drag reduction and that a quadratic relationship exists between the parameters and drag reduction. The plotted data in Figs. 5-6 suggest that such quadratic relationships exist in elliptical cylinders in addition to the circular models in [1].