Drag reduction on grooved cylinders in the critical Reynolds number regime

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Abstract

Experiments show that significant drag reductions may be realized for circular cylinders in cross-flow by using grooves, even at very shallow relative groove depths. It is demonstrated that the total groove area has a significant effect on reducing the critical Reynolds number, whether the area is increased through changing the groove shape, width, or depth. A strong correspondence to the minimum drag coefficient is also observed.

Highlights

► Transition behavior of grooved cylinders in cross-flow was investigated. ► Geometric groove designs were studied to optimize drag reduction at different Re. ► Groove width, depth, and shape were studied. ► Significant drag reductions were realized at very shallow groove depths. ► Established relationship between groove cross area and minimum drag coefficient.

Introduction

It is well known that for cylinders in cross-flow the transition from laminar separation to turbulent separation occurs at a critical Reynolds number Rec. Here, the Reynolds number is defined by Re = U D/ν, where U is the freestream velocity, D is the cylinder diameter, and ν is the fluid kinematic viscosity. The transition is accompanied by a significant reduction in drag. For a smooth cylinder, Rec  200 × 103, but its value diminishes with surface roughness. Roughness elements can cause an early transition to turbulence, which means that a rough cylinder can have a lower drag coefficient than a smooth cylinder at the same Reynolds number.

This mechanism for drag reduction is well known for spheres (see, for example [3]), and it is used widely in sports ball aerodynamics, most effectively in the use of dimples on golf balls. Using surface conditions to trigger early transition is also of significant interest for cylinders in cross flow, as in reducing wind and water loads on cylindrical structures.

Wind tunnel studies [2] have demonstrated that dimples can have a substantial effect at reducing drag on cylinders at low Reynolds numbers. Other recent work including wind tunnel experiments and simulation have focused on the effectiveness of longitudinal grooves in reducing drag. This is important in obvious situations such as heat exchangers, as well as less obvious applications such as turbine blades [6], [7].

Kimura and Tsutahara [5] demonstrated that circular-cross section grooves were effective at reducing drag even at sub-critical Reynolds numbers, where the Reynolds number Re = UD/ν, and ν is the fluid kinematic viscosity, D is the cylinder diameter, and U is the freestream velocity. In addition, studies have been conducted by Yamagishi and Oki [12] comparing the effects of circular-cross section and triangular-cross section grooves (or “V”-shaped grooves). They found there was little observed change in the critical Reynolds number or pre-crisis drag, but a small reduction in post-crisis drag for V-shaped grooves. The same authors later found that increasing the number of grooves (circular cross-section of fixed width) on a cylinder of a given diameter dramatically reduced the critical Reynolds number [13]. Further investigations by Takayama and Aoki [10] demonstrated that increasing the groove depth decreased the critical Reynolds number.

In most cases, the use of longitudinal grooves was significantly more effective at reducing the drag coefficient compared with reported results using sand-type roughness [9]. The drag coefficient CD=FD/12ρU2DL, where FD is the drag force, ρ is the fluid density, and L is the cylinder length.

In summary, three design parameters were tested in our experiments: the number of grooves (more pertinently, the area of the cylinder covered by grooves), the depth of the grooves at fixed width, and (to a limited extent) the shape of the grooves (that is, circular versus V-section). This work seeks to optimize groove shape and width for drag reduction performance at low Reynolds number.

Section snippets

Experiment

Cylinders were fabricated from 2000-series aluminum with a final overall diameter of 57.2 mm (2.25 in.) and a length of 457.2 mm (18 in.), giving a length-to-diameter ratio of 8:1. This aspect ratio is expected to give slightly higher values of drag coefficient compared to the infinite aspect ratio case [11]. Longitudinal grooves were incised in the cylinders using a 4-axis CNC machine to a 0.019 mm (0.00075 in.) profile tolerance. All tests were conducted with the cylinders in cross-flow, with the

Results and discussion

Drag measurements for a smooth, polished cylinder with the same diameter and length as the grooved cylinders resulted in an average drag coefficient between 1.32 and 1.38 over the range 20,000 < Re < 120,000 (see Fig. 4). This is somewhat higher than the expected value of 1.3 [11], and the difference may be due to interference effects due to the end plates.

Drag coefficient results for the experimental grooved cylinders are plotted in subgroups according to groove geometry in Fig. 4, Fig. 5, Fig. 6,

Conclusions

It has been shown that, even at very shallow relative groove depths, significant drag reductions may be realized for circular cylinders in cross-flow. It has further been shown that the total groove area has a significant effect reducing the critical Reynolds number, whether the area is increased through changing the groove shape, width, or depth. There is also a strong, though less significant, correspondence to the minimum drag coefficient.

Acknowledgements

The authors would like to thank Mr. Michael Vocaturo for his time and patience in helping to set up the experiments, and the USGA for funding the research.

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