Active aerodynamic drag reduction on morphable cylinders

We study a mechanism for active aerodynamic drag reduction on morphable grooved cylinders, whose topography can be modified pneumatically. Our design is inspired by the morphology of the Saguaro cactus (Carnegiea gigantea), which possesses an array of axial grooves, thought to help reduce aerodynamic drag, thereby enhancing the structural robustness of the plant under wind loading. Our analog experimental samples comprise a spoked rigid skeleton with axial cavities, covered by a stretched elastomeric film. Decreasing the inner pressure of the sample produces axial grooves, whose depth can be accurately varied, on demand. First, we characterize the relation between groove depth and pneumatic loading through a combination of precision mechanical experiments and finite element simulations. Second, wind tunnel tests are used to measure the aerodynamic drag coefficient (as a function of Reynolds number) of the grooved samples, with different levels of periodicity and groove depths. We focus specifically on the drag crisis and systematically measure the associated minimum drag coefficient and the critical Reynolds number at which it occurs. The results are in agreement with the classic literature of rough cylinders, albeit with an unprecedented level of precision and resolution in varying topography using a single sample. Finally, we leverage the morphable nature of our system to dynamically reduce drag for varying aerodynamic loading conditions. We demonstrate that actively controlling the groove depth yields a drag coefficient that decreases monotonically with Reynolds number and is significantly lower than the fixed sample counterparts. These findings open the possibility for the drag reduction of grooved cylinders to be operated over a wide range of flow conditions.

Figure 1

(a) Representative photograph of a Saguaro cactus (Scottsdale, Arizona) [15]. (b) Photographs of a grooved cylindrical sample covered by a stretched latex film. The surface topography can be morphed pneumatically by increasing the pressure differential between the inside and the outside of the samples: (b1) $\mathrm{\Delta }p=1000\mathrm{Pa}$, (b2) $\mathrm{\Delta }p=5000\mathrm{Pa}$, (b3) $\mathrm{\Delta }p=10,000\mathrm{Pa}$. A laser sheet aligned at ${45}^{\circ }$ with respect to the cross section of the sample is used to measure the depth of the surface grooves.

Figure 2

(a) Photograph of the experimental apparatus used to measure the drag force on a grooved cylindrical sample under aerodynamic loading. The sample (1), mounted across the wind tunnel (2), is rigidly connected to a force sensor (5) via an air bearing (4) to measure the exerted aerodynamic drag forces. The internal pressure of the sample is set by a regulated vacuum pressure source (3). The air flow with average far-field speed $U$ is aligned perpendicularly to the axis of the sample. (b) Schematic diagram of the cross section of the sample (top) comprising a rigid acrylic skeleton (red) covered by a thin latex film (blue, thickness $t=0.25\mathrm{mm}$). Depressurizing ($\mathrm{\Delta }p$) the inner cavity of the shell results in deeper grooves (bottom).

Figure 3

(a) Schematic diagram of a single groove after applying the pneumatic loading by setting the pressure differential to $\mathrm{\Delta }p$. The groove depth, width, and film thickness are represented by $d$, $w$, and $t$, respectively. (b) Results of experiments (solid lines) and FEM simulations (dashed lines) showing the shape of the surface of the latex film at increasing values of $\mathrm{\Delta }p=\{2,4,6,8,10\}\mathrm{kPa}$, for a sample with $N=14$ grooves. The rigid (acrylic) skeleton is represented by the thick black lines. Given the periodicity of the system, only the data for a single groove are shown.

Figure 4

(a) Groove depth, $d$, vs pressure differential, $\mathrm{\Delta }p$, for samples with different numbers of grooves; see legend, which also applies to panel (b). Solids lines and data points correspond to simulations and experiments, respectively. (b) Normalized groove depth, $\overline{d}=d/w$, as a function of normalized pressure, $\mathrm{\Delta }\overline{p}=\mathrm{\Delta }pw/\left[Gt\right]$, for the same data as in panel (a). The slope of the best linear fit to the data is $\alpha =0.152\pm 0.001$.

Figure 5

Drag coefficient, $C_d$, vs Reynolds number, $\text{Re}$, for smooth cylinders of different diameters and thus blockage ratios ranging from $1.90<D\left[\mathrm{cm}\right]<7.62$ and $0.0625<\beta <0.25$, respectively. The solid black corresponds to the classic curve for a smooth cylinder [7]. The solid symbols are the uncorrected experimental results, and the open symbols are the corrected results using Maskell's theory [24] with $\epsilon =0.3453$, which was determined using the procedure described in the text.

Figure 6

Drag coefficients, $C_d$, vs Reynolds number, $\text{Re}$, for grooved cylinders at increasing values of depressurization (and consequently increasing normalized groove depth, $\overline{d}$). Solid black line correspond to the result for a smooth cylinder (W21: Ref. [7]). (a) Fixed samples with $N=24$ grooves at increasing values of normalized groove depth, $\overline{d}$ (circles), and actively controlled sample (squares). The fixed samples range in groove depth from $\overline{d}=0$ to 0.093 in equally spaced increments of $\overline{d}=0.0072$. (b) Actively controlled samples with $N=14$ (circles), $N=16$ (triangles), $N=20$ (diamonds), and $N=24$ (squares).

Figure 7

(a) Minimum drag coefficient, $C_{\mathrm{d}}^{*}$, of each $C_{\mathrm{d}}\left(\text{Re}\right)$ curve in Fig. 6, vs normalized groove depth, $\overline{d}$, for samples with different numbers of grooves (see legend). (b) Critical Reynolds number, ${\text{Re}}^{*}$, vs normalized groove depth, $\overline{d}$, for the same samples used in panel (a). Inset: Log-log version of the same data suggesting consistency with the power-law scaling ${\text{Re}}^{*}\sim {\overline{d}}^{-1/2}$ (solid line).