**1. Introduction**

The power that can be extracted from the wind is primarily driven by three factors, the cross-sectional area that is being used to capture the wind, the velocity of the captured wind, and the power coefficient of the turbine blades. This relationship is described by:

$$P = \frac{1}{2} \rho \pi R^2 \mathcal{U}\_{fs}^3 \mathcal{C}\_{p\text{ov}} \tag{1}$$

Here *Cpow* is the coefficient of power for the wind turbine, *Ufs* is the free stream wind speed, and *R* is the rotor radius [1]. Note that in this work *Cp* is used to define the pressure coefficient rather than the coefficient of power. One can, therefore, increase the harvested power by increasing the blade radius, the wind speed, or the coefficient of power, which is representative of the aerodynamic efficiency of the wind turbine. Equation (1) indicates that the rotor area is a strong driver of the power of a wind turbine. This has led to increased rotor sizes, especially for commercial scale wind turbines. However, wind turbine sizes are ultimately bounded by structural limitations and other practical considerations such as the need to transport parts. Power is also a function of the coefficient of power of the system which has an upper limit defined by the Betz limit (59.3%) for free wind turbines, limiting potential gains through increased aerodynamic efficiency.

Equation (1) indicates that a wind turbine's extracted power has a cubic relationship with wind speed. This leads to the strategy of increasing the velocity of the wind at the rotor plane to increase the power extraction. Increased wind speed is typically accomplished by siting turbines in locations with high wind speeds or by increasing the tower height. This, however, limits the number of economically viable siting locations. Alternately, one could attempt to modify the local wind stream to achieve higher velocities at the rotor plane. This approach is attractive in that relatively small changes in the local wind speed can lead to significant increases in harvested energy.

"Accelerated wind" is a general term for such strategies and is normally accomplished by adding a structure near the rotor to locally increase the flow velocity. The most common example is seen in diffuser augmented wind turbines (DAWT). A DAWT's structure lowers the pressure downstream of the blades to draw a greater mass of air through the rotor plane and thus generate more power than a similarly sized horizontal axis wind turbine (HAWT) [1–10]. A less explored accelerated wind concept is to place rotors near structures that increase the local wind speed. Examples of this include building augmented wind turbines [11–13] and specially designed tower structures [14–16]. This study explores the concept of placing wind turbine rotors next to a cylindrical structure, see Figure 1. The cylindrical structure serves to act as both the wind turbine tower and a method to increase the velocity at the rotor plane.

**Figure 1.** Conceptual views of (**a**) original Optiwind 150 kW wind turbine design. (**b**) Conceptual smooth cylinder design. Rotors shown schematically by dotted circles. In application, direction of wind would be into the page so that turbine blades are at ±90◦ with respect to the wind direction.

Duffy and Jaran [12] reported on what they named a "toroidal accelerator rotor platform" (TARP). The TARP concept used a toroidal channel around the outside of a cylinder to accelerate the wind into rotor blades that were mounted in the channel. The TARP was intended to be either an add-on attachment to grain silos, water towers, etc. or as a standalone structure. This concept was extended to the WARP, or wind amplified rotor platform, consisting of a number of stacked TARP modules [13]. A prototype was built and briefly tested in Belgium; however, a viable commercial product does not exist today.

A similar concept, the Optiwind "Accelerator Platform", shown in Figure 1a, formed the motivation for the current study. This concept was a finite span (aspect ratio, AR = 0.93) corrugated circular cylinder where the rotor blades would also sit in isolated channels. The channels were conceived of as aerodynamic structures to direct the wind into the wind turbine blades, which would also isolate the wind turbine blades from each other. This is strategically different from DWATs in that the channels were not intended to be traditional diffusers, but more specifically as flow directors. Flow acceleration was provided by the surface curvature. This concept was the motivation for the first model used in the current study. The second model, shown in Figure 1b, was a smooth circular cylinder with the same aspect ratio and a diameter equal to the outer diameter of the corrugated cylinder. The location of the rotor placement for both designs is indicated by the dashed circles. Both models were intended to accelerate the wind prior to entering rotors; however, the smooth cylinder lacked the "flow directing" channels as shown. The high level goal of the project was to design a mid-range, scalable wind turbine for the renewable energy market [15]. In both cases the number of stack turbines, three shown in Figure 1 and used for testing, could be chosen arbitrarily depending on the power requirements.

This work details experiments performed on the two tower models: a 1:80 scale model of the Optiwind Accelerator Platform (i.e., the "corrugated cylinder model") and a smooth circular cylinder with the same aspect ratio as the corrugated model. The surface pressures and tangential velocity, *V*<sup>θ</sup> (*r*), profiles were acquired experimentally for both platform models. The location and magnitude of the minimum pressure coefficient (*Cp,min*) and the mean flow velocities were used as metrics in determining the effectiveness of the potential designs for accelerating the flow. The minimum pressure coefficient, *Cp,min*, serves as one basis for discussion of the performance in this work in two ways. First, the location of the *Cp,min* is indicative of where the surface flow curvature has changed and the flow is no longer following the surface shape. It can be used to determine if the separation point has moved forward or aft between cases. Second, the magnitude of *Cp,min* correlates with the increase in flow velocity, and it can again be used comparatively between cases.

The motivation for this work was to assess the potential of the two shapes for accelerated wind applications. The goal of the current work was to compare, in a quantitative manner, the flow around low aspect ratio cylinders with smooth and corrugated surfaces. Within the larger project, the results of this study were used to down select the platform shape and guide the continued design/development of the prototype wind accelerator platform within the larger project. It is acknowledged that the presence of rotors, which were not investigated in this work, would change the flow conditions around both the corrugated and smooth cylinders. This effect is the subject of future studies for the following reasons. First, rotors are typically designed to provide a specific pressure drop that optimizes the power extraction. Because this study was used to down select the platform geometry, the rotors have not yet been designed. Second, this study provides a canonical case comparing short aspect ratio cylinders with and without surface corrugations. These conditions, without the rotors, therefore represent the upper limit on the potential performance.

#### **2. Materials and Methods**

## *2.1. Experimental Models and Facility*

The corrugated cylinder was constructed using stereolithography as a 1:80 scaled model of the proposed Optiwind Accelerator Platform design with three rows of corrugations, as shown in Figure 2. The key dimensions of the model were as follows: major diameter, *Dmaj* = 0.269 m; minor diameter *Dmin* = 0.164 m; length, *L* = 0.249 m; and the aspect ratio based on the major diameter *L*/*Dmaj* = 0.93. Pressure taps were added circumferentially along the minor diameter (i.e., in the "valley" of the channel) of the model and along the corrugation walls, as shown in Figure 3, for all three channels. The surface of the corrugated cylinder was sanded to smooth the steps in the surface resulting from the stereolithography fabrication.

A smooth cylinder with the same diameter as the major diameter and aspect ratio of the corrugated cylinder provided a second potential platform design as well as a canonical baseline reference case. The smooth cylinder was fabricated from a 0.27 m diameter PVC pipe cut to the same length as the corrugated cylinder, which provided an aspect ratio equal to the platform model, *L*/*D* = 0.93. Pressure taps were machined into the cylinder at the mid-height.

Experiments were performed in the Clarkson University High Speed Aerodynamic Wind Tunnel. The tunnel is an open loop tunnel with a 1.2 × 0.9 × 1.8 m long test section. The tunnel blockage due to the models was 6.7% based on the major diameter and length of the corrugated cylinder model. Experimental flow speeds ranged from *Ufs* = 10 to 50 m/s. The turbulence level of the tunnel free stream was measured via hotwire anemometry to be approximately 1.2% within the velocity range investigated. The Reynolds number was computed based on the major diameter of the corrugated

cylinder and the test section free stream speed. Experimental Reynolds numbers covered a range of Re = *Ufs Dmaj*/<sup>υ</sup> = 1.9 <sup>×</sup> 105 to 8.9 <sup>×</sup> 105 for this study. It is noted that the Reynolds number for the full scale device was expected to be nominally 50–100 <sup>×</sup> <sup>10</sup>5. The upper end of the experimental Reynolds number was limited in this work by the flow facility (i.e., cross sectional area of the test section and maximum flow speed). While this was approximately an order of magnitude lower than the device Reynolds number that motivated the study, the results show a decreasing dependence on the Reynolds number, and the results were expected to be qualitatively similar and therefore informative. The lowest Reynolds number was investigated to allow for Reynolds number trends to be investigated. Both models were placed in the wind tunnel with a 0.15 m vertical offset from the bottom floor of the test section, as shown in Figure 4. The tops and bottoms of the models were closed.

**Figure 2.** Schematic of corrugated cylinder model. All dimensions are in meters.

**Figure 3.** Schematic of side wall pressure taps.

**Figure 4.** Experimental set-up for the (**a**) corrugated and (**b**) smooth models.

#### *2.2. Pressure Measurements*

The models contained pressure taps with 1 mm diameter openings at the surface starting at the leading edge (θ = 0◦) and extending around the diameter of the models in 10◦ increments. Stainless steel tubing (1.58mm outer diameter, 1.32 mm inner diameter) was pressed into each tap to allow for connection with the pressure transducer via Tygon tubing. The corrugated cylinder model also had rows of pressure taps along the channel walls at φ = 42◦ and 98◦ up from the horizontal as shown in Figure 3. Pressure surveys were conducted using an Omega model PX653-10BD5V pressure transducer with a ±2.5 kPa range. Data were acquired with a National Instruments PCI-6024E 12 bit A/D card. Each pressure measurement consisted of 96,000 data points at a sampling rate of 2400 Hz. A ScaniValve solenoid controller was used to index through the model pressure taps sequentially after sampling at a given location was completed. Uncertainty in the pressure measurements was estimated to be 0.025 kPa, which corresponded to an uncertainty level in the reported pressure coefficients of *Cp* = ±0.03.

The pressure data reported in this work are the average surface pressure values in non-dimensional form. The pressure coefficient, *CP*, was calculated using:

$$\mathcal{C}\_p = \frac{\overline{P}\_S - \overline{P}\_{S,T,\text{unucl}}}{\frac{1}{2}\rho L l\_{fs}^2} \tag{2}$$

where *PS* is the average pressure at a tap location and *PS*,*Tunnel* is the static pressure in the test section upstream of the model. The dynamic pressure of the free stream was measured using a pitot-static probe upstream of the models.
