Fluid Mechanics Division, TSI Incorporated, USA
dtroolin@tsi.com 2
Research Institute of Marine Systems Engineering, Seoul National University
sj38.lee@gmail.com
3
Mechanical Science and Engineering, University of Illinois, Urbana
lpchamo@illinois.edu
ABSTRACT
Instantaneous and time-averaged volumetric velocity fields were obtained in the wake of a single, three-bladed hydrokinetic turbine model placed in a water flume at St. Anthony Falls Laboratory at the University of Minnesota, under subcritical conditions. A cylinder was placed upstream of the turbine in order to introduce large coherent motions into the incoming flow. Six unique configurations were tested, including a base flow characterization, the wake with the turbine-only, the wake of the turbine with a cylinder placed 5 diameters upstream, the wake of the turbine with a cylinder placed 8 diameters upstream, the wake of only the cylinder at the 5 diameters upstream position, and the wake of only the cylinder at the 8 diameters upstream position. The Q-criterion and vorticity as well as the volumetric velocity fields were used to study the interaction between energetic coherent motions generated by the cylinder and tip vortices generated by the turbine. Vortex shedding from the cylinder produced specific coherent vortical structures that affected the turbine wake by increasing the disorder of the otherwise relatively orderly helical downstream wake. Other relevant insights on the tip vortex dynamics, and flow characteristics in the turbine wake are discussed.
1. INTRODUCTION
Recently, underwater hydrokinetic turbines (using tidal, river, and marine currents among others) have received increased interest, and several studies have aimed to characterize the performance and downstream wake of such turbines [e.g. 1, 2]. Fundamental understanding of the turbulent flow around hydrokinetic turbines is important for predicting the effects on the local aquatic environment, flow turbulence, and power available. Of particular relevance are the effects of upstream obstructions on the turbine wake. Several examples of common obstructions upstream include bridge piers, additional turbines, and complex bathymetry. The aim of the current study is to understand the effects of energetic coherent motions propagating from upstream and interacting with the turbine blades and the resulting wake. This is accomplished by performing three-dimensional velocity field measurements in the wake of a miniature turbine under various flow conditions. A circular cylinder was placed vertically at 5 and 8 cylinder diameters upstream of the miniature turbine also along the centerline of the flume with the purpose of introducing energetic coherent motions in the flow toward the turbine.
2. METHODS
A schematic of the experimental arrangements can be seen in fig. 1, which follows the concept of Chamorro et al [1, 2]. A miniature three-bladed axial-flow turbine was placed along the centerline of a water flume at the St. Anthony Falls Laboratory, University of Minnesota. The turbine had a 0.126 m rotor diameter, variable pitch, and dynamic load system. The rotor hub was mounted at a distance of 0.11 m from the floor of the flume. The test section of the flume was 0.5 m wide, 0.7 m height and 10 m long. The flume mean velocity at the turbine hub height was approximately 0.265 m/s. A circular cylinder was placed vertically at five, and separately at eight, cylinder diameters upstream of the turbine hub along the flume centerline with the purpose of inducing energetic coherent structures into the flow. The cylinder extended from the floor of the flume up to and beyond the free surface and consequently introduced energetic coherent structures in the flow that convected toward the turbine from upstream.
Figure 1 Schematic of the experimental arrangement showing the cylinder-only (left), the turbine-only (center), and with both obstructions in the flow (right). In this case the cylinder was placed at 5 and 8 cylinder diameters (dc) upstream of the turbine. The
cases with the cylinder at 5 diameters upstream are not shown in the schematic, but follow the same arrangement.
The flow immediately downstream of the turbine was illuminated by a dual-head Nd:YAG pulsed laser with 100 mJ/pulse, that was mounted above the water tunnel. The laser beam was directed through an articulated light arm with mirrors at each joint, so that the beam was aiming downward into the flume. A transparent Plexiglas plate was mounted at the surface of the water to limit free-surface effects. Two cylindrical lenses were mounted at the light arm exit in perpendicular orientations to produce an ellipsoidal cone of laser light. The volumetric 3-component velocimetry (V3V) technique [3, 4] was used to acquire volumetric velocity fields at a rate of 50 Hz (100 camera frames/sec). Three cameras were mounted in a triangular configuration at 90° to the illuminating light. Pairs of laser pulses were separated by 2000 µs, and 65 micron ceramic sphere tracer particles were identified and tracked in 3D space. A photograph of the experimental setup can be seen in fig. 2.
Figure 2 Photograph of the experimental setup, showing the locations of the cameras (blue) measurement volume (green), turbine (gray), and cylinder (yellow)
The resulting measurement volume was a rectangular prism 96mm × 100mm × 54mm, which encompassed approximately half of the downstream wake in the span-wise direction, and 0.8dT downstream of the turbine. In all cases, the location of the measurement volume remained fixed. A typical single capture yielded approximately 15,000 independent randomly-spaced velocity vectors. The vectors were interpolated onto a rectangular grid using Gaussian-weighting. The average spatial resolution for the instantaneous velocity fields was approximately 3.25mm. For each configuration, over 1200 vector fields were acquired.
3. RESULTS
In this section we present the coherent motions formed by the rotating blades of the model hydrokinetics turbine (the tip vortices) and those generated by a vertical cylinder (the von Karman vortices) as well as the interaction between these two flow structures. The analysis is focused within the first rotor diameter, as illustrated in the schematic of fig. 1. A total of six sub-cases consisting of combinations of turbine and cylinder are studied to understand the role of coherent motions within the turbine wake. The sub-cases are defined as follows: i) base flow with no obstructions, ii) turbine wake, iii) cylinder wake at x/dc=5, iv) cylinder wake at x/dc=8, v) both cylinder at x/dc=5 and turbine wake, and finally, vi) both cylinder at x/dc=8 and turbine wake. To illustrate the spatial and temporal characteristics of the dominant vortical structures within the first rotor diameter downstream of the model hydrokinetic turbine, a temporal sequence of the tip vortices is computed using a widely used vortex recognition technique, the Q-criterion. Figure 3 illustrates iso-contours of Q=5 at four time instances; every other frame is shown to illustrate the motion of the structures. The
Figure 3 Sequence of the advection of the tip vortices from the model hydrokinetic turbine.
As indicated, a vertical cylinder was positioned upstream to add energetic coherent structures into the flow. To visualize the effect of such coherent motions (the von Karman vortex street) on the tip vortices, we follow the same analysis used in determining the tip vortices from the turbine (fig. 3), namely the use of the Q-criterion. The interaction between the two types of vortical structures, which in general exist in different orientations, is evidenced in fig. 4. The vortices shed by the cylinder interact with the turbine tip vortices by deforming, intertwining, and increasing the disorder of the downstream wake and broadening the range of spatial scales within the wake. The increased disorder and deformation of the tip vortices as influenced by the von Karman shedding is clear when comparing the general disorder, size and spatial displacements of vortex structures between figs 3 and 4. A breakdown of the turbine tip vortices occurs in the presence of the von Karman vortices, and due to this process, the wake dynamics are modified. For example, in the top sequence at t = t0, structures consistent with the tip vortices are seen with a longer streamwise oriented vortex structure
spanning the measurement volume at approximately z/d = 0.3 and y/d = 0.4. The case ‘cylinder A’ (i.e., x/dc=8) appears to be more effective in destabilizing the tip vortices, consistent with results at larger-scale experiments, currently underway in the flow facility, as well as the fact that structures resembling tip vortices are more readily identifiable in the turbine with cylinder B (bottom), case.
Figure 4 Sequence of the advection of the coherent motions. Cylinder is located 8 (cyl. A case) and 5 (cyl. B case) cylinder diameters upstream of the turbine.
Due to the interaction between the vortices, it can be difficult to differentiate between the von Karman and tip vortex structures. In order to clarify the identification of the von Karman shedding, various planes within the interrogation volume are plotted and the x- and z-vorticity computed. The results for all the sub-cases are shown in figs. 5-8. Specifically, fig. 5 shows horizontal and vertical planes, where the velocity vectors are inspected in detail. The velocity field in the planes is shown in fig. 6. There, we observe the signature of the tip vortices adjacent to one another with the same rotation direction (turbine only), the counter-rotating vortex pairs of the von Karman vortices (cylinder only) and the distortion and breakdown of the vortical structures in the combined cases of turbine and cylinder, which lends evidence to the vortex-to-vortex interactions.
The visualization of the x- and z-vorticity components for all cases are shown in figs. 7 and 8, which allows the examination into the process by which the von Karman structures enter through the turbine wake (fig. 7) and interact (fig. 8) with the tip vortices.
Figure 5 Tip vortices and von Karman vortices visualized with the Q- criterium (Q=5). Details of the velocity field within the vertical and horizontal planes are detailed in fig. 6.
Figure 7 Streamwise (x-) vorticity (ωx=±5). Positive and negative vorticity are shown in red and blue, respectively.
Further, to quantify the damping of the tip vortex signature due to the von Karman structures, the pre-multiplied spectrum was calculated for the flow in the wake of the turbine (fig. 9, left) and in the wake of the turbine with the cylinder (fig. 9, right) at x/d=0.8 and at the polar coordinate (r,θ)=(R,π/4), with θ=0 corresponding to the vertical. The turbine frequency (fT) and blade passing frequency (fbpf) are clear in the wake of the turbine. Those peaks, which are the
signature of the tip vortices, are massively damped by the structures shed by the cylinder (fig. 9, right).
Figure 9 Pre-multiplied spectrum of the spanwise velocity component at x/d=0.8 in the wake of the turbine (left) and cylinder and turbine.
Finally, to stress the effect of strong coherent motions into the wake, iso-velocity contours of the streamwise velocity component are plotted in fig. 10. The plotted isosurface is at a value of U/Uhub=0.9, where Uhub is the approach velocity at the turbine hub height. An increased disorder and the signature of small scale features are observed in the combined cases (cylinder with turbine).
REFERENCES
[1] Chamorro L.P., Troolin D.R., Lee S., Arndt R.E.A. and Sotiropoulos F. (2013) Three-dimensional flow visualization in the wake of a miniature axial-flow hydrokinetic turbine. Exp. in Fluids, 54:1459
[2] Chamorro L.P., Hill C., Morton S., Ellis C., Arndt R.E.A. and Sotiropoulos F. (2012) On the interaction between a turbulent open channel flow and an axial-flow turbine. J Fluid Mech, 716, 658-670.
[3] Pereira F, Stuer H, Graff E C, Gharib M (2006) Two-frame 3D particle tracking. Meas. Sci. Technol. 17:1680-92.
[4] Troolin D; Longmire E (2009) “Volumetric Velocity Measurements of Vortex Rings from Inclined Exits," Experiments in Fluids, 48(3), pp. 409-420.
