This makes understanding the post-recovery process extremely important for optimizing wind farm efficiency. The results provide insight into the recovery mechanism of VAWT and possible means to control it.
Motivation
This provides evidence that the wake interactions between individual VAWTs could enhance, rather than purely diminish, the overall performance of an array. Exploiting such constructive wake interactions would represent a paradigm shift in the design of efficient wind farms.
A brief overview of VAWTs
A major difficulty, however, lies in the fact that the aerodynamics of the VAWT wake are not well understood, thus providing an opportunity for further investigation. Despite this history, VAWTs have not seen as much commercial success as HAWTs in modern times, and a consequence of this has been a lag in the literature focused on improving their design.
Scope of the current work
Specifically, the speed in the wake of three different turbine models is compared with that of a circular cylinder with the same aspect ratio. The results also demonstrate a link between the dynamic and stable characteristics of the VAWT wake, which has important implications for energy production within a wind farm.
Analytical model
However, a branch of potential flow theory known as free flow theory has been successfully used to estimate drag and the shape of a uniform wake in cavity flows (Birkhoff & Zarantonello, 1957) and behind steep bodies (Wu, 1962). A basic assumption of both F¨opple's system and free-stream theory is that the non-zero resistance to a body in a potential flow requires explicit modeling of the wake region; this is a feature of the LRB model.
Experimental Methods
- Field site and wind turbines
- Wind velocity measurements
- Power measurements
- LRB Model Calibration
Calibration of the sink spacing model parameter, ss. a) Least squares fit to the field data for the single VAWT. Comparison of the LRB model with meteorological tower streamwise velocity measurements for the four-turbine array.
Results
LRB model prediction of individual turbine performance
The effect of wind direction on turbine performance for the four turbine array indicated. a) Schematic of the array with wind direction bins. Qualitatively, there is good agreement between plots of field data and those of the LRB model.
LRB model prediction of turbine array performance
Also of interest is that the LRB model appears to under-predict the performance of turbines 5 and 14, which are on the outer corners of the array. The total array performance as a function of the position of turbine A is shown in Figure 2.12 (d).
Robustness of LRB model prediction of array performance
Parameter study of the LRB model prediction of array performance with varying sink spacing, ss, model parameter. The purpose of this section is to provide additional background information and details on the development of the LRB model.
Conclusions
It is prudent to note that this simplified model is not intended to capture the complex structure and dynamics of the three-dimensional turbulent flow found in wind farms, e.g. The other effect is that of the turbine slack, which slows the flow locally and leads to a decrease in performance for downstream turbines.
Description of experimental test cases
Flow-driven turbine
Here the net torque due to lift, Tlift, balances the net torque due to drag, Tdrag. Here the net torque due to lift, Tlift, of the blades exceeds the torque due to drag, Tdrag, and is offset by the torque added by an applied load, Tload.
Motor-driven turbine
The torque components contributing to the total axle torque are shown in each regime with colored arrows. Note that only torques due to engine and aerodynamics are considered, i.e. friction is neglected. In the following, the near-wake characteristics of a 3-bladed VAWT are evaluated across all three regimes and compared with flow-driven cases when possible.
Experimental Setup
Model turbine
The turbine diameter was 0.3 m, measured by a circle tangent to the chord of each airfoil. The turbine stall ratio, based on the frontal projected area, varied between 8 and 16% during one revolution.
Water channel facility
Diagnostics
A sample free-stream velocity profile in the downstream direction is shown in Figure 3.8(b), corresponding to a pump speed of 15.5 Hz. In the flow-driven cases, the torque sensor end shaft either rotated freely or was slowed by a brake, as shown in Figure 3.9(a). In the motor cases, the torque sensor final shaft was connected to a DC motor (Pittman GM14904S013-R1) as shown in Figure 3.9(b) and was controlled by a constant voltage power supply (Mastech HY3005F-3) capable of providing 0- 30V at 0-5A.
Experimental procedure
- Turbine neutral curve
- PIV measurement conditions
- Calculation of wake statistics
- PIV error analysis
The 'driver' of the turbine rotation is indicated as either 'flow' for flow-driven or. The PIV measurements of the track were used to investigate both its steady-state and dynamic characteristics. The circulation, Γ, in the wake of the turbine was evaluated by numerically integrating the vortex within a rectangular area bounded by the contour, C (cf. Figure 3.15).
Results
PIV measurements on or below the neutral curve
It is interesting to note in Figure 3.17(a) a change in the trend of speed recovery as it increases. Comparing figures 3.17 and 3.19, it is interesting to note the similarity between the trend in the development of the flow profile of the velocity with the dependence of the spatial averages. Examining Figures 3.19 and 3.20, it is evident that the spanwise asymmetry in the velocity profile is reflected in the asymmetry of the spanwise Reynolds stress distributions.
Measurements on or above the neutral curve
However, it is still interesting to note from Figure 3.23 that the shape of the velocity profile remains a strong function of λ in this regime. A somewhat surprising result is that the velocity profile of the engine-driven turbine (dashed green line) operating above the neutral curve closely matches the profile of the flow-driven turbine (solid red line) at almost the same λ but higher Reynolds number .
Circulation and torque measurements
However, the trace corresponding to the motor-driven case at λ= 2.02 is unphysical as a current-driven turbine representation. Turbine shaft torque measurements are shown in Figure 3.26 for the same flow conditions as the circulation in Figure 3.25. For this reason, crossing the zero torque value provides a conservative estimate of the theoretical maximum λ for an engine-driven turbine that still gives reliable wake measurements.
Conclusion
This is attributed to a stronger shear layer developing on the side of the turbine where the blades move upstream and is reflected in an asymmetric Reynolds stress distribution across the span. The conclusions of this chapter suggest that the kinematics and aerodynamic properties of the turbine are the only factors determining wake dynamics, regardless of the means of moving the turbine blades. Some changes have been made to the text to bring it into line with the rest of the work presented in this thesis.
Introduction
Recent work by Rolin & Port'e-Agel (2015) has examined the far flow of a VAWT, up to approximately 7 rotor diameters downstream of the turbine. They noted that the effect of the boundary layer on the wave core was to re-energize the region with a downward momentum sink. The dynamic characteristics of the wake velocity are analyzed using spectral analysis and appropriate orthogonal decomposition.
Experimental methods
- Turbine rotor and cylinder geometry
- PIV setup
- Experimental procedure
- Turbine and cylinder power coefficient, C p
- PIV measurement conditions
- Calculation of wake statistics
In both cases, vorticity is shed in the wake due to the interaction of the flow with the turbine blades;. In addition, a segment of the time series of v0, the velocity component used in the spectral analysis, is shown in Figure 4.7. The power spectra for the spanwise component of the velocity fluctuations (v0) were calculated by the method of Welch (1967).
Results & discussion
PIV measurements for load-free shaft conditions
In the near wake region of the turbine there is a sharp spectral peak corresponding to the blade passing frequency. An analysis of the dominant POD mode illustrates the spatiotemporal variation of the velocity fluctuations in the wake. Right half: contours of the spanwise component (v0) of the dominant POD mode for the velocity fluctuations at the blade passage frequency for the (b) 2-blade VAWT, (d) 3-blade VAWT, and (f) 5-blade VAWT.
PIV measurements for loaded-shaft conditions
Dynamic solidity of a VAWT
The dotted circle in the turbine diagrams is for reference only and corresponds to the turbine diameter. We first define a characteristic length scale, l, as the sum of the holes in the circumference of the turbine rotor, that is, l =πD(1−σ). The ratio tV/tconv represents the percentage of convection time required to close the gaps between the blades, with a smaller percentage resulting in the turbine appearing more solid to the incident flow.
Effect of dynamic solidity on wake transition
Vertical dashed lines correspond to the location of the streamwise transition points in each case, i.e. X/D transition. It was found that a strong relationship exists between the dynamic solidity, σD, and the downstream transition location, X/Dtransition, as shown in Figure 4.18. When the abscissa for each case in Figure 4.17 is normalized by X/D transition, given by Equation 4.2, and the ordinate by the non-dimensional blade passage frequency in each case, Stblade, defined as.
Effect of dynamic solidity on velocity recovery
Referring to Prandtl's mixing length hypothesis, Schlichting (1960) derived an expression for the recovery of the centerline velocity deficit, viz. minimum, after a bluffed body. Note that the curves have been fitted to the measured data for the absolute minimum velocity for each case. All the measured values, including the cylinder data, are shown in Figure 4.25 with the proposed scaling of the ordinate axis.
Insight into three-dimensional effects
Measurements are shown along the Z-axis normalized by the rotor height, H, where Z/H = 0.64 at mid-span of the rotor. An important question to answer, however, is how the Reynolds stresses compare in different measurement planes, as this is more telling of which direction makes the larger contribution to wake recovery. This suggests that although vertical velocity fluctuations play an important role in track dynamics and recovery, the dominant effect may be characterized by spanwise fluctuations, as was done in this analysis.
Rotating cylinder comparison
It is evident from these figures that the vertical shear stress, i.e., < u0w0 >, is approximately the same as the spatial shear stress, i.e.,
Concluding remarks
This indicates that the dominant effect of velocity fluctuations on wave recovery can be characterized by the present analysis in the UV plane. Furthermore, it is reasonable to assume that the aspect ratio of the turbine plays an important role in the wave structure, just as it does for circular cylinders. Furthermore, a coordinate transformation was proposed using σD in which the velocity recovery profiles of the VAWT wake matched that of the cylinder wake, suggesting that bluff body oscillations are more favorable for wave energy capture .
Avenues for future work
U2 is taken as the potential flow velocity just upstream of the turbine center at the position x = −ru in the LRB model. 2015 PIV measurements and CFD simulation of the performance and flow physics of a small-scale vertical axis wind turbine. 2000 A DPIV study of the underlying vortex elements of the blades of a horizontal axis wind turbine in yaw motion.
