On the Evolution of the Integral Time Scale within Wind Farms

Abstract

A wind-tunnel investigation was carried out to characterize the spatial distribution of the integral time scale (T u ) within, and in the vicinity of, two model wind farms. The turbine arrays were placed over a rough wall and operated under high turbulence. The two layouts consisted of aligned units distinguished only by the streamwise spacing (∆x T ) between the devices, set at five and ten rotor diameters d T (or S x = ∆x T /d T = 5 and 10). They shared the same spanwise spacing between turbines of 2.5d T ; this resulted in arrays of 8 × 3 and 5 × 3 horizontal-axis turbines. Hotwire anemometry was used to characterize the instantaneous velocity at various vertical and transverse locations along the central column of the wind farms. Results show that T u was modulated by the wind farm layout. It was significantly reduced within the wind farms and right above them, where the internal boundary layer develops. The undisturbed levels above the wind farms were recovered only at ≈d T /2 above the top tip. This quantity appeared to reach adjusted values starting the fifth row of turbines in the S x = 5 wind farm, and earlier in the S x = 10 counterpart. Within the adjusted zone, the distribution of T u at hub height exhibited a negligible growth in the S x = 5 case; whereas it underwent a mild growth in the S x = 10 wind farm. In addition, the flow impinging the inner turbines exhibited T u /T u inc < 1, where T u inc is the integral time scale of the overall incoming flow. Specifically, T u → βT u inc at z = z hub , where β < 1 within standard layouts of wind farms, in particular β ≈ 0.5 and 0.7 for S x = 5 and 10.

Multiple Wind Turbine Wakes Modeling Considering the Faster Wake Recovery in Overlapped Wakes

“…This expression meets two requirements: First, the coefficient is always less than 1 characterizing less total loss in the wake overlay area due to the higher turbulence level. Second, according to some experimental results [39,40], smaller upwind turbine spacing could lead to larger turbulence intensity in the superimposed area. So the mixing coefficient tends to be smaller with denser upwind turbines, which means faster velocity recovery.…”

Wind Turbines with Truncated Blades May Be a Possibility for Dense Wind Farms

“…Independent electric stepper motors are used to rotate the rods at a frequency of 0.1 Hz with random direction changes; additional information of the TG setup can be found in Jin et al [23]. The resulting turbulence structure contained a well-developed inertial subrange spanning approximately two decades [24]. Surface roughness was also added to promote the development of the turbulent boundary layer (TBL); it consisted of 5 mm bulk diameter chains placed in the spanwise direction every 0.2 m along the test section [25].…”

Spatiotemporal Correlations in the Power Output of Wind Farms: On the Impact of Atmospheric Stability

“…The RSH makes the assumption that the sweeping velocity occurs at length and time scales that are very large compared to turbulence scales of interest. This is a valid assumption for large-scale atmospheric motions, which may be kilometers long and last over timescales on the order of tens of minutes, as compared to typical ∼1 km interturbine separations in wind farms, and the resultant advection time of ∼60 s. However, this is not true for wake-added turbulent motions, which are typically over timescales an order of magnitude higher than the time it takes for the rotor to complete one revolution and smaller [31,32], so that the wake-added motions are similar or smaller in scale to the advection time scale, allowing them to nonlinearly interact. Wake-added motions may then not be expected to contribute to the coherence between turbine pairs, with the coherence instead being dominated by the impinging of turbulent motions from above.…”