Enhanced wind-farm performance using windbreaks

The flow speedup generated by windbreaks can be used to increase the power production of wind turbines. However, due to the increased drag imposed by the windbreaks, their use in large wind turbine arrays has been questioned. We use large eddy simulations to show that windbreaks can increase the power production of large wind farms. A crucial finding is that windbreaks in a wind farm should be much lower than in the single-turbine case. In fact, the optimal windbreak for an isolated turbine can reduce wind-farm performance. The optimal windbreak height in a wind farm namely depends on the right balance between the flow speedup over the windbreak and the drag imposed by all windbreaks in the farm. The increased performance is a result of the favorable total pressure flux created by the windbreaks.

Figure 1

(a) Horizontal and (b) vertical profiles of the normalized streamwise velocity $U/U_h$. Lines, LES data; symbols, field data taken from Finnigan and Bradley [13] as presented in the reanalysis by Wilson [14]. (c) Streamline pattern for flow through a windbreak with porosity $\eta =0.5$. The background color indicates $U/U_h$ and the solid line denotes the windbreak.

Figure 2

Schematic of the layout of a wind farm with windbreaks. In this study, the streamwise and spanwise turbine spacings are $S_x=8D$ and $S_y=5D$, and the values of the windbreak width $b$, the windbreak height $h$, and the spacing between the windbreak and turbine $x_t$ are varied. The effects of the windbreak porosity and the number of windbreaks are also studied (not shown in the figure). The background color presents the instantaneous streamwise velocity distribution from case 39 (see Table 1). The blue color levels are between $[-1,18]$ such that dark blue denotes the windbreak wake and light blue denotes the turbine wake. A video showing the development of the flow field is provided in the Supplemental Material [37].

Figure 3

(a) Streamline pattern for flow through a windbreak with porosity $\eta =0.03$. The background color shows the estimated power increase according to the first equality in Eq. (5). The solid line denotes the windbreak. (b) Power production increase for a turbine located at $x_t/h=2$ (blue), $x_t/h=4$ (yellow), and $x_t/h=6$ (red). Solid lines indicate the predicted power production increase calculated from the flow field over a windbreak obtained from LESs; see (a). Dashed lines are fits to solid lines using the second equality in Eq. (5) with $\beta =0$ and $\alpha =1.9$ (blue), $\alpha =2.4$ (yellow), and $\alpha =2.3$ (red). Symbols indicate the results from simulations in which both the windbreaks and the wind turbines are included.

Figure 4

Normalized power production $P/P_0$ as a function of the downwind position for different values of $x_t$ (see Fig. 2), where $P_0$ is the power production of a stand-alone wind turbine without windbreaks. The windbreak porosity is $\eta =0.03$ and its height is (a) $h/z_h=0.12$, (b) $h/z_h=0.24$, (c) $h/z_h=0.36$, and (d) $h/z_h=0.48$. Values are also listed in Table 1.

Figure 5

The normalized (a) wind-farm $P_{\mathrm{t}}/P_{\mathrm{r}}$ and (b) first-row $P_1/P_0$ power production as a function of the distance $x_t/h$ (see Fig. 2). Here $P_{\mathrm{r}}$ and $P_0$ are the power production of a wind farm and a stand-alone wind turbine without windbreaks, respectively. The windbreak porosity is $\eta =0.03$.

Figure 6

(a), (b) Normalized wind turbine power production $P/P_0$ as a function of the downwind position using a different number of windbreaks $N_{\mathrm{wb}}$ with $\eta =0.03$ located at (a) $x_t/h=6,h/z_h=0.12$ and (b) $x_t/h=4,h/z_h=0.24$. (c) The corresponding normalized wind-farm power production ($P_{\mathrm{t}}/P_{\mathrm{r}}$; filled symbols) and the first-row power production ($P_1/P_0$; open symbols) as a function of the number of windbreaks.

Figure 7

Normalized streamwise velocity deficit $(U-U_{\mathrm{ABL}})/U_{\mathrm{hub}}$ in the midplane of the turbine. The distance between the windbreak and the turbine is $x_t/h=4$. The windbreak porosity is $\eta =0.03$ and its height is (a) $h/z_h=0$, (b) $h/z_h=0.12$, (c) $h/z_h=0.24$, (d) $h/z_h=0.36$, and (e) $h/z_h=0.48$. Solid lines indicate turbine and windbreak locations.

Figure 8

Normalized streamwise velocity variance ${\sigma }_u/U_{\mathrm{hub}}$ in the midplane of the turbine. The distance between the windbreak and the turbine is $x_t/h=4$. The windbreak porosity is $\eta =0.03$ and its height is (a) $h/z_h=0$, (b) $h/z_h=0.12$, (c) $h/z_h=0.24$, (d) $h/z_h=0.36$, and (e) $h/z_h=0.48$. Solid lines indicate turbine and windbreak locations.

Figure 9

Energy budget for wind farms with different windbreak heights $h$ as a function of the downwind position. The windbreak is located $x_t=4h$ upwind of the turbines. Each term in the energy budget equation, (9), is normalized with the power production of an isolated wind turbine $P_0$. The windbreak is two-dimensional and has a porosity $\eta =0.03$.

Figure 10

Normalized vertical kinetic energy flux $-{10}^3\overline{{\tilde{u}}^{\prime }{\tilde{w}}^{\prime }}\overline{\tilde{u}}/U_{\mathrm{hub}}^3$ in the midplane of the turbine. The distance between the windbreak and the turbine is $x_t/h=4$. The windbreak height is (a) $h/z_h=0$, (b) $h/z_h=0.12$, (c) $h/z_h=0.24$, (d) $h/z_h=0.36$, and (e) $h/z_h=0.48$. The windbreak porosity is $\eta =0.03$. Solid lines indicate turbine and windbreak positions.

Figure 11

(a), (b) Normalized wind turbine power production $P/P_0$ as a function of the downwind position for different windbreak porosities when (a) $x_t/h=6,h/z_h=0.12$ and (b) $x_t/h=2,h/z_h=0.24$. (c) The corresponding normalized wind-farm ($P_{\mathrm{t}}/P_{\mathrm{r}}$; filled symbols) and first-row ($P_1/P_0$; open symbols) power production as a function of the windbreak porosity.

Figure 12

(a), (b) Normalized wind turbine power production $P/P_0$ as a function of the downwind position for different windbreak widths $b$ with (a) $x_t/h=6, h/z_h=0.12$ and (b) $x_t/h=2, h/z_h=0.24$. (c) The corresponding normalized wind-farm power production ($P_{\mathrm{t}}/P_{\mathrm{r}}$; filled symbols) and the first-row power production ($P_1/P_0$; open symbols) as a function of the windbreak width. The porosity is $\eta =0.03$.