Wakes behind surface-mounted obstacles: Impact of aspect ratio, incident angle, and surface roughness

The so-called wake-moment coefficient ${\tilde{C}}_h$ and lateral wake deflection of three-dimensional windbreaks are explored in the near and far wake. Wind-tunnel experiments were performed to study the functional dependence of ${\tilde{C}}_h$ with windbreak aspect ratio, incidence angle, and the ratio of the windbreak height and surface roughness $\left(h/z_0\right)$. Supported with the data, we also propose basic models for the wake deflection of the windbreak in the near and far fields. The near-wake model is based on momentum conservation considering the drag on the windbreak, whereas the far-wake counterpart is based on existing models for wakes behind surface-mounted obstacles. Results show that ${\tilde{C}}_h$ does not change with windbreak aspect ratios of 10 or greater; however, it may be lower for an aspect ratio of 5. ${\tilde{C}}_h$ is found to change roughly with the cosine of the incidence angle, and to depend strongly on $h/z_0$. The data broadly support the proposed wake-deflection models, though better predictions could be made with improved knowledge of the windbreak drag coefficient.

Figure 1

Basic schematic of the experimental setup. Symbols $\mathrm{\Phi },\delta$, and $\theta$ denote porosity, boundary layer, and inclination angle. The origin of the coordinate system $(x,y,z)=(0,0,0)$ is set at the windbreak center.

Figure 2

Normalized cutoff location $x_c/h$ between near and far wakes of a windbreak as a function of $h/z_0$.

Figure 3

Near- and far-wake estimation from the proposed models for wake deflection of a windbreak. Solid black line indicates $\beta =1$, whereas dashed lines indicate $\beta =1\pm 0.25$.

Figure 4

A moment that is not aligned with the axis will lead to a perturbation velocity which is not aligned with the axis of the wind.

Figure 5

Wake-moment coefficient ${\tilde{C}}_h$ for the tested $A=b/h$ and $\theta$.

Figure 6

Measured wake-moment coefficient ${\tilde{C}}_h$ as a function of $h/z_0$.

Figure 7

Measurements (symbols) and predictions (solid lines) of the normalized wake deflection $\left(\delta /h\right)$ for all tested $A\left(=b/h\right)$ and $\theta$: (a) $x/h=55$ and (b) $x/h=105$.

Figure 8

Measured (+) and predicted (solid line for $\beta =1$, dashed line for $\beta =1.1)$ normalized wake deflection $\left(\delta /h\right)$ at several downstream locations for a windbreak with $A=10$ and $\theta ={30}^{\circ }$.