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A wind tunnel simulation of the mean velocity fields behind upright porous fences
Agricultural and Forest Meteorology 146 (2007) 82–93 www.elsevier.com/locate/agrformet
A wind tunnel simulation of the mean velocity fields behind upright porous fences Zhibao Dong *, Wanyin Luo, Guangqiang Qian, Hongtao Wang Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 260 West Donggang Road, Lanzhou, Gansu Province 730000, China Received 20 February 2007; received in revised form 27 April 2007; accepted 18 May 2007
Abstract Porosity is the most important parameter that determines the efficiency of wind fences. The present study provided a deeper understanding of mean flow regime behind fences with different porosities at different wind velocities by means of a scaled wind tunnel simulation. Velocities were measured using particle image velocimetry and the mean velocity field was obtained and discussed. The mean velocity fields obtained at different wind velocities were similar. Analyzing the streamline patterns revealed an inherent link between fence porosity and mean airflow characteristics behind the fence. The optimal fence porosity is considered to be the critical porosity above or below which airflow characteristics differ strongly. According to the present study, the optimal porosity is found to be around 0.2 or 0.3, which corresponds to a critical porosity above which bleed flow dominates and below which reversed flow becomes significant. The parameters characterizing the reverse cell behind fences were well correlated with porosity. The velocity profiles revealed seven typical flow regions behind fences, characterized by different velocity gradients. The airflow becomes less complicated and the number of flow regions decreases as fence porosity increases. Some regions, especially the reverse cell and small vortex, disappear when the porosity exceeds a certain value. The flow regions gradually merge as the distance downwind increases, and eventually recover a single velocity profile due to downward transfer of momentum from overlying layers. The recovery distance decreases with increasing fence porosity. # 2007 Elsevier B.V. All rights reserved. Keywords: Upright porous fences; Mean velocity regime; Streamline patterns; Flow regions; Optimal fence porosity
1. Introduction Windbreaks are the earliest devices used to improve windy climatic conditions to serve human needs. They are widely used in coastal, arid, and cold areas to retard wind and to check sand and snow drift, and have been studied in a systematic manner since the 1940s with the goal of finding the optimal windbreak—one that yields optimal protection at the minimum cost (Plate, 1971).
* Corresponding author. Tel.: +86 0 931 8271167; fax: +86 0 931 8277169. E-mail address: [email protected] (Z. Dong). 0168-1923/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2007.05.009
However, there is as yet no clear optimal design for windbreaks (Cornelis and Gabriels, 2005). Fences that are always constructed to have optical porosities greater than zero (Guan et al., 2003) are important artificial windbreaks. They can be classified as upright, horizontal, griddled, holed-plank, and windscreened (Fig. 1), depending on the available materials. Upright fences, usually made of wood bars, bunches of straws or reeds, or tree branches, are widely used to check drifting sand and drifting snow because of their easy availability, low cost, and simple construction. For example, upright fences made of reed bunches are used in the frontal edge of the shelter system that has been constructed along more than 400 km of highway
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Fig. 1. Types of fences: A. Upright fence; B. Horizontal fence; C. Gridded fence; D. Holed-plank fence; E. Wind screen.
crossing the shifting dune fields of China’s Taklimakan Desert (Fig. 2). The most important structural feature of a fence is its porosity (Heisler and Dewalle, 1988). The function of a windbreak is to reduce wind velocity within a certain distance. Maximum wind reductions are closely related to porosity, with low porosity producing high maximum
Fig. 2. The blowing-sand shelter system along the highway crossing China’s Taklimakan Desert: The shelter system consists mainly of checkerboard reed barriers that fix shifting dunes, with fences constructed from reed bunches set at the frontal edge of the shelter system to check drifting sand and extend the expected working life of the reed check barriers.
reductions. However, fences with very low porosity create more turbulence downwind than medium- and high-porosity fences. The higher turbulence produced by low-porosity fences may result in the recovery of mean horizontal wind velocities to levels equal to upwind velocities at a distance closer to the fence, thereby decreasing the shelter distance. Consequently, all else being equal, there should be a fence porosity that provides the optimal shelter effect by balancing the reduction of wind speed with the effects on shelter distance. Since at least the 1970s, considerable effort has been devoted to defining the optimal porosity of fences and other windbreaks. These efforts have included field measurements (e.g., Hagen and Skidmore, 1971a,b; Miller et al., 1975; Jacobs, 1985; Bofah and Alhinai, 1986; Schwartz et al., 1995; Wilson, 1997; Boldes et al., 2001), wind tunnel simulations (e.g., Iversen, 1981; Ranga Raju, 1988; Papesch, 1992; Boldes et al., 1995; Judd et al., 1996; Yaragal et al., 1997; Lee et al., 2002; Guan et al., 2003; Park and Lee, 2003), and numerical simulations (e.g., Wilson, 1985; Fang and Wang, 1997; Pattone et al., 1998; Packwood, 2000; Vigiak et al., 2003; Alhajraf, 2004). A common physical way to express the aerodynamic effect of a windbreak is in terms of its resistance to the flow, or in terms of a
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dimensionless parameter such as a drag coefficient (Raine and Stevenson, 1977; Jacobs, 1985). All published results have shown that the drag coefficient decreases with increasing fence porosity (Hoerner, 1965; Hagen and Skidmore, 1971b; Seginer, 1972; Wilson, 1985; Guan et al., 2003). This implies that fences with lower porosity provide a better shelter effect, and that solid fences would have the best efficiency. This obviously contradicts the observed facts. Thus, the drag coefficient alone is unable to provide significant information for defining optimal porosity, though it is an important parameter in characterizing the disturbance of airflow by fences. There must be other factors that can better characterize the shelter effect created by fences. A review of published results shows that the optimal porosity ranges from 0.3 to 0.5. Hagen and Skidmore’s (1971a) field measurements indicated that a windbreak with a porosity of 0.4 produced the lowest wind velocity over the largest downwind area. Lin et al.’s (1984) field test on the southeastern edge of China’s Tengger Desert suggested that porosities of 0.3–0.4 should be used for fences 0.8–1.0 m tall to avoid sand accumulation upwind of the fence. Lee et al.’s (2002) wind tunnel results showed that a porous wind fence with a porosity of 0.3 was the most effective for abating windblown sand particles because this fence had the maximum threshold velocity (i.e., produced the greatest increase in the wind velocity required to initiate sand movement behind the fence) among the porous fences in their study. Dong et al.’s (2006) wind tunnel simulation indicated that fences with porosities of 0.3–0.5 (depending on fence height) had the maximum relative threshold wind velocity and maximum effective shelter distance, and were thus, most suitable for controlling wind erosion. Researchers believe that there must be some inherent link between shelter efficiency and the flow regime characteristics behind fences, but how these parameters are correlated is not yet clear. Several researchers (e.g., Perera, 1981; Borges and Viegas, 1988; Wilson, 1997; Lee and Kim, 1998; Lee and Park, 1999; Dong et al., 2006) attempted to define the optimal porosity by measuring and analyzing the velocity, turbulence, shear stress, pressure, and sediment susceptibility to wind transport behind fences. They found noticeable changes in the flow characteristics at a porosity around 0.3 or 0.4. For example, Raine and Stevenson (1977) demonstrated in their tests that a fence with a porosity of 0.2 gave the best overall reduction in leeward mean velocity. Perera (1981) found that the Reynolds shear stress and turbulent kinetic energy were strong behind
the fence when the porosity was less than 0.3, whereas the bleed flow (i.e., air passing through the fence rather than over it) was strong when the porosity was greater than 0.4. By measuring the velocity field and surface pressure distributions, which directly influence the shelter effect produced by wind fences, Lee and Kim (1998, 1999) found a porous fence with a porosity of 0.3–0.4 to be the most effective for reducing the mean velocity and surface pressure fluctuations. However, limitations in measurement technology have prevented precise measurement of the characteristics of flow regimes, particularly near fences. The leeward wind used to be measured using conventional anemometers, but hot-wire anemometers provided much more detailed information about the leeward flow turbulence and were soon used by researchers. However, both conventional anemometers and hot-wire anemometers have difficulties in obtaining detailed measurements close to fences, and both may influence the flow field to some extent. The development of particle image velocimetry (PIV) improves our ability to measure the flow velocity field because the technique is non-intrusive, and as a result, it is finding ever more applications in theoretical studies (Stanislas et al., 2000). This unique optical method can capture the whole velocity field of flowing air within a fraction of a millisecond. We thus, believe that it should be an appropriate tool to study the velocity fields behind fences. In the present paper, we present the results of a scaled wind tunnel simulation study in which we obtained airflow fields and wind-velocity profiles at different locations behind fences with different porosities by means of PIV. This approach has the advantage over other commonly used methods of providing simultaneous non-intrusive velocity measurements within the whole target area. PIV can provide more detailed information on the airflow fields behind fences, enabling measurement of the mean velocity field, turbulence structure, shear stress, and pressure. The mean velocity field is discussed in this paper; the turbulence structure, shear stress, and pressure will be discussed in a future paper. We have also attempted to relate the mean flow characteristics to the optimal fence porosity so as to provide a deeper understanding of the aerodynamics of wind fences. 2. Scaled wind tunnel simulation 2.1. Experimental set-up The scaled simulation experiments were carried out in a blowing sand wind tunnel at the Key Laboratory of
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Desert and Desertification of the Chinese Academy of Sciences. The blow-type non-circulating wind tunnel has a total length of 37.8 m, with a 16.2-m long test section. The cross-sectional area of the test section is 0.6 1.0 m. The free-stream wind velocity in the wind tunnel ranges from 1 to 40 m s 1. The thickness of the boundary layer in the test section is typically more than 120 mm. The experimental set-up is shown in Fig. 3. We constructed fence models from rigid stainless-steel wires 1.2 mm in diameter. Wires were cut into straight segments of the required length to produce the desired fence height. The wire segments were then inserted in a row into a bed made of talcum powder paste contained in a wooden groove that was 1 m long (equal to the cross-sectional width of the wind tunnel) by 50 mm wide to create the fence (Fig. 3). The vertical wires were spaced at regular intervals, and the porosities of the fences were adjusted by changing the spacing between wire segments. We created a total of 11 fence models, with the height held constant at 20 mm and spacing varied to create 11 optical porosities (h = 0.05, 0.10, 0.15, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90) that were defined using the ratio between the total open area between the wires and the total area (i.e., 0.02 m2) occupied by the fence. In our test, these porosity values were defined by subtracting the total width of the wires from the 1-m width of the fence, and expressing the
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result as a ratio of the 1-m width of the fence. A solid fence (zero porosity) was also tested using a 1-m long, 2-mm thick piece of plywood. During testing, the fence models were positioned 12 m downwind from the start of the test section of the wind tunnel to ensure the development of consistent airflow. We measured wind velocity field behind the model fences using a PIV device provided by the Beijing Cubic World Science & Technology Development Co., Ltd. This newly developed measurement technique is based on laser imaging technology and digital image processing; for more details concerning the measurement principle, refer to Stanislas et al. (2000). We used very fine talcum powder (with a mean diameter less than 10 mm) as a seeding material. The wind velocity measurements obtained by PIV using this kind of seeding material were calibrated using a Pitot static tube before the test, and the difference between the two measurements was found to be less than 0.5%. An electric duster sprayed the powder from the side of the wind tunnel at the entrance of the test section so that the tracer powder moved with the wind. The CCD (charge-coupled device) camera of the PIV system was set 0.55 m from the light sheet, resulting in a target measurement area 136 mm wide by 102 mm tall (producing a 1600 1200 pixel image with a magnification coefficient of 0.085). By setting the CCD camera at different positions and combining the
Fig. 3. Schematic diagram of the experimental set-up.
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measurement results, the measurement area reached 950 mm wide by 102 mm tall and provided sufficient information about the lee airflow pattern. The image acquisition rate was set at 20 frames per second. The final wind velocity represented the average of the values recorded over a period of 40 s (i.e., 800 frames). Each pair of two frames yields a wind-velocity dataset. The final measurement results thus, represent the average of 400 records, ensuring its statistical significance. 2.2. Similarity considerations The present test intends to investigate the airflow around the reed-bunch fences used along the highway in China’s Taklimakan Desert, which have a height about 1.0–1.2 m and a diameter of 50–60 mm for the reed bunches. Consequently, the geometric scaling of the models was about 1:50, and the Reynolds number scaling for dynamic similarity was impossible to attain. However, the simulation scale tried to meet the general requirements of ‘‘Reynolds number independence’’ recommended by White (1996). For example, the chosen height of the models produced a characteristic scale height to surface boundary layer height ratio of 0.17. Thus, it could be assumed that the wind tunnel’s flow depth posed little restriction on boundary layer development above the fence models (White, 1996). During the testing, the prepared fence models were positioned 12 m downwind from the leading edge of the test section of the wind tunnel, which is 100 times the boundary layer thickness and thus, meets the general rule for matching mean velocity profiles (White, 1996). Four wind velocities that are typically observed causing sand motion in the Taklimakan Desert were investigated (8, 10, 12, and 14 m s 1) so that the flow Reynolds numbers defined by thickness of the boundary layer (Re = Ud/v, where Re is the flow Reynolds number, U is the free-stream wind velocity, d is the thickness of the boundary layer, 0.12 m, and v is the kinematic viscosity of air, 1.4 10 5 m2 s 1) were sufficiently high, and ranged from 6.9 104 to 12.0 104. In addition, wind profiles measured over the bare tunnel floor yielded estimates of roughness Reynolds numbers defined by the aerodynamic roughness length (Rer = Uz0/v, where Rer is roughness Reynolds number, z0 is the aerodynamic roughness length that ranges from 0.0036 to 0.004 mm) ranging from 2.3 to 3.6 (corresponding to real flow Reynolds numbers defined by the height of work section of the wind tunnel ranging from 3.4 105 to 6.0 105) for the velocity range from 8 to 14 m s 1, respectively. Under these conditions, wind tunnel flows simulated the full-scale aerodynamically rough condi-
tions and Reynolds number independence existed (Townsend, 1956; Snyder, 1972; White, 1996). 3. Results and discussion 3.1. Streamline patterns Airflow fields behind porous fences are complicated by the presence of both the bleed flow that passes through the gaps in the fences and the displaced flow that passes over the fences. The relative significance of bleed flow and displaced flow differs as the fence porosity changes. For a solid fence, no bleed flow exists, whereas this flow is dominant for highly porous fences. The typical streamline patterns behind a porous fence are illustrated in Fig. 4. As airflow approaches the fence, the streamlines are lifted to different extents and produce a higher velocity above the fence (Fig. 5), although the streamline lift is very slight when the porosity is greater than 0.6. A high-velocity region forms above the fence. The wind’s momentum is transported to higher levels, resulting in a region with low wind velocity behind the fence. The flow lift grows stronger but the bleed flow becomes weaker as porosity decreases. In particular, flow separation is initiated from the top of the fence and the separation line extends downstream 8–16 times the fence height (i.e., to a distance of 8–16H) when the porosity is less than 0.3, depending on the fence porosity. Since the shape ratio (thickness/height) of the fence models was only 0.06, the flow can be regarded as a ‘‘thin fence flow’’ (Durst and Rastogi, 1980). The shear layer that separates from the leading edge of the fence does not reattach at the upper surface of the fence. Immediately leeward of the point of flow separation is a separation cell characterized by the presence of a back-eddy, which represents
Fig. 4. A typical streamline patterns behind a porous fence (h = 0.10, U = 10 m s 1). l is the reattachment distance, h is the height of the reverse cell above the floor of the wind tunnel, R is the reattachment point.
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Fig. 5. A typical iso-wind velocity chart behind a porous fence (h = 0.10, U = 10 m s 1).
Fig. 6. Typical streamlines, showing the reattachment point (R in Fig. 4) for h = 0.05 and U = 10 m s 1.
an area of reversed flow with a negative wind velocity (Figs. 4 and 5). The maximum fence porosity below which flow separation and reversal occurs is defined as the critical porosity. Experimental results reveals that the critical porosity should be between 0.2 and 0.3, though we cannot offer a more precise value because no tests were made between these two porosities. This is in good agreement with Baltaxe’s (1967) field observations and Lee et al.’s (2002) wind tunnel results. In accordance with their results, the critical porosity was around 0.25 and 0.30. The critical porosity revealed in current study is less than those proposed by Perera (1981), Lee and Kim (1999), and Dong et al. (2006). According to their results, the critical porosity should be 0.3–0.4. The lower critical porosity proposed by Baltaxe (1967) and Lee et al. (2002) and confirmed by the present study than that reported by other authors is because that the flow field was observed at some distance above the ground so that any flow reversal close to the surface would not be revealed. Baltaxe’s (1967) field observations with a rotating vane did not provide data near the ground surface. Lee et al. (2002) defined the reversed flow by observing backward movement of particles on a sand pile behind a fence. The lowest level at which wind flow was detected in the present study was about 3 mm, or 15% of the fence height above the ground. Taking this factor into account, the critical porosity should be over 0.2 or around 0.3. Above this critical porosity, bleed flow is dominant. From these results, it can be concluded that the widely proposed optimal fence porosity of 0.3–0.4 should correspond to the critical porosity above which bleed flow is dominant. The shape of the reverse cell resembles an ellipse when the porosity is less than 0.3. Flow begins to recover some distance downwind from the reverse cell. We chose four parameters to characterize the reverse cell: reattachment distance (l), height above the floor of the wind tunnel (h), area (S), and aspect ratio (A). The
reattachment point is determined by examining the horizontal velocity component at ground level to determine the point where the horizontal velocity changes sign from upwind (negative) to downwind (positive) (Fig. 6). The reattachment distance characterizes the long (horizontal axis) of the reverse cell. Theoretically, the downwind apex of the reverse cell and the reattachment point are located at different positions. The former can be above the surface but the latter must be at the surface. In practice, the difference in their positions should be so small that it can be neglected and the locations of both the downwind apex of the reverse cell and reattachment point can thus, be characterized by a single parameter: the reattachment distance. The height of the reverse cell can be roughly defined by the position of the uppermost boundary of the closed streamlines. This height characterizes the short (vertical) axis of the reverse cell. The area of the reverse cell is defined as the area enclosed by the outermost boundary of the flow lines that define the reverse cell and represents the magnitude of the development of flow reversal. The aspect ratio is defined as the ratio of the height of the reverse cell to the reattachment distance, and thus, characterizes the degree of vertical flatness of the reverse cell. The remainder of this section will discuss these parameters, especially in terms of their variation as a function of fence porosity. The reattachment distance and height of the reverse cell are expressed as multiples of fence height (H), and the area of the reverse cell is converted to a dimensionless relative area expressed as S/H2. Fig. 7 shows that the reattachment distance varies as a function of both fence porosity and wind velocity. The reattachment distance ranged from 8.4 to 16H for a porosity of 0.2 or less. The variation as a function of fence porosity is much more pronounced than that with respect to the wind velocity. The maximum difference in the reattachment distances for the four wind velocities equaled 2.9H, whereas the difference as a
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function of the different porosities was generally greater than 4.5H. The reattachment distance reaches a maximum at a porosity of 0.10 for all four wind velocities. It increases with increasing fence porosity when porosity is less than 0.10 but decreases with increasing fence porosity when the porosity is greater than 0.10. Fang and Wang’s (1997) numerical simulation results showed that the reversed cell extended farther downstream as the fence became more porous, but they did not report a decrease in the reattachment distance with increasing porosity when the fence porosity was greater than a certain value. Dong et al. (2006) defined the reattachment distance by observing the direction of particle movement. Their results are compared with those obtained in the present study in Fig. 8. The results are well correlated, but the reattachment distance defined based on particle move-
ment is always greater than that defined by means of PIV. This is because the reattachment distance defined based on particle movement represents the reattachment distance on the ground, whereas that obtained in the present study represents the result at some distance above the surface. Fig. 9 shows the variation in the dimensionless height of the reverse cell as a function of fence porosity and wind velocity. The dimensionless height of the reverse cell ranged from 0.5 to 1.85H for a porosity of 0.2 or less. As was the case for the reattachment distance, the height of the reverse cell changes more pronouncedly with changing fence porosity than with respect to wind velocity. In general, the height of the reverse cell decreases with increasing fence porosity. This suggests that the downward transfer of wind momentum behind fences becomes faster as the porosity increases. The fence with a porosity of 0.05 has almost the same height of the reverse cell as the solid fence (h = 0). The height of the reverse cell decreases sharply as the fence porosity increases from 0.10 to 0.15. The reverse cell is lower than the fence when porosity is 0.15 or greater but higher than the fence when porosity is 0.10 or less. This is consistent with Fang and Wang’s (1997) numerical simulation results, which showed that the upper bound of the ‘‘vortex area’’ (what we have called the reverse cell) tended to move closer to the ground as the fence porosity increased. Fig. 10 shows the change in the dimensionless area of the reverse cell as a function of porosity and wind velocity. The area of the reverse cell with a porosity of 0.05 is slightly greater than that of the solid fence, and decreases with increasing porosity when the porosity is
Fig. 8. Comparison of the reattachment distance obtained using the PIV method in the current study and the particle movement method described in Dong et al. (2006).
Fig. 9. Variation in the dimensionless height of the reverse cell as a function of fence porosity and wind velocity.
Fig. 7. Variation of reattachment distance as a function of fence porosity and wind velocity.
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Fig. 10. Variation in the dimensionless area of the reverse cell as a function of fence porosity and wind velocity.
Fig. 12. A small vortex developed immediately behind the solid fence and fences with a porosity of 0.05. This example is for h = 0.05 and U = 10 m s 1.
greater than 0.05. Again, the change with respect to porosity is greater than the change with respect to wind velocity. Fig. 11 shows changes in the aspect ratio as a function of the same two parameters. The aspect ratios of the solid fence and of the fences with porosities of 0.05 and 0.10 are relatively constant, but the ratio changes thereafter. The aspect ratios for fences with a porosity of 0.15 and 0.20 vary relatively widely among wind velocities, with no clear pattern. In the presence of a reverse cell, the reattachment point represents the location of flow divergence. However, our results showed that another small vortex developed immediately behind a solid fence and two low-porosity (0.00 and 0.05) fences (Fig. 12), resulting in forward stream in the near-surface layer immediately downwind from the fence. For porous fences, the forward stream was facilitated by the bleed flow that passes through gaps in the fence. The greater the fence’s
porosity, the stronger the bleed flow. This forward air stream meets the reversed backward stream to form a flow-convergence zone. The position of this convergence changes as a function of fence porosity since the relative strengths of the forward flow and the reversed backward flow changes with changing fence porosity (Fig. 13). The forward air stream resulting from the small vortex behind a solid or low-porosity fence is sufficiently strong that the flow convergence zone behind a solid fence extends farther downwind than that behind a fence with a porosity of 0.05. However, the bleed flow strengthens as porosity increases, resulting in an increase of the flow convergence distance with increasing porosity. Dong et al. (2006) observed the
Fig. 11. Variation in the aspect ratio of the reverse cell as a function of fence porosity and wind velocity.
Fig. 13. Variation in the position of the flow convergence zone as a function of fence porosity and wind velocity.
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Fig. 14. Comparison of the positions of flow convergence obtained using the PIV method (current study) and the particle movement method (Dong et al., 2006).
phenomenon of flow convergence by observing particle movement. Their results are compared with those obtained in the present study in Fig. 14. This comparison reveals that the position of flow convergence obtained by the two methods is poorly correlated. This is because the particle movement method defined the position of flow convergence on the ground whereas the PIV method used in the present study defined the position of flow convergence at some distance above the surface. Unlike the reattachment distance, which is always greater on the ground surface than above the surface, the distance of flow convergence may be greater or less on the ground surface than above the surface because it shifts in accordance with the relative strength of the forward and backward air flows. 3.2. Velocity profiles and flow regions The iso-velocity chart (Fig. 5) shows that the airflow behind fences has a different velocity gradient at different locations. The airflow pattern is generally divided into several regions with different aerodynamic behavior, which are characterized by different wind shear and velocity profiles. Fig. 15 shows the typical velocity profiles obtained by means of PIV behind a fence with a porosity of 0.10 and a free-stream wind velocity of 10 m s 1. The smooth curves in Fig. 15 suggest that PIV is a reliable tool for measuring wind velocity above model fences. Velocity profiles deviate from the logarithmic law when the airflow approaches a fence. The deviation increases downwind from the windward side and begins to recover at some distance downwind. Based upon the overall non-log-linear velocity profiles, in which segments of profiles are characterized by their velocity gradients, seven tentative
Fig. 15. An illustration of typical wind velocity profiles and flow regions behind fences (h = 0.10, U = 10 m s 1): A, outer flow; B, overflow; C1, upper wake; C2, lower wake; D, internal boundary layer; E, reverse cell; F, small vortex.
typical layers or regions of airflow can be roughly identified. These are an outer flow region (Fig. 15A), an overflow region (Fig. 15B), a wake region with two layers (Fig. 15C1 and C2), an internal boundary layer (Fig. 15D) that extends downwind from the point of reattachment, a reverse cell (Fig. 15E), and a small vortex (Fig. 15F). Accurate division of these regions is difficult because they are gradually transitional. This is only a tentative division because it is based only on wind profiles and not supported by other data such as momentum fluxes. It must be emphasized that these flow regions are typical for the fully developed airflow behind low-porosity (dense) or solid fences, and that some regions disappear when the fence porosity increases. For example, the small vortex immediately behind the fence disappears when the fence porosity is greater than 0.10, and the reverse cell disappears when the porosity is greater than 0.20. Only two regions can be identified clearly behind a fence with a porosity of 0.90, and they merge to form a uniform logarithmic velocity profile within a distance of 10H. Since the reverse cell was discussed in detail in Section 3.1, the remaining discussion will focus on the other regions. The outer flow region (region A) is characterized by a relatively low velocity gradient and the flow is mostly determined by the conditions in the undisturbed boundary layer far upstream from the fence. Immediately below the outer flow region is an overflow region, which represents a transitional region between the outer flow and the wake region (regions C1 and C2). The height of the boundary between the outer flow region and the overflow region increases gradually as the distance downwind from the fence increases. The velocity gradient in the overflow region is greater than that in the upper part of the outflow region. The velocity gradient in the overflow region tends to increase with increasing distance downwind. Regions C1 and C2
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constitute a wake region below the overflow region and above the internal boundary layer and the reversed cell. The wake region can be viewed as a region of flow recovery in which, overall, the flow is accelerated downwind by downward transfer of momentum from the overlying layers with higher wind velocities. The wake region has an overall S-shaped velocity curve, with the gradient decreasing downwind. It is divided into two sub-regions (C1 and C2) based on differences in the velocity gradient. Region C1 has faster winds and a steeper velocity gradient, whereas region C2 has slower winds and a lower velocity gradient. The division between regions C1 and C2 becomes indistinct and tends to disappear as the distance downwind increases. This results from momentum transfer between the wake region and the overlying or underlying regions. The steep gradient in the upper wake region reflects the rapid downward turbulent momentum transfer from the accelerated overflow region (region B), whereas the less-steep velocity gradient of the lower wake region relates to momentum exchanges with the slower, sheltered flow of the reverse cell (region E). In general, the wake flow expands downwind, resulting in merger of the upper and lower wakes. The wake region is usually considered to be an area of flow recovery where accelerated and displaced flow eventually dissipates turbulent energy downwind via eddy shedding and flow expansion. The upper and lower wake regions in Fig. 15 tend to merge at a certain distance downwind to form a single wind velocity profile with a uniform gradient. This distance increases with decreasing fence porosity. Behind a solid fence, they tend to merge at a dimensionless distance of about 50H, whereas behind the fence with a porosity of 0.90, they tend to merge at a dimensionless distance of 4H. In general, the merge distance decreases as the porosity increases because the airflow recovers faster for highly porous fences. The lowest region (region D) is the internal boundary layer characterized by increasing shear and thickness with increasing distance downwind. The velocity profiles in the internal boundary layer and in the wake region above this layer become more uniform in shape with increasing distance downwind from the point of flow reattachment. The distance required for them to reach equilibrium varies with fence porosity. They typically require a significant distance to reach equilibrium for solid and low-porosity (dense) fences. Judged by the wind velocity profiles, the boundary layer behind the solid fence and the fences with a porosity of 0.10 and 0.20 had not recovered completely within the
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tested leeward distances. The recovery distance is thus, greater than 50H. In contrast, the recovery distance was about 25 and 10H, respectively, for the fences with a porosity of 0.60 and 0.90. In the reverse cell (region E), the velocity gradient increases with the downwind distance to a certain distance, but then decreases. A small vortex (region F) developed behind the solid fence and the fence with a porosity of 0.05. Its extent is much smaller than that of the reverse cell. Its height is lower than the fence and it extends downwind less than 1H. The small vortex results from the high pressure immediately behind the fence, where the wind is almost stagnant. It disappears when the fence porosity is greater than 0.05. 4. Conclusions The mean velocity field behind fences with different porosities was simulated using scaled models in a wind tunnel to provide a deeper understanding of the aerodynamics of porous fences and the optimal porosity. A state of the art non-intrusive PIV technique was employed to obtain precise velocity measurements near the simulated fences. This approach provided rich velocity measurements that enabled a detailed analysis of airflow. A complex velocity field arises behind fences in the presence of both bleed flow and displaced flow (particularly, reversed flow). Porosity is an important parameter in defining the leeward velocity field, whereas wind velocity has a much smaller effect on the velocity field. The relative significance of bleed flow and reversed flow varies as porosity changes. By analyzing the streamline patterns, we revealed an inherent link between the fence’s porosity and the airflow characteristics behind the fence. There is a critical porosity above or below which the airflow characteristics differ strongly. All published results and those obtained in the present study suggest that the optimal porosity is around 0.2–0.3. This optimal porosity corresponds to the critical porosity above which the bleed flow is dominant, and the bleed flow balances the reversed flow at this optimal porosity. The design of wind fences should avoid both a strong bleed flow and a strong reversed flow. In accordance with the previous published results, our results showed that a strong bleed flow, results in insufficient reduction in wind velocity and that a strong reversed flow facilitates the development of turbulent stress, and thus, decreases the shelter distance. Optimal porosity thus, represents a compromise between reduction in wind velocity and shelter distance. Bleed flow and reversed flow must results in the differences of the magnitude and
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directions forces exerted on fences. Further analysis of the forces exerted on fences with different porosity will give us deeper explanation of the aerodynamics of porous fences. This will be a future research need. This paper only relates the optimal fence porosity to the mean velocity field behind fences. There should be a causal relationship between the optimal fence porosity and the patterns of other parameters such as turbulence, shear stress, and pressure. Analysis of different aspects of all these parameters in future research will provide a more thorough understanding of the aerodynamics of wind fences and of the optimal fence porosity. Acknowledgements We gratefully acknowledge the funding received from the Knowledge Innovation Project of the Chinese Academy of Sciences (KZCX3-SW-341), and the National Science Fund for Distinguished Young Scholars of the Natural Science Foundation of China (40225003). References Alhajraf, S., 2004. Computational fluid dynamic modeling of drifting particles at porous fences. Environ. Model. Softw. 19, 163–170. Baltaxe, R., 1967. Airflow patterns in the lee of model windbreaks. Archiv Meteorologie, Geophysik, und Bioklimatologie, Series B: Au¨gemeine und biologische Klimatologie, Band 15, Hefi 3, 26 pp (in German, with English summary). Bofah, K.K., Alhinai, K.G., 1986. Field tests of porous fences in the regime of sand laden wind. J. Wind Eng. Ind. Aerodynamics 23, 309–319. Boldes, U., Colman, J., Maranon, J., Leo, D., 2001. Field study of the flow behind single and double row herbaceous windbreaks. J. Wind Eng. Ind. Aerodynamics 89, 665–687. Boldes, U., Colman, J., Nadal Mora, V., Zumarraga, A., 1995. Velocity fluctuations in the wake behind wind breakers and at the edge of the shear layer, and their correlations with the free stream. J. Wind Eng. Ind. Aerodynamics 58, 217–229. Borges, A.R., Viegas, D.X., 1988. Shelter effects on a row of coal piles to prevent wind erosion. J. Wind Eng. Ind. Aerodynamics 29, 145– 154. Cornelis, W.M., Gabriels, D., 2005. Optimal windbreak design for wind-erosion control. J. Arid Environ. 61, 315–332. Dong, Z., Qian, G., Luo, W., Wang, H., 2006. Threshold velocity for wind erosion: the effects of porous fences. Environ. Geol. 51, 471– 475. Durst, F., Rastogi, A.K., 1980. Turbulent Shear Flows 2. Springer, Berlin, pp. 231–281. Fang, F.M., Wang, D.Y., 1997. On the flow around a vertical porous fence. J. Wind Eng. Ind. Aerodynamics 67–68, 415–424. Guan, D., Zhang, Y., Zhu, T., 2003. A wind-tunnel study of windbreak drag. Agric. Forest Meteorology 118, 75–84. Hagen, L.J., Skidmore, E.L., 1971a. Turbulent velocity fluctuations and vertical flow as affected by windbreak porosity. Trans. ASAE 14 (4), 634–637.
Hagen, L.J., Skidmore, E.L., 1971b. Windbreak drag as influenced by porosity. Trans. ASAE 14, 464–465. Heisler, G.M., Dewalle, D.R., 1988. 2. Effects of windbreak structure on wind flow. Agric., Ecosystems Environ. 22–23, 41–69. Hoerner, S.F., 1965. Fluid Dynamic Drag. Midland Park, NJ, USA, 452 pp. Iversen, J.D., 1981. Comparison of wind tunnel modeling and fullscale snow fence drifts. J. Wind Eng. Ind. Aerodynamics 8, 231– 249. Jacobs, A., 1985. The normal force coefficient on a thin closed fence. Boundary-Layer Meteorology 32, 329–335. Judd, M.J., Raupach, M.R., Finnigan, J.J., 1996. A wind tunnel study of turbulent flow around single and multiple windbreaks, part I: velocity fields. Boundary-Layer Meteorology 80 (1/2), 127–165. Lee, S.J., Kim, H.B., 1998. Velocity field measurements of flow around a triangular prism behind a porous fence. J. Wind Eng. Ind. Aerodynamics 77/78, 521–530. Lee, S.J., Kim, H.B., 1999. Laboratory measurements of velocity and turbulence field behind porous fences. J. Wind Eng. Ind. Aerodynamics 80, 311–326. Lee, S.J., Park, C.W., 1999. Surface pressure characteristics on a triangular prism located behind a porous fence. J. Wind Eng. Ind. Aerodynamics 80, 69–83. Lee, S.J., Park, K.C., Park, C.W., 2002. Wind tunnel observations about the shelter effect of porous fences on the sand particle movements. Atmos. Environ. 36, 1453–1463. Lin, Y., Jin, J., Zou, B., Cong, Z., Wen, X., Tu, X., Ye, J., 1984. Effect of fence techniques in leveling sand accumulation around sandbreaks. J. Desert Res. 4 (3), 16–25 (in Chinese with English abstract). Miller, D.R., Rosenborg, N.J., Bragley, W.T., 1975. Wind reduction by a highly permeable tree shelter belt. Agric. Forest Meteorology 14, 321–333. Packwood, A.R., 2000. Flow through porous fences in thick boundary layers: comparisons between laboratory and numerical experiments. J. Eng. Ind. Aerodynamics 88, 75–90. Papesch, J.G., 1992. Wind tunnel test to optimize barrier spacing and porosity to reduce wind damage in horticultural shelter systems. J. Wind Eng. Ind. Aerodynamics 44, 2631–2642. Park, C.W., Lee, S.J., 2003. Experimental study on surface pressure and flow structure around a triangular prism located behind a porous fence. J. Wind Eng. Ind. Aerodynamics 91, 165–184. Pattone, E.G., Shaw, R.H., Judd, M.J., Raupach, M.R., 1998. Largeeddy simulation of windbreak flow. Boundary-Layer Meteorology 87, 275–306. Perera, M.D.A.E.S., 1981. Shelter behind two-dimensional solid and porous fences. J. Wind Eng. Ind. Aerodynamics 8, 93–104. Plate, E.J., 1971. The aerodynamics of shelterbelts. Agric. Meteorology 8, 203–222. Ranga Raju, K.G., Garde, R.J., Singh, S.K., Singh, N., 1988. Experimental study on characteristics of flow past porous fences. Jo. Wind Eng. Ind. Aerodynamics 29, 155–163. Raine, J.K., Stevenson, D.C., 1977. Wind protection by model fences in a simulated atmospheric boundary layer. J. Ind. Aerodynamics 2, 159–180. Schwartz, R.C., Fryrear, D.W., Harris, B.L., Bilbro, J.D., Juo, A.S.R., 1995. Mean flow and shear stress distributions as influenced by vegetative windbreak structure. Agric. Forest Meteorology 75, 1– 22. Seginer, I.D.O., 1972. Windbreak drag calculated from the horizontal velocity field. Boundary-Layer Meteorology 3, 87–97.
Z. Dong et al. / Agricultural and Forest Meteorology 146 (2007) 82–93 Snyder, W.H., 1972. Similarity criteria for the application of fluid models to the study of air pollution meteorology. Boundary-Layer Meteorology 3, 113–134. Stanislas, M., Kompenhas, J., Westerweel, J., 2000. Particle Image Velocimetry: Progress Towards Industrial Application. Kluwer Academic Publishers, Dordrecht, The Netherlands. Townsend, A.A., 1956. The Structure of Turbulent Shear Flow. Cambridge University Press, Cambridge. Vigiak, O., Sterk, G., Warren, A., Hagen, L.J., 2003. Spatial modeling of wind speed around windbreaks. Catena 52, 273–288.
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White, B.R., 1996. Laboratory simulation of aeolian sand transport and physical modeling of flow around dunes. Annals Arid Zone 35, 187–213. Wilson, J.D., 1985. Numerical studies of flow through a windbreak. J. Wind Eng. Ind. Aerodynamics 21, 119–154. Wilson, J.D., 1997. A field study of the mean pressure about a windbreak. Boundary-Layer Meteorology 85, 327–358. Yaragal, S.C., Ram, H.S.G., Murthy, K.K., 1997. An experimental investigation of flow fields downstream of solid and porous fences. J. Wind Eng. Ind. Aerodynamics 66, 127–140.
A wind tunnel simulation of the mean velocity fields behind upright porous fences Zhibao Dong *, Wanyin Luo, Guangqiang Qian, Hongtao Wang Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, 260 West Donggang Road, Lanzhou, Gansu Province 730000, China Received 20 February 2007; received in revised form 27 April 2007; accepted 18 May 2007
Abstract Porosity is the most important parameter that determines the efficiency of wind fences. The present study provided a deeper understanding of mean flow regime behind fences with different porosities at different wind velocities by means of a scaled wind tunnel simulation. Velocities were measured using particle image velocimetry and the mean velocity field was obtained and discussed. The mean velocity fields obtained at different wind velocities were similar. Analyzing the streamline patterns revealed an inherent link between fence porosity and mean airflow characteristics behind the fence. The optimal fence porosity is considered to be the critical porosity above or below which airflow characteristics differ strongly. According to the present study, the optimal porosity is found to be around 0.2 or 0.3, which corresponds to a critical porosity above which bleed flow dominates and below which reversed flow becomes significant. The parameters characterizing the reverse cell behind fences were well correlated with porosity. The velocity profiles revealed seven typical flow regions behind fences, characterized by different velocity gradients. The airflow becomes less complicated and the number of flow regions decreases as fence porosity increases. Some regions, especially the reverse cell and small vortex, disappear when the porosity exceeds a certain value. The flow regions gradually merge as the distance downwind increases, and eventually recover a single velocity profile due to downward transfer of momentum from overlying layers. The recovery distance decreases with increasing fence porosity. # 2007 Elsevier B.V. All rights reserved. Keywords: Upright porous fences; Mean velocity regime; Streamline patterns; Flow regions; Optimal fence porosity
1. Introduction Windbreaks are the earliest devices used to improve windy climatic conditions to serve human needs. They are widely used in coastal, arid, and cold areas to retard wind and to check sand and snow drift, and have been studied in a systematic manner since the 1940s with the goal of finding the optimal windbreak—one that yields optimal protection at the minimum cost (Plate, 1971).
* Corresponding author. Tel.: +86 0 931 8271167; fax: +86 0 931 8277169. E-mail address: [email protected] (Z. Dong). 0168-1923/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2007.05.009
However, there is as yet no clear optimal design for windbreaks (Cornelis and Gabriels, 2005). Fences that are always constructed to have optical porosities greater than zero (Guan et al., 2003) are important artificial windbreaks. They can be classified as upright, horizontal, griddled, holed-plank, and windscreened (Fig. 1), depending on the available materials. Upright fences, usually made of wood bars, bunches of straws or reeds, or tree branches, are widely used to check drifting sand and drifting snow because of their easy availability, low cost, and simple construction. For example, upright fences made of reed bunches are used in the frontal edge of the shelter system that has been constructed along more than 400 km of highway
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Fig. 1. Types of fences: A. Upright fence; B. Horizontal fence; C. Gridded fence; D. Holed-plank fence; E. Wind screen.
crossing the shifting dune fields of China’s Taklimakan Desert (Fig. 2). The most important structural feature of a fence is its porosity (Heisler and Dewalle, 1988). The function of a windbreak is to reduce wind velocity within a certain distance. Maximum wind reductions are closely related to porosity, with low porosity producing high maximum
Fig. 2. The blowing-sand shelter system along the highway crossing China’s Taklimakan Desert: The shelter system consists mainly of checkerboard reed barriers that fix shifting dunes, with fences constructed from reed bunches set at the frontal edge of the shelter system to check drifting sand and extend the expected working life of the reed check barriers.
reductions. However, fences with very low porosity create more turbulence downwind than medium- and high-porosity fences. The higher turbulence produced by low-porosity fences may result in the recovery of mean horizontal wind velocities to levels equal to upwind velocities at a distance closer to the fence, thereby decreasing the shelter distance. Consequently, all else being equal, there should be a fence porosity that provides the optimal shelter effect by balancing the reduction of wind speed with the effects on shelter distance. Since at least the 1970s, considerable effort has been devoted to defining the optimal porosity of fences and other windbreaks. These efforts have included field measurements (e.g., Hagen and Skidmore, 1971a,b; Miller et al., 1975; Jacobs, 1985; Bofah and Alhinai, 1986; Schwartz et al., 1995; Wilson, 1997; Boldes et al., 2001), wind tunnel simulations (e.g., Iversen, 1981; Ranga Raju, 1988; Papesch, 1992; Boldes et al., 1995; Judd et al., 1996; Yaragal et al., 1997; Lee et al., 2002; Guan et al., 2003; Park and Lee, 2003), and numerical simulations (e.g., Wilson, 1985; Fang and Wang, 1997; Pattone et al., 1998; Packwood, 2000; Vigiak et al., 2003; Alhajraf, 2004). A common physical way to express the aerodynamic effect of a windbreak is in terms of its resistance to the flow, or in terms of a
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dimensionless parameter such as a drag coefficient (Raine and Stevenson, 1977; Jacobs, 1985). All published results have shown that the drag coefficient decreases with increasing fence porosity (Hoerner, 1965; Hagen and Skidmore, 1971b; Seginer, 1972; Wilson, 1985; Guan et al., 2003). This implies that fences with lower porosity provide a better shelter effect, and that solid fences would have the best efficiency. This obviously contradicts the observed facts. Thus, the drag coefficient alone is unable to provide significant information for defining optimal porosity, though it is an important parameter in characterizing the disturbance of airflow by fences. There must be other factors that can better characterize the shelter effect created by fences. A review of published results shows that the optimal porosity ranges from 0.3 to 0.5. Hagen and Skidmore’s (1971a) field measurements indicated that a windbreak with a porosity of 0.4 produced the lowest wind velocity over the largest downwind area. Lin et al.’s (1984) field test on the southeastern edge of China’s Tengger Desert suggested that porosities of 0.3–0.4 should be used for fences 0.8–1.0 m tall to avoid sand accumulation upwind of the fence. Lee et al.’s (2002) wind tunnel results showed that a porous wind fence with a porosity of 0.3 was the most effective for abating windblown sand particles because this fence had the maximum threshold velocity (i.e., produced the greatest increase in the wind velocity required to initiate sand movement behind the fence) among the porous fences in their study. Dong et al.’s (2006) wind tunnel simulation indicated that fences with porosities of 0.3–0.5 (depending on fence height) had the maximum relative threshold wind velocity and maximum effective shelter distance, and were thus, most suitable for controlling wind erosion. Researchers believe that there must be some inherent link between shelter efficiency and the flow regime characteristics behind fences, but how these parameters are correlated is not yet clear. Several researchers (e.g., Perera, 1981; Borges and Viegas, 1988; Wilson, 1997; Lee and Kim, 1998; Lee and Park, 1999; Dong et al., 2006) attempted to define the optimal porosity by measuring and analyzing the velocity, turbulence, shear stress, pressure, and sediment susceptibility to wind transport behind fences. They found noticeable changes in the flow characteristics at a porosity around 0.3 or 0.4. For example, Raine and Stevenson (1977) demonstrated in their tests that a fence with a porosity of 0.2 gave the best overall reduction in leeward mean velocity. Perera (1981) found that the Reynolds shear stress and turbulent kinetic energy were strong behind
the fence when the porosity was less than 0.3, whereas the bleed flow (i.e., air passing through the fence rather than over it) was strong when the porosity was greater than 0.4. By measuring the velocity field and surface pressure distributions, which directly influence the shelter effect produced by wind fences, Lee and Kim (1998, 1999) found a porous fence with a porosity of 0.3–0.4 to be the most effective for reducing the mean velocity and surface pressure fluctuations. However, limitations in measurement technology have prevented precise measurement of the characteristics of flow regimes, particularly near fences. The leeward wind used to be measured using conventional anemometers, but hot-wire anemometers provided much more detailed information about the leeward flow turbulence and were soon used by researchers. However, both conventional anemometers and hot-wire anemometers have difficulties in obtaining detailed measurements close to fences, and both may influence the flow field to some extent. The development of particle image velocimetry (PIV) improves our ability to measure the flow velocity field because the technique is non-intrusive, and as a result, it is finding ever more applications in theoretical studies (Stanislas et al., 2000). This unique optical method can capture the whole velocity field of flowing air within a fraction of a millisecond. We thus, believe that it should be an appropriate tool to study the velocity fields behind fences. In the present paper, we present the results of a scaled wind tunnel simulation study in which we obtained airflow fields and wind-velocity profiles at different locations behind fences with different porosities by means of PIV. This approach has the advantage over other commonly used methods of providing simultaneous non-intrusive velocity measurements within the whole target area. PIV can provide more detailed information on the airflow fields behind fences, enabling measurement of the mean velocity field, turbulence structure, shear stress, and pressure. The mean velocity field is discussed in this paper; the turbulence structure, shear stress, and pressure will be discussed in a future paper. We have also attempted to relate the mean flow characteristics to the optimal fence porosity so as to provide a deeper understanding of the aerodynamics of wind fences. 2. Scaled wind tunnel simulation 2.1. Experimental set-up The scaled simulation experiments were carried out in a blowing sand wind tunnel at the Key Laboratory of
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Desert and Desertification of the Chinese Academy of Sciences. The blow-type non-circulating wind tunnel has a total length of 37.8 m, with a 16.2-m long test section. The cross-sectional area of the test section is 0.6 1.0 m. The free-stream wind velocity in the wind tunnel ranges from 1 to 40 m s 1. The thickness of the boundary layer in the test section is typically more than 120 mm. The experimental set-up is shown in Fig. 3. We constructed fence models from rigid stainless-steel wires 1.2 mm in diameter. Wires were cut into straight segments of the required length to produce the desired fence height. The wire segments were then inserted in a row into a bed made of talcum powder paste contained in a wooden groove that was 1 m long (equal to the cross-sectional width of the wind tunnel) by 50 mm wide to create the fence (Fig. 3). The vertical wires were spaced at regular intervals, and the porosities of the fences were adjusted by changing the spacing between wire segments. We created a total of 11 fence models, with the height held constant at 20 mm and spacing varied to create 11 optical porosities (h = 0.05, 0.10, 0.15, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, and 0.90) that were defined using the ratio between the total open area between the wires and the total area (i.e., 0.02 m2) occupied by the fence. In our test, these porosity values were defined by subtracting the total width of the wires from the 1-m width of the fence, and expressing the
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result as a ratio of the 1-m width of the fence. A solid fence (zero porosity) was also tested using a 1-m long, 2-mm thick piece of plywood. During testing, the fence models were positioned 12 m downwind from the start of the test section of the wind tunnel to ensure the development of consistent airflow. We measured wind velocity field behind the model fences using a PIV device provided by the Beijing Cubic World Science & Technology Development Co., Ltd. This newly developed measurement technique is based on laser imaging technology and digital image processing; for more details concerning the measurement principle, refer to Stanislas et al. (2000). We used very fine talcum powder (with a mean diameter less than 10 mm) as a seeding material. The wind velocity measurements obtained by PIV using this kind of seeding material were calibrated using a Pitot static tube before the test, and the difference between the two measurements was found to be less than 0.5%. An electric duster sprayed the powder from the side of the wind tunnel at the entrance of the test section so that the tracer powder moved with the wind. The CCD (charge-coupled device) camera of the PIV system was set 0.55 m from the light sheet, resulting in a target measurement area 136 mm wide by 102 mm tall (producing a 1600 1200 pixel image with a magnification coefficient of 0.085). By setting the CCD camera at different positions and combining the
Fig. 3. Schematic diagram of the experimental set-up.
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measurement results, the measurement area reached 950 mm wide by 102 mm tall and provided sufficient information about the lee airflow pattern. The image acquisition rate was set at 20 frames per second. The final wind velocity represented the average of the values recorded over a period of 40 s (i.e., 800 frames). Each pair of two frames yields a wind-velocity dataset. The final measurement results thus, represent the average of 400 records, ensuring its statistical significance. 2.2. Similarity considerations The present test intends to investigate the airflow around the reed-bunch fences used along the highway in China’s Taklimakan Desert, which have a height about 1.0–1.2 m and a diameter of 50–60 mm for the reed bunches. Consequently, the geometric scaling of the models was about 1:50, and the Reynolds number scaling for dynamic similarity was impossible to attain. However, the simulation scale tried to meet the general requirements of ‘‘Reynolds number independence’’ recommended by White (1996). For example, the chosen height of the models produced a characteristic scale height to surface boundary layer height ratio of 0.17. Thus, it could be assumed that the wind tunnel’s flow depth posed little restriction on boundary layer development above the fence models (White, 1996). During the testing, the prepared fence models were positioned 12 m downwind from the leading edge of the test section of the wind tunnel, which is 100 times the boundary layer thickness and thus, meets the general rule for matching mean velocity profiles (White, 1996). Four wind velocities that are typically observed causing sand motion in the Taklimakan Desert were investigated (8, 10, 12, and 14 m s 1) so that the flow Reynolds numbers defined by thickness of the boundary layer (Re = Ud/v, where Re is the flow Reynolds number, U is the free-stream wind velocity, d is the thickness of the boundary layer, 0.12 m, and v is the kinematic viscosity of air, 1.4 10 5 m2 s 1) were sufficiently high, and ranged from 6.9 104 to 12.0 104. In addition, wind profiles measured over the bare tunnel floor yielded estimates of roughness Reynolds numbers defined by the aerodynamic roughness length (Rer = Uz0/v, where Rer is roughness Reynolds number, z0 is the aerodynamic roughness length that ranges from 0.0036 to 0.004 mm) ranging from 2.3 to 3.6 (corresponding to real flow Reynolds numbers defined by the height of work section of the wind tunnel ranging from 3.4 105 to 6.0 105) for the velocity range from 8 to 14 m s 1, respectively. Under these conditions, wind tunnel flows simulated the full-scale aerodynamically rough condi-
tions and Reynolds number independence existed (Townsend, 1956; Snyder, 1972; White, 1996). 3. Results and discussion 3.1. Streamline patterns Airflow fields behind porous fences are complicated by the presence of both the bleed flow that passes through the gaps in the fences and the displaced flow that passes over the fences. The relative significance of bleed flow and displaced flow differs as the fence porosity changes. For a solid fence, no bleed flow exists, whereas this flow is dominant for highly porous fences. The typical streamline patterns behind a porous fence are illustrated in Fig. 4. As airflow approaches the fence, the streamlines are lifted to different extents and produce a higher velocity above the fence (Fig. 5), although the streamline lift is very slight when the porosity is greater than 0.6. A high-velocity region forms above the fence. The wind’s momentum is transported to higher levels, resulting in a region with low wind velocity behind the fence. The flow lift grows stronger but the bleed flow becomes weaker as porosity decreases. In particular, flow separation is initiated from the top of the fence and the separation line extends downstream 8–16 times the fence height (i.e., to a distance of 8–16H) when the porosity is less than 0.3, depending on the fence porosity. Since the shape ratio (thickness/height) of the fence models was only 0.06, the flow can be regarded as a ‘‘thin fence flow’’ (Durst and Rastogi, 1980). The shear layer that separates from the leading edge of the fence does not reattach at the upper surface of the fence. Immediately leeward of the point of flow separation is a separation cell characterized by the presence of a back-eddy, which represents
Fig. 4. A typical streamline patterns behind a porous fence (h = 0.10, U = 10 m s 1). l is the reattachment distance, h is the height of the reverse cell above the floor of the wind tunnel, R is the reattachment point.
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Fig. 5. A typical iso-wind velocity chart behind a porous fence (h = 0.10, U = 10 m s 1).
Fig. 6. Typical streamlines, showing the reattachment point (R in Fig. 4) for h = 0.05 and U = 10 m s 1.
an area of reversed flow with a negative wind velocity (Figs. 4 and 5). The maximum fence porosity below which flow separation and reversal occurs is defined as the critical porosity. Experimental results reveals that the critical porosity should be between 0.2 and 0.3, though we cannot offer a more precise value because no tests were made between these two porosities. This is in good agreement with Baltaxe’s (1967) field observations and Lee et al.’s (2002) wind tunnel results. In accordance with their results, the critical porosity was around 0.25 and 0.30. The critical porosity revealed in current study is less than those proposed by Perera (1981), Lee and Kim (1999), and Dong et al. (2006). According to their results, the critical porosity should be 0.3–0.4. The lower critical porosity proposed by Baltaxe (1967) and Lee et al. (2002) and confirmed by the present study than that reported by other authors is because that the flow field was observed at some distance above the ground so that any flow reversal close to the surface would not be revealed. Baltaxe’s (1967) field observations with a rotating vane did not provide data near the ground surface. Lee et al. (2002) defined the reversed flow by observing backward movement of particles on a sand pile behind a fence. The lowest level at which wind flow was detected in the present study was about 3 mm, or 15% of the fence height above the ground. Taking this factor into account, the critical porosity should be over 0.2 or around 0.3. Above this critical porosity, bleed flow is dominant. From these results, it can be concluded that the widely proposed optimal fence porosity of 0.3–0.4 should correspond to the critical porosity above which bleed flow is dominant. The shape of the reverse cell resembles an ellipse when the porosity is less than 0.3. Flow begins to recover some distance downwind from the reverse cell. We chose four parameters to characterize the reverse cell: reattachment distance (l), height above the floor of the wind tunnel (h), area (S), and aspect ratio (A). The
reattachment point is determined by examining the horizontal velocity component at ground level to determine the point where the horizontal velocity changes sign from upwind (negative) to downwind (positive) (Fig. 6). The reattachment distance characterizes the long (horizontal axis) of the reverse cell. Theoretically, the downwind apex of the reverse cell and the reattachment point are located at different positions. The former can be above the surface but the latter must be at the surface. In practice, the difference in their positions should be so small that it can be neglected and the locations of both the downwind apex of the reverse cell and reattachment point can thus, be characterized by a single parameter: the reattachment distance. The height of the reverse cell can be roughly defined by the position of the uppermost boundary of the closed streamlines. This height characterizes the short (vertical) axis of the reverse cell. The area of the reverse cell is defined as the area enclosed by the outermost boundary of the flow lines that define the reverse cell and represents the magnitude of the development of flow reversal. The aspect ratio is defined as the ratio of the height of the reverse cell to the reattachment distance, and thus, characterizes the degree of vertical flatness of the reverse cell. The remainder of this section will discuss these parameters, especially in terms of their variation as a function of fence porosity. The reattachment distance and height of the reverse cell are expressed as multiples of fence height (H), and the area of the reverse cell is converted to a dimensionless relative area expressed as S/H2. Fig. 7 shows that the reattachment distance varies as a function of both fence porosity and wind velocity. The reattachment distance ranged from 8.4 to 16H for a porosity of 0.2 or less. The variation as a function of fence porosity is much more pronounced than that with respect to the wind velocity. The maximum difference in the reattachment distances for the four wind velocities equaled 2.9H, whereas the difference as a
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function of the different porosities was generally greater than 4.5H. The reattachment distance reaches a maximum at a porosity of 0.10 for all four wind velocities. It increases with increasing fence porosity when porosity is less than 0.10 but decreases with increasing fence porosity when the porosity is greater than 0.10. Fang and Wang’s (1997) numerical simulation results showed that the reversed cell extended farther downstream as the fence became more porous, but they did not report a decrease in the reattachment distance with increasing porosity when the fence porosity was greater than a certain value. Dong et al. (2006) defined the reattachment distance by observing the direction of particle movement. Their results are compared with those obtained in the present study in Fig. 8. The results are well correlated, but the reattachment distance defined based on particle move-
ment is always greater than that defined by means of PIV. This is because the reattachment distance defined based on particle movement represents the reattachment distance on the ground, whereas that obtained in the present study represents the result at some distance above the surface. Fig. 9 shows the variation in the dimensionless height of the reverse cell as a function of fence porosity and wind velocity. The dimensionless height of the reverse cell ranged from 0.5 to 1.85H for a porosity of 0.2 or less. As was the case for the reattachment distance, the height of the reverse cell changes more pronouncedly with changing fence porosity than with respect to wind velocity. In general, the height of the reverse cell decreases with increasing fence porosity. This suggests that the downward transfer of wind momentum behind fences becomes faster as the porosity increases. The fence with a porosity of 0.05 has almost the same height of the reverse cell as the solid fence (h = 0). The height of the reverse cell decreases sharply as the fence porosity increases from 0.10 to 0.15. The reverse cell is lower than the fence when porosity is 0.15 or greater but higher than the fence when porosity is 0.10 or less. This is consistent with Fang and Wang’s (1997) numerical simulation results, which showed that the upper bound of the ‘‘vortex area’’ (what we have called the reverse cell) tended to move closer to the ground as the fence porosity increased. Fig. 10 shows the change in the dimensionless area of the reverse cell as a function of porosity and wind velocity. The area of the reverse cell with a porosity of 0.05 is slightly greater than that of the solid fence, and decreases with increasing porosity when the porosity is
Fig. 8. Comparison of the reattachment distance obtained using the PIV method in the current study and the particle movement method described in Dong et al. (2006).
Fig. 9. Variation in the dimensionless height of the reverse cell as a function of fence porosity and wind velocity.
Fig. 7. Variation of reattachment distance as a function of fence porosity and wind velocity.
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Fig. 10. Variation in the dimensionless area of the reverse cell as a function of fence porosity and wind velocity.
Fig. 12. A small vortex developed immediately behind the solid fence and fences with a porosity of 0.05. This example is for h = 0.05 and U = 10 m s 1.
greater than 0.05. Again, the change with respect to porosity is greater than the change with respect to wind velocity. Fig. 11 shows changes in the aspect ratio as a function of the same two parameters. The aspect ratios of the solid fence and of the fences with porosities of 0.05 and 0.10 are relatively constant, but the ratio changes thereafter. The aspect ratios for fences with a porosity of 0.15 and 0.20 vary relatively widely among wind velocities, with no clear pattern. In the presence of a reverse cell, the reattachment point represents the location of flow divergence. However, our results showed that another small vortex developed immediately behind a solid fence and two low-porosity (0.00 and 0.05) fences (Fig. 12), resulting in forward stream in the near-surface layer immediately downwind from the fence. For porous fences, the forward stream was facilitated by the bleed flow that passes through gaps in the fence. The greater the fence’s
porosity, the stronger the bleed flow. This forward air stream meets the reversed backward stream to form a flow-convergence zone. The position of this convergence changes as a function of fence porosity since the relative strengths of the forward flow and the reversed backward flow changes with changing fence porosity (Fig. 13). The forward air stream resulting from the small vortex behind a solid or low-porosity fence is sufficiently strong that the flow convergence zone behind a solid fence extends farther downwind than that behind a fence with a porosity of 0.05. However, the bleed flow strengthens as porosity increases, resulting in an increase of the flow convergence distance with increasing porosity. Dong et al. (2006) observed the
Fig. 11. Variation in the aspect ratio of the reverse cell as a function of fence porosity and wind velocity.
Fig. 13. Variation in the position of the flow convergence zone as a function of fence porosity and wind velocity.
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Fig. 14. Comparison of the positions of flow convergence obtained using the PIV method (current study) and the particle movement method (Dong et al., 2006).
phenomenon of flow convergence by observing particle movement. Their results are compared with those obtained in the present study in Fig. 14. This comparison reveals that the position of flow convergence obtained by the two methods is poorly correlated. This is because the particle movement method defined the position of flow convergence on the ground whereas the PIV method used in the present study defined the position of flow convergence at some distance above the surface. Unlike the reattachment distance, which is always greater on the ground surface than above the surface, the distance of flow convergence may be greater or less on the ground surface than above the surface because it shifts in accordance with the relative strength of the forward and backward air flows. 3.2. Velocity profiles and flow regions The iso-velocity chart (Fig. 5) shows that the airflow behind fences has a different velocity gradient at different locations. The airflow pattern is generally divided into several regions with different aerodynamic behavior, which are characterized by different wind shear and velocity profiles. Fig. 15 shows the typical velocity profiles obtained by means of PIV behind a fence with a porosity of 0.10 and a free-stream wind velocity of 10 m s 1. The smooth curves in Fig. 15 suggest that PIV is a reliable tool for measuring wind velocity above model fences. Velocity profiles deviate from the logarithmic law when the airflow approaches a fence. The deviation increases downwind from the windward side and begins to recover at some distance downwind. Based upon the overall non-log-linear velocity profiles, in which segments of profiles are characterized by their velocity gradients, seven tentative
Fig. 15. An illustration of typical wind velocity profiles and flow regions behind fences (h = 0.10, U = 10 m s 1): A, outer flow; B, overflow; C1, upper wake; C2, lower wake; D, internal boundary layer; E, reverse cell; F, small vortex.
typical layers or regions of airflow can be roughly identified. These are an outer flow region (Fig. 15A), an overflow region (Fig. 15B), a wake region with two layers (Fig. 15C1 and C2), an internal boundary layer (Fig. 15D) that extends downwind from the point of reattachment, a reverse cell (Fig. 15E), and a small vortex (Fig. 15F). Accurate division of these regions is difficult because they are gradually transitional. This is only a tentative division because it is based only on wind profiles and not supported by other data such as momentum fluxes. It must be emphasized that these flow regions are typical for the fully developed airflow behind low-porosity (dense) or solid fences, and that some regions disappear when the fence porosity increases. For example, the small vortex immediately behind the fence disappears when the fence porosity is greater than 0.10, and the reverse cell disappears when the porosity is greater than 0.20. Only two regions can be identified clearly behind a fence with a porosity of 0.90, and they merge to form a uniform logarithmic velocity profile within a distance of 10H. Since the reverse cell was discussed in detail in Section 3.1, the remaining discussion will focus on the other regions. The outer flow region (region A) is characterized by a relatively low velocity gradient and the flow is mostly determined by the conditions in the undisturbed boundary layer far upstream from the fence. Immediately below the outer flow region is an overflow region, which represents a transitional region between the outer flow and the wake region (regions C1 and C2). The height of the boundary between the outer flow region and the overflow region increases gradually as the distance downwind from the fence increases. The velocity gradient in the overflow region is greater than that in the upper part of the outflow region. The velocity gradient in the overflow region tends to increase with increasing distance downwind. Regions C1 and C2
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constitute a wake region below the overflow region and above the internal boundary layer and the reversed cell. The wake region can be viewed as a region of flow recovery in which, overall, the flow is accelerated downwind by downward transfer of momentum from the overlying layers with higher wind velocities. The wake region has an overall S-shaped velocity curve, with the gradient decreasing downwind. It is divided into two sub-regions (C1 and C2) based on differences in the velocity gradient. Region C1 has faster winds and a steeper velocity gradient, whereas region C2 has slower winds and a lower velocity gradient. The division between regions C1 and C2 becomes indistinct and tends to disappear as the distance downwind increases. This results from momentum transfer between the wake region and the overlying or underlying regions. The steep gradient in the upper wake region reflects the rapid downward turbulent momentum transfer from the accelerated overflow region (region B), whereas the less-steep velocity gradient of the lower wake region relates to momentum exchanges with the slower, sheltered flow of the reverse cell (region E). In general, the wake flow expands downwind, resulting in merger of the upper and lower wakes. The wake region is usually considered to be an area of flow recovery where accelerated and displaced flow eventually dissipates turbulent energy downwind via eddy shedding and flow expansion. The upper and lower wake regions in Fig. 15 tend to merge at a certain distance downwind to form a single wind velocity profile with a uniform gradient. This distance increases with decreasing fence porosity. Behind a solid fence, they tend to merge at a dimensionless distance of about 50H, whereas behind the fence with a porosity of 0.90, they tend to merge at a dimensionless distance of 4H. In general, the merge distance decreases as the porosity increases because the airflow recovers faster for highly porous fences. The lowest region (region D) is the internal boundary layer characterized by increasing shear and thickness with increasing distance downwind. The velocity profiles in the internal boundary layer and in the wake region above this layer become more uniform in shape with increasing distance downwind from the point of flow reattachment. The distance required for them to reach equilibrium varies with fence porosity. They typically require a significant distance to reach equilibrium for solid and low-porosity (dense) fences. Judged by the wind velocity profiles, the boundary layer behind the solid fence and the fences with a porosity of 0.10 and 0.20 had not recovered completely within the
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tested leeward distances. The recovery distance is thus, greater than 50H. In contrast, the recovery distance was about 25 and 10H, respectively, for the fences with a porosity of 0.60 and 0.90. In the reverse cell (region E), the velocity gradient increases with the downwind distance to a certain distance, but then decreases. A small vortex (region F) developed behind the solid fence and the fence with a porosity of 0.05. Its extent is much smaller than that of the reverse cell. Its height is lower than the fence and it extends downwind less than 1H. The small vortex results from the high pressure immediately behind the fence, where the wind is almost stagnant. It disappears when the fence porosity is greater than 0.05. 4. Conclusions The mean velocity field behind fences with different porosities was simulated using scaled models in a wind tunnel to provide a deeper understanding of the aerodynamics of porous fences and the optimal porosity. A state of the art non-intrusive PIV technique was employed to obtain precise velocity measurements near the simulated fences. This approach provided rich velocity measurements that enabled a detailed analysis of airflow. A complex velocity field arises behind fences in the presence of both bleed flow and displaced flow (particularly, reversed flow). Porosity is an important parameter in defining the leeward velocity field, whereas wind velocity has a much smaller effect on the velocity field. The relative significance of bleed flow and reversed flow varies as porosity changes. By analyzing the streamline patterns, we revealed an inherent link between the fence’s porosity and the airflow characteristics behind the fence. There is a critical porosity above or below which the airflow characteristics differ strongly. All published results and those obtained in the present study suggest that the optimal porosity is around 0.2–0.3. This optimal porosity corresponds to the critical porosity above which the bleed flow is dominant, and the bleed flow balances the reversed flow at this optimal porosity. The design of wind fences should avoid both a strong bleed flow and a strong reversed flow. In accordance with the previous published results, our results showed that a strong bleed flow, results in insufficient reduction in wind velocity and that a strong reversed flow facilitates the development of turbulent stress, and thus, decreases the shelter distance. Optimal porosity thus, represents a compromise between reduction in wind velocity and shelter distance. Bleed flow and reversed flow must results in the differences of the magnitude and
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