Evaluating the optimal porosity of fences for reducing wind erosion

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, Lanzhou, Gansu 730000, China

*Correspondence to: ZhiBao Dong, Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences. No. 320, West Donggang Road, Lanzhou, Gansu 730000, China.Email: zbdong@lzb.ac.cn

Evaluating the optimal porosity of fences for reducing wind erosion

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, Lanzhou, Gansu 730000, China

*Correspondence to: ZhiBao Dong, Key Laboratory of Desert and Desertification, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences. No. 320, West Donggang Road, Lanzhou, Gansu 730000, China.Email: zbdong@lzb.ac.cn

Porosity is the most important parameter determining the shelter efficiency of fences. Wind measurements were made around fence models with different porosities in a wind tunnel. The optimal fence porosity is evaluated by means of Gandemer’s method that combines the effects of wind reduction and turbulence fields on the shelter efficiency for abating wind erosion. Defining the optimal porosity must take into account of its own purposes, required shelter degree and area to be sheltered. Turbulence has profound impacts on the shelter efficiency of high degree. Two concepts: absolute optimal porosity and practical optimal porosity concerning optimal porosity are proposed. Choosing the practical optimal porosity means reducing cost without significant expense of shelter efficiency.According to the evaluation in present study, the absolute optimal porosity for providing high degree of shelter to abate wind erosion is 0.20 while the practical optimal porosity is around 0.40. If a less shelter degree but over wider area is required, the absolute optimal porosity ranges from 0.05 to 0.10 and the practical optimal porosity is 0.10. For any degree of shelter for abating wind erosion effectively, the fence porosity must be less than or equal 0.40.

windbreak; shelter efficiency; optimal design

1. Introduction

Wind fences are artificial structures designed to reduce the hazards caused by wind. Their presence in the airflow reduces the effect of wind velocity not only at the system itself but also at a certain windward and leeward distance.The aerodynamic action of a wind fence is simple in principle (Cornelis and Gabriels, 2005). A wind fence exerts a drag force on the wind field, causing a net loss of momentum in the incompressible airflow and thus a sheltering effect. However, there is no clear optimal design that yields optimal protection at the minimum cost (Plate, 1971) for wind fences or other windbreaks though they have been studied in a systematic manner since the 1940s. At first, the optimal design of fences is determined by its own purposes.For example, the wind fences constructed along the railway from Hami to Urumqi in China to protect trains against strong winds are required to create a maximum reduction of wind drag on a train behind fences. However, the wind fences constructed in the frontal edge of the shelter system along the highway crossing the Taklimakan Desert of China are required to reduce the wind shear on the ground surface behind the fences and hence wind erosion (Donget al.,2007). The definition of optimal fence design is also complicated by the variations in velocity and turbulence fields behind fences with fence parameters. It has been found that the shelter efficiency of fences is determined by factors that include fence height, overall porosity, porosity distribution,and orientation (Cornelis and Gabriels, 2005). For fences that are long relative to their height, the most important structural feature is porosity (Heisler and Dewalle, 1988).Seginer’s (1972) field measurements showed that the porosity of the fence was the most influential parameter on the wake characteristics behind the fence, compared to other factors that need to be considered for the fence design.Hence, optimal design of wind fences in most cases is to choose the optimal porosity.

The shelter efficiency of a wind fence is usually defined in terms of reduction of wind velocity, turbulence intensity,and the effective shelter distance (i.e., the distance downwind of the fence in which wind velocity is reduced below the threshold required to initiate sand movement). Maximum wind reductions are closely related to porosity, with low porosity producing high maximum 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.

Field observations of the shelter effect of wind fences to determine the optimal porosity date back to 1938 (Bofah and Al-Hinai, 1986). Ever since, considerable efforts have 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; Milleret al., 1975;Jacobs, 1985; Bofah and Alhinai, 1986; Schwartzet al.,1995; Wilson, 1997; Boldeset al., 2001), wind tunnel simulations (e.g., Iversen, 1981; Ranga Raju, 1988; Papesch, 1992; Boldeset al., 1995; Juddet al., 1996; Yaragalet al., 1997; Leeet al., 2002; Guanet al., 2003; Park and Lee, 2003; Cornelis and Gabriels, 2005), and numerical simulations (e.g., Wilson, 1985; Fang and Wang, 1997;Pattoneet al., 1998; Packwood, 2000; Vigiaket al., 2003;Alhajraf, 2004). A review of published results shows that the optimal porosity ranges from 0.1 to 0.66. Bofah and Al-Hinai (1986) attributed the large spread of optimal porosity reported by various investigators to the fence application, wind characteristics, topographical relief, surface roughness and the investigator’s definition of shelter efficiency. Schultz and Kelly (1960) found an optimal porosity of 0.25 for a 1.22m high snow fence measured atz/H=0.5(wherezis the height above surface, andHis the height of fences). Hagen and Skidmore (1971a), measuring atz/H=0.125, found an optimal porosity of 0.4 because it produced the lowest wind velocity overx/H=2 tox/H=20(wherexis the downwind distance from fence). However,their graphed data indicate that if the overall reduction in wind speed was evaluated in several heights, their 0.20 porous fences would have been the optimum (Raine and Stevenson, 1977). Raine and Stevenson (1977) evaluated the total velocity withinz/H=1.5 andx/H=45, and found that the best overall wind velocity reduction was given by 0.20 porous fence. Cermaket al. (1982) and Bofah and Alhinai (1986) defined the optimal fence porosity in terms of the sand drift that was entrapped by fences in wind tunnel and field tests. They found that the optimal porosity was around 0.5. Grant and Nickling’s (1998) field observation showed that the optimal porosity was around 0.3 because it had the greatest drag coefficient. Leeet 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.Cornelis and Gabriels (2005) evaluated the shelter efficiency of wind fences in terms of the total wind velocity reduction atz/H=0.25 and found that the optimal porosity ranged from 0.20 to 0.35.

The diversity in many reports of optimal fence porosity shows a need to specify clearly the definition of optimal porosity and an accurate method to evaluate it. In wind erosion control, an appropriate definition of optimal porosity is that it produces effective shelter to the ground surface over the longest distance, or the longest effective shelter distance.The present paper attempts to evaluate the optimal porosity of fences for reducing wind erosion based on wind measurements around model fences in a wind tunnel.

2. Wind tunnel tests

To make an aerodynamic evaluation of the optimal fence porosity, experiments were conducted in a blowing sand wind tunnel at the Key Laboratory of 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 0.6m×1.0m. The free-stream wind velocity in the wind tunnel ranges from 1 to 40 m/s. The thickness of the boundary layer in the test section is typically more than 120 mm.

Particle image velocimetry (PIV) was employed to obtain the data on mean velocity and turbulence fields required to evaluate the optimal porosity. The PIV system was provided by the Beijing Cubic World Science & Technology Development Co., Ltd. It has five key components: a double pulsed laser (two laser pulses that illuminated the saltating particles with short time difference), light sheet optics (optics that transformed the laser light into a thin light plane guided into the saltating cloud), a CCD (Charge Coupled Device)camera (fast frame-transfer CCD that captured two frames exposed by laser pulses), a synchronizer (timing controller that used highly accurate electronics to control the laser and camera), and software that processed, displayed and stored data on a computer. Figure 1 illustrates the layout of the experimentation. For more details concerning the measurement principle, refer to Stanislaset al. (2000). We used very fine talcum powder (with a mean diameter less than 10 µm) 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 camera of the PIV system was set 0.55 m from the light sheet to capture the flow images with resolution of 1600×1200 pixels, resulting in a target measurement area 136 mm wide by 102 mm tall (the magnification coefficient of was 0.085). The measurements were performed in seven consecutive cross-sections so that the measurement area reached 950 mm wide by 102 mm tall and provided sufficient information about the upwind and lee airflow patterns around the fence models. The measurement sections were perpendicular to fence models along the middle line of the work section of wind tunnel. 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 seconds (i.e., 800 frames). Each pair of two frames yields a wind-velocity dataset. The final measurement results thus represented the average of 400 records, ensuring its statistical significance. The instantaneous velocity vectors at random locations were interpolated to regularly spaced grid points with intervals of 2.7 mm in both the horizontal(δx) and the vertical (δz) directions.

The tests were conducted at four free-stream wind velocities: 8, 10, 12 and 14 m/s. The results at one wind velocity (10 m/s) are discussed in the present paper because it has revealed that the patterns of the wake flow behind fences were almost independent of free-stream wind velocity or Reynolds number at the tested Reynolds number range from 6.9×104to 12.0×104(Donget al., 2007).

Figure 1 Layout of the experimentation

3. Approaching airflow

The secondary flows that develop in the presence of dunes are formed by modification of the approaching flow.The velocity profiles of the approaching wind, free of obstacles, were measured before the scaled tests of the transverse dunes and their turbulence intensity was calculated (Figure 2). More than 140 mm of turbulent boundary layer was generated by the approaching flow. The vertical and lateral velocity components of the approaching wind were negligible compared with the longitudinal velocity component. The velocity profiles in the turbulent boundary layer of the approaching flow were successfully fitted using a logarithmic expression (r2＞ 0.99):

whereu(z) is the mean longitudinal wind velocity,Uis the mean free-stream wind velocity,zis the height above the ground surface,z0is the aerodynamic roughness length,u*is the friction velocity, andkis the von Karman constant. The friction velocities corresponding to the four free-stream wind velocities (8, 10, 12, and 14 m/s) were 0.30, 0.37, 0.46,and 0.55 m/s, respectively. The aerodynamic roughness lengths corresponding to these four free-stream wind velocities were 0.19, 0.17, 0.16, and 0.14 mm, and decreased with increasing free-stream wind velocity.

The turbulence intensity generally decreases with in-creasing height, though some irregular changes were noticed above 100 mm for the free-stream wind velocity of 12 m/s.The turbulence intensity close to the ground surface ranged from 11% to 13%.

Figure 2 Velocity and turbulence intensity profiles of the approaching flow as a function of height.(a) velocity profiles and (b) turbulence intensity profiles.

4. Wind reduction

Cornelis and Gabreils (2005) proposed a dimensionless wind reduction coefficientRcΔx,z= 1-uΔx,z/u0Δx,zto express the efficiency of fences in reducing wind velocity at a given height above the surface and distance windward or leeward from the fence. WhereRcΔx,zis the wind reduction coefficient, Δxis the distance from the fence (in fence heightH),zis the height above the surface (in fence heightH),uΔx,zis the time-averaged wind velocity disturbed by the fence (m/s),andu0Δx,zis the time-averaged wind velocity in the absence of a fence (m/s). The overall wind-velocity reduction at a given height was expressed as the average overall reduction coefficient:

whereMis the number of observations.

We used Cornelis and Gariels’s (2005) method to calculate the wind reduction coefficient as a function of fence porosity. The wind reduction coefficient is calculated at four heights:z=0.2H,z=0.5H,z=0.75Handz=0.9H. Figure 3 shows the variation of wind reduction coefficients at four heights with fence porosity, distance from the fence and height above the surface. The variation patterns at every height are similar. They are also similar to that obtained by Cornelis and Gabriels (2005). The wind reduction coefficients for porosities 0, 0.1, 0.2, 0.4 and 0.5 are close and are much greater than those for porosities 0.6 and 0.7. Porosity 0.1 provides the longest sheltering zone,i. e. zone where the wind reduction coefficient is greater than 0.5. The overall wind reduction coefficients at the four heights are calculated by equation(2)and plotted against fence porosity in figure 4.They are very close at the four heights. It is readily apparent that the optimal porosity for wind reduction ranges from 0 to 0.2, with a peak wind reduction coefficient at fence porosity 0.10, which is in accordance with values found by Perera(1981). Similar to Cornelis and Gabriels’ (2005) curve, the data in figure 4 fits the Gaussian peak function (Equation(3))well, but the peak in their curve was observed at porosity around 0.30. In an economic view, porosity 0.2 is an ideal value for reducing wind speed.

Figure 3 Variation of wind reduction coefficient with downwind distance at four heights for different fence porosities

Figure 4 Variation of overall wind reduction factor with fence porosity

5. Turbulence intensity

Turbulence intensity of the streamwise and vertical velocity components can be calculated using equation(2)from the velocity measurements:

whereTuandTvare the turbulence intensity of the streamwise and vertical velocity components (respectively),Uis the mean free-stream wind velocity, andu׳ andv׳ are the fluctuation velocity of the streamwise and vertical velocity components(respectively), and are derived usingu′=u-andv′=v-, where (u,w) is the instantaneous velocity field,and(,) is the mean turbulent velocity field.

Figure 5 shows a typical contour plot of turbulence intensity for the porosityη=0.30 at free-stream wind velocityU=10 m/s. Two highly turbulent regions can be identified.One is located immediately adjacent to the fence and the other lies in the near-surface atx=13-16H, in the vicinity of flow reattachment (Donget al., 2007). Donget al.’s (2007)analysis of the mean velocity fields revealed that the reattachment point was located atx=14.5Hfor the same fence porosity at the same free-stream wind velocity.

Figure 5 A typical contour map of turbulence intensity behind a model fence for U = 10 m/s and η = 0.1.H = the height of the fence, z = height above the bed, and x = distance downwind of the fence.

Figures 6 and 7 show the turbulence intensity profiles of the streamwise and vertical velocity components (respectively) as a function of the fence porosity. The fence wake generally has higher turbulence as the porosity decreases though this trend is not apparent atx=0Handx=0.5H. The variation with height of turbulence intensity becomes more complex as it gets closer to the fence. Beyondx=10H, the streamwise turbulence intensity decreases with height monotonically. Atx≤ 10H, the streamwise turbulence intensity profiles have one or two local maximum values except for the porosityη=0.8. The streamwise turbulence intensity profiles have two local maximum points atx≤ 1.5H, one is close to the surface and the other is located at 1Hto 1.5Habove the surface. Ranga-Rajuet al. (1988) and Lee and Kim (1999) also found the two peaks in the streamwise turbulence intensity profiles though the spatial ranges in which two-peak turbulence intensity profiles occur are different.Ranga rajuet al. (1988) found that the two-peak turbulence intensity profiles occurred withinx＜5H, while Lee and Kim(1999) found that the two-peak turbulence intensity profiles occurred withinx≤ 2H, close to the present study. Atx=3H,5Hand 10H, the streamwise turbulence intensity profiles forη≤0.20 have one peak but those for the other porosities have no peak.

The vertical turbulence intensity profiles for all porosities have a peak located at 1.0Hto 1.2Habove the surface.The peaks are located at 0.5Hto 0.8Hforx=0Handx=0.5H.The vertical turbulence intensity for all porosities is less than the streamwise turbulence intensity (Figure 7) betweenx=1.5Handx=25H. The maximum values of vertical turbulence intensity are generally less than 60% of those of streamwise turbulence intensity betweenx=1.5Handx=15H.Lee and Kim (1999) observed the similar phenomena in the near-wake region ofx＜2Hand concluded that the turbulence structure of the wake flow behind fences seemed to be anisotropic. Their experimental results showed that the turbulent structure gradually recovered its isotropic characteristics beyondx=3H. But the present study show that it takes much longer distance for the turbulent structure to recover its isotropic characteristics, at least beyondx=35H. The differences can at least partly be attributed to experimental conditions. Lee and Kim’s (1999) experiment used holed fences in a water channel while the present experiment used upright fences in a wind tunnel.

The fence porosities fall into two groups in both streamwise and vertical turbulence intensity. One group that has higher turbulence intensity includesη=0,η=0.05 andη=0.1. The other group that has lower turbulence intensity includesη=0.3 andη=0.4. The fence withη=0.2 usually has intermediate turbulence intensity between the higher and lower. It is thought that high turbulence intensity will reduce the shelter efficiency of fences. The fence porosity should be over 0.1 or 0.2 to effectively reduce the turbulence intensity behind fences.

Figure 6 Variations in the turbulence intensity profiles of the horizontal velocity component as a function of fence porosity for U = 10 m/s.H = the height of the fence, z = height above the bed, and x = distance downwind of the fence.

6. Comprehensive evaluation

It is thought that neither wind reduction nor turbulence intensity alone is directly related to the optimal fence porosity for reducing wind erosion because both mean wind speed and turbulence influence the shelter efficiency. Gandemer(1979) introduced a dimensionless protection factor to account for the combination effect of mean speed reduction and turbulence on the shelter effect.

wherefis the dimensionless protection factor,u0(z) andσ0(z)are the mean wind speed and standard deviation at heightzupstream from the fence at an undisturbed zone,u(z) andσ(z)are the mean wind speed and standard deviation at heightzbehind fences in the disturbed zone.

Gandemer (1979) defined the degree of protection in terms of protection factor and protection area. He found that the optimal porosity differed depending on whether the aim was a high degree of comfort (f=2 and 3) or less high (f=1.2)over the maximum protection area. A homogeneous porosity of the order of 0.2 was an optimum for the first case, whilst a homogeneous porosity of about 0.5 corresponded to the second case.

Perera (1981) made extensive measurements in the wakes of two-dimensional solid and porous fences immersed in the constant-stress region of a simulated rural atmospheric boundary-layer, using a pulsed-wire anemometer. He used the inverse of Gandemer’s (1979) protection factor to define the optimal porosity and found that away from the vicinity of the fence, the fence of porosity 0.1 provided the best overall shelter, in contrast with the higher values suggested by Gandemer.

Gandemer’s (1979) and Perera’s (1981) parameters re-flected only the streamwise and mean velocity and turbulence intensity. Kim and Lee (2002) suggested that the vertical velocity component must be considered in addition to the streamwise velocity component to obtain an accurate shelter parameter although the vertical velocity component was relatively small compared with the streamwise velocity component. Therefore, in their study, a modified shelter parameter that took into account both the streamwise and vertical velocity components was defined as follows:

In this study, we use equation(6)to evaluate the shelter effect of fences and to define the optimal porosity. Figure 8 shows contour plots of the shelter parameter as a function of fence porosity. The shelter parameter above 2Hshows similar contour irrespective of the porosity. The region displaying significant values expands as the flow goes downstream.The shelter parameter in the bleed flow region just behind the fence has small values except for the solid fence.

In accordance with Gandemer’s (1979) suggestion, we divide the shelter region as high shelter region withψ=0.3(corresponding tof=3), moderate shelter region withψ=0.5(corresponding tof=2) and low shelter region withψ=0.8(corresponding tof=1.2). We use shelter distancedinstead of shelter area suggested in previous studies (Gandemer,1979; Perera, 1981; Kim and Lee, 2002) to define the optimal porosity because shelter on the ground surface is most significant for wind erosion. Figure 9 shows the variation with fence porosity of shelter distance with different shelter extent. The shelter distance is a function of shelter degree.The less the shelter degree is required, the greater the shelter distance will be provided. The optimal fence porosity that provides the longest shelter distance is also a function of shelter degree. Turbulence has profound impacts on the shelter efficiency of high degree. Adding a turbulence term to the evaluation equation shifts the optimal fence porosity to higher values. However, for the shelter efficiency of moderate and low shelter degree, the optimal porosity is mainly determined by wind reduction so that adding a turbulence term to the evaluation equation has little influence on the optimal porosity. The optimal porosity for high shelter degree(ψ=0.2 andψ=0.3 in figure 9) ranges from 0.15 to 0.40. In the economic view, fences with porosityη=0.4 can greatly reduce wind erosion. The optimal porosity for moderate and less shelter degrees (ψ=0.5 andψ=0.8) ranges from 0.05 to 0.10.For any shelter degree, the shelter distance decreases rapidly when the porosity is greater than 0.40. A practical conclusion is that the fence porosity should be less than 0.40 to provide shelter of any degree to control wind erosion.

Figure 8 Contour plots of shelter parameter for different fence porosities (to be continued)

Figure 8 Contour plots of shelter parameter for different fence porosities (continuation)

Figure 9 Variation of shelter distance with fence porosity for different shelter degree

7. Conclusions

Wind measurements around fence models with different porosity were made in a wind tunnel and used to evaluate the optimal porosity of fences for abating wind erosion in terms of shelter efficiency. The wind reduction parameter and turbulence fields behind fences were analyzed. However neither the wind reduction nor the turbulence field alone can provide sufficient information to determine the optimal fence porosity. It has been shown that the fence with porosityη=0.20 has good performance (Perera, 1981; Lee and Kim, 1999) in reducing wind velocity. However, achieving low turbulence in the wake region behind fences in addition to mean velocity reduction is also important for the purpose of abating wind erosion. The criteria to define the optimal fence porosity must be comprehensive ones that incorporate several parameters. Therefore, the combination effects of wind reduction and turbulence fields on shelter efficiency were evaluated in terms of the shelter parameter proposed by Gandemer (1979) and modified by Kim and Lee (2002).

The definition of shelter efficiency and hence optimal porosity of wind fences at first is determined by its own purposes, including the required shelter type and degree. The optimal porosity is also an issue that balances the shelter efficiency and cost. The cost of fences increases with decreasing fence porosity. We must distinguish between the absolute optimal porosity and practical optimal porosity. The former is the porosity with best shelter efficiency while the latter is the critical porosity below which the shelter efficiency has no significant increase with decreasing porosity.Choosing the practical optimal porosity means reducing cost without significant expense of shelter efficiency. According to the evaluation in present study, the absolute optimal porosity for providing high degree of shelter to abate wind erosion is 0.20 while the practical optimal porosity is around 0.40. If a less shelter degree but over wider area is required,the absolute optimal porosity is from 0.05 to 0.10 and the practical optimal porosity is 0.10. For any degree of shelter for abating wind erosion effectively, the fence porosity must be less than or equal 0.40.

We gratefully acknowledge funding from the Knowledge Innovation Project of the Chinese Academy of Science(KZCX2-YW-329), and the National Natural Science Foundation of China (40638038).

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10.3724/SP.J.1226.2011.00001

15 July 2010 Accepted: 10 September 2010