Research on Wind Flow Control by Windbreak Fence for a Large Radio Telescope Site Based on Numerical Simulations

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Introduction
Te larger the efective receiving area of the radio telescope antenna, the higher its sensitivity and resolution [1]. However, on the one hand, with the increase of antenna aperture, the wind area of the antenna refector surface increases, which leads to the increase of wind load on the antenna; on the other hand, with the improvement of comprehensive performance of the antenna, the requirement of pointing accuracy also increased, so that the infuence of site wind disturbance on pointing accuracy cannot be ignored. Terefore, the efect of wind disturbance on the efciency and pointing accuracy of large antennas becomes more obvious and more difcult to solve. According to the 100 m aperture fully steerable radio telescope GBT (the Green Bank Telescope) report [2], the antenna pointing accuracy up to 1.5" at wind speeds below 2.5 m/s; when the wind speed is greater than 3 m/s, the pointing error caused by wind disturbance will afect the observation of greater than 40 GHz; when the wind speed is greater than 5 m/s, observations greater than 20 GHz will be limited; and when the wind speed continues to exceed 11 m/s, all the observations will stop.
Currently, antenna wind resistance methods mainly include the following methods: for small-and medium-sized radio telescopes with high pointing accuracy, a radome can be built outside the antenna to prevent wind disturbance, such as 13.7 m Delingha telescope in China [3] and 36 m Haystack telescope in the United States [4]. However, the radome will refect and absorb radio signals, afecting the antenna performance. And, with the increase of antenna aperture, the engineering cost of radome increases geometrically. Terefore, radome is not suitable for the wind resistance of large aperture antennas. For large aperture antennas, mesh refectors can be used to reduce wind load, such as the 64 m Parkes telescope in Australia [5]. However, because high-frequency waves will directly penetrate the mesh surface, the design of the mesh refector is not suitable for high-frequency antennas. Facing the urgent needs of wind resistance for large aperture and high frequency antennas, many scholars try to reduce the infuence of wind disturbance on electrical performance of antennas by controlling compensation. NASA (National Aeronautics and Space Administration) designed the LQG (Linear Quadratic Gaussian) controller for the 70 m antenna, and the simulation results show that this method can efectively reduce the rotational axis error caused by wind disturbance [6]. Gawronski and Souccar [7] discussed the efect of PID (Proportional Integral Derivative) control, LQG control, and H∞ control for suppressing wind disturbance. H∞ control has the best performance, but its practical use is limited by antenna hardware performance. Ukita et al. [8] applied a fxed compensation method to reduce the telescope beam pointing error caused by steady-state wind disturbance for the 10 m Atacama Cosmology Telescope (ACT) in Chile. However, the previous methods of control compensation are still passive, and it is difcult to fast control the time-varying wind disturbance. Terefore, the problem of wind disturbance that afects the performance of large radio telescopes needs further study.
By studying the terrain for the site of some large radio telescopes, it is found that most of these sites are located in valleys or basins. Te GBT site, for example, is located in a valley 800 m above sea level at 38.4°north latitude, surrounded by mountains 1,400 m above sea level [9]; the 100 m Efelsberg Radio Telescope is located about 40 km southwest of Bonn in a valley surrounded by mountains [10]; and the 110 m aperture fully steerable radio telescope QTT, which is under construction in Qitai County, Xinjiang, China, is located in a basin surrounded by mountains with an elevation of 1760 m [11]. Te height of the mountain around the site ranges from 1860 to 2250 m. Such terrain can not only efectively shield electromagnetic interference but also block wind disturbances. However, the natural mountain barrier does not completely block the infow of wind. Tere will still be some directions of the incoming wind blowing to the antenna area, and the direction of the incoming wind is mostly concentrated at the mountain gap. Te QTT site incoming wind statistics are taken as an example, as shown in Figure 1; the wind from the mountain gap accounts for more than 55% of all incoming winds. And, the wind direction with relatively high speed is mainly located in the mountain gap. Based on the previous fndings, antenna wind resistance research can be carried out from the perspective of improving the wind environment at the site.
Te windbreak fence is often used in port material yard [12], highway bridge [13], Gobi Desert [14] etc. It has a certain porosity, which can have a certain blocking efect on the wind, to change the direction of the wind and consume wind energy, so that the wind speed behind the fence is attenuated [15]. Research on the theory of wind and dust suppression by the windbreak fence was carried out earlier in the United States, the United Kingdom, and New Zealand [16][17][18]. After 1990, China gradually carried out application research in the windbreak fence project for the coal storage yard of Qinhuangdao Harbor [19], coal open yard of Jingtang Harbor [20], and the Taiyuan Coal Gasifcation Company [21]. Te sheltering efect of the windbreak fence is afected by its porosity, surface shape, height,  distance from the target area, etc. [22]. Fang et al. [23] studied the optimal porosity for wind barrier design based on numerical simulations, and the result showed that a porosity of 0.35 is optimal and a porosity of 0.3∼0.4 can provide the longest sheltering distance. Yu et al. [24] studied the infuence of porosity and height of fences on blocking efect based on the wind tunnel experiment. Sand fences with porosity of 0.36 had the highest blocking efciency (reducing wind speed by 70%) and the longest blocking distance (9 times the distance of the fence height) among fences with porosities of 0.75, 0.63, 0.56, and 0.36, and the higher the fence, the better blocking efect. Wang et al. [25] studied the sheltering efect of punching plate and wire mesh fences with the same porosity, and the results showed that punching plate fences reduced wind speed more than wire mesh fences. At present, the resisting wind efect of fences is studied based on numerical simulation and it is low cost and fast. Meanwhile, the reliability of the fence model in numerical simulation can be ensured by verifed with measured data in wind tunnel [26,27]. According to previous studies, wind fow control by a windbreak fence can improve the wind environment at the site to some extent. But the application of windbreak fence in astronomy is diferent from other felds. In the working conditions of the mineral storage yard, the windbreak fence can be very close to the target area and completely shield the target area in terms of height, thus greatly reducing wind speed and dust emission [12]. However, for the telescope site, the windbreak fence cannot block the view of the antenna, which means that the fence must be a certain distance from the antenna position, so the shielding efect will be weakened to some extent. But the wind speed of the site is relatively small. Te direction of the incoming wind and the location of the tuyere are relatively clear [28]. So, there is no need to completely cover the antenna area with the windbreak fence. In order to reduce the infuence of wind disturbance on the electrical performance of the antenna, a method to control wind fow at the site is proposed based on the precise arrangement of the windbreak fence through the analysis of the terrain and wind characteristics of the site. Te wind speed in the antenna area is expected to be reduced by accurately arranging the windbreak fence so as to increase the efective observation time of the radio telescope. Te framework chart of the article is shown in Figure 2. It reduces the number of calculations, and the turbulence model is used to guarantee the accuracy of the simulation, which meets the requirements of engineering calculations. In this paper, the RANS method is used. Several turbulence models have been developed for this method. Among them, the standard k-ε model was proposed by Launder and Spalding in 1972 [29]. It is widely used in industrial applications because its computational convergence and accuracy meet the needs of engineering calculations. Subsequently, the RNG k-ε model [30] and the realizable k-ε model [31] were developed. Te realizable k-ε model is relatively new, which not only has higher accuracy but is also more consistent with the actual physical situation of the fow. Santiago et al. [32] used the standard k-ε model, the RNG k-ε model, and the realizable k-ε model to simulate the wind fow behind the fence and compared with the result of the wind tunnel experiment, while the root mean square (RMS) of the realizable k-ε model was relatively smaller. Bourdin and Wilson [33] simulated the air fow around the windbreak fence to study the applicability of fuid dynamics to windbreak aerodynamics, and the simulation result of the realizable k-ε model was consistent with the observation result. In this paper, the realizable k-ε model is used for numerical simulation. Te air fow follows three laws of conservation of mass, conservation of momentum, and conservation of energy. Te numerical simulation method is established based on the basic governing equations. Te energy equation is not used because the local thermal efect has little efect on the numerical simulation of this study condition. Te basic Advances in Astronomy governing equations for CFD numerical simulation are as follows:

Construction and
where ρ is the air density, t is time, v → is the wind velocity vector, p is the static pressure, τ is the stress tensor, ρ g → is the gravitational body, and S is the momentum source term. Te fnite-volume method (FVM) is used to discretize the governing equations. Te second order upwind is used to spatially discretize the characteristic quantities of momentum, turbulent kinetic energy, and turbulent dissipation rate. Te SIMPLEC (semi-implicit method for pressure-linked equations consistent) algorithm is used to solve the discrete equation system. Te solution is considered to have convergent when the iterative dimensionless residuals of all characteristic quantities are reduced to less than 10 −5 and the velocity of the fow feld near the monitoring point no longer changes signifcantly. Te overall schematic diagram of the numerical simulation is shown in Figure 3.

Construction of the Computational Domain of the Windbreak Fence Simulation Model.
In order to verify the reliability of the windbreak fence model in the simulation, the experimental data of the windbreak fence in the wind tunnel are cited for verifcation. Tis article uses the wind speed reduction data of the windbreak fence conducted by Wang Zetao at the Wind Tunnel Laboratory, Dalian University of Technology [34]. Te butterfy-type windbreak fence is 0.5 m in height, 0.0016 m in thickness, and 0.40 and 0.33 in porosity, respectively. Te simulation computational domain for the windbreak fence is shown in Figure 4. Te computational domain area is 5 m * 25 m. Te inlet boundary type is "velocity-inlet," the outlet boundary type is "outfow," the top boundary type is "symmetry," and the bottom boundary type is "wall." Te windbreak fence is placed 5 m from the entrance.

Te Model Construction and Parameter Setting of the Windbreak Fence.
In the wind fow simulation, the windbreak fence can be simplifed to a porous medium and the porous jump model can be used. Te essence of the porous jump model is to add a momentum source term to the momentum equation to simulate the obstruction of wind fow by porous materials. Te momentum source term consists of the viscous resistance term and the inertia loss term. Te formula is as follows: where μ is the fuid viscosity, α is the permeability coefcient, v is the fuid velocity, and C 2 is the pressure-jump coefcient.
Te parameter α and C 2 of porous jump model are set according to the property of the windbreak fence. Te model parameter α and C 2 can be obtained by physical experiments. For example, the resistance coefcient a 1 and a 2 are calculated by using the relationship between pressure drop ∆p and velocity v before and after the fence. Te ftting formula is as follows: Te source term of the momentum equation is the pressure drop per unit length, namely, where ∆n is the thickness of porous medium.
In the absence of measured data, the C 2 can be obtained according to the equation of Smith et al. [35,36]: where A p is the area of the plate, A f is total area of the holes, and C is a coefcient that has been tabulated for various Reynolds number ranges and for the ratio of hole diameter to plate thickness. According to the measured data in the wind tunnel [15], it is known that the permeability of the windbreak fence is about the magnitude of 10 − 5 . In the simulation, the infuence of changing permeability parameters on the simulation result is very small, so the viscous resistance term is not paid much attention to the simulation process.

Grid Division.
A structured grid is used for the grid division in paper. Te grid is encrypted around the windbreak fence and in the terrain area, and the density of the grid can be appropriately reduced away from the area of concern. Te meshing of the computational domain (Figure 4) is shown in Figure 5. A uniform distribution of the grid below the height of the fence along the y-axis is presented, with a grid size of 0.025 m. Te grid length above the height of the fence is increased by the "geometric law" method with a growth factor of 1.033. Te maximum grid length is 0.087 m. Along the x-axis, the grid from the inlet to the fence is reduced by the "geometric law" method with a reduction factor of 0.992. Te size of the grid around the fence is 0.01 m. Te grid from fence to outlet is growth with a growth factor of 1.007. Te maximum grid length is 0.143 m. Te number of grids is below 38,000.

Boundary Conditions of the Atmospheric Boundary Layer.
In the atmospheric boundary layer, the law of variation of the wind speed with height is called the mean wind speed gradient, which is usually described by a mathematical formula of the power or logarithmic law. In this paper, the power law profle formula is adopted for the wind speed condition at the inlet: the terrain of the site belongs to class B; roughness of the index β takes 0.15; z is the altitude, set z 0 as 10 m and V 0 as 15 m/s. Te empirical formula of the turbulence intensity is based on Type II of the Architectural Institute of Japan (AIJ): where z g is 350 m. Te turbulent kinetic energy k and the turbulent dissipation rate ε are set according to the following formulas: where l is the turbulence length scale, l � (0.07L/C μ (3/4) ); L taken as the top height of the computational domain; C μ � 0.09.

Verifcation of Numerical Simulation
where λ is the coefcient of reducing wind speed, V e is the wind speed without fence, and V n is the wind speed with fences.
Te results comparing simulation and wind tunnel experiment are shown in Figure 6. As can be seen from the fgure, the coefcient of reducing wind speed in wind tunnel experiment increases frst and then decreases with the distance after the fence, and the simulation result fully conforms to this trend. Te mean error of the results between the simulation and the wind tunnel experiment is shown in Table 1. In results with a height of 0.5 H, the mean error of both is relatively small. In the wind tunnel  Advances in Astronomy experiment, the curves of the two porosities are intertwined after a distance of 7 H; in the simulation, the diference value, which is the coefcient of reducing wind speed with two fences, decreases with the increase of the distance after the fence, but two curves do not intersect. Tis is due to the inherent turbulence efect of wind. Tere will be a certain degree of volatility, although incoming wind conditions are to some extent artifcially controllable in the wind tunnel experiment. Te numerical simulation is a more ideal experiment, and the results are smoother. Te average error of this study is at the minimum of 3.7% and at the maximum of 13.5%. Terefore, the windbreak fence model is reliable.

Te Top Height of the Computational Domain.
Te determination of the boundary of the computational domain is very important for the wind fow simulation, especially the infuence of the top height of the computational domain on the simulation result. If the top boundary is set too low, it will compress the bottom fow feld and afect the accuracy of the fow feld structure. Considering the terrain of the site, the top height of the computational domain is constructed as 1200, 2000, and 3000 m, respectively. Te length of the computational domain is set to 6000 m. Te windbreak fence is 120 m high and is located 1200 m from the entrance. Te computational domain is similar to Figure 4. Te simulation result is shown in Figure 7.
As can be seen in Figure 7, the simulation result of multiple computational domain models with diferent top heights set based on real working conditions of the site are completely consistent with the simulation result of Section 2.6, which fully demonstrates that the windbreak fence model constructed in this study is robust enough. Te coefcient of reducing wind speed of fences changes almost the same with the distance after the fence for diferent top heights of the computational domain, and there is a slight diference between the values. It indicates that the setting of the top height above 1200 m can guarantee the full development of the bottom fow feld. Terefore, the top height of the computational domain is set as 1200 m in the simulation of the actual working conditions for the site.

Construction of the Model and Simulation for the Slope
Terrain of the Site. Along the north-south direction of the antenna position (the blue dotted line in Figure 1), the 2dimensional topographic data of the site area are extracted, as shown in Figure 8. Point 0 of the horizontal coordinate is the antenna position; the vertical coordinate indicates the relative altitude. In the fgure, both the north and south ends are at the bottom of the canyon. In terms of terrain, the topography of the site is high in the south and low in the north.
Te more realistic the terrain model is constructed, the more it can fully refect the infuence of the terrain on the wind fow. However, small bumps and depressions in the ground will also be retained in the model. Tese structures have a weak efect on the wind fow but are extremely detrimental to grid division, consuming a large amount of Distance afer the windbreak fence (H) Figure 7: Infuence of the top height on reducing wind speed. "NS40-0.5 H" and "NS33-0.5 H" are the simulation results of Section 2.6. "NS" is numerical simulation. "40" and "33" are porosities. "0.5 H" is the height. "1200," "2000," and "3000" are the top heights of the computational domain.
working time and computational resources. Terefore, it is essential to determine the efect of local microtopography on wind fow to optimize the terrain model. Te simplifed terrain model (named the S model) and the real terrain model (named the R model) are constructed by analyzing the terrain of the site, as shown in Figure 9. In the computational domain model, the upstream and downstream terrains of the slope are replaced by straight lines. Te slope terrain in the S model is replaced by the oblique line. And, the slope factor is obtained by ftting the actual terrain data. Te slope terrain in the R model is constructed from actual terrain data.
Te grid length in the terrain area is set to 3 m, and the grid outside the terrain area is increased by the "geometric law" method with a growth factor of 1.005. Te maximum grid length is 7.735 m and the number of grids is less than 380,000. Te fence with 0.33 porosity and no fence is set in computational domain models of the site, and then the wind fow simulation is performed separately. Te simulation results are shown in Figure 10. Te antenna position is 6.7 H behind the fence. Te changing trend of the curve that is the coefcient of reducing wind speed in S and R models is completely the same with two heights relative to the ground. Due to the fuctuation of the actual ground, there is a slight diference between the reducing coefcients of two terrain models.
Te simulation results of the S and R models are extracted separately to make diagrams of the wind speed distribution, as shown in Figure 11. In the condition without windbreak fence, as in Figure 11(a), the wind speed gradient is evenly distributed due to the fat ground; as in Figure 11(b), there are sporadic disturbances in the wind speed gradient distribution near the ground due to the slight fuctuation of the real ground, but the fow feld structure is the same as in Figure 11(a). In the condition with the windbreak fence, the wind speed distributions in Figures 11(c) and 11(d) are almost the same. Tis is because the fence is also one of the obstacles on the ground, and the height of the fence is much higher than the height diference of the ground fuctuation. Terefore, the infuence of the small ground undulation on the wind fow is no longer obvious. Trough the analysis of Figures 10 and 11, it is concluded that the construction of the terrain model can properly smooth the local microstructure on the basis of retaining the original terrain contour, which can not only save the workload and computing resources but also not afect the simulation accuracy.

Analysis and Discussion of the Simulation Results at the
Site. Te frequency of incoming winds from the south and north (N and S directions in Figure 1) is also very high. Along the north-south direction, the terrain is high in the south and low in the north. Wind from north, the windbreak fence is arranged in low terrain, and the sheltering efect of the fence will be weakened. Furthermore, the location of the fence is in the wind mouth of the river valley, which is the most extreme working condition of the wind fence to control the wind fow. Based on the terrain data in the interval of x = −1350∼600 m in Figure 8, the computational domain model of the extreme condition of the site is constructed and the simulation of the wind feld is performed.
Te simulation results are shown in Figure 12, from which it can be seen that the reducing wind coefcient of the fence increases frst and then decreases in the Distance afer the windbreak fence (H) Figure 10: Te reducing coefcient of the terrain of the site. "NS40-0.5 H" and "NS33-0.5 H" are the simulation results of Section 2.6. "S" is the simplifed terrain model and "R" is the real terrain model. "33" is porosity. "0.5 H" and "0.8 H" are diferent heights relative to the ground. Te antenna position is 6.7 H behind the fence.
working conditions of the site terrain. Due to the impact of the slope terrain, the reducing wind coefcient of the fence that is placed at the bottom of the slope is smaller than that placed on the fat ground. And, as the distance behind the fence increases, the sheltering efect decreases faster. Te distribution of wind speed with and without fence working conditions is shown in Figure 13. It can be seen from the fgure that the area of low wind speed downstream is signifcantly larger in the condition without the windbreak fence ( Figure 11(b) compared to Figure 13(a)) due to the shading of the hill at x � 1000 m position; while the area of low wind speed downstream of the windbreak fence is signifcantly smaller in the condition with the windbreak fence ( Figure 11(d) compared to Figure 13(b)). In terms of wind shielding efciency, the coefcient of reducing wind speed at the antenna position (antenna position at x � 2200 m) is reduced by 5%.

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In general, because the windbreak fence is far from the antenna position, the windbreak fence has a relatively weak sheltering ability to the antenna position, and the optimal sheltering position is x � 1600∼2000 m, as shown in Figure 13(b). Te analysis concluded that slope terrain will weaken the sheltering efect of the windbreak fence at the bottom of the slope. However, based on the current assumption of the height and location of the windbreak fence, the coefcient of reducing wind speed at the antenna area can still reach more than 30% after control of the windbreak fence, that is, the wind coming from 5 m/s can be efectively reduced to within 3.5 m/s. Tis shows that wind fow can be controlled even if the windbreak fence is placed at the bottom of the slope. As can be seen in Figure 1, the mountain to the north of the antenna is relatively high. Within the lowest pitch angle of view, it is possible to try to place the windbreak fence closer to the antenna position, while reducing the height of the windbreak fence to achieve the optimal shielding efect of the antenna area.

Conclusions
Te larger the aperture and the higher the observation frequency, the more afected the observation efciency of the radio telescope is by wind disturbance of the site. In this paper, we summarize the terrain characteristic of some large radio telescope sites. And, the QTT site is taken as the research object. Trough the analysis of terrain characteristics and incoming wind characteristics, it is found that the direction of incoming wind with a high frequency and relatively high speed is located mainly in the mountain gap outside the antenna. Terefore, a method for controlling the wind fow of the site is proposed by windbreak fences.
Te windbreak fence simulation model is constructed based on the theory of porous jumps. Te mean error between the simulation result and the measured wind tunnel data is less than 14%. And, it has a strong reliability in the simulation for working conditions at the site. Te infuence of the top height of the computational domain on the simulation results is considered. Based on analysis of the simulation results with the top height of 1200, 2000, and 3000 m, the top height with 1200 m can meet the requirements. In addition, the simplifed terrain model and the real terrain model of the site are constructed, respectively. Te reducing wind coefcient of the windbreak fence is almost the same in two terrain models, and there is a slight diference between the values. Terefore, when constructing the terrain model, the microtopographic structure with small infuence on wind fow can be smoothed appropriately.
Based on the current assumption of the height and location of the windbreak fence, even if the windbreak fence is placed at the bottom of the slope, after control of the windbreak fence, the wind speed at antenna position can still be weakened by more than 30%. Tis shows that the windbreak fence can play a role in optimizing the wind environment at the telescope site. Tis study verifes the feasibility of the method for the windbreak fence controlling the wind fow of the site and also provides a method reference for the subsequent design of more accurate windbreak fence arrangement schemes. In the next phase, we will conduct a more detailed study of the windbreak fence in the 3D model. For example, the infuence of parameters such as the width of the fence in the horizontal wind direction, the width of the fence in the downwind direction, the diferent wind angle, and the diferent angles of wind attack on the downstream wind blocking efect.

Data Availability
Te experimental data of the wind tunnel are from a master dissertation (sources cited in the article). Other data supporting the fndings of this study are available from the corresponding author (xuqian@xao.ac.cn) upon reasonable request.

Conflicts of Interest
Te authors declare that they have no conficts of interest.