Effect of shelter porosity on downwind ﬂow characteristics

. Previous wind-tunnel studies were focused mainly on lonely standing windbreaks or wind fences with respect to their wind velocity reduction e ﬃ ciency and e ﬀ ective shelter distance. In presented wind-tunnel study, we investigated the e ﬀ ects of a three di ﬀ erent fence porosities (0.5, 0.25 and 0) embodied in a shelter-like building for coal convey by means of two-component Laser Doppler Anemometry (LDA). The turbulent ﬂow characteristics behind the fences were compared with those performed without the fence. For characterization of the fence e ﬀ ectiveness we used following quantities: wind-speed and turbulence kinetic energy reduction, and time fractions of the turbulent coherent structures associated with the sediment transport (sweeps and outward interactions). Results from mentioned quantities revealed that for the case of embodied fence the shelter construction has signiﬁcant impact on the ﬂow characteristics behind. The fence of the 0.5 porosity has been indicated as the most shelter e ﬀ ective considering the studied quantities.


Introduction
The windbreaks or wind fences have been studied since the 1940th. The main objectives of these studies remain the same: shelter efficiency and the factors that help to optimize the windbreak or wind fence design with respect to control the particle sedimentation (sand, dust, snow, etc.). The fence shelter efficiency is evaluated as the reduction of the wind velocity and downwind distance for which wind velocity remains below the threshold velocity [1]. Here the threshold velocity relates to the particle movement initiation. Previous studies (e.g. [2]) observed that the shelter efficiency is mainly influenced by the fence geometry and porosity. As one might expected, lower porosity brings about higher wind velocity reduction. However, higher turbulent intensities, shear stresses and pressures are produced as well. These flow turbulent characteristics are unfavourable to fence efficiency since decreasing the fence shelter distance and enhancing the particle uplift just downstream the fence.
In this paper, we present twofold extension relating to the fence shelter efficiency analysis: construction complexity and turbulent coherent structures. Previous wind-tunnel studies were mainly focused on a lonely standing windbreaks or wind fences. However, there are many practical fence applications. Thus, in present study, we considered the fence integration into the shelter for avoiding the coal dust escape from an convey belt to the surrounding area. This will give a better insight into a practical fence utilization.
The second fence shelter efficiency analysis extension follows the experimental study on aeolian sediment transa e-mail: nosek@it.cas.cz port over a sand dune [9], which revealed that the turbulent coherent structures, sweeps and outward interactions, have a dominant influence on sand transport. This finding is in contrast to research in fluvial domain where turbulent structures associated with the bursting processes, sweeps and ejections, were found to be dominant for sediment transport [3].

Experimental setup
The experiment was carried out in the low-speed Environmental wind-tunnel of the Institute of Thermomechanics of the Czech academy of sciences in Nový Knín. For detailed wind-tunnel description see [4]. The schema of the shelter model for convey belt of scale 1:100 positioned at the wind-tunnel test section with respect to the wind-tunnel coordinates is presented in figure 1a. Detail of the model, where the measures are normalised by the shelter model characteristic height H = 90 mm (H = 9 m at full scale), is presented in figure 1b. The fence, made of polypropylene fibres, was positioned at the leeward side of the shelter at x/H = 0 and z/H = 0.17 and runs along the entire lateral shelter leeward side (from y/H = −8.3 to y/H = 8.3). The gap that arisen between the bottom of the wind tunnel and the fence is necessary for dust explosiveness prevention. We investigated the following fence porosities = 0, 0.25 and 0.5, defined according to [5] as where B is the fence opening width and D is the fence fibre diameter. The wind-tunnel free stream velocity was maintained at 6 m s −1 during the whole experiment. For the characteristic height of the shelter model the Reynolds number was sufficiently high (Re = 34600) to fulfill the Reynolds number independence (Re crit = 11000), recommended by [6]. The free stream velocity also fulfil the criterium for the fence porosity independence on pressure drop according to [7].
The turbulent boundary layer simulating the moderately rough atmospheric boundary layer for the area of the interest (e.g. moderate hills, shrubs) was developed along the 20 m long wind-tunnel development section. Four vortex generators were spaced laterally at the beginning of the development section and the remaining part was covered by the roughness elements. The boundary layer characteristics were measured at the model entrance with the twodimensional Laser Doppler Anemometry (LDA) based on DANTEC BSA F-60 burst processor. The parameters of the longitudinal velocity profile (roughness length z 0 , displacement length d 0 and friction velocity u * ) were derived from the logarithmic law and are compared with those recommended by the VDI guidelines [8] in table 1. The parameters of the longitudinal velocity profile as well as the longitudinal and vertical turbulent profiles (not shown here) were in accordance with the VDI guidelines [8].

Data Analysis
The data were collected from the measured grid of the vertical plane xz downstream from the fence by LDA system at a rate ranging from 1 to 2 kHz. The sampling time for The origin of the coordinate system for the measurement grid is depicted in figure 1b, where the scheme of the vertical cut at y = 0 is presented. We measured at 6 heights 13 points downstream from the fence for each fence porosity and without the fence. One extra height (z/H = 0.1), consisting of 5 downstream points, was measured to provide the data below the fence gap (z/H < 0.17, see figure 1b) for each model type as well.
For analysing the fence effectiveness, we used a dimensionless wind-speed reduction coefficient according to [2] where U dim = U/U re f is the dimensionless mean velocity measured at a given point and fence porosity and  was applied for the dimensionless turbulent kinetic energy reduction coefficient Here, we assumed that the turbulent flow is a quasi twodimensional and used the following formulas for dimensionless turbulent kinetic energies where u and w is the fluctuation of the longitudinal and vertical velocity, respectively, is the time averaging and the zero index denotes the case without the fence. If R U and R T KE are equal to one, the fence reduces the windspeed and turbulent kinetic energy to zero and is 100% efficient. The negative values mean that the fence is increasing the wind-speed and turbulent kinetic energy, respectively.
Assuming the same approach for the sand transport [9], we performed the quadrant analysis according to [10] in order to identify turbulent coherent structures. This conditioning technique separates the flow into four discrete categories according to four quadrants of the scatter plots of two turbulent quantities, u and w : 1. outward interactions (u > 0, w > 0), 2. sweeps (u > 0, w < 0), 3. inward interactions (u < 0, w < 0) and 4. ejections (u < 0, w > 0). We used the hole quadrant analysis in order to filter insignificant events such that the attribution of the flow structure occurred if |u w | > σ uw , where σ uw is the standard deviation of the kinematic stress u w and represents the selected "hole threshold".
We analysed the fence porosity efficiency with respect to relevant events for sediment transport (sweeps and outward interactions) by means of their time fraction to the total sampling time T defined by [11] as where D 2 and D 1 is total sweep and outward interaction durations within T , respectively, and I i is the indicator function, where I i = 1, if u w is within quadrant i = 1, 2 and I i = 0, otherwise.

Reduction coefficients
The dimensionless longitudinal velocity reduction coefficient, R U , of three fence porosities as a function of the dimensionless streamwise distance from the fence, x/H, is presented in figure 2. The four graphs of R U are plotted for dimensionless height z/H = 0.2, 0.4, 0.7 and 0.9, respectively.
As one expected, the solid wall, = 0 (square symbols in figure 2), has the highest wind-speed reduction.  However, this reduction is absolute (for all investigated heights) only at the fence vicinity (x/H = 0.1). For heights z/H > 0.4 we can observe that R U decreases with the increasing downstream distance and height. The R U is even lower than the R U of the fence with the highest porosity ( = 0.5) for x/H > 1.5 and z/H > 0.2. The values of R U in case of the solid wall means that the backward wind direction (vortex) is present. The wind-speed reduction is independent on the dimensionless downstream distance x/H from ceratin value of x/H. We can observe that the higher the height the shorter the downstream distance is for the wind-speed reduction independence on downstream distance.

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Another parameter for determining the fence effectiveness, the dimensionless turbulent kinetic energy reduction coefficient R T KE , is presented in figure 3. The meanings of the symbols and coordinates are the same as in figure 2.
From R T KE point of view, the solid wall is even the worst case with respect to the sediment transport behind the shelter. It increases the turbulent kinetic energy If we observe the effect of a necessary vertical gap between the fence and the bottom of the model (z/H = 0.1), we can see from the figure 4a and figure 4b that strong wind-speed accelerations and not so strong turbulent kinetic energy reductions occur for all investigated porosities, respectively. Thus, the simulated vertical gap has unfavourable effect for sediment transport.
Because of better wind-speed and turbulent kinetic energy reductions are attained by fence of 0.25 and 0.5 porosity, respectively, the most favorable porosity cannot be stated. Hence, turbulent coherent structure analysis at following chapter would give a better insight to the fence porosity effectiveness.

Turbulent coherent structures analysis
Because the presented turbulent coherent structures are the partitions of the total vertical momentum flux u w , we present the dimensionless momentum flux u w /U 2 re f in figure 5 as well. As in previous presented results, the vertical momentum flux is plotted as a function of dimension-

Conclusions
The presented wind-tunnel experiment on porous shelter model revealed the impact of the geometry and porosity on downstream flow quantities. We demonstrated that not only the wind-speed and turbulent kinetic reduction coefficients but also the vertical momentum flux and its partitions should be taken into account for the shelter efficiency determination with respect to the aeolian sediment transport. According to these turbulent quantities the non-porous shelter shows the most unfavourable flow for the sediment transport, hence the worse shelter efficiency. The necessary shelter construction arrangement, comprising the vertical gap below the shelter porous/non-porous leeward wall, has unfavourable effect on shelter efficiency of all investigated shelter porosities. The best shelter performance associated with the highest turbulent kinetic reduction, the lowest total vertical momentum fluxes, and very low dominant turbulent coherent structures time fractions were observed for the shelter of 50% porosity. This porosity was worse than others only for the wind-speed reduction coefficient and have slightly lower values of the dominant coherent structures time fractions than the fence of 25% porosity. These results for the very high fence porosity suggest that the vertical gap at the shelter leeward wall would be unnecessary considering the dust explosiveness limits, hence improve sheltering effect.