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Experimental and computational study on the surface friction coefficient on a flat roof with solar panels Almerindo D. Ferreira1, Thomas Thiis2, Nuno A. Freire1 ADAI-LAETA, Department of Mechanical Engineering, University of Coimbra, Portugal 2 Department of Mathematical Science and Technology, Norwegian University of Life Sciences, Norway email:
[email protected],
[email protected],
[email protected] 1
ABSTRACT: This work aims to contribute for a better understanding of how solar panels affect the wind flow over a building with a flat roof, and how they affect the aeolian erosion of fine particles, like snow drifting. The work comprises wind tunnel experiments and three-dimensional CFD simulations. Several configurations are studied, varying the number of panels, and the gap between the panels and the roof, and wind orientation. The accuracy of these simulations is examined by comparing the predicted results with wind tunnel experiments conducted by the authors. It is confirmed that numerical simulations by means of the SST model capture the tendency of the surface pressure and surface friction on the roof when using a fine mesh around the model. It is found that wall friction is considerably affected by the presence of panels and, consequently, the wind erosion process and, therefore, snow drifting on the roof. The applicability of the numerical method in practical situations is discussed. KEY WORDS: Wind Erosion; Solar Panels; Snow Load; CFD; Surface Friction Coefficient; Surface Pressure. 1
INTRODUCTION
Snow load on buildings results from snow accumulation on the roof deposited by multiple snow events during the winter season. In between snow events, roofs may lose some snow due to wind erosion, or by melting. The eroded quantity depends on several parameters, such as snow packing, building and roof geometries, wind exposure, existence of obstacles on the roof, among others. Due to the continuously increasing energy demand, the installation of solar photovoltaic panels (PV) or solar collectors on flat roofs has increased also in areas with cold climate and snow. While this brings PV systems out of the public space and uses areas that otherwise would have been unused, it is susceptible to create some drawbacks. Indeed, the placing of solar panels on roofs changes significantly the local wind flow pattern. As well known, the roof is significantly more exposed to higher wind speeds than the ground. This has been investigated thoroughly and there are now several guidelines on wind load on solar panels, e.g., NVN 7250 [1] and BRE Digest 489 [2]. Snow load on roofs is usually a combination of a drift load and a balanced load (ISO 4355) [3]. Usually, the drift load consists of the snow that is accumulated in sheltered areas of the roof and the balanced load that is calculated as the fraction of the ground snow load which is not eroded by wind. For flat roofs with no drift load, this fraction is ranging from 70% for a wind y exposed roof, 84% on a normally exposed roof, and 96% for a sheltered roof. The corresponding fractions in the Eurocode (CEN) [4] are 64% for an exposed roof, 80% for a normal roof, and 96% on a sheltered roof. When placing obstructions to the wind flow, such as solar panels, on a flat roof, there will be sheltered zones where snow can accumulate in snow drifts. The snow load standards describe how to calculate snow load around such obstructions if they are continuous all the way down to the roof. As discussed in [5], when PV cells are mounted, snow loads constitute a variable load that needs to be taken into consideration. If solar panel arrays are mounted at an angle to the roof surface, snow is distributed in a variety of ways. For example, in [5] it is also indicated that snow tend to drift along the roof and accumulate along the backside of the PV modules, increasing locally the load on the roof. Furthermore, it is also likely for the solar panel array to collect snow during snow storms, and then shed it, which will increase the overall loading inside the array. This study aims to investigate the wind exposure of a flat roof surface when equipped with solar photovoltaic panels. Several configurations will be analyzed, varying various parameters, such as the spacing between rows of panels, gap size between the roof and the solar collector, and wind direction. Since the erosion is an important mechanism in determining the snow load on roofs, this might be a support in developing future provisions for snow load codes.
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015
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METHODOLOGY
For this study two methods are employed, namely experimental wind tunnel studies and computational simulations, as described in sections 2.2 and 2.3, respectively. 2.1
Building model
The parallelepiped model used in this study represents a typical three-story building with solar collectors installed on its flat roof. The model has dimensions H x W x L = 0.3 m x 1.2 m x 0.6 m, where H is the height of the building, W the width, and L the length in the streamwise direction, as shown in Figure 1. Assuming a 1:25 scale, this model mimics a full-scale building of 7.5 m height, 30 m width, and 15 m length. The solar panel model has a height of 0.075 m and thickness equal to 0.004 m, which represents a solar collector of approximately 1.9 m height and a thickness of 0.1 m. The gap distance, between the roof and the lowest edge of the solar panel, varied from 8 mm to 16 mm and 24 mm, corresponding to 0.2 m, 0.4 m and 0.6 m in full scale. The angle of the solar collectors, relatively to the horizontal, was set equal to 70º, assuming a relatively high latitude. In this study the undisturbed wind direction is assumed perpendicular to the longest side of the model and thus also to the solar panels. Two wind directions are considered, namely a positive (P) inclination when the solar panel is leaning against the wind, and also a negative (N) inclination. Combinations of 2, 3 and 5 rows of solar panels are tested. In the case of 2 rows of panels, panels no. I and V were used (see Figure 1). The case of 3 rows used rows no. I, III and V, whereas the last case included all rows of solar panels. The internal distance between the rows of panels is 105 mm (2.6 m in full scale). The model is symmetric relatively to the y=0 plane (coordinate system adopted is shown in Figure 1).
Figure 1. Model equipped with five rows of solar panels and for the case of negative inclination (dimensions in m). 2.2
Wind tunnel experiments
The experimental tests were conducted in the wind-tunnel installed in the Industrial Aerodynamics Laboratory - University of Coimbra, Portugal. The test chamber of the wind-tunnel is 5 m long, and no roughness elements were used to control the boundary layer thickness and shape due such relatively short length. The approaching wind profile, measured at a distance of 2.3 m from the inlet of the test section (where the windward face of the model is located in the experiments), can be fitted by a power law: (1) u z U0 where U0 is the undisturbed wind speed, and is the boundary layer thickness, and the exponent (equal to 0.4 m, and 0.11, respectively). The equipment and method used is similar to what was used in Ferreira [6]. Three different sets of experiments are performed. For the first set, the sand-erosion technique [7] was employed, in which a 1 mm layer of sieved and calibrated sand, spread over the building’s roof, is exposed to gradually higher wind speeds. The sand used has a prevailing grain diameter equal to 0.5 mm, to which corresponds a threshold shear velocity, u*t, of approximately 0.33 m/s (which corresponds to Cf=1.77×10-3, assuming U0=11.1 m/s, as explained ahead) [8]. This value is valid for loose sand grains disposed on a relatively long horizontal surface. Each selected wind speed was maintained for 120 seconds, which was the observed time interval necessary to define a stabilized eroded contour. This time interval is twice as long as the one adopted
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in [9], where it is stated that, after one minute, sand contours are stable and do not depend much on the initial sand thickness non-uniformities. The eroded contours were recorded continuously using a digital video camera, for later image treatment. Only the contours, each one of them defined after 120 s of exposition to a constant wind speed, are shown in this work. In the post processing of the data, the erosion on the building model without solar panels was used as a reference to normalize the data. Since friction velocity is directly proportional to velocity following the logarithmic wind profile close to the boundary, it is possible to determine the relative friction velocity at which sand erodes, u*REL, as given by Eq. (2): (2) ue 0 u*REL uePANEL where ue0 is the undisturbed velocity in the wind tunnel, upwind the model at roof height, without solar panels at which sand erodes on a specific part of the roof and uePANEL the undisturbed velocity necessary to erode the sand, at the same spot, but with solar panels mounted. This method was proposed by Thiis et al. [18] and the tests using the erosion technique can provide valuable qualitative information about the magnitude of the local speed-up. In the second experimental setup it was intended to analyze how solar panels affect the static pressure distribution along the roof. To accomplish so, thirty nine pressure taps were approximately uniformly distributed along line y=±0.05 m (depending on the wind orientation), on the roof (i.e., z=0.3 m). For the third experimental set, twenty two Irwin probes [10], placed along the center of model’s roof (z=0.3 m), were installed to measure the shear stress distribution. In order to reduce the interference between sensors, the probes were mounted alternately along three parallel lines, one coincident with the half-width (i.e., y=0), and the other two placed symmetrically at a crosswise distance of 25 mm, i.e., y=±0.025 m, respectively (see Figure 2). An Irwin probe consists essentially of two concentric pressure taps, one of them flush with the surface and the other protruding 2 mm above the surface. The pressure difference ( p) between these two taps is used to estimate the wall shear stress, and then the friction velocity, as intended in this work. In wind tunnel testing, the Irwin sensors are frequently used to estimate the wind speed close to the ground-level (e.g., [8], [11], [12]). The Irwin sensors are simple in design, do not require alignment as they are omnidirectional, and allow the measurement at numerous closely spaced locations. Based on the calibration of the probes [11], performed for favorable pressure gradient conditions, the local wall shear stress, w [Pa], is related to the pressure difference, p [Pa], by the following equation: (3) w 0.0373 p0.768 Such data is presented and discussed here, in a non-dimensional form, using the friction coefficient (Cf), defined as: w Cf 1 U 02 2
(4)
where is the air density.
Figure 2. Close view of (left picture) roof with Irwin-type probes distributed three central lines and pressure taps (line on the right hand side) along the roof without panels; (right picture) view of the model with three rows of panels installed, for a gap of 8 mm and positive wind orientation. In wind erosion tests it is frequent to use the concept of friction velocity (u*), which is related to the friction coefficient through: (5) Cf u* w U 0 2
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Second and third experimental set-ups were performed only for an undisturbed wind speed of U0=11.1 m/s, with the main intention to obtain data for the benchmark of the computational simulations. 2.3
Computational modeling
For the CFD modeling the open-source code OpenFOAM®, version 2.3.0, [13] was used. The computational modeling considers the same model dimensions and conditions as described in section 2.1. Steady state and incompressible conditions are assumed for the simulations, and two turbulence models, namely standard high Reynolds k- [14] and k- SST [15] are tested. The size of the computational domain, and axis system adopted, is shown in Figure 3. Only two wind directions are being considered in this work (as in the experiments). Therefore, a symmetry condition was imposed on the mid longitudinal vertical plane (i.e., y=0). For the boundary conditions, the influence of two wind profiles imposed at the inlet is evaluated. One of the situations considers a uniform profile (UP), where the wind speed (U0) is set as uniform across the entire boundary. In the other situation, the inlet profile reproduces a boundary layer (BL), as given by Eq. (1). Regardless of the inlet velocity profile, the turbulence intensity is assumed uniform in height, and equal to 10%, which was imposed at the inlet. Zero gradient is assumed at the outlet for all variables, except pressure, which was imposed equal to a fixed value of 0 Pa (zero gradient was imposed for pressure at the inlet).
Figure 3. Domain considered in the computational simulations. 3
COMPUTATIONAL BENCHMARK TESTS
Some preliminary tests were performed to evaluate the performance of the computational modeling, and select the turbulence model. Two benchmark cases were selected, namely the experiments of Castro and Robins [16] and the present wind tunnel measurements of surface pressure, and surface friction, performed in the building described in section 2.1. 3.1
Flow around a surface-mounted cube
The wind tunnel data, measured in the experiments of Castro and Robins [16], concerning the case of a surface-mounted cube, is used here to benchmark the CFD performance. The authors considered two situations for the inlet boundary profile, namely: “Case A”, which has a uniform upstream profile, i.e., constant velocity in height; and “Case B”, with a turbulent upstream boundary-layer flow. In both cases, the height of the cube considered here is H=1 m. The simulations were accomplished using OpenFOAM®, and the same grid was used to test the performance of the two selected turbulence models. For the simulations an undisturbed wind speed of U0=1 m/s (Re=7.9×104), was considered which, in accordance with the experimental observation of Castro and Robins [16], is high enough to ensure Reynolds independency (Re higher than 3×104). Additionally, several tests were conducted to ensure grid independency. Surface static pressure results on the cube are presented in the non-dimensional form of a pressure coefficient defined by:
Cp
ps p0 1 U 02 2
14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015
(6)
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where ps is the static pressure, and p0 and U0 refer to reference conditions. Figure 4 shows the pressure coefficient (Cp) distribution along the symmetry lines of the cube (line A: 0< /H
