Numerical Study on Flow Field for a Solar Collector at Various Inflow Incidence Angles *

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1 Journal of Aeronautics, Astronautics and Aviation, Vol.46, No.4 pp (2014) 241 DOI: / Numerical Study on Flow Field for a Solar Collector at Various Inflow Incidence Angles * Uzu-Kuei Hsu, Keh-Chin Chang ** and Chung-Chin Chuang Department of Aircraft Engineering, Air Force Institute of Technology No. 1, Jyulun Road, Gangshan Dist, Kaohsiung 82063, Taiwan, R.O.C. Institute of Aeronautics and Astronautics, National Cheng Kung University No. 1, University Road, Tainan 70101, Taiwan, R.O.C. Department of Aircraft Maintemance & Repair, Air Force Institute of Technology No. 1, Jyulun Road, Gangshan Dist, Kaohsiung City 82063, Taiwan, R.O.C. ABSTRACT Previous studies on solar water heaters (SWHs) have primarily focused on the thermal efficiency of a solar collector and structural safety. This study applied a numerical simulation method to examine the characteristics of flowfield. In addition, a solar collector of a SWH was employed to investigate the distribution of average surface pressure and vortex structure for various inflow incidence angles as well as the influence of two types of spoiler. This study adopted a computational fluid dynamics fluid mechanics method, an incompressible flow algorithm (i.e., semi-implicit method for pressure-linked equation [SIMPLE]), to simulate the flow field of the solar collector. A turbulence model (realizable k-ε model) was adopted. The obtained numerical values were compared with the experimental results. Because the simulation data were approximated to the experimental results, the turbulence strength and length were set as 11.7% and 0.12, respectively. The parameter for this study was inflow angle (θ = 15, 22.5, 30, 37.5, and V = 35 m/s). The characteristics of the flow field for various spoilers at inflow angle (θ) = 22.5 were examined. According to the numerical simulation results, the low-pressure area on the upper surface of the solar collector first enlarged and then diminished as the inflow angle increased. The largest low-pressure area occurred at the wind incidence angle (θ) = 30. Because the cross-sectional aspect ratio in the frontal view changed, the overall lift force increased as the angle θ increased. Because the vertical inflow cross-sectional area changed, air resistance gradually reduced. After spoilers of various sizes were installed, inflow airflow directly hit the solar collector, thereby reducing the pressure difference between the upper and lower surfaces of the solar collector. When the length of the spoiler increased, the shielding effect was enhanced; therefore, the increased size of the spoiler gradually reduced the lift force. Keywords: Solar collector, Incidence angle, Spoiler, Semi-implicit method for pressure-linked equation (SIMPLE) algorithm, Turbulence I. INTRODUCTION Taiwan is situated in a subtropical region and is thus suitable for developing solar thermal technology. In recent years, the government has endeavored to promote the installation and application of solar water heaters * Manuscript received, July 28, 2014, final revision, October 2, 2014(2014 Aeronautic Technology and Flight Safety Conference) ** To whom correspondence should be addressed, kcchang@mail.ncku.edu.tw

2 242 Uzu-Kuei Hsu Keh-Chin Chang Chung-Chin Chuang (SWHs). A typical SWH consists of a solar collector and water cylinder, and a flat-plate solar collector has a glass cover. Taiwan is on the typhoon path of the Northwest Pacific area. From 1911 to 2010, 397 violent typhoons hit Taiwan (on average, three to four typhoons hit Taiwan per year) [1]. The lift force produced by a typhoon often causes damage to the solar collectors of SWHs [2, 3]. Therefore, reducing the lift force of a solar collector by elevating a solar collector from the ground or installing a spoiler can reduce damage caused by a typhoon [4]. Previous studies on SWHs have mainly focused on the thermal efficiency of solar collectors or structural safety [5, 6]. The support structure of an SWH is rigid and can bear strong wind loads but can damage the glass cover and deform the case of the solar collector. Radu and Axinte [7] used an experimental method to measure the pressure coefficient when wind power influenced a flat-plate solar collector. Chang et al. [1] compared the effects of off- and on-ground solar collector models. The results revealed that no difference existed between the two models regarding the central line (the Cp curve) on the upper surface of the solar collector. Regarding the lower surface, air could not escape from the end of the on-ground model and was therefore obstructed, forming a high-pressure zone. In this aspect, the on-ground model substantially differed from the off-ground model. The maximal pressure of the airflow in the hit area of the solar collector occurred at the minimal value of Cp. Chung et al. [9] conducted an experiment in which a bucket was installed at the upper front end of a solar collector. They observed that when no bucket was installed, the lift force increased as the attack angle increased. After a spoiler was installed, the lift force decreased as the area in which the spoiler was installed increased. The results are consistent with those of Hsu et al. [10]. Hsu et al. used the Fluent software to numerically simulate the standard k-εmodel coupled with the enhanced wall function. According to experimental results, the lift force for the model in which a bucket was installed was lower than that for the model in which no bucket was installed. Installing a spoiler on a solar collector reduces damage caused by lift force because of strong wind [4, 9]. Previous studies have determined that the cavity between a spoiler and solar collector apparently influenced the surface pressure distributions on the upper and lower surfaces of solar collectors. Wind incidence was a crucial parameter that influenced the aerodynamic characteristics of a model. Previous studies have indicated that a change in wind incidence caused a change in average pressure or pressure fluctuations. This change formed a suction area on the roof of a low-rise building or long-spanned cantilever roof and caused a change in lift force. Lam and Zhao [11] observed that when wind flowed in from the front side, the separation zone that formed spanned the front edge of the surface of the cantilever roof. Increasing the inflow wind angle changed the shape of the negative pressure zone. In addition, a high suction zone formed at the front edge of the upper roof surface near the windward angle [12]. Increasing the inflow wind angle from 0 to 30 gradually produced a conical vortex at the windward roof corner, increased the strength of the suction zone, and moved the suction zone from the windward roof to a corner [13]. According to the aforementioned studies, several characteristics can be summarized as follows: (1) A SWH must be a blunt body, and when airflow passes an SWH, a wake flow and low-pressure area can occur. (2) When the attack angle for the solar collector is large, the cross-sectional area of the sheltered flow field increases. When the low-pressure area on the surface of the solar collector increases, the difference between upper and lower surface pressures also increases. (3) Elevating the solar collector from the ground can effectively reduce the lower surface pressure of the solar collector and decrease the difference between upper and lower surface pressures. (4) Regarding the model in which a spoiler is installed, when the projected area of the spoiler in a vertical airflow direction is large, the lift force of the model can be effectively reduced. In Taiwan, SWHs are typically installed on the top of unsheltered buildings, face southward, and form an angle of 20 to 30 for an optimal thermal efficiency. In the event of a typhoon, wind gusts influence a solar collector and a pressure change on the solar collector occurs. A large difference between upper and lower surface pressures may damage the structure of the solar collector. Therefore, to determine how a change in wind incidence influences a solar collector, this study constructed a solar collector model and simulated various inflow incidence angles to investigate the change in flow field. In addition, this study examined the pressure change for specific angles after a spoiler was installed. II. PHYSICAL MODEL AND GRID SYSTEM This study employed a 60% scaled single solar collector model equipped without bucket for a SWH used in a previous study [9] (L = 1.2 m, W = 0.6 m, and H = m). The solar collector was elevated 0.03 m from the ground (0.025 L, where L denotes the length of the solar collector and equals 1.2 m), forming an attack angle (α) of 25 with the ground, as shown in Figure 1. In the first part of this study, four wind inflow angles were examined (i.e., when θ equaled 15 (E01), 22.5 (E02), 30 (E03), or 37.5 (E04)). According to previous studies, within a wind speed of m/s, the influence of a change in wind speed (i.e., the Reynolds number) was small. Therefore, the wind speed for the experiment was set to 35 m/s for simulating the situation in which a solar collector was influenced by a moderate typhoon. In the second part of the study, two spoilers of different sizes (S01 [i.e., 17.5 cm] and S02 [i.e., 35.0 cm]) were added to the model to examine whether a spoiler can effectively reduce the lift force of the solar collector at a specific wind incidence angle. Tables 1 and 2 show related parameters. Regarding the computational domain, refer to the size of atmospheric boundary layer wind tunnel (L = 13.2 m, W = 4.0 m, and H = 2.6 m) proposed by Architecture and Building Research Institute, Ministry of the Interior. As shown in Figure 1, the 2L distance model for the upwind area was used to ensure the

3 Numerical Study on Flowfield for a Solar Collector at Various Inflow Incidence Angles 243 stability of intake airflow. The length of the downwind area was 8L for self-preserving or fully developed conditions at the rear end. The working fluid was defined as air. The mainstream direction of the fluid was the X axis, vertical direction was the Y axis, and cross-mainstream direction was the Z axis. The grids were divided into 43 blocks. A grid system that underwent a grid independence test was used. The number of grids was 2,033,765. Eight personal computers (PC) were used to perform message passing interface parallel computing. The specifications of the PCs were 4-cores 3.2 GHz CPU / 8 4 GB RAM. Table 1 Matrix of research case θ V(m/s) Guiding plate (cm) α E E or 0 E E S S L Table 2 Lift and Drag Force coefficient in different spoiler length Model E02 (0 cm) S01 (17.5cm) S02 (35 cm) Guiding Plate Area (m 2 ) Lift Coefficient Drag Coefficient Figure 1 Computational domain size and angle of heat collector Top view of models in different incidence inflow Spoiler size Computational domain III. NUMERICAL METHOD The computational fluid dynamics software, Fluent, was used for numerical simulation. The basic assumption was three-dimensional steady-state viscous and incompressible flow. Reynolds-averaged Navier Stokes (RANS) equations were used as governing equations. Mass and momentum conservation equations were adopted without considering energy equations. Continuity equation: Momentum equation: ( ν ) = 0 (1) V ρ + V v = p + µ 2 V + f (2) t The turbulence model was the realizable k-εmodel [14], which included RANS equations in addition to a turbulent kinetic energy equation (k) and turbulent kinetic

4 244 Uzu-Kuei Hsu Keh-Chin Chang Chung-Chin Chuang energy dissipation rate equation ( ε ). The discrete method, the finite volume method, was adopted. Based on conservation laws, any grid produced a control volume. When a physical quantity entered the control volume, the physical quantity had to comply with physical conservation to obtain a discrete solution by using a conservation rate in integral form. Regarding solving momentum equations, the second order upwind scheme and central difference scheme were used to compute the convection and diffusion terms, respectively. The semi-implicit method for pressure-linked equation (SIMPLE) was used for pressure and velocity coupling [15]. After the pressure correction equation was identified, the discrete momentum equation was used to solve the velocity field. A convergent solution was obtained by repeating the procedure. IV. BOUNDARY CONDITIONS Boundary conditions are described as follows: (1). The inlet boundary was set to uniform flow. The gauge total pressure of pressure inlet was 101,325 Pa, and the initial gauge pressure was set to 100,549 Pa. (2) The outlet boundary condition was pressure outlet, and the outlet gauge pressure was 100,549 Pa. In contrast to the value for pressure inlet, based on Bernoulli s law, pressure difference was converted into a velocity of 35 m/s, which was equivalent to the wind speed of a moderate typhoon. (3) Wall boundary included a solar collector and wind tunnel boundary. Stationary wall, no slip, non-penetrating, adiabatic boundary conditions and a wall velocity of 0 were assumed. grid system D02 D03 D04 Y + for BL cells ~97 ~56 ~36 Y + range 42~320 33~276 26~254 Total cells 1,022,899 2,033,765 4,067,551 Figure 2 Cp distribution along the longitudinal central line of the collector lower surface in different grid system. (Vin= 35m/s,T.I.= 11.7%) 5.2 Comparison of various inflow wind angles Analysis of the change in streamlines of a flow field V. BOUNDARY CONDITIONS 5.1 Grid dependence test and flowfield verification The experimental results obtained from numerically simulating a flow field in a previous study on wind tunnel [9] (i.e., the streamwise (x axis) velocity of u) served as a reference value for this study. The derived experimental values are listed as follows: Turbulent Intensity = 11.7% and Length Scale = 0.12 m. As shown in Figure 2, grid points distributed at three densities were used for a grid dependence test. This study employed a 60% scaled solar collector model, the wind incidence angle (θ) of which was 0, attack angle (α) was 25, length was 1.2 m, width was 0.6 m, and height was m for the grid independence test. Because the RNG k-ε Turbulence Model was adopted and the standard wall function was used to simulate the near-the-wall state, the range of the y+ value was 30 < y+ < 300. Figure 2 shows the Cp values of four grid systems (D01 D04) at the lower surface of the solar collector below the central line. No significant difference existed between the simulated curves for D03 and D04. Therefore, grid independence was verified, and D03 was the grid system used for subsequent studies. The total grid numbers were 2,033,765. Figure 3 Streamlines over heat collector in different incidence inflow. (Vin= 35m/s,T.I.= 11.7%)

5 Numerical Study on Flowfield for a Solar Collector at Various Inflow Incidence Angles 245 Figure 3 shows the simulated streamlines of a flow field. As shown in Figure 3, Streamline A indicated that a corner vortex occurred after airflow passed the acute angle at the left side of the solar collector. The streamline whirled from the left side of the figure to the center and flowed out downstream along the edge of the solar collector. Streamline C flowed in from the upper right corner of the solar collector, passed the solar collector, formed a recirculation zone above the solar collector, flowed toward the left low-pressure area, and finally merged with the corner vortex. Streamline B was the airflow across the recirculation zone, passed the upper left corner of the solar collector, and flowed out toward the lower right corner. Streamline B was slightly influenced by the low-pressure area. Streamline D whirled from the right side of the figure to the center after passing the right acute angle. When streamline D passed the middle area of the solar collector, Streamline D moved toward the central area and finally merged with Streamline B and passed the solar collector. Streamline E showed the airflow state in the recirculation zone at the upper right part of the solar collector. Because of the influence of the airflow that passed the solar collector, an eddy current system was formed. Four inflow wind angles (θ) were compared. Streamline A showed that a corner vortex occurred after airflow passed the left acute angle and whirled from the left side to the center. As shown in Figures 3 and, Streamline C initially flowed in from the right side of the solar collector. Streamline C was influenced by the low-pressure area above and gradually moved toward the left side and merged with the left corner vortex. As shown in Figures 3 and, after the angle θ increased, Streamline C was influenced by the right recirculation zone and enlarged, thereby changing its path and flowing in the right recirculation zone Analysis of numerical oil flow Figure 4 shows numerical oil flow on the solar collector. The area above the dotted line is the recirculation zone in which the streamline direction is opposite to the inflow direction. The recirculation zone is a low-pressure area. In the downstream area of the solar collector, a corner-edge vortex was formed because of the right and left acute angles. After the corner-edge vortex flowed through the recirculation zone, collided with the airflow in the recirculation zone, and left traces below the dotted line, the corner-edge vortex moved toward the lower part, right side, and left side of the solar collector. Therefore, the re-attached region can be depicted using dotted lines according to the collision boundary opposite to the airflow direction. The airflow below the re-attached region moved downstream. The oil flow diagrams of four inflow incidence angles of the solar collector were compared, and the results revealed that the re-attached area apparently moved toward the right side of the solar collector as the inflow wind angle increased. As shown in Figures 4 and, the re-attached region moved slightly toward the upstream area. Figure 4 Numerical oil flow visualization in different incidence inflow. (Vin= 35m/s,T.I.= 11.7%) Effect of inflow incidence angle As shown in Figure 5, the Cp distributions of various inflow incidence angles of the solar collector were compared. In the figure, blue indicates low pressure and red indicates high pressure. The Cp value for the lowest pressure on the upper part of the solar collector was less than The upper left and lower right corners of the solar collector were the low- and high-pressure areas, respectively. A comparison of four low-pressure areas showed that the low-pressure areas first increased and then decreased. As angle θ increased from 15 to 30, the low-pressure areas gradually increased. As shown in Figure 5, the largest low-pressure area on the solar collector occurred at θ = 30. When angle θ increased to 37.5, the low-pressure area began to diminish. Regarding the reason for the decrease in pressure, according to Figures 3 and, Streamline C merged with Streamline A and influenced the vortex strength of Streamline A; therefore, the flow rate of Streamline A reduced, and the pressure increased. According to Figures 3 and, Streamline C changed its original path and merged with the vortex zone at the right side of the figure. The vortex generated by Streamline A was not influenced, and thus, the flow rate of Streamline C increased, and the pressure reduced. The high-pressure area formed on the upper surface of the solar collector was located in the lower right zone. As shown in Figures 3 and, no significant difference existed among the high-pressure

6 246 Uzu-Kuei Hsu Keh-Chin Chang Chung-Chin Chuang areas. The high-pressure areas diminished as angle θ increased, as shown in Figure 3. The reason may be that as angle θ increased to 30, the path of Streamline B was distant from the downstream area of the solar collector, and the airflow did not collide with the solar collector or cause a change in the pressure at the surface of the solar collector. Therefore, the high-pressure area diminished. cross-sectional area located at the left side of the solar collector and impacted by airflow increased as angle θ increased. Therefore, the high-pressure area moved left as angle θ increased. The high-pressure area originally located at the center diminished because angle θ changed and airflow was obstructed. Therefore, as angle θ increased, the high-pressure area apparently enlarged, indicating that a large area on the lower surface of the solar collector was under pressure. In particular, the pressure focused on the left side of the solar collector, yielding uneven pressure at the right and left sides of the solar collector. Figure 5 Cp distribution on collector upper surface (Vin= 35m/s,T.I.= 11.7%) Figure 6 shows the distribution of pressure to the lower surface of the solar collector. As shown in the figure, the airflow passed the lower part of the solar collector and directly collided with the surface of the solar collector, yielding a larger pressure change at the lower surface than at the upper surface. The overall streamline direction deviated according to the inflow angle, and thus, an uneven and asymmetric distribution formed. According to Figures 6 and, high-pressure areas were located at the centers of the upstream and downstream zones on the surface of the solar collector. As angle θ increased, the high-pressure area slightly enlarged and moved left. This phenomenon occurred because the windward side in the upstream zone on the surface of the solar collector was impacted by airflow. In addition, the airflow on the lower surface of the solar collector was obstructed. When angle θ exceeded 30, the high-pressure areas shown in Figures 6 and moved to the left side of the solar collector. In addition, the Cp value of the overall pressure to the surface of the solar collector was higher than 0.6. At the windward side, the Figure 6 Cp distribution on collector lower surface (Vin= 35m/s,T.I.= 11.7%) 5.3 Influence of spoilers of various sizes Analysis of the change in streamlines of a flowfield Figure 7 shows the streamline distribution on the upper surface of the S01 model. After Streamline A passed the left corner of the solar collector, airflow whirled from the outside to the center, and a corner vortex occurred. According to Figures 7 and, Streamline A whirled to the re-attached region of the solar collector. The re-attached region was located at three-fourths of the downstream area of the solar collector. Streamline E moved from the lower part to the back of the spoiler after the airflow hit the spoiler. Because of the influence of the low-pressure area, airflow flowed from the lateral part to the upper part of the solar collector, and a recirculation zone formed in the upstream area of the solar collector. In addition, the airflow moved from right to left and then merged with the corner vortex

7 Numerical Study on Flowfield for a Solar Collector at Various Inflow Incidence Angles 247 of Streamline A and flowed out. Streamline D showed the corner vortex at the right side of the solar collector. After passing through the corner, the airflow moved from outside to inside, lifted upward, passed across the upstream recirculation zone of the solar collector, and flowed out. After hitting the front edge of the solar collector, Streamlines B and C lifted upward and passed across the recirculation zone formed by Streamline E. Subsequently, the airflow contacted the solar collector again in the downstream area. toward the downstream area. In particular, for the upstream area at the right side of the dotted line, the boundary of the re-attached region extended toward the upper right corner before a spoiler was installed. After a spoiler was installed, the re-attached region was replaced by a recirculation zone. Regarding the numerical oil flow on the lower surface of the S01 model as shown in Figure 10, an apparent recirculation zone existed in the upper left corner of the solar collector. The streamline in the upstream area moved from left to right in the figure and flowed out from the upper right corner. The path can be compared with that of Streamline E shown in Figure 7. The streamlines in the midstream and downstream areas flowed out along the deviated inflow angle. Figure 7 Streamlines over heat collector with spoiler Figure 8 shows the streamline distribution on the lower surface of the S01 model. Streamline A flowed near the lower surface of the solar collector after passing a spoiler. At the midstream area of the solar collector, Streamline A moved inwardly from the right edge to the area above the solar collector. After passing a spoiler, Streamline B hit the upstream area on the lower surface of the solar collector and flowed near the lower surface of the solar collector to the downstream area of the solar collector and then moved upward out from the left edge. Because of the shielding effect at the back of the spoiler, Streamline D formed a closed low-pressure recirculation zone. Figure 9 Numerical oil flow visualization on collector upper surface with different spoiler (Vin= 35m/s,T.I.= 11.7%) Figure 8 Streamlines under heat collector with spoiler Analysis of numerical oil flow Figure 9 shows numerical oil flow on the upper surface of the solar collector. In the figure, a dotted line was used to indicate the location of the re-attached region (θ = 22.5 ). The numerical oil flow diagrams of the models with a spoiler installed (S01) and without a spoiler installed (E02) were compared. The results showed that the re-attached region evidently moved Figure 10 Numerical oil flow visualization on collector lower surface with different spoiler (Vin= 35m/s,T.I.= 11.7%) 5.4 Comparison of lift force and air resistance Table 2 shows the influence of the spoilers of various sizes on the lift force and air resistance of a solar collector under two conditions (constant wind speed = 35 m/s and inflow wind angle (θ) = 22.5 ). In the table, E02 is the model with no spoiler installed; S01 and S02 are the models equipped with spoilers 17.5 cm and 35 cm in length, respectively. The lift forces and air resistances of the S01 and S02 models decreased by 18% and 45% and increased by 17% and 46%, respectively, compared with the model with no spoiler installed. Therefore, installing

8 248 Uzu-Kuei Hsu Keh-Chin Chang Chung-Chin Chuang a spoiler effectively reduced overall lift force. VI. CONCLUSION Under the condition of constant wind speed, the numerical oil flow diagrams for various inflow wind angles (θ) were compared. The results showed that the re-attached region moved slightly toward the upstream area as an inflow angle increased from 15 to Regarding the distribution of pressure, the low-pressure area on the upper surface of the solar collector first enlarged and then diminished as angle θ increased. The largest low-pressure area occurred at wind incidence angle (θ) = 30. After the angle exceeded 30, the low-pressure area started to diminish. The high-pressure area on the upper surface of the solar collector slightly diminished as angle θ increased; no substantial difference existed. Regarding the lower surface of the solar collector, the high-pressure area was located at the left side of the solar collector and increased as angle θ increased. Regarding the lift force and air resistance of the solar collector, the overall lift force of the solar collector gradually increased as the inflow angle θ increased from 15 to Under two conditions (constant wind speed (V) = 35 m/s and inflow wind angle (θ) = 22.5 ), the models with spoilers of various sizes installed were compared. According to the numerical oil flow diagrams of the two models, the boundary of the re-attached region on the upper surface of the solar collector apparently moved toward the downstream area as the length of the spoiler increased. The extension of the re-attached region at the upper right corner of the solar collector was replaced by a recirculation zone. After the length of the spoiler increased, the area replaced by a recirculation zone increased. Regarding the lower surface of the solar collector, the recirculation zone occurred in the upstream area because of the obstruction of the spoiler and increased as the size of the spoiler increased. The results were consistent with the numerical oil flow diagrams. According to the distribution of pressure, because the length of the spoiler increased, the vertical inflow cross-sectional area enlarged. Accordingly, overall airflow was effectively obstructed, and the pressure caused by the collision of the airflow with the solar collector was effectively reduced, thereby reducing the pressure difference of the solar collector. Thus, the overall lift force of the solar collector was lower than that of the model with no spoiler installed. The lift force of S01 and S02 decreased by 18% and 45%, respectively, and the air resistance of S01 and S02 increased by 17% and 46%, respectively. [3] Kopp, G. A., Surry, D, and Chen, K. Wind Loads on a Solar Array, Wind and Structures, Vol.5, No.5, pp , [4] Chung, K. M., Chang, K. C., and Liu, Y. M., Reduction of Wind uplift of a Solar Collector Model, Journal of Wind Engineering and Industrial Aerodynamics, Vol.96, No.8 9, pp , [5] Oliphant M. Measurement of Wind Speed across Solar Collectors. Solar Energy, Vol.24, pp , [6] Kalogirous S., Solar Thermal Collectors and Applications, Proceedings of Energy Combust. Sci., Vol.20, pp , [7] Radu A, and Axinte E., Wind Forces on Structures Supporting Solar Collectors, Journal of Wind Engineering and Industrial Aerodynamics, Vol.32, pp , [8] Chang, K. C., Hsu, U. K., Wang, W. C., and Tyan, R. H., Flow Visualization and Wind Uplift Analysis of a Suspended Solar Water Heater, Procedia Engineering, Vol.31, pp.3-8, [9] Chung, K. M., Chang, K. C., and Chou, C. C.. Wind load on residential and large-scale solar collector models, Journal of wind engineering and industrial aerodynamics, Vol.99, No.1, pp.59 64, [10] Hsu, U. K., Chang, K. C., Tyan, O. H., Wang WC, Liu YC. Numerical Studies of the Uplift Effect over a Solar Water Heater in Strong Wind, Journal of Air Force Institute of Technology, Vol.10, No.1, pp , 2011 [11] Lam, K. M., and Zhao, J. G., Occurrence of peak lifting actions on a large horizontal cantilevered roof, Journal of Wind Engineering and Industrial Aerodynamics, Vol.90, pp , [12] Lam, K. M., and To, A. P., Generation of wind loads on a horizontal grandstand roof of large aspect ratio, Journal of Wind Engineering and Industrial Aerodynamics Vol.54, pp , [13] Zhao, J. G., and Lam, K. M., Characteristics of wind pressures on large cantilevered roofs: effect of roof inclination, Journal of Wind Engineering and Industrial Aerodynamics, Vol.90, pp , [14] Shih, T. H., Liou, W. W., Shabbir A, Yang Z, and Zhu J. A., New k-εeddy-viscosity Model for High Reynolds Number Turbulent Flows, Model Development and Validation. Computers Fluids, 24(3): , [15] Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere. Ch. 6, REFERENCES [1] The Meteorological Research and Development Center. [2] Wood G. S., Denoon R.O., and Kwok K., Wind Loads on Industrial Solar Panel Arrays and Supporting Roof Structures, Wind and Structures, Vol.4, No.6, pp , 2001.