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Three dimensional numerical investigation of air flow over domed roofs
ARTICLE IN PRESS J. Wind Eng. Ind. Aerodyn. 98 (2010) 161–168
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Three dimensional numerical investigation of air flow over domed roofs Ahmadreza K. Faghih, Mehdi N. Bahadori School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e in fo
abstract
Article history: Received 1 May 2008 Received in revised form 12 October 2009 Accepted 16 October 2009 Available online 10 November 2009
Domed roofs have been used in Iran and many other countries to cover large buildings such as mosques, shrines, churches, schools, etc. However their favorable thermal performance made them to be employed in other buildings such as bazaars, or market places, in Iran. The aim of this study was to determine the air pressure distribution over domed roofs, employing a numerical method. In this investigation, a three-dimensional model and a laminar inlet air flow were considered. The k-e RNG method was employed for the turbulent flow simulation method. Simulation was run under three conditions of windows and a hole on top of the dome being open, or closed. The results were compared with the results obtained by an experimental investigation of the same domed-roof model. The results of this research can be employed to determine the heat transfer coefficient of wind blowing on domed roofs and the passive cooling effect of such structures. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Domed roof Numerical solution Experimental investigation Wind pressure distribution
1. Introduction Domed roofs have traditionally been employed to cover buildings with large areas. These roofs have played an important role in Iranian architecture, and have had a great effect on the reduction of the buildings’ cooling loads. Preliminary research shows that the solar energy received by a domed roof is roughly equal to that of the flat roof of the same base area (Serpoushan and Yaghoubi, 2002). The solar energy absorbed causes the roof temperature to increase in comparison with the ambient air. With wind flowing over a dome, some of the heat is removed from the roof through convection, and the rest goes through the roof by conduction and can be transferred to the inside air by convection, and to the surrounding surfaces of the occupied space by radiation. The geometrical configuration of these domed roofs causes the wind velocity to increase over them, resulting in an increase in the convection heat transfer coefficient. Also, the heat transfer from these roofs is accentuated by the fact that the area of a domed configuration is greater than a flat one. Passive cooling can be achieved by inserting a hole on top of the dome. In the presence of this hole, the negative pressure over it makes an airflow emanating from the building’s openings towards it. This airflow decreases the inside roof temperature, resulting in a lower heat transfer by convection and radiation. Fig. 1 shows a schematic pattern of airflow in a building with a domed roof (Bahadori, 1978). In addition to large buildings, domed roofs have been used in Iran to cover large cisterns. In the cistern shown in Fig. 2, the pressure difference between the air entering the space above the Corresponding author. Tel.: + 98 21 66 16 55 08.
E-mail address: [email protected] (M.N. Bahadori). 0167-6105/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2009.10.012
water level from the wind towers and the air leaving from the top of the dome causes a natural airflow over the water surface. This process causes evaporation of water and its cooling. Air flow pattern on domed roof building has been investigated by means of numerical and experimental methods. Ogawa et al. (1993) developed a two-dimensional finite element analysis for turbulent flow over cylindrical domed roofs. Velayati and Yaghoubi (2004) and Hadadvand et al. (2008) simulated air flow over cylindrical domed roofs, assuming two-dimensional flow, and using control volume method. Blessmann (1971), Taniguchi et al. (1982), Cheung (1983), Cheung and Melbourne (1983), Toy et al. (1983), Newman et al. (1984), Savory and Toy (1986), Taylor (1991), Yaghoubi (1991), Sabzevari and Yaghoubi (1992), Tsugawa et al. (1992), Franchini et al. (2005), and Faghih and Bahadori (2009a) investigated air flow over domed roof buildings experimentally. The purpose of this investigation was to determine the wind pressure coefficient over a domed roof. This information can be used for the thermal performance evaluation of domed roofs. In this research the air pressure distribution over a domed roof model was studied, considering the presence of windows in the walls and a hole on top of the dome. A boundary layer air flow was considered. There are many famous buildings in the world with domed roofs. Figs. 3–5 show a few of such buildings. In this investigation, the dome located in Yazd, Iran, was considered.
2. Numerical analysis of the problem A commercially-available software was employed in this numerical investigation. As compared with the standard methods
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Nomenclature X, Y, Z t h, H Vh VH
coordinates the height of building height wind velocity at height h wind velocity at height H
of analysis, the RNG k-e model for turbulence simulation was adopted in this study, due to its higher accuracy. First order upwind method was used to make the related equations discrete. The solution method was a control volume, using incompressible model. Pressure and velocity dependency method was SIMPLE and near wall treatment was non-equilibrium wall function (Pope, 2000). To make sure of the accuracy associated with employing this software, it was decided to use it in conjunction with a structure for which experimental results were known, or other investigators had already obtained valid data. It was first used to obtain the wind pressure coefficients over wind towers for which experimental data were available. There was a fairly good agreement between the numerical and experimental results (Faghih and Bahadori, 2007).
y, b, j a V P Cp
r
angles constant wind velocity pressure pressure coefficient density
In the second step of the numerical study, it was applied to the domed roof models. To compare the results with those of Hadadvand et al. (2008), the length of the air circulation behind the building shown in Fig. 6 was obtained to be equal to 6.6, with Hadadvand simulation, and equivalent of 6.8 in the current analysis, for Re = 5 105. In this figure, X and Y are dimensionless as defined below, and t is the height of building’s wall which is equal to 1 in this simulation X ¼ x=t
ð1Þ
Y ¼ y=t
ð2Þ
The pressure difference between the middle of the front wall and the top of the domed roof was 18, in this simulation, and it was 16.01, as was reported by Hadadvand et al. (2008).
Fig. 1. Air flow in a building with domed roof with an opening on its cap (Bahadori, 1978).
Fig. 3. Domed roof of Taj Mahal in Agra, India.
Fig. 2. Air flow in a cistern equipped with a domed roof and several pairs of wind towers (Bahadori, 1978).
Fig. 4. Domed roof of St Peter’s Church in Rome, Italy.
ARTICLE IN PRESS A.K. Faghih, M.N. Bahadori / J. Wind Eng. Ind. Aerodyn. 98 (2010) 161–168
163
1 Numerical Experimental
Cp
0.5 0 -0.5
0
30
60
90
120
150
180
-1 -1.5
(Degrees)
Fig. 8. Numerical results of Cp along the b =0 in comparison with Taylor’s experimental results (Taylor, 1991).
1 Numerical Experimental
0.5 Cp
Fig. 5. Domed roof of Sheikh Lotfollah Mosque in Isfahan, Iran.
0
0
30
60
90
-0.5 -1 -1.5
(Degrees)
Fig. 9. Numerical results of Cp along the b = 90 in comparison with Taylor’s experimental results (Taylor, 1991).
Fig. 6. The length of the circulating area obtained in this analysis, employing the model of Hadadvand et al. (2008).
reaches the model. A high pressure zone is created on the windward side, pushing the air around the sides and up over the top of the dome. A portion of the air flows downward, and around the model, creating an eddy at the leeward side. The turbulent flow produced in this area is considerable. As the result, we can expect an uncertainty and a difference between the experimental and the numerical values of Cp obtained for this region. It should be mentioned that neither the experimental, nor the numerical results give the exact amounts of Cp.
3. Numerical analysis of a domed roof
Fig. 7. The model of the dome employed by Taylor (1991).
In the third step, experimental model by Taylor (1991) was considered for the numerical analysis verification. Fig. 7 shows the Taylor model used for numerical simulation. Figs. 8 and 9 compare the numerical and experimental results. The data are for the wind pressure coefficients of the roof, for Re = 3.1 105. Wind blowing normal to the model decreases in velocity when it
Having obtained fairly good agreement between the numerical results from the software under consideration with the numerical or experimental data of other investigators (Hadadvand et al., 2008; Taylor, 1991; Faghih and Bahadori, 2007), it was decided to employ the software for an actual domed roof. To obtain the wind pressure coefficients over an actual dome, a simple 3-D model of a domed roof geometry was generated by employing its picture. In this investigation, a 1/10 scale model of the dome of the School of Theology located in Yazd, Iran, was considered. Two cross sections of this dome are shown in Fig. 10. In this research, the air flow velocity and the wind pressure distributions around and inside this 3-D domed roof were studied too, assuming the presence of 12 openings in the walls, and a hole on top of the dome. Fig. 11 shows the geometrical model of the domed roof employed in this investigation. The presence of 12 openings in the cylindrical wall, and a hole on top of the dome along with their dimensions are shown in this figure. In the next step, meshed area of the solution zone was prepared. In this simulation, optimized cell dimensions near domed roof and the wall were defined to have optimized CPU time by means of y + parameter (Pope, 2000). The mesh size near the roof and the wall was decreased step by step till y + of all
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Fig. 10. A 3-D model of the domed roof of the School of Theology considered in this study.
Fig. 12. A slice of the three-dimensional meshed area for the domed roof building model, with all the windows and the hole on top being open.
Fig. 11. The model of the dome employed in the present study.
nodes on the roof and wall were between 30 and 60. Tetragonal cells of 20, 12, 6 and 3 mm in dimension were generated near the wall and the roof, and finally 3 mm cell size was selected in this investigation. Fig. 12 shows a slice of the three dimensional meshed areas for when all windows and the hole on the top are open. Fig. 13 is similar to Fig. 12, for when all the openings are closed. Dimension of the solution domain, as well as the boundary conditions, are shown in Fig. 14 and Table 1. Only half of the model was used for simulation because of symmetry. Therefore, the boundary condition of all lateral surfaces is symmetrical. Boundary conditions of ground, roof and wall of the building are considered as WALL. No slip assumption used for wall shear condition. The roughness height was 0, and roughness constant was 0.5 for the wall boundary condition. Outlet boundary condition was outflow. For inlet surface, the wind velocity profile near the ground, used in the
Fig. 13. A slice of the three-dimensional meshed area for the domed roof building model with all the windows and the hole on top being closed.
simulation, could be expressed by: a Vh h ¼ VH H
ð3Þ
where Vh is the wind velocity at elevation h, VH the wind velocity at height H, and ‘a’ a constant. Above the height H there is a
ARTICLE IN PRESS A.K. Faghih, M.N. Bahadori / J. Wind Eng. Ind. Aerodyn. 98 (2010) 161–168
165
Fig. 14. Dimensions of the solution domain, and the boundary conditions.
Table 1 Dimensions of the solution domain, in mm. 1800 4500 1800 2550
700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
Fig. 16. A photograph of the model tested in a boundary-layer wind tunnel.
0 6. 0 7. 0 8. 0 9. 0 10 .0 11 .0 12 .0 13 .0 14 .0 15 .0 16 .0
0
5.
0
4.
0
3.
2.
1.
0.
0
The simulation was conducted under three conditions, as described below. 0
Elevation, h (mm)
X1 X2 Y Z
V (m/s) Fig. 15. Air flow profile at the inlet.
uniform wind flow. For small towns, it is recommended that H= 400 m and a =0.28 (Penwarden and Wise, 1975). The desired wind velocity profile is therefore given by: 0:28 Vh h ¼ V400 400
ð4Þ
In this simulation, V400 =48.6 m/s were assumed. Fig. 15 shows the wind profile at the inlet. The height of domed model is 0.6 m (as it is shown in Fig. 11) which is 1/10 scale model of the actual dome. The air flow velocity on top of the roof (6 m) is 15 m/s (Re =5.8 105) according to Eq. 4. Turbulent intensity was 0.13% and turbulent viscosity ratio was 10 for the inlet boundary condition. The prepared meshed areas with the specified boundary conditions were the input data for the numerical simulation.
(A) All openings, including the hole on top of the dome and the windows are closed. (B) All openings, including the hole on top of the dome and the windows are open, and the middle of one of the windows is directly facing the wind. (C) All openings, including the hole on top of the dome and windows are open, but the model is turned by 151, so that the line between the two adjacent windows is facing the wind.
4. Results The most important result of this study was to obtain the air pressure distribution on the domed roof, and inside the building. They will be used to calculate convection heat transfer coefficients over and beneath the roof, and also the natural air flow in the building. For verification of the results of this study, it was decided to compare them with the experimental data, obtained by testing of the model of the domed roof in a boundary-layer wind tunnel (Faghih and Bahadori, 2009a). Figs. 16 and 17 show the model. Fig. 17 shows the longitudes and latitudes considered on the
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domed roof model in order to identify the pressure tabs. The pressure tabs are at the intersections of the latitudes and longitudes as shown in this figure. The wind pressure coefficient Cp at various points on the dome was determined from the following equation: P ¼ Cp 12rV 2
ð5Þ
1.5 1
Numerical Experimental
0.5
Cp
0 -0.5
0
30
60
90
120
150
180
-1 -1.5 -2 Fig. 17. The model of the dome with the longitudes and latitudes considered on it. The pressure tabs are installed at the intersection of the longitudes and latitudes.
-2.5
Fig. 20. Numerical results of Cp along the longitudes 5 and 9 for condition A in comparison with the experimental results.
1.5 Experimental
0.5
-0.5
1
Numerical
0.5
0
30
60
90
120
150
180
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
Experimental
0 Cp
Cp
0
1.5
Numerical
1
0
30
60
90
120
150
180
-2
-2.5
Fig. 18. Numerical results of Cp along the longitudes 1 and 13 for condition A in comparison with the experimental results.
Fig. 21. Numerical results of Cp along the longitude 7 for condition A in comparison with the experimental results.
1.5
1
1
Numerical
-0.5
Experimental 0
0
30
60
90
120
150
180
-1
Cp
Cp
0
Numerical
0.5
Experimental
0.5
0
30
60
90
120
150
180
-0.5 -1
-1.5 -1.5
-2 -2.5
Fig. 19. Numerical results of Cp along the longitudes 3 and 11 for condition A in comparison with the experimental results.
-2
Fig. 22. Numerical results of Cp along the longitudes 1 and 13 for condition B in comparison with the experimental results.
ARTICLE IN PRESS A.K. Faghih, M.N. Bahadori / J. Wind Eng. Ind. Aerodyn. 98 (2010) 161–168
The velocity in this equation was 15 m/s, which was measured at the height of the dome, which was 0.6 m. Figs. 18–21 show the values of Cp obtained at various points along the longitudes on the dome, when all openings in the dome are closed (condition A). The angle phi (j) in these figures shows the position of the pressure tabs on each longitude, which is 0 for the windward side and 180 for the leeward side. On the dome apex, j is equal to 90. These figures show that the maximum value of Cp is for point 1f (see Fig. 18), and it is about 1, as obtained from the experimental investigation, and 0.75, as obtained in this analysis. The minimum value is at point a, and is 2.3, obtained experimentally, and 2.1 obtained numerically,
when all openings are closed. Obviously, because the maximum speed occurs at point a, on top of the dome, therefore the minimum pressure occurs at this point. Neither the experimental, nor the numerical results are exact; so a difference between these results can be expected. Nevertheless, because of separation taking place behind the dome
1
Cp
Cp
Numerical
0.5
Experimental 0
30
60
90
120
150
180
90
120
150
180
-1
Fig. 26. Numerical results of Cp along the longitudes 3 and 13 for condition C in comparison with the experimental results.
-2
1
Fig. 23. Numerical results of Cp along the longitudes 3 and 11 for condition B in comparison with the experimental results.
0 Numerical
0.5
Cp
0 30
60
90
120
150
Experimental 0
30
60
90
120
150
180
-0.5
Experimental 0
Numerical
0.5
1
Cp
60
-2.5
-1.5
180
-1 -1.5
-0.5
-2
-1
-2.5
-1.5 -2
Fig. 27. Numerical results of Cp along the longitudes 5 and 11 for condition C in comparison with the experimental results.
Fig. 24. Numerical results of Cp along the longitudes 5 and 9 for condition B in comparison with the experimental results.
1 Numerical
0.5
1 Numerical
0.5
Cp
30
-2
-1
0
Experimental
Experimental 0
30
60
90
120
150
180
0
30
60
90
120
150
180
Cp
-0.5 -1
-1
-1.5
-1.5
-2
-2
0
-1.5
-0.5
-0.5
Experimental
-0.5
1
0
Numerical
0.5 0
0
167
Fig. 25. Numerical results of Cp along the longitude 7 for condition B in comparison with the experimental results.
-2.5
Fig. 28. Numerical results of Cp along the longitudes 7 and 9 for condition C in comparison with the experimental results.
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(j 490), so a difference between the two sets of data can be expected. Taylor (1991) reported an amount of Cp of 0.75 for point 1f and 1.35 for point a, when Re =3.2 105. Separation occurs behind the roof because of high Reynolds number. So a difference between the numerical and the experimental results in this area seems to be acceptable. As can be seen from the following figures, the amount of Cp obtained from the numerical simulation is greater than those of the experimental data, except for front of the dome. The minimum difference between the two sets of data occurs on the longitude 7. Figs. 22–25 show the values of Cp obtained at various points along the longitudes on the dome, when all openings in the dome are open (condition B). In this case, the numerical results show that the wind pressure coefficient at the opening a, on top of the dome, increases from 2.1 to 1. However, this is not the minimum value of Cp on the dome in this case. This is due to the fact that there is a flow of air between the open windows and this hole. The minimum Cp is around 1.9, which occurs along the longitude 7. The maximum Cp has been decreased slightly, and it is less than 1 in the same position (1f), in comparison with the condition A. The largest difference between the experimental and the numerical results was obtained behind the model. This was due to a separation taking place there. Figs. 26–28 show the values of Cp obtained at various points along the longitudes on the dome under condition C, or when the model is turned by 151, so that the longitude running between two adjacent windows (shown by number 2 in Fig. 17) is facing the wind in the wind tunnel. In this condition, the numerical results show that the pressure coefficient at the opening a, on top of the dome, decrease from 1 to 1.2 in comparison with the condition B. Similar to previous conditions, the greatest difference was obtained behind the model because of separation.
5. Conclusion Wind pressure coefficients were determined numerically at various points on a domed roof model. The model included 12 windows at the collar of the dome and a hole on its apex. It was found that when the windows and the hole at the apex of the dome are all closed we obtain a value of 2.1, for Cp at the apex. When they are all open, this value increases to about 1. Comparing the results of this investigation with those of the experiment carried by the authors, one can find a good agreement between these data. Behind the dome, right after the apex, air separation occurs, so the maximum error in all figures can be found around this area. The numerical evaluation of the air flow pattern around domed roof buildings is the first step for the thermal performance analysis of such buildings. In that analysis, convection heat transfer coefficients will be determined for both outside and
inside areas of the dome. With solar radiation determined for the domed building (Faghih and Bahadori, 2009b), one can estimate the total heat transferred through the dome, and compare it with that of a flat roof of similar area.
Acknowledgement The authors wish to thank the Iranian National Science Foundation (INSF) for financially supporting this research. References Bahadori, M.N., 1978. Passive cooling systems in Iranian architecture. Scientific American 238, 144–154. Blessmann, J., 1971. Pressure on domes with several wind profiles. Wind Effects on Building and Structures, 317–326. Cheung, J.C.K., 1983. Effects of turbulence on the aerodynamics and response of a circular structure in wind flow. Ph.D. Thesis. Monash University. Cheung, J.C.K., Melbourne, W.H., 1983. Turbulence effects on some aerodynamic effects of circular cylinder at supercritical Reynolds numbers. Journal of Wind Engineering and Industrial Aerodynamics 14, 399–410. Faghih, A.K., Bahadori, M.N., 2007. Three dimensional numerical simulation of air flow over domed roofs. International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece. Faghih, A.K., Bahadori, M.N., 2009a. Experimental investigation of air flow over domed roofs. Iranian Journal of Science and Technology; Transaction B: Engineering 33 (B3), 207–216. Faghih, A.K., Bahadori, M.N., 2009b. Solar radiation on domed roofs. Energy and Buildings 41, 1238–1245. Franchini, S., Pindado, S., Mesegure, J., Sanz-Andres, A., 2005. A parametric, experimental analysis of conical vortices on curved roofs of low-rise buildings. Journal of Wind Engineering and Industrial Aerodynamics 93, 639–650. Hadadvand, M., Yaghoubi, M., Emdad, H., 2008. Thermal analysis of vaulted roofs. Energy and Building 40, 265–275. Newman, B.G., Ganguli, U., Shrivasatava, S.C., 1984. Flow over spherical inflated building. Journal of Wind Engineering and Industrial Aerodynamics 17, 305–327. Ogawa, T., Suzuki, T., Fukuoka, Y., 1993. Large eddy simulation of wind flow around dome structures by the finite element method. Journal of Wind Engineering and Industrial Aerodynamics 46, 47, 461–470. Penwarden, A.D., Wise, A.F.E., 1975. Wind Environment around Buildings. Bldg. Res. Estab., London. Pope, S.B., 2000. Turbulent Flows. Cambridge University Press, UK. Sabzevari, A., Yaghoubi, M., 1992. Air flow behavior in and around domed roof buildings. Wind Engineering 16, 27–34. Savory, E., Toy, N., 1986. Hemispheres and hemispherical cylinders in turbulent boundary layers. Journal of Wind Engineering and Industrial Aerodynamics. 23, 345–364. Serpoushan, S., Yaghoubi, M., 2002. Solar energy calculation on 3D surfaces. Iranian Journal of Energy 13, 3–21 (in Persian). Taniguchi, S., Sakamoto, H., Kiya, M., Arie, M., 1982. Time-averaged aerodynamic forces acting on a hemisphere immersed in a turbulent boundary. Journal of Wind Engineering and Industrial Aerodynamics 9, 257–273. Taylor, T.J., 1991. Wind pressures on a hemispherical dome. Journal of Wind Engineering and Industrial Aerodynamics 40, 199–213. Toy, N., Moss, W.D., Savory, E., 1983. Wind tunnel studies on a dome in turbulent boundary layers. Journal of Wind Engineering and Industrial Aerodynamics 11, 201–212. Tsugawa, T., Hongo, T., Suzuki, M., 1992. Experimental study of wind pressure and wind force characteristics on dome shaped openable roofs. Journal of Wind Engineering and Industrial Aerodynamics 41–44, 1509–1510. Velayati, E., Yaghoubi, M., 2004. Analysis of wind flow around various domed-type roofs. IMEC, Kuwait. Yaghoubi, M., 1991. Air flow pattern around domed roof buildings. Renewable Energy 1 (3/4), 345.
Contents lists available at ScienceDirect
Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Three dimensional numerical investigation of air flow over domed roofs Ahmadreza K. Faghih, Mehdi N. Bahadori School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e in fo
abstract
Article history: Received 1 May 2008 Received in revised form 12 October 2009 Accepted 16 October 2009 Available online 10 November 2009
Domed roofs have been used in Iran and many other countries to cover large buildings such as mosques, shrines, churches, schools, etc. However their favorable thermal performance made them to be employed in other buildings such as bazaars, or market places, in Iran. The aim of this study was to determine the air pressure distribution over domed roofs, employing a numerical method. In this investigation, a three-dimensional model and a laminar inlet air flow were considered. The k-e RNG method was employed for the turbulent flow simulation method. Simulation was run under three conditions of windows and a hole on top of the dome being open, or closed. The results were compared with the results obtained by an experimental investigation of the same domed-roof model. The results of this research can be employed to determine the heat transfer coefficient of wind blowing on domed roofs and the passive cooling effect of such structures. & 2009 Elsevier Ltd. All rights reserved.
Keywords: Domed roof Numerical solution Experimental investigation Wind pressure distribution
1. Introduction Domed roofs have traditionally been employed to cover buildings with large areas. These roofs have played an important role in Iranian architecture, and have had a great effect on the reduction of the buildings’ cooling loads. Preliminary research shows that the solar energy received by a domed roof is roughly equal to that of the flat roof of the same base area (Serpoushan and Yaghoubi, 2002). The solar energy absorbed causes the roof temperature to increase in comparison with the ambient air. With wind flowing over a dome, some of the heat is removed from the roof through convection, and the rest goes through the roof by conduction and can be transferred to the inside air by convection, and to the surrounding surfaces of the occupied space by radiation. The geometrical configuration of these domed roofs causes the wind velocity to increase over them, resulting in an increase in the convection heat transfer coefficient. Also, the heat transfer from these roofs is accentuated by the fact that the area of a domed configuration is greater than a flat one. Passive cooling can be achieved by inserting a hole on top of the dome. In the presence of this hole, the negative pressure over it makes an airflow emanating from the building’s openings towards it. This airflow decreases the inside roof temperature, resulting in a lower heat transfer by convection and radiation. Fig. 1 shows a schematic pattern of airflow in a building with a domed roof (Bahadori, 1978). In addition to large buildings, domed roofs have been used in Iran to cover large cisterns. In the cistern shown in Fig. 2, the pressure difference between the air entering the space above the Corresponding author. Tel.: + 98 21 66 16 55 08.
E-mail address: [email protected] (M.N. Bahadori). 0167-6105/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2009.10.012
water level from the wind towers and the air leaving from the top of the dome causes a natural airflow over the water surface. This process causes evaporation of water and its cooling. Air flow pattern on domed roof building has been investigated by means of numerical and experimental methods. Ogawa et al. (1993) developed a two-dimensional finite element analysis for turbulent flow over cylindrical domed roofs. Velayati and Yaghoubi (2004) and Hadadvand et al. (2008) simulated air flow over cylindrical domed roofs, assuming two-dimensional flow, and using control volume method. Blessmann (1971), Taniguchi et al. (1982), Cheung (1983), Cheung and Melbourne (1983), Toy et al. (1983), Newman et al. (1984), Savory and Toy (1986), Taylor (1991), Yaghoubi (1991), Sabzevari and Yaghoubi (1992), Tsugawa et al. (1992), Franchini et al. (2005), and Faghih and Bahadori (2009a) investigated air flow over domed roof buildings experimentally. The purpose of this investigation was to determine the wind pressure coefficient over a domed roof. This information can be used for the thermal performance evaluation of domed roofs. In this research the air pressure distribution over a domed roof model was studied, considering the presence of windows in the walls and a hole on top of the dome. A boundary layer air flow was considered. There are many famous buildings in the world with domed roofs. Figs. 3–5 show a few of such buildings. In this investigation, the dome located in Yazd, Iran, was considered.
2. Numerical analysis of the problem A commercially-available software was employed in this numerical investigation. As compared with the standard methods
ARTICLE IN PRESS 162
A.K. Faghih, M.N. Bahadori / J. Wind Eng. Ind. Aerodyn. 98 (2010) 161–168
Nomenclature X, Y, Z t h, H Vh VH
coordinates the height of building height wind velocity at height h wind velocity at height H
of analysis, the RNG k-e model for turbulence simulation was adopted in this study, due to its higher accuracy. First order upwind method was used to make the related equations discrete. The solution method was a control volume, using incompressible model. Pressure and velocity dependency method was SIMPLE and near wall treatment was non-equilibrium wall function (Pope, 2000). To make sure of the accuracy associated with employing this software, it was decided to use it in conjunction with a structure for which experimental results were known, or other investigators had already obtained valid data. It was first used to obtain the wind pressure coefficients over wind towers for which experimental data were available. There was a fairly good agreement between the numerical and experimental results (Faghih and Bahadori, 2007).
y, b, j a V P Cp
r
angles constant wind velocity pressure pressure coefficient density
In the second step of the numerical study, it was applied to the domed roof models. To compare the results with those of Hadadvand et al. (2008), the length of the air circulation behind the building shown in Fig. 6 was obtained to be equal to 6.6, with Hadadvand simulation, and equivalent of 6.8 in the current analysis, for Re = 5 105. In this figure, X and Y are dimensionless as defined below, and t is the height of building’s wall which is equal to 1 in this simulation X ¼ x=t
ð1Þ
Y ¼ y=t
ð2Þ
The pressure difference between the middle of the front wall and the top of the domed roof was 18, in this simulation, and it was 16.01, as was reported by Hadadvand et al. (2008).
Fig. 1. Air flow in a building with domed roof with an opening on its cap (Bahadori, 1978).
Fig. 3. Domed roof of Taj Mahal in Agra, India.
Fig. 2. Air flow in a cistern equipped with a domed roof and several pairs of wind towers (Bahadori, 1978).
Fig. 4. Domed roof of St Peter’s Church in Rome, Italy.
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163
1 Numerical Experimental
Cp
0.5 0 -0.5
0
30
60
90
120
150
180
-1 -1.5
(Degrees)
Fig. 8. Numerical results of Cp along the b =0 in comparison with Taylor’s experimental results (Taylor, 1991).
1 Numerical Experimental
0.5 Cp
Fig. 5. Domed roof of Sheikh Lotfollah Mosque in Isfahan, Iran.
0
0
30
60
90
-0.5 -1 -1.5
(Degrees)
Fig. 9. Numerical results of Cp along the b = 90 in comparison with Taylor’s experimental results (Taylor, 1991).
Fig. 6. The length of the circulating area obtained in this analysis, employing the model of Hadadvand et al. (2008).
reaches the model. A high pressure zone is created on the windward side, pushing the air around the sides and up over the top of the dome. A portion of the air flows downward, and around the model, creating an eddy at the leeward side. The turbulent flow produced in this area is considerable. As the result, we can expect an uncertainty and a difference between the experimental and the numerical values of Cp obtained for this region. It should be mentioned that neither the experimental, nor the numerical results give the exact amounts of Cp.
3. Numerical analysis of a domed roof
Fig. 7. The model of the dome employed by Taylor (1991).
In the third step, experimental model by Taylor (1991) was considered for the numerical analysis verification. Fig. 7 shows the Taylor model used for numerical simulation. Figs. 8 and 9 compare the numerical and experimental results. The data are for the wind pressure coefficients of the roof, for Re = 3.1 105. Wind blowing normal to the model decreases in velocity when it
Having obtained fairly good agreement between the numerical results from the software under consideration with the numerical or experimental data of other investigators (Hadadvand et al., 2008; Taylor, 1991; Faghih and Bahadori, 2007), it was decided to employ the software for an actual domed roof. To obtain the wind pressure coefficients over an actual dome, a simple 3-D model of a domed roof geometry was generated by employing its picture. In this investigation, a 1/10 scale model of the dome of the School of Theology located in Yazd, Iran, was considered. Two cross sections of this dome are shown in Fig. 10. In this research, the air flow velocity and the wind pressure distributions around and inside this 3-D domed roof were studied too, assuming the presence of 12 openings in the walls, and a hole on top of the dome. Fig. 11 shows the geometrical model of the domed roof employed in this investigation. The presence of 12 openings in the cylindrical wall, and a hole on top of the dome along with their dimensions are shown in this figure. In the next step, meshed area of the solution zone was prepared. In this simulation, optimized cell dimensions near domed roof and the wall were defined to have optimized CPU time by means of y + parameter (Pope, 2000). The mesh size near the roof and the wall was decreased step by step till y + of all
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Fig. 10. A 3-D model of the domed roof of the School of Theology considered in this study.
Fig. 12. A slice of the three-dimensional meshed area for the domed roof building model, with all the windows and the hole on top being open.
Fig. 11. The model of the dome employed in the present study.
nodes on the roof and wall were between 30 and 60. Tetragonal cells of 20, 12, 6 and 3 mm in dimension were generated near the wall and the roof, and finally 3 mm cell size was selected in this investigation. Fig. 12 shows a slice of the three dimensional meshed areas for when all windows and the hole on the top are open. Fig. 13 is similar to Fig. 12, for when all the openings are closed. Dimension of the solution domain, as well as the boundary conditions, are shown in Fig. 14 and Table 1. Only half of the model was used for simulation because of symmetry. Therefore, the boundary condition of all lateral surfaces is symmetrical. Boundary conditions of ground, roof and wall of the building are considered as WALL. No slip assumption used for wall shear condition. The roughness height was 0, and roughness constant was 0.5 for the wall boundary condition. Outlet boundary condition was outflow. For inlet surface, the wind velocity profile near the ground, used in the
Fig. 13. A slice of the three-dimensional meshed area for the domed roof building model with all the windows and the hole on top being closed.
simulation, could be expressed by: a Vh h ¼ VH H
ð3Þ
where Vh is the wind velocity at elevation h, VH the wind velocity at height H, and ‘a’ a constant. Above the height H there is a
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165
Fig. 14. Dimensions of the solution domain, and the boundary conditions.
Table 1 Dimensions of the solution domain, in mm. 1800 4500 1800 2550
700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
Fig. 16. A photograph of the model tested in a boundary-layer wind tunnel.
0 6. 0 7. 0 8. 0 9. 0 10 .0 11 .0 12 .0 13 .0 14 .0 15 .0 16 .0
0
5.
0
4.
0
3.
2.
1.
0.
0
The simulation was conducted under three conditions, as described below. 0
Elevation, h (mm)
X1 X2 Y Z
V (m/s) Fig. 15. Air flow profile at the inlet.
uniform wind flow. For small towns, it is recommended that H= 400 m and a =0.28 (Penwarden and Wise, 1975). The desired wind velocity profile is therefore given by: 0:28 Vh h ¼ V400 400
ð4Þ
In this simulation, V400 =48.6 m/s were assumed. Fig. 15 shows the wind profile at the inlet. The height of domed model is 0.6 m (as it is shown in Fig. 11) which is 1/10 scale model of the actual dome. The air flow velocity on top of the roof (6 m) is 15 m/s (Re =5.8 105) according to Eq. 4. Turbulent intensity was 0.13% and turbulent viscosity ratio was 10 for the inlet boundary condition. The prepared meshed areas with the specified boundary conditions were the input data for the numerical simulation.
(A) All openings, including the hole on top of the dome and the windows are closed. (B) All openings, including the hole on top of the dome and the windows are open, and the middle of one of the windows is directly facing the wind. (C) All openings, including the hole on top of the dome and windows are open, but the model is turned by 151, so that the line between the two adjacent windows is facing the wind.
4. Results The most important result of this study was to obtain the air pressure distribution on the domed roof, and inside the building. They will be used to calculate convection heat transfer coefficients over and beneath the roof, and also the natural air flow in the building. For verification of the results of this study, it was decided to compare them with the experimental data, obtained by testing of the model of the domed roof in a boundary-layer wind tunnel (Faghih and Bahadori, 2009a). Figs. 16 and 17 show the model. Fig. 17 shows the longitudes and latitudes considered on the
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domed roof model in order to identify the pressure tabs. The pressure tabs are at the intersections of the latitudes and longitudes as shown in this figure. The wind pressure coefficient Cp at various points on the dome was determined from the following equation: P ¼ Cp 12rV 2
ð5Þ
1.5 1
Numerical Experimental
0.5
Cp
0 -0.5
0
30
60
90
120
150
180
-1 -1.5 -2 Fig. 17. The model of the dome with the longitudes and latitudes considered on it. The pressure tabs are installed at the intersection of the longitudes and latitudes.
-2.5
Fig. 20. Numerical results of Cp along the longitudes 5 and 9 for condition A in comparison with the experimental results.
1.5 Experimental
0.5
-0.5
1
Numerical
0.5
0
30
60
90
120
150
180
-1
-0.5
-1.5
-1
-2
-1.5
-2.5
Experimental
0 Cp
Cp
0
1.5
Numerical
1
0
30
60
90
120
150
180
-2
-2.5
Fig. 18. Numerical results of Cp along the longitudes 1 and 13 for condition A in comparison with the experimental results.
Fig. 21. Numerical results of Cp along the longitude 7 for condition A in comparison with the experimental results.
1.5
1
1
Numerical
-0.5
Experimental 0
0
30
60
90
120
150
180
-1
Cp
Cp
0
Numerical
0.5
Experimental
0.5
0
30
60
90
120
150
180
-0.5 -1
-1.5 -1.5
-2 -2.5
Fig. 19. Numerical results of Cp along the longitudes 3 and 11 for condition A in comparison with the experimental results.
-2
Fig. 22. Numerical results of Cp along the longitudes 1 and 13 for condition B in comparison with the experimental results.
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The velocity in this equation was 15 m/s, which was measured at the height of the dome, which was 0.6 m. Figs. 18–21 show the values of Cp obtained at various points along the longitudes on the dome, when all openings in the dome are closed (condition A). The angle phi (j) in these figures shows the position of the pressure tabs on each longitude, which is 0 for the windward side and 180 for the leeward side. On the dome apex, j is equal to 90. These figures show that the maximum value of Cp is for point 1f (see Fig. 18), and it is about 1, as obtained from the experimental investigation, and 0.75, as obtained in this analysis. The minimum value is at point a, and is 2.3, obtained experimentally, and 2.1 obtained numerically,
when all openings are closed. Obviously, because the maximum speed occurs at point a, on top of the dome, therefore the minimum pressure occurs at this point. Neither the experimental, nor the numerical results are exact; so a difference between these results can be expected. Nevertheless, because of separation taking place behind the dome
1
Cp
Cp
Numerical
0.5
Experimental 0
30
60
90
120
150
180
90
120
150
180
-1
Fig. 26. Numerical results of Cp along the longitudes 3 and 13 for condition C in comparison with the experimental results.
-2
1
Fig. 23. Numerical results of Cp along the longitudes 3 and 11 for condition B in comparison with the experimental results.
0 Numerical
0.5
Cp
0 30
60
90
120
150
Experimental 0
30
60
90
120
150
180
-0.5
Experimental 0
Numerical
0.5
1
Cp
60
-2.5
-1.5
180
-1 -1.5
-0.5
-2
-1
-2.5
-1.5 -2
Fig. 27. Numerical results of Cp along the longitudes 5 and 11 for condition C in comparison with the experimental results.
Fig. 24. Numerical results of Cp along the longitudes 5 and 9 for condition B in comparison with the experimental results.
1 Numerical
0.5
1 Numerical
0.5
Cp
30
-2
-1
0
Experimental
Experimental 0
30
60
90
120
150
180
0
30
60
90
120
150
180
Cp
-0.5 -1
-1
-1.5
-1.5
-2
-2
0
-1.5
-0.5
-0.5
Experimental
-0.5
1
0
Numerical
0.5 0
0
167
Fig. 25. Numerical results of Cp along the longitude 7 for condition B in comparison with the experimental results.
-2.5
Fig. 28. Numerical results of Cp along the longitudes 7 and 9 for condition C in comparison with the experimental results.
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(j 490), so a difference between the two sets of data can be expected. Taylor (1991) reported an amount of Cp of 0.75 for point 1f and 1.35 for point a, when Re =3.2 105. Separation occurs behind the roof because of high Reynolds number. So a difference between the numerical and the experimental results in this area seems to be acceptable. As can be seen from the following figures, the amount of Cp obtained from the numerical simulation is greater than those of the experimental data, except for front of the dome. The minimum difference between the two sets of data occurs on the longitude 7. Figs. 22–25 show the values of Cp obtained at various points along the longitudes on the dome, when all openings in the dome are open (condition B). In this case, the numerical results show that the wind pressure coefficient at the opening a, on top of the dome, increases from 2.1 to 1. However, this is not the minimum value of Cp on the dome in this case. This is due to the fact that there is a flow of air between the open windows and this hole. The minimum Cp is around 1.9, which occurs along the longitude 7. The maximum Cp has been decreased slightly, and it is less than 1 in the same position (1f), in comparison with the condition A. The largest difference between the experimental and the numerical results was obtained behind the model. This was due to a separation taking place there. Figs. 26–28 show the values of Cp obtained at various points along the longitudes on the dome under condition C, or when the model is turned by 151, so that the longitude running between two adjacent windows (shown by number 2 in Fig. 17) is facing the wind in the wind tunnel. In this condition, the numerical results show that the pressure coefficient at the opening a, on top of the dome, decrease from 1 to 1.2 in comparison with the condition B. Similar to previous conditions, the greatest difference was obtained behind the model because of separation.
5. Conclusion Wind pressure coefficients were determined numerically at various points on a domed roof model. The model included 12 windows at the collar of the dome and a hole on its apex. It was found that when the windows and the hole at the apex of the dome are all closed we obtain a value of 2.1, for Cp at the apex. When they are all open, this value increases to about 1. Comparing the results of this investigation with those of the experiment carried by the authors, one can find a good agreement between these data. Behind the dome, right after the apex, air separation occurs, so the maximum error in all figures can be found around this area. The numerical evaluation of the air flow pattern around domed roof buildings is the first step for the thermal performance analysis of such buildings. In that analysis, convection heat transfer coefficients will be determined for both outside and
inside areas of the dome. With solar radiation determined for the domed building (Faghih and Bahadori, 2009b), one can estimate the total heat transferred through the dome, and compare it with that of a flat roof of similar area.
Acknowledgement The authors wish to thank the Iranian National Science Foundation (INSF) for financially supporting this research. References Bahadori, M.N., 1978. Passive cooling systems in Iranian architecture. Scientific American 238, 144–154. Blessmann, J., 1971. Pressure on domes with several wind profiles. Wind Effects on Building and Structures, 317–326. Cheung, J.C.K., 1983. Effects of turbulence on the aerodynamics and response of a circular structure in wind flow. Ph.D. Thesis. Monash University. Cheung, J.C.K., Melbourne, W.H., 1983. Turbulence effects on some aerodynamic effects of circular cylinder at supercritical Reynolds numbers. Journal of Wind Engineering and Industrial Aerodynamics 14, 399–410. Faghih, A.K., Bahadori, M.N., 2007. Three dimensional numerical simulation of air flow over domed roofs. International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece. Faghih, A.K., Bahadori, M.N., 2009a. Experimental investigation of air flow over domed roofs. Iranian Journal of Science and Technology; Transaction B: Engineering 33 (B3), 207–216. Faghih, A.K., Bahadori, M.N., 2009b. Solar radiation on domed roofs. Energy and Buildings 41, 1238–1245. Franchini, S., Pindado, S., Mesegure, J., Sanz-Andres, A., 2005. A parametric, experimental analysis of conical vortices on curved roofs of low-rise buildings. Journal of Wind Engineering and Industrial Aerodynamics 93, 639–650. Hadadvand, M., Yaghoubi, M., Emdad, H., 2008. Thermal analysis of vaulted roofs. Energy and Building 40, 265–275. Newman, B.G., Ganguli, U., Shrivasatava, S.C., 1984. Flow over spherical inflated building. Journal of Wind Engineering and Industrial Aerodynamics 17, 305–327. Ogawa, T., Suzuki, T., Fukuoka, Y., 1993. Large eddy simulation of wind flow around dome structures by the finite element method. Journal of Wind Engineering and Industrial Aerodynamics 46, 47, 461–470. Penwarden, A.D., Wise, A.F.E., 1975. Wind Environment around Buildings. Bldg. Res. Estab., London. Pope, S.B., 2000. Turbulent Flows. Cambridge University Press, UK. Sabzevari, A., Yaghoubi, M., 1992. Air flow behavior in and around domed roof buildings. Wind Engineering 16, 27–34. Savory, E., Toy, N., 1986. Hemispheres and hemispherical cylinders in turbulent boundary layers. Journal of Wind Engineering and Industrial Aerodynamics. 23, 345–364. Serpoushan, S., Yaghoubi, M., 2002. Solar energy calculation on 3D surfaces. Iranian Journal of Energy 13, 3–21 (in Persian). Taniguchi, S., Sakamoto, H., Kiya, M., Arie, M., 1982. Time-averaged aerodynamic forces acting on a hemisphere immersed in a turbulent boundary. Journal of Wind Engineering and Industrial Aerodynamics 9, 257–273. Taylor, T.J., 1991. Wind pressures on a hemispherical dome. Journal of Wind Engineering and Industrial Aerodynamics 40, 199–213. Toy, N., Moss, W.D., Savory, E., 1983. Wind tunnel studies on a dome in turbulent boundary layers. Journal of Wind Engineering and Industrial Aerodynamics 11, 201–212. Tsugawa, T., Hongo, T., Suzuki, M., 1992. Experimental study of wind pressure and wind force characteristics on dome shaped openable roofs. Journal of Wind Engineering and Industrial Aerodynamics 41–44, 1509–1510. Velayati, E., Yaghoubi, M., 2004. Analysis of wind flow around various domed-type roofs. IMEC, Kuwait. Yaghoubi, M., 1991. Air flow pattern around domed roof buildings. Renewable Energy 1 (3/4), 345.