- Email: [email protected]
Computational study of natural ventilation
Journal of Wind Engineering and Industrial Aerodynamics 82 (1999) 49} 68
Computational study of natural ventilation Samir S. Ayad Faculty of Engineering at Shoubra, Zagazig University, Cairo, Egypt Received 30 July 1997; received in revised form 1 September 1998; accepted 30 November 1998
Abstract The object of the present work is to use computational #uid dynamics (CFD) to study the ventilation properties for a room with di!erent opening con"gurations. The "nite volume method is used to solve the basic equations of mass and momentum conservation in the primitive form together with the two-equation turbulence model. The model is veri"ed by comparing the results for steady two-dimensional #ow around a long square cylinder immersed in the atmospheric boundary layer with experimental values. Internal #ows are then simulated in a single-room building with di!erent opening con"gurations. Six examples are considered for internal #ows. The results include mean velocity vectors, stream lines, and pressure distribution around the building as well as the mean velocity vectors, streamlines and turbulent eddy viscosity inside the room are considered. The placement of openings in relation to one another may enhance or reduce mean velocity at certain locations inside the room. The model can help in assigning comfortable locations for humans inside the room. For a given upstream wind speed the in-room mean velocity vectors are found to be sensitive to upstream wind direction while the e!ect of upstream turbulence level on in-room wind speed is shown to be negligible. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Natural ventilation; CFD; Finite volume method
Nomenclature C , C and Ck constants for two equation turbulence model C pressure coe$cient N E constant used in the logarithmic wall function k kinetic energy of turbulence ¸ dimension of the building or the room considered l characteristic length scale P pressure ; mean wind speed in the i direction G u #uctuating wind speed in direction i G uH shear velocity 0167-6105/99/$ } see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 2 1 0 - 4
50
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Greek letters e k 2 k l o p I p C
rate of dissipation of turbulence energy turbulent eddy viscosity e!ective viscosity kinematic viscosity density Prandtl number for kinetic energy of turbulence Prandtl number for rate of dissipation
1. Introduction With the increase of energy costs; passive cooling of houses using natural wind is coming back as an attractive alternative for mechanical air conditioning. Wind has been regarded as the most popular passive cooling resource against hot and humid climates in summer. Good ventilation has positive e!ects on occupants' comfort and indoor-air quality. The alteration of wind #ow by the designer can result in a climatically comfortable residence. The human comfort can be predicted on the basis of internal air speed. The ventilation e!ectiveness can be related to spatial distribution of fresh air necessary for minimum health requirements. Tsutsumi et al. [1] used full-scale measurements and numerical simulation to evaluate thermal comfort of common houses in Japan. Wind ventilated houses were shown to be in the comfort zone while unventilated houses were uncomfortable. Movements of smoke during "re development can also be of extreme importance in relation to building evacuation routes and times. The con"gurations of building rooms and especially the location of inlet and outlet openings in relation to dominant wind direction at the site, have major e!ects on the ventilation rates in buildings. Locating Inlet openings near high-pressure surfaces of a building and exit openings at low-pressure ones produces higher #ow rates through windows. Accordingly, an understanding of air #ow around the building is necessary to design well-ventilated residences. External #ows around buildings are very complicated involving severe pressure gradients, streamline curvature, swirl, separation and reattachment together with the resulting e!ects of enhancing and suppression of turbulence. Several authors have examined time-averaged #ow "eld around buildings both experimentally and numerically. Castro and Robins [2] measured velocities near and pressures around surface mounted cubes in both uniform and shear turbulent #ows. They demonstrated major e!ects of upstream turbulence on the reattachment of separating shear layer on the top of the body. Baines [3] reported pressure measurements around a cube block in steady turbulent #ows with wind normal to one face of the block. Paterson and Apelt [4], Paterson [5], Murakami and Mochida [6] and Murakami et al. [7] all reported numerical models for steady #ow around building with di!erent degrees of complexity. Murakami and Kato, [8] and Baker and Kelso [9] both considered numerical models for in-room #ows.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
51
The use of wind tunnel models to study natural ventilation was evaluated by Smith [10] and more recently by Cermak et al. [11]. In order to achieve Reynolds number independent #ow around and inside blu! buildings and at the same time to avoid tunnel blockage, a large tunnel section is needed. In view of enormous costs and time required for "eld or wind tunnel studies, the present work is aimed to employ computational #uid dynamics to determine the distribution of time-averaged, steady, two-dimensional and turbulent in-room #ow "eld at the mid plane of openings. Although the e!ects of neighboring buildings can be signi"cant, only an isolated room is considered for the present work to test the basic natural ventilation rules as a!ected by relative opening location and di!erent upstream wind conditions. The two-equation turbulence model is used. Air speed, circulation zones and turbulent di!usion coe$cients are the parameters considered for the evaluation of natural ventilation.
2. Governing equations An understanding of air #ow around buildings with complete details on surface pressures is necessary to design well-ventilated buildings. Accordingly, in the present work two con"gurations are considered. The "rst deals with external #ow and the second concentrates on internal room #ow. Steady, turbulent and two-dimensional #ow around a building immersed in an atmospheric boundary layer is considered. Building aspect ratio equals 1 and the #ow domain extends from two building lengths upstream of building windward face to ten building lengths downstream of the building leeward face. The domain height is 4 times the building height. The #ow domain is shown in Fig. 1. The second con"guration considers the in-room #ow in the mid plane of the room at the openings level. Six examples with di!erent locations of openings are shown in Fig. 2. Since air movements are considered as the natural cooling resource, the computations are carried out for isothermal conditions.
Fig. 1. Con"guration 1 for boundary layer #ow around long square cylinder.
52
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 2. Con"guration II for in-room #ow model with six examples: (1) cross ventilation, (2) cross ventilation with larger exit opening, (3) cross ventilation with two exit openings, (4) ventilation with exit opening at adjacent walls, (5) ventilation with openings at the far ends of adjacent walls with normal wind, and (6) ventilation with openings at far ends of adjacent walls with 303 incidence wind.
Equations of mass and momentum conservation are given by *(o; ) G "0, (1) *X G *P * *; *(o; ; ) G H "! G!ou u , # k (2) G H *X *X *X *X G G H H where ; , i"1, 2 are the mean velocity components in the streamwise and normal G directions, respectively. u , i"1, 2 and 3 are turbulent #ow #uctuating components in G the x, y and z directions, respectively. k is the molecular viscosity and o is the #uid density. The Reynolds stress in Eq. (2) is modeled by the use of Boussinesq's turbulent viscosity, which is evaluated as a function of the turbulence kinetic energy k and its rate of dissipation e; [12]:
ok k "C , R I e
(3)
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
d uu k" GH G H, 2
53
(4)
*u *u G H. (5) *X *X H G k and e are obtained by solving the following transport equations simultaneously with the mean #ow equations: e"l
* * k *k (; k)" #G!oeC , (6) B *X p *X *X H H H H I * * k *e G e o (; e)" #C e !C o , (7) k k *X p *X *X H H H C H *; *; *; G G# H , G"k (8) R *X *X *X H H G k "k #k, (9) R where G is the production of turbulence energy due to work of the mean #ow on the turbulent Reynolds stress. k is the e!ective viscosity. The constants appearing in the above equations are given by o
C "1.44,
C "1.92,
C "0.09, I
p "1 and p "1.3. I C
(10)
2.1. Boundary conditions Undisturbed streamwise velocity is assumed to obey the () power-law variation with z for the "rst con"guration while uniform #ow is considered at inlet opening for the second con"guration: ;(z)"; (Z/2¸) for Z(2¸, ;(Z)"; for Z'2¸, k"0.0036;,
(11) (12)
e"C k /l, (13) I l is the characteristic length and is taken to be 0.2¸. At the upper boundary of con"guration I, all derivatives of dependent variables are assumed to vanish. Correcting the outlet velocity components strictly imposes the overall mass conservation through the #ow domain. Near the ground as well as at the inner or outer building surface constant, stress layers are assumed to exist and the wall function is used in order to avoid the need for large number of nodal points usually required for a region with large velocity gradients. At the "rst nodal point next to a wall the mean velocity, the shear stress,
54
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
turbulence production and rate of dissipation are respectively, given by
u yu o ;" H ln E H , s k
(14)
yu o q "so(C ) (k/ ln E H , U I k G"q
*; *l # #2k U *y *x
*; *l # , *x *y
C k e" I , s y
(15) (16) (17)
s"0.41, E"8.331. In the above equations y is the normal distance between the "rst nodal point and the wall. It is exchanged with x for windward and leeward faces of the building as well as for normal walls of in-room #ow. 3. Solution procedure The method of "nite volume integration of Patanker [13] is used on a rectangular Cartesian grid. Smaller grid size is used near the walls and the ground. A stretching factor of 1.1 is used. Control volumes of size 52;62 are used for the "rst con"guration, while 60;30 was used for the second con"guration half room. Fig. 3 shows an example of the grid employed for half room #ows with the "rst three examples of con"guration II. Following Peric et al. [14], the co-located variable arrangement is employed. All dependent variables are stored at the same location in the integration domain. The mass #uxes are interpolated from the dependent variables and stored at the control volume faces. A special interpolation procedure is used for the cell-face velocities to suppress oscillatory solutions, which might otherwise arise from the co-located storage. The QUICK scheme of Leonard [15] for space discretization is used to avoid the large numerical di!usion of the widely used upwind di!erence scheme. Predictor}corrector method is considered for obtaining the velocity components. The pressure distribution is obtained using SIMPLEC procedure of van Doormal [16] and the "nite-di!erence linear system is solved by the strongly implicit method of Stone [17]. 4. Results 4.1. Boundary layer yow around the long square cylinder The results of pressure contour, mean velocity vector plots and streams for the #ow around the long square cylinder are shown in Fig. 4. The model captures the
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
55
Fig. 3. An example of grid used for half-room #ows examples 1}3 of con"guration II.
recirculating zone downstream of the building, which extends about six building length downstream. The results show the circulation zones near the lower corner of upwind cylinder surface and at the upwind top corner. The values of pressure coe$cients are also compared with the experimental values of Castro and Robins [2]. Since their experiment was carried for a three-dimensional object, mid plane values are used for comparison with the present two-dimensional results in order to avoid the end e!ects on surface values of pressure. The present results have the same trend as the experimental surface pressure values. The pressure coe$cient is de"ned as (P!P ) . C" N 0.5(o; ) The pressure at the far-left top of the domain is taken as the reference pressure. Fig. 5 shows a favorable comparison between the present calculations and mid-plane experimental values. The trend of variations is generally close to the experimental one. The discrepancies at the top surface and leeward surfaces can be explained by the di!erence in the boundary layer thickness as well as the turbulence intensity of the approach #ow. Their results were measured for atmospheric boundaries layer thickness ten times the building height. Based on their measurements as the boundary layer thickness decreases the magnitude of negative pressure coe$cient at the mid-top of the building increases. It should be noted that the present calculations are carried out for boundary layer height that is twice the building height. The results of solid body surface pressure distribution are very important from the ventilation
56
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 4. Pressure contours, velocity vector and streams for #ow around long square cylinder.
point of view. They are used to locate the optimum locations of inlet and exit openings. The results show that the upwind vertical surface would be appropriate for inlet openings while top surface as well as the leeward surface opening serves as exit ones.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
57
Fig. 5. Comparison of present results with experimental values of surface pressure coe$cient around a long square cylinder.
This idea was employed and tested in a meteorological wind tunnel by Cermak et al. [11]. 4.2. In-room -ow examples Figs. 6}8 show the vector plots as well as streamlines for in-room #ows, for examples one to three of con"guration II. As given in Fig. 2, these examples have symmetric #ows around the room centerline of plan view. Accordingly half the room only is shown. The #ow in Fig. 6 presents cross ventilation with equal inlet and exit openings. It can be seen that only the area spanned by the cylindrical stream tube is actually ventilated. The idea of increasing exit area opening by Smith [10] is simulated in Fig. 7. The exit area is increased to 37.5% of wall area, which is 50% larger than the inlet opening. The plan of the ventilated zone seems to have larger area at exit and looks like a trapezoid. Air momentum transport seems to be carried mainly by convection and hardly by turbulent di!usion. This idea will be discussed later while looking at the e!ect of upstream turbulence. In order to enhance convection, example three is considered with two exit openings at the ends of leeward wall with a total area which equals 25% of wall area in order to increase the length of the streamtube. Fig. 8
58
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 6. Velocity vectors and streams for example 1 (cross ventilation with equal openings).
shows a considerable increase of velocity vector and a reduced area of the calm zone that does not bring fresh air. Fig. 9 shows the air #ow vectors and streamlines in a room of example four. The supply window is placed at the center of one room side and exhaust window is located at the end of the adjacent room side wall. The diagram shows two medium size circulation zones; one at each side of the main wind #ow path. Velocity vectors seem to have larger magnitudes especially, at locations within the circulation zone but away from their centers. Fig. 10 presents the velocity vector and streams of example "ve.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
59
Fig. 7. Velocity vectors and streams for example 2 (cross ventilation with larger exit openings).
Openings are located at the far ends of the adjacent walls. As shown in the "gure when one circulation zone increases the other diminishes. In Fig. 11 incident wind with 303 to normal is considered. Again two circulation zones are shown but the one close to exit opening has a smaller size. Fig. 12a and 12b shows contour plots for the magnitude of wind speed magnitude as a fraction of inlet opening speed. Large zone of speed less than 20% of inlet value is shown for examples 1 and 2. Such calm zones are decreased for example 3 with shifted openings of cross-ventilation. Considerable reduction of non-ventilated zones is shown for #ows of examples 4, 5 and 6. Depending
60
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 8. Velocity vectors and streams for example 3 (cross ventilation with shifted openings).
on the locations of humans inside the room and the dominant wind direction the designer should be able to locate ventilation openings. 4.2.1. Turbulence Eddy viscosity Fig. 13 shows contour plots for the turbulence eddy viscosity. Except for areas near inlet and exit openings and walls the eddy viscosity has very small values. Momentum transfer does not seem to alter the velocity vectors outside the stream tube. An increase of incoming kinetic energy of turbulence from 6% to 12% does not cause any
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 9. Velocity vectors and streams for example 4 (ventilation with openings at adjacent walls).
61
62
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 10. Velocity vectors and streams for example 5 (ventilation with openings at the far ends of the adjacent walls).
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 11. Velocity vector and streams for example 6 (Ventilation with thirty degrees incident wind).
63
64
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 12. Contour plots for the magnitude of in-room wind velocity. (a) Shaded areas have wind speed less than or equal to 20% of inlet wind speed for examples 1}3. (b) Shaded areas have wind speed less than or equal to 20% of inlet wind speed for examples 4 }6.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 12 (continued).
65
66
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 13. Contour plots for in-room turbulent Eddy viscosity.
considerable increase of velocity vectors outside the main stream tube. The e!ect of upstream turbulence and boundary layer thickness must not be underestimated. Although the present results of Fig. 13 show no e!ect on in-room eddy viscosity, upstream turbulence has been shown to strongly in#uence the external surface pressure thus a!ecting the upstream mean wind speed at inlet openings, and this provides a ventilation driving mechanism. Increased turbulence promotes re-attachment.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
67
The vortex formed at top windward corner causes an increase in velocity and a decrease in pressure. Further, the shear layer re-attachment e!ectively seals o! bubble from direct venting to free stream causing an increased magnitude of negative pressure there.
5. Conclusions (1) The model for #ow around a building captures the circulating bubbles upstream and downstream of the building, and the steady #ow pressure coe$cient has the same trend as the experimental ones. (2) The two-equation turbulence model is a useful tool for predicting in-room #ows. (3) Cross ventilation is useful for ventilating the areas passed by the stream tube between inlet and exit openings, but outside the stream tube recirculation zones with no fresh air dominate. The low turbulence level is not enough to enhance momentum transfer from the stream tube to the otherwise stand still air outside the tube. (4) Depending upon the locations of humans inside the room, the wind incidence angle can cause an increase in velocity magnitude and reduction of calm air zones inside the room. (5) For the same upstream wind speed, the incoming turbulence intensity does not have signi"cant e!ects on either mean velocity vector or on in room turbulent eddy coe$cient. It should be noticed that upstream turbulence has considerable e!ects on external #ow reattachment and surface pressure coe$cients, which will ultimately a!ect #ow through building openings. An extended explanation of e!ects of upstream turbulence and boundary layer thickness on surface pressure is given in Castro and Robins [2].
Acknowledgements The author would like to express his deep thanks and gratitude to J.E. Cermak, distinguished university professor at Colorado State University for his continuing support. His ideas and suggestions made this work possible.
References [1] J. Tsutsum, T. Katayama, A. Ishii, P. He, T. Hayashi, Investigation of wind e!ects on thermal comfort in a house, J. Wind Eng. Ind. Aerodyn. 60 (1996) 267}280. [2] I.P. Castro, A.G. Robins, The #ow around a surface mounted cube in uniform #ow and turbulent streams, J. Fluid Mech. 79 (1977) 307}335. [3] W.D. Baines, E!ects of velocity distribution on wind loads and #ow patterns on buildings, Wind E!ects on Build. Struct. 1 (1965) 198. [4] D.A. Paterson, C.J. Apelt, Simulation of #ow past a cube in a turbulent #ow, J. Wind Eng. Ind. Aerodyn. 35 (1990) 149}176.
68
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
[5] D.A. Paterson, Computation of wind #ows over three dimensional buildings, Ph.D. Thesis, University of Queensland, 1986. [6] S. Murakami, A. Mochida, Three dimensional numerical simulation of air #ow around a cube model by means of K-? model, J. Wind Eng. Ind. Aerodyn. 31 (1988) 283}303. [7] S. Murakami, A. Mochida, K. Hibi, Three dimensional numerical simulation of air #ow around a cube model by means of large eddy simulation, J. Wind Eng. Ind. Aerodyn. 25 (1987) 291}305. [8] S. Murakami, S. Kato, Current status of numerical and experimental methods for analyzing #ow "eld and di!usion "eld in a room, Proc. Building Systems Room Air and Air Contaminant Distribution ASHRAE Atlanta, 1989, 39}56. [9] A.J. Baker, R.M. Kelso, On validation of computational #uid dynamics procedure for room air motion prediction, ASHRAE Trans. 96 (1990) 760}774. [10] E.G. Smith, The feasibility of using models for predetermining natural ventilation, Research Report C 26, Texas Eng. Exp. Station, Texas A&M, June 1951. [11] J.E. Cermak, M. Poreh, J. Peterka, S. Ayad, Wind tunnel investigations of natural ventilation, J. Transp. Eng. ASCE Trans. 110 (1) (1984) 67}79. [12] W.P. Jones, B.E. Launder, The prediction of laminarization with two equation model of turbulence, Int. J. Heat Mass Transfer 15 (1972) 301}314. [13] S.V. Patanker, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980, p. 197. [14] M. Peric, R. Kessler, G. Scheuerer, Comparison of "nite-volume numerical methods with staggered and co-located grids, Comput. Fluids 4 (1988) 389}403. [15] B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19 (1979) 59}98. [16] J.P. Van Doormal, C.D. Raithby, Enhancement of the SIMPLE method for predicting incompressible #uid #ow, Numer. Heat Transfer 7 (1984) 147}163. [17] H.L. Stone, Iterative solution of implicit approximation of multidimensional partial di!erential equations, SIAM J. Numer. Anal. 5 (1968) 530}560.
Computational study of natural ventilation Samir S. Ayad Faculty of Engineering at Shoubra, Zagazig University, Cairo, Egypt Received 30 July 1997; received in revised form 1 September 1998; accepted 30 November 1998
Abstract The object of the present work is to use computational #uid dynamics (CFD) to study the ventilation properties for a room with di!erent opening con"gurations. The "nite volume method is used to solve the basic equations of mass and momentum conservation in the primitive form together with the two-equation turbulence model. The model is veri"ed by comparing the results for steady two-dimensional #ow around a long square cylinder immersed in the atmospheric boundary layer with experimental values. Internal #ows are then simulated in a single-room building with di!erent opening con"gurations. Six examples are considered for internal #ows. The results include mean velocity vectors, stream lines, and pressure distribution around the building as well as the mean velocity vectors, streamlines and turbulent eddy viscosity inside the room are considered. The placement of openings in relation to one another may enhance or reduce mean velocity at certain locations inside the room. The model can help in assigning comfortable locations for humans inside the room. For a given upstream wind speed the in-room mean velocity vectors are found to be sensitive to upstream wind direction while the e!ect of upstream turbulence level on in-room wind speed is shown to be negligible. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Natural ventilation; CFD; Finite volume method
Nomenclature C , C and Ck constants for two equation turbulence model C pressure coe$cient N E constant used in the logarithmic wall function k kinetic energy of turbulence ¸ dimension of the building or the room considered l characteristic length scale P pressure ; mean wind speed in the i direction G u #uctuating wind speed in direction i G uH shear velocity 0167-6105/99/$ } see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 8 ) 0 0 2 1 0 - 4
50
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Greek letters e k 2 k l o p I p C
rate of dissipation of turbulence energy turbulent eddy viscosity e!ective viscosity kinematic viscosity density Prandtl number for kinetic energy of turbulence Prandtl number for rate of dissipation
1. Introduction With the increase of energy costs; passive cooling of houses using natural wind is coming back as an attractive alternative for mechanical air conditioning. Wind has been regarded as the most popular passive cooling resource against hot and humid climates in summer. Good ventilation has positive e!ects on occupants' comfort and indoor-air quality. The alteration of wind #ow by the designer can result in a climatically comfortable residence. The human comfort can be predicted on the basis of internal air speed. The ventilation e!ectiveness can be related to spatial distribution of fresh air necessary for minimum health requirements. Tsutsumi et al. [1] used full-scale measurements and numerical simulation to evaluate thermal comfort of common houses in Japan. Wind ventilated houses were shown to be in the comfort zone while unventilated houses were uncomfortable. Movements of smoke during "re development can also be of extreme importance in relation to building evacuation routes and times. The con"gurations of building rooms and especially the location of inlet and outlet openings in relation to dominant wind direction at the site, have major e!ects on the ventilation rates in buildings. Locating Inlet openings near high-pressure surfaces of a building and exit openings at low-pressure ones produces higher #ow rates through windows. Accordingly, an understanding of air #ow around the building is necessary to design well-ventilated residences. External #ows around buildings are very complicated involving severe pressure gradients, streamline curvature, swirl, separation and reattachment together with the resulting e!ects of enhancing and suppression of turbulence. Several authors have examined time-averaged #ow "eld around buildings both experimentally and numerically. Castro and Robins [2] measured velocities near and pressures around surface mounted cubes in both uniform and shear turbulent #ows. They demonstrated major e!ects of upstream turbulence on the reattachment of separating shear layer on the top of the body. Baines [3] reported pressure measurements around a cube block in steady turbulent #ows with wind normal to one face of the block. Paterson and Apelt [4], Paterson [5], Murakami and Mochida [6] and Murakami et al. [7] all reported numerical models for steady #ow around building with di!erent degrees of complexity. Murakami and Kato, [8] and Baker and Kelso [9] both considered numerical models for in-room #ows.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
51
The use of wind tunnel models to study natural ventilation was evaluated by Smith [10] and more recently by Cermak et al. [11]. In order to achieve Reynolds number independent #ow around and inside blu! buildings and at the same time to avoid tunnel blockage, a large tunnel section is needed. In view of enormous costs and time required for "eld or wind tunnel studies, the present work is aimed to employ computational #uid dynamics to determine the distribution of time-averaged, steady, two-dimensional and turbulent in-room #ow "eld at the mid plane of openings. Although the e!ects of neighboring buildings can be signi"cant, only an isolated room is considered for the present work to test the basic natural ventilation rules as a!ected by relative opening location and di!erent upstream wind conditions. The two-equation turbulence model is used. Air speed, circulation zones and turbulent di!usion coe$cients are the parameters considered for the evaluation of natural ventilation.
2. Governing equations An understanding of air #ow around buildings with complete details on surface pressures is necessary to design well-ventilated buildings. Accordingly, in the present work two con"gurations are considered. The "rst deals with external #ow and the second concentrates on internal room #ow. Steady, turbulent and two-dimensional #ow around a building immersed in an atmospheric boundary layer is considered. Building aspect ratio equals 1 and the #ow domain extends from two building lengths upstream of building windward face to ten building lengths downstream of the building leeward face. The domain height is 4 times the building height. The #ow domain is shown in Fig. 1. The second con"guration considers the in-room #ow in the mid plane of the room at the openings level. Six examples with di!erent locations of openings are shown in Fig. 2. Since air movements are considered as the natural cooling resource, the computations are carried out for isothermal conditions.
Fig. 1. Con"guration 1 for boundary layer #ow around long square cylinder.
52
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 2. Con"guration II for in-room #ow model with six examples: (1) cross ventilation, (2) cross ventilation with larger exit opening, (3) cross ventilation with two exit openings, (4) ventilation with exit opening at adjacent walls, (5) ventilation with openings at the far ends of adjacent walls with normal wind, and (6) ventilation with openings at far ends of adjacent walls with 303 incidence wind.
Equations of mass and momentum conservation are given by *(o; ) G "0, (1) *X G *P * *; *(o; ; ) G H "! G!ou u , # k (2) G H *X *X *X *X G G H H where ; , i"1, 2 are the mean velocity components in the streamwise and normal G directions, respectively. u , i"1, 2 and 3 are turbulent #ow #uctuating components in G the x, y and z directions, respectively. k is the molecular viscosity and o is the #uid density. The Reynolds stress in Eq. (2) is modeled by the use of Boussinesq's turbulent viscosity, which is evaluated as a function of the turbulence kinetic energy k and its rate of dissipation e; [12]:
ok k "C , R I e
(3)
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
d uu k" GH G H, 2
53
(4)
*u *u G H. (5) *X *X H G k and e are obtained by solving the following transport equations simultaneously with the mean #ow equations: e"l
* * k *k (; k)" #G!oeC , (6) B *X p *X *X H H H H I * * k *e G e o (; e)" #C e !C o , (7) k k *X p *X *X H H H C H *; *; *; G G# H , G"k (8) R *X *X *X H H G k "k #k, (9) R where G is the production of turbulence energy due to work of the mean #ow on the turbulent Reynolds stress. k is the e!ective viscosity. The constants appearing in the above equations are given by o
C "1.44,
C "1.92,
C "0.09, I
p "1 and p "1.3. I C
(10)
2.1. Boundary conditions Undisturbed streamwise velocity is assumed to obey the () power-law variation with z for the "rst con"guration while uniform #ow is considered at inlet opening for the second con"guration: ;(z)"; (Z/2¸) for Z(2¸, ;(Z)"; for Z'2¸, k"0.0036;,
(11) (12)
e"C k /l, (13) I l is the characteristic length and is taken to be 0.2¸. At the upper boundary of con"guration I, all derivatives of dependent variables are assumed to vanish. Correcting the outlet velocity components strictly imposes the overall mass conservation through the #ow domain. Near the ground as well as at the inner or outer building surface constant, stress layers are assumed to exist and the wall function is used in order to avoid the need for large number of nodal points usually required for a region with large velocity gradients. At the "rst nodal point next to a wall the mean velocity, the shear stress,
54
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
turbulence production and rate of dissipation are respectively, given by
u yu o ;" H ln E H , s k
(14)
yu o q "so(C ) (k/ ln E H , U I k G"q
*; *l # #2k U *y *x
*; *l # , *x *y
C k e" I , s y
(15) (16) (17)
s"0.41, E"8.331. In the above equations y is the normal distance between the "rst nodal point and the wall. It is exchanged with x for windward and leeward faces of the building as well as for normal walls of in-room #ow. 3. Solution procedure The method of "nite volume integration of Patanker [13] is used on a rectangular Cartesian grid. Smaller grid size is used near the walls and the ground. A stretching factor of 1.1 is used. Control volumes of size 52;62 are used for the "rst con"guration, while 60;30 was used for the second con"guration half room. Fig. 3 shows an example of the grid employed for half room #ows with the "rst three examples of con"guration II. Following Peric et al. [14], the co-located variable arrangement is employed. All dependent variables are stored at the same location in the integration domain. The mass #uxes are interpolated from the dependent variables and stored at the control volume faces. A special interpolation procedure is used for the cell-face velocities to suppress oscillatory solutions, which might otherwise arise from the co-located storage. The QUICK scheme of Leonard [15] for space discretization is used to avoid the large numerical di!usion of the widely used upwind di!erence scheme. Predictor}corrector method is considered for obtaining the velocity components. The pressure distribution is obtained using SIMPLEC procedure of van Doormal [16] and the "nite-di!erence linear system is solved by the strongly implicit method of Stone [17]. 4. Results 4.1. Boundary layer yow around the long square cylinder The results of pressure contour, mean velocity vector plots and streams for the #ow around the long square cylinder are shown in Fig. 4. The model captures the
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
55
Fig. 3. An example of grid used for half-room #ows examples 1}3 of con"guration II.
recirculating zone downstream of the building, which extends about six building length downstream. The results show the circulation zones near the lower corner of upwind cylinder surface and at the upwind top corner. The values of pressure coe$cients are also compared with the experimental values of Castro and Robins [2]. Since their experiment was carried for a three-dimensional object, mid plane values are used for comparison with the present two-dimensional results in order to avoid the end e!ects on surface values of pressure. The present results have the same trend as the experimental surface pressure values. The pressure coe$cient is de"ned as (P!P ) . C" N 0.5(o; ) The pressure at the far-left top of the domain is taken as the reference pressure. Fig. 5 shows a favorable comparison between the present calculations and mid-plane experimental values. The trend of variations is generally close to the experimental one. The discrepancies at the top surface and leeward surfaces can be explained by the di!erence in the boundary layer thickness as well as the turbulence intensity of the approach #ow. Their results were measured for atmospheric boundaries layer thickness ten times the building height. Based on their measurements as the boundary layer thickness decreases the magnitude of negative pressure coe$cient at the mid-top of the building increases. It should be noted that the present calculations are carried out for boundary layer height that is twice the building height. The results of solid body surface pressure distribution are very important from the ventilation
56
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 4. Pressure contours, velocity vector and streams for #ow around long square cylinder.
point of view. They are used to locate the optimum locations of inlet and exit openings. The results show that the upwind vertical surface would be appropriate for inlet openings while top surface as well as the leeward surface opening serves as exit ones.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
57
Fig. 5. Comparison of present results with experimental values of surface pressure coe$cient around a long square cylinder.
This idea was employed and tested in a meteorological wind tunnel by Cermak et al. [11]. 4.2. In-room -ow examples Figs. 6}8 show the vector plots as well as streamlines for in-room #ows, for examples one to three of con"guration II. As given in Fig. 2, these examples have symmetric #ows around the room centerline of plan view. Accordingly half the room only is shown. The #ow in Fig. 6 presents cross ventilation with equal inlet and exit openings. It can be seen that only the area spanned by the cylindrical stream tube is actually ventilated. The idea of increasing exit area opening by Smith [10] is simulated in Fig. 7. The exit area is increased to 37.5% of wall area, which is 50% larger than the inlet opening. The plan of the ventilated zone seems to have larger area at exit and looks like a trapezoid. Air momentum transport seems to be carried mainly by convection and hardly by turbulent di!usion. This idea will be discussed later while looking at the e!ect of upstream turbulence. In order to enhance convection, example three is considered with two exit openings at the ends of leeward wall with a total area which equals 25% of wall area in order to increase the length of the streamtube. Fig. 8
58
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 6. Velocity vectors and streams for example 1 (cross ventilation with equal openings).
shows a considerable increase of velocity vector and a reduced area of the calm zone that does not bring fresh air. Fig. 9 shows the air #ow vectors and streamlines in a room of example four. The supply window is placed at the center of one room side and exhaust window is located at the end of the adjacent room side wall. The diagram shows two medium size circulation zones; one at each side of the main wind #ow path. Velocity vectors seem to have larger magnitudes especially, at locations within the circulation zone but away from their centers. Fig. 10 presents the velocity vector and streams of example "ve.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
59
Fig. 7. Velocity vectors and streams for example 2 (cross ventilation with larger exit openings).
Openings are located at the far ends of the adjacent walls. As shown in the "gure when one circulation zone increases the other diminishes. In Fig. 11 incident wind with 303 to normal is considered. Again two circulation zones are shown but the one close to exit opening has a smaller size. Fig. 12a and 12b shows contour plots for the magnitude of wind speed magnitude as a fraction of inlet opening speed. Large zone of speed less than 20% of inlet value is shown for examples 1 and 2. Such calm zones are decreased for example 3 with shifted openings of cross-ventilation. Considerable reduction of non-ventilated zones is shown for #ows of examples 4, 5 and 6. Depending
60
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 8. Velocity vectors and streams for example 3 (cross ventilation with shifted openings).
on the locations of humans inside the room and the dominant wind direction the designer should be able to locate ventilation openings. 4.2.1. Turbulence Eddy viscosity Fig. 13 shows contour plots for the turbulence eddy viscosity. Except for areas near inlet and exit openings and walls the eddy viscosity has very small values. Momentum transfer does not seem to alter the velocity vectors outside the stream tube. An increase of incoming kinetic energy of turbulence from 6% to 12% does not cause any
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 9. Velocity vectors and streams for example 4 (ventilation with openings at adjacent walls).
61
62
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 10. Velocity vectors and streams for example 5 (ventilation with openings at the far ends of the adjacent walls).
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 11. Velocity vector and streams for example 6 (Ventilation with thirty degrees incident wind).
63
64
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 12. Contour plots for the magnitude of in-room wind velocity. (a) Shaded areas have wind speed less than or equal to 20% of inlet wind speed for examples 1}3. (b) Shaded areas have wind speed less than or equal to 20% of inlet wind speed for examples 4 }6.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 12 (continued).
65
66
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
Fig. 13. Contour plots for in-room turbulent Eddy viscosity.
considerable increase of velocity vectors outside the main stream tube. The e!ect of upstream turbulence and boundary layer thickness must not be underestimated. Although the present results of Fig. 13 show no e!ect on in-room eddy viscosity, upstream turbulence has been shown to strongly in#uence the external surface pressure thus a!ecting the upstream mean wind speed at inlet openings, and this provides a ventilation driving mechanism. Increased turbulence promotes re-attachment.
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
67
The vortex formed at top windward corner causes an increase in velocity and a decrease in pressure. Further, the shear layer re-attachment e!ectively seals o! bubble from direct venting to free stream causing an increased magnitude of negative pressure there.
5. Conclusions (1) The model for #ow around a building captures the circulating bubbles upstream and downstream of the building, and the steady #ow pressure coe$cient has the same trend as the experimental ones. (2) The two-equation turbulence model is a useful tool for predicting in-room #ows. (3) Cross ventilation is useful for ventilating the areas passed by the stream tube between inlet and exit openings, but outside the stream tube recirculation zones with no fresh air dominate. The low turbulence level is not enough to enhance momentum transfer from the stream tube to the otherwise stand still air outside the tube. (4) Depending upon the locations of humans inside the room, the wind incidence angle can cause an increase in velocity magnitude and reduction of calm air zones inside the room. (5) For the same upstream wind speed, the incoming turbulence intensity does not have signi"cant e!ects on either mean velocity vector or on in room turbulent eddy coe$cient. It should be noticed that upstream turbulence has considerable e!ects on external #ow reattachment and surface pressure coe$cients, which will ultimately a!ect #ow through building openings. An extended explanation of e!ects of upstream turbulence and boundary layer thickness on surface pressure is given in Castro and Robins [2].
Acknowledgements The author would like to express his deep thanks and gratitude to J.E. Cermak, distinguished university professor at Colorado State University for his continuing support. His ideas and suggestions made this work possible.
References [1] J. Tsutsum, T. Katayama, A. Ishii, P. He, T. Hayashi, Investigation of wind e!ects on thermal comfort in a house, J. Wind Eng. Ind. Aerodyn. 60 (1996) 267}280. [2] I.P. Castro, A.G. Robins, The #ow around a surface mounted cube in uniform #ow and turbulent streams, J. Fluid Mech. 79 (1977) 307}335. [3] W.D. Baines, E!ects of velocity distribution on wind loads and #ow patterns on buildings, Wind E!ects on Build. Struct. 1 (1965) 198. [4] D.A. Paterson, C.J. Apelt, Simulation of #ow past a cube in a turbulent #ow, J. Wind Eng. Ind. Aerodyn. 35 (1990) 149}176.
68
S.S. Ayad/J. Wind Eng. Ind. Aerodyn. 82 (1999) 49 }68
[5] D.A. Paterson, Computation of wind #ows over three dimensional buildings, Ph.D. Thesis, University of Queensland, 1986. [6] S. Murakami, A. Mochida, Three dimensional numerical simulation of air #ow around a cube model by means of K-? model, J. Wind Eng. Ind. Aerodyn. 31 (1988) 283}303. [7] S. Murakami, A. Mochida, K. Hibi, Three dimensional numerical simulation of air #ow around a cube model by means of large eddy simulation, J. Wind Eng. Ind. Aerodyn. 25 (1987) 291}305. [8] S. Murakami, S. Kato, Current status of numerical and experimental methods for analyzing #ow "eld and di!usion "eld in a room, Proc. Building Systems Room Air and Air Contaminant Distribution ASHRAE Atlanta, 1989, 39}56. [9] A.J. Baker, R.M. Kelso, On validation of computational #uid dynamics procedure for room air motion prediction, ASHRAE Trans. 96 (1990) 760}774. [10] E.G. Smith, The feasibility of using models for predetermining natural ventilation, Research Report C 26, Texas Eng. Exp. Station, Texas A&M, June 1951. [11] J.E. Cermak, M. Poreh, J. Peterka, S. Ayad, Wind tunnel investigations of natural ventilation, J. Transp. Eng. ASCE Trans. 110 (1) (1984) 67}79. [12] W.P. Jones, B.E. Launder, The prediction of laminarization with two equation model of turbulence, Int. J. Heat Mass Transfer 15 (1972) 301}314. [13] S.V. Patanker, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980, p. 197. [14] M. Peric, R. Kessler, G. Scheuerer, Comparison of "nite-volume numerical methods with staggered and co-located grids, Comput. Fluids 4 (1988) 389}403. [15] B.P. Leonard, A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19 (1979) 59}98. [16] J.P. Van Doormal, C.D. Raithby, Enhancement of the SIMPLE method for predicting incompressible #uid #ow, Numer. Heat Transfer 7 (1984) 147}163. [17] H.L. Stone, Iterative solution of implicit approximation of multidimensional partial di!erential equations, SIAM J. Numer. Anal. 5 (1968) 530}560.