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Effect of building re-entrant shape on performance of air-cooled condensing units
Energy and Buildings 32 Ž2000. 143–152 www.elsevier.comrlocaterenbuild
Effect of building re-entrant shape on performance of air-cooled condensing units T.T. Chow a,) , Z. Lin a , Q.W. Wang b a
DiÕision of Building Science & Technology, City UniÕersity of Hong Kong, Tat Chee AÕenue, Kowloon, Hongkong, People’s Republic of China b School of Energy and Power Engineering, Xi’an Jiaotong UniÕersity, Xi’an, Shaanxi ProÕince, People’s Republic of China Received 15 March 1999; accepted 25 November 1999
Abstract Provision of split-type air-conditioners in high-rise residential buildings has become fashionable in Hong Kong. Building re-entrants are most popular for placing the outdoor condensing units. Heat energy dissipated by these condensing units induces a buoyant airflow. Inadequate displacement of air may lead to an elevated temperature environment at the re-entrant, which could significantly affect the condenser performance at the upper floors and subsequently result in a degradation of the overall capacity and efficiency of the air-conditioners. In recent years, some innovative building designers go for sustainable housing design. Re-entrants of various shapes thus evolve. One of their concerns is whether these various shapes would incur more difficulties in the airflow and thereby, would intensify the condenser heat dissipation problem. This paper describes some investigations on different re-entrant shapes making use of the computational fluid dynamics ŽCFD. techniques together with an energy evaluation model. The results show no evidence that the new re-entrant shapes will have adverse effects in comparison with the conventional design. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Air-conditioner performance; Energy and flow simulation
1. Introduction Residential buildings in Hong Kong are typically comprised of a number of domestic towers standing on a common podium garden. Underneath the podium are supportive and recreational facilities such as covered car park, clubhouse, or shopping mall. Patterns of tower arrangements generally vary depending on the prevailing climate and topography. Fig. 1 shows a model of a current building project under construction. Residential towers can be seen at the left-hand side of the site. The widespread development based on a ‘‘cruciform’’ plan for an individual tower is essentially a product of Building ŽPlanning. Regulations w1,2x. Public space, including lift lobbies and corridors, is usually squeezed to a minimum at the building core. With its four wings radiating out from the core, typically, a residential tower consists of eight apartments on a single floor, with two at each wing. A deep, narrow
)
Corresponding author. Tel.: q852-2788-7089; fax: q852-2788-9716. E-mail address: [email protected] ŽT.T. Chow..
‘‘I-shaped’’ re-entrant exists at each wing between the neighboring flats. According to the building regulations, the width of a re-entrant should not be less than 2.3 m. Windows of the kitchens and bathrooms are open towards the re-entrants for sources of natural lighting and ventilation. On some occasions, innovative architects go for sustainable housing design. The concept of sustainability refers to a careful management of energy and entropy, including reduced consumption, recycling and self-sufficiency w3x. Instead of the conventional cruciform plans, linear plan forms are sometimes adopted to enhance natural ventilation for not only apartments but also lobbies and corridors w4x. Other re-entrant shapes thus occur, such as ‘‘T’’ and ‘‘L’’. There is also a recent trend for property developers in Hong Kong to provide split-type air-conditioners to serve the livingrdining rooms and the bedrooms in new apartments. A split-type Žor multi-split-type. unit consists of one outdoor condensing unit Žthat houses the air-cooled condenser and the refrigerant compressor. and one or more indoor unitŽs. Žthat houses the evaporating coil and blower..
0378-7788r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 Ž 9 9 . 0 0 0 4 8 - 1
144
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
lines for the use of building practitioners. One of the concerns is that while the sustainable architectural design attempts to create the most balanced approach to environmental, economic and social factors, whether the various re-entrant shapes will have an impact on the condenser performance or not still needs to be evaluated. The following report some findings via a computational fluid dynamics ŽCFD. study in association with an energy evaluation model.
3. Simulation model Fig. 1. Model of a new combined commercial and residential project under construction in Hong Kong.
The distinct advantages of split-type units lie in the quiet operation and the flexibility in multi-room services. From a marketing point of view, the provision attracts the customers by promoting a deluxe image of the apartments and a delightful external view of the building. The recessed re-entrants of the residential towers are therefore favorite locations for placing the outdoor condensing units. Fig. 2 shows some of the outdoor condensing units being installed at an L-shaped re-entrant. According to a recent survey on new residential buildings in Hong Kong that are served with split-type air-conditioners, about 40% of their re-entrants are in I-shaped, 18% are in T-shaped, 14% are in L-shaped, 2% are in Y-shaped, and 26% are in irregular shapes w5x. The first three account for 72% of the total. These 111 re-entrants in the survey cover a floor plan area ranging from 10 to 70 m2 each, with the average value at around 30 m2 .
The driving effects of air movement at a re-entrant are basically the wind, the condenser fans and the thermal buoyancy. CFD is known to be the most common numerical technique applying to similar studies, for instance, the works of Aynsley w6x, Lovatt and Wilson w7x, and Boyer et al. w8x. Here, the investigations were carried out based on the placement of the same number Žtotally 120. of identical condensing units into three different re-entrants of shapes: ‘‘I’’, ‘‘T’’ and ‘‘L’’, respectively. It was believed that Y-shaped re-entrants, by the nature of geometry, would have the effectsrattributes somewhere between those of the I-shaped and T-shaped. All three re-entrants under study were having the same floor plan area of 30 m2 , the same width of 3 m, and the same building height of 82.05 m Žrepresenting 30 floor levels of 2.735 m each.. A previous work w9x has shown that for high-rise residential buildings, the building height alone does not have a significant effect on the elevation of condenser on-coil temperature. This is because the buoyancy effect caused by
2. Condenser heat dissipation problem It is known that for a split-type unit, effective cooling performance of the indoor air-conditioner requires effective heat rejection at the outdoor condensing unit. For a 30-storey residential building, over a hundred of these condensing units can exist inside a single re-entrant. Heat energy released from the condensers induces a natural rise of warm air plume. The accumulating effect of heat energy pick-up as the plume rises could result in a substantial temperature rise at upper floor levels. The direct consequences of elevated on-coil temperature at the condensing units are the degradation of air-conditioner performance and a waste of electrical energy. For a proposed layout of condensing units in a re-entrant, the design engineer often finds it difficult to assess accurately the air-conditioner performance of individual units or as a group. A research project has been launched to study this effect and aims at introducing design guide-
Fig. 2. Arrays of outdoor condensing units in an L-shaped re-entrant.
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
the increased heat dissipation with an increase in building height will eventually incur additional airflow. In this study, each floor level was provided with four numbers of condensing units that were arranged symmetrically with two at each side, as shown in Fig. 3. Only one side is shown in Fig. 3Ža. and Žc. up to the center plan in the cases of I- and T-shapes. The condensing units were tentatively being placed at the interior of the re-entrants. Each condensing unit had a rated heat dissipation rate of 4.5 kW and a cooling air discharge rate of 1.53 m3rs. Prediction of the actual working conditions of the condens-
145
ing units can be complicated because of the dynamics involved, such as:
1. not necessarily all air-conditioners are in operation at the same time; 2. those air-conditioners in operation are most likely under partial loads; 3. the climatic conditions, e.g., incoming wind and outdoor temperature, are changing and affect the airflow all the time.
Fig. 3. Arrangements of condensing units in the re-entrants: Ža. I-shaped, Žb. L-shaped, Žc. T-shaped.
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T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
the k– ´ turbulence model in a 3D vector space are listed in Table 1 w12,13x. Some validation work using the CFX software in solving related thermal problems in buildings had been reported w14x. In the analyses related to the I- and T-shaped conditions, only one-half of the re-entrants Žup to the central plans. were modeled using a 3D rectangular grid, taking advantage of the symmetry in the re-entrant shapes and the condenser arrangements. The ‘‘casing’’ of each condensing unit was represented by four thin surfaces, leaving the front and rear ends open for cooling airflow. The coolingair fan was modeled by adding appropriate body force to the enclosed cells. Volumetric heat energy was specified to the enclosed cells to represent the condenser heat dissipation. In the numerical simulation, symmetry boundaries were used at the center plans Žin the I- and T-shaped cases. and at 13.5 m away from the front edges of the re-entrants. See Fig. 4 for the T-shaped case. Mass flow boundaries were used at 5 m above the re-entrant top and at 5 m downstream the rear wall. Mass flow boundaries are types of Neumann boundary conditions in which the normal gradients of all the transported variables are imposed on the boundaries. All the transported quantities are given zero normal gradients, with the exception of velocity, which is given constant normal gradient to maintain global mass continuity in the computational region. To simulate the no-wind condition, a zero-velocity boundary ŽDirichlet type. was specified at an upstream distance of 100 m from the building front wall. This was replaced later on by a power–law wind profile assuming urban terrain during the
Simplifications and assumptions were adopted to form a steady-state computational model to enable the analysis. These include: 1. all air-conditioners are assumed in operation; 2. the condensing units are having the same steady heat dissipation rate at 60% of the rated capacity, and the same cooling-air discharge rate; 3. all wall surfaces of the re-entrants are flat, and without openings for possible air exchange; in particular, the effects of kitchen and toilet air exhausts are negligible; 4. the effect of solar radiation on the wall surfaces is negligible; and 5. outdoor temperature and air movement remain steady. Two different wind conditions had been evaluated. First, a no-wind condition was examined. This was regarded as the worst situation in terms of dispersion of heat energy from the condensers. In this case, the heat energy induced a buoyant flow of air within the re-entrant, and caused ingress of outside-air at the front of the re-entrant. Second, a case of steady-wind was examined. The wind was assumed to be approaching at a horizontal speed of 4 mrs at a reference height of 10 m above the ground, and at the zero-degree direction with the front of the re-entrant facing upwind w10x. The CFX-4.2 software w11x was used in the CFD study. The numerical simulation was based on the two-equation k– ´ model, assuming steady incompressible flow. For solving a steady-flow thermal problem with the Boussinesq approximation, the five basic transport equations of
Table 1 Transport equations of the k– ´ turbulence model in a 3D vector space Continuity Momentum
EUirE X i s 0
Uj
EUj
1 EP sy
E
Žn q nt .
q
r E Xi
E Xj
E Xj
EUj
ž
E Xi
ž
E Xi
EUi
q
/
E Xi
y b giu
Thermal energy Eu Ui
E s
E Xi
E Xi
ž
kq
nt su
/
Eu E Xi
q qu
Turbulence kinetic energy Ek Uj
E s
E Xj
E Xj
ž
nq
ž
nq
nt sk
/
Ek E Xj
q nt
EUj
q
EUi
EUi
/
E Xj
q
EUi
E Xj
q b gi
n t Eu su E X i
y´
Dissipation rate of turbulence kinetic energy E´ Uj
Eddy viscosity
E s
E Xj
E Xj
Õt s C D Žk 2 r´ )
nt s´
/
E´
´ q
E Xj
k
C1 n t
ž
EUj E Xi
E Xj
/
EUi E Xj
´2 y C2
k
´ q C3
k
b gi
n t Eu s0 E Xi
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
147
Fig. 4. Airflow boundaries used in no-wind conditions of a T-shaped re-entrant Žnot to scale..
steady-wind simulation. The variation of wind speed Ž u. with the elevation Ž z . is governed by u s u m 0.35 z 0.25
Ž 1.
where u m is the mean wind speed at a height of 10 m w15x. Multi-block representation was used in order to reduce the overall grid size. Structured grids of 171,600, 333,060 and 191,520 cells were finally used in the I-, L- and T-shaped cases, respectively. Fig. 5 shows the isometric views of the grid systems used in the cases of Ža. T-shaped, and Žb. L-shaped re-entrants, respectively.
4. Results of
CFD
analysis
4.1. No-wind Fig. 6Ža. to Žc. shows the simulation results of the I-, Land T-shaped re-entrants, respectively. The variations of
on-coil temperature at the condensing units at different floor levels are shown. With the increase in floor level, it can be seen that a temperature curve generally climbs up until a maximum is reached at one of the top Ž27–29. levels, and then declines. The decline is owing to the entry of outside-air above the re-entrant top. Comparatively, the temperature condition is the worst for the I-shaped, and followed by the L-shaped. The T-shaped appears the best among the three; this is because the two pairs of condensing units in the T-shaped re-entrant are separated far apart, while the four condensing units are close together in the I-shaped and L-shaped situations. 4.2. Steady-wind Fig. 7Ža. to Žc. shows the simulation results of the I-, Land T-shaped re-entrants, respectively. It can be observed that there is no obvious trend for the temperature curves. Nevertheless, the temperature conditions at the I- and
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T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
A, and thus results in a lower on-coil temperature at Condenser A. The discussions above gave a basic picture about the performance of the air-conditioners in different conditions. An energy performance model is introduced below, which is able to give more precise and direct evaluations of the specific cases.
5. Energy evaluation Energy performance of an air-conditioner can be described by its coefficient of performance ŽCOP., which in a broad sense, is the ratio of the unit cooling capacity to the overall power input. The COP of a split-type unit varies with its operating conditions, in particular, the room air condition and the condenser cooling condition. An air-conditioner performs better at higher room temperature ŽTr . and lower condenser on-coil temperature ŽTo .. At a given room temperature, the COP of a split-type unit can be related to To by COPT r s a y bTo ,
Ž 2.
where a and b are constants. Statistical analysis applying to manufacturing data has shown that when Tr s 258C, COP25 s 5.153 y 0.0738To .
Fig. 5. Computational spaces used to study Ža. T-shaped, and Žb. L-shaped re-entrants, with numerical grids on horizontal plan shown.
L-shaped re-entrants appear to be more affected by the incoming wind. Their maximum temperature points are shifted to the lower portion of the re-entrants. Similar to the no-wind situation, the worst temperature condition appears in the I-shaped, followed by the L-shaped, and then the T-shaped. As one illustration example to visualize the wind effect, Fig. 8 shows the patterns of air temperature contours Žisotherms. at the 20rF Ži.e., two-third of the building height. of the L-shaped re-entrant and at the level where the four condensing units are located. These isotherms are plotted assuming an outdoor temperature of 338C, which is the summer design condition of Hong Kong. Fig. 8Ža. shows the no-wind situation and the steady-wind situation in Fig. 8Žb.. Fig. 9 gives the air velocity profile corresponding to the steady incoming wind situation in Fig. 8Žb.. It can be seen that for the latter, while the vertical velocity component dominates the flow pattern, there is a turn of the incoming wind at a region close to Condenser
Ž 3.
This linear regression was derived from catalogue data of several commercial products, and with a high sample coefficient of determination of 0.991 w5x. It applies well in the range of To from 258C to 458C for single speed units. A condenser on-coil temperature higher than 458C may lead to a trip of the air-conditioner, owing to excessive condenser working pressure. Hence, if the on-coil temperatures of individual condensing units have been determined by CFD simulation, the working conditions of the air-conditioners can be predicted. When To is at 338C, i.e., at the summer design condition, Eq. Ž3. gives a COP value of 2.72. To consider the performance of ‘‘n’’ number of air-conditioning units working together as a group, say those operating inside one single re-entrant, a Condenser Group Performance Indicator ŽCGPI. can be used, which is defined as: CGPI T rŽ Tref . s
100 n
n
Ý is1
½
1y
COPT rŽ To . COPT rŽ Tref .
i
5
.
Ž 4.
This term describes the average percentage drop in COP of all air-conditioners under consideration, with respect to referenced on-coil temperature Tref and room temperature Tr . Tref can be an outdoor temperature arbitrarily assigned w16x.
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
149
Fig. 6. Results of condenser on-coil temperatures of the three re-entrant shapes Žno-wind.: Ža. I-shaped, Žb. L-shaped, Žc. T-shaped.
It can be shown by working with Eqs. Ž3. and Ž4. that for Tr s 258C and Tref s 38C, the corresponding CGPI expression is given by CGPI 25 Ž 33 . s 2.72Tom y 89.76,
formance in the L-shaped re-entrant is closer to the I-shaped re-entrant in the case of no-wind, but closer to the T-shaped re-entrant in the case of steady-wind.
Ž 5.
where Tom is the mean on-coil temperature of all air-conditioners. Table 2 lists the calculated CGPI values based on Eq. Ž5. for the six specific cases in this study. It can be seen that for all three re-entrants that CGPI is lower in the steady-wind than the no-wind conditions. And, independent of the wind conditions, the results of the overall performance assessment of the air-conditioners are consistent — the best appears in the T-shaped re-entrant, and the worst appears in the I-shaped re-entrant. The overall per-
6. Conclusions Going for sustainability is a global trend. Investigations were done on the condenser heat dissipation situations in each of the three different re-entrants, based on the same equipment operation data. While the I-shaped re-entrant represents the convention cruciform building design, the L-shaped and T-shaped represent the new innovative linear building design. The development of a steady-state thermal
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T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
Fig. 7. Results of condenser on-coil temperatures of the three re-entrant shapes Žsteady-wind.: Ža. I-shaped, Žb. L-shaped, Žc. T-shaped.
model made possible the examinations of condenser on-coil temperature conditions via CFD analysis. Further, the use of an energy evaluation model enabled systematic and generalized result comparisons. The derivation of the CGPI allows an assessment of the overall performance; whereby, multiple effects can be monitored by a single parameter. The analysis showed that, with the assumed operating conditions, the energy performance of the split-type airconditioners is the best in the T-shaped re-entrant and the worst in the I-shaped re-entrant. The same conclusion was reached from the studies of both no-wind and steady-wind conditions. Hence, the findings here do not support that these new building design concepts would intensify the
condenser heat dissipation problem, but instead, may improve the situation.
7. Nomenclature a, b C1 , C 2 C3 CD CGPI
constants empirical constant in generationrdestruction term of ´-equation empirical constant in buoyant term of ´-equation empirical constant for eddy viscosity condenser group performance indicator
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
151
Fig. 8. Air temperature contours at 20rF level of L-shaped re-entrant.
COP gi k n
coefficient of performance gravitational constant in X i-direction Žmrs 2 . mean turbulent kinetic energy Žm2rs 2 . number
p qu T
mean static pressure ŽNrm2 . mean volumetric heat source generation rate ŽkWrm3 . temperature Ž8C.
Fig. 9. Air velocity profile at 20rF level of L-shaped re-entrant for the case of steady-wind.
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
152
Table 2 Calculated values of CGPI for the six specific cases
I-shaped L-shaped T-shaped
u Ui
Uj
Xi , X j z
No-wind
Steady-wind
25.5 22.9 14.3
16.5 11.2 9.4
speed Žmrs. mean velocity component in X i-direction Žmrs. mean velocity component in X j-direction Žmrs. distance in cartesian coordinate Žm. height Žm.
Greek letters b volumetric expansion coefficient ŽKy1 . ´ mean dissipation rate of k Žm2rs 3 . u temperature rise above ambient ŽK. k thermal diffusivity Žm2rs. n kinematic molecular viscosity Žm2rs. nt eddy viscosity Žm2rs. P total pressure ŽNrm2 .; P s p q ((2 r k) r 3) r fluid density Žkgrm3 . sk empirical constant of turbulent Prandtl number for k s´ empirical constant of turbulent Prandtl number for ´ su empirical constant of turbulent Prandtl number for u Subscripts m o r ref u
mean on-coil room referenced in u equation
Acknowledgements This research work was financially supported by the Strategic Research Grant of the City University of Hong Kong.
References w1x Building ŽPlanning. Regulations, Part IV: Lighting and Ventilation, Chapter 123, Part IV, 30 Ž1., Hong Kong Government, 1984. w2x D. Cronin, Investigation into the dynamics of waste air dispersal from high-rise residences, in: Proc. 30th Conf. of ANZAScA, Chinese University of Hong Kong, Hong Kong, 1996, pp. 85–92, July. w3x Y. Kato, Research information: regional architecture as a model towards sustainability, Building Research & Information 26 Ž6. Ž1998. 363–369. w4x A. Ng, K.S. Wong, Sustainable housing design in Hong Kong: Verbena Heights ŽTKO Area 19B. and beyond, The Journal of Hong Kong Institute of Architects Ž9. Ž1997. 56–63, 2nd Quarter. w5x T.T. Chow, C.K. Cheng, Survey report on performance of split-type air-conditioners with outdoor units placed at building re-entrants, in: Internal Report, Division of Building Science & Technology, City University of Hong Kong, 1998. w6x R.M. Aynsley, A resistance approach to estimating airflow through buildings with large openings due to wind, ASHRAE Transactions 94 Ž1988. 1661–1669, Part 2. w7x J.E. Lovatt, A.G. Wilson, Stack effect in tall buildings, ASHRAE Transactions 100 Ž1994. 420–431, Part 2. w8x H. Boyer, A.P. Lauret, L. Adelard, T.A. Mara, Building ventilation: a pressure airflow model computer generation and elements of validation, Energy and Buildings 29 Ž1999. 283–292. w9x T.T. Chow, Z. Lin, Prediction of on-coil temperature of condensers installed at tall building re-entrant, Applied Thermal Engineering 19 Ž1999. 117–132. w10x ASHRAE, ASHRAE Handbook: Fundamental, Chapter 14, Atlanta, USA, 1993. w11x AEA, CFX 4.2 Flow Solver User Guide, Computational Fluid Dynamics Services, Harwell Laboratory, UK, 1998. w12x B.E. Launder, D.B. Spalding, The numerical computation of turbulent flow, Computer Methods in Applied Mechanics and Engineering 3 Ž1974. 269–289. w13x J.H. Ferziger, M. Peric, Computational Methods for Fluid Dynamics, Springer, Germany, 1996. w14x T.T. Chow, Z. Lin, Q.W. Wang, W.Z. Lu, Studying thermal performance of split-type air-conditioners at building re-entrant via computer simulation, in: Proc. IBPSA 6th Int. Conf. Building Simulation ’99, University of Kyoto, Japan, 1999, pp. 1357–1363, Sep. w15x T.D. Eastop, W.E. Watson, Mechanical Services for Buildings, Longman, UK, 1992. w16x T.T. Chow, Simulation study of performance of split-type air-conditioners, in: Proc. Mainland–Hong Kong HVAC Seminar ’98, Hong Kong Vol., Beijing, China, 1998, pp. 40–44, Mar.
Effect of building re-entrant shape on performance of air-cooled condensing units T.T. Chow a,) , Z. Lin a , Q.W. Wang b a
DiÕision of Building Science & Technology, City UniÕersity of Hong Kong, Tat Chee AÕenue, Kowloon, Hongkong, People’s Republic of China b School of Energy and Power Engineering, Xi’an Jiaotong UniÕersity, Xi’an, Shaanxi ProÕince, People’s Republic of China Received 15 March 1999; accepted 25 November 1999
Abstract Provision of split-type air-conditioners in high-rise residential buildings has become fashionable in Hong Kong. Building re-entrants are most popular for placing the outdoor condensing units. Heat energy dissipated by these condensing units induces a buoyant airflow. Inadequate displacement of air may lead to an elevated temperature environment at the re-entrant, which could significantly affect the condenser performance at the upper floors and subsequently result in a degradation of the overall capacity and efficiency of the air-conditioners. In recent years, some innovative building designers go for sustainable housing design. Re-entrants of various shapes thus evolve. One of their concerns is whether these various shapes would incur more difficulties in the airflow and thereby, would intensify the condenser heat dissipation problem. This paper describes some investigations on different re-entrant shapes making use of the computational fluid dynamics ŽCFD. techniques together with an energy evaluation model. The results show no evidence that the new re-entrant shapes will have adverse effects in comparison with the conventional design. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Air-conditioner performance; Energy and flow simulation
1. Introduction Residential buildings in Hong Kong are typically comprised of a number of domestic towers standing on a common podium garden. Underneath the podium are supportive and recreational facilities such as covered car park, clubhouse, or shopping mall. Patterns of tower arrangements generally vary depending on the prevailing climate and topography. Fig. 1 shows a model of a current building project under construction. Residential towers can be seen at the left-hand side of the site. The widespread development based on a ‘‘cruciform’’ plan for an individual tower is essentially a product of Building ŽPlanning. Regulations w1,2x. Public space, including lift lobbies and corridors, is usually squeezed to a minimum at the building core. With its four wings radiating out from the core, typically, a residential tower consists of eight apartments on a single floor, with two at each wing. A deep, narrow
)
Corresponding author. Tel.: q852-2788-7089; fax: q852-2788-9716. E-mail address: [email protected] ŽT.T. Chow..
‘‘I-shaped’’ re-entrant exists at each wing between the neighboring flats. According to the building regulations, the width of a re-entrant should not be less than 2.3 m. Windows of the kitchens and bathrooms are open towards the re-entrants for sources of natural lighting and ventilation. On some occasions, innovative architects go for sustainable housing design. The concept of sustainability refers to a careful management of energy and entropy, including reduced consumption, recycling and self-sufficiency w3x. Instead of the conventional cruciform plans, linear plan forms are sometimes adopted to enhance natural ventilation for not only apartments but also lobbies and corridors w4x. Other re-entrant shapes thus occur, such as ‘‘T’’ and ‘‘L’’. There is also a recent trend for property developers in Hong Kong to provide split-type air-conditioners to serve the livingrdining rooms and the bedrooms in new apartments. A split-type Žor multi-split-type. unit consists of one outdoor condensing unit Žthat houses the air-cooled condenser and the refrigerant compressor. and one or more indoor unitŽs. Žthat houses the evaporating coil and blower..
0378-7788r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 Ž 9 9 . 0 0 0 4 8 - 1
144
T.T. Chow et al.r Energy and Buildings 32 (2000) 143–152
lines for the use of building practitioners. One of the concerns is that while the sustainable architectural design attempts to create the most balanced approach to environmental, economic and social factors, whether the various re-entrant shapes will have an impact on the condenser performance or not still needs to be evaluated. The following report some findings via a computational fluid dynamics ŽCFD. study in association with an energy evaluation model.
3. Simulation model Fig. 1. Model of a new combined commercial and residential project under construction in Hong Kong.
The distinct advantages of split-type units lie in the quiet operation and the flexibility in multi-room services. From a marketing point of view, the provision attracts the customers by promoting a deluxe image of the apartments and a delightful external view of the building. The recessed re-entrants of the residential towers are therefore favorite locations for placing the outdoor condensing units. Fig. 2 shows some of the outdoor condensing units being installed at an L-shaped re-entrant. According to a recent survey on new residential buildings in Hong Kong that are served with split-type air-conditioners, about 40% of their re-entrants are in I-shaped, 18% are in T-shaped, 14% are in L-shaped, 2% are in Y-shaped, and 26% are in irregular shapes w5x. The first three account for 72% of the total. These 111 re-entrants in the survey cover a floor plan area ranging from 10 to 70 m2 each, with the average value at around 30 m2 .
The driving effects of air movement at a re-entrant are basically the wind, the condenser fans and the thermal buoyancy. CFD is known to be the most common numerical technique applying to similar studies, for instance, the works of Aynsley w6x, Lovatt and Wilson w7x, and Boyer et al. w8x. Here, the investigations were carried out based on the placement of the same number Žtotally 120. of identical condensing units into three different re-entrants of shapes: ‘‘I’’, ‘‘T’’ and ‘‘L’’, respectively. It was believed that Y-shaped re-entrants, by the nature of geometry, would have the effectsrattributes somewhere between those of the I-shaped and T-shaped. All three re-entrants under study were having the same floor plan area of 30 m2 , the same width of 3 m, and the same building height of 82.05 m Žrepresenting 30 floor levels of 2.735 m each.. A previous work w9x has shown that for high-rise residential buildings, the building height alone does not have a significant effect on the elevation of condenser on-coil temperature. This is because the buoyancy effect caused by
2. Condenser heat dissipation problem It is known that for a split-type unit, effective cooling performance of the indoor air-conditioner requires effective heat rejection at the outdoor condensing unit. For a 30-storey residential building, over a hundred of these condensing units can exist inside a single re-entrant. Heat energy released from the condensers induces a natural rise of warm air plume. The accumulating effect of heat energy pick-up as the plume rises could result in a substantial temperature rise at upper floor levels. The direct consequences of elevated on-coil temperature at the condensing units are the degradation of air-conditioner performance and a waste of electrical energy. For a proposed layout of condensing units in a re-entrant, the design engineer often finds it difficult to assess accurately the air-conditioner performance of individual units or as a group. A research project has been launched to study this effect and aims at introducing design guide-
Fig. 2. Arrays of outdoor condensing units in an L-shaped re-entrant.
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the increased heat dissipation with an increase in building height will eventually incur additional airflow. In this study, each floor level was provided with four numbers of condensing units that were arranged symmetrically with two at each side, as shown in Fig. 3. Only one side is shown in Fig. 3Ža. and Žc. up to the center plan in the cases of I- and T-shapes. The condensing units were tentatively being placed at the interior of the re-entrants. Each condensing unit had a rated heat dissipation rate of 4.5 kW and a cooling air discharge rate of 1.53 m3rs. Prediction of the actual working conditions of the condens-
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ing units can be complicated because of the dynamics involved, such as:
1. not necessarily all air-conditioners are in operation at the same time; 2. those air-conditioners in operation are most likely under partial loads; 3. the climatic conditions, e.g., incoming wind and outdoor temperature, are changing and affect the airflow all the time.
Fig. 3. Arrangements of condensing units in the re-entrants: Ža. I-shaped, Žb. L-shaped, Žc. T-shaped.
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the k– ´ turbulence model in a 3D vector space are listed in Table 1 w12,13x. Some validation work using the CFX software in solving related thermal problems in buildings had been reported w14x. In the analyses related to the I- and T-shaped conditions, only one-half of the re-entrants Žup to the central plans. were modeled using a 3D rectangular grid, taking advantage of the symmetry in the re-entrant shapes and the condenser arrangements. The ‘‘casing’’ of each condensing unit was represented by four thin surfaces, leaving the front and rear ends open for cooling airflow. The coolingair fan was modeled by adding appropriate body force to the enclosed cells. Volumetric heat energy was specified to the enclosed cells to represent the condenser heat dissipation. In the numerical simulation, symmetry boundaries were used at the center plans Žin the I- and T-shaped cases. and at 13.5 m away from the front edges of the re-entrants. See Fig. 4 for the T-shaped case. Mass flow boundaries were used at 5 m above the re-entrant top and at 5 m downstream the rear wall. Mass flow boundaries are types of Neumann boundary conditions in which the normal gradients of all the transported variables are imposed on the boundaries. All the transported quantities are given zero normal gradients, with the exception of velocity, which is given constant normal gradient to maintain global mass continuity in the computational region. To simulate the no-wind condition, a zero-velocity boundary ŽDirichlet type. was specified at an upstream distance of 100 m from the building front wall. This was replaced later on by a power–law wind profile assuming urban terrain during the
Simplifications and assumptions were adopted to form a steady-state computational model to enable the analysis. These include: 1. all air-conditioners are assumed in operation; 2. the condensing units are having the same steady heat dissipation rate at 60% of the rated capacity, and the same cooling-air discharge rate; 3. all wall surfaces of the re-entrants are flat, and without openings for possible air exchange; in particular, the effects of kitchen and toilet air exhausts are negligible; 4. the effect of solar radiation on the wall surfaces is negligible; and 5. outdoor temperature and air movement remain steady. Two different wind conditions had been evaluated. First, a no-wind condition was examined. This was regarded as the worst situation in terms of dispersion of heat energy from the condensers. In this case, the heat energy induced a buoyant flow of air within the re-entrant, and caused ingress of outside-air at the front of the re-entrant. Second, a case of steady-wind was examined. The wind was assumed to be approaching at a horizontal speed of 4 mrs at a reference height of 10 m above the ground, and at the zero-degree direction with the front of the re-entrant facing upwind w10x. The CFX-4.2 software w11x was used in the CFD study. The numerical simulation was based on the two-equation k– ´ model, assuming steady incompressible flow. For solving a steady-flow thermal problem with the Boussinesq approximation, the five basic transport equations of
Table 1 Transport equations of the k– ´ turbulence model in a 3D vector space Continuity Momentum
EUirE X i s 0
Uj
EUj
1 EP sy
E
Žn q nt .
q
r E Xi
E Xj
E Xj
EUj
ž
E Xi
ž
E Xi
EUi
q
/
E Xi
y b giu
Thermal energy Eu Ui
E s
E Xi
E Xi
ž
kq
nt su
/
Eu E Xi
q qu
Turbulence kinetic energy Ek Uj
E s
E Xj
E Xj
ž
nq
ž
nq
nt sk
/
Ek E Xj
q nt
EUj
q
EUi
EUi
/
E Xj
q
EUi
E Xj
q b gi
n t Eu su E X i
y´
Dissipation rate of turbulence kinetic energy E´ Uj
Eddy viscosity
E s
E Xj
E Xj
Õt s C D Žk 2 r´ )
nt s´
/
E´
´ q
E Xj
k
C1 n t
ž
EUj E Xi
E Xj
/
EUi E Xj
´2 y C2
k
´ q C3
k
b gi
n t Eu s0 E Xi
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Fig. 4. Airflow boundaries used in no-wind conditions of a T-shaped re-entrant Žnot to scale..
steady-wind simulation. The variation of wind speed Ž u. with the elevation Ž z . is governed by u s u m 0.35 z 0.25
Ž 1.
where u m is the mean wind speed at a height of 10 m w15x. Multi-block representation was used in order to reduce the overall grid size. Structured grids of 171,600, 333,060 and 191,520 cells were finally used in the I-, L- and T-shaped cases, respectively. Fig. 5 shows the isometric views of the grid systems used in the cases of Ža. T-shaped, and Žb. L-shaped re-entrants, respectively.
4. Results of
CFD
analysis
4.1. No-wind Fig. 6Ža. to Žc. shows the simulation results of the I-, Land T-shaped re-entrants, respectively. The variations of
on-coil temperature at the condensing units at different floor levels are shown. With the increase in floor level, it can be seen that a temperature curve generally climbs up until a maximum is reached at one of the top Ž27–29. levels, and then declines. The decline is owing to the entry of outside-air above the re-entrant top. Comparatively, the temperature condition is the worst for the I-shaped, and followed by the L-shaped. The T-shaped appears the best among the three; this is because the two pairs of condensing units in the T-shaped re-entrant are separated far apart, while the four condensing units are close together in the I-shaped and L-shaped situations. 4.2. Steady-wind Fig. 7Ža. to Žc. shows the simulation results of the I-, Land T-shaped re-entrants, respectively. It can be observed that there is no obvious trend for the temperature curves. Nevertheless, the temperature conditions at the I- and
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A, and thus results in a lower on-coil temperature at Condenser A. The discussions above gave a basic picture about the performance of the air-conditioners in different conditions. An energy performance model is introduced below, which is able to give more precise and direct evaluations of the specific cases.
5. Energy evaluation Energy performance of an air-conditioner can be described by its coefficient of performance ŽCOP., which in a broad sense, is the ratio of the unit cooling capacity to the overall power input. The COP of a split-type unit varies with its operating conditions, in particular, the room air condition and the condenser cooling condition. An air-conditioner performs better at higher room temperature ŽTr . and lower condenser on-coil temperature ŽTo .. At a given room temperature, the COP of a split-type unit can be related to To by COPT r s a y bTo ,
Ž 2.
where a and b are constants. Statistical analysis applying to manufacturing data has shown that when Tr s 258C, COP25 s 5.153 y 0.0738To .
Fig. 5. Computational spaces used to study Ža. T-shaped, and Žb. L-shaped re-entrants, with numerical grids on horizontal plan shown.
L-shaped re-entrants appear to be more affected by the incoming wind. Their maximum temperature points are shifted to the lower portion of the re-entrants. Similar to the no-wind situation, the worst temperature condition appears in the I-shaped, followed by the L-shaped, and then the T-shaped. As one illustration example to visualize the wind effect, Fig. 8 shows the patterns of air temperature contours Žisotherms. at the 20rF Ži.e., two-third of the building height. of the L-shaped re-entrant and at the level where the four condensing units are located. These isotherms are plotted assuming an outdoor temperature of 338C, which is the summer design condition of Hong Kong. Fig. 8Ža. shows the no-wind situation and the steady-wind situation in Fig. 8Žb.. Fig. 9 gives the air velocity profile corresponding to the steady incoming wind situation in Fig. 8Žb.. It can be seen that for the latter, while the vertical velocity component dominates the flow pattern, there is a turn of the incoming wind at a region close to Condenser
Ž 3.
This linear regression was derived from catalogue data of several commercial products, and with a high sample coefficient of determination of 0.991 w5x. It applies well in the range of To from 258C to 458C for single speed units. A condenser on-coil temperature higher than 458C may lead to a trip of the air-conditioner, owing to excessive condenser working pressure. Hence, if the on-coil temperatures of individual condensing units have been determined by CFD simulation, the working conditions of the air-conditioners can be predicted. When To is at 338C, i.e., at the summer design condition, Eq. Ž3. gives a COP value of 2.72. To consider the performance of ‘‘n’’ number of air-conditioning units working together as a group, say those operating inside one single re-entrant, a Condenser Group Performance Indicator ŽCGPI. can be used, which is defined as: CGPI T rŽ Tref . s
100 n
n
Ý is1
½
1y
COPT rŽ To . COPT rŽ Tref .
i
5
.
Ž 4.
This term describes the average percentage drop in COP of all air-conditioners under consideration, with respect to referenced on-coil temperature Tref and room temperature Tr . Tref can be an outdoor temperature arbitrarily assigned w16x.
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Fig. 6. Results of condenser on-coil temperatures of the three re-entrant shapes Žno-wind.: Ža. I-shaped, Žb. L-shaped, Žc. T-shaped.
It can be shown by working with Eqs. Ž3. and Ž4. that for Tr s 258C and Tref s 38C, the corresponding CGPI expression is given by CGPI 25 Ž 33 . s 2.72Tom y 89.76,
formance in the L-shaped re-entrant is closer to the I-shaped re-entrant in the case of no-wind, but closer to the T-shaped re-entrant in the case of steady-wind.
Ž 5.
where Tom is the mean on-coil temperature of all air-conditioners. Table 2 lists the calculated CGPI values based on Eq. Ž5. for the six specific cases in this study. It can be seen that for all three re-entrants that CGPI is lower in the steady-wind than the no-wind conditions. And, independent of the wind conditions, the results of the overall performance assessment of the air-conditioners are consistent — the best appears in the T-shaped re-entrant, and the worst appears in the I-shaped re-entrant. The overall per-
6. Conclusions Going for sustainability is a global trend. Investigations were done on the condenser heat dissipation situations in each of the three different re-entrants, based on the same equipment operation data. While the I-shaped re-entrant represents the convention cruciform building design, the L-shaped and T-shaped represent the new innovative linear building design. The development of a steady-state thermal
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Fig. 7. Results of condenser on-coil temperatures of the three re-entrant shapes Žsteady-wind.: Ža. I-shaped, Žb. L-shaped, Žc. T-shaped.
model made possible the examinations of condenser on-coil temperature conditions via CFD analysis. Further, the use of an energy evaluation model enabled systematic and generalized result comparisons. The derivation of the CGPI allows an assessment of the overall performance; whereby, multiple effects can be monitored by a single parameter. The analysis showed that, with the assumed operating conditions, the energy performance of the split-type airconditioners is the best in the T-shaped re-entrant and the worst in the I-shaped re-entrant. The same conclusion was reached from the studies of both no-wind and steady-wind conditions. Hence, the findings here do not support that these new building design concepts would intensify the
condenser heat dissipation problem, but instead, may improve the situation.
7. Nomenclature a, b C1 , C 2 C3 CD CGPI
constants empirical constant in generationrdestruction term of ´-equation empirical constant in buoyant term of ´-equation empirical constant for eddy viscosity condenser group performance indicator
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Fig. 8. Air temperature contours at 20rF level of L-shaped re-entrant.
COP gi k n
coefficient of performance gravitational constant in X i-direction Žmrs 2 . mean turbulent kinetic energy Žm2rs 2 . number
p qu T
mean static pressure ŽNrm2 . mean volumetric heat source generation rate ŽkWrm3 . temperature Ž8C.
Fig. 9. Air velocity profile at 20rF level of L-shaped re-entrant for the case of steady-wind.
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Table 2 Calculated values of CGPI for the six specific cases
I-shaped L-shaped T-shaped
u Ui
Uj
Xi , X j z
No-wind
Steady-wind
25.5 22.9 14.3
16.5 11.2 9.4
speed Žmrs. mean velocity component in X i-direction Žmrs. mean velocity component in X j-direction Žmrs. distance in cartesian coordinate Žm. height Žm.
Greek letters b volumetric expansion coefficient ŽKy1 . ´ mean dissipation rate of k Žm2rs 3 . u temperature rise above ambient ŽK. k thermal diffusivity Žm2rs. n kinematic molecular viscosity Žm2rs. nt eddy viscosity Žm2rs. P total pressure ŽNrm2 .; P s p q ((2 r k) r 3) r fluid density Žkgrm3 . sk empirical constant of turbulent Prandtl number for k s´ empirical constant of turbulent Prandtl number for ´ su empirical constant of turbulent Prandtl number for u Subscripts m o r ref u
mean on-coil room referenced in u equation
Acknowledgements This research work was financially supported by the Strategic Research Grant of the City University of Hong Kong.
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