- Email: [email protected]
A new integrated design tool for naturally ventilated buildings
EI_=|LG't AI'ID
ELSEVIER
UILDIPIGEnergy and Buildings 23 (1996) 231-236
A new integrated design tool for naturally ventilated buildings P.G. Rousseau, E.H. Mathews Centrefor Experimentalarm Numerical Thermoflow(CENT), Departmentof Mechanical and Aeronautical Engineering, Universityof Pretoria, Pretoria 0002, SouthAfrica
Abstract
In many cases natural ventilation may be sufficient to ensure acceptable comfort levels in occupied buildings. In these cases, installation of energy-intensive active environmental control systems will not be necessary. This will result in considerable energy and cost savings and also indirectly in a reduced burden on the environment, since the use of energy is always associated with the production of waste materials. This paper describes the development of a new model to predict natural ventilation flow rates in buildings. The model is based on the concept of a flow network where openings are represented by non-linear flow resistances. It takes into account the effect of both wind-induced pressures and pressures due to thermal ferces. The model draws on a healthy balance between purely theoretical equations and empirical data. The new flow model was linked to an existing thermal model to produce a new integrated design tool for naturally ventilated buildings. It takes into account the important interaction between the flow model and the thermal model and can therefore be used to predict the natural ventilation flow rates as well as the resulting indoor air temperatures. The applicability of the new tool is illustrated through a case study. From this it is clear that the tool can be used successfully to optimize passive building design. The optimized design illustrated here not only resulted in minimum initial cost, but also ;in improved passive thermal comfort in summertime and a reduction in winter heating energy consumption. Keywords: Natural ventilation; Boildings
1. Introduction
Typical buildings where rtatural ventilation may be applied are factories, workshops, farm buildings, schools, residential buildings and even some offices. A major problem encountered in the design of these buildings is that it is difficult to optimize the ventilation de,;ign. The main reason for this is that there is a complicated interaction between the flow rate and the indoor air temperature which is not accounted for in existing design tools [ 1 ]. In the context of buildings the term ventilation usually refers to flow through purpose-provided openings such as open windows and ventilators caused by natural driving forces. This flow is directly influenced by the pressure distribution on the building envelope and the characteristics of the different openings. The pressure distribution is the driving force for ventilation while the characteristics of each opening, among other things, determine the flow resistance. The pressures on the budding envelope consist of windinduced pressures and pressures arising from the difference in temperature between the indoor and outdoor air. Windinduced pressures are dependent on the geometry of the building, the orientation of the building with respect to the wind direction, the wind speed ~tnd the nature of the terrain surrounding the building. 0378-7788/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved
SSDIO378-7788(95)OO948-W
The pressures due to thermal forces arise from the difference in density between the indoor and outdoor air. This socalled 'stack effect' will theoretically only result in flow if there are at least two openings at different heights connected by a flow path inside the building. In practice a very tall single opening will however also allow flow. The top and bottom parts will in effect act as two different openings. The flow resistance, or conversely the permeability, of each opening is determined by a combination of the area of the opening and the so-called discharge coefficient. The discharge coefficient is dependent on the geometry of the opening and can usually only be determined empirically. Wind-induced pressures and pressures due to the stack effect are not simply additive. The combined effect of these two may in one case be to reduce the total flow rate through the building and in another case to increase it. A good natural ventilation design tool should therefore cater for both of these and also combine their effect in the correct manner. Since the flow rate is dependent on the difference in temperature between the indoor and outdoor air, the tool must be able to predict the indoor air temperatures, taking into account all the important thermal characteristics. The indoor air temperature is in turn dependent on the flow rate. An integrated flow and thermal analysis must therefore be possible.
232
P, G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236
2. Ventilation model 2. I. The flow network If one assumes that the static pressure throughout each zone is constant and that all air entering a zone mixes thoroughly with air already inside, any building may be represented by a flow network consisting of nodes coupled by non-linear flow resistances as shown in Fig. 1. Each internal zone in the building is represented by a single internal node while the outdoor air at each opening on the envelope is represented by a boundary value node. Each external node has a specific total external pressure associated with it. Each opening in an internal dividing wall or on the envelope is represented by a non-linear flow resistance between two given pressure nodes. The air flow rate through an opening can be calculated by employing the energy conservation equation in the following way: I
2.2.1. External pressure due to wind The wind-generated pressure at each opening on the envelope is dependent on the position of the opening on a particular facade, the exact geometry of the building, the wind speed, the shape of the atmospheric boundary layer, the orientation of the building with respect to the wind direction, and the shading effect of nearby buildings. Although the pressure may vary from point to point on the facade, the model will make use of a single averaged value for the pressure at all points on each facade. All openings on the same facade will therefore have the same wind-generated external pressure. Although buildings may have very complex geometries we will assume that all buildings can roughly be approximated by rectangular shapes. The effect of the wind speed is taken into account by expressing the external pressures in terms of the non-dimensional pressure coefficient Cp defined as: Cp =Pwind -- Pref
(3)
! 2
where Q is the flow rate, Ca the non-dimensional discharge coefficient, A the area of the opening, p the density of the air and Ap the pressure difference across the opening. In cases where the flow is fully turbulent, which is typically the case for purpose-provided natural ventilation through component openings, the value of n may be taken as 2. By enforcing mass conservation for each node, i.e. ZQ = 0, the flow network may be solved numerically to find the internal pressure in each zone as well as the airflow rate through each opening. 2.2. The total external pressure
where Pref is the reference pressure, which equals the static pressure of the undisturbed airflow and may be taken as equal to the barometric pressure, and Vh the free-stream velocity at roof height. The free-stream wind velocity is in general measured at a single specified reference height above ground level. The relation between the wind velocity at roof height and at reference height is determined by the shape of the atmospheric boundary layer. The shape of the atmospheric boundary layer is influenced by the relative 'roughness' of the terrain surrounding the building and is described by the power law equation: Vh= Vrc~h--h-]°
(4)
'[..href ]
The total external pressure (Po) at each boundary node in the flow network must include both the wind- and stackinduced pressures. Although the wind-induced and stackinduced flow rates are not additive, the external pressure due to wind (P,i,d) and the 'effective' external pressure due to thermal forces ( p ~ ) are additive [2]. Therefore: po=p,i,d + p ~ -
(2) Po2
Pol
I'lode flow resistance
~ PO4
|
pl:~
Fig. 1. Plan view showing flow network for a typical building.
where h is the roof height, hret the reference height and a the so-called velocity profile exponent. A value for a equal to 0.15 represents open fields such as an airport, and a value of 0.4 represents a densely built-up city environment. The orientation of the building with respect to the wind direction is taken into account by using measured values of pressure coefficients at different azimuth angles. The azimuth angle (0) is defined as the angle between the wind direction and the vector perpendicular to the facade and pointing towards the inside of the building as shown in Fig. 2. The values of pressure coefficients used in the model proposed here are based on measurements in boundary layer wind tunnels made by the present authors combined with extensive measured data published by Akins et al. [ 3 ]. Fig. 3 shows the averaged pressure coefficents as a function of azimuth angle for data representing a range of velocity profile exponents varying between 0.12 and 0.38, building side ratios varying between 0.25 and 1 and aspect ratios varying between 1 and8.
P.G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236
233
2.2.2. E x t e r n a l p r e s s u r e d u e to t h e r m a l f o r c e s
The appropriate equation for P t h ~ can be derived by considering the case where no wind is present but where a difference in temperature exists between the indoor and outaoor air. By employing the ideal gas law to relate the pressure and density of air and by assuming that the difference between the indoor static pressure and the outdoor static pressure is small, the effective external pressure due to thermal forces can be calculated as
Wind dlredlon
F a c ~ d e vector
P ~ , ~ = 0.0342 y p ' f (To - Ti)
/',To
Fig. 2. Definition of the azimuth angle (0). 0.6
•
0.4
)
• 0.2
)
~
~ ............... i
;. . . . . . . .
:
where y is the height of the opening above ground level and T, and To the indoor and outdoor air temperatures, respectively. Eq. (8) will hold true for cases where To> Ti as well as where To < Ti.
•
•
. . . . . . . . . . . . . . i:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E
&
!
................. i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> o
i
(8)
-0.2
............
3. Implementation
mm
•
i ...............
!. . . . .
i .............
C,
i ...................
,, -0.4
•
•
•
• -0.6
,
0
, 60
• 120
=
.......• . . .m. . . . . . .
•
m ~ 180
•
. . . . .
i
? • • 240
300
3fi0
8o
Fig. 3. Averaged facade pressure coefficient as a function of azimuth angle; • = measurements.
The values of Cp for 0 < 90 ° and 0> 270 ° are given by: C v = 0.5994 - 0.1426abs(sinO) - 0 . 8 0 5 5 a b s ( s i n 0) 2 + 2 . 0 1 4 9 a b s ( s i n O ) 3 _. 2 . 1 9 7 2 a b s ( s i n O ) 4
(5)
and for 90 ° < 0 < 270 ° by: Cp = - 0 . 3 3 3 0 0 - O. 1 5 4 4 a b s ( sin 0)
-0.1128abs(sinO) 2
(6)
The pressure coefficient due to wind on the roof of a building is a function of the roof angle and varies across the surface of the roof. The pressure coefficient at all openings, including ventilators, situated on any roof will however be taken as - 1.0.
Soliman [4] investigated the shading effect of nearby buildings. Measurements of the pressure difference over any two faces of the building at different angles of attack were taken for different grouping densities and boundary layer profiles. The grouping density D is defined as the percentage of the total surface area in the immediate surroundings of the building covered by other buildings. From these data it was found that the effect of nearby buildings can be taken into account by multiplying Cp by a factor/3 where: 1
/3 = eO.OSn
(7)
The ventilation model was integrated with the building thermal analysis proposed by Mathews et al. [ 5 ]. The thermal model is based on an electrical analogue design-day calculation procedure and has been implemented in a user-friendly design tool that allows the analysis of a single zone at a time. It includes inter alia the modelling of hourly varying interior convective, radiative and latent loads, direct solar gains taking into account external shading devices and building orientation, multi-layered walls, roofs and high-mass floors either suspended or in ground contact. Given the building geometry and hourly values for climatic temperature, humidity and radiation as well as hourly values for internal loads, the model can be used to predict the resultant hourly indoor air temperatures or to calculate air-conditioning loads for a specified indoor air temperature. The thermal model has been verified successfully for a wide variety of passive buildings. The loads due to air introduced into the zone are also taken into account given the flow rates and the supply air temperatures for each hour. In the case of an air-conditioning system the temperatures and flow rates can be specified. In the case of natural ventilation or infiltration, the supply air temperature would be equal to the specified outdoor air temperatures. The flow rates must be calculated using the appropriate flow model. To provide for the interaction between the thermal and flow models an iterative solution algorithm is employed. The calculation is initiated by guessing values for the indoor air temperatures. These indoor temperatures together with the specified outdoor air temperatures are used as input to the flow model which is then solved for the flow rates. These flow rates are used as input to the thermal model which in turn predicts the indoor air temperatures. This process is repeated until convergence.
2.34
P.G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236 North and south view
West and east view
4. C a s e s t u d y
Fig. 4. Schematic representation of the factory building designed in the case study. 42 38 ~34 ©30
-22 18 14
;
4
8
12
,
16
20
24
hour
Fig. 5. Outdoor air temperatures ) and predicted indoor air temperatures (lq) with no ventilation or insulation provided. 42 38 ~34
$26
$22 I
18 14 0
i 4
~ 8
i 12 hour
i 16
i 20
24
Fig. 6. Outdoor air temperatures ( ) and predicted indoor air temperatures (I-1) with 50 mm thick insulation provided underneath the roof.
42 38 ~34 ® 30'
~26' E $ 22 18 ! 14 ,4 0
4
8
12
' 16
2'o
24
ho~r
Fig. 7. Outdoor air temperatures ( ) and predicted indoor air temperatures (Iq) with no insulation and roof ventilators equal to 10% of the floor area provided.
The building studied here is a factory shown schematically in Fig. 4. The factory is constructed of sheet metal and has a floor area of 1250 m 2 and an internal volume of 18 750 m 3. It contains high interior mass and a total interior load of 100 kW due to machines. The building is occupied by 20 people between 07:00 h and 18:00 h. It has windows along the side of the north and south walls with a total openable area of 150 m 2. The roof may be fitted with ventilators but at this stage the exact geometry is not known. The factory is situated in the East London area in the Cape Province of South Africa. In South Africa the main thermal problem in such a factory is encountered in summertime when outdoor air temperatures are high. For the purpose of the demonstration a windless summer design day will be used. The first simulation carried out with the new tool is the case where no insulation is provided and only unintentional infiltration is allowed. As expected the results given in Fig. 5 show that the indoor air temperature will rise very high during the day with a maximum of almost 42 °C. Two of the most important measures employed in a factory like this to enhance thermal comfort are insulation and natural ventilation. In order to optimize the design the aim will be to minimize the initial cost of the building for the best possible degree of thermal comfort inside. In this respect it is important to note that the capital cost of both insulation and roof ventilators are directly proportional to the area covered. A number of questions should be addressed during the design stage, namely: (i) Will it be worthwhile to spend money on roof insulation? (ii) Will it be worthwhile to spend money on roof ventilators? (iii) Could a combination of insulation and roof ventilators not be used to provide the best solution? (iv) If so, how much money should be spent to provide the optimum amount of ventilation? To investigate the effect of insulation Fig. 6 shows the resultant temperatures for the case where a mineral wool blanket of 50 mm thickness is attached to the bottom of the corrugated iron roof. It is clear that the maximum indoor air temperature is drastically reduced to around 34 °C. It is important to realize that the effect of the roof insulation is mainly to reduce the load induced by radiation on the outside of the roof. The effect of internal loads is however not addressed. As opposed to insulation, ventilation aids in removing internal loads caused by heat generation from the zone. As shown earlier the effectiveness of the ventilation is influenced by the total permeability of the building which is in turn determined by the total discharge area of the ventilation openings. The area of roof ventilators used in a factory such as this is usually expressed as a percentage of the floor area and 10% is usually regarded as an upper limit. To illustrate the effect of ventilation, Fig. 7 shows the predicted
P.G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236
235
ventilators cannot be closed in winter the smaller than usual ventilators will also aid heat retention. The combined effect of these measures will therefore be to reduce winter heating energy consumption. ......................
i .........
i ........
5. Conclusions
E 28
26
~
i
o
2
i
,~
6 flo~
8
~o
oreo
Fig. 8. Predicted maximum indoor air temperatures with 50 mm roof insulation and different roof ventilators expressed as a percentage of the floor area; [] = with insulation.
indoor air temperatures for the factory with no insulation but with roof ventilators with a discharge area equal to 10% of the floor area. The windows are only open during the daytime. The effect of ventilation on the indoor air temperature is even more drastic than that caused by the addition of insulation. The indoor air temperature is reduced from 42 °C to just below 31 °C. The slight increase in temperature at 19:00 h is interesting. It is caused by the stored energy in the building structure and high internal mass and floors which is radiated into the zone even after the occupants have left the building. Remember that the windows are closed after 17:00 h and the loads due to the stored energy are not removed instantly. The effects of insulation and ventilation have up to now been investigated separately. However, the most cost-effective solution could perhal:s be obtained by combining these two. By using a combination insulation and natural ventilation the effect of external radiation on the roof and the removal of internal loads can be addressed simultaneously. The implication of such a strategy on the initial cost of the building must however be considered. To investigate this, simulations were conducted with 50 mm of roof insulation installed together with different sizes of roof ventilator. Fig. 8 presents the results of thi:~ investigation and shows the predicted maximum indoor air temperature versus the roof ventilator area expressed as a percentage of the floor area. As shown in the figure the combination of insulation and ventilation results in much lower temperatures. Maximum temperatures of below 30"C can be achieved. Note the reduction in the relative effectiveness of the ventilators with increased area. Further addition of ventilator areas beyond 4% of the floor area represents improvements of less than 1% on the maximum indoor air temperature. It is therefore possible to fund all or part of the cost of the insulation from money saved by installing less roof ventilators, i.e. 4% instead of 10%. The fact that less roof ventilators are installed together with insulation will of course also have a beneficial effect in the winter. In wintertime internal loads aid in heating the building. Insulation will diminish the heat loss. In the case where
A new ventilation model is proposed that makes use of a healthy balance between empirical data and theoretical equations. The model accounts for the layout of the building, the permeability of openings, the height of different openings above ground level, the wind speed and direction, the difference in temperature between the indoor and outdoor air as well as the effect of the surrounding terrain in which the building is situated. The integration of the new ventilation model into an integrated design tool is also discussed. The design tool provides for the analysis of typical single-zone buildings and uses an iterative solution algorithm in which the thermal and flow models are solved in turn until convergence is obtained. In the case study the complex interaction between the thermal and flow models were illustrated by investigating the combined effect of natural ventilation and roof insulation. The effectiveness of roof ventilator area is reduced gradually with the addition of more area. This means that the optimum amount of ventilator area for each specific design should always be investigated. The highest degree of thermal comfort was obtained with a combination of roof insulation and ventilation. By minimizing the ventilator area the cost of the insulation can be partially or totally funded from the savings in the cost of ventilation devices. The optimized design not only resulted in minimum initial cost, but also in improved passive thermal comfort in summertime and a reduction in winter heating energy consumption.
6. List of symbols A Cd Cp D h p Q T V y
area of opening (m 2) non-dimensional discharge coefficient non-dimensional pressure coefficient grouping density (%) height above ground level (m) pressure (Pa) flow rate (m3/s) temperature (K) velocity ( m / s ) height of opening above ground level (m)
Greek letters a 0 p
non-dimensional velocity profile exponent azimuth angle (°) density ( k g / m 3)
Acknowledgements Financial assistance for this project was given by the following institutions: South African Department of Mineral and
236
P.G. Rousseau. E.H. Mathews / Energy and Buildings 23 (1996) 231-236
Energy Affairs: Energy Branch, University of Pretoria and TEMM International (Pty) Ltd.
References [ 1] E.H. Mathews and P.G. Rousseau, A new integrated design tool for naturally ventilated buildings Part 1: Ventilation model, Build. Environ., 29 (1994) 461-471.
[2] F.W. Sinden, Wind, temperature and natural ventilation theoretical considerations, Energ. Build., 1 (1978) 275-280. [3] R.E. Akins, J.A. Peterka and J.E. Cermak, Averaged pressure coefficients for rectangular buildings, Proc. 5th. Int. Conf. on Wind Engineering, Fort Collins, USA, 1979. [4] B.F. Soliman, The Effect of Building Grouping on Wind lnduced Natural Ventilation, Department of Building Science, University of Sheffield, 1973. [5] E.H. Mathews and P.G. Richards, An efficient tool for future building design, Build. Environ., 28 (1993) 409--417. -
ELSEVIER
UILDIPIGEnergy and Buildings 23 (1996) 231-236
A new integrated design tool for naturally ventilated buildings P.G. Rousseau, E.H. Mathews Centrefor Experimentalarm Numerical Thermoflow(CENT), Departmentof Mechanical and Aeronautical Engineering, Universityof Pretoria, Pretoria 0002, SouthAfrica
Abstract
In many cases natural ventilation may be sufficient to ensure acceptable comfort levels in occupied buildings. In these cases, installation of energy-intensive active environmental control systems will not be necessary. This will result in considerable energy and cost savings and also indirectly in a reduced burden on the environment, since the use of energy is always associated with the production of waste materials. This paper describes the development of a new model to predict natural ventilation flow rates in buildings. The model is based on the concept of a flow network where openings are represented by non-linear flow resistances. It takes into account the effect of both wind-induced pressures and pressures due to thermal ferces. The model draws on a healthy balance between purely theoretical equations and empirical data. The new flow model was linked to an existing thermal model to produce a new integrated design tool for naturally ventilated buildings. It takes into account the important interaction between the flow model and the thermal model and can therefore be used to predict the natural ventilation flow rates as well as the resulting indoor air temperatures. The applicability of the new tool is illustrated through a case study. From this it is clear that the tool can be used successfully to optimize passive building design. The optimized design illustrated here not only resulted in minimum initial cost, but also ;in improved passive thermal comfort in summertime and a reduction in winter heating energy consumption. Keywords: Natural ventilation; Boildings
1. Introduction
Typical buildings where rtatural ventilation may be applied are factories, workshops, farm buildings, schools, residential buildings and even some offices. A major problem encountered in the design of these buildings is that it is difficult to optimize the ventilation de,;ign. The main reason for this is that there is a complicated interaction between the flow rate and the indoor air temperature which is not accounted for in existing design tools [ 1 ]. In the context of buildings the term ventilation usually refers to flow through purpose-provided openings such as open windows and ventilators caused by natural driving forces. This flow is directly influenced by the pressure distribution on the building envelope and the characteristics of the different openings. The pressure distribution is the driving force for ventilation while the characteristics of each opening, among other things, determine the flow resistance. The pressures on the budding envelope consist of windinduced pressures and pressures arising from the difference in temperature between the indoor and outdoor air. Windinduced pressures are dependent on the geometry of the building, the orientation of the building with respect to the wind direction, the wind speed ~tnd the nature of the terrain surrounding the building. 0378-7788/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved
SSDIO378-7788(95)OO948-W
The pressures due to thermal forces arise from the difference in density between the indoor and outdoor air. This socalled 'stack effect' will theoretically only result in flow if there are at least two openings at different heights connected by a flow path inside the building. In practice a very tall single opening will however also allow flow. The top and bottom parts will in effect act as two different openings. The flow resistance, or conversely the permeability, of each opening is determined by a combination of the area of the opening and the so-called discharge coefficient. The discharge coefficient is dependent on the geometry of the opening and can usually only be determined empirically. Wind-induced pressures and pressures due to the stack effect are not simply additive. The combined effect of these two may in one case be to reduce the total flow rate through the building and in another case to increase it. A good natural ventilation design tool should therefore cater for both of these and also combine their effect in the correct manner. Since the flow rate is dependent on the difference in temperature between the indoor and outdoor air, the tool must be able to predict the indoor air temperatures, taking into account all the important thermal characteristics. The indoor air temperature is in turn dependent on the flow rate. An integrated flow and thermal analysis must therefore be possible.
232
P, G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236
2. Ventilation model 2. I. The flow network If one assumes that the static pressure throughout each zone is constant and that all air entering a zone mixes thoroughly with air already inside, any building may be represented by a flow network consisting of nodes coupled by non-linear flow resistances as shown in Fig. 1. Each internal zone in the building is represented by a single internal node while the outdoor air at each opening on the envelope is represented by a boundary value node. Each external node has a specific total external pressure associated with it. Each opening in an internal dividing wall or on the envelope is represented by a non-linear flow resistance between two given pressure nodes. The air flow rate through an opening can be calculated by employing the energy conservation equation in the following way: I
2.2.1. External pressure due to wind The wind-generated pressure at each opening on the envelope is dependent on the position of the opening on a particular facade, the exact geometry of the building, the wind speed, the shape of the atmospheric boundary layer, the orientation of the building with respect to the wind direction, and the shading effect of nearby buildings. Although the pressure may vary from point to point on the facade, the model will make use of a single averaged value for the pressure at all points on each facade. All openings on the same facade will therefore have the same wind-generated external pressure. Although buildings may have very complex geometries we will assume that all buildings can roughly be approximated by rectangular shapes. The effect of the wind speed is taken into account by expressing the external pressures in terms of the non-dimensional pressure coefficient Cp defined as: Cp =Pwind -- Pref
(3)
! 2
where Q is the flow rate, Ca the non-dimensional discharge coefficient, A the area of the opening, p the density of the air and Ap the pressure difference across the opening. In cases where the flow is fully turbulent, which is typically the case for purpose-provided natural ventilation through component openings, the value of n may be taken as 2. By enforcing mass conservation for each node, i.e. ZQ = 0, the flow network may be solved numerically to find the internal pressure in each zone as well as the airflow rate through each opening. 2.2. The total external pressure
where Pref is the reference pressure, which equals the static pressure of the undisturbed airflow and may be taken as equal to the barometric pressure, and Vh the free-stream velocity at roof height. The free-stream wind velocity is in general measured at a single specified reference height above ground level. The relation between the wind velocity at roof height and at reference height is determined by the shape of the atmospheric boundary layer. The shape of the atmospheric boundary layer is influenced by the relative 'roughness' of the terrain surrounding the building and is described by the power law equation: Vh= Vrc~h--h-]°
(4)
'[..href ]
The total external pressure (Po) at each boundary node in the flow network must include both the wind- and stackinduced pressures. Although the wind-induced and stackinduced flow rates are not additive, the external pressure due to wind (P,i,d) and the 'effective' external pressure due to thermal forces ( p ~ ) are additive [2]. Therefore: po=p,i,d + p ~ -
(2) Po2
Pol
I'lode flow resistance
~ PO4
|
pl:~
Fig. 1. Plan view showing flow network for a typical building.
where h is the roof height, hret the reference height and a the so-called velocity profile exponent. A value for a equal to 0.15 represents open fields such as an airport, and a value of 0.4 represents a densely built-up city environment. The orientation of the building with respect to the wind direction is taken into account by using measured values of pressure coefficients at different azimuth angles. The azimuth angle (0) is defined as the angle between the wind direction and the vector perpendicular to the facade and pointing towards the inside of the building as shown in Fig. 2. The values of pressure coefficients used in the model proposed here are based on measurements in boundary layer wind tunnels made by the present authors combined with extensive measured data published by Akins et al. [ 3 ]. Fig. 3 shows the averaged pressure coefficents as a function of azimuth angle for data representing a range of velocity profile exponents varying between 0.12 and 0.38, building side ratios varying between 0.25 and 1 and aspect ratios varying between 1 and8.
P.G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236
233
2.2.2. E x t e r n a l p r e s s u r e d u e to t h e r m a l f o r c e s
The appropriate equation for P t h ~ can be derived by considering the case where no wind is present but where a difference in temperature exists between the indoor and outaoor air. By employing the ideal gas law to relate the pressure and density of air and by assuming that the difference between the indoor static pressure and the outdoor static pressure is small, the effective external pressure due to thermal forces can be calculated as
Wind dlredlon
F a c ~ d e vector
P ~ , ~ = 0.0342 y p ' f (To - Ti)
/',To
Fig. 2. Definition of the azimuth angle (0). 0.6
•
0.4
)
• 0.2
)
~
~ ............... i
;. . . . . . . .
:
where y is the height of the opening above ground level and T, and To the indoor and outdoor air temperatures, respectively. Eq. (8) will hold true for cases where To> Ti as well as where To < Ti.
•
•
. . . . . . . . . . . . . . i:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E
&
!
................. i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> o
i
(8)
-0.2
............
3. Implementation
mm
•
i ...............
!. . . . .
i .............
C,
i ...................
,, -0.4
•
•
•
• -0.6
,
0
, 60
• 120
=
.......• . . .m. . . . . . .
•
m ~ 180
•
. . . . .
i
? • • 240
300
3fi0
8o
Fig. 3. Averaged facade pressure coefficient as a function of azimuth angle; • = measurements.
The values of Cp for 0 < 90 ° and 0> 270 ° are given by: C v = 0.5994 - 0.1426abs(sinO) - 0 . 8 0 5 5 a b s ( s i n 0) 2 + 2 . 0 1 4 9 a b s ( s i n O ) 3 _. 2 . 1 9 7 2 a b s ( s i n O ) 4
(5)
and for 90 ° < 0 < 270 ° by: Cp = - 0 . 3 3 3 0 0 - O. 1 5 4 4 a b s ( sin 0)
-0.1128abs(sinO) 2
(6)
The pressure coefficient due to wind on the roof of a building is a function of the roof angle and varies across the surface of the roof. The pressure coefficient at all openings, including ventilators, situated on any roof will however be taken as - 1.0.
Soliman [4] investigated the shading effect of nearby buildings. Measurements of the pressure difference over any two faces of the building at different angles of attack were taken for different grouping densities and boundary layer profiles. The grouping density D is defined as the percentage of the total surface area in the immediate surroundings of the building covered by other buildings. From these data it was found that the effect of nearby buildings can be taken into account by multiplying Cp by a factor/3 where: 1
/3 = eO.OSn
(7)
The ventilation model was integrated with the building thermal analysis proposed by Mathews et al. [ 5 ]. The thermal model is based on an electrical analogue design-day calculation procedure and has been implemented in a user-friendly design tool that allows the analysis of a single zone at a time. It includes inter alia the modelling of hourly varying interior convective, radiative and latent loads, direct solar gains taking into account external shading devices and building orientation, multi-layered walls, roofs and high-mass floors either suspended or in ground contact. Given the building geometry and hourly values for climatic temperature, humidity and radiation as well as hourly values for internal loads, the model can be used to predict the resultant hourly indoor air temperatures or to calculate air-conditioning loads for a specified indoor air temperature. The thermal model has been verified successfully for a wide variety of passive buildings. The loads due to air introduced into the zone are also taken into account given the flow rates and the supply air temperatures for each hour. In the case of an air-conditioning system the temperatures and flow rates can be specified. In the case of natural ventilation or infiltration, the supply air temperature would be equal to the specified outdoor air temperatures. The flow rates must be calculated using the appropriate flow model. To provide for the interaction between the thermal and flow models an iterative solution algorithm is employed. The calculation is initiated by guessing values for the indoor air temperatures. These indoor temperatures together with the specified outdoor air temperatures are used as input to the flow model which is then solved for the flow rates. These flow rates are used as input to the thermal model which in turn predicts the indoor air temperatures. This process is repeated until convergence.
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P.G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236 North and south view
West and east view
4. C a s e s t u d y
Fig. 4. Schematic representation of the factory building designed in the case study. 42 38 ~34 ©30
-22 18 14
;
4
8
12
,
16
20
24
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Fig. 5. Outdoor air temperatures ) and predicted indoor air temperatures (lq) with no ventilation or insulation provided. 42 38 ~34
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~ 8
i 12 hour
i 16
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Fig. 6. Outdoor air temperatures ( ) and predicted indoor air temperatures (I-1) with 50 mm thick insulation provided underneath the roof.
42 38 ~34 ® 30'
~26' E $ 22 18 ! 14 ,4 0
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Fig. 7. Outdoor air temperatures ( ) and predicted indoor air temperatures (Iq) with no insulation and roof ventilators equal to 10% of the floor area provided.
The building studied here is a factory shown schematically in Fig. 4. The factory is constructed of sheet metal and has a floor area of 1250 m 2 and an internal volume of 18 750 m 3. It contains high interior mass and a total interior load of 100 kW due to machines. The building is occupied by 20 people between 07:00 h and 18:00 h. It has windows along the side of the north and south walls with a total openable area of 150 m 2. The roof may be fitted with ventilators but at this stage the exact geometry is not known. The factory is situated in the East London area in the Cape Province of South Africa. In South Africa the main thermal problem in such a factory is encountered in summertime when outdoor air temperatures are high. For the purpose of the demonstration a windless summer design day will be used. The first simulation carried out with the new tool is the case where no insulation is provided and only unintentional infiltration is allowed. As expected the results given in Fig. 5 show that the indoor air temperature will rise very high during the day with a maximum of almost 42 °C. Two of the most important measures employed in a factory like this to enhance thermal comfort are insulation and natural ventilation. In order to optimize the design the aim will be to minimize the initial cost of the building for the best possible degree of thermal comfort inside. In this respect it is important to note that the capital cost of both insulation and roof ventilators are directly proportional to the area covered. A number of questions should be addressed during the design stage, namely: (i) Will it be worthwhile to spend money on roof insulation? (ii) Will it be worthwhile to spend money on roof ventilators? (iii) Could a combination of insulation and roof ventilators not be used to provide the best solution? (iv) If so, how much money should be spent to provide the optimum amount of ventilation? To investigate the effect of insulation Fig. 6 shows the resultant temperatures for the case where a mineral wool blanket of 50 mm thickness is attached to the bottom of the corrugated iron roof. It is clear that the maximum indoor air temperature is drastically reduced to around 34 °C. It is important to realize that the effect of the roof insulation is mainly to reduce the load induced by radiation on the outside of the roof. The effect of internal loads is however not addressed. As opposed to insulation, ventilation aids in removing internal loads caused by heat generation from the zone. As shown earlier the effectiveness of the ventilation is influenced by the total permeability of the building which is in turn determined by the total discharge area of the ventilation openings. The area of roof ventilators used in a factory such as this is usually expressed as a percentage of the floor area and 10% is usually regarded as an upper limit. To illustrate the effect of ventilation, Fig. 7 shows the predicted
P.G. Rousseau, E.H. Mathews / Energy and Buildings 23 (1996) 231-236
235
ventilators cannot be closed in winter the smaller than usual ventilators will also aid heat retention. The combined effect of these measures will therefore be to reduce winter heating energy consumption. ......................
i .........
i ........
5. Conclusions
E 28
26
~
i
o
2
i
,~
6 flo~
8
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Fig. 8. Predicted maximum indoor air temperatures with 50 mm roof insulation and different roof ventilators expressed as a percentage of the floor area; [] = with insulation.
indoor air temperatures for the factory with no insulation but with roof ventilators with a discharge area equal to 10% of the floor area. The windows are only open during the daytime. The effect of ventilation on the indoor air temperature is even more drastic than that caused by the addition of insulation. The indoor air temperature is reduced from 42 °C to just below 31 °C. The slight increase in temperature at 19:00 h is interesting. It is caused by the stored energy in the building structure and high internal mass and floors which is radiated into the zone even after the occupants have left the building. Remember that the windows are closed after 17:00 h and the loads due to the stored energy are not removed instantly. The effects of insulation and ventilation have up to now been investigated separately. However, the most cost-effective solution could perhal:s be obtained by combining these two. By using a combination insulation and natural ventilation the effect of external radiation on the roof and the removal of internal loads can be addressed simultaneously. The implication of such a strategy on the initial cost of the building must however be considered. To investigate this, simulations were conducted with 50 mm of roof insulation installed together with different sizes of roof ventilator. Fig. 8 presents the results of thi:~ investigation and shows the predicted maximum indoor air temperature versus the roof ventilator area expressed as a percentage of the floor area. As shown in the figure the combination of insulation and ventilation results in much lower temperatures. Maximum temperatures of below 30"C can be achieved. Note the reduction in the relative effectiveness of the ventilators with increased area. Further addition of ventilator areas beyond 4% of the floor area represents improvements of less than 1% on the maximum indoor air temperature. It is therefore possible to fund all or part of the cost of the insulation from money saved by installing less roof ventilators, i.e. 4% instead of 10%. The fact that less roof ventilators are installed together with insulation will of course also have a beneficial effect in the winter. In wintertime internal loads aid in heating the building. Insulation will diminish the heat loss. In the case where
A new ventilation model is proposed that makes use of a healthy balance between empirical data and theoretical equations. The model accounts for the layout of the building, the permeability of openings, the height of different openings above ground level, the wind speed and direction, the difference in temperature between the indoor and outdoor air as well as the effect of the surrounding terrain in which the building is situated. The integration of the new ventilation model into an integrated design tool is also discussed. The design tool provides for the analysis of typical single-zone buildings and uses an iterative solution algorithm in which the thermal and flow models are solved in turn until convergence is obtained. In the case study the complex interaction between the thermal and flow models were illustrated by investigating the combined effect of natural ventilation and roof insulation. The effectiveness of roof ventilator area is reduced gradually with the addition of more area. This means that the optimum amount of ventilator area for each specific design should always be investigated. The highest degree of thermal comfort was obtained with a combination of roof insulation and ventilation. By minimizing the ventilator area the cost of the insulation can be partially or totally funded from the savings in the cost of ventilation devices. The optimized design not only resulted in minimum initial cost, but also in improved passive thermal comfort in summertime and a reduction in winter heating energy consumption.
6. List of symbols A Cd Cp D h p Q T V y
area of opening (m 2) non-dimensional discharge coefficient non-dimensional pressure coefficient grouping density (%) height above ground level (m) pressure (Pa) flow rate (m3/s) temperature (K) velocity ( m / s ) height of opening above ground level (m)
Greek letters a 0 p
non-dimensional velocity profile exponent azimuth angle (°) density ( k g / m 3)
Acknowledgements Financial assistance for this project was given by the following institutions: South African Department of Mineral and
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P.G. Rousseau. E.H. Mathews / Energy and Buildings 23 (1996) 231-236
Energy Affairs: Energy Branch, University of Pretoria and TEMM International (Pty) Ltd.
References [ 1] E.H. Mathews and P.G. Rousseau, A new integrated design tool for naturally ventilated buildings Part 1: Ventilation model, Build. Environ., 29 (1994) 461-471.
[2] F.W. Sinden, Wind, temperature and natural ventilation theoretical considerations, Energ. Build., 1 (1978) 275-280. [3] R.E. Akins, J.A. Peterka and J.E. Cermak, Averaged pressure coefficients for rectangular buildings, Proc. 5th. Int. Conf. on Wind Engineering, Fort Collins, USA, 1979. [4] B.F. Soliman, The Effect of Building Grouping on Wind lnduced Natural Ventilation, Department of Building Science, University of Sheffield, 1973. [5] E.H. Mathews and P.G. Richards, An efficient tool for future building design, Build. Environ., 28 (1993) 409--417. -