A simplified overall thermal transfer value equation for building envelopes

EnergyVol. 13, No. 8, Pp. 657-670,1988 Printedin Great Britain. All rightsreserved

0360-5442/88$3.00+ 0.00 Copyright0 1988Pergamon Press plc

A SIMPLIFIED OVERALL THERMAL TRANSFER VALUE EQUATION FOR BUILDING ENVELOPES S. K. CHout and Y. K. LEE Department of Mechanical & Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511 (Received 20 July 1987; received for publication 26 April 1988)

Abstract-We describe a methodology for determining a simplified overall thermal transfer value (OTI’V) equation for air-conditioned buildings in Singapore. The OTTV equation was formulated by modelling a generic commercial building and using results from DOE-2 computer simulations as a database of heat gains. The new equation increases the weight of the solar heat gain as compared to the currently used OTTY equation. This change yields an improved relation between the O’TTV and the total heat gain through the building envelope

INTRODUCTION

Since 1979, under the Singapore building control regulations,’ a design parameter for building envelopes known as the overall thermal transfer value (O’ITV)2 has been adopted as a mandatory standard. The OlTV requirement, which applies only to air-conditioned buildings, is aimed at achieving adequately designed building envelopes so as to cut down external heat gains and hence reduce the cooling load of air-conditioning systems. The OTTV concept takes into consideration the basic modes of heat gains through the external walls of a building, namely, heat conduction through opaque walls and glass windows, and solar radiation through glass windows. The building control regulations stipulate that all air-conditioned buildings must be designed to have an OTTV below 45 W/m2. For Singapore, the OTTV definition and design calculation methodology are contained in a handbook3 published in 1979 by the Development and Building Control Division, Public Works Department, to assist engineers and architects in meeting the design requirements. In 1985, a study4 conducted at the Lawrence Berkeley Laboratory using input data for Singapore revealed that the total cooling energy use of a building having the same OTTV can vary by as much as 35% for different parametric simulations using the DOE-2 computer program. Furthermore, it was found that the existing OTTV equation (given in Ref. 3 and described in the next section) does not properly account for the relative contributions of the different heat gain components through the building envelope. The study then recommended that the OTI’V equation be redefined to correlate the cooling energy use better with the OTTV of a building. This approach has resulted in the reformulation of the OTTV equation containing only the component of radiation transmitted through windows. The basis of the approach is the aim of correlating the O’ITV only with the cooling energy use of a building. Consequently, by using only the radiative component, better regression of results can be obtained. In this study, we extend the investigations to look first into the influence of building orientation and aspect ratio on energy performance. A generic multi-storey commercial building is modelled and the DOE-2.1A computer program is used as the simulation tool. The OTTV for various building orientations and aspect ratios are calculated using the present OTTV equation given in Ref. 3. Pairs of the OTTV and ‘simulated annual cooling energy-consumption data are examined to check the adequacy of the present OTTV a methodology for obtaining a revised OTTV equation is formulation. Subsequently, attempted, with the objective of correlating the OTTV with the total heat gain through the t To whom all correspondence

should be addressed.

S. K. CHOU and Y. K.

658

LEE

building envelope while retaining the three basic components of the OTTV equation. Also, the new equation will provide a more direct estimation of the annual cooling load due to the heat gain through a building envelope.

METHODOLOGY

The OTTV The OTTV formulation takes into account the following three basic heat-gain components through the external walls of a building: (i) heat conduction through opaque walls, (ii) heat conduction through glass windows, and (iii) solar radiation through glass windows. The OTTV equation for an external wall is given as

OTT&*”

xU,xTD,,)+(A,xU,xAT)+(A,xSCxSF) >

A0

(1)

where A0 = A,,, + Af. Since walls at different orientations receive different amounts of solar radiation, it is necessary, in general, to compute first the OTTVs of individual walls. The OTI’V of the whole building envelope is then obtained by taking the weighted average of these values. To calculate the OTTV for the envelope of a building having n walls, the following formula is used: oTTV=

Aol x OTTV1 + Ao2 x OTTVz + . * . + A,,,, X OTTV,,

(4

Aol+Am+*--+Ao,,

For a square building with four identical walls, Eq. (2) reduces to Ol-IV = TD,, (1 - WWR)(U,)

+ AT(WWR)(U,) + [Afl x SF1 + Aa x SF2 + An x SF3 + 4, *,,I + A,2 + 43

Equation

x SF,](SC)

c3j

+ *w

(3) may be further reduced to O’ITV = TD,,(l

- WWR)(Q,)

+ [(*,,)(SF)(CF,

+ AT(WWR)(Q)

+ CFz + CF3 + CF,)(SC)]I%,

(4)

since Afl = A= = AB = Af4, Aol = A, = Ao3 = Aw, and SF, = SF x CF,, where the solar correction factor CF takes into account the orientation of the facade and the pitch angle of the fenestration component. A set of solar-correction factors, extracted from Ref. 3, is listed in Table 1. The correction factors for other orientations and pitch angles may be found by interpolation. It is seen that, for vertical walls of a square building, the sum of the correction factors for the four orientations is very close to 4. As an illustration, in the case of a square building that has its four walls facing North, East, South, and West, the sum of the correction factors is 0.72 + 1.25 + 0.74 + 1.25 = 3.96. Hence, Eq. (4) may be further simplified to OTTV = TD,,(l - WWR)(U,)

+ AT(WWR)(CJ,) + SF(WWR)(SC).

(5)

Table 1. Solar correction factors for wall.

N

NE

E

SE

s

SW

70”

1.32

1.63

1.89

1.65

1.32

1.65

75O

1.17

1.48

1.75

1.50

1.18

80’

1.03

1.33

1.59

1.35

1.04

85’

0.87

1.17

1.42

1.19

9o”

0.72

1.00

1.25

1.02

W

NW

1.89

1.63

1.50

1.75

1.48

1.35

1.59

1.33

0.89

1.19

1.42

1.17

0.74

1.02

1.25

1.00

659

OTTV equation for building envelopes

To comply with mandatory regulations in Singapore, the authors of Ref. 3 recommend that, for a wall mass per unit area ~195 kg/m2, TD,, = 10, AT = 5, and SF = 130. Hence, for such a square building, OTTV = lO(1 - WWR)( U,,,) + S(WWR)( U,) + 130(WWR)(SC).

(6)

Equation (6) has been in use in Singapore since 1979. It has been found that, in the design or retrofitting of a building envelope, a reduction in the OTTV is not indicative of a corresponding reduction in the annual cooling energy use. Furthermore, it was reported in Ref. 4 that Eq. (6) gives far too much weight to heat conduction through opaque walls and glazings, and underestimates the contribution of solar gains through fenestrations. This procedure led to the use of a single term in redefining the OTIV as OTTV = 215 (WWR)(SC).

(7)

In this study, ?he original form of the OTTV equation [Eq. (5)] has been retained. Values of TD,, 7 AT, and SF are obtained by determining, through computer simulations, the actual contributions to the envelope heat gain due to the three heat-gain components. Thus, this methodology revises the OTTV equation to better reflect the total heat gain through a building envelope under local weather conditions. Also, it provides the advantage of retaining the flexibility of designing to account for heat conduction through opaque walls and glazings. The OTTV may be considered as the average heat transfer rate through the building envelope. In this study, we divide the annual heat gain per unit area of the building envelope by the total operating hours of the air-conditioning system. This has the effect of averaging the loads accumulated during non-operating hours over the operating hours of the air-conditioning system. Thus, the normalized OTTV is larger than the average value based on 8760 h in a year. Thus, the OTTV may be expressed as OlTV

=

total heat gain through envelope (total operating hours) x (envelope

area) ’

(8)

For a generic office building in Singapore, the number of hours of operation is 2816 annually based on 5.5 working days /week. To reflect the actual contributions due to the three heat-gain components, the following relations may be written: T&,(1

wall heat conduction gain - WWR) U., = OTTV total heat gain through the envelope ’

AT(WWR)G= OTTV SF(WWR)SC = OTTV Reference-building

glass heat conduction

(9)

gain

total heat gain through the envelope ’

(10)

solar radiation gain total heat gain through the envelope ’

(11)

description

A 7-storey reference office building has been modelled for simulation. Construction characteristics and operating schedules of the reference building are given in Tables 2 and 3, respectively. The elevation and plan of the building are shown in Fig. 1. The building has a total conditioned area of 3675 m2. On each floor, it has a central unconditioned zone of 100 m2 which is assumed to be thermally insulated from the core area. The floor-to-floor height of the building is 3.05 m and the window-to-wall ratio is 0.44. The lighting power density is 20 W/m* in occupied areas and 80% of the heat from lights is assumed to enter the conditioned space. The air-conditioning system uses variable air volume with an inlet guide-vane controlled fan having a minimum airflow rate ratio of 0.5. A hermetic centrifugal chiller with a coefficient of performance of 4.5 is used in the model to provide chilled water to the air handling units. The fan operating schedule is the inverse of the infiltration schedule as the building is treated as being pressurized when the fans are in operation. When the fans were not operating, however,

660

S. K. CHOU

and Y. K. LEE

Table 2. Reference building description. BUILDING TYPE Multi-storey office building, 3675 m* air-conditioned area

MATERIALS Walls External:

25 cm concrete, 1.9 cm air layers, 028 cm spandrel glass on exterior, Total R = 0.458 m *K/W

Internal:

1.59 cm gypsum board, 10 cm air layer, 1.59 cm gypsum board, Total R = 0.475 ,2-K/W

Roof 1.27 cm roof gravel, 0.95 cm built up roofing, R5 polystyrene insulation, 15.2 cm concrete, lo22 cm air layer, 1.3 cm acoustic tile, Total R = 1.585 •I *K/W Floors 15.2 cm concrete floors, Total R = 0.236 m*.K/W

SOLAR ABSORPTIVITY Walls Roof

: :

0.45 0.30

WINDOWS AND LIGHTING Window-to-wall ratio Shading coefficient Glass-conductance No window setback Lighting power Infiltration

= = =

0.44 0.30 3.2 w/m* *K (double glazing)

= =

Heat-of-light to space ratio

=

20.4 W/m* in occupied areas 0.6 air changes per hour when fans are off 0.8

SYSTEMS Outside air Cooling setpoint Night setback Economizer Chiller COP

= = = = -

7 cfmlperson 25'C 37°C None 4.5

the infiltration is taken to be 0.6 air changes/h. The above specifications for the airconditioning system, plant and internal loads are meant only for the purpose of comparing the cooling energy use due to the change in the OTTV. Computer simulations

The DOE-2.1A computer program5 has been used in this study to generate an energy database for use in Eqs. (8)-(11). The program accepts input data such as the building description, operating schedules, secondary systems and primary plant equipment. DOE-2 simulations can yield information on energy consumption, load contributions, interior space conditions, plant operating hours and part-load operation of equipment. In this study, DOE-2 preprogrammed libraries are used to specify the air-conditioning system, control strategies and building materials with associated thermal properties.

OTTV equation for building envelopes Table 3. Reference building schedules. Monday

HOW

l-5 6 7 a 9-12 13 14-17 18 19 20 21 22 23 24

to

Friday Fans

Inf

OCC

Light

Cool

1 1 1 0 0 0 0 1 1 1 1 1 1 1

0 0 0 0.20 0.95 0.50 0.95 0.30 0.10 0.10 0.10 0.10 0.05 0.05

0.05 0.10 0.10 0.30 0.90 0.80 0.90 0.50 0.30 0.30 0.20 0.20 0.10 0.05

37 37 37 25 25 25 25 37 37 37 37 37 37 37

0 0 0 1 1 1 1 0 0 0 0 0 0 0

37 37 37 25 25 37 37 37 37

0 0 0 1 1 0 0 0 0

37 37 37

0 0 0

Saturday l-5 6 7 a 9-12 13-17 la 19 20-24

1 1 1 0 0 1 1 1 1

0 0 0 0.10 0.90 0.10 0.05 0.05 0

0.05 0.05 0.10 0.10 0.90 0.15 0.05 0.05 0.05 Sunday

l-6 l-18 19-24

1 1 1

0 0.05 0

0.05 0.10 0.05

For Occ (Occupancy) and Light (Lighting) schedules, 0 denotes absence of occupant or switching-off of all lights, 1 denotes presence of all occupants or switching-on of all available lights. Fraction denotes the fraction of all occupants that are present or fraction of available lights that are switched on. For Inf (Infiltration) and Fans schedules, 0 denotes no infiltration or fan is not in operation and 1 denotes presence of infiltration or fan is in operation. Cool denotes the cooling temperature set-point in “C.

,

25m

ELEVATION PLAN Fig. 1. Elevation and plan of reference building.

I

S. K. CHOU and Y. K. LEE

662

Climatic data The tropical oceanic climate of Singapore is characterized by the lack of seasonal variations in temperature and relative humidity. Diurnal changes of the dry-bulb temperature are small with mean daily maximum and minimum values of approx. 31°C (65% r.h.) and 24°C (95% r.h.), respectively. No heating is required and, owing to high relative humidity ratios, the latent heat extraction from outside air is significant. In the simulations, the Singapore climatic data for the year 1979 are used. The DOE-2 weather tape contains hourly data on dry-bulb and wet-bulb temperatures, wind velocity, and measured direct and diffuse solar radiation. RESULTS

AND

DISCUSSION

Base case performance The annual energy use of the reference building is 456.8 MWh and its total cooling load is 716.5 MWh. The components of the energy use and cooling load are given in Tables 4 and 5, respectively. Since miscellaneous equipment has not been specified, the energy used by pumps and fans are attributable to the cooling system, which includes chillers and cooling towers. Typically, the energy consumption due to miscellaneous equipment varies from 5 to 15% of the total. Building orientation and aspect ratio With respect to the reference commercial building, three rectangular buildings having aspect ratios of 4.1, 2.62, and 1.82 have been studied. These three buildings have the same construction characteristics and operating schedules as those of the reference commercial building except for the total building envelope area. Similarly, the internal loads, such as for lighting and occupancy, have been given the same values as those of the reference commercial building. In the simulations, only the orientation of the buildings is varied. Their OTTVs are calculated by using Eqs. (1) and (2), and the methodology given in Ref. 3. For each orientation, all building parameters except the OTTV are kept constant and the energy performance of the building is simulated. The relationship between annual cooling energy

Table 4. Annual energy use (MWh). components

Energy

Use

Percentage

Lights

211.3

46.3

Cooling

161.6

35.4

83.9

18.3

456.8

100.0

Fans,

Pumps

Total

Table 5. Annual cooling load (MWh). Components

Cooling

Load

Percentage

Solar

182. I

25.4

Lights

166.3

23.2

Infiltration

133.1

18.6

Occupants

117.7

16.4

Walls

55.7

7.8

Glass

35.3

4.9

Others

26.3

3.7

716.5

100.0

Total

OTTV equation for building envelopes

663

215

37

38

39

LO

42

OTTV

Fig. 2. Cooling energy variation with OTTV.

consumption predicted by DOE-2 and the OTTV are then compared. Figure 2 shows the relationship between the annual cooling energy consumption and the OTTV. The buildings are orientated from the North-South to the East-West direction based on the surface azimuth of the broader front. As the O’ITV is intended to represent the total heat gain through the building envelope, and when other loads are kept constant in the simulations, the annual cooling energy consumption is expected to increase with increasing OTTV. It may be observed that the annual cooling energy consumption does not always increase with increasing O’ITV. This suggests that the OTIV equation does not properly account for the total heat gain through the building envelope. Hence, we establish the need to revise the existing OTTV equation. Revision of OTTV equation In all simulations, four heat-transfer parameters of the building envelope have been varied. The four parameters are: window-to-wall ratio (WWR), shading coefficient of fenestration (SC), and window and wall U-values (Uf and I!&,). The following ranges of values have been used: WWR, 0.20-0.95; SC, 0.16-0.95; U,, 0.20-4.21 W/m*K; and Uw, 1.49-2.44 W/m’K. The total number of hours of operation of the building and the envelope area have been kept constant at 2816 h and 2135 m2, respectively, in the simulations. Using the database of heat-gain components with Eqs. (8)-(ll), values of OTTV, TD,,, AT, and SF have been calculated for the cases shown in Table 6. As heat gains eventually appear as loads, the correlation of the OTTV with heat gains is achieved through the use of annual loads. The heat-gain components are extracted from the DOE-2 loads summary report as heat-load components summed over an entire year. The heat-load components account for the conduction gain through walls, conduction gain through windows and radiation gain through windows during operating and non-operating hours of the building. For the purpose of comparison, the OTIVs calculated using the present standard3 have been included. Inspection shows that TD,, and SF have values which are approximately constant. However, AT varies between 4.52 and 5.38. By rounding off the values, we obtain TD,, = 11 and SF = 230. The corresponding average value of AT is 4.8. Hence, the revised OTTV equation for a square building may be expressed as OTTV = ll(1

- WWR)U,,, + 4.8(WWR)U, + 230(WWR)(SC).

(12)

It should be noted that the above procedure can readily be employed for walls of different construction and mass. It can be seen that Eq. (12) provides an increase in the weight of the solar heat gain component relative to the conductive heat-gain components across the windows and opaque walls.

Table

C-continued OTTV

cases

(froo Eq. 8

SF

AT

TDeq

OTTV (Ref. 3)

WWR = 0.40 "f = 1.29

SC = 0.50 "W = 2.24

63.2

230.0

4.92

11.0

42.0

WWR = 0.50 "f = 1.52

SC = 0.40 UW - 2.44

62.9

229.9

4.87

11.0

42.0

WWR = 0.60 "f = 4.21

SC = 0.30 "W = 1.49

57.8

229.6

4.64

11.1

42.0

WR Uf

= 0.70 = 2.44

SC = 0.30 "W = 2.06

62.4

230.0

4.74

11.0

42.0

WWR = 0.80 "f = 2.88

SC = 0.25 Uw = 2.24

60.4

229.8

4.66

10.9

42.0

WWR = 0.90 "f = 2.29

SC J 0.25 Uw = 2.44

63.2

230.0

4.69

10.9

42.0

WWR = 0.95 "f = 3.49

SC - 0.20 "W = 1.49

57.6

2X9.5

4.58

10.8

42.0

WWR = 0.85 "f = 1.29

SC = 0.30 "W = 2.24

67.3

230.1

4.80

10.8

42.0

WWR = 0.44 "f = 3.20

SC - 0.47 "W - 2.44

68.6

229.9

4.95

10.9

47.6

WWR = 0.50 "f = 3.06

SC = 0.50 "W = 1.49

72.4

230.2

4.89

11.1

47.6

WWR = 0.52 Uf = 3.40

SC - 0.40 "W = 2.44

68.1

230.2

4.78

11.0

47.6

WWR - 0.60 "f - 3.80

SC - 0.35 "W = 2.24

67.4

230.1

4.69

11.1

47.6

WWR = 0.65 "f = 1.84

SC - 0.40 "W = 2.24

73.9

230.2

4.88

11.0

47.6

WWR - 0.80 "f = 3.80

SC - 0.27 "W = 2.24

66.7

230.1

4.64

11.0

47.6

!JWR = 0.90 "f = 4.00

SC = 0.23 uw = 2.44

64.2

229.8

4.57

10.8

47.6

WWR = 0.70 "f = 4.00

SC = 0.32 uw = 1.49

67.6

230.0

4.69

11.0

47.6

WWR = 0.50 "f = 2.46

SC = 0.45 "W = 2.44

70.6

230.0

4.90

11.0

47.6

WWR = 0.55 "f = 2.14

SC = 0.43 Uw = 2.44

71.8

230.1

5.36

11.1

47.6

WWR = 0.55 "f = 2.91

SC = 0.46 "W = 1.49

72.6

230.4

4.86

11.0

47.6

r

Table

7. OTTO

cases

[Eq. (6)] and heat gain correlation. Annual total gain rhrough en" oPe (X 10YI kWh)

9: increase in total gain through envelope

S. K. CHOU and Y. K. LEE

666 Table

8. OTTV

[Eq. (1211 and beat gain correlation. Annual total gain through en” oPe 9 (x 10 kWh)

CaSeS Reference

total

through

273.1

case

10% increase

in

OTTV

298.9

15% increase

in

OTTV

313.5

25% increase

in

OTTV

339.2

352

in OTTV

366.9

increase

in

gain

:,“:: 1

This has resulted in an increase in the OTI’V of between 40 and 60% over that calculated by following the present standard. In an attempt to test the revised OTTV equation, further simulations have been performed to enable the comparison between the percentage increase in OTTV and the corresponding percentage increase in total heat gain through the building envelope. The OTIVs calculated using Eqs. (6) and (12) are tabulated in Tables 7 and 8, respectively. Upon inspection of Table 7, it can be seen that, by using Eq. (6), the percentage increase in the OTIV does not correspond to the percentage increase in the total heat gain through the building envelope. Comparison between Tables 7 and 8 shows that, for the various cases studied, the percentage increase in total heat gain through the envelope is almost equal to the percentage increase in OTW calculated by the revised OTT’V equation. In other words, the revised equation is better able to correlate the OTIV and the total heat gain through the building envelope. Additionally, the cooling energy consumption of the building has been predicted for various OTTVs calculated by Eq. (12). This result is shown in Fig. 3. It can be seen that better correlation between the annual cooling energy consumption and the OTTV is obtained. It should be noted that this improvement in correlation is secondary compared to the primary objective of correlating the OTIV with the total heat gain through the building envelope. Moreover, the correlation of heat gains or cooling loads with the cooling energy use is greatly dependent on the specifications of the air-conditioning system, plant and control strategy used. Thus, this study does not attempt to correlate the OTTV with cooling energy use. In a further attempt to validate the revised O’ITV equation, DOE-2 simulations have been made on rectangular buildings having aspect ratios of 4.1, 2.62, and 1.82. This is intended to show that although the revised OTW equation has been formulated from simulations on a square building, the equation is equally applicable to rectangular buildings. The buildings are 215

1

0 AS =LlO AS = 262 . AS r 182

d 2

210

-

205

-

3 "': ;

u

5

L5 0

45 5

460

L65

L70

L75

OTTV

Fig. 3. Cooling

energy variation

with O’ITV.

LB0

OTTV equation for building envelopes Table 9. Comparison of OlTVs.

T

I

parameters

Building

(8)

(2) AS

T o-(2)

OnvAV

by Eq.

by Eq. (17) (3)

x

100x

(2)

= 4.1, AN - 152.5

AE = 37.21 WWRN=mE=0.44

42.0

41.2

- 1.9

43.2

42.5

- 1.6

43.9

43.7

- 0.5

63.6

61.4

- 3.5

65.5

63.6

- 2.9

66.6

65.8

- 0.5

76.5

74.4

- 2.7

SC = 0.30, IJf - 3.2 "W = 1.49

A5 = 2.62, AN = 121.7 AE = 46.4 WWRN = WWRE = 0.44 SC = 0.30, Uf = 3.2 IJw = 1.49

AS = 1.82, AN = 101.3 A E = 55.8 WWQ=

WWRE = 0.44

SC = 0.30, IJf = 3.2 uw = 1.49

AS = 4.1, AN = 152.5 A E = 37.21 mN

= WWRE = 0.65

SC = 0.35, Uf = 3.2 Uw = 2.058

AS = 2.62, AN - 121.7 AE - 46.4 MN

- WWRE - 0.65

SC = 0.35, Uf - 3.2 "W = 2.058

AS = 1.82,

AN -101.3

AE * 55.8 WWRN = WWRE - 0.65 SC - 0.35, Uf - 3.2 uw = 2.058

AS = 4.1, AN = 152.5 AE = 37.21 WWRN = WWRE = 0.70 SC = 0.40, Uf = 4.0 "W = 2.237

conrinuedoverleaf

S. K. CHOU and Y. K. LEE

668 Table

9-continued

T Building

parameters

AS = 2.62,

OTTVAV by Eq. (8) (2)

by Eq. (17) (3)

(3)-(2) x (2)

100%

AN = 121.7

AE = 46.4 WWRN= WWRE = 0.70 SC = 0.40, UW = 2.237

AS = 1.82, AE -

u

-

78.9

77.0

-

2.4

80.1

79.7

-

0.5

49.5

50.8

+ 2.6

40.7

49.5

+ 1.6

4.0

f

AN = 101.3

55.8

WwRN = WwRE = 0.70 SC = 0.40,

Uf = 4.0

“W = 2.237

AS = 4.1,

AN = 37.21

AE = 152.5 WWRN= WWRB= 0.44 SC = 0.30,

Uf = 3.2

“W = 1.49

AS = 2.62,

AN = 46.4

AE = 121.7 WWRN= WWRg = 0.44 SC = 0.30,

uf = 3.2

“W = 1.49

AS = 1.82,

AN = 55.8

AE = 101.3 Ww$

47.5

= WwRE = 0.44

SC = 0.30,

uf

+ 1.7

40.3

= 3.2

uw = 1.49

conveniently orientated such that their four vertical walls face the North, East, South, and West. In order to apply Eq. (12) to a rectangular building, the following equations are used for each side of the building: OTTVN = ll(1 - WWR,)Uw

+ 4.8(WWR,)U,

+ 230 x CFN(WWRN)SC,

(13)

OTTVE = ll(1 - WWR,)Uw

+ 4.8(WWR&

+ 230 x CFE(WWRE)SC,

(14)

OTIVs = ll(1 - WWR,)Uw + 4.8(WWRs)U, + 230 x CFs(WWRs)SC, OTIVw = ll(1 - WWR,)Uw

(15)

+ 4.8(WWRw)U, + 230 x CFw(WWRw)SC;

(16)

the average OTI’V is written as OlTVA”

=

A,(O’ITVN)

+ AE(OTTV~) + As(O’=Vs) A,+A,+As+Aw

+ -%v(OI--IVw)

,

(17)

where the subscripts N, E, S, and W represent North, East, South, and West, respectively. Also, AE = Aw, AN = As, WWRN = WWRs and WWRE = WWRw.

669

OTTV equation for building envelopes Table 10. O’ITV [Eq. (18)] and heat gain correlation. Annual total gain through en" ape (x 10'J'kWh)

X increase in total gain through envelope

In each case, two values of the OTTV are calculated. One value is calculated by applying Eq. (8) and the other by using Eqs. (13)-(17). The values are tabulated in Table 9. It can be seen that the differences are within f 4% for all the cases considered. Also, differences are larger for buildings with larger aspect ratios. A final comparison is made between the OTTV equation formulated by the present study and the one recommended in Ref. 4, which reported on a study conducted under the ASEAN-US Energy Project supported by the U.S. Agency for International Development. This comparison is based on the commercial building shown in Fig. 1. In Ref. 4, Turiel et al have recommended that the OTTV equation for an external wall be redefined by a single term taking into account only the radiative component of the heat gain as OlTV=215xWWRxSC.

(18)

Using data obtained from DOE-2 simulations and Eq. (18), the percentage increase in OTTV and the corresponding percentage increase in total heat gain through the building envelope have been calculated and presented in Table 10. It can be seen that, by using Eq. (18), the percentage increase in the simulated total heat gain through the envelope is less than the corresponding percentage increase in the OTTV. That is, Eq. (18) tends to overemphasize any corrective measure to achieve a reduction in the heat gain through the envelope by a reduction in the OTI’V. This result contrasts (see Table 7) with the use of Eq. (6), which tends to underestimate the effects of conservation measures applied to building envelope design. Comparing values in Tables 8 and 10, we may conclude that Eq. (12) provides a better correlation for the heat gain than Eq. (18). It should be noted, however, that Eq. (18) is obtained by a regression of the cooling energy use. Thus, it is not intended to present the proportional contributions of the envelope heat gain components. In order to understand the contributions of the three heat-gain components better, the total gain through the building envelope has been subdivided and presented in Table 11. It may be seen that the two conductive heat-gain components (through walls and windows) contribute about 30% of the total heat gain through the building envelope. Thus, their contributions appear too large to be disregarded.

Table 11. OTIV [Eq. (18)] and heat gain components. heat gain (x IO3 kh'h)

Cases

solar radiation (1)

glass conductance (2)

wall conductance (3)

(2)+(3) (1)+(2)+(3)

10% increase in OTTV

198.6

36.2

54.7

0.31

15% increase in OTTV

207.0

40.1

49.7

0.30

25% increase in OTTV

227.8

47.9

39.7

0.28

35% increase in OTTV

241.1

21.7

74.7

0.29

S. K.

670

CHOU and Y.

K.

LEE

CONCLUSION

It has been shown that the O’ITV equation presently used in Singapore is inadequate in correlating the total heat gain through a building envelope. For the purpose of upgrading existing building energy conservation standards in Singapore, a more accurate formulation of the OTTV equation has been attempted. The methodology adopted applies the definition of the OTTV and makes use of computer simulation results to obtain the three basic heat-gain components of the equation. The revised equation [Eq. (12)] is applicable to most buildings and has been tested against the existing equation [Eq. (6)] and the one recommended in Ref. 4 [Eq. (l&3)]. Results show that the revised equation gives the best correlation between the OTTV and the total heat gain through a building envelope. The equation is found applicable to buildings having an aspect ratio from 1.0 to 4.1. For other classes of buildings, types of construction or locations, the methodology can readily be applied to obtain the OTIV equation. Furthermore, the methodology ensures that the equation obtained by applying the OTTV definition [Eq. (S)] directly gives a more accurate estimate of the total heat gain through a building envelope.

REFERENCES 1. “Building Control Regulations, 1979,” Development and Building Control Division, Ministry of National Development, Singapore 0106, Singapore (1979). 2. “Energy Conservation for New Building Design,” ASHRAE Standard 90-75, American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Atlanta, GA 30329 (1975). 3. “Handbook on Energy Conservation in Buildings and Building Services,” Development and Building Control Division, Ministry of National Development, Singapore 0106, Singapore (1979). 4. I. Turiel, R. Curtis, and M. D. Levine, Energy 10,95 (1985). 5. “DOE-2 Reference Manual,” Parts 1 and 2 (Version 2.1), U.S. Department of Commerce, National Technical Information Service, Springfield, VA 22161 (1980).

NOMENCLATURE Af = Area of fenestration

(m’)

A w = Area of opaque wall (m*) A0 = Gross area of exterior wall (m’)

AS = Aspect ratio of building CF = Solar correction factor O’ITV = Overall thermal transfer value (W/m’) OTTV,, = Average overall thermal transfer value (W/m’) SC = Shading coefficient of fenestration

SF = Solar factor (W/m”) TD,, = Equivalent temperature difference (K) AT = Temperature difference of outdoor and indoor conditions (K) U, = Thermal transmittance of fenestration (W/m’K) U, = Thermal transmittance of opaque wall (W/m2K) WWR = Window-to-wall ratio