Thermal performance of a hollow core concrete floor system for passive cooling

Buildin 9 and Environment, Vol. 23, No. 3, pp. 243-252, 1988. 0360-1323/8853.00+0.00 Printed in Great Britain. © 1988 Pergamon Press plc.

Thermal Performance of a Hollow Core Concrete Floor System for Passive Cooling

R A D U Z M E U R E A N U * P A U L FAZIO*

A preliminary technical study of the thermal performance of a hollow core concrete floor system for passive cooling is presented. Numerical techniques have been used to solve the one- and two- dimensional models of the transient heat transfer throuoh the buildiny components. Computer simulations for a warm and sunny day in Montrbal show that, durin9 occupancy, the hollow core floor system provides thermal comfort without mechanical coolin 9.

c

CLDM ae e

DTsw FE

FSB FSG FSS

h=

h~f

hg

hi ho hR Ic,

IDN IP

IREF

IT ITP

k l

m rh

thl~v

P M V q

QL Q,

QHCS

N O M E N C L A T U R E

specific heat (J kg- ' °C- ' ) total cloud amount characteristic dimension (m) emissivity factor temperature swing of the concrete plate (°C) emissivity factor surface-to-built environment view factor surface-to-ground view factor surface-to-sky view factor convective heat transfer coefficient (W m -2 oc- , ) convective heat transfer coefficient within the hollow core slab (W m 2 °C ~) convective heat transfer coefficient on the inside surface of window (W m -2 °C-i ) film coefficient on interior surface (W m-2 o C-~) film coefficient on exterior surface (W m 2 °C ~) radiative heat transfer coefficient (W m -2 °C ') thermal resistance of clothing (clo) direct normal radiation (W m 2) solar radiation incident on interior surface (W m -2)

solar radiation distributed over the interior surfaces, after the first reflection (W m -2) solar radiation on outside surface (W m -2) solar radiation transmitted through glazing (W m -2)

thermal conductivity (W m -t °C t) width of hollow core slab (m) mass (kg) ventilation air flow rate (kg s ') infiltration air flow rate (kg s- ' ) thermal comfort index heat flow rate (W m -2) power of lighting (W) heat gain due to people and equipment (W) net cooling effect of the hollow core slab (W m 2) fraction of internal heat gain from lighting that is assumed to be convective

* Centre for Building Studies, Concordia University, Montrral, Qurbec, Canada H3G 1M8.

RF1 R W N

S SC SG SR

T t

TDB TG

T1S TMRT

TOS TR TS

U

v

c(

At Ax, Axl,Ayl

q 0 P

pB Pg o"

v

total radiation on horizontal surface (W m 2) ratio between the U value of glazing at night and by day surface area (m 2) shading coefficient glazing area (m 2) sunlit ratio temperature (°C) time (s) outdoor dry-bulb temperature (°C) inside surface temperature of window (°C) inside surface temperature of wall (°C) mean radiant temperature (°C) outside surface temperature of wall (°C) room air temperature (°C) supply air temperature (°C) overall heat transfer coefficient of window between outdoor and indoor air (W m-2 °C-I) velocity (m/s) absorptivity coefficient solar altitude angle (deg.) time increment (s) distance increment (m) thickness (m) efficiency of the air distribution system angle of incidence (deg) density (kg m 3) reflectivity of built environment reflectivity of ground Stephan-Boltzman constant kinematic viscosity of air (m2/s)

1. I N T R O D U C T I O N

O F F I C E buildings consume large quantities of energy for heating and cooling. An analysis of 250 office buildings in the United States and Canada [1, 2] indicates that the annual energy consumption varies between 1000 and 4000 M J / m 2 yr. A recent survey [3] of the office buildings that won awards in the A S H R A E Energy Awards Program, shows that improved design and operation reduced the energy consumption in these buildings to about 700 M J / m 2 yr.

One way of achieving lower energy consumption is to make better use of the thermal storage in the building

B~, 23,3-F 243

244 Radu Z m e u r e a n u and Paul Fazio

Fig. 1. Design alternative using hollow core slab.

mass. Relatively little is known about the effect of the use of thermal mass on the energy consumption in office buildings which differ from houses in size, form, internal loads, control, occupancy profiles and schedules.

The International Energy Agency [4] has started exam- ining the use of passive solar concepts in commercial buildings (retail, office, public and educational), and is developing a handbook with guidelines for incorporating passive solar designs such as atria, daylighting, vertical louvers, special shading devices and passive cooling fea- tures which help to avoid air conditioning.

Some researchers have analyzed the dynamic thermal behaviour of buildings when the convective cooling by nocturnal ventilation was utilized. Givoni [5, 6] analyzed the thermal behaviour of a high mass building ventilated at night, when the outdoor air temperature varied from 19 to 34°C. The building mass, cooled down during the previous night, acted as a heat sink and reduced the cooling load during the daytime. The maximum temperature of the room air during the day, for the space ventilated at night, was 26°C, whereas for the case of the unventilated space it was 28.5°C. Hence, the nocturnal ventilation had reduced the maximum room air temperature by about 15% of the outdoor temperature range. Hoffman et al. [7] simulated the heat storage effect in a concrete building, using the total thermal time constant ( T T T C ) method. The results indicated that the nocturnal ventilation provided annual electricity savings of about 100 kWh/m 2, compared with the conventional design.

Other works report on the increase in the efficiency of the thermal mass when forced air is used.

The Thermo-Deck System (Sweden) and the Ekono- System (Finland) [8, 9] utilize the concrete hollow core slab as air duct and heat storage mass (Fig. 1). During the summer, the concrete slab is cooled at night, and is then used as a heat sink during the day, thus reducing the cooling load. The concrete slab acts as a heat exchanger, reducing the temperature of the outdoor air to be introduced in the room. The system achieves a cooling effect of about 50 W/m 2 at an air flow of 50-100 m3/h for an area of 6 m 2. The refrigeration load is reduced by about 70 percent.

Barnaby et al. [10] used a modified version of the NBSLD program to simulate the thermal behaviour of the hollow core slab in a building of 90,000 m 2 in Sacra- mento. The results indicate that with respect to the conventional design, this system provides energy savings of

about 13% and a 30% reduction of the peak cooling load. Svenberg [11] indicated that the hollow core concrete slabs can store about 1200 kJ/m 2 floor area, while the potential energy storage for a heavy structure with reinforced concrete is about 500 kJ/m 2 floor area. There is no information about the variation in the room air temperature or the slab temperature which led to these values. Block et al. [12] designed a residence in Iowa using a concrete cored slab as a thermal storage mass. He estimated the thermal storage as being 2000-3000 kJ/m 2, based on the assumption of an indoor air temperature of 26°C and a slab temperature of 20"C.

Tamblyn [13] estimated that a hollow core slab is more useful than a flat slab in a 24 hour cycle. His studies indicated that up to a 25% reduction of chiller demand could be obtained with air temperature swings of 3 C during the occupied hours.

Monette [14] analyzed the thermal effect of a composite concrete and steel floor system as a combination of return air plenum and heat storage mass, on the energy requirements of a wood-frame rowhouse. He utilized the TRANSHEAT and HOTCAN programs and obtained annual energy savings of about 6-25%. Allen et al. [15] utilized the ENERPASS program to simulate the effect of a hollow core slab in a low energy passive solar house in Ottawa and obtained energy savings of about 13%.

Birrer [16] designed a six-storey office building in Johannesburg using hollow concrete columns and slabs. The measurements indicated that the floor temperature was between 22 and 23"C and that the cooling load was reduced by about 50 W / m 2 due to the structural storage of heat.

The literature survey indicates, therefore, that important energy savings can be achieved when the building mass is used to cool the building. The use of the hollow core concrete slabs provides a reduction of the cooling load by about 50 W/m ~" and gives energy savings of between 13 and 70%. However, this information is based on metered or simulated energy consumption for a particular building and on weather data, which does not allow the extrapolation of the conclusions to other locations and climatic conditions. Furthermore, the available data do not include such information as the thermal comfort of those people working in offices where the mass such as the hollow core concrete slabs has been cooled.

This paper presents the results of a preliminary technical study on the use of the hollow core slab to reduce the cooling energy requirements of a Montreal office building, while maintaining the thermal comfort within acceptable limits.

A mathematical model of the thermal behaviour of a room with a hollow core concrete floor system is presented. An analysis of the thermal performances of this system is carried out for an office space in Montreal on a warm and sunny day.

2. MATHEMATICAL MODEL

The authors have developed a mathematical model to estimate the hourly variation of the sensible cooling load, the room air temperature and the thermal comfort index for a given configuration of the space and for a particular

Hollow Core Concrete Floor System 245

day. The following thermal processes occurring within the building and between the building and the environment are considered :

(i) transient heat transfer through the building components,

(ii) shortwave solar radiation on exterior and interior surfaces,

(iii) longwave radiation exchange between interior surfaces,

(iv) sensible heat gains from people, lighting and equipment,

(v) air infiltration.

2.1. Heat balance for room air The heat balance equation for the room air includes

terms for the heat transfer through walls and windows, the heat gain/loss due to the supply of air, the convective gain from the lighting, the heat gain/loss due to air infiltration and other gains such as from people or equipment :

Sjhcvj(TlSj- TR) + ~ SGkhg(TGk- TR)

+ qrhc(TS- TR) + rQL + thlNC(TDB- TR) + Q6 = O.

(1)

2.2. Heat transfer through exterior walls The one-dimensional model of the heat transfer

through exterior walls is :

0T k a2T dt pc Ox 2 (2)

which is subjected to the following variable boundary conditions :

(a) on the exterior surface, the heat flow rate has a radiative component due to the solar radiation and a convective component due to the temperature difference between the outdoor air and the wall surface :

07" - k - - = cdT+ho(TDB-- TOS),

dx (3)

(b) on the interior surface, the heat flow rate includes radiation from lights, solar radiation through glazing, radiative heat exchange between interior surfaces and convection between the room air and the interior surfaces :

07" - k - - = aQL + IP~ + IREF

Ox

+ h R ( T M R T - T I S ) + h c ~ ( T R - T I S ) . (4)

The solution of the transient heat transfer equation is obtained using a finite difference technique (Crank- Nicolson's implicit formula), which uses an average of approximations in the j and j + 1 time steps, and is unconditionally stable for all computational time and space increments [17].

a t I hr / / / '

E ~ 27

.g z5

2 3

I I I I I I 0 4 8 12 16 20 24

T ime (hnu r )

Fig. 2. Room temperature variation for different time steps.

-- ~ r~_ I d- (1 +).)T~ +l -- ~ T{+ I

2 = i TL, +(1-~)r~, + 2r~+,

where

(5)

At k (Ax) 2 pc"

A three node model for each layer within the exterior wall is used to define the distance increment Ax.

The selection of the time step At used to analyze the variation in time is subjected to the following constraints :

- - large time step for quick answer, - -smal l time step for high accuracy, --available weather data, which are based on hourly

measurements.

Emery et al. [18] obtained differences of less than 10% when the time step was varied from 1 h to 2 min in calculating the indoor air temperature. The present study (Fig. 2) shows differences of less than 1 °C for the room air temperature when time steps of 1 h and of 15 min are used. Hence, a time step of 1 h is used in the present analysis.

A set of eight simultaneous linear equations is obtained for each exterior wall to calculate the transient heat transfer.

2.3. Lonywave radiation exchange between interior surfaces

The radiant interchange in a room is simulated by the Modified Thermal Balance model [19] in which a fictitious surface is defined as having an area, emissivity and a temperature giving about the same radiant heat transfer as in the real case :

where

qR,(t) = hR,(t)ITMRT(t),- TIS(t)i] (6)

S,,TIS(t-- 1),he m TMRT(t)~ = ,,,,i

Y~ S~e. m # i

hR,(t) = 4FE, a[TMRT(t),] s.

246 Radu Zmeureanu and Paul Fazio

2.4. Shortwave solar radiation on exterior and interior sHr](Ices

The solar radiation on the exterior surfaces of sunlit walls is obtained as the summation of the direct, diffuse and reflected radiation :

-- 1-0 --~ ] IDNcosOSR+

1 CLDM~ ] - - i )tDNsin JFSS+peFSGRF1.

(7)

For shaded surfaces, the total incident solar radiation is:

- - - 10 / IDNpsFSB

[ R F I - ( I C L D M \ I O ] + ) IDNsin f lJFSS. (8)

The solar radiation ITP penetrating through a window is assumed to be uniformly distributed on the interior surfaces

ITP IP . . . . . (9)

Si - SG

and, after the first absorption by the surface, the reflected radiation is assumed to be uniformly distributed on the other interior surfaces. This distributed radiation, which is absorbed entirely by the receiving interior surfaces, is given by :

S, (lO) IREF i -- IP( 1 -- o: i ) ~ Sg -- S /

Hence, the solar radiation striking on the interior surfaces is obtained as a summation of the solar radiation before the first absorption IP and the distributed solar radiation IREF.

The heat balance equation for glazing includes the heat flow between the outdoor air and the inside surface, the convective heat flow between the inside surface and the room air, and the radiative heat flow between the inside surface of the window and the interior surfaces. The increase of the glass temperature due to the solar radiation is neglected :

U*( T D B - TG) = ( T G - TR )hg + ( T G - TMRT)hRu,

(11)

where

1 U ~ ~ . . . . . . . .

1 1

U RWN hi

U* is the overall heat transfer coefficient between the outdoor air and the inside surface of the window. The variable R WN introduces the effect of the night insulating shutters in reducing the U-value of the glazing by night, with respect to the daytime value U.

2.5. Sensible heat gams./?om lights The heat from lighting is split equally into convective

and radiative portions. The former impacts the heat balance of the room while the latter is assumed to be uniformly distributed over the interior surfaces :

0.5 Q aQ, . . 2 )

2.6. Heat transfer through the hollow core slab The heat storing floor slab is to be modeled as shown

in Fig. 3. Since the air temperature must increase or decrease during its passage through the slab, the heat flow within the slab itself has to be modelled in two dimensions, with comparatively large gradients in the y direction and weak gradients in the x direction--that of the air flow.

,3T k (?~2T ~2T~ (13) 8t- - -pC\SX 2 + 8.}'2/"

The Crank-Nicolsons's implicit formula, which is always stable for rectangular fields [17] is used to solve equation (13) :

Tt+ i . , , i --r, ,.- t.j ±ztsl +r , + 1) T,!. + i _ rl T,!+ + t.

- r ~ . 7 ' '+' + 2 ( s , - r , - 1) r~., i--Ti.~+l = rlT~ t.I

+rlTl~ Li+TI.i I+T~.j~f, (14)

where

A y l ) 2 "' = \ A x i / '

Ayl 2 pc S~= At k '

The boundary condition on the nodes +22 to +32 (which describe the temperature of the floor) is given by equation (4). The average temperature of the nodes + 22 to + 32 is used as the temperature of the slab in the heat balance equation (1). The temperature of air entering the hollow core slab is equal to the outdoor air temperature.

The boundary condition on the nodes I to +10 includes the convective heat flow between the concrete surface and the air circulating through the hollow core slab.

The temperature variation of the air circulating through the hollow core slab is determined using the heat balance for the control volume ABCD (Fig. 4).

= m A (Q,+Q, , -Q, I , )d t ~ c d (15)

where

a = :rr~- L ,

Ql = Axl lh,,,,j (T.,i +2 T.,2

rn Oil = ~ cT~,

rn Qm = ~cTi2.

By substitution :

Hollow Core Concrete Floor System 247

I ~ ~l

T S U P L Air f / o w ~

Fig. 3. Schema of hollow core slab.

. . - ~ ~.= . ~ . . . . . . : ,

':: .-,;.~Twz "~;:" O l . ' ' i ' TW~ "~2" "

~" rf, _ A , - ~ A i r ft.ow

Z l x

Fig. 4. Control volume for the heat balance of air within the hollow core slab.

I2h,~fAxll(-Tw'2Tw2 T f l - A) - thcAld t

= mcdA. (16)

In order to simplify the calculations, equation (16) is solved analytically in Appendix B to yield equation (17). This equation defines the temperature variation of the air circulated, and describes in a simple way the boundary condition at the nodes I to + 10.

Tf2 = T f t ( 1 - 2 Q ) + Tw,~+ Tw2Q. (17)

The convective heat transfer coefficient h=f within the hollow core slab is defined using the following formula [20] for forced convection :

Nu = 0.023Re °8 e r T M , (18)

where

Nu - hc~fd~ Re = vde k ' v

By substitution :

and Pr = 0.72.

V 0.8

hcvy = 3.71 dO.2, (19)

where de is the characteristic dimension of an air duct with width l and height b

21b d~ = / + b (20)

A set of 44 simultaneous linear equations is obtained which can be solved to define the heat transfer process within the hollow core slab. This set of equations must be used along with the equations corresponding to the exterior and interior walls, to the windows and to the heat balance of the room air. Thus, the simulation of the thermal behaviour of a room with four exterior walls, four windows and hollow core slabs requires the solution of 81 linear simultaneous equations for each hour.

The initial conditions required for solving the para-

Table I. Fanger's seven point scale of the thermal comfort

PMV Sensation

3 hot 2 warm 1 slightly warm 0 neutral

- 1 slightly cool - 2 cool - 3 cold

bolic type of the partial differential equations are those concerning the temperatures within walls and the room air temperature. Since the temperature history at the beginning of the calculation is unknown, the temperatures are assumed to be equal to 20°C. Then, several identical days are analyzed to eliminate the effect of these initial conditions and only the results for the last day are considered.

2.6. Thermal comfort index The estimation of the thermal comfort is based on

Fanger's model [21], where the Predicted Mean Vote index (PMV) is calculated in terms of activity level, clothing type, air temperature, temperature of inside surfaces, air velocity and relative humidity.

Fanger has correlated physical data with subjective thermal sensation votes, using 1300 Danish and North American subjects in a climatic room, and developed a seven-point scale (Table 1) which is used in the estimation of the thermal comfort. Acceptable thermal comfort environment is expected when the P M V index is between - 0 . 5 and 0.5.

3. NUMERICAL RESULTS

The passive cooling of buildings by circulating outdoor air at night through the space is a common technique. It provides cooled interior surfaces during the day, thus reducing the rise of the air temperature and creating thermal comfort for people. The circulation of the outdoor air both by night and by day through the hollow core slab before it is introduced in the room increases the efficiency of the passive cooling. The purpose of this paper is to evaluate both the increase of the cooling effect due to the circulation of the air through the hollow core slab and the savings with respect to the use of the HVA C system.


Table 2. Weather data in Montreal, 22 July 1979

Dry bulb Solar radiation on temperature Total cloud horizontal plane

Hour ('C) amount (W/m;)

i 18.3 0.2 2 18.3 0.1 3 17.2 0.1 - - 4 16.1 0.2 - - 5 15.0 0.2 6 17.2 0.2 115.0 7 18.3 0.2 272.2 8 20.6 0.1 422.2 9 23.9 0.1 581.4

10 25.6 0.1 706.9 11 26.7 0.2 805.8 12 28.3 0.2 858.1 13 28.9 0.2 810.6 14 29.4 0.2 803.6 15 30.0 0.5 727.8 16 29.4 0.4 605.8 17 28.3 0.4 426.7 18 27.2 0.7 283.6 19 26.7 0.9 50.0 20 24.4 0.6 2.2 21 21.7 0.3 22 23.3 1.0 -- 23 22.8 1.0 24 18.3 0.3

The mathematical models presented in Section 2 have been implemented in the CBS-MASS computer program [22, 23], which has been used in the present analysis.

The simulations have been performed for Montreal, on 22 July 1979 (Table 2), which was a particularly warm and sunny day, with a daily temperature difference of 15"C [24]. The analysis under the climatic conditions of a particular day is the usual procedure for a preliminary evaluation of the thermal behaviour of the passive systems [25-28].

A space 30 x 15 x 3.6 m with three exterior walls, at an intermediate level in an office building has been considered (Table 3). The South wall measures 108 m 2 and the East and the West walls have 54 m 2 each. The glazing- to-wall ratio is 0.5. The hollow core slab has been modeled by two concrete plates of 0.15 m thickness, which bound an air space of 0.05 m, making a total floor- ceiling thickness of 0.35 m and a mass of 690 kg/m 2 floor area.

The ventilation rate corresponds to four air changes per hour during occupancy of the space, and is increased to 12 ac/h between 11:00 p.m. and 7:00 a.m. to cool the building structure.

The following two design alternatives have been compared to evaluate the net cooling effect due to the circulation of the air through the hollow core slab :

(a) The hollow core slab design, where the outdoor air is circulated through the HCS as an air duct before it is introduced in the room; no mechanical cooling is used. Other design alternatives (such as hollow core slabs with no air circulation, or with air circulation but no mixing with room air) have not been included in this analysis since the system must provide the required amount of outdoor air to people during occupancy. One of the advantages of the design alternative which has been considered in the

Table 3. Main characteristics of office space where the Hollow Core Slab design is applied

Exterior wall 0.10 m concrete air cavity 0.10 m insulation 0.01 m gypsum board

glazing-to-wall ratio 0.5 shading coefficient 0.5 window U-value 2.8 W/(m 2 °C)

Interior wall 0.0l m gypsum board 0.02 insulation 0.01 m gypsum board

Air infiltration I ac/h

Occupancy 9:00 a.m. to 5:00 p.m.

Internal heat gains people 10 W/m 2 light 20 W/m 2

Air flow rate during the occupied hours corresponds to 4 ac/h.

3O

~ 2 8 2 6 ~ ~ i o n a t

"" -/1 v \, 2 2 - "-- • \

o o

" O •

18 utdoor air

16 I "~" I I I I I I I I I 3 5 7 9 II 13 15 17 19 21 23

T i m e ( h o u r )

Fig. 5. Comparison between the hollow core slab and the conventional design.

present analysis is that it eliminates the need for installing additional air ducts.

(b) The conventional design using natural cooling, where the outdoor air is introduced in the room through air ducts and it is not circulated through any hollow core slabs; no mechanical cooling system is used.

Figure 5 shows that during occupancy the room air temperature for the hollow core slab design is about 3°C lower than for the conventional design. This is due to the following factors :

(i) The floor and ceiling temperatures are about 2°C lower for the hollow core slab design than for the conventional design (Figs. 6 and 7).

(ii) The hollow core slab acts as a heat exchanger, cooling by day or heating by n ight - - the air which is circulated through it. The higher the ventilation rate at night, the greater the air temperature drop by day (Fig. 8). The maximum temperature difference between the air entering and the air leaving the hollow core slab is between 3°C (ventilation rate corresponding to 4 ac/h, day and night) and 7°C (ventilation rate increased to 12 ac/h at night).

The net cooling effect due to the circulation of the air

H o l l o w C o r e C o n c r e t e F l o o r S y s t e m 249

3 0

28 ~ . . , , ~ . ~ ~.~

\~.~. "--'~_Z;~_~/~ ~ . V \

3 5 7 9 I I 13 1.5 17 19 21 23 Time ( h o u r )

Fig. 6. Thermal behaviour of the hollow core slab design.

~ 2 6

24

o 22

~ 20 I,--

18

2 8

v 2 6

24

E 22

~- 2 0 o o "o c 18

.v. .N

"~-N 4/// ...... ~ ~\.

--\ Room oir/. /

. . . . , 16 I ~ I I I I I I I I I

3 ,5 7 9 I I 13 15 17 19 21 23 Time ( h o u r )

Fig. 7. Thermal behaviour of the conventional design.

8

/ ~ - - - - " ~ \ _ _ 2 4 ach 6 , / .r . . . . . \ X / , / # j "NX

_ e 2 //" / ,

e o / / . . . . \ \ , x l ," / \ / ~'..\.\ r-~

~ -2 r .- ,~IZach \.\,\/.r-? / ./ I - , i

I--- " " ~ . . ~ / ." 0 - 6 "-~" / VentiLation rate at night 4ach ~" "\ \

- 8 --- ' \ , . \ / \

I "'-1': ] I I I I I I I I 3 .5 7 9 I I 13 15 17 19 21 23

Time ( hou r )

Fig. 8. Air temperature drop DTwithin the hollow core slab, as difference between the entering temperature T D B and the leaving

temperature TS.

through the hollow core slab is obtained as the difference between the cooling loads of the design alternatives "a" and "b", keeping the room air temperature at a reference value T R E F . The difference is expressed in Watt per square meter of hollow slabs :

1 t2 O , c s = . - ~ . [vhc( T R c ° N v - T R E F )

( t l - t 2 ) S t,

1 - r h c ( T R n c s - - T R E F ) ] - - -

( t ] - t 2 ) S t 2

× ~ r h c ( T R c ° s V - T R n c s ) (21) t l

I0

2 4 aeh 8

E ",- 7

6 12ach

g 4 5 -- Ventitotion rate at night 4 och

U 2 -

t

O I I 0 .10 0.15 0 . 2 0

Thickness (m)

Fig. 9. Net cooling effect of hollow core slab design vs conventional design.

where

t2--t l is the occupancy duration,

S = Sfloor J r Sceiling,

th is the air flow rate during occupancy.

The net cooling effect for the present case was found to be 5.3 W/m 2. This means that the circulation of the air through the hollow core slab reduces the cooling load of the space during occupancy by 4770 W on the average, in relation to the conventional design. This value is roughly equal to the heat gains obtained from the occupants, or to half of those due to lights. Since these heat gains are significant in an office building, it may be concluded that the circulation of the air through the hollow core slab has a significant effect on the reduction of the cooling load of the space.

The variation of the net cooling effect presented in Fig. 9 shows that the modification of the thickness of the concrete plate has a little effect, while the increase of the ventilation rate at night from 4 ac/h to 24 ac/h increases the net cooling effect, bringing it from 2 W/m 2 to 8 W/m 2.

Figure 10 presents a comparison between the two design alternatives from the point of view of the thermal comfort which provides. For an acceptable standard of comfort, the P M V index should lie between - 0 . 5 and 0.5. It will be seen that the hollow core slab design leads to values between - 0 . 3 and 0.3 so that it appears to give comfort conditions. By contrast, the conventional design leads to P M V values between 0.5 and 1.5; people will feel uncomfortably warm in these conditions. Table 4 shows the effect of other parameters which may affect thermal comfort. They are the ventilation rate by night, the thickness of the concrete slabs and the shading coefficient. It should be noted that thermal comfort can- not be achieved if the ventilation rate is not increased by night. On the other hand, if the ventilation rate at night is increased to 12 ac/h, thermal comfort is achieved for all thickness of the concrete plate, except for the thin plate (0.1 m) and shading coefficient equal to 0.75. Higher ventilation rates and thicker concrete plate should thus be used to obtain thermal comfort during occupancy.

The temperature swing of the median plane (nodes +11 to 21) (Fig. 3) of the concrete plate of 0.15 m thickness varies between 2.8°C (ventilation rate at night 4 ac/h) and 5.0°C (ventilation rate increased to 24 ac/h).


1.41

1.2

1.0

0.8

> 0 . 6

0- 0 . 4

0 , 2

0 . 0

- - 0 . 2

- - 0 , 4

- - 0 , 6

/ \ / / " \

/ \ /" \

/ J C o n v e n t i o n a l \~" / " , , / \

/ \ / \

- - 4 - . . . . -4 /

"- X I A, HCS \ / / / " J . \

\ . / - \ dl

1 ""4 1~" I I I I I I I I 3 5 7 9 I J 13 15 17 19 2~ 2 3

T i m e ( h o u r )

Fig. I0. Thermal comfort index PMV.

Table 4. Variation of the thermal comfort index PMV

Ventilationrate Thickness(m) atnight . . . . . . (ac/h) 0.1 0.15 0.2

4

SC-0.5 0.1 . . . . . 0.8 0.2 . . . . ,0.6 0.1 . . . . . 0.6

12

SC=0 .5 -0 .4 . . . . . 0.4 -0.3 . . . . . 0.3 - 0 . 3 , . . . , 0 . 2 SC=0.75 - 0 . 3 , . . . , 0 . 6 - 0 . 2 , . . . , 0 . 4 -0 .2 . . . . . 0.3

24

SC=0 .5 -0 .7 . . . . . 0.2 -0 .6 , . . . , 0 .1 - 0 . 5 , . . . , 0 SC=0.75 -0 .6 . . . . . 0.3 -0.5 . . . . . 0.2 -0.5 . . . . . 0.1

SC--shading coefficient.

For a concrete plate having a density of 2300 kg/m 3 and a specific heat of 653 J kg ~C, these values lead to a heat storage of 630 kJ/m:, and 1126 kJ/m 2 floor area respectively.

The performance of the passive cooling method applied to a given building depends on meteorological factors such as maximum outdoor temperature, daily variation of the outdoor temperature or solar radiation. A temperature swing of about 15°C in ambient air on a sunny day seems to be effective. However, a smaller temperature swing on a cloudy day can also be effective. As an example, the simulation for 1 July 1979 (CLDM = 0.8, TDBmax = 27.80°C, TDBmin = 23.30°C) in Montr6al shows that the heat storage varies between 405 kJ/m 2 floor area (ventilation rate at night 4 ac/h) and 1255 kJ/m 2 floor area (ventilation rate at night increased at 24 ac/h).

A design alternative using the mechanical cooling to keep the room air temperature at 25 + 1 °C has been simu-

lated in order to estimate the savings due to the use of the hollow core slab design. The air flow rate corresponds to 4 ac/h. The cooling loads of this system represent the savings which can be obtained by the use of the hollow core slab system, since the HCS does not require mechanical cooling to provide the thermal comfort. If the mechanical system operates continuously during the occupied and unoccupied hours, the peak load is 48.4 W/m: (Table 5), and the average cooling load over the occupancy is 39.8 W/m 2. If the system is off during the unoccupied hours, the peak load increases at 51.3 W/m 2, and the average cooling load is 44.2 W/m 2. When free cooling due to the outdoor air is used during thc unoccupied hours, peak load decreases to 40.7 W/m:, and the average cooling load drops to 28.4 W/m 2.

Hence, the use of the hollow core slab design provides savings of 28.4 to 44.2 W/m 2 floor area for the average cooling load in relation to the mechanical cooling system.

Since the present analysis addresses the preliminary technical study of the thermal behaviour of the hollow core slab design, the energy requirements of the fan or the refrigeration equipment, and the capital cost related to the mechanical equipment and the space to install it, have not been taken into consideration.

4. C O N C L U S I O N S

The thermal analysis of the hollow core slab design for that particular sunny and warm day shows the following :

(a) The circulation of the outdoor air through the hollow slab before it is introduced into the space, provides an important reduction of the cooling load with respect to the conventional design. This reduction is equal to the heat gains from the occupants, or to half of those due to the lights.

(b) The hollow core slab design provides thermal comfort during occupancy. The ventilation rate should

be increased at night, from 4 ac/h to 12 ac/h, to cool the structure sufficiently to reduce the cooling loads by day.

(c) The use of the hollow core slab design provides savings of 28.4 to 44.2 W/m 2 floor area for the average cooling load in relation to the mechanical cooling system.

(d) The hollow core slab system should be integrated with a predictive control system to assess the ventilation rate at night based on the forecasting for the next day.

Table 5. Cooling loads of HVAC system

Operation of HVA C system during the unoccupied hours

Daily total Peak load cooling load

(kW) (W/m ~ ) (kWh)

21.8 48.4 201.2 23.1 5[.3 179.1 18.3 40.7 115.0

Continuous operation Shut down Free cooling

Average cooling load over the

occtipancy (kWh) (W/m 2)

161.3 39.8 179.1 44.2 115.0 28.4

Hol low Core Concrete Floor Sys t em 251

REFERENCES

1. A.H. Elmahdy, Recorded Energy Consumption Data on Office Buildings, National Research Council of Canada, Division of Building Research, BRN 182 (1982).

2. J. Syska and A. Hennessy, Energy Conservation in Existing Office Buildings, Phase I, U.S. Energy Research and Development Administration, Contract No. EY-76-C02-2799-0000 (1977).

3. M.A. Piette, L. W. Wall and B. L. Gardiner, Measured performance. ASHRAE J., January (1986). 4. IEA to study use of passive solar in commercial buildings, SOL 50, September~October (1985). 5. B. Givoni, Convective nocturnal cooling. Proc. Second Int. Cong. Building Energy Management,

Iowa State University, Ames, Iowa, U.S.A., 30 May-3 June (1983). 6. B. Givoni, Options and applications of passive cooling. Energy and Build. No. 7 (1984). 7. M. E. Hoffman, M. Gideon, K. Muller and Y. Katz, Ventilation as a means of air-conditioning

power saving in reinforced concrete telephone-exchange buildings--analysis and directions for design. Energy and Build. No. 7 (1984).

8. O. Seppane, Cost effective energy conservation in an office building. Proc. Int. Cong. Povoa de Varzim, Portugal, May (1980).

9. D . J . Croome and B. M. Robert, Air Conditioning and Ventilation of Buildings, 2nd edn, Vol. 1. Pergamon Press, Oxford (1981).

10. Ch. S. Barnaby, D. H. Nall and Ed. Dean, Structural mass cooling in a commercial building using hollow core concrete plank. Proc. National Solar Conf., Amherst, Mass. (1980).

11. S.A. Svenberg, The viability of thermal storage. Energy Technol. Sweden, No. 1 (1982). 12. D .A. Block and L. Hodges, Use of concrete cored slab for passive cooling in an Iowa residence.

Proc. 4th National Passive Solar Conf., Kansas City, October (1979). 13. R.T. Tamblyn, Toward zero energy in buildings. Proc. Int. Cong. Povoa de Varzim, Portugal, May

(1980). 14. M. Monette, Use of a composite concrete and steel floor system as a combination air storage

medium/plenum for enhanced passive solar utilization. Proc. SESCI '84, Calgary, August (1984). 15. G. Allen, M. Kani and St. Carpenter, Mechanically enchanced passive solar thermal storage. Proc.

SESC1 '84, Calgary, August (1984). 16. W.A. Birrer, 'Structural storage as a part of a total system for energy efficient office buildings : two

examples. Proc. First E.C., Conf. Solar Heating, Amsterdam, 30 April-4 May (1984). 17. W.F. Ames, Numerical Methods for Partial Differential Equations. Thomas Nelson, London (1969). 18. A.F . Emery, C. J. Kippenhan, D. R. Heerwagen and G. B. Varey, The simulation of building heat

transfer for passive solar systems. Energy and Build. No. 3 (1981). 19. R. Sullivan, N. Nozaki and O. Cumali, Thermal load and computer simulation run-time comparisons

using a research version of DOE-2. ASHRAE Trans. (1982). 20. M.D. Burghardt, Engineering Thermodynamics With Applications. Harper & Row, New York (1982). 21. P.O. Fanger, Thermal Comfort. McGraw-Hill, New York (1973). 22. P. Fazio and R. Zmeureanu, Research oriented software in building energy analysis. Proc. Canadian

Conf. Industrial Computer Systems, Montreal, 28-30 May (1986). 23. R. Zmeureanu, P. Fazio and F. Haghighat, Analytical and interprogram validation of a building

thermal model. Energy and Build. No. 10 (1987). 24. Documentation of the digital archive of Canadian climatological data (surface) identified by element,

Atmospheric Environment Service, Canadian Climate Centre, Data Management Division, Ontario, April (1985).

25. M.S. Sodha, J. K. Mayak, M. K. Bansal and I. C. Goyal, Thermal performance of a solarium with removable insulation. Build. Environ. 17 (1982).

26. M.M. Bahadori and F. Haghighat, Passive cooling in hot, arid regions in developing countries by employing domed roofs and reducing the temperature of internal surfaces. Build. Environ. 20, No. 2 (1985).

27. M.S. Sodha, S. P. Singh and A. Kumar, Thermal performance of a cool-pool system for passive cooling of a non-conditioned building. Build. Environ. 20, No. 4 (1985).

28. J .K. Nayak, Thermal performance of a water wall. Build. Environ. 22, No. 1 (1987).

APPENDIX A

The effect of different numbers of nodes in the concrete slab on the accuracy of the simulations

In the analysis presented in Section 2.6, the discretization of the concrete slab has been performed using three nodes across the plate. To see the effect of the number of nodes on the room air temperature, a five node model is used in the simulation of the case presented in this paper. The differences in simulating the room air temperature due to the use of the three node model and of the five node model are presented in Table 6. The following observations can be drawn :

(i) During occupancy, when the net cooling effect and the thermal comfort are evaluated, the average difference is about 4%, and the difference in estimating the peak indoor temperature is 0.3°C or 1.1%.

(ii) The three node model yields an average room air temperature of 24.60°C, while the five node model gives 25.6°C, or a difference of 3.9%.

Consequently, the use of the three node model provides results

of acceptable accuracy. Moreover, it requires smaller computer memory and reduces the computing time.

APPENDIX B

Temperature variation of the air circulating through the hollow core slab

The heat balance equation for the control volume ABCD is written as follows :

o r

(16)

dA dt

+Tw2 2h.¢Axl l(Twl 2 - T f l ) -A(rhc+ho, fax l l )

m m e "

(16a)


Table 6. Effect of selecting different numbers of nodes in the concrete slab on the estimation of room air temperature TR (°C)

Difference

Hour 3-nodes 5-nodes :>C %

1 23.8 24.5 0.7 2.9 2 23,4 24.3 0.9 3.7 3 22.8 24.0 1.2 5.0 4 22.1 23.7 1.6 6.8 5 21.4 23.4 2.0 8.5 6 21.2 23.5 2.3 9.8 7 21.2 23.5 2.3 9.8 8 21.8 23.9 2.1 8.8 9 23.7 25.6 1.9 7.4

10 24.3 26.0 1.7 6.5 1 l 24.8 26.3 1.5 5.7 12 25.4 26.7 1.3 4.9 13 25.9 27.0 1.1 4.1 14 26.4 27.3 0.9 3.3 15 27.0 27.6 0.6 2.2 16 27.3 27.8 0.5 1.8 17 27.6 27.9 0.3 1.1 l 8 26.4 26.5 0. l 0.4 19 26.4 26.4 0 0 20 26. l 26.1 0 0 21 25.7 25.8 0.1 0.4 22 25.8 25.9 0.1 0.4 23 25.4 25.7 0.3 1.2 24 24.4 25.1 0.7 2.8

Average 24.6 25.6 1.0 3.9

By integration :

. . . . . . . 7 , . , + ÷ 7 . . . . r,,) { t = e x p - : . (16b)

m c

By further development :

t ' l - a z ( L , + ~w~-2rj,)

' / + (T.~ + T.,2 - 2 T / ~ ) = exp {--(I + Z ) } (16c)

where h.~Axl l

Z ~ . . . . .

ghc

The temperature variation A is thus obtained as :

A = T . , l ~ + T w 2 ~ - 2 T f l ~ (16d) where

A= Ts:- TI,

Z { l - e x p ( - Z i )

Zi = I + Z .

Finally, by substitution, the temperature variation of the air circulated through the hollow core slab is obtained as :

Trz = Ts , ( I -2 f~)+ T,~f~+ T,2~. (17)

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Thermal performance of a hollow core concrete floor system for passive cooling