Thermal performance of a water wall

Buildin 9 and Environment, Vol. 22, No. 1, pp. 83-90, 1987.

0360-1323/87 $3.00+0.00 ~') 1987 Pergamon Journals Ltd.

Printed in Great Britain.

Thermal Performance of a Water Wall J. K. N A Y A K * A comparison of the thermal performance of various types of south facin# water walls has been made in terms of the heat flux entering an air-conditioned space throuyh these walls. Numerical calculations for climatic conditions at Srinaoar (India) show that the Transwall is more effective than the Drum water wall to meet the daytime heating load. But, a Drum water wall is better from the points of view of load levelliny and day-and-niyht performance.

extinction coefficient of water for solar radiation available between the (j)th and ( j - 1)th wavelength region, m- i

NOMENCLATURE dl thickness of first water column, m d2 thickness of second water column, m Eb emissive power of blackbody source, W/m 2 h0 outside heat loss coefficient, W / m 2 °C h l heat transfer coefficient from first water column to semitransparent material, W / m 2 °C h2 heat transfer coefficient from semitransparent material to second water column, W/m 2 °C h3 heat transfer coefficient from wall to living space, W/m 2 °C heat transfer coefficient from outer surface of Drum hwl wall to water, W/m 2 °C heat transfer coefficient from water to concrete, hw2

1. I N T R O D U C T I O N S O U T H facing thermal storage wall is one of the most widely used concepts in solar passive-heated buildings. The storage wall may be made of concrete, adobe, stone or composites of brick, block and sand. Such a wall is known as a mass T r o m b e wall. The wall could also be drums of water stacked up one above the other and is known as a water wall. In this case, the storage being a convective body of water, the transfer of energy to the living space is rapid. The heat transfer can, however, be delayed using suitable controls. Detailed performance studies of water walls have been reported in the literature. N a y a k et al. [1] presents a comparison of the performance of the Drum water wall, mass Trombe wall and solarium. In this communication we compare the thermal performance of various types of south facing water walls shown schematically in Fig. 1. Figure la is a sketch of D r u m water wall. It essentially consists of metallic containers filled with water. One surface of the wall is blackened and glazed while the other surface can be either in direct contact with the living space or separated from it by a thin concrete wall/insulating layer. Figures 1b, c and d show water walls with water in containers made of parallel glass walls. Each wall is provided with a partially absorbing material kept parallel to the glass walls. The semitransparent material may be placed either between the water column and the living space (Fig. lb), between the glazing and the water column (Fig. lc) or in the water column itself (Fig. ld). The configuration shown in Fig. ld is usually known as Transwall [2] and those in Fig. lb and c can be considered as its variations. It may be noted that Fig. lc is equivalent to using a thermal trap over a mass of water kept in glass containers. Solar energy incident on the water walls shown in Fig. lb,c and d is partly absorbed and partly transmitted. While the absorbed part is gradually transferred to the living space, the transmitted fraction causes direct heating as well as illumination of the actual living space. To trap the heat collected during the day, the exposed surface of the wall can

W/m 2 °C

J number of wavelength intervals kc thermal conductivity of concrete, W/m °C ks thermal conductivity of semitransparent material, W/m °C L thickness of semitransparent material, m Lc thickness of concrete, m Mw heat capacity of water in Drum wall per unit wall area, J/m 2 °C Mw~ heat capacity of first water column per unit wall area, J/m 2 °C M,2 heat capacity of second water column per unit wall area, J/m 2 °C Qr solar flux, W/m 2 r reflectance of trap material T(x, t) temperature distribution for any x and t, °C To ambient temperature, °C TR living space temperature, °C Tw temperature of water, °C Tws temperature of outer surface of the water wall, °C Tw, temperature of first water column, °C T~2 temperature of second water column, °C t time coordinate, s X space coordinate, m O~c thermal diffusivity of concrete, m2/s % absorptivity of glass thermal diffusivity of semitransparent material, m2/s

zg transmissivity of glass "Ct transmissivity of container of Transwall 2 wavelength, m tLj absorption coefficient of trap material for solar radiation available between the (j)th and ( j - l)th wavelength region, mvj fractional absorption of solar radiation available between the (j)th and ( j - 1)th wavelength region * Energy Systems Engineering, Mech. Engng Dept, liT, Powai, Bombay-400076, India. 83

J. K. Nayak

84

be covered with a removable insulation during the off'sunshine hours. With the help of appropriate energy balance conditions, corresponding to different configurations, the Fourier equations of heat conduction has been solved to derive the explicit expressions for the heat flux, Q[t] entering the living space as a function of time. Since the ambient temperature and solar radiation vary periodically, the periodic solution for the equation of heat conduction has been considered in the analysis. This leads to closed form solutions. Further, the average behaviour of passive systems, which is the most important aspect from the design angle, can also be predicted from the periodic theory. The use of this theory implies that the meteorological parameters have a consistent time dependence over a period of 48 hr. This is because, according to response function methods the variation of meteorological parameters, before 48 hr or longer, does not affect the thermal performance significantly. The thermal performances of various configurations have been estimated in terms of the heat flux entering the living space through these systems; the living space is assumed to be at constant temperature corresponding to air conditioning. Numerical calculations using meteorological data (averaged over five years) for Srinagar, India on January 17 have been made. The results show that Transwall is more effective than the Drum water wall to meet the day time heating load. But from the load levelling and both day and night performance points of view, a Drum water wall is better.

GLAZ,NG--..__.J~

I~

IRANSWAL

SPACE

L_MOVABLE INSULATION

Schematic sketch of Transwall

~

i>; -" !',',~

| '::I",,~-SEMITRANSPA-'~i~'1 !~i':]

t:..,i::l Fig. lb.

SEM(IRANSPARENI MATERIAL

Fig. lc.

Fig. Id.

Cross section of Transwall

such a system can be written down as follows : [1] at the absorbing surface, the energy balance is

%ZgQT=ho(Tw.~-T.)+hw,(T..~-T.)

Figure 1 shows the schematic sketches of various types of water walls considered here. For the purpose of analysing their relative performances, it is assumed that one side of each wall is exposed to solar radiation and ambient conditions while the other side is in contact with the living space maintained at a constant temperature corresponding to air conditioning. We restrict ourselves to one dimensional heat transfer through these systems into the living space. Hence the temperature distribution in the non-convective medium is governed by one dimensional Fourier equation of heat conduction. During offsunshine hours the exposed surface of the wall is considered to be covered by movable insulation to reduce heat losses.

(1)

and the energy balance of water mass is dT..

Mw dt =h..,(Tw.~--T..)-h..2(T~.~-Tl~=o) 2. ANALYSIS

WATER

(2)

while the boundary conditions at surfaces x = 0 and x = L , can be written as

_ k OT

=h..2(T..~-Tl~=o)

(3)

- k , . ~ x .,=*~.= h3(Tlx=Lc- TR)

(4)

~X

,=0

and

where T(x, t) is the temperature distribution in the nonconvective medium and is governed by ?~2T

1 0T

~x~ = ~,~ ~t "

(5)

The heat flux entering the living space through the wall is given by

A. Drum water wall Figure la gives a schematic sketch of a water wall with metallic containers. The energy balance conditions of

O = h3(Tl~=,.,- TR).

(6)

B. Transwall

~O'tY'~

2f c ~

N

Figures lb and lc are some particular cases ofa Transwall (Fig. ld) and hence their energy balance conditions can be written down from those of a Transwall by incorporating appropriate modifications. Therefore, energy balance conditions of a Transwall have been outlined here. (i) For the first water column :

L-MOVABLE INSULATION Fig. I a. Schematic sketch of Drum water w a i l

dTw, M~, ~ - =

Q, +h,(T]~_o- Tw,)--ho(T..l- T.)

(7)

Thermal Performance of a Water Wall and

where Q ~ is the quantity of solar radiation absorbed by the water column. (ii) For the semitransparent material: - k s t3~-xTx=O = h l ( T ~ l - Tl~=o)

Q4=zgz2(1-r)Qr~j I{EbJ~ bj-' xexp(--/~jL)} { v ~ e x p ( - r b ( d , +d2)}]

(8)

~X x = L

= h2(TI~=L- Tw2)

where the temperature distribution c32T

1 0I

(9)

T(x, t) is given by

1 0T

&x2 k~ Ox - ~ Ot

(10)

I(x,t) = Q2 ~Ebj~-E%-'exp(-~jx)

(11)

with

Q2 is the part of radiation available at the semitransparent material. (iii) For the second water column :

dTw2 M w 2 ~ = Q3+h2(TIx=L-T~2)-h3(Tw2-TR)

(12)

where Q3 is the quantity of radiation absorbed by the water column. The heat flux entering the living space can be written as

(~ = h3(Tw2- TR)+Q,

(13) 3. NUMERICAL RESULTS AND DISCUSSION

where Q4 in the part of radiation transmitted into the living space. Values of Ql, Q2, 03 and 04 can be estimated by considering the absorption and transmission characteristics of water and semitransparent material [3, 4]. They are given by

A quantitative estimate of the thermal performance of various water wall configurations has been made in terms of the hourly variation of the heat flux {) coming into the room, corresponding to a typical winterday (January 17). Meteorological data averaged over five years for Srinagar, India have been used for the purpose. The hourly variations of ambient temperature and solar radiation incident on a horizontal surface have been shown in Fig. 2. The Fourier coefficients corresponding to these data have been calculated using the following expressions :

QI =zgZ,QT[1-~vjexp(-rbd,) 1 J Q2 = rgz,(1 -r)Qr~ [vj exp ( - qsd,)] J

rce -eb, ,

Q, =

(14)

where Qr is the solar flux incident on the wall. Values of j, r/j, #j and (Ebj--Ebj_,)/Eb for different wavelength regions of solar radiation are listed in Table 1. It is assumed that the solar radiation consists of five wavelength regions (j varies from 1 to 5) such that each region has different constant absorption as well as transmission coefficients. For solving the foregoing sets of energy balance conditions, it is considered that the incident solar radiation and ambient temperature vary periodically with time and hence can be expanded as Fourier series in time [1]. During off-sunshine hours if the entire glazing is insulated, then the external loss coefficient instead of being a constant value, becomes time dependent. To a reasonable approximation, it can be assumed to be a rectangular function of time with a constant value during sunshine hours and another value during off-sunshine hours. Such functions can still be expanded as a Fourier series. It has been found that the Fourier series expansions represent the respective functions reasonably accurately if the first six terms in the series are retained [5]. Thus, on the basis of periodic theory, the foregoing energy balance equations can be solved to derive explicit expressions for the heat flux entering the living space as a function of time in respective cases [5].

and

-ks

85

exp(-.,L)

}

+6

f(t) = ~ f, exp(inwt); i= x / ~

J

(15)

.=-6

where f(t) refers to a function in time with f,s as the Fourier coefficients, n is a dummy variable and

x {vj exp ( - r b d 0 } {1 - v j exp ( - r b d 2 ) } ] d

Table 1. Absorption and transmission coefficients Wavelength

interval, j

Wavelength region 0 < 0.36 < 1.06 < 1.3 < 1.6 <

2 2 2 ). 2

< < < < <

0.36 1.06 1.3 1.6 oo

Ebl- Ebj_,

Pj

Eb

( m - 1)

0.081373 0.6688 0.086103 0.0612 0.10244

oo 2.381 12.533 31.004 oo

(m-') 0.237 0.193 0.167 0.179 0.224

0.032 0.450 3.0 35.0 255.0

s6

J. K. Nayak 400

l

I

,

16

300

40u

c~ E

3

2 ~ t.~

1

ta IE

~I00 N Q: 0 -r

0

01

,

0

4

,

, ,

,

8

,

,

12 TIME OF THE D A Y ( h r }

,

, ,

16

,

I-2

2o

2t~

Fig. 2. Hourly variation of solar radiation and ambient temperature.

w = 2z/(time period of the function). In the calculation, first six harmonics have been found to be enough for the good representation of the function. The values used for the thermophysical constants of the building materials and semitransparent material (methylmethacrylate) are listed in Table 2. The following values have been used for other parameters in the calculations : z~ = 0.9

r = 0.04

r, = 0.9

TR = 21.1°C

7~ = 0.9

h 3 = 8.29W/m 2 °C h~ = h2 = 206.5W/m 2°C.

Because of the use of movable insulation over the outer surface during off-sunshine hours, the outside loss coefficient becomes time dependent. The following values have been used in the calculations : ho = 4.23 W/m2 C during sunshine hours = 0.53 W/m 2 :C during off-sunshine hours. Figure 3 shows the hourly variation of the heat flux entering the living space for various thicknesses of total water column of Transwall, keeping the width of the semitransparent material constant at 0.1 m. It is observed that there occurs a sharp rise in the heat flux between 8

and 16 hr. It is due to the transmitted gain of solar radiation coming into the living space. Further, there is no phase shift between the maxima of heat flux and the solar flux, since the magnitude of the transmitted gain is quite significant. Whenever there is water column on both sides of the semitransparent material (Fig. ld) the fluctuations in the heat flux reduces thus improving thermal load levelling. The effect of various parameters in the heat flux through a Transwall system is summarized in Table 3 in terms of maximum, minimum and average heat flux entering the living space. Figure 4 shows the hourly variation of the heat flux for different d2 with a fixed d~ ( = 0.0 m) and L ( = 0.1 m). Figure 5 shows the same thing for different d~ with a fixed d2 ( = 0.0 m) and L ( = 0.1 m). It is observed that for a fixed L as d~ increases, the average heat flux decreases. It is true irrespective of the fact that whether d2 is kept fixed or changed keeping the sum of d~ and d2 constant (Table 3). This is because as dt increases, the quantity of heat stored towards the glazing part of the Transwall increases. Consequently the loss to the ambient increases resulting in a decrease in the heat flux. On the other hand, as d2 increases for a fixed dt and L, the average heat flux remains unchanged. Further, a better load levelling is achieved with the increase of d2. Thus the system shown in Fig. lc performs better than that shown in Fig. lb.

Table 2. Thermophysical constants Material

Thermal conductivity (W/m °C)

Density (kg/m3)

Specific heat (J/kg °C)

Concrete Methylmethacrylate

1.73 0.1729

2403.0 1204.0

837.0 1460.0

Thermal Performance of a Water Wall 160

i

i

i

i

i

I

87

i

I

i

i

I.=0-1 m

uz

d_l

120

dL

I-0,1m

0.1m

II-0"2m

0.2m

III-

0,0

0,2m

IV - 0,2 m

0-0

40

I

I 4

i

I 8

I

I 12

I

TIME O F T H E

DAY(hrl

I 16

I

I

I

20

24

Fig. 3. Hourly variation of heat flux entering the living space for different thicknesses of total water column of Transwall.

The effect of the variation of the width (L) of the semitransparent material can also be noticed from Table 3. With the increase in the width, for fixed values o f dl and d2 there occurs a reduction in the heat flux fluctuation thus leading to load levelling. There is, however, a small reduction in the average heat flux, as expected. Figure 6 shows the effect o f the variation of L on the heat flux in a Transwall system for a fixed d2 ( = 0.1 m) with d~ = 0.0. Table 4 summarizes it in more detail. I n

this case, the semitransparent material acts as a heat trap. Its function can be explained as follows. As the thickness of it increases, the heat loss to the ambient decreases since the resistance to conduction o f heat from the water column (d2) increases. But at the same time, it also reduces the transmission of solar flux. However, the amount of decrease is not the same in both cases. So the average heat flux goes through a m a x i m u m for L = 0.04 m (Table 4). Beyond that the reduction in the trans-

Table 3. Heat flux into the living space in a Transwall system for various parameters Thickness of semitransparent material (m) L

Water column width (m) dl

d2

Heat flux (W/m 2) Maximum

Minimum

Average

0.10

0.0 0.2 135.10 0.05 0.15 83.13 0.10 0.10 80.89 0.15 0.05 84.75 (Total water column is fixed at d, +d2 = 0.20 m)

27.23 21.53 19.40 15.71

60.21 40.98 39.59 38.84

0.10

0.10

0.025 0.05 0.10 0.20

96.23 87.66 80.89 76.58

12.6 15.36 19.40 36.27

39.59 39.59 39.59 39.59

0.10

0.025 0.05 0.10 0.20

0.I0

91.58 85.95 80.89 76.17

18.51 19.05 19.40 19.70

42.49 40.98 39.59 38.27

0.03 0.05 0.07 0.10

0.10

0.10

98.78 92.32 87.20 80.89

18.36 18.93 19.19 19.40

44.67 43.08 41.60 39.59

0.10

0.20

0.20

72.18

23.18

38.27

J. K. Nayak

88

I

L= 0.1m~ d l = 0 " 0

dn I = O'OSm I I = 0.1 III

-

0-3

m rn

i'V = 0.9 rn

E

[ 0

L 4

[ 8

I 12

I 16

I 20

I 24

TIME OF THE DAY ( h r )

Fig. 4. Hourly variation of heat flux entering the living space for different thicknesses of water column between the semitransparent material and the room.

that even if there is a slight decrease in the heat flux, this system is attractive, because it will be less expensive and the maintenance cost will also be less due to the absence of the night insulation. Figure 7 shows the hourly variation of the heat flux entering the living space through a Drum water wall for various water depths and concrete thicknesses. It is noted that even for a no-concrete layer behind the water wall,

mission of solar flux is much more than the reduction in the heat loss thus resulting in a decrease in the heat flux. Because of the fact that the trap material reduces the heat loss to the ambient, there is not much use in having a removable insulation during the off-sunshine hours in the system shown in Fig. lc. Figure 6 shows one such calculation for L = 0.1 m, d2 = 0.1 m and d~ = 0.0 (curve V). More results are shown in Table 5. It may be noted

,6°[ L=0"lrn~ 120

// //

~ /

I -- 0"05 m tz= 0.tin

\\ \

d2=0.0

\\

I I I ~ = O-]m

V = 0.t,m

. eo

/ IV

0

I /*

I I 8 12 TIME OF THE DAY ( h r )

I 16

I 20

~

.'4.

Fig. 5. H o u r l y v a r i a t i o n o f heat f l u x entering the living space f o r different thicknesses o f water c o l u m n between the glazing and the semitransparent material.

Thermal Performance of a Water Wall

89

d 2 = 0.1m ~ d 1 = 0.0

rE(

/....-.-:~...... .."

~'~12C

,.

3

pl

"..

!

0-0

II

0.05 m

Ill

0.1

IV

0,3

m

'Y

0-1

(without night-

m

insulation) Ld

"I" 8(

;;y

&O

IY

o

~

~

,'2

,~

.....

~'o

I

~

TIME OF THE DAY ( h r )

Fig. 6. Hourly variation of heat flux entering the living space for different thicknesses of semitransparent material keeping d~ = 0.0 and d2 = O. 1 m.

DRUM WATERWALL WATER COLUMN CONCRETE W1 0-1 m 0"0 W2 0.3m 0.0 W3 0.gin 0.0 W/. 0-t m 0.1 m WS 0.1 m 0.3 m TANANS WAI.L

T2~.~. ~ / 'X \

90

/

•

/ /

/ • /

E

T 1 1 ....-,.

,,t/"

./

"~

// /

". ; \

.:~

~

\

~

/\?., /

/

~ \\ '~

/

~

11 0.1m ~12 0.0 ~

L

0.1m 0.trn 0.1m 0-3m(WI1HOU1 NIGH1

so

!. I •

w,.

?.

.~,~",'~-----~w2~'

z

~

W3

'

./

~..

~,~..---w2

30

I

i

I

I

4

L

J

,

I,,

0

,

,

I

,

,

12 TIME OF THE DAY ( hr )

,

I

16

I,

,

i

1

20

i

L

J

I

2/..

Fig. 7. Hourly variation of heat flux for different wall thicknesses of Drum watcr wall and Transwall.

J. K. N a y a k

90

Table 4. Average heat flux into the living space for various thicknesses of semitransparent material keeping the water column fixed (dr = 0.0, d2 = 0.1 m) (Fig. lc) Thickness of semitransparent material (m)

Average heat flux into the living space (W/m 2)

0.01 0.02 0,03 0.04 0.05 0.07 0.10 0,20

59.39 60.53 60.95 61.06 61.05 60.88 60.26 56.13

wall (Fig. I b and c) in terms o f the maxinlum, minlmunl and average heat flux entering the living spacc. L rcfers to the thickness of concrete (L,) in the former case, while in the latter systems it corresponds 1o the thickness of s e m i t r a n s p a r e n t material. It is seen that Drum water wall performs better from a load levelling and both day and night performance points of view.

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

a good thermal load levelling is o b t a i n e d with increasing water thickness. To get a n appreciable phase shift it is desirable to have a concrete layer b e h i n d the water wall. F o r the sake o f comparison, heat flux entering the living space t h r o u g h a Transwall has also been plotted in the same figure for the following cases : (i) curve T~: d~ = 0.1 m, d2 = 0.1 m, L = 0,1 m (ii) curve T2 : d t = 0.0, d2 = 0.1 m, L = 0.3 m (without night insulation). It is seen that Transwall system does n o t lead to good load levelling a n d also there occurs very little phase shift. Table 5 summarizes the c o m p a r i s o n of the t h e r m a l p e r f o r m a n c e of the D r u m water wall with that o f Trans-

The applicability of the analysis presented in this p a p e r is subject to the limitations, m e n t i o n e d in the introduction. The calculations have been m a d e corresponding to a typical day of h a r s h N o r t h Indian winter climate. A l t h o u g h no general conclusions for all ranges of meteorological p a r a m e t e r s can be d r a w n from the predictions for a single day, it is instructive to summarize the qualitative features of the results as follows. (i) The Transwall as a passive heating concept is useful when immediate heat transfer is required. So, for buildings like schools, offices a n d business establishments where day time heating load is significant, this wall becomes very promising. Further, it has the added a d v a n t a g e of allowing vision to the exterior. (ii) A D r u m water wall system (water with a thin concrete layer b e h i n d it) ensures a good load levelling a n d significant phase shift. So this system is attractive when b o t h day and night p e r f o r m a n c e as well as load levelling are the prime concern.

Table 5. Maximum(Qm,x), minimum (Omin)and average (Q,v) heat flux (W/m 2) through Transwall and Drum water wall d~ = 0.0 m,

Transwall d 2 = 0.1 m

I

II

d~ = 0.1 m,

d 2 =

0.0 m

Drum water wall water depth = 0.1 m

Thickness (m) L*

I

I

~max

Qmin

~av

Qmax

Qmin

Qav

Qmax

Qrnin

Qav

Qmax

Qmin

Qav

0.0 0.1 0.2 0.3 0.45

190.65 143.90 120.30 101.70 80.22

- 3.07 19.86 26.0 28.12 28.96

50.68 60.26 56.13 51.53 45.26

129.0 109.2 92.53 72.82

17.83 24.52 26.43 26.79

47.08 46.61 43.67 38.80

131.57 103.08 84.03 63.17

9.77 12.28 13.34 13.95

43.53 36.96 32.29 27.14

80.42 55.64 43.87 37.46 32.11

14.28 25.37 28.93 30.14 29.52

43.84 39.90 36.80 34.20 30.97

* Thickness in Drum water wall case refers to that of concrete layer behind the water column and in Transwall case refers to that of semitransparent material. I With night insulation. II Without night insulation.

REFERENCES 1. J. K. Nayak, N. K. Bansal and M. S. Sodha, Analysis of passive heating concepts. Sol. Enerq) 30, (1983). 2. R. Fuchs and J. F. McClelland, Passive solar heating of building using a Transwall structure. Sol. Energy 23, (1979). 3. P. Lumsdaine, Transient solution and criteria for achieving maximum fluid temperature in solar energy applications. Sol. Energy 13, (1970). 4. P. R. Smith and M. H. Cobble, The thermal trap solar energy collector. Tech. Report, New Mexico State Univ., NMI = 2, January (1976). 5. M. S. Sodha, J. K. Nayak, N. K. Bansal and I. C. Goyal, Thermal performance of a solarium with removable insulation. BM Envir. 17, (1982).