Experimental validation of a thermal model of an evaporative cooling system

Energy Convers. Mgnu Vol. 24, No. 4 pp. 305 - 311, 1984 0196-8904/84 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright ¢~) 1984 Pergamon Press Ltd

EXPERIMENTAL VALIDATION OF A THERMAL MODEL OF AN EVAPORATIVE COOLING SYSTEM*

ALOK SRIVASTAVA and G. N. TIWARI

Centre of Energy Studies, Indian Institute of Technology, Hauz Khas, New Delhi- l l0 016, India

(Received 29 June 1983)

Abstract--A periodic thermal model for an evaporative cooling system over the roof has been presented. Open roof pond, water film and flowing water layer are the the special cases of the analysis. The time dependency of solar radiation, ambient air, sol-air and room air temperatures has explicitly been taken into account by expressing as a Fourier series of time for a 24 h cycle. Experimentally observed air temperature of rooms, treated with and without evaporative cooling over the roof, has been found in good agreement with theoretical results.

Solar energy Passive system Evaporative cooling

NOMENCLATURE W = West wall N = North wall

b = breadth, m E = East wall c = specific heat, J/kg°C F = floor

cw = specific heat of water, J/kg°C o = outside caiT = specific heat of air, J/kg°C i = inside

d = thickness of water column, m f = to floor h = heat transfer coefficient, W/m 2 °C ~ = outside of floor to ambient k = thermal conductivity, W/m°C r = radiative L = length of water path, m e = evaporative

Mw = heat capacity of water, J/m 2 °C c = convective MR = heat capacity of room air, J/~C D = door

rh = mass flowing per unit time, kg/s. n = number of harmonic Superscripts p = partial pressure of water vapour at temperature

T, N/m z A = ambient Q(t) = amount of heat flux, W/m 2 R = roof S(t) = intensity of solar radiation, W/m 2 S = South wall

Ti = inlet water temperature assumed as TA(t) W = West wall TA(t) = ambient air temperature, °C N = North wall

Tw = water temperature, *C E = East wall Uo = water flow rate, m/s F = floor vo = wind velocity, m/s x = position coordinate, m X = area, m 2 1. INTRODUCTION

a = absorptivity of surface The authors are engaged in the design of passive r = relative humidity

O(x,t) = temperature distribution *C buildings appropr ia te for the hot and dry climate of o = density, kg/m 3 North India. As a part of this effort , it was considered

p,,. = density of water, kg/m 3 desirable to develop thermal models of various t~ = 2~r/period, s -I passive heating/cooling approaches in the building.

= emissivity of surface The convent ional approaches for the reduct ion of AR = difference between long wave radiation incident

heat flux into the building through the roof (as about on the surface from sky and surroundings and the radiation emitted by a black body at ambient air 60% of the heat flux comes through the roof in temperature co mmo n designs at locations be tween 0 to 35 °

T~ = fraction of solar radiation absorbed by water lati tude) are: provision of insulation and/or false cr = Stefan-Boltzmann constant, 5.6697 x I0 -s W/ ceiling, shading of roof due to vegetable pergola, use

mK 4 c~. = emissivity of water surface of removeable canvas and the use of reflective paints ~, = fraction of solar radiation absorbed by roof over the roof. An unconvent ional and highly effec-

surface tive approach to the p rob lem consists of utilization of d,,~,cb~, = constants, equation (14) evaporat ive cooling over the roof; this can be

Subscripts achieved by an open pond or thin film or flow of water over the surface of the roof.

R = roof Mainly steady state thermal models are available S = South wall for the predict ion of heat flux across the roof with an

* The work is partially supported by the Department of evaporat ive cooling system. These analyses do not Science and Technology, Government of India. consider the t ime dependence of meteorological

305

306 SRIVASTAVA and TIWARI: THERMAL MODEL EVAPORATIVE COOLING SYSTEM EXPERIMENT

conditions and enable one to calculate only the The energy balance for surfaces whose one side is average heat transfer through the fabric without exposed to outside environment and the other being considering the storage effect of building masonry in contact with room air, may be expressed as (U-value method). In the present analysis we have on.i .o0 t,mo of.o ar i too.,ty [ ) ] ambient air, sol-air and room air temperatures by - k O--x x=o = ho Osa (t) - 0 (3) expressing their parameters as Fourier series of time x=0 over a 24 h cycle.

An experimental study of the indoor air tempera- and ture o! a room with evaporative roof cooling treatment has also been performed. Besides the roof - k 00 [ which is studied, the heat gain/loss through different 0x- x=x = h~ [O(x--X,t) - Tn] (4) walls or floor has also been considered and the aggregate of their performances, which enables one where to find the explicit expression for room air temperature. It is found that the observed room air tempera- asS(t) eAR ture is in good agreement with the numerical results OSA - - + T A - - - -

theoretically obtained (Fig. 4.). The open roof pond, ho ho water film and flowing water over the roof surface are the special cases of the model developed, commonly known as sol-air temperature.

In the case of multilayered wall/roof (Fig. 1), the energy balance conditions can be expressed by

2. ANALYSIS assuming continuity of heat flux and temperature across the interfaces, viz.

The schematic sketch of the system is shown in Fig. 1. The temperature distribution in the various walls, 0j (x = Xl,t) = 0i+l (x = Xl , t ) (5) roof and floor is governed by the one dimensional equation of heat conductance viz. and

k 020j = pc ~ (1) -k ) ~ ~=x? 00/+11 Ox 2 Ot Ox - ki+l Ox x=x) (6)

For parameters relevant to common building mate- rials, the characteristic length of the system is less Based on these boundary conditions, one can write than 15 cm; hence, if one considers the transverse the expressions for heat flux coming into the room dimensions to be larger than 50cm, the heat conduc- through the exposed walls/roof in terms of solar tion equation can be assumed one dimensional, intensity, ambient and room air temperatures.

The temperature distribution in the various re- However, if the floor is in contact with the ground, gions may be expressed as [1] the additional boundary condition can be written in

the form

Oj(x,t) = A ~ / + Azjx + Re ~" {Cjn exp(a m x) 0 (x ~ ~, t) is finite (7) n = l

+ Dj~ exp(-aj ,x)} exp(imot) (2) If the floor is not in contact with the ground, or in contact with the ambient air (Fig. 1), the energy balance conditions may be expressed as

where

aj,, = - etj (1 + i) V'ft'- - k 00 I ox ~=x7 hr [ rR (t) - o (x = X l , t)] (8)

and and

_koo c t / = \ 2k i / bx hfi [0(x = X4, t) - TA (t)] (9)

A1j, A2i, Ci, and Dj, are constants to be determined by appropriate energy balance conditions. RegionsI, For the periodic nature of meteorological para- II, III and IV are between (0 ~< x ~< x~), (xl ~< x ~< x2), meters, one can write Fourier series expansions for a (x2 ~ x ~< x3) and (x3 ~ x ~< x4) of the masonry, 24 h cycle, for solar intensity, ambient air, room air respectively, and sol-air temperatures in the form

SRIVASTAVA and TIWARI: THERMAL MODEL EVAPORATIVE COOLING SYSTEM EXPERIMENT 307

S(t}

Wo ler L,'--~.. ~ Weter Concrete .~'~.~:~.-`:~-~.`~!:~-~.~!!-:.:~-~;~!f`~;~`::i~`~!~fh~;~:~::~T:~.~:¢`~4~ x --.0

Brick =: .x x root Lim e - ~ " ~ ~ 2 2 2 2 2 2 2 2 2 2 2 7 7 2 / ~ x - x x

Room oi r

Room o i r \\.~.~ W G l l s

S([) ~ ~ Room o i r

-N x=O X=X¢

Room Q=r

Concrete------............,=. x=O Br ick

• X=X 2 Mudphuska = " " . . . . . . . . . . . . . . . . . . . . x=x 3 L, oncrere '

Ambient o i r

Floor

(b )

Fig. I. (a) Schematic view of the room, roof. walls and floor. (b) Photographic vicw of the roofs with and without cooling system.

S(t) = S¢~ + Re _~" S,, exp(inmt) (I0) Tn(t) = Tt¢o + Re _.\~ Tin, exp(inmt) (12) I ! = I t l ~ [

TA(t) = TAo + Re \" TA. exp(imot) (11) 0~(t) = Oso + Re \f. Os. exp(inwt) (13) n----Z n = ]


where to = 2 ~/period. Therefore, the heat flux + b hi (01 ~=0- T.~) (17) entering the room through different walls can be expressed as

where

Qw(e) = X tu(Oso - rgo) + Re ~ hi [cb~. Os. f

1 .=1 Ts = "~- ['r, S(t) + HITA(t) - R~)Ra(1-r)]

exp(incot)l (14) H = hr + hc + PoRt TR.] J

HI = h r + h c + 3'RoR1

where Ro = 0.013 hc

1 1 + X/ + 1 and M~, = b.d.c.,.pw

- F u ho " K/ hi Equation (17) is a general energy balance equation and d~l,,, d:2. are constants to be determined by energy which can be simplified by putting balance conditions.

Following Tiwari et al. [2], the heat flow through (i) rh., = 0 for open roof pond and (ii) Mw = 0, th., the roof on which an evaporative cooling system is = 0 for water film, spray, gunny bag system.

maintained, can be expressed as follows. If the Thewater temperature (T.,) as a function o fycan be flowing water layer is of thickness d, the energy obtained from equations (17) with the initial bound- balance condition for water moving over the roof ary condition for water temperature viz. along the y direction (Fig. 2) can be expressed as

Tw = T i at y = 0 (18) ( - - cwOT.,I O Tw + thw ---~-y / dy bd Pw cw Ot The temperature of water can also be assumed a

periodic function of time as

=['rt S(t) - Qr - Qc - Qe + hi (01 x=0- T~,)] bdy oo

(15) T.,(y,t) = Two (Y) + Re ~ T.,. exp(intot) (19) n = l

where The amount of heat flux entering the room through the roof with an evaporative cooling system can be

hi = ~ 0.14 (Gr.P) 1/3 + 0.644 (Pr) 1/3 (Re) t/3 [4] expressed as

Qr = h, (Tw - TA) Q. (y,t) = hi [0 x=2 TRI (20)

Q~ = h~ (Tw - TA)

Q~ = 0.013 h~ L o (T.,) - 7p (TA)] Assuming a uniform surface temperature along the

hr = ewcr [(7'w + 273.15) 4 - (7'A + 261.15)4]/ y-direction, the mean heat flux (averaged over y) into the room can be obtained as (7'w- ~,,)

• 1 Io L h~ = 5.678 (1.0 + 0.85 Av). [5] Q~oof (t) = XR - ~ - Q (y,t) dy

Av = vo - Uo (16)

7'wand TA are, respectively, the average values of Tw = XRhi A I 4 X 4 + A24 - TRO + hi Re X n = I

and TA; Gr, Pr and Re are Grashof, Prandtl and f Reynolds numbers, respectively. XRt C4. exp(x4.X4)+ D4n exp(-eq.X4) .

In a narrow temperature range, the saturation vapour pressure of water (p) can be expressed by a } linear relation of the form [6] - TRn exp(intot) (21)

p(T) = R1T + R2 where Ai4, A24, C4. and D4. are unknown constants and can be determined from the energy balance

where R~ and R2 are two constants to be determined conditions. The interaction of room air to ambient air from the saturation vapour pressure data [7] by a through infiltration and ventilation can be expressed least square curve-fitting method. Hence, equation as [8] (15) can be expressed as

0(,)~.,~o.. = v ~ + v ? (7,, - rA) (22) M,,, OT.. OTw

+ th,,,cw - b H (T~ - T.:) Ot Ot where the Ws are defined in Appendix I.


The heat transmission through a door can be expressed 1.72 m were constructed. The roof of both rooms is as tilted slightly at an angle of 10". Figure la schemati-

cally represents the cross-sectional view of the Qo(t) = ho (TR-TA) Xo (23) rooms. The roof is made of traditional construction

(Fig. 1) composed of reinforced cement concrete (5 Opening the door increases the number of air cm), brick (10 cm) and lime plaster (5 cm). The walls changes per second, and this effect is included in the are made of brick of thickness 20 cm. The rooms are Q(t)inf/vent term. located on the roof of the terrace of the main

building, so the floors of the experimental test rooms

3. ENERGY BALANCE FOR INSIDE ROOM AIR are composed of concrete-brick, mudphuska* and concrete exposed to ambient air on the other side.

Now, one can write the energy balance equation The roof of one room was treated with the for room air temperature, which is mainly composed evaporative cooling system, while the other was of components like heat flux entering the room untreated for comparison. Two G.I. pipes were through walls, roof and door and air changes due to spread over the upper end of the roof with tiny holes infiltration/ventilation, viz. in it along the length of the room. One end of each

d TR pipe was connected from a constant level water tank. MR &-t = (~w(t) + (~R + OO(t) -- O.~t) -- Water through tiny holes in pipes spreads over the

Q(t)inf/vem roof. As the roof is slightly tilted at an angle due to (24) gravitational force, the water spreads over the roof.

The flow rate from the pipes was so controlled that it where the LHS represents the change in the heat keeps the roof surface just wet. content of room air. Using equat ions(10)to (13)and As a matter of fact, after a few hours it was (15) to (21) in the energy balance condition from (3) observed that an extra smooth surface is needed just to (9) one obtains to wet the roof by this free movement arrangement of

water, To overcome the problem of dry spots over the surface, thin jute cloth was spread on the roof. It

TRo = Xs Us No + XwUwOs~o + XNUNO~o + XEUeO~o was observed that, with the help of jute cloth and pipes of tiny holes, a uniform water layer over the roof can be maintained. The reason behind this is the

+ X~ hoOsNo + XRURO~o + V A TAd + XohoOSo capillary action and ability of jute cloth/gunny bag to retain the water. Both rooms were exposed to the

/ (X,U~ outside environment for a few days to attain the + X~Uw + XNUN + XFhr + XeUE steady state condition. The temperatures of both rooms were measured by thermocouples, keeping

+ XRUR + Vo A + Xoho the other end of the junction in an ice box. The thermo e.m.f, of the thermocouples were measured

and RRn = B2n/Bln by a potentiometer of least count 0.1°C. The hourly where variation of solar insolation and wind speed were

Bl, = inwMR + X R ~ + X~I~ln + X ~ , measured by Kipp and Zonon pyranometer and an aminometer, respectively. The room air temperature

+ XMI~', + XExI~ + V~ + X,~I~. and ambient air temperature were noted for 1 h intervals. The relative humidity of the outside air was measured with the help of dry/wet bulb thermo- + A~ ho + XSo ho. meter.

The heat and mass transfer from wetted jute cloth

= XR,t,2~0~. + x ~ + xw~2~0~% B2 n R R is identical to that from a free water surface at the

same temperature. Hence, by neglecting the heat ~ N e e capacity of jute cloth, the analytical model for

"F XN~2nOsn + XE~2nOsn stationary water layer case (Mw = th~ = 0) is

+ V~ TAn + X~DhDO~. + Xrc~TA~ applicable in this system. The photograph of the treated room is shown in

+ XsD hD ~ Fig. lb.

TRo is the average and TR~ is the time dependent part 5. NUMERICAL RESULTS AND DISCUSSION

of the room air temperature. Numerical calculations, to verify the experimentally observed results, are performed. The variation of

4. EXPERIMENT solar radiation on different walls are calculated from

To verify the analytical model, a simple experi- the data observed for the horizontal surface using Liu

ment was performed for the stationary water film * Mudphuska is a mud mortar mixed with hay in 35 kg/m 3 case. Two identical rooms of dimensions 5.2 x 2.5 x proportion.


and Jordan relations [9]. These values, then Fourier d = 0.005 m (thickness of jute cloth) analysed for a 24 h cycle, and the corresponding cw = 4190.0 J/kg*C Fourier coefficients are shown in Table I. uo = 0.0 m/s

The following sets of parameters have been used in Rt = 325.17 N/m2°C the calculations. R2 = -5154.89 N/m 2

Pw = 1000 kg/m 3 1. Thermal Concrete Brick Lime Mud- ~2 = 0.54

conductivity plaster phuska "~ = 0.27 (averaged over the day).

(W/m°C)---~ 0.72 0.71 0.731 0.52 Density Figure 1 presents the schematic view of the system. (kg/m 3) ~ 1858.0 1922.4 1446.0 2050.6 There are two identical rooms, one treated with the Specific 837.4 evaporative cooling system while the other is untre- heat---~ 655.2 836.8 1840.0 ated. Two doors of dimensions 1.85 and 1.04 m 2 are (J/kg*C) in the north and south walls, respectively. The roof,

wall and floor is made of traditional construction

2. Heat capacity of room air = 37328.3 J/°C except that the exposed roof surface is extra treated ho = 22.78 W/m2*C(corresponding to average with reinforced cement. The rooms were fairly closed

wind velocity 10.2 kin/h), for a few days during the experiment and one air hr = 8.4 W/m2°C for bare roof surface with heat changeperhour i sassumeddue to inf i l t r a t ionofa i ras

flow downwards suggested in Ref. [8]. = 8.3 W/m2°C for treated roof surface with Figure 2 presents the cross-sectional view of the

heat flow upwards moving water layer as depicted in Fig. 1. = 6.3 W/m2°C for vertical walls. Figure 3 presents the variation of partial vapour

pressure with temperature; marked points are the

For floor Xt = 5 cm; ( X 2 - X 1 ) = 10 cm; experimental values obtained from steam tables [7]. (X3 - X2) = 10 cm The continuous line is plotted by a least square curve and (X4 - X3) = 5 cm. fitting method. It is reasonably good in the small

hr = 8.4 W/m2°C for floor temperature range of interest to express partial and ho = 0.45 W / m 2 ° C for door. vapour pressure by a linear relation.

The variation of ambient and room air tempera- The values of heat transfer coefficients have been ture with and without evaporative cooling system is calculated from relevant expressions given in Ref. shown in Fig. 4. It is seen that the variatiop, of room [10]. air temperature without roof treatment is sufficiently

high and even larger than the ambient air tempera- 3. Areas in (m 2) ture during the day. It is due to the fact that there is XR = 15.43,Xs = 9.08, Xw = 4.3, XN = 7.67 more heat gain through the roof and walls and low Xe = 4.3, Xr = 14.7, X~ = 1.85, X s = 1.024. heat losses to the environment during the sunshine

period. Marked points ( A ) are the correspondingly 4. L = 5.2 m observed values. Room air temperatures with the

b = 296 m roof treated with the evaporative cooling system

Table 1. Fourier coefficients for daily variation of solar radiation on different surfaces and ambient air temperature on 4th June. 1981 at Delhi (Latitude 28°.5 ' N). S~ is amplitude and n is phase factor of solar radian

Fabric n 0 1 2 3 4 5 6

S" (W/m 2) 307.16 470.6 191.37 10.172 21.121 4.62 12.84 Roof nt,~ai~,, ) 3.17 0.1504 2.728 3.91 4.217 0.926

Sooth wall S,; (W/m 2) 78.76 117.33 41.98 5.65 6.64 11.48 4.26 n ~r~d~"~ 3.113 0.006 4.252 0.5861 3.1 6.057

S,' (W/re") 146.18 224.19 128.98 106.31 62.22 24.13 13.958 West wall ntradian ) 3.654 1.453 5.562 2.994 0.591 4.180

S~' (W/m 2) 64.75 93.44 28.6 18.37 25.3 13.25 4.72 North wall n,ad,~n~ 2.677 4.987 5.467 1.239 3.678 3.745

S; (W/m 2) 162.7 249.17 141.08 105.65 50.86 9.601 1.701 East wall n(,,ai,.) 2.499 4.574 0.315 2.683 4.586 4.039

Ambient air T'A, (*C) 28.97 7.081 1.156 0.396 0.22 0.217 0.33 t e m p e r a t u r e A n ~'adiin) 3.724 0.181 0.732 2.512 4.586 5.174

S, = S~' ¢xp ( - in) and T~t, = T'A, exp (-/An)


:~ L • I obtained by present theory is shown by curve ( . . . . ). It / ~- is seen that the room air temperature is substantially ,," lower than that of the o ther room with the untreated

roof. As a mat ter of fact, due to free evaporat ion of ,, water over the roof, the roof (x=0) surface temperature significantly decreased even below the room air

b ;' temperature . Hence , the roof loses heat to the

l / J ' , envi ronment rather than gaining. However , if it is

decided to use the evaporat ive cooling system, it is , good to construct the roof with some bet ter conduct-

ing material to enhance the heat transfer to the envi ronment from room air. Some attention should

~-~ also be given to reduce heat transfer through the dy walls and due to air changes in the room.

Fig. 2. Cross-sectional view of the moving water layer Therefore , it may be concluded that the periodic over the roof. theory successfully eva lua tes the heat t ransfer

through (a) roof with evaporat ive cooling, and (b) different fabrics.

l 8,000 0

7,000 _ y REFERENCES z 1. J. K. Nayak et al, Int. J. Energy Res. 4, 41 (1980).

6,c~o 2. G. N. Tiwari et al, Energy Convers. Mgmt 2,143 (1982). 3. A. Kumar, Physics of solar stills, Ph.D. thesis. Indian 5,000

-~ Institute of Technology, Delhi, (1981). : 4,ooo ~ 4. P. W. D. Callaghan, Building for Energy Conservation.

Pergamon Press, New York (1978). a, ooo 5. H. R. Hay and I. J. Yellot, Mech. Engng 92 (1). z~°%o 22 24 26 2a 30 32 34 36 3s 40 42 6. M. S. Sodhaetal., Solar Energy2, 127(1981).

7. E. Schmidt, Properties of Water and Steam in S.I. Units. Temperoture (*C) ~ Springer, Berlin (1969).

Fig. 3. Values ofpartialvapourpressurewithtemperature 8. E. Shaviv and G. Shaviv, A model for predicting (Schmidt, 1969). Continuous lines obtained by least square thermal performance of buildings, Architectural Scien-

curve fitting for these data. ces and design methods. Working paper number ASDM-B, Faculty of Architeture and Town planning Technion. Israel Institute of Technology (1977).

9. J. A. Duffle and W. A. Beckman, Solar Energy ,5 Thermal Processes. Wiley, New York (1974).

~ /~ Observlld room olr ,em~rolure wllh~t roof trlK='Imenl 10. W. H. McAdams, Heat Transmission. McGraw Hill, 40 ~- 00blervlEI room oir ,em~rof . . . . i,h roof .... ,ment New York (i954).

1 [ ;7 ~ / ~ . ~ - o ~ y - ~% "~ I ./~x~/~. "°" 9"" ~ , APPENDIX I

~- The values of V's are 20 Ambienf a i r

' ~ . . . . . . x - - Room air wifhouf roof treotrne~t

L . . . . R . . . . . . . +,, ,oo, . . . . . . . . V(~ = 2463 MR ( g A + 1~ A) • ARH/Cai, 15

I and i ,o l , ' ' ' ,~ 1; 2; 2~ 1 3 5 7 9 411 13 115

Time of the day (h) ~ VIA = MR ( NA + NoA) (Cair Jr 1.88 ARH)/C c

Fig. 4. Variation of ambient air ( ) and theoretically where N A is the number of air changes per hour due to the calculated rooms air temperatures with (----) and without door ventilation and No A that due to the opening of window; ( - - - ) evaporative cooling system over the roof. Marked ARH is the difference in relative humidity between inside points (O) and (~7) show the correspondingly observed and outside. The superscript A refers to air changes from

room air temperatures, room to ambient air.

gCM 2 4 : 4 - [

Documents

Experimental validation of a thermal model of an evaporative cooling system