The influence of natural convection on the temperature decay of a porous thermal layer

Transport in Porous Media 3 (1988), 437-453. 437 �9 1988 by Kluwer Academic Publishers.

The Influence of Natural Convection on the Temperature Decay of a Porous Thermal Layer

H. SALT and K. J. MAHONEY Commonwealth Scientific and Industrial Research Engineering, Highett 3190, Victoria, Australia

Organisation, Division of Construction and

(Received: 3 February 1987; revised: 9 February 1988)

Abstract. Temperature decay in sealed rockbeds has been recorded. The rockbeds lost energy through the top surface and the results indicated that different natural convective flows occurred in beds of fixed depth and rock size but different lateral dimensions. However, the different flows had no effect on the mean power density dissipated through the top of the beds. A simple numerical conduction model based on the 'power integral method' was used to calculate the temperature decay. The experimental results suggested that an insulated porous lower boundary was appropriate for the model and this gave the best agreement with the experiments.

Key words. Natural convection, heat transfer, flow, critical, Nusselt, power integral method.

1. N o m e n c l a t u r e

a w a v e n u m b e r

B, Blot n u m b e r

c specific heat

d rock d iamete r

E . cons t an t for n th mode of na tura l convec t i on

g g rav i ta t iona l acce le ra t ion

H height of porous layer

h heat t ransfer coefficient

k thermal conduc t iv i ty

kp thermal conduc t iv i ty of porous layer

Nu Nussel t n u m b e r

n mode n u m b e r

T t empera tu re

A T t empera tu re di f ference across porous layer

t t ime

z space coord ina te

Az inc remen ta l space

Greek

T2= vo lumet r i c thermal expans ion coefficient of fluid

a (h + a)

438

6~= K

A 2 2

/~c,n

P

P (pc)i 4,

a(A - a) permeability of porous layer Rayleigh number critical Rayleigh number of nth mode kinematic viscosity of fluid density thermal capacity of fluid void volume fraction of porous layer

Subscript j space increment counter.

H. SALT AND K. J. MAHONEY

2. Introduction

Transient natural convection in a layer of porous material occurs in a number of practical systems. It occurs in all fibrous insulation on equipment and in buildings due to intermittent and variable use. The current work arose from the need to know how natural convect ion within an underfloor rockbed would influence the performance of a solar space heating system (Peck and Proctor, 1983; Salt, 1985; Woodridge and Welch, 1980). The rockbed thermal energy store is located beneath and in good thermal contact with a concrete slab floor. The house is heated by convection and radiation from the floor and thermal energy is transferred from the rockbed to the house by conduction through the concrete. The rockbed is charged by forced convection with hot air from the solar collectors but the fan is switched off when the collectors cannot supply additional energy to the store. The rate at which energy is supplied to the house is determined by the temperature difference between the surface of the concrete and the living area. Over several hours the temperature of the concrete is determined by the rate at which energy is supplied by the rockbed, and therefore on any natural convection within the bed.

In order to investigate transient natural convection within rockbeds, a number of rockbeds were constructed and their discharge observed after being charged using the apparatus described below. The experimental results are reported in this paper.

The expected average annual performance of a solar energy system in any one location is determined by using the system parameters and recorded climatic data to calculate the energy that would have been supplied over each hour. To avoid excessive computer charges, it is important that simple models be used for each component of the system. Such a model has been written to represent the discharge of this rockbed store and the numerical predictions are compared with the experimental results to verify the adequacy of the model for use in system

performance simulations.

THE TEMPERATURE DECAY OF A POROUS THERMAL LAYER 4 3 9

3. Experimental Apparatus

The apparatus, which is shown in Figure 1, was located in a laboratory which was maintained at a nominal 20~ Two contractions were available so that bed

heights of 0.3 or 0.15 m could be used. The variation from the mean values in both velocity and tempera ture were • at the outlet of the contraction for the 0.3 m high beds whereas for the 0.15 m high beds, the variations were +1.0

and • for velocity and temperature , respectively. The rocks were packed into 1 m wide and 1 m long mild steel containers, which were lined internally with

12 mm closed-cell neoprene to minimise channelling between the bed and the walls. The containers sat on a 700 m m thick slab of expanded polystyrene and the

sides and top were insulated with 100 m m of expanded polystyrene.

A matrix of thermistors, which were supplied curve matched to •176 over a tempera ture range of 0 to 70~ was placed in the beds to monitor the fluid

tempera ture during the experiments and a mic rocompute r was used for data

acquisition. The overall accuracy of the tempera ture measuring system was •176 and the a r rangement of the thermistors in the various beds is shown in

Figure 2.

3.1. TOP LOSS COEFFICIENT

For the purpose of predicting a tempera ture decay in the rockbeds, it is necessary to know the value of the heat transfer coefficient through the top of the beds. A

1 m long and 0.3 m deep bed of 23.5 m m crushed basalt rock was constructed. It

was necessary to place a 12 m m thick layer of very light open-cell foam on the

bed of rocks to completely prevent channelling between the rocks and the top of the container when the bed was being charged, since insufficient pressure could

be applied to the container top to force the closed-cell neoprene well down

ORIFICE " MIXERr~S HEATER

_ . /HO E,CO, E,Pr,ON - - I

< I I I I I EAN

ROCKBED tN l m SECTIONS SCREENS

Fig. 1. The experimental apparatus.

440 H. SALT AND K. J. MAHONEY

FLOW

0 150 300 450 600 750 t000 1150 1300 1450 1600 1750 1900

50

Fig. 2(a). Arrangement of thermistors in beds 0.3 m high, 1 m and 2 m long.

O 150 300 450 600 '750 900

Fig. 2(b). Arrangement of thermistors in beds 0.15 m high, 1 m long.

130 93 57 20

around the rocks. The bed was brought to the steady state with the expanded

polystyrene removed from the top of the container, and the transfer coefficient

from the top calculated from the energy lost from the air stream and the mean

temperature of the top plane of thermistors. Results were obtained for air inlet

temperatures of 40 and 60~ with air mass flow rates of 0.011, 0.036, and

0.060 kg s -1, and the mean value of the transfer coefficient was calculated to be

3.11 W m -2 K -1. Using the value of 0.08 m2K W -1 for the surface resistance of

plane surfaces in buildings with internal air movement (Barnard, 1970) and

taking the conductivity of the neoprene sheet as 0 . 0 5 W m -a K -a, the heat

transfer coefficient is calculated as 3.13 W m -2 K -1 thus agreeing with the value calculated from the experimental data.

A similar exercise was carried out with a 1 m long and 0.15 m deep bed filled with 50 mm crushed basalt rock. In this case, it was necessary to place a 25 mm

thick layer of very light open-cell foam on top of the rocks to prevent chan-

nelling. A value of 2 . 7 1 W m 2K-1 was calculated for the top loss coefficient

from the experimental data and the reduction from that for the bed of 25 mm rocks was attributed to the thicker layer of open-cell foam. Subsequently, three flux meters were obtained and these gave a value of 2.68 W m -2 K -1 for the

transfer coefficient through the top of the 0.15 m deep bed. Since the flux meters

THE T E M P E R A T U R E DECAY OF A POROUS THERMA L LAYER 441

were rated at • these two experimental values for the top loss coefficient are

in agreement .

3.2. CONDUCTIVITY OF THE ROCKBEDS

The method of Kunii and Smith (1960) can be used to calculate the thermal conductivity of a packed bed f rom the propert ies of the constituents of the bed.

Taking the thermal conductivity of air as 0.026 W m -1 K -1, the thermal conductivity of basalt as 2.2 W m -1 K -I (Forsythe, 1969) and the emissivity of basalt as 0.9, which is a typical value for nonmetals (Kreith, 1976) then the conductivity of

a bed filled with 23.5 mm rocks is calculated to be 0.27 W m -1 K 1. To test the

applicability of the Kunii and Smith method to a bed of rocks, an experiment was per formed with a small bed of 23.5 mm rocks within a natural convect ion testing

apparatus (Peck, 1984). The apparatus was used with the hot plate on top of the

rocks and the cold plate beneath, thus eliminating any possibility of natural convect ion occurring within the rockbed. The experimental results gave the conductivi ty of the rockbed as 0.31 W m -1 K - l . Considering the complex paths for heat transfer within a rockbed, the agreement between the theoretical and

experimental values of thermal conductivity was considered to be reasonable.

4. Experimental Procedure

The following five rockbeds were constructed and tested:

1 m wide, 1 m long and 0.3 m deep, filled with 23.5 mm crushed basalt rock, 1 m wide, 2 m long and 0.3 m deep, filled with 23.5 m m crushed basalt rock,

1 m wide, 1 m long and 0.3 m deep, filled with 40.0 mm crushed basalt rock,

1 m wide, 2 m long and 0.3 m deep, filled with 40.0 m m crushed basalt rock, 1 m wide, 1 m long and 0.15 m deep, filled with 50.0 mm crushed basalt rock,

The 23.5 mm rock was selected by sieving through 22 and 25 mm screens, the

40 mm through 38 and 42 m m screens, and the 50 mm rock was sieved through 48 and 52 mm screens. The mean value of the screen mesh sizes was taken as the characteristic dimension of the rocks because it would be impossible to determine

a more precise equivalent hydraulic diameter for a bed of randomly shaped rocks.

The beds were fully insulated and raised to a temperature of 60~ by passing heated air through them. The fan was kept running and the rear was sealed before the front of the bed in order to reduce any cooling effects due to the sealing. A 100 mm thick layer of rigid expanded polystyrene was used at each end but steel sheet had to be placed against the wire mesh supporting the rocks before the slab of polystyrene could be slid into place. The steel was removed immediately and the rockbeds were totally sealed within 30 sec, but the effect of the sealing can be seen in some of the results obtained.


5. Experimental Results

Figure 3 shows the decay of the mean temperatures in the four horizontal planes where the thermistors were located. The curves are numbered in sequence with the temperature in the bot tom plane of thermistors being represented by curve 1

and that in the top plane by curve 4. Losses in the inlet ducting could not be

eliminated entirely when the beds were being charged and this is the reason for

the initial temperatures of the charged beds being lower at the bottom. However ,

the salient feature of these results is that the tempera ture of the bot tom plane is never the hottest, suggesting that convect ion occurred within the beds and

70

60

O

5O

=E 40

Fig. 3(a). rock.

., x N \

~ " . . . \ \

231 "-- . . . . . . . ~ . > . . _ .

2L1 412 613 814

ELAPSED TIME - HOURS

Decay of mean horizontal temperatures. ] m long and 0.3 m high bed filled with 23.5 mm

7o I 6O

i 5~

30

20 I 0 21 42 63 84


Fig. 3(b). Decay of mean horizontal temperatures. 2 m long and 0.3 m high bed filled with 23.5 mm rock.

THE TEMPERATURE DECAY OF A POROUS THERMAL LAYER 443

o i

50 :=

o:

40

I.-

~ 4

�9 \

" ' , N N "- . N

211 412 613 ~ 4


Fig. 3(c). Decay of mean horizontal temperatures. 1 in long and 0.3 m high bed filled with 40 mm rock.

continued until each experiment was terminated. Figures 3(a) and 3(b) show the influence of the bed length and Figures 3(a) and 3(c) show the influence of rock

size. The most positive evidence for natural convect ion occurring within the beds is

obtained from examining the tempera ture decay at the individual sensors. Figure 4 shows temperatures at the individual sensors of the columns on the central plane at distances of 0 and 300 m m from the front for the 1 m bed filled with

23.5 m m rocks. The initial fall in temperature of the bot tom sensor for a little more than one hour in Figure 4(b) is a characteristic of the bot tom sensors along the central plane apart f rom the sensor at the very front of the bed, and may be due to the technique used to seal the beds. Since conduction can not cause a

discontinuity in tempera ture gradient, the reversal of the tempera ture gradient for the bot tom sensors within the bed is a clear indication of convect ion occurring throughout the whole bed.

The relative positions of the temperature curves for the top three sensors for the results shown in Figure 4 are to be expected, but the relative positions of the curves for the bot tom sensors are surprising. At the front of the bed the

tempera ture of the bot tom sensor is below that of the next two above it for 28 h and this is presumably due to cooler air flowing from the corners of the bed to the

centre. The discontinuity in the slope of the curve for the lowest sensor in (a) suggests that the flow from the corners was dominant for the first 21 h but that flow down from the sensors above it was dominant after the change. Referring to (b), it is notable that the bot tom sensor becomes the coolest after 48 h. The temperatures of the bot tom sensors along the central plane are shown in Figure 5, clearly showing that the tempera ture at the ends of the bed determines the

temperature at the bot tom of the bed in a manner similar to a temperature front


,o F 60

', "~.\ 50 , ~,,

"" , ~ \ 2 3 . ,\ x.~ / , I/4

30

20 211 412 613 814 ELAPSED TIME - HOURS

Fig. 4(a). Temperature decay at individual sensors along the centre-plane of a 1 • 0.3 m bed filled with 23.5 mm rocks; front.

7~ I

60 ~ , . \

4o ~ / / /

3O

20 211 412 613 814 ELAPSED TIME - HOURS

Fig. 4(b). Temperature decay at individual sensors along the centre-plane of a 1 • 0.3 m bed filled with 23.5 mm rocks; 300 mm into bed.

t rave l l ing a long the b o t t o m of the bed . T h e cu rves for the b o t t o m sensors across

the bed at a p l ane 450 m m f rom the f ront a re p lo t t ed in F i g u r e 6 t o g e t h e r with

the t e m p e r a t u r e cu rve for the b o t t o m sensor at the f ront of the bed on the cen t re

p lane . T h e s e resul ts were surpr i s ing but were conf i rmed when the e x p e r i m e n t was

r e p e a t e d . T h e curves in F igu re 6 ind ica te that the t e m p e r a t u r e f ront d i scussed

a b o v e t ravels m o r e qu ick ly on the cen t ra l p lane a long the bed , sugges t ing that a

c o m p o n e n t of flow across the bed exists but its m a g n i t u d e is less than that a long

the bed . T h e f igures the re fo re sugges t that the flow for the 1 m bed of 23.5 m m

rocks is a spiral a r o u n d a to ro ida l - l i ke shape .

THE TEMPERATURE DECAY OF A POROUS THERMAL LAYER

76

445

54 60 4,5

r 56

30

26 O 211 412 613 814 ELAPSED TIME - HOURS

Fig. 5. Temperature decay at individual sensors along the bottom of the centre-plane of a 1 x 0.3 m bed filled with 23.5 mm rocks; curves are numbered in sequence from the front of the bed.

T h e re su l t s fo r t he i n d i v i d u a l s e n s o r s f r o m the o t h e r b e d s g a v e no i n d i c a t i o n of

a t e m p e r a t u r e f r o n t m o v i n g a l o n g the b o t t o m of t he beds . H o w e v e r , t h e y all

s h o w e d tha t all t he b o t t o m senso r s w e r e a lways c o o l e r than the h i g h e r sensors , as

i n d i c a t e d by F i g u r e 3, and tha t t he s enso r s at the s ides w e r e c o o l e r t han t h o s e at

t he c e n t r e . Al l t he r e su l t s w e r e c o n s i s t e n t w i th w a r m air r i s ing in the m i d d l e of

t he b e d s a n d c o o l a i r f a l l ing at all f o u r s ides a n d t h e n t r a v e l l i n g a l o n g the b o t t o m

of t he b e d s t o w a r d s the m i d d l e .

70

51 60 2 3 ~

50

o. 4O

30 3 ~

~~ 2, ,'2 ;3 ' , 0 ELAPSED TIME - HOURS

Fig. 6. Temperature decay of individual sensors across the bottom of a 1 x 0.3 m bed on a plane 450 mm from front, together with bottom sensor at front of bed; curves are numbered in sequence from 200 mm plane in Figure 2(a).

4 4 6 H. SALT AND K. J. M A H O N E Y

5.1. P A R T L Y - C H A R G E D R O C K B E D

The fully-insulated 0.3 m high and 1 m long bed filled with 25 m m rocks was partly charged by passing 60~ air into it until the plane normal to the flow at 450 mm from the inlet had reached approximately 40~ The ends were then sealed, the airflow stopped, and the insulation removed from the top. Figure 7(a) shows the

J

50

i ,~

3 0 -


Fig. 7(a). Decay of mean temperatures on vertical planes along a partly-charged 1 x 0.3 m bed filled with 23.5 mm rocks.

1"0

0"9

0"8

0"7

0.6 ==

0"5

0"4

0.3 o z

0"2

0.1

Fig. 7(b).

TIME : 0.0 h rs

16.83

25.25

33"67

42-08

' ~ ' ' 4 0.15 O" 0 0'45 0,60 O- 5

DISTANCE ALONG BED (m)

Change in the temperature along the partly-charged bed.


decay of the mean temperatures of the vertical planes with curve 1 representing the front of the bed and curves 2 through 6 representing the planes at 150 mm through 750 mm in 150 mm intervals. The plots in Figure 7(b) have been formed from the data in Figure 7(a) and these plots clearly show that the energy is dissipated through the top far more quickly than it is redistributed throughout the rockbed.

6. Theoretical Results

When the length of the 0.3 m deep beds was increased from 1 to 2 m, only the temperature curve for the bottom plane of thermistors showed any significant change. The fact that there was a difference for the bottom plane suggests that there was a difference in the convective flow; the fact that there was no substantial change for the top three planes suggests that the change in the flow had no significant influence on the transfer of heat from the beds. The mean thermal power density dissipated through the top of the beds was clearly independent of the lateral dimensions and detailed convective flow within the beds. Accordingly, for modelling purposes, it should be possible to represent the beds as infinite layers. The transient behaviour of a one-dimensional conducting layer is described by

OT 02T p c - = k - (1)

Ot O Z 2 "

At each time step in a numerical solution, the effective conductivity of the rockbed was determined by using the 'power integral method' (Malkus and Veronis, 1958) to calculate the mean heat transfer across the rockbed for each possible mode of natural convection within the bed, and then summing the contributions from the modes to give a Nusselt number (Nagagawa, 1960). The method has been used for steady-state natural convection in a porous layer with isothermal impervious boundaries (Combarnous and Bories, 1975) and it has been shown that the method is applicable in porous layers with flux and porous boundaries (Salt, 1988). The Rayleigh number for each time interval was calculated from the temperature difference across the porous layer at the beginning of the time interval and an effective conductivity calculated for the layer for use during that particular time interval. The Nusselt number was calculated using

c , n Nu = 1 + N, 1 ---~-7- , (2)

n = l

where n is the mode number, E~ is a constant for that mode, A2,~ is the critical Rayleigh number of the mode, and A 2 is the Rayleigh number for the time


interval. Rayleigh number is given by

~ 2 = ecga(pc)tH A T (3)

The permeability is given by the Kozeny-Carman relationship (Combarnous and Bories, 1975)

d 2 ~3

K - 172 (1 - ~b) ~" (4)

The critical Rayleigh numbers and the constants in the power integral method are determined by the boundaries. In the rockbed experiments, the upper boundary was impervious with the flux decreasing as the temperature of the bed fell, and the physical lower boundary was impervious with zero flux. The critical Rayleigh numbers can be found from (Salt, 1988),

2y61(cosh y cos 61 - 1) + (~/2 _ 62) sinh 3, sin 61 +

+ 2Bt(y sin 61 cosh 3, + 61 sinh ~/cos 61) = 0 (5)

where y 2 = a ( A + a ) , 6 2 = a ( A - a ) , and Bt is the Biot number at the upper boundary, given by Bt = hH/kp.

The critical Rayleigh numbers are the minima in A as the wavenumber a is varied and the values of E~ can be found from Equations (28), (A5), (A6) and (A7) in (Salt, 1988).

The temperature of the lowest plane of thermistors was always below that of the next lowest plane in all the experiments. Hence, there was a plane near the bottom of the bed, below which the vertical temperature profile created stability and therefore did not contribute to the generation of natural convection flow. Accordingly, a porous lower boundary has also been considered for the theoretical results. For simplicity, it was assumed that any downwards energy flux below the plane could be neglected and that pressure gradients below the plane could also be neglected, thus allowing the lower boundary to be expressed as the easily-represented zero flux porous boundary in contact with a standing fluid (Lapwood, 1948). Examination of the experimental curves shows that the as- sumption of zero flux is a reasonable approximation because the conductivity of the beds was small. The approximation that pressure gradients can be neglected below the plane is not unreasonable because simple calculations based on the total discharge time, the rate of temperature decay and the permeability of the beds indicate that the pressure gradients within the beds were of the order of 1 Pa m -1.

The critical Rayleigh numbers with the porous lower boundary can be found from (Salt, 1988)

y sinh 7 c o s 61 - 61 cosh 7 sin 61 + 2B, cosh 7 c o s ~1 = 0. (6)


Table I. Rockbed parameters

Rock Bed Bed Transfer Biot size conductivity height coefficient number (mm) (Wm IK-l) (m) (Wm-2K 1)

23.5 0.27 0.3 3.1 3.17 40.0 0.36 0.3 3.1 2.38 50.0 0.41 0.15 2.7 0.83

T h e va lues of E , can be found f rom Equa t ions (28), ( A l l ) , (A12) and (A13) in

(Salt, 1988).

T h e r e l e v a n t phys ica l p a r a m e t e r s of the beds with the th ree rock sizes a re

g iven in T a b l e I bu t the b e d he igh ts were r e d u c e d by the th ickness of the

n e o p r e n e l ining for ca l cu la t ing the Biot numbers . T h e dens i ty of the rock was

m e a s u r e d as 2658 kg m -3 and the a v e r a g e vo id f rac t ion f rom a n u m b e r of sample

beds was 0.46, which ag ree s with ea r l i e r pub l i shed work (Close , 1965), g iv ing the

dens i ty of the r o c k b e d s as 1435 kg m 3. T h e specific hea t of the rock was taken

at 880 J kg K -~ (Close , 1965) and the cr i t ica l R a y l e i g h numbe r s and fac tors E~ of

the four lowest m o d e s of na tura l c o n v e c t i o n are g iven in T a b l e II for bo th

i m p e r v i o u s and po rous lower bounda r i e s .

F i g u r e 8 shows the ca l cu l a t ed t e m p e r a t u r e s for c o n d u c t i o n only, and for the

i m pe rv ious and po rous lower b o u n d a r i e s for the 23.5 m m rocks . F o r clar i ty , only

the ca l cu l a t ed t e m p e r a t u r e s for the top p l ane and s e c o n d - l o w e s t p lane of ther -

mis tors a re shown in the f igure but, c lear ly , a o n e - d i m e n s i o n a l m o d e l which

Table II. The first four modes of natural convection with impervious upper and either impervious or porous lower boundaries

Biot Mode Critical Rayleigh E~ for lower boundary number number number for lower boundary

Impervious Porous Impervious Porous

3.17 1 22 8 2.72 2.70 2 117 78 2.31 2.31 3 289 224 2.20 2.19 4 540 448 2.15 2.14

2.38 1 21 8 2.83 2.86 2 116 76 2.33 2.33 3 287 222 2.21 2.20 4 538 446 2.15 2.14

0.83 1 18 6 3.19 3.55 2 112 73 2.36 2.37 3 283 218 2.22 2.21 4 533 441 2.15 2.14

4 5 0 H. SALT A N D K. J, M A H O N E Y

70

- - NO CONVECTION

60 ~. IMPERVIOUS LOWER BOUNDARY . . . . POROUS LOWER BOUNDARY

" ~ ,'-%,~.... 50 , " . \

\ ~ " " ' > . . . . ~ 't 183turn

0 211 412 613 814

ELAPSED TIME HOURS

Fig. 8. Calculated temperature decay in a 0.276 m high layer of 23.5 mm rock on planes 8 and 183 mm from top.

reduces the convective heat transfer to an effective conduction heat transfer can not give a result in which the bottom plane is cooler than the one above. In calculating the Rayleigh number for the case with the porous lower boundary, the height was taken as that of the bed since the plane where the temperature gradient changed was not known precisely and, in a practical situation, the height of the bed would be the only known length parameter which could be used in calculating a Rayleigh number. The cyclical variation in the temperature of the top plane reflects the variation in ambient. The results for the case with no convection clearly do not agree with the experimental results shown in Figure 3(a) and the effect of the smaller value of the lowest critical Rayleigh number with the porous lower boundary is progressively obvious as time increases in this figure. Figure 9 shows the experimental results for the temperature decay in the

i

w 5 0

O. 4o

Fig. 9(a).

- - EXPERIMENTAL

. . . . THEORETICAL ~ ~ TOP PLANE

~ o SECOND LOWEST PLANE

ELAPSED T IME - HOURS

Calculated and experimental temperature decay; 23.5 mm rock.

THE TEMPERATURE DECAY OF A POROUS THERMAL LAYER

7O

451

60

o i

50

30

20 211 412 613 814 E L A P S E D T I M E - H O U R S

Fig. 9(b). Calculated and experimental temperature decay; 40 mm rock.

5O

3O

Fig. 9(c).

21 42 63 84 E L A P S E D T I M E - H O U R S

Calculated and experimental temperature decay; 50 mm rock.

top and the second-lowest planes of thermistors for the 1 m long bed of 23.5 mm rock, the 2 m long bed of 4 0 m m rock and the bed of 5 0 m m rock. The theoretical results from the porous lower boundary case are also plotted and there is reasonable or good agreement between the experimental and calculated curves in all three cases.

7. Conclusions

Experiments have been performed with shallow sealed rockbed thermal energy stores which were discharged by energy transfer through their top surfaces. The


monitored results of temperature decay indicated that natural convection occurred within all the beds over the whole period of every discharge and that the overall flow was one of warm air rising in the middle and cool air falling at the sides over the whole period. Results for a 1 m long, 1 m wide and 0.3 m high bed filled with 23.5 mm rocks, show that a cool temperature front moved along the bottom of the bed. The temperature of the front was the same as the temperature of the sides, which approached the temperature of the top as the bed discharged, and the mean temperature of the bottom of the bed therefore approached the mean temperature of the top of the bed with the middle of the bed remaining warmer. No obvious temperature front can be seen in the results for the other beds but all the experimental evidence suggests that the cool air fell at the sides of the beds and then travelled along the bottom of the beds towards the centre, being heated by the rocks as it did so.

A simple model has been used to satisfactorily calculate the rate of decay of a convecting porous layer, which is insulated at the lower boundary and losing energy through an impervious upper boundary. The model uses the power integral method to reduce the problem to one of one-dimensional conduction for which a numerical solution can be used. The theoretical results, which give the best agreement with the experiments, used an insulated porous lower boundary to calculate the constants required for the solution. The physical justification for considering such a boundary was that the experimental results showed that the temperature at the bottom of the beds was always lower than that in the plane of

sensors above the bottom. Since the experimental results indicate substantial differences in the convection taking place within the different beds, the level of agreement for all cases suggests that the theoretical model can be used to calculate the performance of the much larger rockbeds in the heating system for which this work was done.

An experiment has also been performed showing that in a bed with a large temperature variation along it, the energy redistribution within the bed can be neglected in comparison to the energy dissipated through the top.

Acknowledgement

The authors would like to acknowledge the support of the Victorian Solar Energy Council for this work.

References

Barnard, J. R., revised by O'Brien, L. F., 1970, Thermal Conductivity of Building Materials, Report R.2, Division of Building Research, Commonwealth Scientific and Industrial Kesearch Organization,

Highett, Victoria 3190, Australia. Close, D. J., 1965, Rock pile thermal storage for comfort air conditioning, Mech. & Chem. Eng.

Trans. of the Institution of Engineers, Australia MC1 (1), 11-22.


Combarnous, M. A. and Bories, S. A., 1975, Hydrothermal convection in saturated porous media, Adv. Hydrosci. 10, 231-307.

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Documents

The influence of natural convection on the temperature decay of a porous thermal layer