Solar& Wind Technology Vol. 5, No. l, pp. 15-25, 1988 0741-983X/88 $3.00+.00 Printed in Great Britain. Pergamon Journals Ltd.

E X P E R I M E N T A L T E S T I N G O F F L U I D I Z E D B E D T H E R M A L S T O R A G E

M. M. ELSAYED, I. E. MEGAHED and M. M. EL-REFAEE Mechanical Engineering Departments, P.O. Box 9027, Jeddah 21413, Saudi Arabia

(Received 10 February 1987; accepted 6 May 1987)

AImtraet--An air-sand fluidized bed is designed and tested for thermal storage. The bed has a cylindrical shape of 30 cm in diameter with height varying between 6-15 cm. Measurements are taken for the pressure and temperature along the bed. A data acquisition system is used to collect temperature measurements and to control the supply temperature of the air to the bed according to a pre-specified criterion. Three cases are considered for the supply temperature : constant supply temperature, linear time dependent supply temperature, and exponential time dependent supply temperature. The results are analysed and presented in dimensionless form to study the effect of the supply temperature and height of the bed on the temperature distribution in the bed, average temperature of the bed, storage efficiency and heat recovery efficiency.

1. INTRODUCTION

Thermal storage has been recognized for a long time as a means to store surplus thermal energy for later use when needed. Sensible heat storage (i.e. increasing the temperature of the storage medium) is the most common method of thermal storage.

In solar applications, thermal storages are usually taken as integrated parts of the solar utility system to overcome the operational problems related to the intermittent nature of the solar energy. Commonly, sensible storage is the type of thermal storage used in most thermal applications. In applications with low temperature such as space heating, water heating, solar desalination, etc., liquid storage and rock beds are widely used as for thermal storage (e.g. see [1,2]). Intermediate and high temperature solar applications, such as solar furnaces, central receivers, air heaters for industrial purposes, etc., use molten salt and rock beds among other methods for thermal storage (e.g. s e e [31).

Fluidized beds have been utilized for a long time as a means of improving the combustion process (especially of coal) or as a means of efficient and fast heat exchanging process. Lately it has been considered that fluidized beds could be employed in solar appli- cations. Flamant and Olalde [4] tested and compared the fluidized bed and the packed bed solar receivers. They concluded that the fluidized bed behaves as the best solar absorber. Cranfield [5] tested the use of a fluidized bed for a heat store for power generation and recommended its use as a means for improving the performance. Weast et al. [6] used the fluidized bed thermal storage for waste heat recovery.

15

It is the objective of the present work to exper- imentally study the application of fluidized beds to thermal storage (Fig. 1). Like rock beds, fluidized beds can be utilized for low, intermediate and high temperature solar applications. In addition, the rate of heat exchange between the heat carrying fluid and the storage medium is much faster in fluidized beds than in rock beds; which can be an advantage in several applications.

In the present work, an air-sand test bed model is designed and built. The experimental set-up is used to study the following :

(a) The dependence of the pressure drop across the bed on the bed height and on the fluidizing mass velocity of the bed.

(b) The dependence of the time variation of the bed temperature and the storage efficiency on the initial temperature of the supply air at heat charging mode.

(c) The variation of the bed temperature and heat recovery efficiency with time at the heat dis- charging mode.

2. EXPERIMENTAL CONFIGURATION

Figure 2 shows a layout of the experimental con- figuration which consists of the following major com- ponents: an air blower, a heating chamber and a fluidized bed.

The heating chamber is a cylinder of 46 cm in length and 31 cm diameter. Four heating coils each of 2 kW capacity are installed in the chamber for heating the

16 M. M. ELSAYED et al.

+o<, \

,,o, <̀> \ ",, %o

I

O

Fig. 1.

1 Fluidized

Bed

Thermal Storage

_ _ . f

air. The chamber is manufactured of 12 in. diameter pipe of 6 mm wall thickness and 31 cm inside diameter. Two of the four heating coils are operated manually while the other two can be operated either manually or by a data acquisition system to control the supply air temperature to the fluidized bed.

The fluidized bed has a cylindrical shape with 85 cm overall height and 31 cm inside diameter. The bed is divided into three major sections. The lower section is the calm section, the middle section is the fluidization section and the upper section is the deentrainment section. In the calm section the velocity of the supply air is reduced and its direction is deflected to assure homogeneous flow distribution to the fluidization sec-

tion. The fluidization section and the calm section are separated by a distribution plate of thickness 3 mm and of 10mm diameter holes at 50% blockage. A screen of holes of size less than 100/am is mounted on the top of the distributor plate to prevent the solid particles from entering the calm section. The de- entrainment section is separated from the fluidiz- ation section by a screen of holes of size smaller than 100 pm supported by a 3 mm thick plate with 10 mm diameter holes with 50% blockage. The purpose of the deentrainment section is to separate any en- trained solid particles and to assure homogeneous velocity distribution of air at the exit from the fluidiz- ation section.

'on l liH--gii

I . . . . 4oo_,..~3_oo_ soo

i .... ; 2 Pipe work

Pitot tube traversing mechanism

1

- - - ~----~i

,_2

J i I i l I I I I I I I I t i i i i t l / I L I I I I I I I I I I I t f111111111 I I I I I I I I I I I I l l I f i l l ~1111 t I i l~ I I I I f l l l l f 171 I 77 i ; 7i 7i 7111 i 77t I t i ~71111 I I ; 5'1 t~ i ; f/111 t l i 7 " i l i I, "t I t11~ ~ l l l l l i i l l l I / I /H / i / I ~~It

Dimensions in m m s

Fig. 2.

Fluidized bed thermal storage 17

The static pressure is measured in one station in each of the calm section and deentrainment section and in 11 stations along the fluidization section. At each station, the static pressure is averaged over three pressure taps distributed on the circumference of the fluidized bed cylinder at an angle of 120 °. The pressure lines from the 13 pressure stations are connected to an inclined water manometer. To protect the capillary tubes connecting between the pressure taps and the manometer from being blocked by sand particles, a fine mesh screen is installed on each tap. Pressure is also measured at the two ends of a traversing pitot tube mechanism mounted on the 2 in. pipe to estimate the rate of supply air to the bed.

A temperature probe has been specially designed and manufactured to measure the temperature in the bed at eight various stations at the bed axis. Type- K thermocouple of 0.31 mm diameter with fiberglass insulation is used. In addition, a thermocouple is installed in the calm section to measure the supply air temperature. All thermocouples are connected to a data acquisition system, model 3056DL manu- factured by Hewlett-Packard. A specially designed control circuit is used to regulate the heating rate, in order to control the supply air temperature according to a prespecified time dependent relation; prescribed in the software of the data acquisition system.

3. HYDRODYNAMICS OF FLUIDIZED BED

In this study the pressure distribution inside the bed is measured for different values of air flow and mass of sand. The measurements are used to determine the voidage ~ of the bed.

3.1. Idealized pressure distribution Air enters at point .4 at the bottom of the bed, Fig.

3. The pressure should drop due to friction to point B at the inlet of the distributor plate (or the lower screen) where air should experience a relatively larger pressure drop depending on the distributor design. At point C air has to go through the solid (sand), and due to the requirement of fluidization, the pressure should drop to point D. The fluidization is complete if all the sand weight is counterbalanced by the pressure force. For uniformly fluidized sand the voidage ~ will be constant and also the pressure gradient will be constant. For this reason the pressure distribution curve is a straight line in the region C-D. Air leaves sand at D where it will be subjected to wall friction again and the pressure drops to point E at the inlet of the upper retaining screen. I f the design of the upper screen is similar to that of the distributor plate (as in

the present case), also if sand does not block the upper screen, then the pressure drop from E to F should be similar than that from B to C. Again from F to the bed outlet G the pressure drop is due to wall friction. It should be expected that the pressure drops from A to B, D to E and F to G are very small compared to the overall pressure drop.

3.2. Pressure distribution measurements The pressure distribution inside the bed is measured

for different masses of sand and for different air flow rates. The mass of sand used is varied between 0 and 20 kg, and the inlet air velocity is varied between 0 and 25 m/s. The heaters are switched off and the air enters the bed approximately at room temperature (about 25°C). Seven runs are performed with different masses of sand as shown in Table 1.

During each run, measurements are obtained while increasing the air velocity. Repeatability of the results is checked and found satisfactory especially for the runs from I to 6. For run 7, when the mass of sand is 20 kg, the bed operation is found to be unstable and the large pressure fluctuations destroy the repeatability of the results. The results of run 7 are not reported for this reason.

The results of the first six runs are shown in Fig. 4. The pressure distribution for an empty bed is obtained to show the pressure drops due to wall friction, the distributor plate and the upper retaining screen.

The superficial air mass velocity G (mass flow rate per unit cross-section area of bed) is chosen as a par- ameter in Fig. 4. The interparticles air mass velocity G' (mass flow rate per unit actual area of flow in the bed) is not used because of the lack of information, at the present time, about the bed voidage e.

The obtained data show the main features of the idealized pressure distribution curve shown in Fig. 3. The pressure drop across the distributor plate is not very clear because it is overtaken by the large pressure drop in the sand. The pressure drop in the sand is well defined. The pressure distribution in the sand has a straight line form. The constant pressure gradient in the sand is an indication of the uniformity of the voidage e along the bed height.

The pressure above the sand is approximately con- stant up to the upper retaining screen which shows a pressure drop that is rapidly increasing with the air flow rate. This is very much different from the case when the bed is empty. The reason may be attributed to the very fine sand particles which are carried away by the high velocity air and stick against the upper retaining screen. The flying fine particles block the screen and increase the pressure drop across it. It is also clear from the data that the pressure inside the

18 M.M. ELSAYED et al.

Air out

I

~-~Air in

H

G

i A

Pressure

Fig. 3.

Table 1. Pressure distribution experimental runs

Mass of sand, kg Run no. (ms)

1 0 2 5 3 7,5 4 10 5 12,5 6 15 7 20

bed increases as the air flow rate increases due to the larger pressure drop required.

3.3. Estimate of the expanded bed height and voidage The pressure distribution data are used to estimate

the height of sand inside the bed. Referring to Fig. 3, the idealized pressure distribution, the bed height H is equal to the vertical distance between points C and D as indicated in the figure.

The points corresponding to C and D are located on the measured pressure distribution curves of Fig. 4. Point C is at the lower screen, at the zero bed height, and point D is at the end of the straight dropping line. The bed height H is thus obtained and the results are shown in Fig. 5. In some cases, for high inlet velocities, some problems in defining the top of sand (point D) are faced due to some small deviation from the straight line relationship. This is very clear for

G = 0.150 kg/s m 2. To solve this problem, the straight line relationship is extrapolated and point D is con- sidered at the intersection of the dropping pressure line in the sand and the approximately constant pres- sure line above the sand. It can be seen from Fig. 5 that there is some expansion in the bed height however small it is.

The bed voidage e can now be obtained from the following equation :

TCD~H (1) m, = p , ( l - e ) ~

where ms is the mass of sand in kg, p, is the density of sand which equals 2600 kg/m 3, O b is the bed diameter (0.31 m) anu H is the bed height in m obtained as mentioned above. Using the above numerical values, eqn (1) reduces to

e = 1-5.096 x 10 -3--m-" (2) H

The results obtained for ~ are depicted in Fig. 6. The value of the packed bed voidage, which was calculated and reported in [7], is also shown in the figure.

Examining the results of the bed voidage in Fig. 6, it can be concluded that the fluidized bed voidage does not change much from the packed bed value. This conclusion agrees with those of other investigators, e.g. [5]. If an average value of ~ = 0.42 is used, the interparticles air mass velocity G' is related to the

Fluidized bed thermal storage 19

i

L ~4,

I

4o

• .o 0

0

,,,15 60 . 40

?

c

1

0

N

0

I 10 20 30 40

I I I 50 60 70 80

I I

d 4 4 /

,o, " ~ 0 Q ¶

- ~

I

I I m s = 5 kg

I

_UT!T . % . , = , . ,k ,

0 I _Ioi l0 II

.... I I 0 75 IS 0 225

Fig. 4(a).

90

300

superficial air mass velocity G by the following relation

G' = 1G = 2.381G. (3) e

3.4. Bed pressure drop The variation of the pressure drop across the bed

with the nominal air mass velocity is depicted in Fig.

7. After determining the bed voidage e in the previous section, it becomes more convenient to use the packed bed height H* (at G = 0) as a parameter instead of the mass of sand m,. Figure 7 shows that the general well known features (see e.g. [5, 8, 9]) of the pressure drop in a fluidized bed are well demonstrated by the experimental results obtained. First the pressure drop increases with the increase in the air mass velocity,

20 M, M. ELSAYED et al.

i

,

i I

I1

I

I

m s =10 kg

- - 6 0

~4o

.a 20

0

]

I 1

ms =12.s kg 1 -

o , ,

I I

66

~ 2 o

0 - -

. 1 4

0 • q

i I

m s = 15 kg

t~

I I l

"/5 150 225 Pressure ,mm H 2 0 gage

Fig. 4(b).

u

3 0 0

then it reaches a constant value irrespective of the increase in the air mass velocity. Between these two parts of the curve, a little pressure jump is sensed due to the residual clogging of sand. This jump is clear especially for small heights of sand.

Increasing the height of sand, scatter of data is found to increase, which raised the need for more data

to show the trend of the characteristic curve. For H * = 0.172m (ms = 20kg) the pressure drop data showed no clear trend and therefore the results for this case are excluded in Fig. 7,

F rom the pressure drop data shown in Fig. 7 it can be concluded that the min imum fluidizing air mass velocity for height of sand up to 0.13m is

Fluidized bed thermal storage 21

150

100 -

E E

4) j -

" 0

50-

1.0

' I ' I ' I ' I '

-/.5 k g j ._ .__4_.__--

mass of s a n d = 5 kg

, I , I , I I I m

0.04 0,00 0,12 0.16

Superficial air mass velocity G, k g / s . m 2

Fig. 5.

0.0

0.6

~ 0 .4

" U

o

0.2

Packed bed

i / / o~

0 i 0

I J I ' I ' I ' k e y m s

• 5 kg O "/.5 I , 10 O 12.5 x 15

0 O~[DxO~dll o e A ¢

I , I , I , I

0.04 0.00 0.12 0.16

Superficial air mass velocity G ,kg/s.m 2

Fig. 6.

about 0.0175kg/s m 2 which corresponds to G~,/= 0.179 kg/s m 2. Table 2 compares the present value of G,~ I to the values obtained by other investigators. It is clear that the present value of G~, I agrees very well

200

180

160

140

O -r

120 E E

"O ~ 1 0 0

o v o 8o Q.

"0

~ 0 0 w

Q .

40

20

' I ' ;I ' l ' i ' I

i0..,,,4 2/ i o.,o0 . , . . , )

~ 0 ,085 (10 k g ) -

I !

el o.o64 (7.Sk,)

H')('=0,043m (ms,, 5kg)

/ x ' -X , . , . . x .~x~ xX.F.x x x

E

,'7, _o

, l i .,I I , I ,

0.04 0.08 0.12 0.16 Superficial air mass velocity G. kg/s .m 2

Fig. 7.

with the value obtained by using the theoretical expression of [10].

The pressure drop across the sand required for fluidization (the constant value of Ap) as a function of the height of sand H* is shown in Fig. 8. The experimental results are compared with the ideal theoretical value of the pressure drop required just to overcome the sand weight, which varies linearly with the height of sand. The experimental results prove also this straight line relationship. Moreover, the experimental results give the same inclination of the theoretical relationship. The experimental results of the pressure drop are generally about 20ram H20 less than the theoretical ones. This difference may be attributed to the partial fluidization of sand caused" by bad distribution of the air flow.

22 M.M. ELSAYED et al.

Table 2. Values of G':.

Ref. a ~

Sourcet (kg/s m 2)

[10] [1 l ] [12]

Present work

(e~fl(1- ~,,:)) (d~(p,-p)g/180#) 0.178 O.Ol06(d~p(p~- P)/lO 0,27 l

0.0081 (d~-S[(p~-- p)]°'94/p0.88) 0.166 Fig. 7 and eqn (3) 0,179

I" Nomenclature : p = density of fluid (kg/m3), e,,: = voidage at minimum fluidizing velocity, Ps = density of sand (kg/m 3) and/~ = dynamic viscosity of air (Pa s).

4. HEAT TRANSFER IN FLUIDIZED BED

4.1. Experimental parameters In the following experiments, the bed is heated or

cooled by a flow of air at a constant or a specified pattern supply temperature. The air flow rate is always taken about 1.5 times the min imum required for fluidization.

Several experiments have been carried out to predict the transient bed performance at various parametric conditions, as given in Table 3. As indicated in the table, the three parameters considered in the experi- ments are : the supply air temperature, bed status and height of sand. The constant supply air temperature is taken equal to 85°C when heating the bed and the ambient when cooling the bed. When using linear

0 cq

E fi

r-

o

o. o

o,.

N -o '5

200

100

" I ' I ' I / / ~ / / / ' J

- /// / /

,// ,, i / X ~

. i i 1

O. 04 0.08 0.12 0.16 0.20

Original bed height , H ~ m

Fig. 8.

time dependent supply air temperature, the following relation is used

T,,i = Ti+0.66t , t < 60]

= constant, t > 60~ (4)

where t is the time in min measured from the instant where supply air is connected to the bed, and 7",. is the initial temperature of the bed. The exponential time dependent supply air temperature is described as fol- lows

T,, i = Tmax-(Tmax- Ti)e -°°'3' (5)

where t and T~ are as defined before, and Tm,x is the maximum achievable temperature.

The bed status can be either heating (charging with thermal energy) or cooling (discharging thermal energy). Also as indicated by the previous tabulation Lhe height of sand in the bed is selected at either 0.065 m or 0.13 m.

Before proceeding to the analysis of the exper- imental results it is convenient to introduce the fol- lowing dimensionless temperature and time :

T-- Tmi . o - (6)

Tmax - Tmj°

G'C r - p~H*C~ t (7)

where Tmi. is the min imum temperature of air or sand

Table 3. Heat transfer experimental runs

Run Supply H* no temperature Status (m]

H 1 constant heating 0.065 H 2 constant heating 0.13 H 3 linear in time heating 0.13 H 4 exponential in time heating 0.13 H 5 constant cooling 0.13 H 6 constant cooling 0.13

Fluidizedbed thermal storage 23

(D

£ w

N

1.0

0.8

0.6

0.4

0.2

0

6 12

I I

L i n e a r o o

o

o e

o • o •

o •

o • o t

e o •

'o •

~e • I I S 12 "C

18 24 30 36 I I I /

ee O a e e ag l O e e e e o e e I e

e l . 0 ,, , ; o o o o ~ E x p o n e n t i a l o o o o ° t e e e • • e e e e e

0.8 O O O e O e e

- o • o •

0.6 • o

o 0.4 • •

o • o S u p p l y a i r t e m p e r a t u r e

0 . 2 • • B e d a v e r a g e t e m p e r a t u r e

o e

0 s o I I I I n

6 12 18 24 3 0

D i m e n s i o n l e s s t i m e , "I;

Fig. 9.

36

during the time history of the bed, T~ax is the maximum temperature of air or sand during the time history of the bed, G' is the interparticle average air mass velocity, p is density, C is the specific heat and the subscript s refers to sand.

4.2. Temperature along the bed The results showed that the variation of the tem-

perature along the bed is negligible (less than I°C between sand at bottom and sand at top). This means that unlike the rock bed, the fluidized bed behaves as a well mixed tank, i.e. without any temperature gradient.

4.3. Bed average temperature The bed average temperature 0" b is defined as follows

1 " a~ = ~ ,Y:_ o,, ,C, am,,, (8)

where Am:,j is the mass of the sand segment that is represented by the temperature 0,,,- and n is the number of the sand segments.

The variation of the bed average temperature with time is given in Fig. 9 for linear time dependent supply air temperature and for exponential time dependent supply air temperature. By examining the figure one concludes that during the time interval where the supply temperature is sensibly varied with time, i.e. for 0 < z < 14 with constant temperature and 0 < z < 24 in linear and exponential supply tempera- ture respectively, the bed average temperature varies with time in a similar way as the supply air temperature.

Comparisons of the variation of bed average tem- perature with time for the previous two time depen-

dent supply air temperature and with the case of constant supply air temperature (with H * = 0.065 and 0.13 m) are given in Fig. 10. The figure shows that steady state conditions are achieved earlier in the case of constant supply air temperature than that of time dependent supply air temperature. Also, the cases of constant supply air temperature have identical results for H* = 0.065 and 0.13 m.

The bed storage factor BSF is now defined as the ratio of energy stored in the bed to the maximum possible energy storage in the bed, i.e.

msCs(I"b-- Ti) BSF = - Ob (9) m.Cs(T.,a.- T,)

where mr and C~ are the mass of sand in the bed and the sand specific heat respectively, and Tm,x is the maximum achievable temperature of the supply air. Thus, from eqn (9) it is clear that Figs 9 and 10 also represent BSF. In the constant supply air temperature, BSF becomes higher than 0.9 to z > 12 and higher

i i "° 1.0

I 0.8

s ~6

o 0.4

~ o.2

0

x e e

~ e e

. • A ~i

,!l ~l t I #

t i i Jo

x ° x e e l & & - - 0.8

Supp ly t e m p e r a t u r e " x Cons tan t I - r 'F=O.13m - 0.4

o Constant I - ~ : 0 . 0 6 5 m *& -o • Exponen t ia l in t ime _ 0.2 •

A l i near in t i m e

t f I 0 l l 18 24 30 38

D imens ion leSs l ime i "C

Fig. 10.

24

0.5

O.4

• ~- 0 . 3 .u =~ ~, o.z

O 0.1

M. M. ELSAYED et al.

I i ~ I I

V Supply temperature x Constant l~X'= 0.13m

I x o Constant = H* O.06Sm J ,~ Linear in time - ~ o Exponential in t;~me - O ~

XO x e ~-~ ̂ xo x

,. t 6 1?- I 24 3 36

Dimensionless time , "[

Fig. I 1.

1.38 0b - ~ . ( 1 1 )

r = 0

The previous equation is used to predict the vari- ation of q., with time as indicated in Fig. 11. The highest efficiency is found to occur at early time of operat ion for all cases of supply air temperature where the temperature difference between heating air and sand is at its highest value. For the same reason, the storage efficiencies at early time of operation for the cases of constant supply temperature (CST) are higher than those of the cases of the time dependent supply temperature. In all cases ~/, falls below 15% for

> 12 and below 8% for ~ > 24.

than 0.95 at z > 24. In the two cases o f time dependent supply air BSF becomes higher than 0.9 at r > 24.

4.4. Storage effieieno' One way to evaluate the process of heat storage in

the bed is to estimate the storage efficiency, q.t, which is defined as follows

,.~= - , - - - (10)

ri~,,c ~ (T,,,,- T,)At t = 0

where ~ is the voidage and rh, is the rate of air flow to the bed. The definition of qs relates the heat stored in the bed at a certain time to the amount of input heat (relative to the initial bed temperature) to the bed from the starting time of operation up to that time. The expression of eqn (10) is recast in the following

form (with ~ = 0.42)

4.5. Heat recovery After the bed is heated to its maximum possible

temperature, a cold air flow at the same rate as the original heating flow and at a constant temperature is circulated to the bed. Two cases are considered in the experiments, H* = 0.065 and 0.13 m. Figure 12 shows the time variation of the bed average temperature. As shown in the figure, identical results are obtained for H* = 0.065 and 0.13m. It is also shown in the figure that the bed average temperature did not decrease to 0-~ = 0 as will be the case if the final temperature becomes the same as the original initial temperature of the bed. This occurred because the supply cold air is heated by the fan to a temperature higher than that of ambient by about 5-T'C.

The heat recovery efficiency r/R is defined as follows

1.0 ,¢ 0.8

U

~" 0.6

g 0.4 a

~o 0.2

0

1 . 0 - - , , 1

~ 0.8

i ~ 0 . 6

o 0.4 g

--~0.2 x

x ~x ,~ 0 6 I . 12 24

X ~ :~ ~4DX ~'l lx Xe( xek x e c • • • e t

I I t 3'0 36 6 112 18 24

Dimensionless time , T.

x ~ x xe x x x x x

x e x Xex

x

x H -X" = 0 . 1 3 m x

• H "X" = 0. 065m x~

Fig. 12.

36

Fluidized bed

where Tb ... . is the maximum achievable bed average temperature. Figure 12 depicts the time variation of the heat recovery efficiency. The figure shows that identical results are obtained for H * = 0.065 and 0.13m. More than 70% of the available energy for storage can be recovered after being stored when z > 12. The percentage is increased to more than 80% when z > 24.

5. CONCLUSIONS

An experimental air-sand model is designed and manufactured to test the use of fluidized bed for ther- mal storage. The following have been found :

(1) The average voidage of air-sand bed, with sand of particle diameter less than 400 #m, is about 0.42.

(2) The minimum fluidizing interparticle mass vel- ocity is found about 0.18 kg/s m 2 and this value com- pares very well with the value given by Richardson [10].

(3) At heat storage mode the bed always behaves as a well mixed tank.

(4) The bed average dimensionless temperature does not depend on the mass of sand in the bed when hot air is supplied to the bed at constant temperature.

(5) More than 90% of possible heat storage is obtained after z > 12 with constant supply tem- perature and after z > 24 with linear and exponential time dependent supply temperature.

(6) The storage efficiency in case of constant supply temperature is always higher than that obtained with linear and exponential time dependent supply tem- perature.

(7) Only about 70% of the heat stored is recovered

thermal storage 25

from the bed at z = 12. This ratio is increased to 80% at z = 24.

Acknowledgement--This material is based upon work sup- ported by the College of Engineering of King Abdulaziz University under Grant No. 501/6.

REFERENCES

1. T. J. Jansen, Solar Engineering Technology. Prentice- Hall (1985).

2. E. E. Anderson, Fundamentals of Solar Energy Conver- sion. Addison-Wesley (1983).

3. W. B. Stine and R. W. Harrigan, Solar Energy Fun- damentals and Design. John Wiley (I 985).

4. G. Flamant and G. Olalde, High temperature solar gas heating comparison between packed and fluidized bed receivers--I, Solar Energy 31, 463-471 (1983).

5. R. R. Cranfield, Fluidized bed heat store for power generation. J. Inst. Energy 196 (Dec. 1980).

6. T. E. Weast, L. J. Shannon and K. P. Ananth, Study of thermal energy storage using fluidized bed heat ex- changers. Proc. 15th Int. Energy Conversion Engineer- ing Conf., pp. 619-623 (1980).

7. I. E. Megahed, M. Sabbagh, M. M. Elsayed and M. M. E1-Refaee, Transient performance of fluidized bed for thermal storage of solar energy. Final Report, Project 302-04, Faculty of Engng, King Abdulaziz University, Saudi Arabia (1985).

8. J. S. M. Botterill, Fluid-Bed Heat Transfer. Academic Press, London (1975).

9. J. F. Davidson and D. Harrison, Fluidization. Academic Press, London (1977).

I0. J. F. Richardson, Incipient fluidization and particulate systems, in Fluidization (Edited by J. F. Davidson and D. Harrison), 2nd edn, Chap. 2. Academic Press (1977).

11. J. F. Frantz, in Fluid-Bed Heat Transfer (Edited by J. S. M. Botterill), p. 71. Academic Press (1975).

12. M. I_eva et al., in Fluid-Bed Heat Transfer (Edited by J. S. M. Botterill), p. 70. Academic Press (1975).

13. M. Y. Abubakar, J. L. Sullivan, J. D. Tarasuk and M. A. Berougnou, New approaches and baffled heat transfer studies in fluidized bed heat storage. Proc. 14th Inter- society Energy Conversion Engineering Conf., pp. 899- 904 (1979).