Development of a model compatible with solar assisted cylindrical energy storage tank and variation...

Pergamon Energy Convers. Mgmt Vol. 37, No. 12, pp. 1775-1785, 1996

Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All fights reserved

PII: S0196-8904(96)00035-0 0196-8904/96 $15.00 + 0.00

DEVELOPMENT OF A MODEL COMPATIBLE WITH SOLAR ASSISTED CYLINDRICAL ENERGY STORAGE TANK A N D VARIATION OF STORED ENERGY WITH TIME FOR DIFFERENT PHASE CHANGE MATERIALS

M E H M E T E S E N 1 and T E O M A N A Y H A N 2

~Department of Mechanical Education, Ftrat University, 23119 Elam[~, Turkey and 2Department of Mechanical Erigineering, Karadeniz Technical University, 61080 Trabzon, Turkey

(Received 14 April 1995)

AlaS'act--In this work, the performance of a solar assisted cylindrical energy storage tank is investigated theoretically. A model describing the transient behavior of a phase change energy storage unit is used. The model of the tank holds the numerical description of a short term (by day) beat-storage tank. In the tank, the energy is stored as the latent heat of the phase change material (PCM). In the tank, the PCM is packed in cylinders, and the heat transfer fluid (HTF) flows parallel to it. The basis of the model is the enthalpy method. The resulting set of equations is solved by means of the Gauss--Sddd iteration process. Sdeeted computer simulations are drawn versus some parameters of the model, and the heat storage capacities of different PCMs, which can be used as heat storage materials for domestic heating by heat pumps, were determined and compared. Results show that the PCM, cylinder radius, the mass flow rate, and the inlet temperature of the HTF must be chosen carefully in order to optimize the performance of the tank. Copyright © 1996 Elsevier Science Ltd

Solar energy storage Phase-change materials Latent heat Simulation Heat pump

Enthalpy method

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

A a - -

ak= b k =

CCHH = C 1

C 2

c~= Cpj-- Cp., --

Area (m 2) Thermal diffusivity (me/s) Grid-factor concerning (j, k) and (j, k + l) Grid-factor concerning (j, k) and (j, k - I) CaC126H20 Grid-factor concerning (j, k) and ( j + l, k) Grid-factor concerning (j, k) and ( j - l, k) Specific heat (ld/kg °C) Specific heat of PCM in liquid phase (kJ/kg °C) Specific heat of PCM in solid phase (kJ/kg °C)

E = Energy (El) E E l = Energy content of PCM

,it = Initial energy content of PCM Fo = Fourier number (dimensionless) H = Nondimensional enthalpy

HTF = Heat transfer fluid i = Specific enthalpy (kJ/kg)

Lc = Length of cylinder (m) l = Axial length of control volume dement (m)

M = Number of axial elements (dimensionless) N = Number of radial elements (dimensionless) n = Distance in direction normal to phase change interface (m)

Arc = Number of cylinders (dimensionless) PCM ffi Phase change material

P-WAX = Paraffin wax (P116) Qin,H = Mass flux of HTF flowing from heat source to tank (kg/h)

R = Radial distance (m) R~ = R ~ . = R~out (nonwall cylinder)

R~,, = Inner radius of cylinder (m) R~.o~ t = Outer radius of cylinder (In)

r = Nondimensional radial distance (dimensionless)

1775

1776 ESEN and AYHAN: SOLAR ASSISTED CYLINDRICAL ENERGY STORAGE TANK

r s = Latent heat o f fusion (kJ/kg) SSDH = Na2SO4.10 H20

T = Temperature (°C) Te. v = Environment temperature of storage tank (°C)

Tin. H = Temperature of HTF flowing from heat source to tank (°C) Tml = Lower melting temperature of PCM (°C) Tin2 = Upper melting temperature of PCM (°C) T,t = Initial temperature of storage tank (°C)

t = Time (h) U = Thermal loss of storage tank (kJ/h m 2 °C) V = Volume (m 3)

Vjj, = Control element volume (m 3) V ~ = Total PCM volume in tank (m 3) Vum~ = Inside volume of tank (m 3)

z = Axial distance (m) AT m = Transition range width (°C)

0 = Nondimensional temperature 2 = Thermal conductivity (kJ/m h °C) 21 = Thermal conductivity of PCM in liquid phase (kJ/m h °C) 2, = Thermal conductivity of PCM in solid phase (kJ/m h °C) ) ' t = Thermal conductivity of PCM in transition phase (kJ/m h °C) p = PCM density (kg/m 3)

P. = HTF density (kg/m 3) Pw = Cylinder wall material density (kg/m 3)

Superscripts i = time level inside model

if = final time level inside subroutine itf = final iteration level

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

Energy storage can reduce the time or rate mismatch between energy supply and demand, thereby playing a vital role in energy conservation. Energy storage leads to saving fuel and makes the system more effective by reducing the wastage of energy. It improves the performance of energy saving systems by smoothing and increasing their reliability. Because of this, energy storage is an important element in many utility systems [1]. Recently, many studies on thermal energy storage have been conducted, accompanying the development of efficient energy utilization technology, such as energy conversion from geothermal energy, solar energy and factory exhaust heat.

Among various methods of thermal energy storage, latent heat thermal energy storage is the most attractive due to a high density of heat storage. PCM heat storage can be applied in processes which require heat at an approximately constant temperature level. For instance, the storage tank may be part of a solar assisted heat pump. Heating homes by heat pumps in regions in which the annual average temperature is not below zero in the winter season is more economical. Because the coefficient of performance of the heat pumps is always greater than one, heat pumps give us more energy than the primary energy we use. Energy storage allows the heat pump to operate at night and on cloudy days, during which times or periods there is no solar radiation.

In addition, for practical purposes, the latent heat of fusion is the most important storage parameter since the phase change involves a relatively large quantity of heat that can be stored at a constant temperature with little change in volume.

The use of PCMs for thermal energy storage in solar heating systems has received considerable attention. For liquid based systems, Morrison et al. [2] showed that a system utilizing paraffin wax may require a slightly larger storage volume than a system of comparable performance with a water tank. On the other hand, systems utilizing Na2 SO4.10 H20 require roughly one-half the storage volume of a conventional water tank system. A theoretical model of a shell-and-tube PCM storage unit was reported by Ismail and Alves [3]. In their model, the energy equation for the PCM is written in terms of the enthalpy. The numerical results show the effects of the Biot number, the relative diameters of the tubes, and the inlet fluid temperature on the thermal performance of the unit. Visser [4] developed a component model for numerical description of two different short term heat storage vessels. In both vessels, the energy is stored as the latent heat of PCMs. Both configurations can be described in a cylindrical way, resulting in a two-dimensional mathematical model. The basis of the model is the enthalpy method. The model is validated on the basis of a

ESEN and AYHAN: SOLAR ASSISTED CYLINDRICAL ENERGY STORAGE TANK 1777

comparison between the numerical results of a simple problem and its analytical solution. The agreement is the best in the case of a linear grid in the radial direction of the PCM cylinder. Yimmer and Adami [5] also developed a numerical model for optimizing a basic one-dimensional, shell-and-tube, thermal energy storage system. Again, an enthalpy approach was adopted for the PCM. A parametric study was then conducted to assess the effects of the inner tube and outer shell radii and of the liquid phase thermal conductivity of the PCM on the performance of the unit. Lacroix [6] developed a theoretical model to predict the transient behavior of a shell-and-tube storage unit with the PCM on the shell side and the HTF circulating inside the tubes. Then, parametric studies are performed to assess the effects of various thermal and geometric parameters on the heat transfer process and on the behavior of the system. Other important studies can be found in Refs [7-10].

In this paper, a parametric study is performed to assess the effects of various parameters (T~n,H, Qin.H) and PCMs on the quantity of stored heat energy. First, a computational methodology is presented for predicting the heat transfer between the HTF and the PCM of a cylinder packed latent heat storage tank.

The cylindrical latent heat storage system (tank) which has been considered here is a part of a domestic heating system (Fig. 1). During the charging mode of the PCM, the cylindrical tank is in the closed loop with the flat-plate collectors, and during the discharging mode, the stored energy is extracted by a liquid flowing through the storage unit to the water-source evaporator of the heat pump.

A theoretical model has been developed for such a storage tank. The calculations for the moving boundary and fluid (water) temperatures have been done using latent heat storage materials.

The main objectives of the present study are to develop a model of phase-change energy storage that considers

(i) the heat losses from the storage unit, (ii) the axial conduction in the storage material,

(iii) the radial conduction in the storage material (i.e., the thermal conductivity of the storage material in the radial direction is finite), and

(iv) the local film temperature difference between the fluid and the PCM.

2. CONFIGURATION OF THE STORAGE TANK

Figure 2 shows the configuration chosen for the storage vessel. It consists of a vessel packed in the vertical direction with cylindrical tubes. Besides the phase change material (PCM), the latent

t Storage [ tank

Water circulating pump

®

Evaporator

Compressor

Inlet air

Fan

Condenser

J, Exit air

Fig. 1. Solar-assisted heat pump system with latent heat storage tank.


(a) (b)

From heat source

Vtlnk

L c

t

I

Rc,out

Re inn p

/

PCM I I

/ Cylinder wall

Heat-transfer fluid

To heat source Fig. 2. The cylinder-packed vessel (a) and the model for one cylinder (b).

heat storage system contains a fluid for the heat transfer towards or from the heat-storage material. The PCM and the H T F are separated. The shape of the packing of the PCM and the H T F is of a cylindrical nature. In this study, we consider a configuration of packing of the storage material which is a vessel packed in the vertical direction with cylindrical tubes; the PCM is inside the tubes and the H T F flows parallel to it. We decide to describe the vessel as follows.

For the model, we assume that the HTF which is surrounding the cylinders is situated in cylinder jackets all round the tubes. Of course, the volume of all these cylinder jackets together is equal to the fluid volume in the real storage tank.

The density of the packing is the same anywhere in the tank. To have as much PCM as possible enclosed within a tank of a certain volume, we shall mostly aim at a close packing of the cylinders. However, again, we notice that this is not necessary.

3. D I S C R E T I Z A T I O N OF THE E N T H A L P Y EQ U A TIO N

The thermal energy storage in PCM makes use of the latent heat of the material. The change of state results in a moving boundary: on one side of the interface the material is solid, while on

I I

- i ~ j ' _ - j - j , k z _ -j-1

l kl Ik_ 1 JR

Fig. 3. Definition of the cylindrical control volume element (], k).


the other side it is liquid. This class of problem is known as a Stefan problem. Application of Fourier's law to a small control volume leads to energy conservation:

0T pCp ~ = div(2gradT) (1)

In equation (1), we assume there is no convection and there are no sources of energy inside the control volume. If 2 is direction-independent, equation (1) can be rewritten as follows:

0T 0 t = a.div(gradT) (2)

where a is the thermal diffusivity given by a = 2/pCp. The increase with time of the energy content of an arbitrary volume V, which is fixed in space, has to be equal to the net heat transfer into V through its surrounding surface area A if there are no sources of energy inside V and no external work is performed. Considering that, in the absence of motion, the pressure is time-independent, we find the enthalpy equation:

d f p i d V f A 2 g r a d T . a d A (3) dt v

with ti the outward normal to A. The interface has been removed from equation (3). Another advantage of the enthalpy method

is that it is easy to handle heat-storage materials with a phase change range. We decide to introduce the phase change range(s) by:

i (T )= Cp.sT for T < Tm~, (4)

rs(T - - Tin, ) i(T) = Cp,, T -~ ATm for Tml ~< T ~< Tin2 (5)

and

i(T) = Cp,,T + rs for T > Tm2 (6)

in which ATm is the width of the transition range: ATm = Tin2 - Tm,. With equations (4)-(6), we have achieved a more useful description of the moving boundary

problem. By using a nondimensional enthalpy and temperature, we will further simplify these equations. The nondimensional enthalpy is given by:

i - iml H = - - (7)

rs

and the nondimensional temperature by:

O= Cp~(T- Tm') for T < Tm~ (8) rs

and

o=Cpj(T-Tm~) for T/>Tm~. (9) Is

4. M O D E L L I N G OF THE CYLINDRICAL PROBLEM

To solve the moving boundary problem, we will discretize the enthalpy equation (3). Because of the cylindrical nature of the problem, the discretized equations will also be in cylindrical form. We consider, in this section, a fixed control-volume element (j, k) of phase change material, which is part of the cylinder (see Fig. 3).


Table 1. Physical properties of studied PCMs [12]

Properties CCHH PARAFFIN SSDH P-WAX

Density (kg/m 3) 1710 830 1460 786 Specific heat (kJ/kg °C)

Solid 1.46 1.92 2 2.89 Liquid 2.13 3.26 2 2.89

Thermal conductivity (kJ/m h °C) Solid 3.92 1.85 0.54 0.497 Liquid 1.94 0.805 1.08 0.997 Transition 2.52 1.157 0.72 0.685

Melting temperature (°C) Lower (Tml) 29.7 32 39 46.7 Upper (T~) 29.85 32.1 39.15 46.85 Latent heat of fusion (kJ/kg) 187.49 251 180 209

Application of equation (3) on volume element (j, k) leads to:

L O T 0 T + 2A/ - 2A:_ ~ ~z Oi = - 2Ak - ~ + 2Ak- 1 - ~ 1

The surface areas of element (j, k) are given by:

Ak = 27rRkl

Ak_ t = 2 ; r R , _ t l

and

Aj= A:_, = ~r IR~_I - R2J

and the volume of the element by:

Vy,k= Tr lR2_, -- R211.

We use finite differences in space for OT/OR and OT/Oz:

k i O T Tj,~ -- Tj, k + s -~ = 2

Rk-1 - - Rk+l

--oROT d = 2 Tj~n _- rtT~'k-1 k - J ~ , ~ k - 2

J i i OT _ T:~-- T/+l,k

Oz l

(io)

(11)

(12)

(13)

(14)

05)

(16)

(17)

Table 2. Other simulation parameters

Inside surface area of the storage tank 13 m 2 Thermal loss of the storage tank 2 kJ/h m 2 °C Shape of the storage tank (Lo/D) 2.46 Environment temperature of the storage tank 18°C Initial temperature of the storage tank 18°C Density of the HTF 1000 kg/m 3 Specific heat of the HTF 4.2 kJ/kg °C Density of the cylinder wall material 1200 kg/m 3 Specific heat of the cylinder wall material 0.5 kJ/kg °C Thermal conductivity of the cylinder wall material 0.2 kJ/m h°C Length of cylinder (or the tank) 3.2 m Nightly heat load of heating space 200 MJ Maximum storage time (daytime) 8 hour

E S E N and A Y H A N :

250 - -

~" 2oo

150

O 50

0

Tie H=35"C, R c iw~ ~0"024 m, ' PCM: C ~ H H

• • . • •'*

x • • •

• • • 600 kglh Jm • • 800 kg/h

. j ~ i ~ • • xt l O 0 0 k g / h 1100 kg/h

..dti i l I I I I I 5 10 15 20 25 30 35 40

T i me (h)

SOLAR ASSISTED C Y L I N D R I C A L E N E R G Y STORAGE T A N K

T. - = 4 0 ° C , R . - 0 0 2 4 m i n , H CplRIt "

PCM: CCHH

250 --

~" 2 0 0 - -

1 5 0 - - r, es

o 100 -

~ so -

0 -

(b) x

x •

x •

×

t J ' l 5

X i I • • X • • • • •

• 600 kg/h • 800 kg/h • 1000 kg/h × 1100 kg/h

I i I I 10 15 20 25

Time (h)

1781

300

~, 250

~ 150

'~ 100 o

50

0

Tin H--450C, R ¢ inn=0.024 m, ' PCM: C ~ H H

(c)

Am I •• x xxm •

x:." I" x • • • 600 kg/h • • • • 800 kg/h • • • I000 ks /h

• • x I100 kglh

, 1 : , I I 5 10 15 20

T i me (h)

300

250

--- 200

o 150

~00

m 50

Tin , H=5OoC, R c in• =0"024 m, PCM: C ~ H H

(d)

D

x •

×•@

1 ,

0 5

x2-~t - • • • xAI •

xA• •

x •

• • • • 600 kg/h • 800 kg/h • 1000 ks /h x 1100 kg/h

l I l 10 15 20

Time (h)

o es

~J

200

150

I00

50

Q in H = 1 1 0 0 kg /h , R c inn =0"024 m, ' P C M : P - W ~ X

(e) A m.

• ••me •

Am 0 0 • 0 0 0

• • 50"C • 600C • 70"C

Am

• •

l* I o o 5

I I I I 10 15 20 25

400 --

--~ 3 5 0 -

3 0 0 -

2 5 0 - eb m 2 o o ! -

150 - -

2 t 00 -

50 -

30 0

R e inn=0.024 m, Q in a = 1 1 0 0 kg /h ' PCM: S S b H

(f)

• 0@0 Aim 1 1 • • 0

• 5 0 0 C

,t • 600C • • • 7 0 " C

i I I i I I I 2 4 6 8 10 12 14

T i m e (h) T i m e (h)

Fig. 4a-f.

and

a n d f o r Oi/Ot:

~zTI _ T~,-T~_t, l - I 1 (18)

j,k ~ "i " i - 1 di ty~ - - tj, k

0t At (19)

Combinat ion o f equations (10)-(19) leads to a fully implicit equation which is given in the nondimensional form by:

1782 E S E N and A Y H A N : S O L A R A S S I S T E D C Y L I N D R I C A L E N E R G Y S T O R A G E T A N K

H ~ s , - H ~ ' A F o . [ a k ( Q j a , + , - Q ~ . K ) + ' = bk(Qj .~_, - Q t y . t )

. .~ i i i Cl (Qj+ l,k - - Qj,k) .-I- c 2 ( Q j - l , k Q~s~)]. (20)

Here, A F o is the Fourier number:

A F o = ~.At/pCpR2c,out . ( 2 1 )

The constants ak, bk, C, and c2 are called the grid factors:

a~ = 4rk/ (rk_ l -- rk + l ) (r 2 - , -- r 2), (22)

bk = 4 r k - I / ( r k - 2 - - rk )(r2k-1 - - r2) ( 2 3 )

with rk the nondimensional radial distance and

2 2 cl = c2 = Rc,o.t / l • (24)

The nondimensional radial distance is given by:

r k --.= Rk /Rc ,ou t . ( 2 5 )

The detailed analysis of the numerical method used to solve this problem can be found in Ref. [4]. The energy content with regard to the initial temperature /'st of the PCM is given by:

350

--'- 300

250

2OO e~ o 150 o

I00

50

Tin H =500C ' Q i a H = 1 1 0 0 k g / h ' R e , in=0.~)24 m

( g ) • CCHH - xX x × • Paraffin

~ • P-WAX ~ × SSDH

• ! •, I , I I I 5 10 15 20 25 30

T i m e (h)

350 - -

300 -

250-

e~ 200 -

e-i o 150 -

~ l o o - O

50 -

O . |

Tin , H=60*C, R c inn =0 .024 m, Q ia, H=l I~0 kgPa

(h) • "

• @ P - W ~ • SSDH

I I I I I I 4 6 8 10 12

T i m e (h)

400

350

3 0 0 -

2 5 0 ; - -

o 200

.~ 150 - o } 100 -- r~

50 --

0 0

Tia H=70oC, R ¢ iaa=0.024 m, ' Q ia,H=ll~0 kg/h

( i )

• P-WAX • • SSDH

$ I I I I [ 2 4 6 8 10

v

o es O

o

140

120

I00

80

60

40

20

0 i 2

Tia t l = 5 0 ° C , R e iaa =0 .024 m, ' P C M : p ~ a f f i n

0) x ** × •

x • • @

x a • • • 600 kg/h

X • • • 8 0 0 k g / h

• • • 1000 kg/h × 1100 kg/h

I I I I I I J 4 6 S I0 12 14 16

T i m e (h) T i m e (h)

Fig. 4g-j . Var ia t ion of s tored energy wi th t ime, for different P C M s and values of Qin, H, Tm, H(Vpcm = 0.637 m 3, N c = 110. R~ o.t = 0.025 m) .

ESEN and AYHAN: S OL AR ASSISTED C Y L I N D R I C A L E N E R G Y STORAGE T A N K

R c,laa---0.024 m, T st=lSOC, 60 - PCM: C C H H

~ • 400 kg/h 50 -~ • 600kg/h

. . ~ A 800 kg/h 40 ' ~ ~ × 1000 kg/h

20 - ~ - = ~ _ .

I I I 35 40 45 50

Y i,. n (*C) Fig. 5. Variation of whole PCM melting time with inlet HTF temperature of tank (Tin..) at different values

of Qin, n , for CCHH (Fpcm = 0.637 m ~, R~,o~t = 0.025 m, N c = 110).

1783

M+ 1 N + 2

Epcm = Epcm,,t + N~pr," E E H~tf Vj~ j = 2 k = 3

in which E~m,,t is dependent on the range /'st.

(26)

5 . R E S U L T S A N D D I S C U S S I O N

The transient simulation program [4] is used to determine the performance of the cylindrical energy storage tank which can be used in the solar assisted domestic heating by heat pump system (Fig. 1). The physical properties of the PCMs used in this simulation program are listed in Table 1. Other simulation parameters are given in Table 2. The solar heating system considered in this study is based on water and is shown in Fig. 1. Whenever solar energy is available, it is collected and transferred to the storage unit. Whenever a space heating load is present, it is met by the storage unit and/or the auxiliary energy source. The results given in Figs 4--6 are obtained from computer simulations [11]. Appropriate thermal and geometric parameters for a given heating load can be selected by means of these figures.

Figure 4 shows the variation of stored energy in the PCM with time for various PCMs at different values of Qi.,. and Ti.... Each curve has been generated for constant values of Tin,., Qi,,M and Re,i**. As the mass-flow rate of the H T F (Qin,H) increases at a given time, the stored energy becomes bigger (i.e., more heat is removed from the HTF, and consequently, more heat will be stored in the PCM). In addition Ti,,H causes a similar variation. We suppose that the nightly, and daily required heat load of a heating space and the maximum storage time of solar energy (daytime) are, respectively, 200 M J, 500 MJ and 8 hours. For the nightly load, the heat storage material C C H H is appropriate for values of Qi,,n 1> 800 kg/h, Tin,. I> 50°C o r Qin,H t> 1000 kg/h, Tm,. 1> 45°C. Similarly, when the PCMs P-Wax and SSDH are appropriate, the values are Qi,.H t> 1100 kg/h, Tin,n >t 70°C and Qin.n >/1100 kg/h, Tin.. I> 50°C, respectively. For appropriateness, the paraffin needs much larger values of the Ti,.H and Qm,. than the SSDH (see Fig. 4).

Figure 5 shows that, for melting of all the C C H H in the daytime (i.e. for maximum energy storage), the appropriate values are Qi,../> 1300 kg/h, T.~,. I> 50°C.

The variations of stored energy and whole CCHH melting time with number of cylinders (i.e. mass of the CCHH) at different values of Qin,H and/~,in~ are depicted in Fig. 6. It is seen that, as the radius of the PCM cylinder increases at a constant mass of CCHH, the whole CCHH melting time becomes longer.

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

A parametric study for estimating the stored energy dependence on time in a tank containing PCM has been presented. The following conclusions were obtained.

In this model, although we used relatively high temperatures Ti,,H (60-70°C) and Q~,H, the whole PCM melting time is found to have a high value again. Furthermore, the stored energy is obtained


II

a..lO

~ s • .~ 7

6

,..11

~, 10

9 . . t

S

"" 7 o

6 5

o

O

PCM: CCHH, R c=0.016 m.

_ m

m I - Epc m • • @

• m m / _

• • . • • •/>/*×.. x

• $ •• • m m ~• : ~ xA'×

• • x / - : x t xt x t x f f • t l00kg/h -- - x / • 1300 kg/h

/ • 1500 ks/h 4 - / x 1700kg/h

/ 3 - /

2 / I 100 200

900 l 1

10 800

700 9

• 8 600

7 500

6 400 5

30O 4

2OO 3

I I I I I I too 2 300 400 500 600 700 800 900


- - - Epc m

- • :

• × ^ j • x × /

f

/ f

f _I

I I I I 100 150 200 250 300

-- 900

• • , . , 8 o o [

f 700 ---"

( _ ,00.. - 500

• ltOOkg/h -- 400 • 1300 kg/h .,.,° • 1500 ks/h - 300 x 1700 kg/h - 200

I I I I 100 350 400 450 500 550

Number of cylinders Number of cylinders

PCM: CCHH, R c=0.024 m. - 500

- - - - Epcm • $ O / /

• • 4m

• / • • x

• • ,,F &° X -- • X • / x

• × --

-- X X X / t /

/ • 1100 kg/h -- / • 1300 ks/h

/ • 1500ks/h - 200 -- / x 1700 kg/h _/

) I I I t oo 120 140 160 180 200 220

400

300


• As / • x

x . t . ' x

f

- - - Epc m

1 --

- - • • X X X - - × /

/ /

_ / /

- /

3 1 - 2 I I I I

40 60

• • • $ i , / 0 / / m •

• ~ . )1

× x

x

• 1100 kg/h • 1300 kg/h • 1500 kg/h × 1700 kg/h

800 "-a

7OO & m

- 600~"

- - 500"~ em

- - 4 0 0 o

- 3oo~ 4 o

- 2 0 0 ~ 3

2 I I I I I I I I I I 100 40 60 80 100 80 100 120 140 160 180 200 220 240 260

Number of cylinders Number of cylinders

Fig. 6. Variation of stored energy and whole PCM melting time with number of PCM cylinders at different values of Qi~H and Pc, for CCHH (R~m = P~.out = Pc, Tin.a = 50 °C, Tst = 18 °C).

as not much more. From these considerations, we conclude that the cylinder wall material and radius used were not appropriate. Because the thermal conductivity of the cylinder material is very small, the PCM melting time is lengthened. In addition, the cylinder wall radii are big. To remove these disadvantages, more appropriate cylinder wall materials and dimensions should be selected. Namely, the thermal conductivity of the cylinder material has to be much bigger. The effective thermal conductivity is often increased by placing conducting structures like fins, lamellae or matrix structures into the storage material. Moreover, smaller cylinder radii should be tried. Results show that, for a given type of PCM, these parameters must be selected carefully in order to optimize the performance of the storage tank. The numerical predictions are validated with experimental data.

In this study, only a theoretical analysis was presented. In the future, an experimental analysis of this storage tank with numerical analysis will be presented.

R E F E R E N C E S

1. B. Kilki} and S. Kakaq, NATO ASI Series, p. 1 (1989). 2. D. J. Morrison and S. I. Abdel Khalik, SoL Energy 20, 57 (1978). 3. K. A. R. Ismail and C. L. F. Alves, Analysis of shell-and-tube PCM storage system, Prec. 8th Int. Heat Transfer Conf.,

San Francisco, 1781-1786 (1986). 4. H. Visser, Energy storage in phase-change materials-development of a component model compatible with TRNSYS.,

Final Report. Contract No. 2462-84-09 El) ISPNL. Delft Univ. of Technology, Department of Applied Physics, Delft (1986).

5. B. Yimmer and M. Adami, Parametric study and optimization of phase change thermal energy storage systems, National Heat Transfer Conference, HTD, Multiphase Flow, Heat, and Mass Transfer 109, 1-8 (1989).

6. M. Lacroix, Sol. Energy 50, 357 (1993). 7. A. A. Ghoneim, Sol. Energy 42, 209 (1989).


8. N. Giiltekin, T. Ayhan and K. Kaygusuz, Energy Convers. Mgmt 32, 311 (1991). 9. N. K. Bansai and D. Buddhi, Energy Convers. Mgmt 33, 235 (1992).

10. A. M. Tayeb, Energy Convers. Mgmt 34, 243 (1993). 11. M. Esen, Numerical Simulation of Cylindrical Energy Storage Tank Containing Phase Change Material on the Solar

Assisted Heat Pump System and Comparing with Experimental Results, Doct. Thesis, Dept. of Mechanical Engineering, Karadeniz Technical University, Trabzon, Turkey (1994).

12. D. V. Hale, M. J. Hoover and M. J. O'Neil, Phase Change Materials Handbook. NASA CR 61363 (1971).

Development of a model compatible with solar assisted cylindrical energy storage tank and variation...

Documents

Transcript of Development of a model compatible with solar assisted cylindrical energy storage tank and variation...