pcm two phase flow 2009

8/3/2019 PCM Two Phase Flow 2009

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The 6th Engineering Conference Volume3: Mechanical and

College of Engineering Nuclear Engineering

5-7 April 2009

ANALYSIS OF THERMAL ENERGY STORAGE SYSTEM WITH

TWO PHASE FLOW AND PCM USING FEM

Asst. Prof. Dr. Karima E. Amori*

Ameer K. Baqir*** Univ. of Baghdad , ** MSc. Student Nahrain Univ. , (Mech. Eng. Dept. ), Baghdad/ Iraq

ABSTRACT

The present study explores numerically the energy stored by a phase change material

(PCM) surrounding a tube (to form a thermal energy storage unit TESU) which acts as a

heat sink that receives energy from fluid flowing inside a tube embedded in the PCM.Effect of single or two phase fluid flow on the melting and the temperature distribution

inside the PCMs is performed for different parameters studied such as flowing fluid inlet

temperature ranged from 40C to 80C, the effect of Reynolds number of the flowingfluid ranged from (1500 to 12000), and the type of PCMs employed to investigate the

effect of their thermo-physical properties. In all these cases an axial temperaturedistribution is obtained by adopting a computational transient (3D) simulation usingFEM, and a Fortran-90 computer program is developed to solve the problem. The

program was tested and verified by solving some verification cases. Results show that thetime required to complete phase change (of PCM) becomes shorter with increase in inlet

temperature of flowing fluid. Also the increase in Reynolds No. has a great influence on

the phase transition process of the PCM. The increase in fluid flow rate is translated intoan increase in heat transfer between the flowing fluid and PCM.. It is shown that using

water instead of air as a flowing fluid leads to an increase in energy stored. For two phase

flow the investigation indicates that an increase in the magnitude of mass dryness fraction

leads to increase the energy stored in the PCM and a decrease in time of charging energy

in the unit.

(PCM) (

.))(PCM

((PCM40 ,)1500-12000(, o 80 o.

90(PCM ) . .

. (

(PCM . ) (PCM. ." .

Keywords: heat storage, PCM, melting, two phase, FEM.

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Analysis of Thermal Energy Storage System With Asst Prof. Dr. Karima E. Amori

Two Phase Flow and PCM Using FEM Ameer K. Baqir

INTRODUCTION

Phase change storage systems have been developed for many applications such as icestorage, conservation and transport of temperature sensitive materials, building insulation

applications, etc. Employing the heat released or absorbed at melting/solidification

temperature of phase change material (PCM) in space heating or cooling is an important

feature of this process.A review of thermal energy storage particularly on moving boundary problems in

different heat exchanger constructions is presented by Zalba et. al.(2003). A storage unit

composed of spherical capsules filled with (PCM) placed inside a cylindrical tank isinvestigated numerically and experimentally by Ismail and Heriqniez (2002). They

treated the solidification process using only one dimensional heat conduction employing

finite difference approximation and a moving grid inside the spherical capsules.Zukowski (2007) analyze the heat and mass transferred in a ventilation duct filled with

encapsulated paraffin wax (RII56) for short term heating by adapting three dimensional

fully implicit (FDM).The objective of the present study is to explore numerically in 3-D the melting process

of different phase change material (PCM) in a storage system. The heat is transferred tothis material from a single or two phase flowing fluid inside horizontal tube pass through

this PCM.

MATHEMATICAL MODEL

Assumptions

To establish a convenient mathematical model to analyze the transient temperatures

and heat transfer rates, the following assumptions have been introduced:

The PCM is homogenous and isotropic and the thermo physical properties of solid

phase are different from that of liquid phase.

The thermo physical properties of PCM are independent on temperature and there

is no volume contraction or expansion. Thermal losses from system external boundary and radiation heat transfer inside

the system are ignored.

Forced convection fluid flow inside tubes. The initial temperature of the (PCM) is uniform and assumed at solidifying

temperature (Ts) for melting process.

No Internal chemical reactions or heat sources

Governing Equation

The energy equation for a material undergoing a phase transformation is given as

Zalba et. al.(2003):

sTkHut

H +=+ 2 (1)

For constant thermo physical properties (constant density ) of the PCM and no heat

sources , eq.(1) can be reduced to :

Tkt

H 2=

(2)

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5-7 April 2009

Substituting the left hand side byt

Tcp

, yields:

Tkt

Tcp

2=

(3)

Geometry and Boundary ConditionsThe initial condition specifies a constant temperature field at (To) at time zero. The

boundary conditions, given as:

0=

n

T(4)

at external boundary and plane of symmetry as shown in fig.(1), while that at internal

surface of tube wall :

)( =

TTh

n

Tk i (5)

Heat Transfer Coefficient ( hi )

Single Phase Flow

The internal heat transfer coefficient (hi) is calculated for turbulent single fluid flow

according to (Kays and Crawford 1993)

))1(Pr2/7.121

2/*)1000(Re(

32

+

=

f

f

i

C

C

D

kh (6)

2)639.4ln(Re)236.2(2=fC (7)

Where

fC is Petukhovs friction coefficient for turbulent flow [Kays and Crawford 1993].

Two Phase Flow (Condensation heat transfer coefficient )

The local heat transfer coefficient is dependent on the mass flux G of fluid flowing

through the tube. If G is greater then or equal to (100 kg/ms) the fluid is considered to betransitioning to annular flow and correlation is applied that is [Shah 1979]:

]p

)X1(X8.3)X1[(hhh

38.0

r

04.076.08.0

ltpi

+ (8)Where csatr PPP = ; is the critical pressurecPIf G is less than (100 kg/ms), then the stratified flow portion of the Dobson and Choto(1998) correlation is applied .

}Nu)1(]Ja

PrGa[

X11.11

Re23.0{

D

kh forad

l25.0

l

l

58.0

tt

12.0

vol

tp + (9)

where: : Lockhart- Martinelli parameterttX

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v

vo

GDRe = , (Reynolds No. and Pandtl No. assuming all fluid flowing as vapor)lPr

9.01.0

l

v5.0

l

v

tt )X

X1()()(X

=

(10)

2

l

3

gllc D)(gGa

= (11)

fgwsatpll h/)TT(CJa (12)where Ga is Galileo No. ; is Jakob No.

lJa

l

is the angle formed by extending an imaginary line from the top of the tube to the

liquid level in the bottom of the horizontal tube.l

is related to the void fraction , which

is defined as the ratio of the vapor-flow cross- section area to the total cross section area[Zivi , (1964)]:

2

)2sin( ll (13)Approximate this relationship as [Jaster & Kosky , (1976)]

)12(cos

11

l (14)The forced convection Nusselt number is given as:forcedNu

)X(ClPrRe0195.0Nu ttl4.0

l

8.0

lforce = (15)

2c

tt

1

ttlX

C376.1)X(Cl + For 0 < < 0.7 (16)loFr

2

lolo1 Fr564.1Fr78.5172.4C lo2 Fr69.0773.1C

If > 0.7 then ,loFr 242.7C1 = 655.1C2 =

NUMERICAL ANALYSIS

Descretizing the differential eq.(3) with initial and boundary conditions (eq.s (4) and

(5) respectively) using finite element method, employing Galerkin procedure leads to thefollowing typical components of elemental mass, stiffness matrices, and force vector (M

e

, Ke

and Fe

respectively) which can be defined as:

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5-7 April 2009

= ee

kjp

e

jk dNNCM (17)

+= eee

kjie

jkejk dNNhdNkNK )( (18)

= ee

ki

e

k dNhF (19)

The thermophysical properties during phase change process (melting process) are

calculated as : (using table (1) for different PCM's)

(20)

mss

msss

smp

)F1(F

k)F1(kFk

)TT/(LHC

Where the subscripts (s) and (m) refer to solid phase and melted phase respectively, and

the elemental solid fraction is calculated using linear interpolation as:

sm

s

sTT

TTF

=(21)

where T refers to the elemental average temperature.

The elemental matrices and vector (Me

,Keand F

e) are assembled into global matrices

and global vector to obtain a system of first order time dependent differential equation

[ ] { } [ ]{ } { }FTKTM =+ (22)

A recursive algorithm based on time marching technique (finite difference method) isadopted to solve eq.(22) (Smith and Giffiths 2004), so introducing a linear interpolation

and fixed time step t :

onTTT )1( += (23)

Where are new and old temperature values respectivelyon

TandT

: constant such that 10 (taking =2/3 based on Galerkin approach with

unconditional stability)Substituting eq.(23) in eq.(22) leading to the following result

tFTKtMTtKMon +=+ ])1([][ (24)

Rearranging this equation to get a system of algebraic equations as:

[A] ={B} (25)n

T

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Grid Generation

The mesh shown in fig's. (1.b,c and 2a,b) represents a symmetrical quarter of thermalenergy storage unit composed of 396 nodes (66 nodes per layer) and (250) hexahydral

linear eight nodded elements. The first line (e=1 to 10 in layer 1) of elements adjacent to

fluid represents the copper tube wall while the rest belong to PCM.

Computational ProcedureThe computational steps followed in the present work are:

1- Read input data :a.Thermophysical properties of copper tube and of different PCM's used in the

present work (Table (1)).

b.TES unit size and tube diameter (Table (2)).c.Initial temperature

d.Fluid inlet temperature, and flow rate.

e.Time step.2- Generate nodes coordinates and elemental nodes (local and global) and compute

elemental area.3- At each time step

a. Increment timeb. Compute the local (z direction) internal heat transfer coefficient hi

c. Compute elemental matrices and vector

d. Assemble elemental matrices and vector to global systeme. Modify system matrices to form matrix A and vector B

f. Solve the system of simultaneous equations [eq.(25)] to evaluate

using Gauss Elimination method for symmetrical matrix A

nT

4- Advance to the next time step and repeat step 3

Time required to complete phase change ( melting duration ) can be determined by

subtracting the time required to change the phase of the first node (t1) from that requiredfor the last node ((t2) in the analyzed domain.A Fortran-90 computer program is

developed for the computational approach using. The execution time varies between (7-10 min for time step of (10 s) depending on period of examination) on a personal

computer Pentium 4.

RESULTS AND DISCUSSION

Verification of the Computer Program

The validity of the computational procedure and the computer program developed is

examined by solving a two dimensional phase change problem which is initially at

material fusion temperature (Tf) then suddenly subjected to T1 in order to solidify thematerial as shown in fig.(3). The results obtained are compared with that published by [

Crowley 1978 ]. This comparison shows a good agreement between the computational

and published results with maximum variation of 0.1% .

Single Phase Flowing Fluid:

The Effect of Flowing Fluid Inlet Temperature:

The effect of water inlet temperature on three dimensional melting process of the

PCM around tube for inlet temperatures (40C, 60C and 80C) is shown in figures (4,5&6), respectively (for Re=1500). These figures show the axial temperature distribution

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5-7 April 2009

within PCM (CaCl2.6H2O at initial temperature =27C) along line AA. It is clear that the

melting process started and finished at (Z = 0) while at (Z > 0.4) the PCM was still in

solid phase because the flowing fluid temperature decreases along tube length fordifferent inlet fluid temperature as shown in fig.(7). The PCM needs less time to melt as

inlet fluid temperature increases (6100s, 3800s and 2500s for inlet fluid temperature

40C, 60C and 80C respectively)as shown in fig.(8). fig. (9) shows that the computed

heat stored in PCM during melting process increases with increasing water inlettemperature (70 kJ, 150 kJ and 210 kJ for 40, 60 and 80C respectively). The thermal

behavior recorded above is due to the dependence of heat transfer between PCM (initial

temperature was 27C) and flowing fluid on the temperature difference between them.

The Effect of Reynolds No. (Re):

Figures (5, 10, and 11) show the axial temperature distribution along line AA for

Reynolds numbers 1500, 6000 and 12000 respectively and water inlet temperature equal

to 60C. These figures demonstrate that the melting process started and finished at Z=0faster than other axial position, also increasing Reynolds number leads to decrease the

melting duration of PCM as shown in fig.(12), since the convection heat transfercoefficient is affected by Reynolds number (increase with increasing Reynolds number asgiven in eq.(6) which leads to increase the heat transfer from water to PCM as shown

clearly in fig. (13).

The Effect of Type of the Phase Change Material:

Three types of phase change material are investigated in this work named

CaCl2.6H2O, Lithium Chloride Ethanol and Zn(NO2).6H2O to study their thermal

performance. figs. (5, 14 and 15) show the computational axial temperature distributionof the three types of PCM when water at 60C enters the tube with Re=1500. These

figures show that Lithium Chloride Ethanol has faster thermal response than that of

Zn(NO2).6H2O while CaCl2.6H2O seems to have the slowest response. This is due tothe difference in their thermo physical properties. fig.(16) shows that maximum heat

stored in PCM3 (Zn(NO2).6H2O) compared with the others, since it has the max.

temperature difference between melting and solidifying temperatures , max. density,thermal conductivity and heat capacity as shown in table (1) .

The Effect of Type of Inlet Flowing Fluid:

Two types of flowing fluid were investigated (water and air) as shown in fig.s (5) and(17), for inlet temperature of 60C and Reynolds No. of 1500. From these results it can

be seen that the total heat transfer in case one is more than the heat transfer in case two as

shown in fig.(18) because the heat transfer coefficient is decreased when air is used as a

flowing fluid. The reason for this behavior is due to higher value of density and viscosityof water than that the air, this leads to increase in the heat transfer.

Two Phase Flowing Fluid:

Effect of Mass Dryness Fraction (X):

The two phase flow of saturated water at 60C and (0.2 bar) was studied as a flowing

fluid in TESU with different mass dryness fraction (0.1, 0.3 and 0.5), figs.(19, 20 & 21)show that the total heat transfer from flowing fluid to the PCM will increase and a

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decrease in melting duration time when the mass dryness fraction (X) increases for the

same inlet water temperature of 60C, and Re No. of 1500, since the content of vapor(which moves faster than water) will increase and increases heat transferred.

CONCLUSION

The following concluding remarks can be drawn during this work Increase the temperature of inlet flowing fluid leads to increase the heat stored inPCM and leads to decrease the phase change duration.

Increase the Reynolds No. of the flowing fluid leads to increase the magnitude ofheat transfer and leads to decrease the melting duration.

Increase the difference between melting and solidifying temperature leads toincrease in the heat transfer and melting duration.

Increase in the density and viscosity of flowing fluid leads to increase in the heattransfer, and also decreases the melting duration time.

Increase in the mass dryness fraction of the two phases flowing fluid leads toincrease in the heat transfer and decrease in the melting duration time.

Table (1) Properties of Three PCM Used [Zalba et.al.2003]

Property CaCl2.6H2O

PCM1

Lithium

Chloride

Ethanol PCM2

Zn(NO2).6H2O

PCM3

Latent heat of fusion

LH (kJ/kg) 181.38 188.38 136Solid Liquid solid liquid Solid liquid

Temperature (Co

) 28 28.2 22.7 23 36 36.7 copperDensity (kg/m

3) 789 750 780 700 1937 1828 8954

Thermal Conductivity

(kW/m.K)

0.18 0.19 0.11 0.12 0.464 0.47 386

Specific Heat Cp (kJ/kg) 1800 2400 1500 2200 2300 4000 0.3831

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5-7 April 2009

PCM

Flow InsideTubes

AnalyzedDomaine

(a)

e =

1 - 50 51 - 100 101 - 150 151 - 200 201 -250

node No.=1 67 133 199 265 331

66 132 198 264 330 396

PCM V

Fluid Flowing VPCM

V

V

( b )

VV 20 mm

Vz

A A

(c)

Fig.(1): Division of the Thermal Energy Storage Unit into a)TES Unit, b)Layers ,

c)Elements and nodes

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1

11

12

22

33

44

55

66

23 34 45

56

61

50

39

28

17

6

e=1

e=10

e=50

V

Vx

y 50 mm

50mm

V

VV

V

V

25

mm

0 1 2 3 4 5 6 7 8 9 10

t

0

10

20

30

40

50

60

70

80

90

100

Solid

Fraction

Computed results

Crowley

(a)

b

Fig.(2): Grid Generation (a) First Layer at z = 0 , b) 8-Noded 3_D Element

(b)

85

e=10

96

84

18

30

29

1

2

3

4

5

6

7

19

(a)

T1

T1

Initially

at Tf

Solid

Liquid

0=

n

T

Insulation

L

L

Fig.(3): a) Analyzed Domain ,(b)Comparison of Computational Results and Crowley

Results for Two Dimensional Phase Change Problem

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5-7 April 2009

26.5

27

27.5

28

28.5

29

29.5

30

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time(s)

Temperature(C)

Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig.(4): Temperature Distribution in PCM along Tube for Single Phase Flowing

(40C) Inlet Temperature, Re =1500

26.5

27

27.5

28

28.5

29

29.5

30

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time(s)

Temperature(C)

Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig.(5) :Temperature Distribution in PCM along Tube for Single Phase Flowing Fluid at

(60C) Inlet Temperature, Re =1500

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26.5

27

27.5

28

28.5

29

29.5

30

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time(s)

Temperature(C) Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig.(6) :Temperature Distribution in PCM along Tube for Single Phase Flowing Fluid at(80C) Inlet Temperature, Re =1500

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100 120

Tube Length (cm)

Temperature(C)

Tin=40

Tin=60

Tin=80

Fig.(7): Water Temperature Variation Along Tube Length for Different Inlet

Temperature

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5-7 April 2009

20 40 60 80 100Inlet Temp. ( C)

0

2000

4000

6000

8000

Time(s)

20 40 60 80 100Inlet Temp. ( C)

0

50

100

150

200

250

Heat(kJ)

Fig. (8): Melting Duration Time for Different Fig. (9): Heat Stored within PCMfor Inlet Water Temperature at (Z=0, Re=1500) Different Inlet Water

Temperature

26.5

27

27.5

28

28.5

29

29.5

30

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time(s)

Temperature(C) Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig. (10): Temperature Distribution in PCM Along Tube for Single Phase Flowing Fluidat (60C) Inlet Temperature, Re =6000.

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26.5

27

27.5

28

28.5

29

29.5

30

30.5

0 2000 4000 6000 8000 10000 12000

Time(s)

Temperature(C)

Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig. (11): Temperature Distribution in PCM Along Tube for Single Phase Flowing Fluid

at (60C) Inlet Temperature, Re =12000

0

1000

2000

3000

4000

5000

6000

Time(s)

Re= 1500 6000 12000 0

Heat(kJ)

Re= 1500 6000 12000

Fig.(12): Melting Duration Time for Fig.(13): Heat Stored in PCM for

Different Re No. Different Re No.

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20

21

22

23

24

25

26

27

28

29

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time(s)

Temperature(C)

Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig.(14): Axial Temperature Distribution in PCM for Single Phase Flowing Fluid at

(60C) Inlet Temperature, Re =1500 for Lithium Chloride Ethanol

35.5

36

36.5

37

37.5

38

38.5

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Time(s)

Temperature(C)

Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig.(15): AxialTemperature Distribution in PCM for Single Phase Flowing Fluid at

(60C) Inlet Temperature, Re =1500 for Zn(NO2).6H2O

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0

50

100

150

200

250

300

PCM 1 PCM 2 PCM 3

Different PCM

Heat(kJ)

Fig.(16): Computational Heat Stored in PCM for Different PCM

26.8

27

27.2

27.4

27.6

27.8

28

28.2

28.4

28.6

28.8

29

0 5000 10000 15000 20000 25000 30000 35000

Time(s)

Temperature(C) Z=0

Z=20

Z=40

Z=60

Z=80

Z=100

Fig.(17): Axial Temperature Distribution in PCM for Single Phase Flowing Fluid Air at(60C) Inlet Temperature, Re =1500

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144

146

148

150

152

154

156

158

160

162

water

Two Type of Flowing Fluid

Heat(kJ)

airwatera ir

Fig.(18): Heat Stored in PCM for Two Type of Flowing Fluid

21.5

22

22.5

23

23.5

24

24.5

25

25.5

26

26.5

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time(s)

Temperature(C)

X=0.1

X=0.3

X=0.5

single phase

Fig.(19): Axial Temperature Distribution in PCM2 (Lithium Chloride Ethanol) at Two

Phase Flowing Fluid Water at (60C) Inlet Temperature, Re =1500 and at Z=0

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0

1000

2000

3000

4000

time(s)

0.1 0.3 0.5

Dryness Faction X

0

40

80

120

160

Heat(kJ)

0.1 0.3 0.5

Dryness fraction X

Fig. (20): Melting Time Duration for Fig. (21): Heat Stored in TESU for DifferentDifferent Mass Dryness Fraction Mass Dryness Fraction

REFERENCES:

Crowley A.B., (1978), "Numerical Solution of Stefan Problems", Int.J. Heat MassTransfer, 21, 215

Dobson,M.K., and Chato,J.C. (1998), "Condensation in Smooth Horizontal Tubes",ASME Journal of Heat Transfer,120,193-213.

Ismail Kar; Henriquez, JR., (2002),Numerical and Experimental Study of SphericalCapsules Packed Bed Latent Heat Storage System" Applied thermal engineering 22,

P.P.1705-1716.

Jaster H., Kosky P. G., (1976), Condensation Heat Transfer in a Mixed Flow Regime,

International Journal of Heat and Mass Transfer, 19,95-99.

Kays,W.M. and Crawford,M.E. (1993), "Convective Heat and Mass Transfer", Newyork,

McGraw Hill

Zukowski M. (2007), "Mathematical Modeling and Numerical Simulation of a Short

Term Thermal Energy Storage System Using Phase Change Material for Heating

Applications", Energy Conversion & Management 48, PP. 155-165

Smith, I.M. and Giffiths, D.V. (2004),"Programming the finite element method" ,ThirdEdition, John Wiley & Sons Ltd. England.

Shah M.M., (1979), A General Correlation for Heat Transfer During Film Condensation

Inside Pipe, International Journal of Heat Transfer, 22,547-556.

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5-7 April 2009

Zalba B. ; Marin J.M. ;Cabeza,L.F. and Mehling H.,(2003), "Review on Thermal EnergyStorage with Phase Change Materials, Heat Transfer Analysis and Applications", Applied

thermal engineering 23, PP. 251-283

Zivi S.M., (1964), Estimation of Steady-State Steam Void-Fraction by Mean of thePrinciple of Minimum Entropy Production, ASME Journal of Heat Transfer, V.22;

pp.547.556.

Baqir A.K.,(2008),"Numerical Study Of Two Phase Flow Effect On Thermal BehaviorOf Thermal Energy Storage System", MSc. Thesis, Mechanical Eng. Dept. Al-Nahrain

Univ.

NOMENCLEATURE:

Cp Specific heat J/kg.K Q fluid volumetric flow rate (m3/hr)

D Tube diameter (m) Re Reynolds number

loFr Froude No. of all liquid Pr Prandtl number

{F} Global force vector s Heat source J/m3

h Specific enthalpy J/kg t Time (s)H Enthalpy J T PCM or tube wall temperature (C

o)

k Fluid thermal conductivity(W/m.Co) Tin fluid inlet temperature (C

o)

[K] Global stiffness matrix T fluid bulk temperature (Co)

[M] Global mass matrix u Velocity (m/s)

N Unit normal vector X Mixture dryness fraction

Greek symbols

boundary domain

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pcm two phase flow 2009

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