NUMERICAL SIMULATION AND DISCUSSION

Series of numerical calculations have been carried out in order to analyse transient heat transfer during melting and solidification of the technical grade paraffin used in experimental investigations. Some of the computational results are illustrated further.

Fig. 6 shows radial dimensionless temperature distribution at an axial location of X = 12.73 in different dimensionless times during melting of PCM for laminar HTF flow with Re = 657. Melting of the PCM has occurred non-isothermally within a dimensionless temperature interval 0 to 0.42. The regions of HTF, tube wall and a PCM are indicated in the figure.

Fig. 6. Radial dimensionless temperature distribution at X = 12.73 in different times during melting

Melting of the paraffin starts on the HTF tube wall surface and expands inside the PCM storage tank. As melting front progresses, the temperature curve moves upward. The fluid velocity profile reaches a steady state quickly, while the temperature profile never reaches a fully developed state due to the moving melting front. This clearly approves that the use of empirical correlations for the convective heat transfer can result in a significant error.

Radial dimensionless temperature distribution at an axial location of X = 12.73 in different times during PCM solidification, for laminar HTF flow with Re = 657, is shown in Fig. 7. Solidification has occurred isothermally. Solidification fronts in different times are the intersections of the dimensionless temperature 0 = 0 and the corresponding temperature curves. Solidification of the PCM starts on the HTF tube wall surface and spreads inside PCM tank. Temperature curve moves downward due to a solidification front progression.

The propagation of the solidification front is shown in Fig. 8. The solidification front moves in the axial direction of the PCM container faster than in the radial direction. Due to the relatively large Prandtl numbers (small thermal conductivity) of the water as HTF, a large amount of heat is carried downstream, while a relatively small amount of heat is transferred directly to the paraffin as PCM upstream. The solidification zones are indicated in the figure. At dimensionless time t= 10909, the PCM is mainly in the solid phase.

Spatial dimensionless temperature distributions of HTF, tube wall and PCM inside the latent storage unit in different times during PCM solidification are shown in Fig. 9.

CONCLUSION

A numerical and experimental study of transient phase-change heat transfer during charging and discharging of the shell-and-tube latent thermal energy storage unit, with HTF circulating inside the tube and PCM filling the shell side, has been performed. Numerical predictions coincide quite well with the experimental results. Non-isothermal melting and isothermal solidification of technical grade paraffin, which has been used as PCM, have been observed by experimental investigations. Unsteady temperature distributions of HTF, tube wall and PCM have been calculated numerically. The results of numerical analysis underline that HTF velocities reach a steady state condition quickly, while temperatures change with moving of the melting/solidification interface, so it is necessary to treat the phase-change and fluid flow and heat transfer as a conjugate problem and solve them simultaneously as one domain. The usage of empirical correlations in expressing a convective heat transfer should be avoided. Due to the relatively large Prandtl numbers of the water as HTF, a large amount of heat is carried downstream, while a relatively small amount of heat is transferred directly to the paraffin as PCM upstream. The developed numerical procedure could be efficiently used for the simulation of transient thermal behaviour during charging and discharging of a latent thermal energy storage unit. Obtained numerical results provide guidelines for its design optimisation.

NOMENCLATURE

Symbols Subscripts

a

thermal diffusivity, m2/s

f

HTF

c

specific heat, J/(kgK)

i

inside radius of the tube

D

diameter of the tube, m

in

inlet

H

volume enthalpy, J/m3

init

initial

L

length of the tube, m

l

liquid phase of the PCM

m

mass flow rate, kg/s

m

melting / solification

Nu

Nusselt number

o

outer surface of the latent

P

dimensionless pressure

storage unit

P

pressure, Pa

out

outlet

Pr

Prandtl number

p

PCM

q

latent heat capacity, J/kg

R

dimensionless coordinate

R

dimensionless coordinate along the radial direction

along the radial direction

r

coordinate along the radial direction, m

r

coordinate along the

Re

Reynolds number

radial direction

St

Stefan number

s

solid phase of the PCM

T

thermodynamic temperature, K

w

wall

t

time, s

X

dimensionless coordinate

W

dimensionless velocity

along the axial direction

w

velocity, m/s

x

coordinate along the axial

X

dimensionless coordinate along the axial direction

direction

x

coordinate along the axial direction, m

а

convective heat transfer coefficient, W/(m2K)

X

dimensionless enthalpy

$

temperature, °C

X

thermal conductivity, W/(mK)

в

dimensionless temperature

P

density, kg/m3

T

dimensionless time

и

kinematic viscosity, m2/s

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