Heat and Mass Transfer

, 47:1027 | Cite as

Shell-and-tube type latent heat thermal energy storage: numerical analysis and comparison with experiments

Original

Abstract

The melting process of industrial grade paraffin wax inside a shell-and-tube storage is analyzed by means of numerical simulation and experimental results. For this purpose, the enthalpy porosity method is extended by a continuous liquid fraction function. The extended method is tested using results gained from a gallium melt test inside a rectangular enclosure.

Abbreviations

LHTES

Latent heat thermal energy storage

PCM

Phase change material

HTF

Heat transfer fluid

CFD

Computational fluid dynamics

List of symbols

A

Porosity function in Darcy type source term, kg/m³ s

b

Small numerical constant in porosity function

C

Large constant in Darcy type source term, kg/m³ s

c

Heat capacity, J/kg K

Co

Courant number

d

Diameter, m

g

Gravitational force, m²/s

h

Specific enthalpy, J/kg

L

Latent heat of fusion, J/kg

l

Length, m

p

Pressure, Pa

Sh

Source term in enthalpy equation, J/m³ s

Sm

Darcy type source term in x and y momentum equation, kg/m² s²

Sb

Buoyancy source term in y momentum equation, kg/m² s²

T

Temperature, K or °C

t

Time, s

u

Velocity in x coordinate, m/s

v

Velocity in y coordinate, m/s

x

Horizontal coordinate

y

Vertical coordinate

X

Width of simulation domain

Y

Height of simulation domain

Greek letters

β

Volumetric thermal expansion coefficient

γ

Liquid fraction

η

Dynamic viscosity, kg/m s

λ

Thermal conductivity, W/m K

ρ

Density, kg/m³

Subscripts

erf

Error function

hot

Hot wall

ini

Initial

l

Liquid

m

Melting

ref

Reference

s

Sensible, solid

References

  1. 1.
    Zalba B, Marína JM, Cabeza LF, Mehling H (2003) Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Appl Therm Eng 23:251–283CrossRefGoogle Scholar
  2. 2.
    Cao Y, Faghri A, Chang WS (1998) A numerical analysis of Stefan problems for generalized multi-dimensional phase-change structures using the enthalpy transforming model. Int J Heat Mass Transf 32:1289–1298CrossRefGoogle Scholar
  3. 3.
    Lacroix M (1993) Numerical simulation of a shell-and-tube latent heat thermal energy storage unit. Sol Energy 50:357–367CrossRefGoogle Scholar
  4. 4.
    Gong Z-X, Mujumdar AS (1997) Finite-element analysis of cyclic heat transfer in a shell-and-tube latent heat energy storage exchanger. Appl Therm Eng 17:583–591CrossRefGoogle Scholar
  5. 5.
    Trp A (2005) An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit. Sol Energy 79:648–660CrossRefGoogle Scholar
  6. 6.
    Voller VR, Prakash C (1987) A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems. Int J Heat Mass Transf 30:1709–1719CrossRefGoogle Scholar
  7. 7.
    Ng KW, Gong ZX, Mujumdar AS (1998) Heat transfer in free convection-dominated melting of a phase change material in a horizontal annulus. Int Commun Heat Mass 25:631–640CrossRefGoogle Scholar
  8. 8.
    Khillarkar DB, Gong Z-X, Mujumdar AS (2000) Melting of a phase change material in concentric horizontal annuli of arbitrary cross-section. Appl Therm Eng 20:893–912CrossRefGoogle Scholar
  9. 9.
    Sasaguchi K, Kusano K, Viskanta R (1997) A numerical analysis of solid-liquid phase change heat transfer around a single and two horizontal, vertically spaced cylinders in a rectangular cavity. Int J Heat Mass Transf 40:1343–1354MATHCrossRefGoogle Scholar
  10. 10.
    Sugawara M, Beer H (2009) Numerical analysis for freezing/melting around vertically arranged four cylinders. Heat Mass Transf 45:1223–1231CrossRefGoogle Scholar
  11. 11.
    Brent AD, Voller VR, Reid KJ (1988) Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of pure metal. Numer Heat Transf 13:297–318CrossRefGoogle Scholar
  12. 12.
    Voller VR (1985) Implicit Finite—difference Solutions of the Enthalpy Formulation of Stefan Problems. IMA J Numer Anal 5:201–214MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Voller VR, Cross M, Markatos NC (1987) An enthalpy method for convection/diffusion phase change. Int J Numer Methods Eng 24:271–284MATHCrossRefGoogle Scholar
  14. 14.
    OpenCFD Ltd (2010) OpenFOAM 1.7.1. http://www.openfoam.com/
  15. 15.
    Shmueli H, Ziskind G, Letan R (2010) Melting in a vertical cylindrical tube: numerical investigation and comparison with experiments. Int J Heat Mass Transf 53:4082–4091MATHCrossRefGoogle Scholar
  16. 16.
    Gau C, Viskanta R (1986) Melting and solidification of a pure metal on a vertical wall. J Heat Transf 108:174–181CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Lehrstuhl für Technische Thermodynamik und Transportprozesse (LTTT)Universität BayreuthBayreuthGermany

Personalised recommendations