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Three-dimensional freezing of water in a copper foils porous layer around a coolant-carrying tube

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Abstract

Three-dimensional freezing of water around a coolant carrying horizontal tube placed in an adiabatic rectangular cavity partially including copper foils is investigated numerically and by experiment. Both, enhancement of freezing and a uniform freezing rate are achieved. The present numerical analysis predicts well the transient solid fraction found by experiments.

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Abbreviations

c :

Specific heat

C :

Coefficient in the PCM flow resistance (=−10−6, Eq. 8)

d 1 :

Diameter of the domain 1 without copper foils

d i :

Inner diameter of the tube (=17.05 mm)

d o :

Outer diameter of the tube (=19.05 mm)

DTF :

Temperature range (0.05 °C) in the mushy zone (0 < f s < 1)

f :

Mass fraction

F :

Flow resistance per unite area perpendicular to the flow direction (Eq. 8)

h f :

Latent heat of freezing

H :

Height/width of the rectangular cavity (=12 cm)

k :

(effective) Thermal conductivity

L :

Tube length (=40 cm)

n :

Copper foil number

p :

Copper foil thickness (=35 μm)

P :

Coefficient in the flow resistance of the copper foils porous layer (Eq. 9)

r 1 :

Distance in the domain 1 (=(d 1 − d o )/2, without copper foils, see Fig. 1)

Fig. 1
figure 1

Physical model and coordinate system

Full size image
t :

Time

T :

Temperature

T ph :

Freezing temperature (=0 °C)

U :

x-Component velocity

v :

y-Component velocity

V PCM :

PCM volume \( ( = L[\gamma_{f2} (H^{2} - \pi d_{1}^{2} /4) + \pi \gamma_{f1} (d_{1}^{2} - d_{o}^{2} )4]) \)

V bare :

Bare volume of the cavity (\( = L[H^{2} - \pi d_{o}^{2} /4],\,\gamma {}_{f1} = \gamma_{f2} = 1 \) in V PCM)

w :

z-Component velocity

w m :

Mean velocity of the coolant in the tube (=0.0245 m/s)

x :

Horizontal coordinate

y :

Vertical coordinate

z :

Axial coordinate

γ:

Volume fraction

γ f :

Porosity, PCM volume fraction (i.e., = γ s+γℓ = 1 − γ c )

ρ:

Density

υ:

Kinematic viscosity

1:

Domain 1

2:

Domain 2

c:

Copper

clt:

Coolant

f:

PCM

ini:

Initial

inlt:

Inlet

ℓ:

Liquid (water)

s :

Solid (ice)

x :

x-Direction

y :

y-Direction

z :

z-Direction

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Acknowledgments

The authors wish to acknowledge support for this study by the technical official T. Fujita.

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Authors and Affiliations

  1. Faculty of Engineering and Resource Science, Mineral Industry Museum, Akita University, Akita, 010-8502, Japan

    M. Sugawara

  2. Department of Mechanical Engineering, Faculty of Engineering and Resource Science, Akita University, Akita, 010-8502, Japan

    Y. Komatsu & D. Onodera

  3. Institut fur Technische Thermodynamik, Technische Universitat Darmstadt, Petersenstrasse 30, 64287, Darmstadt, Germany

    H. Beer

Authors
  1. M. Sugawara
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  2. Y. Komatsu
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  3. D. Onodera
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  4. H. Beer
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Correspondence to M. Sugawara.

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Sugawara, M., Komatsu, Y., Onodera, D. et al. Three-dimensional freezing of water in a copper foils porous layer around a coolant-carrying tube. Heat Mass Transfer 48, 1847–1854 (2012). https://doi.org/10.1007/s00231-012-1030-x

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