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TECHNICAL PAPERS: Melting and Solidification

Ice Block Melting Into a Binary Solution: Coupling of the Interfacial Equilibrium and the Flow Structures

[+] Author and Article Information
Sophie Mergui, Sandrine Geoffroy, Christine Bénard

FAST-UMR CNRS 7608 (Universities Paris VI and Paris XI), Campus Universitaire-Ba⁁timent 502, 91405 Orsay Cedex, France

J. Heat Transfer 124(6), 1147-1157 (Dec 03, 2002) (11 pages) doi:10.1115/1.1513572 History: Received July 10, 2001; Revised May 06, 2002; Online December 03, 2002
Copyright © 2002 by ASME
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References

Figures

Grahic Jump Location
Time evolution of the dimensionless experimental height of the upper zone: 1.5×107≤RaT≤2.3×108,−172≤N≤−8(3×1010≤RaS≤3×1012).
Grahic Jump Location
Numerical simulation of the onset and the development of the first thermosolutal cell. Streaklines. Particles are released in the cavity at 9 locations specified by the coordinates (x*/Hi,z*/Hi): in the hot boundary layer – – – (9.6 10−5,0.70), [[dashed_line]](4.7 10−3,0.70); in the cold boundary layer [[dashed_line]](0.3296, 0.80), [[dashed_line]](0.3291, 0.80), [[dashed_line]](0.3285, 0.80), [[dashed_line]](0.3276, 0.80), [[dashed_line]](0.3265, 0.70), [[dashed_line]](0.3265, 0.80); near the cold wall: [[dashed_line]](0.2817, 0.85). RaT=2.3×108;N=−24;A=3; Pr=11.2; Le=189.
Grahic Jump Location
Concentration, temperature and density fields in the upper zone before the destabilization (t*=6050 s).RaT=2.3×108;N=−24;A=3; Pr=11.2; Le=189.
Grahic Jump Location
Experimental dimensionless height of the stagnant zone at the onset of the destabilization as a function of the theoretical one
Grahic Jump Location
Development of the structure of the fluid phase: (a) initial state; (b) build up of the thermal cell and development of an ascending solutal layer along the ice front; (c) growth of the upper low velocity and low concentration zone filled up by the ascending flow along the ice front. The thermal cell remains at the initial concentration and its temperature field is vertically stratified; (d) destabilization of the bottom part of the upper zone through a succession of corotating vortices; (e) the growing vortices merge into a wide horizontal rotating layer; and (f) the same destabilization process is reproduced several times.
Grahic Jump Location
Position and shape of the ice front are shown for two experiments at a same melting characteristic time, tm=0.63. The measured relative melted volumes are the same in both cases. These photographs show the weak velocity upper zone and the high velocity thermal cell (exposure time ≈20 s). The relative volumes of the upper zone are very different in both cases because the filling characteristic times tC are very different. Destabilization takes place at the cold side (case (a)) or at the hot side (case (b)).
Grahic Jump Location
Sketch of the experimental cell
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CL/(Ci−CL) as a function of 1/Ste. Local values of the front concentration CL are obtained from local interface temperature measurements, local thermodynamic equilibrium being assumed (Eq. (2.10)). zc is the corresponding height range of the convective cell (valid for Fig. 5 and Fig. 6).
Grahic Jump Location
Le−1/2Ras1/4/Nu as a function of Ste, where Nu is the local Nusselt number obtained from local front velocity measurements in the upper stagnant zone or in the convective zone. This figure shows the correlation between the local Nusselt number in the convective zone with Ras1/4 and its independence from Ste.
Grahic Jump Location
Dimensionless front velocity in the upper stagnant zone, VS, and in the convective zone, VC, as a function of Ste Le−1/2RaS1/4. For the convective zone, a straight line of slope 0.41±0.01 is obtained by linear regression (correlation coefficient J=0.99). For the upper zone, the straight line obtained by linear regression leads to a slope of 0.09±0.01 (correlation coefficient J=0.6).
Grahic Jump Location
Time evolution of the dimensionless experimental height of the upper zone: N=−23,RaS≈7.5×1010,2≤A≤3.1. For Δ and for ○, a secondary cell (sc) appears around t*=2100 s and t*=2164 s respectively. For □ and ⊞ no time is reached that corresponds to a secondary cell.
Grahic Jump Location
Dimensionless time evolution of the dimensionless experimental height of the upper zone: N=−23,RaS≈7.5×1010,2≤A≤3.1.
Grahic Jump Location
Dimensionless time evolution of the dimensionless experimental height of the upper zone: 1.5×107≤RaT≤2.3×108,−172≤N≤−8(3×1010≤RaS≤3×1012).

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