MODULES
Mushy Region Phase Change Problem With Convection
Problem Definition:
This is a general phase change problem with natural convection. In this case, phase change occurs over a temperature range (e.g. alloys). To solve two-dimensional problem (1 × 1) in three-dimensional code, one cell is used in the z-direction. A cubical enclosure is filled with the liquid having initial temperature T=0.5. The following properties of the liquid are taken in the simulation Voller and Prakash [1].
• specific heat (cp)=1
• thermal conductivity (κ)=0.001
• dynamic viscosity (μ)=0.01
• density (ρ)=1
• volume expansion (β)=0.01
• half-mushy range (ǫ)=0.1
• latent heat (L) =5.0
• melting temperature(Tm)=0.0
These parameters leads to Ra=104, Pr=10 and St=5.0. At time t > 0 left wall temperature is reduced to −0.5 which is below the melting point temperature and right wall is kept at its initial temperature. All the other faces are having adiabatic boundary condition. As a result, solidification occurs in the presence of natural convection and the mushy zone is moving in the positive x direction. The solver finds the position of the mushy zone at different times. The problem is actually taken from , but they have taken very high Pr (Pr=1000). A very high Pr liquid demands a high computational time [2]. Therefore to reduce the time for the present case Pr=10 has been taken.
Figure 4.1: Geometry of Turbulent mixed convection
Numerical simulation is performed on 50 × 50 uniform hexahedral grid. The zone lies between the solidus and liquidus lines is known as mushy zone. In this zone, both liquid and solid co-exists as shown in Fig. 1.2(a). This is an unsteady problem and therefore the mushy zone is moving as the time passes as shown in Fig. 1.2(b). Figures 1.3(a) and (b) show the comparison of u-velocity at different y section and solidus & liquidus lines at t=1000 sec respectively with the result of Anupravaha I.
(a)
(b)
Figure 1.2: Mushy zone and vector plot at (a) t=200 sec, (b) t=600 sec
(a)
(a)
Figure 1.3: (a) u-velocity comparison at t=500sec, (b) solidus and liquidus lines comparison at t=1000sec
[1] Voller V. and Prakash C. (1987) ‘A fixed grid numerical modelling methodology for convection-diffusion mushy region phase change problems’, Int. J. Heat mass transfer, vol. 30(8), pp. 1709–1719.
[2] Babu A.B. (2006) ‘Numerical simulation of solidification and melting problems, iit kanpur’, Master’s thesis.
