BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI
buletinul institutului politehnic din iaşi - Universitatea Tehnică ...
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82 Gelu Coman and Valeriu Damian<br />
h<br />
⎧CT T<<br />
T<br />
s<br />
f<br />
= ⎨<br />
CT<br />
l<br />
T ≥ T<br />
⎬<br />
f<br />
⎩<br />
⎫<br />
, (6)<br />
⎭<br />
h= h + ∫ c dT<br />
, (7)<br />
ref<br />
T<br />
Tref<br />
p<br />
where: T f – solidification temperature, C s ,C l – specific heat for the solid and<br />
liquid phases, h – sensitive enthalpy, T ref – reference temperature.h ref – reference<br />
enthalpy, c p – specific heat at constant pressure<br />
3. Numerical Results<br />
With numerical simulation of ice formation around the pipe submerged in<br />
water, a number of 25 210 iterations were made at a time step τ = 10 seconds.<br />
The total process running time was 7 hours, considering the process conclusion<br />
at the ice free surface temperature of -5,55 0 C. For the pipe is buried in sand a<br />
number of 18.000 iterations at a time step of 10 s were carried out . The time<br />
taken for solidification process was 5 hours, considering the process complete at<br />
an ice free surface temperature of -4,62 0 C.<br />
Initialized parameters in the mathematical model were:<br />
a) water temperature on the skating track t apa = 10 0 C<br />
b) air temperature at the water free surface t aer = 10 0 C<br />
c) temperature of the refrigerating agent inside the pipe t agent = -10 0 C<br />
d) mass flow fate fo the refrugerating agent m = 0.185 kg/s<br />
e) convection coefficient in the pipe α agent = 550 W/m 2 K<br />
f) air Convection coefficient on water surface α aer = 15W/m 2 K<br />
g) heat flow density o the track foundation board q= 10W/m 2 .<br />
Figs. 2 and 3 illustrate the time variation of the water surface<br />
temperature in the two cases analyzed: tube submerged in the water and pipe<br />
buried in sand. When immersed in water (Fig. 2) there is a sharp decrease in<br />
temperature in the nodes above the pipe and a slower decrease in the points<br />
located midway between the pipes. Under isothermal 0 0 C after τ = 300min,<br />
there is an almost constant distribution in nodes.<br />
When the pipe is buried in the sand Fig.3 there is a more rapid decrease<br />
in temperature compated with the pipe submerged in water. Isothermal 0 0 C<br />
reaches the water surface after approximately 90 minutes. Temperature<br />
distribution in the water surface nodes is almost uniform under isothermal 0 0 C,<br />
indicating a high quality of the ice.