BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

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