Page 91 - Defrosting for Air Source Heat Pump

Modeling study on uneven defrosting 83

h c
h D ¼ (4.37)
2
c p ρ LeÞ 3
ð
a
where Le is the Lewis number for air and water vapor mixtures and a fixed value of
0.845 was used in this section [24].
Model 2 development (only Stage 3)
Schematics of mass and energy flows in defrosting Stages 1, 2, and 4 for Model 2 are
the same as those for Model 1 shown in Fig. 4.2, except that in Stage 3 in Model 2,
which is shown in Fig. 4.3. Hence, for Model 2, all the equations for Stages 1, 2, and 4
were identical to those in Model 1, except those for Stage 3.
In Stage 3, energy conservation in Control Volume j yielded:

dT w, j
q j ¼ L sf m f, j + c p M w,max + c p m w, j T w, j + h c,w T w, j T a A f a + q Me j ¼ 1 3ð Þ
dt
(4.38)

where M w, max is the maximum of the melted frost held on the surface of Circuit j.
Mass conservation in Control Volume j was:

m w, j ¼ m f, j j ¼ 1 3ð Þ (4.39)

Modeling a water-collecting tray and a water-collecting cylinder
As part of the entire setup of the three-circuit outdoor coil, a mathematical submodel
for the heat and mass flows on a water-collecting tray and a water-collecting cylinder
was also developed, and used together with the two models. As seen from Fig. 4.1, for
Model 1, the melted frost flowing away from the three circuits was collected by Cyl-
inder C via Collecting Tray C. However, for Model 2, the melted frost flowing away
from Circuits 1 to 3 was collected by Cylinders A, B, and C, via Collecting Trays A, B,
and C, respectively. As shown in Fig. 4.4, there were three steps for the process of the
mass and energy flows in a water-collecting tray during defrosting. Step 1 started dur-
ing Stage 3 defrosting and the melted frost started to flow away from a refrigerant
circuit and into a water-collecting tray.
The energy conservation of the melted frost collected on the tray in Step 1 required:

ð
dM tw T tw Þ
c p m w, j T w, j ¼ c p
dt
ð
h c A tw T a T tw Þ j ¼ 3 forModel1 and j ¼ 1 3 for Model2ð Þ
(4.40)
where M tw is the accumulated mass of the retained melted frost in the water-collecting
tray, which can be evaluated using Eq. (4.3). In addition, T w, j is the temperature of the
retained water on the surface of the tubes and fins of each circuit (as shown in Fig. 4.1),