Page 84 - Defrosting for Air Source Heat Pump

76 Defrosting for Air Source Heat Pump

(b) At 40 s into defrosting, the preheating stage (first stage) was over.
(c) At 90 s into defrosting, the frost melting without water flowing away from a circuit stage
(second stage) was over.
(d) The following experimentally measured refrigerant flow rate, tube surface temperatures at
the inlets and outlets of each circuit, temperature of the ambient air surrounding the outdoor
coil, and compressor discharge pressure during defrosting were used as the inputs to the
models developed.

4.2.1.2 Model development
As mentioned, two semiempirical models were developed for the two settings of with
and without the use of water-collecting trays between circuits. The use of trays would
stop the melted frost from flowing into the circuits (or control volumes) underneath in
Stage 3. Therefore, the two models were identical for Stages 1, 2, and 4, with only the
modeling work in Stage 3 being different. In this section, for simplicity, the complete
development of Model 1 is first presented. For Model 2, only the modeling work in
Stage 3 is reported.

Model 1 development (all four stages)
The model was developed by applying the energy and mass conservation in each of the
three control volumes at each of the fourth defrosting stages.

First stage: Preheating As shown in Fig. 4.1A, the energy and mass conservation in
Control Volume j yielded:

q j Δt ¼ L sf m f, j Δt + c p Δ M w, j T w, j + q Me Δtj ¼ 1 3ð Þ (4.1)
As Δt ! 0, Eq. (4.1) can be written as

dM w, j T w, j
q j ¼ L sf m f, j + c p + q Me j ¼ 1 3ð Þ (4.2)
dt
whereM w, j istheaccumulatedmassoftheretainedmeltedfrostintheControlVolumej :
ð t
M w, j ¼ m f, j dt j ¼ 1 3Þ (4.3)
ð
0

where t is the ending time of Stage 1 defrosting and T w, j the temperature of the melted
frost on the surface of Circuit j (as shown in Fig. 1).
On the other hand, the heat transferred from the water layer to the frost layer for
frost melting was:

h w T w, j T tp A 0 ¼ L s, f m f , j j ¼ 1 3ð Þ (4.4)
where T tp is the triple point of water and A 0 the equivalent airside surface area of a
refrigerant circuit.