Page 353 - Defrosting for Air Source Heat Pump

Appendices 349

Appendix C: Metal energy storage effect

The metal energy storage (MES) effect was used to evaluate the influence of the ther-
mal energy stored in the metal of the indoor and outdoor coils on the defrosting per-
formance. It was defined as the ratio of the net amount of energy from the indoor and
outdoor coils to the total amount of energy available from the system outside during an
entire defrosting operation, as follows:

Q i,MES Q o,MES
η ¼ 100% (C.1)
m
E comp + E i, fan + Q i,air
in which, E comp and E i, fan are the power inputs to the compressor and indoor air fan
during defrosting, respectively. Q i, fan is the thermal energy supply from the indoor air.
Q i, MES and Q o, MES are the MES values of the indoor and outdoor coils, respectively.
The total mass of frost accumulation during the experiment, m f , could be calculated
with the density of the air in the outdoor frosting space and the volumetric flow rate of
the air passing through the outdoor coil, as shown in the following equations.

t f
ð
X
m f ¼ Δm f dt ¼ Δm f Δt (C.2)
0
Δm f ¼ ρ o,a V o,a Δt ω o,o ω o,i Þ (C.3)
ð
In Eqs. (C.2) and (C.3), ρ o, a and V o, a are the density and volume of outdoor air, and
ω o, o and ω o, i are the moisture content of the air at the outlet and inlet of the outdoor
coil. Δt and t f are the measuring time interval and frosting duration, respectively.
The total mass of vaporized water, m v , was expressed by

(C.4)
m v ¼ m f m m ¼ m f m tf m rw
in which, m cf is the total mass of the melted frost collected in the cylinders, and m rw the
total mass of the retained water.
In Eqs. (A.1) and (C.1), Q i, a is the thermal energy transferred from the indoor air,
which was evaluated by:

ð d t
X
ð
Q i,a ¼ c i,a m i,a dT ¼ c i,a ρ V i,a Δt T ind,in T ind,out Þ (C.5)
i,a
0
where, c i, a is the specific heat of the indoor air and m i, a the mass rate of the indoor air.
ρ i, a is the density of the air in the indoor heated space, and V i, a the volumetric flow
rate of the air passing through the indoor coil. T ind, in and T ind, out are the measured air
temperature at the inlet and outlet of the indoor coil, respectively.