Fault Detection and Diagnostics for Rooftop Air Conditioners

37
L
2 1
P
cond
= Pdis
− 0 ( fvdx+
v −v
= P
D
∫ 2 1)
2
0
After the system stops, at least one of the condenser and evaporator coils will be
filled with two-phase refrigerant and the refrigerant will not be subcooled anywhere. For
a TXV system, since the TXV has the ability to shut off the refrigerant flow when the
compressor stops, the refrigerant in both coils could remain in a two-phase condition. For
a fixed-orifice system, after the system has been off for a long time in the daytime, the
refrigerant in the condenser will normally be superheated. However, it takes some time
for the high and low sides to reach a balance and for the refrigerant to become
superheated. In addition, in the nighttime at many locations the outdoor temperature is
normally lower than the indoor temperature, so the refrigerant in the condenser will be
two-phase mixture when the system is off. Consequently, it is safe to assume that the
refrigerant in the condenser would be saturated at some time when the system is off and
the following derivation holds.
T = T ( P ) = T ( P )
(1-13)
cond, pred sat cond sat dis
∆T = T − T = T − T ( P ) 0
(1-14)
cond, norm cond,
meas cond,
pred cond,
meas sat dis
=
However, when there is non-condensable gas in the system and according to
Dalton’s law,
P
ref , vapor
= Pdis
− Pncg
= (1 − yncg
) Pdis
, yncg
>> 0
(1-15)
dis
y
ncg
=
P
P
ncg
dis
=
=
( N
1+
( N
1
=
χ
1+
r
ref
ncg
N
ncg
ref , vapor
ncg
1
N
N
ncg
+ N
N
ref , vapor
ref , total
ref , total
)
)
=
( N
ncg
N
( N
ref , total
ncg
N
) + ( N
ref , total
)
ref , vapor
N
ref , total
)
where,
P
ref , vapor
is the refrigerant partial pressure,
ncg
P is non-condensable gas partial
pressure,
y
ncg
is the mole fraction of non-condensable gas in the refrigerant vapor-gas
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