Fault Detection and Diagnostics for Rooftop Air Conditioners

38
mixture,
χ
ref
is known as the quality or the mole fraction of vapor refrigerant in the
refrigerant liquid-vapor mixture, r
ncg
is the mole ratio of non-condensable gas over total
refrigerant, and
N
ncg
,
ref vapor
N −
, and N
ref , total
are the numbers of moles of noncondensable
gas, vapor refrigerant, and total refrigerant.
where,
According to the Clapeyron equation,
dP
( )
dT
sat
h
=
Tv
⇒ ∆T ≈ ∆P
fg
h
fg
Tv
h
fg
is the enthalpy of vaporization, v
fg
is specific volume change, and T is
absolute temperature for vaporization. So, equation (1-14) can be modified to,
∆T
cond,
abnorm
= T
= { T
= T
cond,
meas
cond,
meas
sat
= ( P
= −(1
− y
− r
=
χ
ncg
ref
( P
ref , vapor
ref , vapor
ncg
1
= (1 −
1 − y
P
ncg
−T
−T
− P
Pdisv
)
h
ref , vapor
cond,
pred
fg
P
)
sat
) −T
dis
fg
fg
( P
T
)
ref , vapor
sat
ref , vapor
( T
h
T
cond,
meas
= T
( P
dis
cond,
meas
h
fg
fg
cond,
meas
( T
h
fg
fg
fg
cond,
meas
fg
)} + { T
)
v
cond,
meas
) v
T
) v
−T
fg
sat
T
cond,
meas
sat
( P
( P
dis
)
ref , vapor
cond,
meas
) −T
sat
( P
dis
)}
. (1-16)
For an air conditioning application,
P ) v
ref , vapor
( Tcond,
meas
h
fg
fg
can be approximated as
a constant, 0.125, and if the Celsius scale is used, equation (1-16) can be reduced to be,
rncg
∆T cond abnorm
= − ( 0.125)(273.15 + Tcond,
χ
, meas
ref
rncg
= ( − )(34.14 + 0.125Tcond,meas)
χ
ref
)
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