Fault Detection and Diagnostics for Rooftop Air Conditioners

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devices. An equation for liquid mass flow rate across an orifice could be derived from
Bernoulli’s equation (ASHRAE 1997) as,
4
m& C A 2ρ(
P − P ) /(1 − β )
(A1-1)
=
d
up down
2
where, C
d
is discharge coefficient, A = πD is the throat area, ρ is density, P
up
is the
4
upstream pressure, P
down
is the downstream pressure, and β is the ratio of the orifice
diameter, D , to the upstream tube diameter. Since β varies from 0.1 to 0.2, raising β
4
to the fourth power results in a very small number. Therefore, the term of (1 − β ) could
be dropped from the equation.
m& = C A ρ(
P − P )
(A1-2)
d
2
up down
Benjamin and Miller (1941) conducted experiments of sharp-edged orifices of
L / D = 0.28 ~1 with saturated water at various upstream pressures and found that
1. Orifices having L / D < 1 did not choke the flow at normal operating conditions and
therefore could not be used as refrigerant expansion devices.
2. The discharge coefficient found for a two-phase water mixture was approximately
the same as that for cold liquid water.
Some other researchers (Roming et al., 1966; Davies and Daniels, 1973) refined
the above equation to deal with two-phase situations more accurately by adding an
expansion factor, y , which is unity if no vaporization occurs.
m& = C yA ρ(
P − P )
(A1-3)
d
2
up down
In summary, the mass flow rate equation of orifices can be generalized as,
m& = CA ρ(
P up
− P )
(A1-4)
2
down
It should be pointed out that some researchers (Chisholm, 1967; Krakow and Lin
1988) observed that the mass flow rate of a refrigerant through an orifice in a heat pump
was primarily dependent on the upstream conditions, which indicates that the flow was
choked. This warrants further investigation.
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