Fault Detection and Diagnostics for Rooftop Air Conditioners

99
Figure A1-7 shows the geometric model of valve type III. It is very easy to obtain
the expression as,
A = πDh ,
h
D
Figure A1-7 Geometric model of valve type III
It is obvious that throat-area, A , is a linear function of valve position, h .
A1.2.3 Valve Position Expression
The valve position for a EXV can be calculated easily by the control signal. As to
a TXV, it is the function of superheat. Assume that the pressure difference is a linear
function of superheat,
= , P = k ( x ) .
P
open
k1T sh , operating
close 2 static
+ h
Since the forces exerted on the valve are balanced,
k
1Tsh , operating 2 static
+ h
= k ( x ) ,
Rearranging the above equation gives an expression for valve position,
k
h =
k
1
2
= kT
= kT
T
sh,
operating
sh,
operating
sh,
opening
− x
− kT
static
sh,
static
= kT
= k(
T
sh,
operating
− x
sh,
operating
static
−T
sh,
static
As shown in Figure A1-8, it is obvious that the valve position is a linear function
of opening superheat.
).
99