Technical characteristics of this system
This mobile cooling plant is required to supply up to 5g/s of liquid
C3F8 sub-cooled to temperatures as low as -30°C in order to remove a
heat load of up to 500W by full evaporation the flow.
The following pressure-enthalpy diagram depicts the
thermodynamic cycle envisaged for this unit.
Fig.1
The pressure corresponding to evaporation at -30°C is
1350mbar(a). The compressor was tested with this inlet pressure and the
mass flow was measured. As shown in Fig.2, the mass flow satisfies the
user requirements of 5g/s.
The compressor speed is adjusted by a PID controller in order to
maintain a constant buffer tank pressure.
C3F8 mass flow vs Inlet pressure for Haug SOGX
50 compressor at 60Hz
14
13
12
11
10
mass flow (g/s)
9
Pcond=10bar(a)
8
Pcond=6bar(a)
7
6
5
4
3
2
1
0
500
600
700
800
900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500
Inlet Pressure (mbar)
Fig.2
Comments:
It can be seen that the mass flow is a function of both inlet and outlet pressures:
m& = f ( Pin , Pout )
And also that it depends more on Pin than on Pout,
∂m&
5−2
≈
= 0.75 gs −1 / bar
∂POUT 10 − 6
∂m&
4−2
≈
= 6.7 gs −1 / bar
∂PIN 1.6 − 1.3
Theoretical background
Let p be the percent clearance of the compressor,
p=
Vc
× 100
VMAX − Vc
(a)
Where:
• VMAX is the maximum volume in the cylinder, which occurs when the piston is at
one end of its stroke.
• Vc is the minimum volume, or clearance volume, which occurs at the other end of
the piston stroke
The clearance volumetric efficiency is
ηVC =
Volume _ of _ vapour _ drawn _ in VMAX − VOPEN
× 100
=
swept _ volume
VMAX − VC
(b)
Where VOPEN is the volume in the cylinder at which the pressure is low enough for the
suction valve to open. (VMAX -VOPEN) is the volume of gas drawn into the cylinder
and (VMAX -VC) is the total volume swept by the cylinder.
(a) and (b) can be combined to give:
V

ηVC = 100 − p OPEN − 1
 VC

(c)
If an isentropic expansion is assumed for the gas trapped in the clearance
volume, i.e. between Vc and VOPEN,
P
VOPEN
ρ
= OUT =  OUT
VC
ρ IN
 PIN



1/ K
(d)
Where ρIN is the density at the compressor inlet and ρOUT at its outlet and k is the
coefficient of isentropic expansion
Thus,
ηVC

ρ
= 100 − p OUT − 1 = 100 −

 ρ IN
 P
p  OUT
  PIN




1/ k

− 1


(e)
The volumetric flow is:
V& = N × VSWEPT
(f)
Where, as seen above VSWEPT = VMAX-VC and N is the number of cycles per second
The mass flow is
m& = V& × ηVC × ρ IN = N × VSWEPT

× 100 −


ρIN is of course, a function of PIN.
 P
p  OUT
  PIN




1/ k

− 1 × ρ IN


(g)