Transcript Document

VESSEL DECOMPRESSION
MODEL
Prepared by Catalina Alupoaei
December 9, 2001
INTRODUCTION TO VACUUM TECHNOLOGY
The vacuum environment plays a basic and indispensable role in present
day technology
It has an extensive range of applications in industrial production, and in
research and development laboratories, where it is used by engineers, scientists and
technologists for a variety of purposes.
Some of the applications:
1.
An early application of vacuum technology came around 1900 when the first
major industrial use was for light bulbs and TV tube production (later on).
2.
The second major application is in the electronic industry. Many processes that
occur in a semiconductor fabrication facility require vacuums of different levels,
including the deposition of thin films of material on computer chips.
3.
Another major application is in space technology. The main issue in space
technology is how to design the space station or shuttle in order to maintain a
pressurized cabin. Also, it is important to design safe space-suits to protect
astronauts during their missions in open space.
EXPERIMENTAL PROTOCOL
The experiments were conducted at HCC’s Vacuum Technology Laboratory to
develop a model for a vacuum system
The system used for conducting the experiments consists of a chamber with a
single vacuum pump connected to it. The pump removes the gas from the chamber
as function of time
The vacuum station allow to automatically monitor the drop in the vacuum
chamber pressure as function of time. In addition, the station has a mass flow
controller that precisely meters gas into the chamber at various desired mass flow
rates
Experiments were conducted at different percentage of mass flow (between 10100%)
MATHEMATICAL MODEL
Is based on on the ideal gas law
S = pumping speed
dV
S
dt
V = volume of gas removed
t = time
p = pressure at the inlet
dV
Q  pS  p
dt
Q = throughput
Assumptions:
 constant pumping speed, S
 no additional gas load to that in volume V, at ant time Q = pS
 the process is isothermal
MATHEMATICAL MODEL
pS  V
dp
dt
For initial condition:
t=0
 p = po
Results the measured vacuum chamber pressure change as function of time is given by:
 S
p  p0 exp   t
 V
A program has been written in Matlab for fitting the exponential function for
pressure (P/Po) as function of time.
Measured vacuum pressure versus time (at different % mass flow)
1000
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
900
800
Pressure (torr)
700
600
500
400
300
200
100
0
0
5
10
15
20
25
30
Time (sec)
35
40
45
50
DATA PROCESSING
 The region selected for the fitting :
• From time corresponding to P maximum to time = 30 seconds
 The selected region of data for each experiment was shifted to the origin,
so the time corresponding to the P maximum is now considered time zero
 The pressure data were normalized (P/Po)
 The estimation of the time constant (S/V) was accomplished solving the
corresponding linear least square problem
 The measured and calculated data for the selected range have been plotted together
for each experiment
Comparison between measured and calculated vacuum
chamber pressure versus time
10% mass flow rate
100% mass flow rate
Estimates for the time constant (S/V) and for the
standard deviations
% mass flow rate
10
20
30
40
50
60
70
80
90
100
Parameter estimates
S/V
Standard deviation
-0.2405
0.3787 x 1.0e-3
-0.2517
0.3263 x 1.0e-3
-0.2493
0.3241 x 1.0e-3
-0.2509
0.3090 x 1.0e-3
-0.2459
0.2921 x 1.0e-3
-0.2479
0.3295 x 1.0e-3
-0.2499
0.2968 x 1.0e-3
-0.2506
0.2982 x 1.0e-3
-0.2465
0.2723 x 1.0e-3
-0.2505
0.2918 x 1.0e-3
The pump time constant (S/V) versus different percentage
of mass flow rate together with ± 2 standard deviations
The pump-down time
The time required to pump-down a vacuum system from atmospheric pressure to a
specified pressure is called the time of evacuation or pump-down time
Time 
2.3  Volume
2.3  V

Pumping speed
S
The pump-down time Tf estimated from the model as 99% of the pressure drop
corresponds to,
Tf 
ln 0.99
S

V
Pumping speed versus pump-down time for various volumes [3]
The pump-down estimates from the model
 could be used with Figure above to obtain the volume or the speed to specify a pump
CONCLUSIONS
 There is a significant variability in the experimental data relative to the time interval
required to reach the maximum pressure and in the order of the experiments relative to the
percent of mass flow rate
 The parameter values reported in Table above also reflect this variability
 Nevertheless, the estimates of the variance of the model lack of fit (calculated from the
residual sum of squares) suggest that the parameters are statistically different
The model gives an adequate representation of the trend of the pressure versus time data,
but is clearly not complete
 The data appears to have an exponential decay, followed by a plateau (probably the rate
of mass flow decreases), continued by a second exponential decay
 This behavior could be explained on the basis of temperature. Initially the system is
isothermal, as the gas is extracted, the temperature drops, reducing the pressure and the
mass flow, as the temperature equilibrates, the rate of mass flow increases again.
Temperature data would be very helpful to improve the reproducibility and the control of
the system.
REFERENCES
1.
Rajka Krstic, Jennifer Trelewicz and Veena Mahesh, Introduction to Vacuum
Technology
2.
Chambers, A., Basic vacuum technology, 1998
3.
Andrew Guthrie, Vacuum Technology, Alameda State College, California, John
Wiley and Sons, Inc. 1965
4.
L. Holland, W. Steckelmacher and J. Yarwood, Vacuum Manual, E. & F. N. Spon
London, 1974
NOTE
The document in Word provides the program that has been written in Matlab for
fitting the exponential function for pressure (P/Po) as function of time
Also, it provides all the figures with the comparison between measured and
calculated vacuum chamber pressure versus time for the different range of mass flow
rate