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PDE equations (1) and (2). Comparisons between
simulation and experiment results are as shown in
Figure 4.
Figure 4: Comparisons between Simulation and Experiment
Results (PS=Simulated Pressure)
DISCUSSION
The transmission line diameter calibration experi‐
ment shows that the relationship between the di‐
ameter and the exerted pressure is close to linear.
This is then applied to the simulation algorithm to
investigate the influence of the working pressure
on the transmission line diameter expansion as
shown in Figure 2.
Figure 3 shows the pressure response in the
transmission line after the valve is closed. When
the valve is fully closed, the air will continue to
flow downstream of the transmission line due to
the presence of higher pressure and momentum
at the upstream of the transmission line. There‐
fore the pressure downstream of the transmis‐
sion line will continue to increase until it reaches
a peak value at which the velocity downstream is
close to zero. The fluid then starts to flow in the
opposite direction in the transmission line since
the pressure downstream is larger than the pres‐
sure upstream. When the upstream pressure
reaches new peak value, the fluid flows down‐
stream again. This process repeats itself though
the peak pressure values reached as the time
progresses at different transmission line posi‐
tions will gradually decreases due to the viscosity
effect imposed on the travelling air. Finally, the
system reaches a new steady state in which all
the pressures along the transmission line arrived
at a same constant value.
A combined transmission line model is proposed
in this paper. The simulation is based on the com‐
bination of finite difference model McCloy (1980)
and lumped model (Xue and Yusop, 2005). The
lumped model is used to update the boundary
MIMET Technical Bulletin Volume 1 (2) 2010
conditions, which is then applied to the first and
the last segments. The parameters for the other
segments are updated by means of finite differ‐
ence model in the simulation algorithm.
Simulation results show good consistency com‐
pared with the experiment data especially in the
pressure frequency response. The simulation re‐
sults also show that the air in the transmission
line took a longer time to reach a new steady
state compared with the experiment results. This
is due to the fact that perfect gas is assumed. Per‐
fect gas assumes that the force between the at‐
oms or molecules in the gas is negligible. The oc‐
cupied volume of the atoms or molecules in the
gas is also omitted under perfect gas conditions.
On the other hand, under real gas conditions, due
to the existence of the aforementioned factors,
the influence of friction on the working fluid is
larger. Furthermore when the atoms or molecules
in the air hit the blocked end of the transmission
line with a certain momentum, some of these at‐
oms or molecules are bounced back from the
blocked end of the transmission line which is in
the opposite direction of the air flow. The direct
influence of this is a reduction in the total air en‐
ergy and this result in an earlier dissipation of the
pressure wave in the captured data compared to
the simulated results.
CONCLUSION
A time domain model describing the dynamics of air
in a pneumatic transmission line is presented by con‐
sidering changes in air density, pressure and mass
flow rate. The combined models are proposed to
simulate the dynamics of trapped air in a blocked
transmission line. In order to update the boundary
conditions, the first and the last segments are consid‐
ered as two lumped volumes and these are then con‐
nected to the transmission line segments using an
orifice model. The transmission line segments are
expressed by means of finite difference model. The
effectiveness of the proposed model is depicted
| MARINE FRONTIER @ UniKL
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