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used to model the pneumatic transmission line
Tannehill et al. (1997), which combines the
lumped model (Xue and Yusop, 2005) to simulate
the air dynamics in the transmission line. The
experiment set‐up is shown in Figure 1.
Figure 1: Experiment Set‐Up
The valve is opened until the transmission line
reaches a steady state. The valve is then closed
and the system is allowed to reach a different
steady state. Pressure transducers are used to
record the pressure during this process. At the
same time a mass flow meter is used to record
the steady state mass flow rate. The simulation
is then performed to verify the transient proc‐
ess of the fluid in the transmission line after the
valve is fully closed.
The blocked transmission line is considered to
have N number of segments. Hence N numbers
of pressure transducers are needed to capture
the changes in air pressures along a 4m polyure‐
thane pneumatic transmission line which has an
internal diameter of 5.0mm and a thickness of
1.5mm. The change in system temperature is not
considered in this study and the temperature is
assumed to be constant at an ambient tempera‐
ture of 20°C. The change in transmission line di‐
ameter due to high system pressure is consid‐
ered during the simulation.
MIMET Technical Bulletin Volume 1 (2) 2010
MATHEMATICAL MODEL
For a general three‐dimensional Navier‐Stokes
equation, the following assumptions are made:
1. The swirl of the working fluid in each cross sec‐
tion along the transmission line is omitted.
2. The change in fluid properties along the radial
direction is omitted.
3. Perfect gas is considered ‐
The equations are then reduced to one‐dimensional
format as follows:
For continuity equation:
��
�
�t
�
�x
��u��0 x
and for momentum equation:
p � � RT
where ρ is the density, ux being the velocity
along the axial direction, p is the pressure, R is
the gas constant, T is the system temperature
and μ is the dynamic viscosity.
(1)
(2)
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