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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) | MARINE FRONTIER @ UniKL 107
In order to update the boundary conditions, the first and the last segments are considered as two volumes (Xue and Yuzri, 2005). The equation used to calculate the mass flow rate passing through the orifice is used, which is: M� � C � C � A � P d m where the mass flow parameter is as shown below in equation (4). C m � d 2� R ��1� M d is the mass flow rate passing the orifice while Cd is the discharge coefficient. A is the ori‐ fice cross‐sectional area, Pu is the upstream stag‐ nation pressure (absolute), Tu is the upstream stagnation temperature (absolute), γ is the spe‐ cific heat ratio and Pvc is the static pressure at the vena contracta or throat. � Equation 4 is only valid when Otherwise the flow is considered to be choked and Cm will be constant at a value of 0.0405. Note that the ratio of specific heats g for air is 1.4. EXPERIMENT AND SIMULATION u �� P � � � �� P vc u T The transmission line diameter is first calibrated by experiment to determine the influence of the system pressure onto changes in its radial dimen‐ sion. Highly incompressible liquid (water) is in‐ jected into a polyurethane transmission line which is blocked at one end. Different pressures are then applied to the other end. By recording changes in the liquid height, the transmission line u � � � � 2 � � P � � � � P ��1� (3) (4) MIMET Technical Bulletin Volume 1 (2) 2010 P vc vc u P s � � � � � � � 0 . 528 � � �� diameter changes can then be determined. Ex‐ periment results are listed in Table 1. Pressure [bar] Liquid Height [mm] Table 1: Transmission Line Diameter Calibrations It is assumed that the high pressure applied only ex‐ pands the transmission line along the radial direction and do not influence the dimension along the axial direction. The initial volume occupied by the water is 1. 88 �10 m 3 . Based on the assumption above, the relationship between the applied pressure and the internal diameter of the transmission line is as shown in Figure 2. 0 95.82 1 94.46 2 93.72 3 92.32 4 91.59 5 90.85 6 89.27 7 88.37 �6 | MARINE FRONTIER @ UniKL 108
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NO SHIP NAME OWNER/OPERATOR GRT DWT
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MIMET Technical Bulletin Volume 1 (
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Page 72 and 73: METHODOLOGY Description of Apparatu
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