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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 111
through comparisons of simulated pressure re‐ sponses against pressures measured by practical ex‐ periments. The simulated results can be concluded to be successful since it does match well with the cap‐ tured experimental data though the simulated results show longer system transient state. REFERENCES 1. Franco, W. and Sorli, M. (2004). Time‐domain Models for Pneumatic Transmission Lines. Power Transmission and Motion Control (PTMC 2004). 257‐269. 2. Krus, P. (1999). Distributed Modelling for Simulation of Pneumatic Systems. 4 th JHPS International Sympo‐ sium. 443‐452. 3. Manning, J.R. (1968). Computerized Method of Char‐ acteristics Calculations for Unsteady Pneumatic Line Flows. Transactions of the ASME, Journal of Basic Engineering. 231‐240. 4. McCloy, D. (1980). Control of Fluid Power: Analysis and Design. 2 nd Edition, John Wiley & Sons. 5. Tannehill, J.C., Anderson, D.A. and Pletcher, R.H. (1997). Computational Fluid Mechanics and Heat Transfer. 2 nd Edition. Taylor & Francis. 6. Xue Y. and Yusop M.Y.M. (2005). Time Domain Simula‐ tion of Air Transmission Lines. 8 th International Sympo‐ sium on Fluid Control, Measurement and Visualization (FLUCOME). Paper 277. MIMET Technical Bulletin Volume 1 (2) 2010 | MARINE FRONTIER @ UniKL 112
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EDITORIAL CHIEF EDITOR Prof. Dato
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DIRECTIONAL STABILITY ANALYSIS IN S
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The determinant from equations (3)
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Table 1 ‐ Results of Stability Cr
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Skeg Effectiveness Skeg Effectivene
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