| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 103 === Nowadays, underwater pipeline has been widely applied to transport resources. If the pipeline is located on the sea bed, the related units must maintain the pipeline regularly due to the tough environment. Despite this, there are still lots of unexpected damages and the following maintenance costs much efforts, resources and money. To solve this problem, understanding of the reasons of the injuries would be an effective method.
Above several reasons of the damages, Chang (2012) considered that the scour around the pipes is the main reason and the erosion process could be related to piping effect. Chang came up with an idea that cladding porous media outside the pipe to protect it from the scour of current or wave. The study turned the idea into a numerical model and the results indicated that the increase of permeability of the pipe would significantly reduce the gradient of pressure around the pipe which drive the flow in the porous media.
In this study, we continue to develop the conceptual model created by Chang, potential theory and Darcy’s law are adopted to investigate the potential field in water and in porous media respectively. Use the regular perturbation method to deal with the ill-conditioned problem caused by the permeability of porous media (Wang et al., 2010). We apply multiple parameters perturbation to classify the original problem into several boundary value problems (B.V.P.) based on the order of physical quantities and the regions. Use the boundary element method (B.E.M.) to simulate the potential field, velocity and pressure profile around the pipe on the bed.
We believe there is an important relation between permeability of artificial porous media and flow around the pipe. In this study, we regard these two permeability of porous media as two different order and describe them with two small perturbation parameters. But under the situations that the order difference in these two small parameters is too large to ignore. After executing the order analysis, it turns out that the boundary condition of continuity of mass flux between these two kind of porous media becomes no flux condition. It’s not rational and we will not know the utility of artificial porous media. So we make a correction to the boundary condition and assume there is a thin layer on the boundary of the relatively impermeable porous media. Use the continuity equation to prove the rationality of the thin layer.
There are many physical parameters affect the flow nearby the pipe. It’s hard to search the optimized arrangement of the remedy for piping of pipelines. We both consider the reality of engineering and analysis of the modeling results to reduce the possible parameter combinations and discuss the relation between parameters and piping effect. Further, simulate the limited cases to seek for the optimized arrangement of model. In the end, for the future designs and works, we provide engineers reference materials on the basis of physical theory and numerical results.
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