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The axial vibration of liquid-pipes, considering the fluid-structure interaction (FSI), can be described by a four-equation model consisting of two equations for the fluid and the other two for the pipe wall. When distributed friction and damping were neglected, the model could be solved with an exact solution developed from the method of characteristics (MOC). The exact solution with a simple recursion process was presented instead of meshing the distance-time plane, introducing no numerical error, while the only weakness was the high time cost. An improved method based on this exact solution is proposed in this work, using the time-line interpolation rather than the recursive algorithm to speed the calculation. As numerical diffusion and oscillation affect the accuracy a lot, various interpolation techniques are investigated and compared. The mean absolute error (MAE) and the structural similarity index measure (SSIM) are employed to assess the accuracy of proposed methods, and the latter was originally developed for the image quality assessment. A hybrid interpolation scheme, mixing the cubic spline and linear interpolation, is proposed and achieves the highest accuracy and the quadratic-linear interpolation is found to be a good choice considering both accuracy and efficiency. The solution method developed here improves the efficiency significantly while retains an acceptable level of the accuracy, especially suitable for the long duration event. [ABSTRACT FROM AUTHOR]

Abstract: Complex pipelines may have various structural supports and boundary conditions, as well as branches. To analyse the vibrational characteristics of piping systems, frequency modelling and solution methods considering complex constraints are developed here. A fourteen-equation model and Transfer Matrix Method (TMM) are employed to describe Fluid–Structure Interaction (FSI) in liquid-filled pipes. A general solution for the multi-branch pipe is proposed in this paper, offering a methodology to predict frequency responses of the complex piping system. Some branched pipe systems are built for the purpose of validation, indicating good agreement with calculated results. [Copyright &y& Elsevier]

The axial vibration of the liquid-filled pipes can be represented with a four-equation fluid–structure interaction (FSI) model. When distributed friction was neglected, this model could be solved with an exact solution without computational grid, while the only weakness was the high time cost. A fast meshless solution (FMS) developed earlier used the time-line interpolation rather than the recursive algorithm, to speed the calculation. For the purpose of practical applications, the FMS for supports at pipe end and middle position is proposed, and series connection is also studied in this paper. The support is described by the complex constraint including elastic, damping and inertial effects. A numerical case of the double-pipe water hammer is employed to validate the series connection and end supports. The FMS for the middle support is validated by an existing experiment, where the support can be described by the dry friction. Both numerical and experimental cases indicate the effectiveness and the efficiency of the proposed solution method. • The fast meshless solution for the double pipe is proposed. • Complex constraints at pipe supports are incorporated and solved. • Calculation efficiency is improved significantly and high accuracy is achieved. [ABSTRACT FROM AUTHOR]