Planned transient waves can be beneficially used in the detection of defects in pipelines. Such applications show that the higher is the frequency of the injected wave the better is the detection. Finite volume (FV) methods have recently been applied to waterhammer problems and are known to be well suited for high frequency waves. However, FV methods are formulated for simple boundary conditions such no-flux or no-slip, but not for typical boundary conditions in pressurized pipeline systems (e.g., junctions, control valves, orifices, tanks, and servoirs). In the instances in the literature where FV has been applied to waterhammer problems, the approach has been to use FV for internal sections and the Method of Characteristics (MOC) at the boundaries. This global order of accuracy of the...[ Read more ]

Planned transient waves can be beneficially used in the detection of defects in pipelines. Such applications show that the higher is the frequency of the injected wave the better is the detection. Finite volume (FV) methods have recently been applied to waterhammer problems and are known to be well suited for high frequency waves. However, FV methods are formulated for simple boundary conditions such no-flux or no-slip, but not for typical boundary conditions in pressurized pipeline systems (e.g., junctions, control valves, orifices, tanks, and servoirs). In the instances in the literature where FV has been applied to waterhammer problems, the approach has been to use FV for internal sections and the Method of Characteristics (MOC) at the boundaries. This global order of accuracy of the FV-MOC is governed by the MOC solution. This thesis is a first attempt in handling boundary conditions within the FV framework. The approach places the boundary element within a FV to enforce mass and momentum conservation within this volume. The fluxes between the FV and the adjacent elements are then formulated in the usual manner. The approach is illustrated for the case of a valve, a reservoir and a junction. The finite volume method used is the Boltzmann-type scheme, which is a mesoscopic model.

In particular, the 1st and 2nd-order collisionless Boltzmann-type scheme (i.e., the kinetic flux vector splitting (KFVS)) and the 2nd-order Bhatnagar-Gross-Krook (BGK) Boltzmann scheme are formulated and applied to one-dimensional transient flows. The accuracy and efficiency of all schemes with the proposed non-iterative FV formulation of the boundary conditions are demonstrated through the following test cases: (i) problems due to sudden closing of a valve, (ii) wave interactions with a junction boundary characterized by a geometric discontinuity, (iii) wave interactions with a junction boundary characterized by a discontinuity in the value of wave speed, and (iv) wave interactions with a junction characterized by a flow rate discontinuity. The pure FV formulation guarantees the mass and momentum conservation. The Boltzmann-based FV schemes capture the discontinuity as well as wave interaction with boundary elements accurately. The stability of the proposed FV schemes is satisfied when Cr < 0.5. The comparison between the efficiency of the conventional scheme (i.e., the Fix-MOC and Godunov schemes) and those of the mesoscopic-based schemes (i.e., the KFVS and BGK schemes) reveals that none of the proposed schemes is better than the 2nd-order Godunov scheme for classical waterhammer. Nevertheless, it is found that the CPU time needed by the 2nd-order BGK scheme to achieve a predefined degree of accuracy is not too far from that by the 2nd-order Godunov scheme. The KFVS scheme is more dissipative than the BGK scheme due to the lack of particle collisions in the formulation.