The use of interpolations in time, rather than the more widely used spatial interpolations, demonstrates several benefits in the application of the method of characteristics to wave problems in hydraulics. Two such time-line schemes are presented and analyzed in the solution of a linearized water hammer problem. Reachback time-line interpolations, where the characteristic lines are projected back before the current time step, demonstrate less damping than the corresponding spatial interpolation scheme at the same discretization. Implicit time-line interpolations, where the characteristic line is projected into the current time step, permit relaxation of the restrictive time step required by the Courant condition. An error analysis and numerical experiments demonstrate the degree of damping and dispersion introduced by both reachback and implicit time-line interpolation methods. The error analyses and their verification may encourage further application of these methods in appropriate problem domains.

Characteristics Method Using Time‐Line Interpolations

This thesis describes the development of a numerical simulation based on the method of characteristics (MOC) for full bore rupture (FBR) of long pipelines containing high pressure hydrocarbons. The Peng-Robinson equation of state coupled with the assumption of thermal equilibrium and homogeneous flow are used to generate the appropriate vapour/liquid equilibrium data. A variety of solution techniques including the use of a second order MOC in conjunction with a nested grid system have been developed in order to investigate their effects on computation run times and accuracy. The above, together with the use of a DEC Workstation, has allowed for the first time, the validation of a MOC model by comparison with intact end pressure data logged for 20,000s following FBR of the Piper-Alpha main riser. Excellent agreement is obtained. Comparison with field data obtained following FBR of LPG pipelines also gives good agreement. The main part of the thesis describes the application of the simulation for the study of the dynamic response of ball valves and check valves following hypothetical FBR of a long pipeline containing either gas or a two-phase mixture. A variety of scenarios including the effects of valve proximity to the rupture plane and the delay in closure on the total amount of inventory released prior to pipeline isolation are analysed. The accompanying pressure oscillations and surges are also accounted for. The results are in turn used to recommend guidelines regarding the appropriate choice of emergency shut-down valve depending on the failure scenario.

Modelling the dynamic response of emergency shut-down valves following full bore rupture of long pipelines

One-dimensional implicit characteristic method for compressible two-phase coolant flow

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One-dimensional implicit characteristic method for compressible two-phase coolant flow