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Computation of state variables of one‐dimensional non‐stationary pipe flow at orifices on pipe ends
Author(s) -
Niessner Herbert
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510290
Subject(s) - body orifice , nonlinear system , mathematics , boundary value problem , state variable , computation , finite difference , outflow , mathematical analysis , finite difference method , mechanics , riemann problem , entropy (arrow of time) , physics , riemann hypothesis , engineering , thermodynamics , mechanical engineering , algorithm , quantum mechanics , meteorology
Boundary conditions of orifices in conjunction with the graphical method of characteristics given in [1] are reformulated and made ready to be used with finite difference methods. Orifice flow to the apparent narrowest cross‐section is assumed conserving entropy and energy, thereafter not recovering pressure without exceeding sound speed. These conditions allow to eliminate state variables at the narrowest cross‐section. Additional equations stem from mass conservation and a balance of the Riemann variable over the outgoing cross‐characteristic and either further energy conservation or a balance of entropy over the outgoing particle path. They permit to determine the state at the boundary of the computational grid for usual finite difference methods. A single nonlinear equation has to be solved only in case of outflow. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)