Modelling gas dynamics in 1D ducts with abrupt area change |
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Authors: | R Menina R Saurel M Zereg L Houas |
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Institution: | (1) Courant Institute, New York University, 251 Mercer Street, New York, NY 10012-1185, USA |
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Abstract: | Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This
poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative
term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from
a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical
standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the
present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations
expressing the energy and turbulent pressure stored in the vortices generated by the abrupt area variation. The turbulent
energy created by the flow–area change interaction is determined by a specific estimate of the surface pressure integral.
Model’s predictions are compared with 2D-averaged results from numerical solution of the Euler equations. Comparison with
shock tube experiments is also presented. The new 1D-averaged model improves the conventional cross-section-averaged Euler
equations and is able to reproduce the main flow features. |
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