Modelling gas dynamics in 1D ducts with abrupt area change

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 integra...

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Bibliographic Details
Published in:Shock waves 2011-09, Vol.21 (5), p.451-466
Main Authors: Menina, R., Saurel, R., Zereg, M., Houas, L.
Format: Article
Language:English
Subjects:
Acoustics
Computational fluid dynamics
Condensed Matter Physics
Cross-sections
Discontinuity
Ducts
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Euler-Lagrange equation
Fluid flow
Fluid- and Aerodynamics
Gas dynamics
Heat and Mass Transfer
Integrals
Mathematical models
Momentum
Original Article
Physics
Pressure
Thermodynamics
Turbulent flow
Two dimensional models
Vortices
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Summary: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.
ISSN:0938-1287
1432-2153
DOI:10.1007/s00193-011-0321-3