Abstract
The analysis and the numerical simulation of turbulent volume variable flows require a mathematical description of physical variables in a statistical model. A closed set of statistical equations describing correctly the evolution of this specific flows is needed for the resolution. The variability of the mass volume increases significantly the complexity of this set of equations, enhancing a strong connection between all of them. The writing of balance laws per unit of volume for the volume variable turbulent flows using Reynolds averaging leads to an open set of equation. These equations, while exact, are unclosed; they contain correlation that are not exactly determinable, with physical signification and modelling steel complicated. Favre (1965) used density-weighted averages to reduce the mathematical complexity of this set. However, conditioned averages restrict the physical analysis and then the modelling framework. At the same time, other authors have developped other ways of investigation using hybrid decompositions like Chassaing (1985) or HaMinh and al. (1981). This work takes again the Reynolds averaging’s trail and postulates that the compressible situation can be described like a deviation of the incompressible situation. Then, we can identify the different physical mechanisms and separate the incompressible terms. Consequently, we identify the “deviatoric terms” where the variation and fluctuation of volume appear. The Boussinesq assumptions are not adopted.
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References
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© 1997 Springer Science+Business Media Dordrecht
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Aurier, T., Rey, C., Sini, JF. (1997). Second-Order Turbulence Modelling and Numerical Simulation of Volume Variable Turbulent Flows. In: Fulachier, L., Lumley, J.L., Anselmet, F. (eds) IUTAM Symposium on Variable Density Low-Speed Turbulent Flows. Fluid Mechanics and Its Applications, vol 41. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5474-1_11
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DOI: https://doi.org/10.1007/978-94-011-5474-1_11
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