Claude Rey

Analyse des effets de variation de volume des gaz dans les équations générales de bilan

Resume Chaque bilan, de masse, de forces et d’energie, est ecrit par unite de masse du fluide. La continuite introduit un nouveau parametre Θ= ln U U r appele ici parametre de variation volumique, U est le volume massique, U r une valeur de reference constante. Si |Θ| ln 2 , ce parametre conduit a un decoupage des equations de bilan en deux equations distinctes. La premiere equation est invariable en ecriture par rapport a une situation incompressible; en particulier l’ordre de correlation des termes des equations reste inchange. La deuxieme equation est directement liee a la variation de volume. Si la loi d’etat des gaz parfaits est appliquee, la pression n’est plus une variable du systeme. Une classification des ecoulements donne les differents cas qui autorisent l’utilisation de ce decoupage.

Total energy balance in a natural convection flow

Purpose The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance. Design/methodology/approach The thermodynamic analysis comprises a number of numerical simulations where some terms, typically ignored by the commonly used approximations, are removed from the total energy equation to quantify the effects in the flow and heat transfer fields. The case study is the differentially heated square cavity flow, in which the effects of work done by the pressure forces contribute significantly to the energy balance. Because local magnitudes are computed here for discussion, the dimensional form of the governing equations is preferred and a numerical model without any restrictive approximation about the role of the pressure is used. Findings The results show that the work of gravity forces term is in perfect balance with the work of pressure forces term, and thus, ignoring the contribution of one of them yields an incorrect solution. In addition, it is shown that the assumption of zero divergence of the Boussinesq approximation can be erroneous, even for a natural convection flow case where the temperature difference is very small. Research limitations/implications As the flow and heat transfer governing equations are complex, simplifying assumptions are generally used; that is, the Boussinesq and low Mach number approximations. These assumptions are systematically adopted without any validation process and without considering that they modify the physical meaning of one or more of the thermodynamic quantities, particularly the pressure. This fact results in inconsistencies of the different forms of energy. Originality/value This is the first time that the terms of the total energy balance are quantified in such a way, in a differentially heated square cavity flow, which is a case study addressed by several authors.

Spectral Analysis of Chaos Transition in a Dynamic System: Application to Backward Facing Step Flow in Mixed Convection

This work focuses on the study of the transition from steady to chaotic behavior in mixed convection flow over a backward-facing step. Direct numerical simulations are performed in a two-dimensional horizontal channel of expansion ratio ER = 2 at step level. The effects of the temperature difference between the heated bottom wall and the inflow temperature are investigated by keeping constant the Richardson number at 1. The covered range of Grashof and Reynolds numbers is respectively 3.31 × 104 ≤ Gr ≤ 2.72 × 105 and 182.03 ≤ Re ≤ 521.34. The thermodynamic instabilities which cause the onset of unsteady flow are described in detail. A spectral and phase portrait analysis of the temperature time series allows us to observe that the transition from steady to chaotic flow occurs by period-doubling bifurcations.