Evaluation of non-equilibrium by the Crocco theorem

Abstract

The quantification of non-equilibrium is important both in computational fluid dynamics to identify regions where the flow field can be considered isentropic or not and in direct simulation Monte Carlo (DSMC) method to identify regions where the number of molecular collisions should be more or less high. As it is well known, thermodynamic non-equilibrium and anisotropy are two aspects of non-equilibrium. The parameters quantifying thermodynamic non-equilibrium rely on the difference of the local values of the translational temperature with respect to the rotational and vibrational temperatures. The parameters, quantifying anisotropy, rely on the difference of the local values of the three spatial components of the translational temperature. A measure of ‘global’ non-equilibrium relying on just one parameter that includes thermodynamic non-equilibrium and anisotropy at the same time could be preferable from an operative point of view. Such a single parameter has been already introduced; this is the entropy generation rate that identifies the non-equilibrium regions, whereas a positive entropy generation exists. In this study, a ‘new’ parameter is proposed. The method obtaining this new parameter relies on the assumption that a theoretical equation, based on the hypotheses of equilibrium, is not verified in non-equilibrium. The equation of the Crocco theorem showed to be proper for this purpose; the new parameter is defined as the difference of the terms forming the equation. This parameter verified to be more effective than the parameters based on the temperature differences because it was able to identify the non-equilibrium regions in a more precise and evident way. Computing tests considered a slab normal to the free stream velocity in the whole transitional regime. For this reason, the runs have been carried out by a DSMC code.