While the Navier-Stokes-Fourier set of equations are the common fluid flow equations, their physical validity rests on an existence of a local-equilibrium in the flows. This set fails in the description of several engineering flow configurations: flows in micro-nano devices, rarefied gas flows, rapid granular flows. To extend the classical continuum model into areas where it fails, the tradition in gases consists of deriving so-called extended hydrodynamic models by solving the Boltzmann’s kinetic equation of dilute gases to a high order using small parameter expansion. These extended hydrodynamics equations are now recognized to be thermodynamically inconsistent. During this talk I will present our new construction of continuum flow equations beyond the Navier-Stokes-Fourier model that accounts for local disequilibrium and non-continuum effects. This will be followed by simulations of different flow configurations that include: natural convection in a nano-cavity, pressure drop prediction in a fluidized bed rector and others.
References:
N. Wolchover, Famous Fluid Equations are Incomplete, Quanta Magazine, 21 July 2015
SK Dadzie, (2013) A Thermo-Mechanically Consistent Burnett Regime Continuum Flow Equation Without Chapman-Enskog Expansion, Journal of Fluid Mechanics 716, R6-11
H Brenner, (2012) Beyond Navier-Stokes, International Journal of Engineering Science 54, 67-98
D Bresch, B Desjardins, E Zatorska, (2015) Two-velocity hydrodynamics in fluid mechanics, Journal de Mathématiques Pures et Appliquées, 104, 801–836