Navier–Stokes equations with rovibrational state-resolved transport flux closure

Abstract

In the time since the Navier–Stokes equations were introduced more than two centuries ago, their application to problems involving real gas effects has relied on appropriate closure for the mass, momentum, and energy transport fluxes via the constitutive laws. Determination of the corresponding transport coefficients, most readily obtained through generalized Chapman–Enskog theory, requires knowledge of the intermolecular potentials for rotationally and vibrationally excited molecules. Recent advances in computational chemistry provide extraordinary detail of interactions involving rovibrationally excited molecules, offering a means for transport flux closure with unprecedented accuracy. Here, the bracket integrals for rovibrationally resolved molecular states are developed, and the resulting transport flux closure is presented for the rovibrationally resolved Navier–Stokes equations. The accompanying continuum breakdown parameters are also derived as a rigorous metric to establish the range of applicability of the aforementioned equations in flow conditions approaching the rarefied regime.