Closed form for the equations of chemically reacting flows under local thermodynamic equilibrium

Abstract

We present a closed form for the governing equations of chemically reacting flows under local thermodynamic equilibrium, which rigorously takes into account effects of elemental (de)mixing. To this end, we show that when chemistry is fast, the diffusion fluxes of elements and species enthalpies can be expressed as explicit linear functions of gradients of elemental mass fractions and temperature. Our formulation is a natural extension of classical work on local equilibrium flows by other authors and yields results equivalent with a recent fully rigorous mathematical theory in a straightforward and physically appealing manner. The obtained set of equations is well-suited for numerical implementations and does not require the computationally expensive evaluation of thermodynamic derivatives using finite differences. The new transport coefficients that appear in the equations allow quantitative predictions and help to gain deeper insight into the physics of chemically reacting flows at and near local equilibrium.

Ionization and dissociation effects on boundary-layer stability

“…The reactions that are and are not accounted for depend on the list of species comprising the mixture. Authors performing analyses in LTE, such as Malik & Anderson (1991) or Stuckert & Reed (1994), neglected elemental demixing, observed to be negligible unless high temperatures are reached (see Rini, Vanden Abeele & Degrez 2005;Rini & Vanden Abeele 2007). The acronym LTE is thus kept for such a traditional set of hypotheses, hereinafter referring to LTE with elemental demixing as LTEED.…”

Study of photometric properties of high-pressure mercury discharge with thallium iodide additives (HgTℓI) using the ray-tracing method

“…One of the first 2D models of MH lamps [3] used a perturbation method to describe the diffusion of different species between cells, and since that time an extensive literature has developed in modelling of de-mixing in arcs (e.g. [22]) and MH lamps [23].…”

Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

“…We will show that with the proposed coupled exponential scheme, the mass constraint can be satisfied exactly. 1 The structure of this paper is as follows. Section 2 introduces the continuity equations and the Stefan-Maxwell equations.…”

“…In plasmas in local thermodynamic equilibrium (LTE), where both the internal and reactive processes are at equilibrium, the diffusion model is used to account for the effects of elemental demixing or to calculate the reactive contribution to the thermal conductivity [1][2][3]. In combustion simulations and simulations of plasmas that are not in local thermodynamic equilibrium (NLTE), the diffusive flux is needed in the species continuity equations.…”