Advection-modulated gaseous diffusion through an orifice

TL;DR

This paper presents an analytical and numerical study of gas flow and mixing through an orifice, considering advection and diffusion effects, with applications to hydrogen-air and hydrogen-water vapor mixtures.

Contribution

It provides a combined analytical and numerical framework for understanding advection-modulated diffusion in orifice flows, including explicit solutions at small Péclet numbers.

Findings

Explicit analytical solution for small Pe flows.

Numerical results for Pe = O(1) flows.

Large gas-molecular-weight differences significantly affect flow and mixing.

Abstract

We examine flow and transport through an orifice in a flat wall separating semi-infinite atmospheres of two dissimilar gases. The analysis assumes steady conditions and order-unity values of the Schmidt number Sc and P\'eclet number Pe, such that advection and diffusion contribute comparably to mass and momentum transport. Mixing between the two gases induces order-unity variations in viscosity and density, resulting in coupled concentration and velocity fields. The solution yields the mass transfer rates of both gases, expressed in terms of an appropriately defined Sherwood number, as well as the overpressure required to sustain the flow, all as functions of Sc and Pe. An explicit analytical solution is obtained in the limit of small Pe, while numerical integration is used to describe flows with Pe = O(1). The mixing of hydrogen and air is used as an illustrative example that serves to highlight the influence of large gas-molecular-weight differences on the flow structure and associated mixing rate, with additional selected results given for the case of hydrogen and water vapor.