# Studies of Mixing Processes in Gases and Effects on Combustion and Stability

Summer 1995

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Mathematics & Statistics

## Program/Concentration

Computational and Applied Mathematics

## Committee Director

D. Glenn Lasseigne

Thomas Jackson

Fang Hu

## Committee Member

Chester E. Grosch

## Abstract

Three physical models of laminar mixing of initially separated gases are studied. Two models study the effects of the mixing dynamics on the chemical reactions between the gases. The third model studies the structure and stability of a laminar mixing layer in a binary gas. The three models are:

1. Two ideal and incompressible gases representing fuel and oxidizer are initially at rest and separated across an infinite linear interface in a two dimensional system. Combustion, expected as the gases mix, will lead to a rapid rise in temperature in a localized area, i.e. ignition. The mixing of the gases is enhanced by two counter-rotating vortices with centers located on the initial interface. The ignition process is studied by an asymptotic analysis.

Ignition times for the double vortex lay between the no vortex and the single vortex times. As the distance between the two counter-rotating vortices gets smaller, ignition times approach the no vortex case, for increasing distance the ignition times approach the single vortex case.

2. Laminar mixing of compressible gases representing two reduced chemical systems is studied. The gases are initially separated into two semi-infinite planes and have different freestream flow velocities. Combustion is followed through ignition to the post-ignition steady flame.

The ignition distance is an inverse logarithmic function of the initially required loading of a non-fuel, non-oxidizer radical. The post-ignition flame temperature is not effected by the initial radical concentration.

3. Laminar compressible non-reacting mixing of two real gases of different free-stream temperatures and flow velocities is studied. Realistic values of transport properties are obtained from various tables or calculated from theory. The transport properties are dynamically calculated as functions of the changing temperature and gas concentrations across the mixing layer. A steady state mixed solution is found. Items of interest are the stability characteristics, the profiles of temperature and gas concentrations and the variations of the Prandtl and Lewis numbers.

The Lewis number and Prandtl numbers may vary significantly through the mixing layer. Neutral phase speeds and growth rates for spatial stability are also shown to be effected by the molecular weights and physical properties.

## Rights

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## DOI

10.25777/pvp1-1y02

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