Relation between flame speed and stretch for a premixed flame in a stagnation point flow

Displacement speed of a flame is a hydrodynamic concept, and it is defined as the normal component of the velocity of the incoming flow evaluated on the unburned side of the flame. Except for a steadily propagating flame with zero stretch (planar flame), this definition is ambiguous because the mass flux and, consequently, the gas velocity vary across the thickness of the flame represented by the flame/thermo-diffusive/pre-heat zone. In other words, the flame displacement speed has different values when evaluated at different locations within the flame zone. This has led to confusion about the position within the flame that must be used for measuring flame speed. Additionally, according to the hydrodynamic theory, the flame speed of weakly stretched flames is dependent on the flame stretch and the position/isotherm chosen within the flame zone through a parameter known as the Markstein Length. It is the objective of this study to provide a recommendation for the position/isotherm within the flame zone for measuring gas velocity in experiments that provides a flame speed value consistent with the hydrodynamic theory. In this regard, a premixed flame in an axisymmetric laminar stagnation point flow is studied using the hydrodynamic theory. First, the outer or hydrodynamic solution is obtained by solving modified Euler equations along with jump conditions resulting from conservation laws. Thereafter, the structure of the flame zone is resolved by rescaling the coordinate and the inner solution obtained using asymptotic theory is presented. Having obtained the outer and inner solutions, a uniformly valid composite expression for the mass flux across the flame is derived and presented. Finally, flame speeds are evaluated at different isotherms/positions within the flame zone, and a recommendation for the position to measure gas velocity in experiments is provided.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Joy, Midhun Jacob

Contributors dc:contributor

• Matalon, Moshe

• Stagnation
• Flame
• Flame displacement speed (FDS)
• Flame speed
• Markstein length
• Hydrodynamic theory

Statement dc:rights

• Copyright 2017 Midhun Joy

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/99416

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F99416