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The Effects of a Vortex Field on Flames with Finite Reaction Rates


Norton, Olin Perry (1983) The Effects of a Vortex Field on Flames with Finite Reaction Rates. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7vn8-4078.


A diffusion flame, supported by a one-step chemical reaction, is initiated along the horizontal axis between a fuel occupying the upper half-plane and an oxidizer below. Simultaneously, a vortex of circulation Γ is established at the origin. As time progresses the flame is extended and "wound up" by the vortex flow field. The effect of distortion of the flame is locally described by the time-dependent straining of a one-dimensional flame. The rate of chemical reaction is represented by the characteristic chemical reaction time, tch, of the system. The combustion field then consists of a totally reacted core region and an external flame region consisting of a pair of spiral arms extending off at large radii toward their original positions.

The presence of the vortex increases the rate of fuel consumption of the flame. For large values of Γ/D, the augmentation of fuel consumption due to the vortex is proportional to ρΓ2/3D1/3, and is a function of t/tch which approaches a constant value as t → ∞. The growth of the fuel consumption rate from zero to its steady value for large times is governed by the time scale tch. If the products of combustion occupy more volume than the original reactants, then the spiral flame will appear as an unsteady volume dilitation for times on the order of the chemical time. An unsteady volume dilitation acts as an acoustic source, so the interaction of a vortex and a diffusion flame is shown to result in the generation of a pressure pulse; the peak pressure occurring after a delay proportional to the chemical time, and the strength of the pulse proportional to Γ2/3D1/3 and inversely proportional to √tch.

These results are valid for hypergolic reaction systems in which the reactant temperature does not significantly effect the rates of the chemical reactions. For systems described as having "large activation energy", the rates are strongly temperature dependent and another description is appropriate. For these systems, a vortex established on an already ignited flame exhibits, in addition to the features described above, an extinct core of unburned reactants if the circulation of the vortex is large.

The results provide the fundamental structure for the mechanism of combustion instability proposed by Rogers and Marble in 1956.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mechanical Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marble, Frank E.
Thesis Committee:
  • Kubota, Toshi (chair)
  • Marble, Frank E.
  • Roshko, Anatol
  • Sabersky, Rolf H.
  • Zukoski, Edward E.
Defense Date:9 August 1982
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)AFOSR-80-0265
Record Number:CaltechETD:etd-09112006-111139
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3457
Deposited By: Imported from ETD-db
Deposited On:26 Sep 2006
Last Modified:16 Apr 2021 23:06

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