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Rutland and Ferziger (1991): Flame-Vortex interactions
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**Title**

Simulations of Flame-Vortex Interactions

**Authors**

Christopher J. Rutland and Joel H. Ferziger


**Summary**

Full numerical simulations to study the interaction of a vortex and a premixed flame as a model problem. The effects of heat release and the importance of the relative length and time scales of the vortex and flames are examined. Changes in the internal structure and overall shape of the flame are studied.

Different approaches are studied to isolate various effects and aid in understand the full interaction.

(1) Frozen flame

(2) Frozen vortex

(3) Full flame-vortex interaction: combination of above two frozen cases


- Non-dimensional parameters:

(1) :math:`\sigma`: Initial vortex size. Ratio of vortex and flame length scales.

(2) Damkohler number (Da): Ratio of time scales. Nondimensional vortex time scale.



- Fronzen flame

  - The frozen flame isolates the effects of the flame on the fluid mechanics. The momentum equation, but not the energy equation, is integrated in time. The temperature and density fields remain fixed as their initial conditions. This approximates high ``Damkohler`` number flows in which the vortex passes through the flame quickly, experiencing very little turnover.

  - The fluid is assumed to be inviscid.

  - Baroclinic torque acts as a source of vorticity whenever the density gradient and the pressure gradient are not aligned. 

  - The density gradient is normal to the flame surface. And the pressure gradient is initially radial from the vortex center.

  - The principal effects appear to be elongation of the vortex in direction normal to the flame surface.

  - For high Da, the time scale of the vortex is much longer than the flame: The vortex rotates very little as it passes through the flame. Thus the main effect is expansion of the vorticity distribution normal to the flame. (See Fig. 5)

  - Effect of heat release on vorticity elongation: As heat release increases, voriticy elongation increa


Under review...