# Vortex-Flame Interactions

The interaction of a premixed flame with the transient vortical structures in a turbulent flow can have a profound effect on the flame. Time dependent effects of stretch and strain can alter chemical pathways and may result in flame quenching. To quantify these effects we have applied our low Mach number modeling methodology with detailed chemistry and preferential diffusion to a series of flow configurations of increasing complexity.

Reduced Domain for Premixed Flame Calculations

### Hydrogen Flame

The simplest example of flame-vortex interactions involves a counter-rotating vortex pair impinging on an established premixed flame. Our first example of this type of flow considers a nitrogen diluted hydrogen-air flame. The flow geometry, depicted on the left, has inflow at the bottom and outflow at the top; symmetry is imposed along the sides. Over the steady premixed flame solution, we superimpose a velocity field due to a periodic array of strong vortex pairs; the vortices start below the flame at t=0 and propagate through the flame sheet due to an upward-directed self-induced velocity. Only the left vortex of a pair is computed; the right vortex, and the remaining pairs appear as image vortices through the symmetry boundary conditions. This simulation includes 9 chemical species and 27 fundamental reactions to describe the hydrogen chemistry. The flame surface breaks and reconnects behind the passing vortex, leaving a pocket of unburned fuel to propagate through the burned-fuel region and out the top of the domain.

The animation to the right illustrates the time evolution of the H2O2 mole fraction. An LIC image (line integral convolution) illustrates the velocity and enthalpy fields about 1/3 of the way through the calculation, and MPEG movies of the entire calculation are available for Temperature, and Enthalpy. The dynamically adapting grids follow regions of vorticity and high H2O2 concentration. In the animations, the rectangular boxes overlaying the solution indicate the bounds of fine grid patches. The orange boxes indicate grid refined by a factor of two over the base (the base grid covers the entire domain). The blue boxes indicate regions that have been refined by an additional factor of two.

## Experimental Methane Flame

For comparisons against experimental data, a similar computation was performed using a nitrogen-diluted methane flame for a range of stoichiometries as the fuel. The vortex and flow conditions were set to closely match conditions measured in a related vortex/flame experiment carried out at Sandia National Laboratory (Nguyen and Paul, Proc. Combust. Symp. 26, p.357-364 (1996)). In the experiment, PLIF imaging techniques were used to obtain the time-dependent CH profile throughout the interaction. Using a computational setup similar to the hydrogen flame considered above, we carried out detailed simulations using the GRI-Mech 1.2 for reactions, thermodynamics and transport properties. GRI-Mech 1.2 contains 32 species and 177 fundamental reactions. In the figure, we show the evolution of the CH model fraction over time for 5 different inflow stoichiometries. We were able to predict a rapid decline in the CH radical that was observed in the experiment under rich conditions. The results of a number of computations show that the the dynamical behavior of the flame's radical production is modulated by a fluid-dynamical ``scouring'' mechanism. The vortex pair modifies the gas composition ahead of the flame, and in fuel-rich cases, significantly alters the chemical pathways that lead to CH formation. This scouring effect depends on the radicals that can diffuse into the pre-heat zone in front of the flame, which in turn, depend on the inlet fuel equivalence ratio.

* Discussion of these and related observations appear in more detail in Bell, et al, Proc. Combus.Symp. 28, 2000

## Vortex Interactions with a Laboratory-Scale V-Flame

Although our results captured some of the experimentally observed features of the flame, such as the CH decline for rich mixtures, the computations did not match other key measurements. In particular, the results failed to reproduce a dramatic increase in OH as the vortex disrupts the flame. Our group and other researchers have explored alternative chemical mechanisms to explain this phenomena without success.

 Another explanation of the discrepancy is the differences between the experimental flow configuration and the idealized flat flame. In the V-flame configuration (such as the one shown here), a premixed flame wraps around a heated wire as reactants are fueled at a rate somewhat larger than the laminar flame speed. Since the flow is laminar, and the heating element is a straight wire, the resulting flame is essentially two-dimensional. PLIF data is obtained by passing a laser sheet normal to the flame surface, and imaging the flame end-on. A two-dimensional vortical structure is generated by pulsing fuel through a slot along the width of the device. The vortex is propelled toward the flame, and temporarily perturbs the otherwise steady structure. Time-dependent laser diagnostics are simulated by repeating the experiment, and adjusting the lag between speaker pulse and laser imaging.
Exercising the AMR (adaptive) capabilities of our algorithm, we can effectively simulate the full experiment. In the following image, the vortex-flame interation was computed over half of the V-flame vessel (the flame here is assumed symmetric across a vertical plane through the wire). There is a significant vertical flow component not included in earlier calculations, and an associated stretching of the flame. We have also included an optically thin radiation model to assess radiation effects on this Vflame. To date however, explanation of the OH spike remains illusive. We are currently implementing full matrix preferential diffusion.