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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

# Displacement Speed Statistics for Stratified Mixture Combustion in an Igniting Turbulent Planar Jet

[+] Author and Article Information
Henrik Hesse, Sean P. Malkeson

Department of Aeronautics,  Imperial College, London, South Kensington Campus, SW7 2AZ, UKEngineering Department,  University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK

Nilanjan Chakraborty1

School of Mechanical and Systems Engineering,  Newcastle University, Claremont Road, Newcastle-Upon-Tyne, NE1 7RU, UK e-mail: nilanjan.chakraborty@newcastle.ac.uk

1

Corresponding author.

J. Eng. Gas Turbines Power 134(5), 051502 (Feb 29, 2012) (14 pages) doi:10.1115/1.4005214 History: Received March 01, 2011; Revised September 10, 2011; Published February 29, 2012; Online February 29, 2012

## Abstract

The statistics of the density-weighted displacement speed of the reaction progress variable $c$ isosurfaces for stratified mixture combustion arising from localized ignition in a turbulent planar coflowing jet have been studied based on 3D Direct Numerical Simulation data where the jet is considered to be fuel-rich and the coflow is taken to be fuel-lean. The resulting flame following successful ignition shows the premixed mode of combustion in fuel-rich and fuel-lean zones although an additional diffusion flame branch was also observed on the stoichiometric mixture isosurface at early times of flame evolution. The flame propagation characteristics have been analyzed in terms of the reaction, normal diffusion and tangential diffusion components of the density-weighted displacement speed for different values of reaction progress variables across the flame brush. It has been found that the reaction, normal diffusion and tangential diffusion components of density-weighted displacement speed, remain the major contributors to the density-weighted displacement speed at all stages of flame evolution as the magnitude of the component which originates due to mixture inhomogeneity remains negligible in comparison to the magnitudes of other components in accordance with previous experimental studies. It has been demonstrated that curvature and tangential strain rate dependences of the reaction progress variable gradient play key roles in determining strain rate dependences of the reaction and normal diffusion components of the density-weighted displacement speed. It has been shown that the interrelation between tangential strain rate and curvature affects the strain rate dependence of tangential diffusion component of the density-weighted displacement speed. The density-weighted displacement speed and curvature are found to be predominantly negatively correlated throughout the flame brush at all stages of the flame evolution. The relative strengths of the tangential strain rate dependence of the reaction, normal diffusion and tangential diffusion components of the density-weighted displacement speed ultimately determine the nature of correlation between the density-weighted displacement speed and the tangential strain rate. The strain rate and curvature dependences of the density-weighted displacement speed in stratified mixtures are found to be qualitatively similar to the statistics previously obtained for turbulent premixed flames.

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## Figures

Figure 1

Schematic diagram of the flow configuration

Figure 2

Distributions of (a) T={0.1,0.3,0.5,0.7,0.9}, (b) |w·F|xD0/ρ0SL2={0.01,0.025,0.05,0.075} at the middle of the domain in the span-wise direction at times t = 1.00tsp (brown), 4.20tsp (red) and 7.40 tsp (green) and (c) |u1|/SL at 7.40tsp . Temporal evolution of (d) Tmax and (e) |w·F|maxxD0/ρ0SL2. (f) Distribution of χcxD0/SL2 and ξ with the distance along the slot height (x2  = y-direction) through the center of the flame kernel at x/H=0.75 for t=1.00tsp, x/H=4.38 for t=4.20tsp, x/H=7.5 for t=7.40tsp.

Figure 3

PDFs of Sd*/SL on the c=0.3,0.5,0.7 and 0.9 isosurfaces at (a) t=1.0tsp, (b) t=4.20tsp and (c) t=7.40tsp

Figure 4

PDFs of Sr*/SL,Sn*/SL and St*/SL on different c isosurfaces at (a) t=1.0tsp, (b) t=4.20tsp and (c) t=7.40tsp. PDFs of Sξ*/SL on different c isosurfaces at (d) t=1.0tsp, (e) t=4.20tsp and (f) t=7.40tsp. The black vertical line corresponding to Sr*/SL=0,Sn*/SL=0 and St*/SL=0 are shown in (a), (b) and (c), respectively.

Figure 5

(a) Variation of mean values of |∇c|×lF conditional on aT×lF/SL values; variations of mean values of (b) |∇c|×lF and (c) aT×lF/SL conditional on κm×lF values. The variations in this and subsequent plots are shown for the c=0.3,0.5,0.7 and 0.9 isosurfaces at t=1.0tsp, 4.20tsp and 7.40tsp.

Figure 6

Variations of mean values of (a) Sd*/SL, (b) Sr*/SL and (c) Sn*/SL conditional on κm×lF values

Figure 7

Variations of mean values of (a) (Sr*+Sn*)/SL, (b) St*/SL and (c) Sd*/SL conditional on aT×lF/SL values

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