Dynamics of diffusion flames in a very low strain rate flow field: from transient one-dimensional to stationary two-dimensional regime

Abstract

The present work describes the transition of transient one-dimensional diffusion flame into a steady two-dimensional regime in a new flow field configuration. To that end, a cylindrical burner from which fuel is ejected radially and uniformly is positioned in the middle of two impinging flows. The chosen conditions are such that the strain rate is very low. The majority of the flame is located in a region of the flow field where spatial coordinates are scaled with the reciprocal of the square root of the strain rate, and the velocities are scaled with the square root of the strain rate. To simplify the model, a potential flow is assumed, with its results compared with those from a more detailed incompressible Navier–Stokes flow solution. The evolution of the flame is similar in both cases, which shows that the idealised potential flow describes well the flow field in such a geometry. Mixture fraction and excess enthalpy variables are employed to describe the infinitely fast chemical reaction, and therefore, fuel mass fraction, oxidiser mass fraction, and temperature fields. Results show that the initial flame displacement is controlled by the radial transport of fuel near the burner, where the impinging flows have a negligible influence. After that region, the flame is strongly influenced by the impinging flows where its acceleration is observed. Moreover, the proposed asymptotic solutions highlight the main transport mechanisms of reactants to the flame under different conditions and show the dependence of the flame on the chemical and flow field parameters. The stationary solution presents a diffusion flame with continuous geometric variation, from the counterflow to the coflow regime.

Keywords:

• diffusion flame
• diffusion flame dynamics
• double Tsuji flame
• flame with continuous geometric variation
• 1D transient flame to 2D stationary flame

Acknowledgements

The authors thank Professor Vinicius Maron Sauer (California State University, Northridge) for the fruitful discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The arc length is defined by $L_i:={\int }_0^{x_f}[1+(\mathrm{d}y/\mathrm{d}x{)}_{Z=1}^2{]}^{1/2}\mathrm{d}x(i\in \{POT,NS\left\}\right)$.

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Codes 1782258, 88882.444539/2019-01, 1700552 and 88887.363086/2019-00, and by CNPq, under grant numbers 302717/2016-1 and 307922/2019-7.