LES/PDF for premixed combustion in the DNS limit

Abstract

We investigated the behaviour of the composition probability density function (PDF) model equations used in a large-eddy simulation (LES) of turbulent combustion in the direct numerical simulation (DNS) limit; that is, in the limit of the LES resolution length scale Δ (and the numerical mesh spacing h) being small compared to the smallest flow length scale, so that the resolution is sufficient to perform a DNS. The correct behaviour of a PDF model in the DNS limit is that the resolved composition fields satisfy the DNS equations, and there are no residual fluctuations (i.e. the PDF is everywhere a delta function). In the DNS limit, the treatment of molecular diffusion in the PDF equations is crucial, and both the ‘random-walk’ and ‘mean-drift’ models for molecular diffusion are investigated. Two test cases are considered, both of premixed laminar flames (of thickness δ_L). We examine the solutions of the model PDF equations for these test cases as functions of Δ/δ_L and h/δ_L. Each of the two PDF models has advantages and disadvantages. The mean-drift model behaves correctly in the DNS limit, but it is more difficult to implement and computationally more expensive. The random-walk model does not have the correct behaviour in the DNS limit in that it produces non-zero residual fluctuations. However, if the specified mixing rate Ω normalised by the reaction timescale τ_c is sufficiently large (Ωτ_c ≳ 1), then the residual fluctuations are less than 10% and the observed flame speed and thickness are close to their laminar values. Away from the DNS limit (i.e. h/δ_L ≳ 1), the observed flame thickness scales with the mesh spacing h, and the flame speed scales with Ωh. For this case it is possible to construct a non-general specification of the mixing rate Ω such that the flame speed matches the laminar flame speed.

Keywords:

• PDF methods
• large-eddy simulation
• turbulent combustion
• DNS limit
• premixed flames

Acknowledgements

We gratefully acknowledge the California Institute of Technology, the University of Colorado at Boulder and Stanford University for licensing the NGA code used in this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This material is based upon work supported by the US Department of Energy Office of Science, Office of Basic Energy Sciences [Award Number DE-FG02-90ER14128].