Scaling of Second-Order Structure Functions in Turbulent Premixed Flames in the Flamelet Combustion Regime

Peter Brearley,Umair Ahmed,Markus Klein,Nilanjan Chakraborty

doi:10.3390/fluids5020089

Peter Brearley, Umair Ahmed + Show 2 more

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https://doi.org/10.3390/fluids5020089

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Abstract

The second-order velocity structure function statistics have been analysed using a DNS database of statistically planar turbulent premixed flames subjected to unburned gas forcing. The flames considered here represent combustion for moderate values of Karlovitz number from the wrinkled flamelets to the thin reaction zones regimes of turbulent premixed combustion. It has been found that the second-order structure functions exhibit the theoretical asymptotic scalings in the dissipative and (relatively short) inertial ranges. However, the constant of proportionality for the theoretical asymptotic variation for the inertial range changes from one case to another, and this value also changes with structure function orientation. The variation of the structure functions for small length scale separation remains proportional to the square of the separation distance. However, the constant of proportionality for the limiting behaviour according to the separation distance square remains significantly different from the theoretical value obtained in isotropic turbulence. The disagreement increases with increasing turbulence intensity. It has been found that turbulent velocity fluctuations within the flame brush remain anisotropic for all cases considered here and this tendency strengthens towards the trailing edge of the flame brush. It indicates that the turbulence models derived based on the assumptions of homogeneous isotropic turbulence may not be fully valid for turbulent premixed flames.

Highlights

Velocity structure functions (SFs) take a central role in turbulence theory [1,2,3,4,5,6], where they are mostly used to analyse the scale invariance of fully developed turbulence, characterized by a sequence of scaling exponents [7]
It is worthwhile to consider the relations based on non-reacting homogeneous isotropic turbulence so that it can be ascertained if DLL (r, t)/hεr i2/3 and DTT (r, t)/hεr i2/3 remain independent of r for η < r < ` where η = [μ3 /ρ3 hεi]1/4 is the Kolmogorov length scale
As the analysis focuses on the velocity statistics, the simplification related to the chemical reaction is not expected to play a major role

Summary

Introduction

Velocity structure functions (SFs) take a central role in turbulence theory [1,2,3,4,5,6], where they are mostly used to analyse the scale invariance of fully developed turbulence, characterized by a sequence of scaling exponents [7]. As SFs depend only on velocity differences separated by spatial distances and do not rely upon Fourier transform to present the information in the spectral space, they have the potential to be more accessible than energy spectra to analyse turbulent flow structures in premixed turbulent combustion [12,13,14,15]. Analysed SFs conditioned on the flame normal and tangential directions for high turbulence intensities representative of high Karlovitz number, thin reaction zones regime combustion and indicated that. The unburned gas turbulence is subject to isotropic forcing, which ensures desired values of both turbulence intensity and integral length scale upstream of the flame

Mathematical Background and Numerical Implementation

Results and Discussion

Conclusions