Vorticity transformation in high Karlovitz number premixed flames

Abstract

To better understand the two-way coupling between turbulence and chemistry, the changes in turbulence characteristics through a premixed flame are investigated. Specifically, this study focuses on vorticity, ω, which is characteristic of the smallest length and time scales of turbulence, analyzing its behavior within and across high Karlovitz number (Ka) premixed flames. This is accomplished through a series of direct numerical simulations (DNS) of premixed n-heptane/air flames, modeled with a 35-species finite-rate chemical mechanism, whose conditions span a wide range of unburnt Karlovitz numbers and flame density ratios. The behavior of the terms in the enstrophy, ω2 = ω ⋅ ω, transport equation is analyzed, and a scaling is proposed for each term. The resulting normalized enstrophy transport equation involves only a small set of parameters. Specifically, the theoretical analysis and DNS results support that, at high Karlovitz number, enstrophy transport obtains a balance of the viscous dissipation and production/vortex stretching terms. It is shown that, as a result, vorticity scales in the same manner as in homogeneous, isotropic turbulence within and across the flame, namely, scaling with the inverse of the Kolmogorov time scale, τη. As τη is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulent flames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration.

Vorticity isotropy in high Karlovitz number premixed flames

“…The analysis in this study is based on the recent DNS of high Karlovitz number statistically planar flames by Bobbitt et al 6 The physical and numerical setup of these DNSs are reviewed here briefly. For additional details, the reader is referred to Bobbitt et al 6 …”

“…This is particularly relevant to consider as it was found that temperature dependent viscosity is central to correctly capturing enstrophy transport through the flame. 6 Despite these previous contributions, it still remains unclear if and when the smallest turbulent scales are isotropic within the flame. Additionally, it is uncertain what mechanism is responsible for producing small scale anisotropy and how this is impacted by different parameters.…”

“…The focus of this study is on high Ka premixed flames. Building on our previous work, 6 the present study focuses on the isotropy of the smallest turbulent scales by considering the vorticity vector. The vorticity vector is chosen as it is characteristic of the smallest turbulent scales [19][20][21] and comparison of its three components may be used to assess flow isotropy.…”

“…Recently, the validity of Kolmogorov's first similarity hypothesis was addressed in high Karlovitz number (Ka) turbulent premixed flames. 6 It was found that enstrophy, Ω = ω · ω, where ω is the vorticity vector, scales with the inverse of the Kolmogorov time scale, Ω ∝ 1/τ 2 η (which is a function of the dissipation rate, ϵ, and kinematic viscosity, ν, alone) given a sufficiently high Karlovitz number. The current work aims to investigate the isotropy of the small scale turbulence, which relates to Kolmogorov's hypothesis of local isotropy.…”

“…The final goal is to determine how different parameters (such as Ka u and l/l F ) impact small scale anisotropy. These goals are accomplished by analyzing a series of DNS with varying Karlovitz numbers, Reynolds numbers, and flame density ratios previously performed by Bobbitt et al 6 The simulations are of statistically one-dimensional, slightly lean n-heptane/air flames using either finite-rate chemistry or tabulated chemistry. Simplified chemical and transport models are often used in numerical simulations of premixed turbulent combustion to reduce the computation cost, 15,16,18,22,23,25 but their impact on vorticity isotropy is not known.…”