Turbulence effects on cellular burning structures in lean premixed hydrogen flames

doi:10.1016/j.combustflame.2008.10.029

Combustion and Flame

Volume 156, Issue 5, May 2009, Pages 1035-1045

https://doi.org/10.1016/j.combustflame.2008.10.029 Get rights and content

Abstract

We present numerical simulations of lean hydrogen flames interacting with turbulence. The simulations are performed in an idealized setting using an adaptive low Mach number model with a numerical feedback control algorithm to stabilize the flame. At the conditions considered here, hydrogen flames are thermodiffusively unstable, and burn in cellular structures. For that reason, we consider two levels of turbulence intensity and a case without turbulence whose dynamics is driven by the natural flame instability. An overview of the flame structure shows that the burning in the cellular structures is quite intense, with the burning patches separated by regions in which the flame is effectively extinguished. We explore the geometry of the flame surface in detail, quantifying the mean and Gaussian curvature distributions and the distribution of the cell sizes. We next characterize the local flame speed to quantify the effect of flame intensification on local propagation speed. We then introduce several diagnostics aimed at quantifying both the level of intensification and diffusive mechanisms that lead to the intensification.

Introduction

There has been considerable recent interest in the development of premixed burners capable of stably burning hydrogen at lean conditions. Operating at fuel-lean conditions minimizes combustion exhaust gas temperatures, which in turn reduces the formation of nitrogen-based emissions downstream of the flame. However, lean premixed flames, and hydrogen–air mixtures in particular, are subject to a variety of flame-induced hydrodynamic and combustion instabilities that render robust flame stabilization difficult. The present study is concerned with the behavior of lean premixed hydrogen–air flames in a turbulent environment. We focus on flames at atmospheric pressure and in relatively low levels of turbulence characteristic of low-swirl burner experiments [1]. Under these conditions, lean hydrogen–air flames form cellular burning structures due to preferential diffusive thermal instabilities [2], [3].

Premixed hydrogen combustion has been the subject of numerous experimental and numerical investigations. Goix et al. [4], [5] looked at fractal properties of the flame front. Wu et al. [6], [7] studied effects of preferential diffusion. Goix et al. [8] and Kwon et al. [9] studied the turbulent flame brush. Turbulent burning velocity has been measured by Kido et al. [10] and Aung et al. [11]. Cellular structures have been observed in dilute H₂/O₂ mixtures by Bregeon et al. [12] and Mitani and Williams [13]. A related phenomena is the tip opening in lean Bunsen flames observed by Mizomoto et al. [14] and Katta and Roquemore [15]. Lee et al. [16], [17] observe strong dependence on curvature in the interaction of lean premixed hydrogen flames with Karman vortex streets. Chen and Bilger [18] present data showing cellular structures in a turbulent Bunsen flame and provide detailed scalar measurements of a progress variable, OH and scalar dissipation rate at lean conditions.

Hydrogen combustion has also been studied using DNS techniques with detailed chemistry in an idealized configuration. Two-dimensional examples include Baum et al. [19], Chen and Im [20], de Charntenay and Ern [21], and Im and Chen [22]. More recently Tanahashi et al. [23], [24] performed simulations for turbulent premixed hydrogen flames at stoichiometric conditions with detailed hydrogen chemistry in three dimensions.

In this study, we use numerical simulation to obtain a detailed characterization of lean premixed hydrogen flames in three dimensions, allowing us to quantify the interplay between the turbulent fluctuations and hydrogen's natural instabilities, in terms of global flame propagation properties, three-dimensional flame geometry, and detailed chemical structures. In order to minimize analysis complexity, we conduct this study using an idealized computational configuration similar to the studies cited above. A time-dependent three-dimensional flame propagates toward an inflow boundary where turbulent fluctuations have been superimposed on a mean flow. The fluctuations are chosen to match (in terms of integral scale and intensity) those observed in related laboratory experiments. For this study, the mean inflow velocity is adjusted dynamically using an automatic control algorithm [25] to hold the mean position of the flame a fixed distance above the inflow face. The procedure allows the simulation of a weakly turbulent flame in a quasi-steady configuration without the need to simulate a pilot or some geometric stabilization device. Bell et al. [26] used this control algorithm to explore Lewis number effects in two dimensions.

The goal here is to quantitatively characterize the geometry of the cellular burning front and local burning properties along that front. Capturing this behavior requires that we resolve the interplay of chemistry and transport processes with the turbulent flow, which, in turn, requires detailed models for transport and chemistry. Moreover, the evolution involves a large range of temporal and spatial scales, both in terms of the turbulent spectra and the local flame structure. Here, the simulations are performed using a well-established low Mach number integration methodology that is summarized briefly in the next section. The subsequent section describes the details of the simulation study. Analysis of the simulation results is presented in Section 4.

Section snippets

Computational methodology

The simulations presented here are based on a low Mach number formulation [27] of the reacting flow equations. The methodology treats the fluid as a mixture of perfect gases. We use a mixture-averaged model for differential species diffusion (see [28] for complete discussion of this approximation) and ignore Soret, Dufour, gravity and radiative transport processes. With these assumptions, the low Mach number equations for an open domain are $\frac{\partial ρ U}{\partial t} + \nabla \cdot ρ U U = - \nabla π + \nabla \cdot τ,$ $\frac{\partial ρ Y_{m}}{\partial t} + \nabla \cdot U ρ Y_{m} = \nabla \cdot ρ D_{m} \nabla Y_{m} - ω_{m},$ $\frac{\partial ρ h}{\partial t} + \nabla \cdot U ρ$

Case study

The idealized flow configuration we consider, schematically identical to that used by Tanahashi and coworkers (see [23, Fig. 1]), initializes a slightly perturbed, flat, laminar flame in a rectangular domain oriented so that the flame propagates downward (since gravity is not included, the direction is for orientation only). A cold ( $T = 298 K$ ) turbulent H₂–air premixture ( $ϕ = 0.37$ ) enters the domain through the square bottom boundary, which measures 3 cm on a side. Hot combustion products exit the

Results

In the following, we characterize the time-dependent evolution of the three quasi-stationary lean hydrogen–air flames in three ways. First, we provide a qualitative description of the salient features of the flames, and discuss global propagation characteristics and how they are affected by the level of inlet turbulence. We then discuss the flame geometry including a topological analysis of the cellular flame surface to capture the distribution of cell sizes associated with these flames.

Conclusions

We have numerically stabilized lean premixed hydrogen flames in a turbulent fuel stream using a feedback control algorithm. Depending on the turbulence level, we observe flames that propagate globally at 3–8 times the speed predicted by a one-dimensional idealization of these thermodiffusively unstable flames. The quasi-steady flames burn intensely in time-dependent cellular structures that are separated by fuel-depleted regions that do not burn. The cellular structures tend to be convex with

Acknowledgments

The calculations were performed under Award SMD-05-A-0126, “Interaction of Turbulence and Chemistry in Lean Premixed Combustion,” for the National Leadership Computing System initiative on the “Columbia” supercomputer at the NASA Ames Research Center. A portion of the post-processing was carried out on the “Davinci” server at NERSC. The authors were supported by the Office of Science through the Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational

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Turbulence effects on cellular burning structures in lean premixed hydrogen flames

Abstract

Introduction

Section snippets

Computational methodology

Case study

Results

Conclusions

Acknowledgments

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