Flame resolved simulation of a turbulent premixed bluff-body burner experiment. Part I: Analysis of the reaction zone dynamics with tabulated chemistry
Introduction
Direct numerical simulations (DNS) have been used over the last decades to gain a deeper understanding of the governing physical mechanisms of turbulent combustion. DNS provides three-dimensional velocity and scalar fields, which are resolved in space and time. These results are useful to complement experimental observations and are also the key element in the development of combustion models for Reynolds-averaged Navier–Stokes simulations (RANS) and large eddy simulations (LES) – which will both be the only viable tools for the computation of technically relevant combustors in the foreseeable future. Recent overviews on the topic of combustion DNS are given by Chen [1] and by Poinsot and Veynante [2].
When focusing on premixed turbulent combustion, DNS simulations can be categorized in groups based on the complexity of the chemical mechanism, the type and strength of turbulence occurring, and the complexity of the geometry. A large amount of early and recent work was performed for planar or spherical flames interacting with canonical flow configurations, mostly either homogeneous turbulence or larger single vortices, with reduced chemical mechanisms or tabulated chemistry [3], [4], [5], [6], [7], [8], [9], [10], more detailed chemical mechanisms [11], [12], [13] or detailed chemical mechanisms [14].
Another group of direct numerical simulations deals with more complex slot- or Bunsen-flames, applying more detailed chemical mechanisms [15], [16], [17], [18], [19]. Although these configurations are more realistic than the canonical cases, they are still compact enough to resolve all flame- and velocity scales properly in a DNS sense.
Classically, combustion models can be developed based on DNS results of the aforementioned simplified flame configurations. Nevertheless, the turbulent flow structures in technically relevant burners are usually more complex than in these simplified configurations. It is therefore mandatory to validate the obtained models also in more realistic flame configurations, as occurring in lab-scale experiments. A classical DNS of these experiments would be computationally too expensive, therefore LES or RANS simulations are performed with the developed combustion models instead. The performance of the models is then judged by comparing (time-averaged) simulation results against experimental measurements. One serious issue with this approach is that, due to the complex interaction of sub-filter closures for the unresolved velocity scales and the sub-filter flame wrinkling, errors might compensate or amplify. Therefore, a clear and definitive judgment of the combustion model performance is hardly possible, which makes a further development of these models based on such comparisons questionable.
However, if the focus is on the development of sub-filter closures for models based on strongly reduced or tabulated chemistry, as they are applied in the vast majority of LES or RANS computations, flame resolved simulations are possible with the computational power available today. The saving of computational time with respect to a classical DNS has two major reasons. First, the chemical species that need to be transported for the strongly reduced or tabulated chemistry can be resolved on a significantly coarser grid than it is required for a more detailed chemical mechanism. Second, the Kolmogorov length scale increases significantly from the unburned to the burned side of the flame, due to the increase in viscosity. As the main focus in the development of models for premixed combustion is on the influence of a given level of velocity fluctuations on the flame propagation, a slight under-resolution of the Kolmogorov scales in the fresh gases can be tolerated when full resolution of the signals is secured in the reaction zone. This kind of simulation has the potential to fill the gap in-between highly resolved ‘classical DNS’ for simpler configurations on the one hand, and LES (for real technical configurations) on the other hand, and may be termed as ‘quasi DNS’ or ‘flame resolved simulation’, where the latter term is chosen for the remainder of the paper. This new paradigm in turbulent flame simulation allows for comparing flame resolved simulation data against experiments and to carefully validate the simulated flow physics, as it has been done for ‘classical DNS’ of non-reactive flows for quite some years [20], [21]. The main advantage is that the lab-scale configurations considered enable a further validation of the simulations and the applied combustion models under much more realistic flow conditions, in which the unsteady motion develops according to real turbulent flow properties. Compare to ‘classical DNS’, an additional and essential validation step may thus be performed, in which it is verified that the statistical flow properties of the DNS fields agree well with experimental measurements.
The first flame resolved simulation for a lab-scale experiment was presented by Moureau et al. [22], it was performed with a finest grid resolution of and tabulated chemistry for a lean premixed methane-air swirl burner, which has been previously investigated experimentally by Meier et al. [23]. The applied grid resolution was sufficient to resolve the progress variable field as well as the velocity field inside the relevant flame region. (A small amount of unresolved velocity scales were still present in the unburned gas close to the walls of the swirler, which were dissipated by the numerical scheme.) A good agreement between simulation and measurement data was demonstrated, the results were then used for developing the filtered laminar flame probability density function (FLF–PDF) modeling approach, in which the unresolved fluctuations of the progress variable are related to an explicit filtering operation applied to one-dimensional flamelets.
In the present paper, a flame resolved simulation of a lab-scale flame is presented for a lean premixed methane-air bluff-body burner investigated experimentally at the University of Cambridge and the Sandia National Laboratories by Hochgreb and co-workers and Barlow and co-workers [24], [25], [26], [27], [28], [29], and also numerically with LES by various groups [30], [31], [32], [33], [34]. In contrast to the work of Moureau et al. [22], the focus of the present paper lies on the analysis of the reaction zone dynamics and the turbulence-flame interaction based on the un-filtered progress variable and velocity fields, rather than on a-priori model development, a topic which is considered in a subsequent paper [35]. The goal is to analyze the flame resolved simulation results for a lab-scale burner with respect to the findings from previous DNS performed in much simpler configurations.
The details of the modeling and the experimental and numerical setup are described in the first section of the paper. Afterwards, a careful analysis of the resolution of flame- and velocity scales is presented and the statistically converged mean and rms profiles obtained from the simulation are compared against the available experimental data. Ensemble-averaged conditioned probability density functions (PDFs) and conditioned joint probability density functions (JPDFs) are then evaluated based on all available data points from the last time step of the simulation. It is shown that a conditioning on the height above the burner and the progress of reaction is necessary to obtain a maximum of information from the data. In the near burner region, the flame is only weakly affected by turbulence. This changes further downstream, due to the interaction of the reaction zone with the turbulence originating from the outer stream and the shear layer between the two streams. The correlations between the strain rate components and the progress variable field are investigated, where the focus is on the comparison with the reference laminar flame structure, used in topology-based subgrid-scale models. The progress variable field is characterized by its gradient, curvature and the local displacement speed of its iso-surfaces. Furthermore, various properties related to the reaction zones are extracted and examined for further analysis.
Section snippets
Premixed flame modeling
The goal of this work is to provide and investigate a database of a flame resolved simulation of a lab-scale burner experiment, which can be used for future validation and development of sub-filter closures for LES or RANS combustion models. Such LES or RANS computations are very often performed with tabulated chemistry, most of the reported LES studies for the investigated burner have been carried out with this approach [30], [31], [32], [33]. Therefore, tabulated chemistry was also used for
Experimental and numerical setup
The experimental setup of the investigated burner is presented in Fig. 2. The measurements have been carried out by Hochgreb and co-workers at the University of Cambridge and Barlow and co-workers at the Sandia National Laboratories [24], [25], [26], [27], [28], [29]. The central bluff-body is surrounded by two co-annular premixed methane-air streams at ambient conditions, which are embedded in a co-flow of air with a velocity of 0.4 m/s. For further details please refer to Table 1.
Resolution of flame- and velocity scales
The sufficient resolution of the velocity scales on the computational grid is checked by two different measures, on the one hand based on the estimated Kolmogorov length scales, and on the other hand based on the remaining turbulent viscosity as predicted from the σ-model. The level of resolution of the progress variable source term on the computational grid is addressed also, to conclude on the quality of the reaction zone description.
Comparisons of time-averaged statistics against measurements
To check the validity of the modeling approach and the general quality of the simulation results, statistical quantities (mean and rms) along sample lines are compared against experimental measurements. The sampling was started after 0.34 seconds, which corresponds to more than one flow-through time with respect to the co-flow velocity of 0.4 m/s. The sampling was carried out for another 0.14 seconds, which corresponds to more than 10 flow-through times with respect to the mean inner stream
Analysis of the turbulent flame structure
This section presents a detailed analysis of the turbulence-flame interaction in the investigated lab-scale burner, with respect to the findings from DNS of much simpler flow configurations. The main focus is on the comparison of the resulting turbulent flame structure to the laminar one, to progress in the context of flamelet-like sub-grid scale modeling. The first step is a phenomenological analysis of the flame structure based on instantaneous two-dimensional and three-dimensional contour
Conclusions
An unsteady simulation of a lab-scale turbulent premixed flame experiment was presented, where the combustion process was modeled with the premixed flamelet generated manifold (PGFM) chemistry tabulation approach. It has been demonstrated that the applied grid resolution of was indeed sufficient to resolve the flame without any sub-filter modeling and all velocity scales inside and in the vicinity of the flame region. Only on the unburned side of the flame, a small amount of unresolved
Acknowledgments
The authors gratefully acknowledge the funding from the state of North Rhine–Westphalia and the compute time granted on JUQUEEN at Jülich Supercomputing Centre (JSC), through the John von Neumann Institute for Computing (NIC). We also would like to thank Vincent Moureau and Martin Rieth for valuable discussions.
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