Stabilization and liftoff length of a non-premixed methane/air jet flame discharging into a high-temperature environment: An accelerated transported PDF method
Introduction
Turbulent lifted flames are relevant in many practical combustion devices, including direct injection (DI) internal combustion (IC) engines, gas turbines and industrial furnaces. Three different mechanisms for the stabilization of lifted flames have been proposed in the literature. These mechanisms are: (1) fuel and oxidizer are premixed within the liftoff height such that the base of a lifted flame burns as a turbulent premixed-flame [1], which implies that a lifted flame is stabilized where the turbulent flame speed is balanced by the incoming reactant velocity [2]; (2) fuel and oxidizer remain non-premixed within the liftoff height such that the base of a lifted-flame burns as a diffusion-flame [3], which implies that a lifted-flame is stabilized at the location where the local scalar dissipation rate is equal to the critical dissipation rate at extinction; and (3) fuel and oxidizer are partially premixed within the liftoff height such that a lifted-flame at its base burns as an edge-flame [4] which is made up of a lean premixed branch, a rich premixed branch and a diffusion flame (the so-called triple-flame) that intersect at the triple-point. The main difference between propagation of an edge-flame and that of a stoichiometric premixed-flame is that the incoming reactant stream diverges significantly due to the heat release from the edge-flame; therefore, the effective flame-front-normal component of the incoming velocity at the base of an edge-flame is smaller than that of the main stream velocity further upstream in the flow [5]. Together with curvature effects, this leads to a propagation speed that is significantly larger than the propagation speed of an unstrained stoichiometric premixed-flame [4], [5], [6].
The lifted turbulent flame base structure was studied by Muiz and Mungal [7]. Many experiments, such as those of Phillips [8], Watson et al. [9] and Upatnieks et al. [10], appear to support the claim that the base of a lifted-flame burns as an edge-flame while discounting the other two above-mentioned mechanisms. However, the evidence was not conclusive. For example, it is difficult to show in the experiments that the base of lifted flames burns at locally stoichiometric conditions and has a triple-flame structure with a lean-premixed, a rich-premixed and a diffusion flame meeting at the flame base. Another limitation in the experiments is that they covered only a limited range of conditions. For example, in the Watson et al. [9] and Upatnieks et al. [10] experiments, the lifted-flame was stabilized above a nozzle that discharged a fuel jet at relatively low or moderate Reynolds numbers (less than 8500), into a low-velocity coflow stream at room temperature. Higher Reynolds number lifted jet flames may be stabilized by elevating the coflow stream temperature. Cabra et al. [11] investigated such conditions by using a burner in which a fuel jet centered at the middle of a coaxial flow of hot combustion products from a lean premixed H2/air flame, known as a Berkeley burner [12], formed a partially premixed lifted jet flame. This type of flame is referred to as a lifted jet flame in a vitiated coflow. The fuel-jet Reynolds number in Berkeley flames exceeds 28,000.
The flame structure and stabilization mechanism for a jet flame in a vitiated coflow may be different from those in the Watson et al. [9] and Upatnieks et al. [10] experiments. For example, the strong sensitivity of the liftoff height to small variations in the coflow temperature (a few degrees Kelvin) in the Cabra et al. [11] experiments is still not fully understood. It cannot be explained by the edge-flame theory and the hypothesis [5], [10] that the liftoff height is inversely correlated to the laminar burning velocity of the stoichiometric flame. Previous studies have shown that the liftoff height of the Berkeley flames is primarily controlled by the auto-ignition process in the gases before the stabilization position [11], [13], [14].
Several authors have performed numerical simulations for these cases in the past. Gorden et al. [13] used a Fluent/Lagragian particle composition PDF method. It was concluded that auto-ignition is the main stabilization mechanism by transport budget analysis and time history of radicals. A hybrid second-moments-closure/Lagrangian particle composition PDF method was used by Gkagkas and Lindstedt [15] to study the same flame. A detailed 44-species mechanism was used in the study. It was concluded that the flame was stabilized by autoignition and importance of different species in the pre-ignition zone was analyzed. Both of the above studies found that the details of mixing model was not very important in capturing the autoignition phenomena. Cabra et al. [11] also studied the same flame using a joint-scalar PDF method, and exercised with different mixing models. It was also seen in this work all mixing models could capture the sensitivity of liftoff height to coflow temperature. However, the detailed scatter plot of temperature versus mixture fraction has different structures among different mixing models. Other than PDF-based methods, LES simulation with chemistry tabulations [16], [17], LES simulation with unsteady flamelet/progress (UFP) variable method [18], and a conditional moment closure approach [19] were all exercised on the same flame, partly for the purpose of validation of the proposed models. Regardless of the kinetic mechanisms that were used in these studies, all of them concluded that auto-ignition is the primary stabilization mechanism under the Berkeley flames conditions. However, the structure of the flames and sensitivity of the liftoff height to the coflow temperature were not fully demonstrated.
In this study, we revisit the question of stabilization mechanisms of lifted-flames in vitiated coflow via modeling Berkeley methane/air flames at different coflow temperatures. The approach in this paper is a particle-based transported PDF method within an URANS formulation. A well-known shortcoming of a transported PDF method is its high computational cost, especially when coupled with realistic chemistry, which is expected to be necessary to capture multiple combustion regions, e.g., partially premixed combustion involving both auto-ignition and flame propagation processes. In general, any measure that accelerates the integration of the chemistry ODEs proportionally reduces the overall computational cost. Chemical mechanism reduction and chemistry tabulation/storage/retrieval approach [20] are common examples of such techniques. In situ adaptive tabulation (ISAT) [21] is an example of tabulation/storage/retrieval approach. While ISAT can significantly reduce the computational costs in statistically stationary flows, it is less efficient in non-stationary flows. Transient spray combustion and combustion in internal combustion (IC) engines are examples of applications where the advantage of ISAT have proven elusive.
To address this issue, a key original aspect of the approach proposed here is the employment of the newly developed chemistry coordinate mapping (CCM) technique [22], [23], [24] to accelerate the transported PDF method (hereinafter the PDF-CCM method). Moreover, in contrast to previous studies, here we focus on the structure of the combustion at and above the liftoff position, and on the role of coflow temperature in the stabilization mechanism. This paper thus has two purposes: (1) to validate the PDF-CCM approach for partially premixed modes of combustion; and (2) to provide an improved understanding of the effects of ambient temperature on the structure of combustion and the stabilization mechanism for lifted jet flames discharging into high-temperature environments.
It is important to recognize that CCM (like ISAT, for example) is a numerical strategy to accelerate the calculation of the chemical source terms; it is not a physical model. Here the turbulent combustion model in all cases is a transported composition PDF method. The speedup performance of CCM is assessed by comparing the computational time for a PDF method with CCM (PDF-CCM) to that of a PDF method without CCM (PDF), and accuracy is quantified by comparing PDF-CCM and PDF results.
Section snippets
Mathematical model: CCM for LPEM PDF method
The PDF-code that is used here employs a consistent hybrid Lagrangian particle/Eulerian mesh method (LPEM) [25]. The code has been developed and validated in earlier modeling studies [26], [27], [28]. The CCM approach as proposed in [22], [23] is adopted for chemistry acceleration. For PDF-CCM, instead of identifying and clustering CFD cells into the CCM zones, the notional Lagrangian particles that are in similar thermodynamic states are identified and clustered into the phase-space zones. CCM
Validation and performance of PDF-CCM
RANS/PDF is targeted for initial PDF-CCM validation in this paper, and Sandia flames D and F [36] are adopted as the first test cases. Sandia flames are ideal test cases because there are publicly available high-quality experimental database for these flames [36]. Detailed measurements of mean and rms temperature, velocities and gas-phase compositions are available for comparison.
The Sandia nonpremixed piloted methane-air flames consist of three flow streams: a fuel jet with an inner diameter
Interrelation between CCM and chemistry tabulation techniques
The steady non-premixed flamelet equation for species mass fraction can be written as follows [40]:Temperature is governed by the same form of equation. Usually a functional form is presumed, where subscript “st” denotes the stoichiometric conditions. Eq. (12) indicates that the mass fractions of chemical species and temperature are only functions of mixture fraction and the scalar dissipation rate at the stoichiometric condition. This is the basic idea
Application of PDF-CCM: Berkeley flames
Numerical simulations using the above-described PDF-CCM method are carried out for CH4/air flames of the Berkeley burner. The burner consists of a fuel jet with an inner diameter of = 4.57 mm and wall thickness 0.89 mm which is located at the center of a perforated disk with a diameter of 2100 mm and having 2100 holes with a diameter of 1.58 mm. Each hole stabilizes a lean premixed hydrogen/air flame to provide a hot co-flow stream. The fuel-jet tube extends 70 mm downstream of the plane of the
Conclusions
PDF-CCM has been formulated to accelerate particle-based PDF methods, and the method has been validated using Sandia flames D and F test cases. In PDF-CCM, the thermodynamic states of all particles are mapped into a multidimensional discretized phase space to identify particles that are at similar thermodynamic states. Many PDF particles may fall into one cell of the CCM phase space (zone). Integration of the stiff ODEs is performed in the zones, and the results are then mapped back to the
Acknowledgments
This work was sponsored by the Swedish Research Council (VR), the Competence Center for Combustion Process at Lund University (KC-FP), and the National Center for Combustion Science and Technology (CeCOST). The computation was performed using Abisko cluster at High Performance Computing Center North (HPC2N) and the Swedish National Infrastructures for Computing (SNIC).
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