Transport budgets in turbulent lifted flames of methane autoigniting in a vitiated co-flow
Introduction
This paper addresses the autoignition of methane, the simplest of the hydrocarbons, and also a possible fuel for gas turbines, dual-fuel diesel engines, supersonic combustion ramjets, and HCCI engines. In some of these applications, autoignition is required to occur rapidly, while for others, designers wish to delay it to allow flame propagation into the flammable mixture [1]. Methane exhibits a relatively long ignition delay that can be reduced by the addition of higher hydrocarbons or hydrogen [2], [3] and increased in to the presence of water vapor [4].
Research in this area has recently intensified, with measurements and kinetic studies of ignition delays being made over ranges of pressures and fuel mixtures in engines, combustion bombs, and shock tubes [2], [3], [4], [5], [6]. Numerical studies of autoignition using direct numerical simulation (DNS) for relatively simple fuels have shown that the fuel does not necessarily ignite under stoichiometric conditions, but rather at mixture fractions where the fluid is “most reactive” yet the scalar dissipation rate is relatively low and the residence times are adequate [7], [8], [9], [10].
Intermediate in complexity between difficult measurements in real engines and expensive DNS studies is a simple laboratory-scale vitiated co-flow burner, which has been established as an excellent model problem for studying autoignition in an environment that is well controlled, yet possessing the characteristics of practical devices. The flow here is dominantly in the axial direction (with no recirculation), and the fuel jet and co-flow properties may be varied to change the liftoff height and the autoignition delay times. Recent extensive measurements in selected flames of hydrogen and methane fuels have been conducted and the data are now available on the Web [11], [12].
The hybrid RANS–PDF approach has recently been used with detailed chemistry to successfully compute the structure of flames of hydrogen (both with composition PDF transport [13] and with joint velocity-turbulence frequency-composition PDF transport [14]) and methane [15] stabilized on this vitiated co-flow burner. Comparisons with available measurements are very encouraging. This implies that the confidence level in the computations of these flames is now sufficiently high so that other aspects of autoignition that are difficult to test experimentally may be studied. A greater understanding of the preignition processes may be gleaned from examining the profiles of minor species leading up to the mean flame base. Further, species transport budgets, while very difficult to measure experimentally, may be very revealing. This has been established for simple flames of hydrogen fuels where the convection, diffusion, and reaction terms are calculated and the balance of these terms is used as an indicator of the dominant stabilizing mechanism [16]. A similar approach has been adopted by de Charentenay et al. [17] using 2-D DNS of a detached laminar flame.
This approach is extended here to more complex turbulent flames of hydrocarbon fuel, which display the following different physical characteristics compared to the hydrogen/nitrogen flames: (i) the liftoff height varies linearly with co-flow temperatures, which are also higher than those used for H2/N2, (ii) the flames are significantly noisier, and (iii) the fluctuations in the liftoff height are large (up to 10 diameters at the greatest liftoff heights). Detailed methane chemistries are used for two flames with different co-flow temperatures and liftoff heights. Budgets for convection, diffusion, and reaction are computed at the base of these flames, as well as for two simple models representing autoignition and premixed flame propagation. The key precursors for autoignition are identified in all cases and discussed with respect to the convective–reactive balance that prevails during this process.
Section snippets
The turbulent combustion model
All computations presented here use the FLUENT 6.2 code, which solves Reynolds averaged Navier–Stokes (RANS) equations for the mean conservation of mass, momentum, and energy, together with the turbulence model using the standard constants, except for , which is set to 1.6 to compensate for the round-jet/plane-jet anomaly. A modeled transport equation for the composition PDF is coupled and solved using a Lagrangian particle-based Monte Carlo method. The EMST mixing model is used, with
Numerical and modeling issues
Mixture fraction for the cases run with the ARM2 mechanism was calculated from the Bilger formulation [28], The mass fractions, Y, and elemental masses, M, of carbon, hydrogen, and oxygen, along with the values at the fuel and co-flow inlets (subscripts 1 and 2, respectively) determine the mixture fraction. For the base-case conditions listed in Table 2, the stoichiometric mixture fraction is 0.17. It should, however, be
Radial profiles
Profiles for mean and RMS temperature and mixture fraction at are shown in Fig. 6. It is clear that the calculations near the jet exit plane are well matched to the experimental data.
Radial profiles at axial locations of , 30, 40, 50, and 70 are shown for mean and RMS temperature and mixture fraction (Fig. 7), and mean and RMS velocity and OH mass fraction profiles are shown for , 30, and 40 in Fig. 8, Fig. 9, respectively. The experimental data at 1355 K co-flow has been
Results: test cases
The objective of showing results for these test cases is to highlight the differences between the phenomenon of autoignition and that of premixed flame propagation, as these are the two most plausible mechanisms for flame stabilization for the turbulent lifted flames under investigation. These differences may be marked by a buildup of a radical pool prior to ignition or by a different balance of transport processes in the stabilization region. With autoignition, a balance is expected between
Results: turbulent lifted flames
The autoignition indicators discussed earlier are applied here to two selected turbulent flames with a fuel jet velocity of 100 m s−1 and different co-flow temperatures, and 1430 K. These flames correspond to high and low liftoff heights and are marked by (a) and (b) in Fig. 2.
The liftoff height is determined by first defining an axial line that starts at the jet exit plane and intersects the most upstream location of the contour of mean mass fraction of .
Conclusions
The hybrid PDF-RANS method is used here with detailed chemistry to compute the species concentrations and their transport budgets of convection, diffusion, and reaction (CDR) in turbulent lifted flames of methane issuing in vitiated co-flows. Several chemical mechanisms are tested and results for the ARM2 mechanism compare favorably with both experimental results and the GRI2.11 mechanism. Test cases representing autoignition and premixed flame stabilization are developed as platforms for
Acknowledgements
This work is supported by the Australian Research Council and the US Air Force Office of Scientific Research Grant No. F49620-00-1-0171. Aspects of this research were conducted using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, federal agencies, foundations, and corporate partners.
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