Parametric direct numerical simulations (DNS) of turbulent premixed flames burning methane in the thin reaction zone regime have been performed relying on complex physicochemical models and taking into account volume viscosity (

Both the availability of electrical energy and all transportation systems are controlled to a large extent by turbulent combustion processes, such as in gas turbines or Internal Combustion engines, burning either fossil or renewable fuels. Optimizing further such well-known systems is only possible with a much better understanding of all relevant processes involved. Detailed quantitative experiments are needed and very useful, but sometimes impossible and usually limited to only a few flame quantities. As a complement, detailed (direct) numerical simulations (DNSs) are increasingly gaining grounds as a reliable tool for detailed investigations towards fundamental understanding of a variety of turbulent combustion phenomena [

There are in fact only two possibilities to obtain statistically significant results. Ensemble averaging is the most straightforward way, based on a repetition of the same “numerical experiment,” then averaging the observations [

More generally, the need for accurate physical models in practical combustion computations has been demonstrated clearly for various flame configurations (see, e.g., [

Neglecting the volume viscosity term in computational models seems logical at very low Mach number and for boundary layer flows. In practice, the additional computational cost associated with its evaluation in multi-component mixtures also contributes to a larger extent for such exclusions. Even more importantly, an overconfidence in the partly misleading suggestion of Stokes [

Since single isolated DNS simulations might sometimes be misleading, systematic DNS computations has been realized in order to carry out ensemble-averaging and obtain a high statistical significance [

Three main challenges have therefore been finally addressed in the present work: the chemical and transport complexity has been stepped up by considering methane flames and volume viscosity effects, respectively, while increasing simultaneously the turbulence intensity. To the authors knowledge, such a combination of numerical, physical, and flow conditions has never been taken into account simultaneously in the same analysis.

In the next section (Section

The DNS approach consists in solving as exactly as possible all the physical space and time scales embedded in the representative flow equations, without adding any model for turbulence. A DNS must thus provide an exact solution for both fluid dynamics and flame structure. Even though this method requires prohibitive numerical costs for practical configurations, it offers an excellent complement to experiments in order to assess the importance of various physical mechanisms, to obtain complementary information on flame structure and therefore to improve turbulent combustion modeling [

The DNS code employed in this work is the massively parallel flame solver,

The above system of governing equations is solved in

In order to access higher values of

The second major issue that needed attention towards fine-grain parallelism is that of efficient, fully parallel data input/output (I/O). The traditional sequential I/O approaches have been replaced by a fully parallel I/O (via MPI-I/O), where multiple processes of the parallel program access data (for read/write) from a common, shared file. This provides both higher performance (speedup in time needed for writing/reading all files by a factor of at least 3) and single (restart/solution) data files.

A stoichiometric spherical premixed methane-air flame is considered in all computations, within a cubic computational domain of sides

Methane oxidation is modeled by a 25-step skeletal scheme comprising 16 species (CH_{4}, O_{2}, H_{2}, H_{2}O, CH_{2}O, CO, CO_{2}, HO_{2}, OH, H, O, CH_{3}, HCO, H_{2}O_{2}, CH_{3}O, N_{2}) [_{2} and higher carbon-chain reactions, the reason why

The initial system is a stationary hot (

To investigate the influence of the turbulent Reynolds number ^{2}/s, the laminar flame speed

Initial turbulence parameters.

case | Ka | |||
---|---|---|---|---|

1 | 5.95 | 3.18 | 615 | 4.87 |

2 | 11.90 | 1.60 | 1 230 | 13.78 |

3 | 17.86 | 1.06 | 1 845 | 25.31 |

4 | 23.81 | 0.80 | 2 460 | 38.97 |

Based on these turbulence characteristics, the flames considered here all fall within the thin reaction zone (TRZ) regime according to the modified regime diagram of Peters [

Modified combustion diagram of Peters [

The general view of the configuration is illustrated in Figure _{2}O_{2} slices and CO_{2} slices with stream lines (thin white lines) is shown, revealing the heavily wrinkled flame front after interacting with the three-dimensional time-decaying homogeneous isotropic synthetic turbulent velocity field for 0.8 millisecond.

General view of the configuration for the direct simulation, showing (a) the iso-surface of temperature with H_{2}O_{2} slices and (b) CO_{2} slices with stream lines (thin white lines), revealing the heavily wrinkled flame front after interacting with the three-dimensional time-decaying homogeneous isotropic synthetic turbulent velocity field for 0.8 millisecond.

A total number of computing cores ranging between 512 and 4 096 were employed to solve the problems on the

The obtained DNS datasets are processed using an in-house postprocessing library called

Instantaneous solutions are analyzed in terms of conditional statistics of quantities relevant for modeling such as temperature, heat release, and selected mass fractions illustrating the turbulence-impaired flame structure. The impact of volume viscosity is assessed by comparing the above profiles for each of the twin computations of

First, a laminar case (referred hereafter as _{2}O_{2} at different times (_{2}O, H_{2}O_{2}, and HO_{2} are shown at _{2}O_{2} and HO_{2} as well as global flame quantities like

Instantaneous contours of the mass fraction of H_{2}O_{2} (along the

Instantaneous profiles of laminar premixed methane-air flame with (circle points) and without (solid line) volume viscosity in the reaction progress variable space, showing the (a) heat release rate and H_{2}O mass fraction and (b) HO_{2}, H_{2}O_{2}, O, and OH radicals at

Temporal evolution of the laminar fuel consumption and integrated heat release rates for

The above observations are not surprising and fully confirm the findings in [

Highly turbulent conditions (

Time evolution of the iso-contours of temperature (along the

The iso-contours of the OH radical closely follow those of the temperature and are shown in Figure

Instantaneous iso-contours of OH mass fraction (along the

For a first assessment of the impact of the volume viscosity on the turbulent flame structure, Figure

Instantaneous flame front defined by the iso-contours of the mass fraction of OH (along the

Two particularly important global flame quantities—the burning rate

The temporal evolution of these two global quantities is shown in Figure

Temporal evolution of the scaled (a) fuel consumption and (b) integrated heat release rates at different turbulence intensities for stoichiometric premixed methane-air flames with (circle points:

Considering now the effect of volume viscosity, the temporal profiles show no noticeable impact of this term. For

Conditional analysis is of central importance for many turbulent combustion models. Hence, conditional mean values have been computed for different variables characterizing flame behavior as a function of turbulence intensity (Figure _{2}O_{2} mass fraction show a noticeable dependency on turbulence intensity, with progressively lowered peaks. The decrease of the conditional mean _{2}O_{2}) as well as major species (not shown) are indifferent in the presence of volume viscosity, irrespective of ensemble averaging. Volume viscosity effects are noticeable on the mean

Conditional profiles of mean (a) progress variable gradient, _{2}O_{2}, conditioned on the progress variable

Progress in numerical techniques as well as computational power now allows quantitative investigations of turbulent reacting flows for increasingly realistic conditions including detailed physicochemical models. Direct Numerical Simulations of stoichiometric premixed methane flames have been considered in a parametric study including a case with six pairs of computations for

The flame speed is found to rapidly increase with increasing turbulence stirring, associated with a noticeable flame thickening. Simultaneously, peak conditional profiles of heat release and major and minor species mass fractions are systematically lowered with increasing turbulence intensity. In all considered cases, premixed methane flames show a negligible impact of volume viscosity. No differences at all are found in laminar computations, confirming theoretical findings for low Mach number conditions. Previous observations for turbulent hydrogen flames, revealing a clear impact of volume viscosity, do not apply for the present methane flames at all Reynolds numbers considered in the study. To save computing resources, the inclusion of volume viscosity effects in multicomponent multidimensional turbulent flame computations burning methane and probably higher hydrocarbons as well is therefore discouraged, as long as low Mach numbers are considered.

This study demonstrates also the importance of repeating DNS realizations in order to obtain statistically significant data. Single realizations might lead to spurious discrepancies, rapidly smoothed out when averaging over several results, as observed here when comparing the findings for

The computational resources have been provided by the DEISA Extreme Computing Initiative (DECI), as part of the 7th Framework program financed by the European Union. The authors are grateful for the support of the DEISA help desk.

_{2}, CO, CH

_{4}and CD

_{4}between 77 and 300 K