By Graham Goldin, Lead Development Engineer, Fluent Inc.

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Iso-surface of voritcal structures, colored by temperature

Reynolds-Averaged Navier-Stokes (RANS) turbulence models have a long history of success for modeling turbulent combustion. When combined with reaction models ranging from simple to complex, they have demonstrated reliable performance that has been documented in dozens of case studies. As the cost of computer hardware has dropped and the speed of processors has increased, however, large eddy simulation (LES) has become an especially attractive alternative for modeling reacting flows. When compared to RANS, LES offers several unique advantages:

1. RANS turbulence models, such as k-ε, have limited accuracy when predicting common combusting flow features such as free jets, swirling jets, jets in cross-flow, and buoyancy-induced structures. Accurate RANS simulations often require tuning turbulence model constants. LES predicts such flow features more accurately than RANS and has fewer, if any, adjustable constants.


2. In contrast to RANS, LES modeling error decreases as the grid resolution increases. The predictions of a grid-independent RANS solution will not improve with further refinement, but LES results tend toward the exact direct numerical simulation (DNS) solution with further refinement.


3. Combustion is often controlled by the rate at which the largest and most energetic eddies mix reactants and products, and these large eddies are directly resolved by LES.


4. Combustion modelers are often unconcerned about flow details near walls, where LES has difficulties (there are no large eddies near walls).


5. For inherently unsteady simulations, such as combustor instability and firespread, the computational cost of LES does not greatly exceed the cost of unsteady RANS simulations.

For these reasons, it is likely that LES will become more prevalent in the computational combustion community in the future. In FLUENT, all of the RANS combustion models are also available for LES, including the finite-rate species transport, non-premixed, premixed, and partially-premixed models.

Axial profiles of mean and RMS temperature, compared to experiment

Axial profiles of mean and RMS NO, compared to experiment

A popular and widely accepted turbulent combustion validation is the Sandia experimental piloted jet flame D, which consists of a partially-premixed methane-air main jet and a burnt pilot to keep the flame attached. An LES simulation of this flame has been performed using the dynamic Smagorinsky subgridscale model and a spectral synthesizer turbulence inflow generator. A 19-species reduced kinetic mechanism was used with ISAT (in-situ adaptive tabulation (1)) to accelerate the chemistry. ISAT provides a 25-fold speed-up: in fact, with ISAT, only half the computational time is spent integrating the chemistry, making realistic chemistry affordable in LES.

Pathlines colored by temperature

The results, in general, are in very good agreement with experimental data, and offer insight where steady or unsteady RANS calculations cannot. For example, pathlines, emitted from a rake at the base of the flame and colored by temperature show unsteady eddy structures that develop and grow. An iso-surface of vortical structures, colored by temperature, illustrates the three-dimensional nature of these coherent structures. Profiles of the mean and RMS temperatures along the axis of the flame show that the mixing rate is correctly predicted since the peak (stochiometric) temperature location agrees with the experiment. There are no adjustable constants in the LES model, so, unlike comparable RANS simulations,the mixing rates are not "tuned."

Axial profiles of mean and RMS CO, compared to experiment

Axial profiles of mean and RMS OH, compared to experiment

Despite the fact that the mean temperature agreement is so good, the CFD model over-predicts the RMS and mean values of nitrous oxide (NO), which is sensitive to the maximum temperature values. Had radiation been included in the simulation, the agreement would be better. The predicted axial profiles of other species, however, are very impressive when compared to experimental data. The mean and RMS values of carbon monoxide (CO) and hydroxide (OH) mass fraction, for example, are in excellent agreement with experiment. CO is particularly difficult to predict since it is often far from chemical equilibrium. Because it is not a trace species like NO, it cannot simply be post-processed.

Reference:

1. S.B. Pope, Combust. Theor. Model. 1997, 1, 41-64.

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