تجزیه و تحلیل حساسیت از پیش بینی های LES-CMC از شعله های آتش جت با سرنشین

The sensitivity of Large Eddy Simulation with Conditional Moment Closure (LES–CMC) simulations of the Sandia piloted jet Flames D and F to various parameters have been investigated. It was found that while an LES grid may sufficiently resolve velocity fields, the conditional scalar dissipation rate obtained may still be affected by grid size due to the calculation of sub-grid scalar dissipation rate, and this can affect the degree of localised extinction predicted. A study of the relative size of the terms in the CMC equation during an extinction/reignition event showed that transport, including in the cross stream direction, plays a key role. The results are sensitive to the choice of inlet boundary conditions as extinction is only observed when the inert-mixing distributions in mixture fraction space are used as inlet conditions for the CMC equation in the primary jet and air jets.

Due to its superior ability to predict the details of turbulent mixing, large eddy simulation is increasingly being used to study turbulent combustion in a variety of industrial applications. Even with the greater spatial resolution of LES compared to RANS the combustion process still takes place on a scale which cannot be resolved by the grid, and as such some form of turbulent combustion modelling must be employed. These include steady (Di Mare et al., 2004) and unsteady (Pitsch and Steiner, 2000) flamelet models, the flamelet/progress variable (FPV) model (Pierce and Moin, 2004) and the stochastic fields or Eulerian Monte Carlo method (Mustata et al., 2006). The Conditional Moment Closure model, discussed later, is another advanced model that is being used for flames with strong turbulence-chemistry interactions. In order for any such model to become a useful engineering tool it is important that they are validated against detailed measurements and that the models’ sensitivity to modelling choices and parameters are investigated. The Sandia piloted jet flames (Barlow and Frank, 1998) provide detailed experimental data for both scalar and velocity fields and consequently have been widely used for this sort of validation work. Data is available for conditions ranging from a flame with very little local extinction (Flame D) to one that is close to global extinction (Flame F). RANS – Muliple Mapping Conditioning (MMC) simulations of Flame D have been performed by Vogiatzaki et al. (2011) in order to determine the value of modelling parameters which give the best agreement with conditional variance of temperature and various species mass fractions. Previous studies using transported PDF methods in RANS have produced good agreement with experiment (Lindstedt et al., 2000 and Xu and Pope, 2000) for Flame F and also revealed the sensitivity of this Flame F to the chosen chemical mechanism (Cao and Pope, 2005). These studies were useful in determining the parameters needed in RANS–PDF modelling to give accurate results, a process that is now being undertaken for LES studies. The presence of localised extinction in Flame E has successfully been predicted in Ihme and Pitsch (2008) using the FPV model. The Eulerian stochastic fields PDF method has been used in Jones and Prasad (2010) to successfully predict the presence of localised extinctions in Flame F. Conditional Moment Closure (CMC), which is the subject of this paper, has previously been used in an LES context for Sandia Flame D (Navarro-Martinez et al., 2005), bluff-body steady flames (Navarro-Martinez and Kronenburg, 2007), autoigniting jets (Navarro-Martinez and Kronenburg, 2009) and for spark ignition problems (Triantafyllidis et al., 2009). An LES–CMC formulation solving the CMC equations on a 3D grid (i.e. resolving variations of conditional average in three dimensions rather than using cross stream averaging) has been used to successfully predict the presence of localised extinction and reignition events in both Sandia Flame F (Garmory and Mastorakos, 2011) and the Delft III piloted jet flame (Ayache and Mastorakos, 2012). It was shown that the model can successfully predict the occurence of localised extinction, and the resulting statistics of species mass fractions and temperature. The purpose of this paper is to revisit the simulations of Sandia Flames D and F in order to investigate the sensitivity of the results to the modelling choices used. This will build confidence to the use of the LES–CMC approach for more complex flames of practical significance. An extended discussion of how the CMC method predicts extinction/reignition and how this may influence its accuracy is also presented. In the next section the formulation of the LES–CMC method is briefly covered and its numerical implementation is discussed. Particular emphasis is placed on modelling choices where more than one option is employed here. This is followed by results obtained using these choices with a discussion of them. The conclusions of this work are summarised in the last section of the paper.

The sensitivity of the LES–CMC method to various factors has been investigated in the context of simulating the Sandia piloted jet Flames D and F. It was found that for Flame D the LES results for velocity fields were very similar for both the fine and coarse LES grids employed here. This shows that the results seen in this work for these quantities can be regarded as grid insensitive. However, it was seen that the conditional scalar dissipation rate extracted from the LES for use in the CMC code was sensitive to the LES mesh. It is likely that using a finer grid improves results for this quantity as it reduces the influence of the modelled sub-grid terms. This suggests that more work is needed on the modelling of unresolved scalar dissipation rate in order to avoid the need to use very fine LES meshes to capture conditional scalar dissipation rate. By studying the relative size of individual terms in the CMC equation we have been able to show that transport, including in the cross stream direction, plays a key role in the prediction of localised extinction in Flame F. This means that the numerical treatment of transport in the CMC code is of great importance. Changing the CMC grid and the differencing scheme has been seen to have some effect on the results here. But in order to transport extinctions downstream to 15 jet diameters and beyond, where they are seen in Flame F, it may be necessary to have much finer CMC grid spacing in the axial direction. With the orthogonal structured CMC formulation here it would be very difficult to achieve this without reducing cross stream resolution or making the computational load very high. An unstructured CMC grid may be advantageous in this situation. The biggest sensitivity of these results was seen to be to the choice of CMC boundary conditions. The results using burning flamelets right across the inlet plane rather than only in the pilot region showed an almost complete absence of localised extinction in the Flame F results. As mentioned above, transport in the cross stream direction plays a key role in extinguishing CMC cells and if burning flamelets are injected into the primary jet rather than inert flamlets this mechanism is effectively switched off. The present simulations highlight further the capabilities of the LES–CMC approach to capture flames very close to extinction and suggest that further research is needed for modelling the scalar dissipation rate.