Direct simulation and modelisation of premixed flame propagation in heterogeneous or stratified mixture.


The technological context of this thesis subject deals with gas turbine, industrial burner and Gasoline Direct Injection engines Stratified spark-ignition engines that use direct fuel injection into the combustion chamber feature both small- and large-scale spatial variations in unburnt mixture composition. In these configurations, the spark-ignited turbulent flame propagates into a mixture with variable equivalence ratio.

Modelisation context  
Until recent years, most works interested in simplified models description (see figure): the perfectly case, where is considered a total mixing before reaction ; the non premixed case, where no mixing is considered before reaction. In many practical situations, one has to deal with partial premixing. A typical example is the problem of the stabilization of jet flames : fuel and oxidizer are introduced separately and a triple flames devellopes in the mixing layer. An other example is the spark ignited flame propagation in piston direct injection system.The study of this particular combustion regime, sometimes called 'stratified flames', is the purpose of the present thesis.

The major purposes of this thesis work are :

to model the sub-grid effects for averaged reactive code .

An adapted tool to answer these questions is Direct Numerical Simulation (DNS) . DNS are used in the present study to bring basic information onto turbulent mixing, effects of partial premixing both on the turbulent flame topology and the overall mean reaction rate, and to determinate if and how flamelet combustion models should be modified to account for these effects.  

2D laminar flame/blob interaction

This figure shows a typical result of a 2D simulation of a laminar flame embedding in a lean mixture interacting with a (single here) rich pocket of gas. The background color corresponds to the equivalence ratio (blue :lean; red : rich). ISO-lines of reaction rate are plotted. (click here or on the image for animation , or click here for comments )
The difference of equivalence ratio (and consequently the difference of local flame velocity) wrinkles the premixed flame front.  
Under lean-rich conditions, the reaction zone can be described as a staged combustion system with a first stage corresponding to a propagating premixed flame front followed by a second stage corresponding to multiple post-diffusion flames that burn the remaining excess fuel and excess oxidizer.

Direct Numerical Simulations


Direct numerical Simulations (DNS) have become one of the major tools to study and model turbulent flows. Even though these techniques have demonstrated high accuracy in many flows, their application has been often limited to simple geometries (cubes), using simplified Navier-Stokes equations (incompressible flows), low Reynolds numbers and high-order numerical techniques (spectral methods). Extending DNS to more complex flows, more complex physics or higher Reynolds numbers requires further improvements of DNS tools. We use here NTMIX code  

Flame-turbulence interaction

Theses snapshots show a typical interaction between a 3D isotropic turbulence and an (initialy plane) flame front. The left images correspond to a time equivalent to one eddy turn over time, the right ones at four eddy turn over times. The top set represents the low pressure nodes (blue) and the flame front (red). The backward set represents the hight vorticity worms (green). The turbulence (free in these compressible simulations) decreases as it wrinkles the flame front, creating surface increasing. The turbulent Reynolds number is near 100, the integral turbulent/flame front velocities ratio is fixed to 7.5, the integral turbulent/flame front lengths ratio is fixed to 7.5. 

Heterogeneous mixture

We have studied first the turbulent mixing of an heterogeneous scalar field without combustion to characterize the temporal decrease of scalar fluctuations.
Secondly, a reactive database has been realized. A heterogeneous scalar field (fuel/oxidizer mass fraction ratio)is surimposed to a turbulent velocity field. The numerical configuration corresponds to three-dimensional partially premixed flames propagating into a temporally decaying turbulent flow. The simulations use different degrees of scalar inhomogeneity around mean stoichiometric conditions. 

This figure illustrates the database developed for this thesis work. Here, fluctuations of the oxidizer/ratio (equivalently, the so-called mixture fraction) are surimposed in the fresh gas to the turbulent velocity field. The red surface represents the premixed-mode flame front identified here as an iso scalar surface. The grey surface represents the post diffusion mode flames identified as an iso-value of reaction rate. The sign of the projection of the gradients of fuel mass fraction and oxidizer mass fraction is used to discriminate the two combustion modes (premixed/diffusion). (see more on the DNS parameters)

It has been found that :
  1. partial premixing has a net negative impact on the overall mean premixed reaction rate.
  2. This effect is related to the reduced values of mean flamelet mass burning rate per unit flame surface area observed in partially premixed configurations compared to perfectly premixed flames.
  3. Wrinkling of the premixed flame surface is shown as the result of turbulent stretch, effects of inhomogeneities are found negligible for u'/sl>1, with u' the RMS velocity fluctuations of the turbulent field and sl the laminar flame velocity (at stoichiometry).
  4. The fuel consumption rate has been found as highly correlated with the local equivalence ratio. The joint pdf is shown to correspond to the laminar value. The mean fuel consumption rate can be approach as the sum on the mixture fraction probability density of the laminar fuel consumption rate.

  5. The unburnt products reacts in the hot gases in a diffusion flame. This post-combustion stage has not evident effects on the first combustion stage.

RANS Modeling

A RANS model has been developed to : We use conditional sampling to distinguish between fluid in the unburnt gas from fluid in the partially burnt gas :

Modifications of the Coherent Flame Model are proposed. One dimensional simulations have been run. The results are coherent with KPP analysis. The right side figure shows the evolution of the turbulent flame speed with the mixture fraction (the unburnt fuel mass fraction) fluctuations made non dimensional by the mean mixture fraction. The left side figure shows typical profiles of mass fraction

RANS simulations of GDI engines

The study described above is used for simulation of real stratified DISI engines. The model is implemented in the KIVA KMB code, an extended version of the improved KIVA 2 code, and applied to realistic chemistry including pollutant formation and variable dilution (EGR), on the basis of Baritaud, Duclos and Fusco [26th Symp. (int) on Combustion, 1996]. Typical stratified combustion parameters are investigated, such as spray injection and ignition times, leading to large and small scale mixture composition changes. The results are compared to the experimental data. Strong effects of local quenching modeling and post-combustion modelisation are found on the first stage. Effects of A/F ratio fluctuations on engine bahavior are demonstrated.

Keywords : premixed turbulent combustion - Direct Numerical Simulation (DNS) - modelisation - stratified turbulent combustion - direct injection - mixture. -

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