2.2 LES of two phase reacting flows
- Numerical Approach (J.-B. Mossa, B. Cuenot, S. Pascaud, A. Kaufmann, O. Simonin)
- Modelling aspects (B. Cuenot, E. Riber, A. Kaufmann, O. Simonin)
- Applications (S. Pascaud, J.-B. Mossa, B. Cuenot, T. Poinsot)
Most industrial combustors burn liquid fuel, that goes through an injector producing
a spray of droplets of varying size and velocity. The presence of liquid droplets in
the burner strongly influences its behavior: the turbulence field is modified,
liquid films may form on the walls and evaporation occurs before (or while) burning,
leading to a non-homogeneous gaseous fuel field. All these effects have to be taken
into account in the simulations of combustion chambers and a project has been
launched in 2000 to develop a two-phase flow solver based on AVBP.
2.2.1 Numerical Approach (J.-B. Mossa, B. Cuenot, S. Pascaud, A. Kaufmann, O. Simonin)
There are two classes of numerical methods to compute two-phase flows:
-
The lagrangian approach calculates the trajectories of the inclusions (bubbles
or droplets), including models for rupture or coalescence, evaporation, etc ...The
main advantage of this approach is that the system of equations describing the
dispersed phase is relatively easy to write. On the other hand the coupling between
a discrete system and a continuous phase raises some delicate questions.
In typical combustion applications the number of droplets that are simultaneously
present in a system is very large. This number may be reduced by a stochastic approach,
in which the set of droplets is interpreted as a statistical sampling of the dispersed
phase. However the minimum number of
samples remains high to reach a reasonable accuracy, as required by LES simulations.
One of the
main difficulties of lagrangian methods is therefore to compute efficiently (through
vectoral or parallel algorithms) a large number of trajectories.
- In the eulerian approach, the dispersed phase is viewed as a continuous phase
and described by continuous fields of variables. This allows to benefit from the
same numerical algorithm as used for the gaseous phase (in particular the
parallelism can be directly extended) and to facilitate the coupling between the two
phases. In this approach the system of equations for the dispersed phase is obtained
from the individual droplet equations through an averaging operation. This leads
classically to unclosed non-linear terms for which models must be developed and
validated.
In the AVBP-TPF project, the eulerian approach has been chosen for its
implementation facility. It has also
demonstrated less difficulties than the lagrangian approach in flame
computations. Note that the lagrangian approach is also investigated, mainly in terms of
computing efficiency and parallel algorithms development.
The project is made of two parts:
-
Models development: as mentioned above, the eulerian approach requires models
for some unclosed terms in the equations, related to the small-scale movement of the
droplets.
- Code development and validation: the code AVBP-TPF has been developed on the
basis of AVBP-5.1, under the control of CVS and with a quality procedure.
2.2.2 Modelling aspects (B. Cuenot, E. Riber, A. Kaufmann, O. Simonin)
Modelling aspects have been addressed in the framework of
a collaboration with O. Simonin (IMFT)
[Kaufmann, 2002].
The most needed model for computations to be stable and meaningful is the so-called
"Quasi-Brownian Model" (QBM). This model is developed to take into account the small
scale uncorrelated movement (called the Quasi-Brownian movement)
of the droplets, droped during the
averaging operation. This small
scale movement plays an essential role in the larger scale droplet dynamics, to some
extent similar to the small scale turbulent movement of the gas. For intermediate
Stokes numbers (around 1), the omission of the Quasi-Brownian movement leads to
excessive segregation and high compressibility effects. A conservation equation has
been derived for the Quasi-Brownian energy, including transport terms, source
and sink terms and a diffusion-like term. Validation with DNS
of decreasing homogeneous isotropic turbulence has shown that the QBM is able to
capture qualitatively the overall droplet behavior and dynamics (see Fig. 2.5).
However the use of
this model in the framework of LES is still an open question.
Figure 2.5: Two-phase Direct Numerical Simulation of Homogeneous and Isotropic Turbulence: number density
field. Left: lagrangian approach; Right: eulerian approach.
2.2.3 Applications (S. Pascaud, J.-B. Mossa, B. Cuenot, T. Poinsot)
Two applications have been computed with the first version of AVBP-TPF. Both are gas
turbines combustion chambers. One is the M88
chamber used on the "Rafale" aircraft. The other application is
the chamber of the VESTA, designed by Turbomeca. The geometry, as well as inlet
and operating conditions have been supplied by the industrial partner.
For the M88 case, calculations with evaporation have been performed. Fig. 2.6
shows droplet trajectories and evaporation. It appears that evaporation is almost
completed in the dilution zone (where the flame is usually located). The associated
fuel vapor field is displayed in Fig. 2.7 in terms of equivalence ratio.
As expected the resulting fresh gas mixture is strongly inhomogeneous. This will
have an important impact on the turbulent flame propagation and modelling.
To see the impact of the Stokes number, the VESTA chamber has been computed with two
different droplet sizes. In the case
of 1 µm droplets, the Stokes number is very small and the velocity field of the
dispersed phase is similar to the gaseous velocity field (Fig. 2.8a). The droplet
number density field shows that the droplets have not enough inertia to go through
the strong dilution jets and concentrate in the area close to the injector
(Fig. 2.8b). The
associated Quasi-Brownian energy field shows that the small size droplets
have no uncorrelated movement: the Quasi-Brownian energy is depleted below the
default value (used in the purely gaseous regions) (Fig. 2.8c).
This is in accordance with the
fact that the movement of these droplets is fully correlated with the gaseous
velocity field.
The results are quite different for 100 µm droplets, as shown in Fig. 2.8a to
Fig. 2.8c. The droplets have too much inertia to be significantly affected by the
gaseous velocity field and go through the chamber along ballistic trajectories.
This also shows on the droplets velocity field and on the Quasi-Brownian energy
field, where the high maximum level illustrates the strong uncorrelated movement.
Figure 2.6: Computation of the M88 geometry with evaporating droplets: droplet trajectories.The initial size is 20 µm.
Figure 2.7: Computation of the M88 geometry with evaporating droplets: equivalence ratio.
The initial size is 20 µm.
(a)
(b)
(c)
Figure 2.8: Computation of the VESTA geometry with a droplet size of 100 µm
(left column) and 1 µm (right column).(a):
liquid velocity field;(b): number density field;(c):Quasi-Brownian energy field.
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