2.2 LES of two-phase reacting flows
- Turbulent dispersion of particles (E. Riber, O. Simonin,
B. Cuenot, T. Poinsot)
- LES of turbulent two-phase flames in aeronautical combustors (M. Boileau, S. Pascaud, B. Cuenot, T.Poinsot)
- Ignition of two-phase combustors (M. Boileau, S. Pascaud, B. Cuenot, T.Poinsot)
- Polydisperse sprays (J. Lavédrine, J.-B. Mossa,
B. Cuenot)
Most aeronautical combustors burn liquid fuel using injectors which atomise the liquid jet
or film in small droplets of size 10-200 µ m.
These droplets are dispersed by the turbulent flow, partially vaporised and finally mixed with
air. Modelling the liquid phase in a LES solver is a difficult issue for which two main classes of methods are available: the Euler framework (EF) and the Lagrange framework (LF).
The LF describes the liquid phase as a large but finite number of droplets with their own
trajectory, velocity, temperature and diameter while the EF considers the dispersed phase as
a continuous field whose characteristics are determined through a set of conservation
equations for the liquid volume fraction, the liquid phase velocity and temperature, and the
first/second order moments of the size distribution.
Because it is easier to implement, parallelise and couple with the gas flow solver, the EF
has been first chosen to study turbulent two-phase combustion with AVBP.
A first EF prototype (AVBP-TPF) has been validated in 2004 and allowed to demonstrate the feasability of two-phase reacting flow LES in industrial gas turbines. The potential of LES for these systems was particularly highlighted by the simulation of ignition sequences in helicopter and aircraft engines. In a second phase of development, a new version of AVBP-TPF has been written that includes a number of improved models, in particular for particle dispersion and polydisperse sprays, and a better control of numerical error. In 2005 the development of a LF solver has also been started with the PhD of M. García, in collaboration with Stanford University.
2.2.1 Turbulent dispersion of particles (E. Riber, O. Simonin,
B. Cuenot, T. Poinsot)
Large-Eddy Simulations (LES) of turbulent two-phase flows in combustion chambers with
AVBP-TPF are based on the Mesoscopic formalism [1]. This approach uses first conditional
ensemble averaging and then volume filtering. It leads to a transport equation for the
so-called Mesoscopic Eulerian Particle Velocity (MEPV)
which represents the local instantaneous velocity field shared by all the droplets or
particles at the same spatial location.
5mm
Figure 2.5: Instantaneous fields of axial gas velocity and particle volume fraction, configuration of Hishida et al. [2] (collaboration with IMF Toulouse).
The remaining part of each single particle velocity, called the Random Uncorrelated Velocity
(RUV), leads to a stress term in the MEPV equation which needs to be modelled.
The volume filtering adds standard subgrid stress (SGS) terms, closed with
a Smagorinsky-like model which proved to be successful in a priori
testing on Homogeneous Isotropic Turbulence.
Special care is required to solve the Eulerian equations because
the dispersed phase implies the resolution of sharp particle concentration
gradients. 3rd order accurate schemes (TTGC,TTG4A) have been implemented and tested in the code
AVBP for the dispersed phase, while artificial dissipative terms have been adapted, to damp spurious modes in regions containing sharp gradients.
In collaboration with IMF Toulouse, two experimental configurations have been selected to study droplets dispersion and validate its modeling. One is the gas-solid turbulent
confined round jet experimentally investigated by Hishida et al. [2]. The other configuration is a
'bluff body' type flow experimentally investigated by Boree et al. [3] which is closer to
combustion chamber devices. Results are very
encouraging: the particle mass flux and radial velocity fluctuation
predicted profiles are used to characterize the effect and the accuracy of the particle RUV and subgrid
stress modelling. Besides, the predictions are found to be very sensitive to particle inlet
conditions and special care has been devoted to improve them. In particular, a turbulent
velocity component, partially correlated with the fluid one, has been added to the mean inlet
MEPV.
[1] Février, P., Simonin, O. & Squires, K. D. , "Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially-uncorrelated random distribution: theoretical formalism and numerical study", J. Fluid Mech., in press (2006).
[2] Hishida, K., Takemoto, K. & Maeda, M., "Turbulent characteristics of gas-solids twophase confined jet", Japanese Journal of Multiphase Flow, 1(1):56-69 (1987).
[3] Borée, J., Ishima, T. & Flour, I., "The effect of mass loading and inter-particle collisions on the development of the polydispersed two-phase flow downstream of a confined bluff body", J. Fluid.Mech., 443:129-165 (2001).
2.2.2 LES of turbulent two-phase flames in aeronautical combustors (M. Boileau, S. Pascaud, B. Cuenot, T.Poinsot)
Depending on the droplets diameters, the flames observed in liquid-fueled combustors may be either purely gaseous (for small droplets) or non-homogeneous, in which case droplets may burn in clusters or even individually. But even in the simplest case of gaseous flames, the presence of a dispersed phase leads to very high local variation of the fuel vapor and therefore of equivalence ratio.
To evaluate the capacity of AVBP to capture all these phenomena, a two-phase reacting LES of an industrial combustion chamber has been performed. Figure 2.6 shows the result of a calculation of the reacting flow inside one sector
of a realistic aircraft combustor, fed with liquid kerosene.
Like in the true geometry, air is entering through swirling inlets, cooling films
and dilution holes. Results show that the overall shape of the flame is captured. The
gaseous flame structure, behind the evaporation zone, is very similar to the classical
gaseous flame found in a swirled burner. The main difference is in the stabilisation
mechanism, controlled by the evaporation in the two-phase flame.
Figure 2.6: Steady two-phase combustion in a SNECMA combustor.
2.2.3 Ignition of two-phase combustors (M. Boileau, S. Pascaud, B. Cuenot, T.Poinsot)
In the performance of an aeronautical gas turbine, the capability of ignition and
altitude re-ignition is a crucial criteria. For a helicopter or an aircraft engine, a fast
and reliable lightup is required for various altitudes, i.e. different atmospherical
conditions of pressure and temperature.
In that context, a comprehensive understanding of the physics involved in the ignition
process is a useful gain for combustor designers.
The principle of ignition is to give an initial input of energy, able to initiate the
combustion and set a stable flame.
This energy can be provided either by a spark plug or by the use of an additional ignition
injector. In both cases, ignition sequences are transient phenomena that can be
computed by LES.
To be accurate, such simulations have to take into account the effects of the presence
of liquid fuel as a dispersed phase.
AVBP has been used to compute two-phase ignition in
realistic combustors.
Figure 2.7 shows a snapshot of the ignition sequence calculation in one periodic
sector of a helicopter annular combustor.
In this simulation, the ignition burner injects hot gases on the left and right periodic planes of the computational domain.
After a certain induction time, the main injector ignites and hot gases appear in this zone too. The complete ignition sequence lasts approximately 50 ms.
Figure 2.7: Snapshot of the ignition sequence in a Turbomeca combustor.
2.2.4 Polydisperse sprays (J. Lavédrine, J.-B. Mossa,
B. Cuenot)
Sprays issued from the injectors used in gas turbines or in piston engines are not monodisperse
and present diameter distributions of different shapes, depending on the atomisation process. The
polydisperse characteristic of a spray has a great influence on all the variables describing the
liquid phase, as the drag force and the evaporation are strongly linked to the size of the
droplets.
In the eulerian framework described in the previous sections, there are two main ways to take into
account a size distribution in a spray: either through a series of classes of droplets of the same
size, or through the computation of evolution of the local size distribution. For compatibility
and feasability reasons, the second approach has been retained (Thesis of J.-B. Mossa), assuming a presumed shape for the
size distribution and computing its moments.
The methodology has been validated on the simple case of a liquid jet in a transverse gas flow,
for which analytical results are available. It has been then applied to a full burner, which
allowed to demonstrate its capability to capture the main effects of polydispersion. With this
model, the implementation of droplets break-down and coalescence is straightforward.
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