1. C. Habchi, B. M. Devassy, R. Kumar, N. Gillet, A.Velghe, J. Bohbot
LES of in-nozzle flows and liquid jet atomization using a two-surfaces density model
C. Habchi, B. M. Devassy, R. Kumar,
N. Gillet, A.Velghe, J. Bohbot
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

2. The CFD Grand Challenge (1)
Without
String Cavitation
With
String Cavitation
Experimental images taken from :
A. Andriotis and M. Gavaises Atomization and Sprays, 19(3):247–261, 2009
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

3. The CFD Grand Challenge (2)
Computing Cavitation and Atomization
What are the main ingredients to compute cavitation and liquid jet atomization ?
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

4. Outline Two-phase flow, Cavitation and Atomization models description
Application of these models to the understanding of in-nozzle flows in Marine Diesel injectors
Summary and Future work
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

5. The two-fluid model
A generalized turbulent multi-species formulation of the highly compressible two-fluid 7-Equations model.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

6. The Gibbs Energy Relaxation Model (GERM) Relaxation procedures for interfacial terms
The velocity, pressure and temperature interfacial terms
are modeled using quasi-instantaneous relaxation procedures
toward equilibrium:
Procedures for SV and SP , see :
Saurel R. & Abgrall R. (1999), JCP,150,
Saurel R. et al. (2008)
JFM, 607,
Procedures for ST and Sg , see :
Zein A. et al. (2010), JCP, 229,
Habchi C. (2014), AAS
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

7. Main features of the GERM cavitation model(*)
GERM cavitation model does not use adjustable constants
GERM model can predicts two cavitation regimes:
Gaseous cavitation regime
The gaseous cavitation regime : it appears in region in which the static pressure is close to but above the liquid saturation pressure
Vaporous cavitation regime
The vaporous cavitation regime : it may happen when the static pressure goes below the liquid saturation pressure.
* C. Habchi , Atomization and Sprays , DOI: /AtomizSpr , 2014.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

8. Closures of the two-fluid model
Equations of state (EOS)
Multi-species gas phase are closed by the perfect gas EOS:
Single-species liquid phase is closed by the Stiffened Gas SG-EOS:
For liquid n-dodecane: g
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

9. SGS Turbulence Model for the Two-Phase System
Smagorinsky model
l= (liquid or gas)
0.2
Sij is the rate of strain tensor and D is the local cell size
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

10. Scenario for the modeling of primary atomization
Second image
First image
Exp observation of ligament breakup by Marmottant & Villermaux (2004)
Liquid
Gas
ligaments
Liquid
Gas
droplets
Liquid
Gas
Control Volume
Ligaments are assumed to be formed due to the stretching of the interface mainly by the fluctuating rate of strain normal to the interface.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

11. The Two Surface Density (TwoSD) Atomization Model
Surface density definitions Sd Ss
Liquid core (index s)
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

12. The TwoSD atomization model*
Primary atomization of the liquid core (index s)
Interface
Stretching
Primary
atomization
Relaxation
of P,T,g
Secondary breakup of the droplets (index d) +
Droplets breakup, coalescance
* B. M. Devassy, C. Habchi, E. Daniel, Atomization and Sprays, DOI: /AtomizSpr , vol. 25, 2014.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

13. Two-phase flow (TPF) numerical solver*
IFP-C3D
start
Red arrows for TPF solver
TwoSD
Atomization&breakup model
Lagrangian
Atomization model
Liquid phase
Solver
Time: 1st order
Space: quasi-2nd order
Single gas phase
Solver
Time: 1st order
Space: quasi-2nd order
Stiff relaxation procedures
for interfacial terms:
GERM
cavitation model
End
* J. Bohbot et al., Oil & Gas Science and Technology, vol. 64, 2009
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

14. Numerical investigation of in-nozzle flows in large marine Diesel injectors
Fuel inlet
3 Million cells
Discharge pipe
Spray
Combustion
Chamber
Injection
hole
Cells size = 25 microns
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

15. Numerical investigation of nozzle orifices eccentricity
Simulations have been carried out :
Simulation 1 : hole eccentricity (e=0)
Simulation 2 : hole eccentricity (e=0.8)
Cross-section A-A through the injection orifice (middle).
Cross-section B-B through the injector bore (right)
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

16. Initial & boundary conditions
Pinj = 700 bar
Initial velocity = 0 m/s
Pgas = 40 bar
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

17. Non-eccentric nozzle(cross-section B-B): Liquid volume fraction
Cavitation leads to:
A reduced flow rate (Cd decreases down to around 0.6)
A deviated liquid jet (which corroborates the experiments)
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

18. Eccentric nozzle (cross-section B-B): Liquid volume fraction
The cavitation pocket is smaller than for e=0
No liquid jet deviation (which corroborates the experiments)
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

19. Eccentric nozzle (cross-section A-A): Liquid volume fraction
A liquid jet deviation is obtained (which corroborates the experiments)
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

20. Eccentric nozzle : Liquid core and velocity field
al=0.5
Cavitation
Liquid core
deviation
The fluid circumvents the cavitation pocket in the hole
The liquid is clearly deviated from the hole axis
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

21. Eccentric nozzle (cross-section B-B): Spray droplets diameter
The smallest droplets (around 1 micron) are atomized at the cavitation pocket side.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

22. Conclusion
In this study, simultaneous simulations of the in-nozzle cavitation and of the atomization of the liquid jet have been carried out.
In this aim, the GERM cavitation model and the TwoSD atomization model, recently developed have been used.
The impacts of the cavitation on the liquid spray characteristics of large marine injectors have been highlighted.
Particularly, it has been shown that
cavitation is at the origin of the spray deviation observed experimentally.
The smallest droplets are atomized at the cavitation pocket side.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

23. Future work
will focus on quantitative validation of the GERM and TwoSD models.
In addition, more accurate numerical schemes will be investigated in the context of the LES simulations of two-phase highly compressible flows.
LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France

24. LES4ICE, 4-5 Dec. 2014, Rueil-Malmaison - France