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Stochastic modeling of primary atomization : application to Diesel spray .

CNRS – UNIVERSITE et INSA de Rouen. Stochastic modeling of primary atomization : application to Diesel spray. J. Jouanguy & A. Chtab & M. Gorokhovski. Introduction. Atomization : main phenomena: Turbulence in liquid and gaz phase, cavitation, cycle by cycle variations

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Stochastic modeling of primary atomization : application to Diesel spray .

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  1. CNRS – UNIVERSITE et INSA de Rouen Stochastic modeling of primary atomization : application to Diesel spray. J. Jouanguy & A. Chtab & M. Gorokhovski

  2. Introduction. Atomization: main phenomena: • Turbulence in liquid and gaz phase, cavitation, cycle by cycle variations • Deterministic description of such atomization is very diffcult task. • Stochastic approach => Application to primary atomization. Sacadura,CORIA

  3. Time t1 Time t2 radial direction radial direction r Liq. r Liq. axial direction axial direction radial direction radial direction Liq. r Liq. r axial direction radial direction axial direction radial direction Liq. r Liq. r axial direction axial direction Floating cutter particles.

  4. Scaling symetry for thickness of liquid core. • Life time. • Ensemble of n particles. y Fragmentation intensity spectrum r(x,t) r(x,t) r(x,t) r(x,t + dt ) liq. x The main asumption: scaling symetry for thickness.

  5. Knowledge of and Equation for the distribution function Theory of Fragmentation under Scaling symetry (Gorokhovski & Saveliev 2003, Phys. Fluids). Evolution equation Knowledge of Fokker Planck type equation Log brownian stochastic process Langevin type equation Equation for one realisation y rc =critical length scale r* =typical length scale liq x

  6. Time scale Identifiction of main parameters. Transverse instability = Rayleigh Taylor instability Liquid Formation of droplets through a minimal size rcr Shearing instability rc =critical radiusrcr r* =Rayleigh Taylor scale => (Reitz 1987)

  7. Radial direction Path of stochastic particle Grid Stochastic particle position Liquid zone Injector radius Gaz zone Axial direction Realization of stochastic process; « Stochastic floating cutter particles ». Motion of particules In the radial direction: In the axial direction: Staitistics of liquid core boundary =>

  8. Experimental setup. C. Arcoumanis, M. Gavaises, B. French SAE Technical Paper Series, 970799 (1997). Gaz initial conditions: Atmospheric conditions Liquid initial conditions:

  9. Injection of droplets Radius: Radius of the injector Injection velocity Probability to get liquid core; formation of discret blobs using presumed distribution: Statistics of liquid core boundary Mass flow rate conservation Motion of droplets => Standard KIVA procedure with velocity conditionned on the presence of liquid Initial conditions

  10. Example of distribution of formed blobs.

  11. Computed mean sauter diameter. Sauter Mean Diameter

  12. Symbols = experiment Line = simulation Centerline droplet mean axial velocity.

  13. Symbols = experiment Line = simulation Centerline Sauter Mean Diameter (SMD).

  14. Ug = 60 m/s, Ul = 1.36 m/s Ug = 60 m/s, Ul = 0.68 m/s Application to Air-Blast atomization. Experiment => mean liquid volume fraction (Stepowski & Werquin 2001) Simulation => statistics of liquid core boundary Key parameter:

  15. f Drag coefficient , Stp particle Stokes number Drop injection and lagrangian tracking. Typical size resulting from primary atomization Motion of the drops injected. Modification of the gas velocity field: Lagrangian tracking : Pl probability of presence of liquid

  16. Distribution of formed blobs. Experiments(Lasheras & al 1998) Ug = 140 m/s Ul = 0.13 m/s Examples of instantaneous distribution of formed droplets with instantaneous conditionned velocity of gaz and liquid core Ul = 2.8 m/s

  17. Shearing Turbulence Collisions Computation in the far field. => Secondary processes: Fragmentation or coalescence Example of instantaneous distribution of formed droplets ug = 140 m/s , ul = 0.55 m/s

  18. Comparison in the far field. Ug = 140 m/s

  19. Conclusion. • Simple enginering model for primary atomization is proposed. • This allows to form the blobs in the near-injector region. Future work. • Comparison with experiments in Brighton (trying different main mechanisms for fragmentation).

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