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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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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

  • Deterministic description of such atomization is very diffcult task.

  • Stochastic approach

    => Application to primary atomization.

Sacadura,CORIA


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.


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.


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


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)


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

=>


Experimental setup.

C. Arcoumanis, M. Gavaises, B. French SAE Technical Paper Series, 970799 (1997).

Gaz initial conditions:

Atmospheric conditions

Liquid initial conditions:


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



Computed mean sauter diameter.

Sauter Mean Diameter


Symbols = experiment

Line = simulation

Centerline droplet mean axial velocity.


Symbols = experiment

Line = simulation

Centerline Sauter Mean Diameter (SMD).


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:


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


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


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



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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