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Stochastic modeling of primary atomization : application to Diesel spray .

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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

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 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.

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.

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

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)

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

=>

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

Gaz initial conditions:

Atmospheric conditions

Liquid initial conditions:

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

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

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

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

Ug = 140 m/s

- 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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