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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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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


Stochastic modeling of primary atomization application to diesel spray

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


Stochastic modeling of primary atomization application to diesel spray

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.


Stochastic modeling of primary atomization application to diesel spray

  • 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.


Stochastic modeling of primary atomization application to diesel spray

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


Stochastic modeling of primary atomization application to diesel spray

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)


Stochastic modeling of primary atomization application to diesel spray

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

=>


Stochastic modeling of primary atomization application to diesel spray

Experimental setup.

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

Gaz initial conditions:

Atmospheric conditions

Liquid initial conditions:


Stochastic modeling of primary atomization application to diesel spray

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


Stochastic modeling of primary atomization application to diesel spray

Example of distribution of formed blobs.


Stochastic modeling of primary atomization application to diesel spray

Computed mean sauter diameter.

Sauter Mean Diameter


Stochastic modeling of primary atomization application to diesel spray

Symbols = experiment

Line = simulation

Centerline droplet mean axial velocity.


Stochastic modeling of primary atomization application to diesel spray

Symbols = experiment

Line = simulation

Centerline Sauter Mean Diameter (SMD).


Stochastic modeling of primary atomization application to diesel spray

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:


Stochastic modeling of primary atomization application to diesel spray

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


Stochastic modeling of primary atomization application to diesel spray

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


Stochastic modeling of primary atomization application to diesel spray

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


Stochastic modeling of primary atomization application to diesel spray

Comparison in the far field.

Ug = 140 m/s


Stochastic modeling of primary atomization application to diesel spray

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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