Theoretical and experimental study (linear stability and Malvern

granulometry) on electrified jets of diesel oil in atomization regime

L. Priol, P. Baudel, C. Louste, H. RomatLaboratoire d’Etudes Aérodynamiques

Poitiers,FranceLaurent.Priol@lea.univ-poitiers.fr

Christophe.Louste@lea.univ-poitiers.fr

Summary

• Introduction

• Linear stability theory for charged jets– Dispersion relation– Numerical results

• Experiments– Experimental device– Experimental results (laser granulometry)

• Conclusion

Introduction

• The dynamic of fuel droplets: a critical importance in the behaviour of liquid fuel disintegration in combustion system

• Effects of electric charges, velocity, viscosity and electrostatic forces on the stability of an electrified jet

• Measurement of the size distribution of droplets with Malvern’s Spraytec ®

Decrease particle size by 10%

Decrease unburned carbon by 35%

Linear stability analysis

• Disturbance on the surface of an axisymmetrical liquid jet

U)cos()exp(0 kzt

IR with

Linear stability analysis

• Dispersion relation between ω and k, found by Reitz1

)()(

)()(

)(

)(1

)(

)(

)(

)(2

)(

)(2

10

0122

222

2

1

2

0

122

2222

21

1

1

0

122

0

121

2

kaKkaI

kaKkaI

kl

klk

kiU

kaI

kaI

kl

klak

a

k

laI

laI

kaI

kaI

kl

kl

kaI

kaIk

1 R.D. Reitz and F.V. Bracco, Mechanism of breakup of round liquid jets, Encyclopedia of Fluid Mechanics, Gulf Pub., N.J., vol. 3, pp.233-249, 1986

Linear stability analysis

• Dispersion relation between ω and k

)()(

)()(

)(

)(1

)(

)(

)(

)(2

)(

)(2

10

0122

222

2

1

2

0

122

2222

21

1

1

0

122

0

121

2

kaKkaI

kaKkaI

kl

klk

kiU

kaI

kaI

kl

klak

a

k

laI

laI

kaI

kaI

kl

kl

kaI

kaIk

kakaK

kaK

kaI

kaI

kl

kl

laI

laI

kaI

kaI

kl

kl

kaI

kaI

kl

kk 1

)(

)(

)(

)(

)(

)(

)(

)(

)(

)(

0

1

0

122

22

1

1

0

122

0

122

2

10

220

22110

20 1

4 kl

Numerical treatment of the dispersion relation

•Dimensionless growth rate

•Dimensionless wave number ka

•Initial charge density σ0 =3 10-4 C/m²

3

1aR

The electrical charges destabilize the jet

With electric charges:

Higher growth rate

Smaller diameter droplets

Experimental device

pump

liquid tank

pressure fluctuation absorber

recirculation pump

manometer

gate

Injector

Reception tank

Electrification system

Electrified high pressure jet

Diesel oil inlet

needle connected to the high voltage source

grounded counter electrode

x

z

Pressure 70 bars, Potential -30kV

Malvern granulometry experiments

•Malvern measures droplets from 1 µm to 250 µm

•Measurements based on Mie’s diffraction theory

•Real time spray measurement at up to 2500 Hz

•Laser beam diameter of 10 mm

Experimental results

Real time evolution of different “diameters” of droplets for p=80 bars, z=40 mm and x=0 mm

Injection of charges

Dv(90)=182.73Dv(90)=351.46

Experimental results

• Droplet size distribution for a driving pressure of 120 bars at z=30 mm, x=0 mm (center of the jet)

Potential 0kV Potential -25kV

Vol

um

e cu

mul

ate

dist

ribu

tion

(%)

Diameters µm Vol

um

e of

th

e cl

ass

diam

eter

(%

)

Vol

um

e cu

mul

ate

dist

ribu

tion

(%)

Diameters µm Vol

um

e of

th

e cl

ass

diam

eter

(%

)

Experimental results

• Droplet size distribution for a driving pressure of 120 bars at z=30 mm, x=5 mm (edge of jet)

Potential 0kV Potential -25kV

Vol

um

e cu

mul

ate

dist

ribu

tion

(%)

Vol

um

e cu

mul

ate

dist

ribu

tion

(%)

Vol

um

e of

th

e cl

ass

diam

eter

(%

)

Vol

um

e of

th

e cl

ass

diam

eter

(%

)

Diameters µm Diameters µm

Conclusion

• Dispersion relation with electrostatic forces shows the destabilizing role of the electric charges in the jet

• For an electrical charged jet the theory predicts a decrease of the droplet mean diameter

• Theoretical results confirmed by experimental measurements obtained by laser granulometry

Better atomization of a jet thanks to the

injection of electric charges