VORTEX RING-LIKE STRUCTURES IN GASOLINE FUEL SPRAYS:

MODELLING AND OBSERVATIONS

Sergei SAZHIN*,

Felix KAPLANSKI**, Steven BEGG*, Morgan HEIKAL*

*Sir Harry Ricardo Laboratories, Internal Combustion Engines Group, School of Environment and Technology, Faculty of Science and Engineering, University of Brighton, Brighton, BN2 4GJ, UK

** Laboratory of Multiphase Physics, Tallinn University of Technology, Tallinn 19086, Estonia

2

Presentation overview

• VORTEX RING-LIKE STUCTURES IN ENGINES

• VORTEX RING MODELS• MODELLING VERSUS EXPERIMENTS• OTHER RECENT RESULTS

3

VORTEX RING-LIKE STUCTURES IN ENGINES

4

A typical spray in Diesel engines

5

Typical vortex ring-like structure in a gasoline fuel spray

Piston crown position

6

Schematic view of vortex ring generatorSchematic view of vortex ring generator ((Gharib Gharib et al.,et al.,1998 )1998 )

7

Formation stage (Gharib et al.,1998 )

L/D<4 L/D<4

L/D>4L/D>4

L/DL/D44‘‘optimal’ ringoptimal’ ring

8

Gasoline engine injectors

Injector A BFuel injector type Port (PFI) Direct (G-DI) Nominal fuel pressure 3.5 bar 100 barFuel temperature 22 °C 22 °CFuel type Iso-octane (2,2,4 TMP) Iso-octane (2,2,4 TMP)Injection frequency 1 Hz 1 HzInjection duration 5 ms 2 msAir pressure 1 bar 1 barAir temperature 20 °C 20 °C Orifice size 200 μm 250 μm

9

VORTEX RING-LIKE STRUCTURE IS GASOLINE ENGINE

(injector A)

,

10

VORTEX RING-LIKE STRUCTURE IS GASOLINE ENGINE

(injector B)

,

Injector axis

Penetration depth

Spray width

Vx1

Vx3

Vx2

2Ro

x

rl

11

The region of maximal vorticity

,

12

VORTEX RING MODELS

,

13

Schematic view of a vortex ring

Formulation of the problem

22

2

2

2 1

rrrrxu

xv

rt

,

)( tUrr

u 1

,,xr

v1

rrrxr

1

2

2

2

2 0

0002122

,:)(

,,,/rx

xx

0

2 dxdrrI

cb tRMAat

(t)x-xr

),,(,

, ,= ,= ,

00

03

0

0

dt

tdxtU

)()( 0

I

M

0R

=

ring-to-core radiusring-to-core radius

Approximate solution

11

Re][* b

c

t

b

22

2

2

2 1

*

20 /Re

..),,(Re),,(Re);,,( 21

..),,(Re),,(Re);,,( 21

, , I2

1exp 1

2221 3bc

122'*

btba.2/14/1 b

Velocity of the centroid at r=0

,

0

00

2

2

dxdrr

dxdrxr

x

dt

tdxVtU x

)()( 0

17

Velocity of the centroid at r=0

,

1222exp3

22

1

2 Iv

VU

n

xx

2

22 ;3,2

5;

2

3,

2

3 F

,;2

7,2;

2

5,

2

3

5

3 222

2

F

,!)()(

)()(;,;,

0 21

21212122

k kk

kkk

kbb

xaaxbbaaF

,;)(;1)( 10 ),2()1().........1()( kkk

,4

Γ

4,

0

030

20

RR

Mv

Rn

18

Velocity of the centroid at r=0 (short times)

,

),2/3(2

3ln

xU

,d

)(logd)(

x

xΓx

γ ≈ 0.57721566 is the Euler constant, ψ(x) is the di-gamma function

19

Velocity of the centroid at r=0 (long times)

,

.30

7 3xU

20

Velocity of the region of maximal vorticity

,

,d)(2

erfc2 01

0

2 JJUU xx

,d)exp(2

)(erfc 2

x

ttx

21

Velocity of the region of maximal vorticity at long

times

,

,2

1)(1 J

.d)()2

(erfc30

7 30

0

2

JU x

Θ 3 ~ t-3b 2/14/1 b

22

MODELLING VERSUS EXPERIMENTS

23

Velocity of the region of maximal vorticity

,

initial/ ttt

)(/)( initialtVtVV xxx

24

Velocity of the region of maximal vorticity

,

xV

25

Conclusions

1. A generalised vortex ring model is based on the assumption that the time dependence of the vortex ring thickness ℓ is given by the relation atb, where a is an arbitrary positive number, and 1/4 ≤b ≤ 1/2 is suggested.

2. The predictions of the model are compared with the results of experimental studies of vortex ring-like structures in gasoline engine-like conditions with a high pressure (100 bar) G-DI injector and a low-pressure (3.5 bar) port fuel injector (PFI). The G-DI results has shown good agreement with the model. In contrast, the agreement of the PFI results with the model has been poor.

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OTHER RECENT RESULTS

27

Transient heating of a semitransparent spherical body

Sazhin, S.S., Krutitskii, P.A., Martynov, S.B., Mason, D., Heikal, M.R., Sazhina, E.M. (2007) Transient heating of a semitransparent

spherical body, Int J Thermal Science, 46(5), 444-457.

22

( , )T T

R P t Rt R R R

/l l l lk c when R Rd

/g g g gk c when Rd<R<Rg

28

Evaporation of droplets into a background gas: kinetic modelling

Sazhin, S.S., Shishkova, I.N., Kryukov, A.P., Levashov, V.Yu., Heikal, M.R. (2007) Evaporation of droplets into a background gas: kinetic modelling, Int J Heat Mass Transfer, 50, 2675-2691.

1 2

Ts, s

x

TRd , Rd

Kinetic region

Hydrodynamic region

Rd

jV q

29

Approximate analysis of thermal radiation absorption in fuel droplets

22

( , )T T

R P t Rt R R R

/l l l lk c when R Rd

/g g g gk c when Rd<R<Rg

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Approximate analysis of thermal radiation absorption in fuel droplets

Sazhin, S.S., Kristyadi T., Abdelghaffar, W.A., Begg, S., Heikal, M.R., Mikhalovsky, S.V., Meikle S.T., Al-Hanbali, O. (2007) Approximate analysis of thermal radiation absorption in fuel droplets, ASME J Heat Transfer, 129, 1246-1255.

6 43 10d

bd R l lR R

P R a R c

where θR is the radiation temperature, Rd is the droplet radius,

3 3 20 1 R 2 R= b + b /10 b ( /10 ) ,b

θR can be assumed equal to the external temperature Text in the case of an optically thin gas in the whole domain. The coefficients depend on the range of radii

0dR R

P R

3 3 20 1 R 2 R= a + a /10 a ( /10 ) ,a

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Particle grouping in oscillating flows

.

Sazhin S.S., Shakked, T., Sobolev, V., Katoshevski, D. (2008) Particle grouping in oscillating flows, European J of Mechanics B/Fluids, 27, 131-149.

Katoshevski, D., Shakked, T., Sazhin, S.S., Crua, C., Heikal, M.R. (2008) Grouping and trapping of evaporating droplets in an oscillating gas flow, International J of Heat and Fluid Flow, 29, 415-426.

dgd uu

Std

du

1

Vd (m/s)

X (mm),

||3

4

dggD

dl

vvC

DSt

dgd uu

Std

du

1

Velocities are normalised by ω/k, the distance by 1/k and the time by 1/ω

32

Acknowledgements

The authors are grateful to EPSRC (Project EP/E047912/1) for financial support.

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Thank you for your attention

Any comments or suggestions

would be highly appreciated

VORTEX RING-LIKE STRUCTURES IN GASOLINE FUEL SPRAYS:

MODELLING AND OBSERVATIONS

Sergei SAZHIN*,

Felix KAPLANSKI**, Steven BEGG*, Morgan HEIKAL*

*Sir Harry Ricardo Laboratories, Internal Combustion Engines Group, School of Environment and Technology, Faculty of Science and Engineering, University of Brighton, Brighton, BN2 4GJ, UK

** Laboratory of Multiphase Physics, Tallinn University of Technology, Tallinn 19086, Estonia

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