Spray dynamics as a multirate process

1
Spray dynamics as a multi-rate process

• Sergei SAZHIN, Sergey MARTYNOV,
• Felix KAPLANSKI, Steven BEGG
• 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
• Department of Mechanical Engineering,
  University College London, Torrington Place,
  London, WC1E 7JE, UK
• Laboratory of Multiphase Physics, Tallinn
  University of Technology, Tallinn 19086, Estonia

2
Presentation overview

• INTRODUCTION
• SPRAY BREAK-UP MODELS
• VORTEX RING MODELS
• OTHER RECENT RESULTS

3
INTRODUCTION Processes in Direct Injection
Internal Combustion Engines (Diesel and Gasoline)

• Formation of a liquid fuel spray
• Fuel spray penetration
• Droplet break-up
• Vortex ring formation (gasoline engines)
• Heating of fuel droplets
• Evaporation of fuel droplets
• Ignition of fuel vapour / air mixture

4
Ignition (experiment)
160 MPa injection into 10 MPa gas
140 MPa injection into 10 MPa gas
100 MPa injection into 10 MPa gas
5
A typical spray in Diesel engines
6
Typical vortex ring-like structure in a gasoline
fuel spray
7
Typical Scales (lengths)

• Spray Length 0.03-0.1 m
• Diameter of the Nozzle 10-4 m
• Droplet Diameter 10-5 m

8
Typical Scales (times)

• Spray Penetration 3 10-3 s
• Injection Duration 10-3 s
• Droplet Break-up Time 10-5 s

9
SPRAY BREAK-UP MODELS

• WAVE model
• TAB (Taylor Analogy Breakup) model
• Stochastic model

,
10
WAVE model
where

and
11
TAB (Taylor Analogy Breakup) model
where

and
12
Stochastic model
where
The break-up of parent particles into secondary
particles does not depend on the instantaneous
sizes of the parent particles (Kolmogorov, 1941).

and
is the normalised droplet distribution function
by radii
is the frequency of production of new droplets
is the break-up operator
13
Stochastic model
where
is the probable number of new droplets in the
interval

and
?0 is the number of break-ups per unit time
14
Stochastic model
where
The previous equation cannot be solved but we
can use the expansion

and
the third and higher logarithmic moments are set
to be zero for large times
is the number distribution function
15
Stochastic model
where

and
16
Comparison of the results
where

and
Gas pressure is 2 MPa, injection pressure is 60
MPa, B1v31.73
17
Modified WAVE model
where

and
18
Comparison of the results
where

and
Gas pressure is 2 MPa, injection pressure is 60
MPa
19
Comparison of the results
where

and
Gas pressure is 2 MPa, injection pressure is 60
MPa (b) Modified WAVE c,d) conventional WAVE
B110 B160
20
SPRAY BREAK-UP MODELS (Conclusions)

• The modified WAVE model can explain the main
  properties of sprays at the initial stage of
  penetration
• The development of more rigorous physical and
  mathematical versions of this model is essential
• (Martynov, S.B., Sazhin, S.S., Gorokhovski, M.A.,
  Chtab, A., Karimi, K,
• Crua, C, Heikal, M.R. (2008) A modified
  wave model for transient liquid sprays,
  Atomization and Sprays, (submitted).
• Sazhin, S.S., Martynov, S.B., Kristyadi, T.,
  Crua, C., Heikal, M.R. (2008) Diesel fuel spray
  penetration, heating, evaporation and ignition
  modelling versus experimentation, International J
  of Engineering Systems Modelling and Simulation,
  1(1) (in press)).

,
21
VORTEX RING MODELS


,
22
Schematic view of vortex ring generator (Gharib
et al.,1998 )
23
Formation stage (Gharib et al.,1998 )
L/Dlt4
optimal ring
L/D4
L/Dgt4
24
Gasoline engine injectors
Injector A B Fuel injector type Port
(PFI) Direct (G-DI) Nominal fuel pressure 3.5
bar 100 bar Fuel temperature 22 C 22
C Fuel type Iso-octane (2,2,4 TMP) Iso-octane
(2,2,4 TMP) Injection frequency 1 Hz 1
Hz Injection duration 5 ms 2 ms Air
pressure 1 bar 1 bar Air temperature 20
C 20 C Orifice size 200 µm
250 µm
25
VORTEX RING-LIKE STRUCTURE IS GASOLINE ENGINE
(injector A)


,
26
VORTEX RING-LIKE STRUCTURE IS GASOLINE ENGINE
(injector B)


,
27
Schematic view of a vortex ring
28
Schematic view of a vortex ring
29
VORTEX RING MODELS


,
30
Formulation of the problem
,
ring-to-core radius
31
Approximate solution
32
Velocity of the centroid at r0
,
33
Velocity of the centroid at r0


,
34
Velocity of the centroid at r0 (short times)


,
? 0.57721566 is the Euler constant, ?(x) is the
di-gamma function
35
Velocity of the centroid at r0 (long times)


,
36
The region of maximal vorticity


,
37
Velocity of the region of maximal vorticity


,
38
Velocity of the region of maximal vorticity at
long times


,
T 3 t-3b
39
Velocity of the region of maximal vorticity

,
40
Velocity of the region of maximal vorticity

,
41
VORTEX RING MODELS (Conclusions)

• 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. In the case when av2?, where ? is the
  laminar kinematic viscosity, and b1/2, the
  predictions of the generalised model are
  identical with the predictions of the
  conventional model.
• The predictions of the model are compared with
  the results of experimental studies of vortex
  rings 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.

42
Other Recent Results
43
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.

when RdltRltRg
44
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.

45
Approximate analysis of thermal radiation
absorption in fuel droplets
when RdltRltRg
46
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.

47
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.

Velocities are normalised by ?/k, the distance by
1/k and the time by 1/?
48
Monodisperse droplet heating and evaporation
experimental study and modelling

• Maqua, C., Castanet, G., Grisch, F., Lemoine, F.,
  Kristyadi, T., Sazhin, S.S. (2008) Monodisperse
  droplet heating and evaporation experimental
  study and modelling, International J of Heat and
  Mass Transfer (in press).

Plots of ethanol droplet temperature Td, measured
experimentally (solid triangles) and predicted by
the model (Tds droplet temperatures at the
surface of the droplet, Tdav average droplet
temperature, and Tdc droplet temperature at the
centre of the droplet) and gas temperature Tg for
the initial conditions Rdo 118.65 µm, Tdo294 K,
C3.97
49
Acknowledgements

• The authors are grateful to the European Regional
  Development Fund Franco-British INTERREG IIIa
  (Project Ref 162/025/247) and EPSRC (Project
  EP/E047912/1) for financial support.

50
Thank you for your attentionAny comments or
suggestionswould be highly appreciated

51
Spray dynamics as a multi-rate process

• Sergei SAZHIN, Sergey MARTYNOV,
• Felix KAPLANSKI, Steven BEGG
• 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
• Department of Mechanical Engineering,
  University College London, Torrington Place,
  London, WC1E 7JE, UK
• Laboratory of Multiphase Physics, Tallinn
  University of Technology, Tallinn 19086, Estonia

52
(No Transcript)