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Modelling of non-isothermal spray flows using a combined viscous-
vortex, thermal-blob and Lagrangian approaches
CAE Research Workshop 1 December, 2014
Oyuna Rybdylova, A.N. Osiptsov, S.S. Sazhin,
S. Begg, M. Heikal
The Sir Harry Ricardo Laboratories Centre for Automotive Engineering
Outline
• Introduction
• Two-phase vortex ring flow, non-evaporating
droplets
• 2D cold two-phase jet injection, evaporating
droplets
• Conclusion
2
Motivation
3
Formation of a Vortex Ring exiting a gun muzzle as captured by Dr. Lyons with spark photography upon firing a blank 40mm grenade (1997)
A typical high-speed photograph
of a G-DI spray (Begg et al 2009)
EPSRC project “Development of the full Lagrangian approach for the analysis of vortex ring-like structures in disperse media: application to gasoline engines”
Outline
• Introduction
• Two-phase vortex ring flow, non-evaporating
droplets
• 2D cold two-phase jet injection, evaporating
droplets
• Conclusion
4
Vortex ring flow. Formulation
5
00Re
• Carrier phase: Kaplanski solution (Fukumoto &
Kaplanski, 2008)
• Dispersed phase: FLA (Osiptsov, 2000)
Dimensionless parameters: 2
0
0
6 R
m
0
0 0
FrR gR
0
0
0
2Res
R
0Re Res s s v v
2/3
2
1 11 Re
6 Fr
dd s
d
dt
vv v j
dd
d
dt
rv
0 0d dn r J n r ij
ij
Jq
t
1 2
1 2
ij i ij j ij
q v vJ J q
t x x
0
idij
j
xJ
x
0
idij
j
vq
x
1
2
r
z
Droplets: numerical simulation
0
3
Re 0.7s
Two-phase jet, Re = 100
0
0.13
Re 3.3s
0 05 0, , , v 0, 1, 0.01d vc d du u z t n t
Outline
• Introduction
• Two-phase vortex ring flow, non-evaporating
droplets
• 2D cold two-phase jet injection, evaporating
droplets
• Conclusion
7
Problem formulation • 2D transient flow
• One-way coupled two-fluid approach
– Carrier phase: incompressible viscous fluid (droplet
liquid vapour)
– Dispersed phase: identical droplets, pressureless
continuum
• Force acting on a single particle:
• Heat rate
8
2/316 1 Re
6s s s
f v v
* * * 1/3 1/24 1 0.3Pr Res s sq T T
Non-dimensional parameters
9
6 similarity parameters: Re, γ, Pr, β, δ, Res0
Problem formulation
10
Initial conditions Boundary conditions
11
VVB (Andronov, Guvernyuk,
Dynnikova, 2006 Cottet &
Koumoutsakos, 2000)
Thermal blobs
(Ogami, 1999)
Carrier phase
Lagrangian approach (Osiptsov, 2000)
Dispersed phase
Numerical algorithm
VVM TBM
12
Numerical algorithm
13
Ω ≠ 0
Ω = 0
Γi
Numerical algorithm
14
Biot-Savart law and the mollified kernel:
Lamb vortex
15
2
2
,, 1 exp Re
2 4
y xu v
t
rv
rRe 100
0 1t
Two-phase jet injection
17
Initial conditions:
y
u
VB: [−3.84; 0]×[0.24; 0.56]U[−3.84; 0]×[−0.56;−0.24] TB: [−3.84; 0]×[−0.5; 0.5] Dr: [−3.84; 0]×[−0.4; 0.4]
Two-phase jet injection
18
Motion of viscous-vortex and thermal blobs
Viscous-vortex blobs and velocity field
Two-phase jet injection
19
Droplet distributions and their sizes β = 0.05, δ = 0.0014
Two-phase jet injection
20
Droplet distributions and their sizes β = 0.21, δ = 0.006
Two-phase jet injection
21
Droplet distributions and their sizes β = 5.5, δ = 0.14
Conclusions: • Unsteady axially symmetric two phase vortex ring flow modelled
using FLA and Kaplanski analytical solution
• A meshless method based on a combination of the viscous-vortex
and thermal-blob methods for the carrier phase and the Lagrangian
approach for the dispersed phase is developed. It can be applied for
modelling unsteady 2D flows of ‘gas-evaporating droplets’ systems
• The injection of a cold ‘vapour – droplet’ jet into a hot quiescent
gas was studied; three regimes corresponding to various droplet
sizes were observed
The authors are grateful to the EPSRC (grant EP/K005758/1) (UK) for the
financial support of this project.
