Reciprocating Internal Combustion Engines
Prof. Rolf D. Reitz,
Engine Research Center,
University of Wisconsin-Madison
2012 Princeton-CEFRC
Summer Program on Combustion
Course Length: 9 hrs
(Wed., Thur., Fri., June 27-29)
Hour 4
Copyright ©2012 by Rolf D. Reitz.
This material is not to be sold, reproduced or distributed without
prior written permission of the owner, Rolf D. Reitz.
1
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Short course outine:
Engine fundamentals and performance metrics, computer modeling supported
by in-depth understanding of fundamental engine processes and detailed
experiments in engine design optimization.
Day 1 (Engine fundamentals)
Hour 1: IC Engine Review, 0, 1 and 3-D modeling
Hour 2: Turbochargers, Engine Performance Metrics
Hour 3: Chemical Kinetics, HCCI & SI Combustion
Day 2 (Spray combustion modeling)
Hour 4: Atomization, Drop Breakup/Coalescence
Hour 5: Drop Drag/Wall Impinge/Vaporization
Hour 6: Heat transfer, NOx and Soot Emissions
Day 3 (Applications)
Hour 7: Diesel combustion and SI knock modeling
Hour 8: Optimization and Low Temperature Combustion
Hour 9: Automotive applications and the Future
2
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Resolution – predictive models
10 cm
Finite
difference
mesh
1-D 104 grid points
3-D 1012 grid points
10 m
Models will not be entirely predictive over next decade
Accurate submodels will be needed for detailed spray processes
(e.g., drop drag, drop turbulence interaction, vaporization, atomization,
drop breakup, collision and coalescence, and spray/wall interaction)
3
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Amsden et al. 1997
Governing Equations
f = f (x, v, r, Td; t)
Gas phase
Liquid phase
Turbulence
x, v, r, Td
Gas void fraction and drop number density
4 3
1
(
r f dr dv dTd )dVol / Vol


3
Vol
Current spray
models:
– drops
occupy no
volume >0.9
Two-Phase Flow Regimes
Computational cell
Drop parcels
Intact
Churning
Thin
Thick
4
Very thin
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Spray Modeling
Dukowicz 1980
• Concept of using “drop parcels”
For typical heavy-duty diesel, injected fuel per cycle (75% load): 0.160 g
One spray plume: mfuel=0.160/6=0.0267 g
If average SMD=10 m  mdrop =3.8x10-10 g
# of drops in the domain=0.0267g/m drop=7.1x107
Impractical to track individual fuel drops – group identical drops into ‘parcels’
What you see in graphs:
drop
nozzle
Grid size
parcel
5
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Eulerian Gas Phase
Amsden et al. 1997
Mass conservation (species)

2

(u) 

4

r
R f dr dv dT d
l


t
R = dr/dt - Vapor source
Momentum conservation
u
2
s

( uu ) p ( 3 k ) F g
t
Turbulent and viscous stress
Rate of momentum gain due to spray – drop drag
6
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Gas Phase (2)
Amsden et al. 1989
Combustion
heat release
Internal energy conservation

I
c
s
+ uI = -P
u - 
J + + Q + Q

t
Turbulence
dissipation
Energy due to
Spray - vaporization
Heat flux
J T D hm(m / )
m
Equations of state
p RT m / W m
m
Specific heat, enthalpy from JANAF data
7
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Liquid Phase
Amsden, 1997
.
Spray drop number conservation f = f (x, v, r, Td, y, y; t)
.
.
f

 .

 .
+ x fv + v fF + (fR ) +
fT d +
fy +
fy = f coll + f bu
t
r
T d
y
y
F=dv/dt
drop drag
R = dr/dt
Vaporization and
heating
Drop
distortion
Drop breakup,
coalescence
Spray exchange functions
Fs = s
Q =-
fd 4/3 r 3F ' + 4r 2Rv dv dr dT d dy d y
f d 4 r 2 R I l + 1 v -u
2
Work done by drop drag forces
2
+ 4/3 r 3 c l T d + F ' v - u - u '
s
W =8
d v dr d T d dy d y
fd 4/3 r 3 F '
u ' dv dr dT d dy dy
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Lagrangian drop - liquid phase
Amsden, 1997
Discrete Drop Model
u'
u
drop position
dx
v
dt
drop velocity
l
dv
F
dt
v
drop size
dr
R
dt
Spray submodels provide:
F - Drag, R – Vaporize
.
Turbulence model
provides: l, u’
t
.
f coll + f bu - breakup/collide
t+dt
Initial data:
v, r, T d – Atomization model
9
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Turbulence Model (RANS)
Amsden, 1997
Kinetic energy
Dissipation




k
2
s
.

( uk) 3 k
u 
u (
)k WÝ




t

Pr k


Production due
to mean flow
Rate of work to
disperse drops
Dissipation rate


+ u= t
2C
1
3
- C 3 
u + 


Pr 
+  C 1 :u - C 2 + C s W
k
Turbulence diffusivity
Eddy size
D C  k / 
2
s
Turbulence intensity
3/2
l = C k /
10
u’2= (2 k/3)
CEFRC4 June 28, 2012
UW-ERC Multidimensional CFD models
Submodel
Los Alamos
intake flow
heat transfer
turbulence
nozzle flow
atomization
assumed initial flow
law-of-the-wall
standard k-
none
Taylor Analogy
drop breakup
drop drag
wall impinge
Taylor Analogy
rigid sphere
none
collision/coalesce O’Rourke
vaporization single component
low pressure
ignition
Arrhenius
combustion
Arrhenius
NOx
soot
Zeldo’vich
none
11
UW-Updated
References
compute intake flow
compressible, unsteady
RNG k-/LES
cavitation modeling
surface-wave-growth
Kelvin Hemholtz
Rayleigh Taylor
Rayleigh Taylor
drop distortion
rebound-slide model
wall film/splash
shattering collisions
multicomponent fuels
high pressure
reduced chemistry
CTC/GAMUT
reduced kinetics
Extended Zeldo’vich
Hiroyasu & Surovkin
Nagle Strickland oxidation
11
SAE 951200
SAE 960633
CST 106, 1995
SAE 1999-01-0912
SAE 960633
SAE 980131
CST 171, 1998
Atom. Sprays 1996
SAE 960861
SAE 880107
SAE 982584
Atom. Sprays 1999
SAE 2000-01-0269
SAE 2001-01-0998
SAE 2004-01-0558
SAE 2004-01-0102
SAE 2003-01-1087
SAE 940523
SAE 960633
SAE 980549
ERC RCCI
Research
CEFRC4
June 28,
2012
Hour 4: Atomization, Drop Breakup/Coalescence
Review of atomization models (Single Hole Nozzle)
Reitz & Bracco, 1982
Four main jet breakup regimes:
Rayleigh, first wind-induced, second wind-induced and atomization
a.) Rayleigh breakup
Drop diameters > jet diameter.
Breakup far downstream nozzle
b.) First wind-induced regime
Drop diameter ~ jet diameter.
Breakup far downstream of nozzle
c.) Second wind-induced regime
Drop sizes < jet diameter.
Breakup starts close to nozzle exit
d.) Atomization regime
Drop sizes << jet diameter.
Breakup at nozzle exit.
Growth of small disturbances
initiates liquid breakup
12
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Nozzle flow - cavitation
Homogeneous Equilibrium Model
- single phase mixture of vapor and liquid
- considers variable compressibility of mixture.
(1) Sonic Speed of mixture
: function of void fraction
  α=0 for pure liquid
 l
l v α=1 for pure vapor

1
1 

v (1 ) l  2  2 
a2
l al 
v av
Sonic Velocity (m/sec)
Lee & Reitz, 2010
Theory (γ)
1.4 (Adiabatic)
1.0 (Isothermal)
(Wallis, 1967)
(2) Equation of State of mixture
: by integrating dP a 2 d (Schmidt, 1997)
P Pl
sat
 v av 2 

l 
v l 

Pvl log 
2
2
2 


a



a


a
l v v
v v
l l


a a 
 
Pvl  v v 2 l 2 l v2 2 l
v av l al
2


2
Pl
sat
Pv
sat
pure
liquid
Void fraction, α
pure
vapor
Sonic velocity in bubbly air/water
mixture at atmospheric pressure
Brennen (1995)
v 2 av 2 
Pvl log  2 2 
l al 
13
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Nozzle flow - cavitation
Lee & Reitz, 2010
max velocity at exit, cm/s
min. density at exit, g/cm3
Max ρ
Max V
(sec)
(sec)
density and
iso-surface
(ρ=0.35g/cm3)
streamline and exit velocity
14
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Cavitation Inception
Cavitation if
Yes
Umean
P < Pv
P2 / P1 
Cavitation
region
r/d
Account for effects of
nozzle geometry
1
vena
Cc
Initial
D
2
l/d
No
Sarre SAE 1999-01-0912
1

2( Cc Cc2 )
Non-cavitating flow
Cc
1.0
0.9
cc
Cavitating flow
Contraction coefficient (Nurick (1976)
1 2
C c [(
) 11.4 r / d ] 1 / 2
0 .62
0.8
sharp inlet
nozzle
0.7
0.6
0.00
0.04
0.08
0.12
r/d
15
CEFRC4 June 28, 2012
0.16
Hour 4: Atomization, Drop Breakup/Coalescence
ERC Nozzle Flow Model
Cavitating flow
Yes
P2 / P1 
Nozzle discharge coefficient
C d C c
Nozzle discharge coefficient
Lichtarowicz (1965)
p1 p v
p1 p 2
C d 0.827 0.0085 l
Effective injection velocity
ueff
d
Effective injection velocity
2 C P P2 (1 2Cc ) Pv
 c 1
Cc 2 ( P1 Pv )
ueff Cd
Effective nozzle area
Aeff
Non-cavitating flow
No
2( P1 P2 )

Effective nozzle area
2Cc2 ( P1 Pv )

A
2 Cc P1 P2 (1 2Cc ) Pv
Aeff A
Sarre SAE 1999-01-0912
16
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Atomization - “Wave” breakup model
Taylor & Hoyt, 1983
High speed photograph of water jet close to nozzle exit
(at top) in the second wind-induced breakup regime
showing surface wave instability growth and breakup
Reitz & Bracco, 1982
Kelvin Helmholtz Jet Breakup Model


= R 0 e ikz +t
Linear Stability Theory:
Cylindrical liquid jet issuing from a circular orifice into a stationary,
incompressible gas.
Relate growth rate, , of perturbation to wavelength 


k
17
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
e t
2B 0

Linearized analysis
Reitz & Bracco, 1982
r
U = Jet velocity
2a
Surface waves breakup on jet or "blob"
Z
1
2
= R 0 e ikz +t
U(r)
Equation of liquid surface: r = a+,
Axisymmetric fluctuating pressure, axial velocity, and radial velocity for both liquid
and gas phases.
Fluctuations described by continuity equation
ui 1 

(rvi ) 0
z r r
plus linearized equations of motion for the liquid and the gas,
Axial:
u
u
1 p
 2 u 1  u 
i
i
i
i
U (r) i v

 i

r i



i
i
t
z
dr
 z  z 2 r r  r 
dU
i
18
i
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Reitz & Bracco, 1982
Analysis (Cont.)
Radial:
vi

vi
1 pi i 2 vi 
1 rvi 

U i (r)

 

2


t
z
r
z


i  

r r r 

i 
Gas is assumed to be inviscid U(r) = U - slip
With 
<<a, the gas equations give the pressure at the interface r = a
p2 2 (U i
 2 K0 (ka )
) k
k
K1(ka)
Boundary conditionsKinematic, tangential and normal stress at the interface:

v1 w  ,

t

u1
v1

r

z
2
v1 
2 
) p2 0
p1 21 1
 2 (a
2
r a
z


19
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Reitz, 1988
Dispersion Relationship
2
I 1' ka
I 1 ka I 1' la
2kl
+ 2v 1 k 
I 0 ka k 2 +l 2 I 0 ka I 0 la
2
2
2 I 1 ka
= k 1 - k 2 a 2 l - k
1 a 2
l 2 + k 2 I 0 ka
2
2 I 1 ka K0 ka
2
2 2
+  U - i /k k l2 - k 2
1
l + k I 0 ka K1 ka
Weber
Ohnesorge
Maximum wave growth rate
characterizes fastest growing
waves which are responsible
for breakup
(as a function of Weber
and Ohnesorge numbers)
Maximum wave growth rate
and length scale:  and 
20
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Curvefit of Dispersion Equation
0.5 1 + 0.4 0.7
T
= 9.02 1 + 0.45 Z
a
0.6
1 + 0.87 We21.67
where
Reitz, 1988
1 a3
 
0.5
1.5
0.34
+
0.38
We
2
=
1 + Z 1 + 1.4T 0.6
2
2
0.5

U
a

We
0.5
2U a
1
1
Z=
; T=ZWe2 ; We1=  ; We2=  ; Re1=Ua
v1
Re1
Maximum growth rate increases and wavelength decreases with We
Increased viscosity reduces growth rate and increases wave length
Wavelength
Ohnesorge
number, Z
growth rate
Weber number, We2
Weber number, We2
21
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
“Wave” atomization model
Drop size:
Reitz, 1988
r B
Breakup time: ~ 
v ~ 


U
Spray angle prediction:
v
Tan 
U

1
4 (
A

g
)1 / 2 f ( T )

Breakup length of the core (Taylor, 1940):

L C a 1 / f (T )
2
where
f(T)=
l
3
f 
T  
1 exp
10T 

6
22
T=
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
X-ray Phase-contrast imaging of high-pressure sprays
ANL Synchrotron-Based Ultrafast (150 ps) Single-Shot images
Surface instability waves produce ligaments
Breakup sensitive to injection pressure, fuel properties
(Hydroground nozzle, biodiesel, 1 ms injection duration in quasi-steady state)
Gao, 2010
23
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Drop breakup
Mechanisms of drop breakup at high velocities
poorly understood - Conflicting theories
Bag, 'Shear' and 'Catastrophic' breakup regimes
Breakup due to capillary
surface waves
Hinze Chem Eng (1955) and
Engel Nat. Bureau Stds (1958)
Boundary Layer Stripping
due to Shear at the interface
Ranger and Nicolls AIAA J. (1969)
Reinecke and Waldman AVCO Rep (1970)

(x)
Delplanque & Sirignano Atom Sprays (1994)
Stretching and thinning – drop
distortion - Liu and Reitz IJMF (1997)
24
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Low velocity drop breakup
Liu & Reitz, 1993
Gas
Liquid
injection
orifice
1.27
Nozzle
Liquid drop
25
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
High speed drop breakup mechanism
Double pulse images
Air jet
RT
waves
KH
waves
RT

KH

Drops
Rayleigh Taylor
Breakup
RT
Product
drops
gt = acceleration
Hwang, 1996
26
2

3 
g   
RT 
3
t
l
g
2
l g
g t 
l g 
3
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Drop Breakup Regimes
Breakup
stages
First
breakup
stage
Deformation or
breakup regimes
(1) Deformation
and flattening
(b) Bag breakup
Breakup process
12 We 100
(including the
Bag-and-Stamen
breakup)
Pilch and Erdman
Air
We 80
Ranger and
Nicolls 1969
Air
100 We 350
Liu and Reitz 1997
Air
350 We
Hwang et al. 1996
Air
Bag burst
Rim burst
(e) Catastrophic
breakup
l
Second
breakup
stage
(d) Stretching and
thinning
breakup
References
We 12
Air
Bag growth
(c) Shear breakup
Weber number
Flattening
and thinning
RT
waves
KH waves
Lee & Reitz, 2001
27
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
O’Rourke PhD thesis 1981
Drop collision modeling
Collision frequency
12  N 2 (r 1  r 2 ) E 12 | v 1  v 2 | / Vol
2
1
r1
v2
2
v1
Number of collisions from
Poisson process
p(n) = e -12t 12 t n /n!
Collision efficiency
2

 K


E12 


~ 1
K 1 / 2 
0 < p <1
random number
2 l v1 v2 r22
K
9
g r1
28
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Drop collision and coalescence
Munnannur, 2007
1. Reflexive vs. surface energy
2. Kinetic energy of unaffected part vs. surface energy
3. Drops cannot expel trapped gas film (bounce apart)
4. Drops form combined mass (coalesce)
1
2
3
4
B=
δ
We 
ρLU 2 d s
σ
2b
B
,
( d s d l )
,
29
d
Δ s
dl
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Drop coalescence
Ashgriz & Poo, 1990
Grazing-coalescence boundary
Drops fly apart if rotational energy of colliding pair exceeds
surface energy of combined pair
6
1
2
2
1




12

 2

3 3
1
1

3 


5 We 
1 





3
Bx 
11
0 < Bx <1
random number
B
30
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Grazing - Stretching Separation
Ashgriz & Poo, 1990
Energy and angular momentum conservation:
Grazing – drops move in same direction but at reduced velocity
Coalescence – mass average properties of colliding drops
B
31
CEFRC4 June 28, 2012
Hour 4: Atomization, Drop Breakup/Coalescence
Reflexive Separation
²=1


²=0.75

²=0.5
0.25
Tennison, SAE 980810



3
6 1 2 
3
4
1 2 
7
1 3 
0







1

2
2 We
3 2
2
1
 
1 2 
1
1 
2
2
1
2
with
1
2
0.15
0.1
 
2 2 

2 2
Coalescence
0.2
0.05
3
Reflexive separation
0
1
 Bx 
1
/2
2
0
10
20
30
40
50
2*We
60
70
80
90
Ashgriz & Poo, 1990
B
32
CEFRC4 June 28, 2012
100
Hour 4: Atomization, Drop Breakup/Coalescence
Summary
The Lagrangian Drop/Eulerian Fluid (LDEF) Discrete Drop model is the workhorse approach in commercial codes for simulating 2-phase flows.
Detailed models are available for use in engine CFD models to describe the
effects of injector nozzle flow, and liquid and gas properties on spray formation
and drop breakup physics.
Due to the importance of sprays in applications, research is still needed. Recent
experimental and modeling work can be accessed through ILASS and ICLASS
conference papers and the Atomization and Sprays journal.
Significant progress is being made using LES/DNS spray modeling with high
resolution experimental diagnostics to validate engine CFD spray models.
Ballistic imaging: Linne, 2009; X-Ray imaging: Liu SAE paper 2010-01-0877
LES: Villiers & Gosman, LES Primary Diesel Spray Atomization, SAE 2004-01-0100
DNS: Near field spray modeling (Trujillo - ERC)
Reitz, Pickett & Trujillo, 2012
33
CEFRC4 June 28, 2012