A new spark model for SI engine in STAR-CD : The Imposed Stretch Spark Ignition Model - Concept and preliminary validations to SI-GDI combustion

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Feb 22, 2014 (3 years and 5 months ago)

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A new spark model for SI engine in STAR
-
CD : The Imposed
Stretch

Spark Ignition Model
-

Concept and preliminary
v
alidations to SI
-
GDI combustion




M. Zellat
,
G. Desoutter
,

D. Abouri, A. Desportes
, J.

Hira


CD
-
adapco, 203
-
213 avenue Paul Vaillant Couturier, BOBIGNY, 93000, FRANCE







Abstract


Gasoline Direct Injection (GDI) appe
ars to be the most relevant way to improve fuel efficiency of SI engines. The
development of such engines is difficult. Every parameter, such as piston shape, injector inclination, or mixing
process for example, has to be carefully adapted. CFD is a useful

tool to understand the processes taking place in
the combustion chamber and the correlation between parameters and, therefore, a way to support the design.
However, CFD will require specific sub
-
models able to describe the spray and its evaporation, the m
ixing process
and stratification, and the combustion process including auto
-
ignition.
Modelling spark ignition and initial flame
kernel growths plays a key role in the development of the whole combustion processes of SI engine.

An ignition model based on
an Imposed Stretch in an Euler
ia
n form is presented in th
i
s paper. This

model

developed at IFP [1]

is implemented in the CD
-
adap
co engine code STAR
-
CD. Preliminar
y
validations under
constant volume chamber as well as engine configurations are

presented
.



1.

INTRODUCTION:

A
Global overview of the
ISSIM model

The Imposed Stretch Spark Ignition Model (ISSIM) is
an Eulerian spark
-
ignition model for 3D RANS
simulations of internal combustion engine
applications.
The sphe
rical kernel equation is no more
resolved in a 0D way, but is instead directly used in
the Eulerian transport equations, therefore allowing a
local description of all phenomena. The usage of the
Flame surface density equation naturally allows the
simulatio
n of multi
-
spark ignitions and of the flame
holder effect, not addressed by previous models. Both
the flame growth and wrinkling are modelled by the
ECFM equation.
This model

is

coupled
to both
ECFM
-
3Z and ECFM
-
CLEH
combustion model
s in
STAR
-
CD
code
.


The
following sections describe
the electrical system
model of ISSIM
, the spark and flame kernel coupling

and t
he modelling of the
flame kernel growth using
ISSIM
.







The electrical system model of ISSI
M
is based on the
el
ectrical circuit model of AKTIM a
nd

includes the
most recent experimental correlations. Assuming an
inductive ignition system, the model provides the
amount of energy transferred to the gas during the
glow phase and the evolution of the spark, which is
convected and wrinkled by the flow.
At the instant of
electrical breakdown, an initial burned gases profile is
created on the 3D mesh. From this instant on, and
unlike what
is

done in AKTIM, the reaction rate is
directly controlled by the F
lame surface density

equation.
In order to allow
fla
me surface density
(FSD)
equation to correctly describe
evolution
of
combustion
during early flame ignition
, few
adaptations are performed on the FSD equation
.





2


2.

Electrical circuit model

A schematic of
the real inductive ignition system for
spark plug is

given in
Figure
1
. The main parts of
interests
for
modelling are:




The coil:
st
o
res the energy and also

acts as a
voltage transformer. The coil has a primary
(inductance L
p
) and a secondary (inductance
L
s
) side



a capacitor C
p

:
can be added to obt
ain a fast
current interruption



Different resistances (of the secondary coil
windings, ca
ble).



the spark plug.



Figure
1
. Simplified electrical scheme of a coil
ignition system and the spark plug


The purpose of a spark

ignition system is to provide
enough energy into a small gas volume,
in the vicinity
of the electrode

gap, to ensure a successful initiation
of the combustion process.

This energy is initially
stored as electrical energy in the ignition system and is
converted into thermal energy when released into the
spark gap.

The evolut
ion of the electrical energy of
the secondary circuit

s
E

is given by:



2
( )
( ) ( )
s
s s spk s
dE t
R i t V i t
dt
  


w
here

s
spk
i
V
,

and
s
R

are
the inter
-
electrodes
tension
, intensity and resistance of the secondary
circuit respectively
.


The energy is not entirely transferred to the spark: a
substantial part is los
t

by
J
oule effect.


The intensity
in the secondary circuit can
be estimated

follo
wing:

2 ( )
( )
s
s
s
E t
i t
L


At breakdown, the spark length is equal
to the spark
gap d
ie
. Then, the spark is stretched by convection
mean
spk
l

and by the turbulent motion of the flow

turb
spk

.
The total length of the spark reads:


turb mean
spk spk spk
l l



The spark wrinkling evolution
e
quation
of
turb
spk


takes
the form
:

,,
1 1
( )
2
turb
spk
spk T spk M
turb
spk
d
K K
dt

 

,


where
K
spk,T

and
K
spk,M

are the spark strain by the
turbulent and by the mean flow respectively.
K
spk,T
correspond
s

to the effect of the turbulent eddies
greater than the
arc thickness and lower than the half
length of the spark
.

The computation of the strain
K
spk,T

is similar to the ITNFS


function

in the equation
of the flame
surface density
equation.



During arc and glow phases, only a fraction of the
spark

energy is r
eleased to the gas. The
energy
released

in a thin region near the electrodes is
essentially lost by fall voltage
as illustrated in
Figure

2
.
The potential difference between both electrodes,
also called spark volta
ge is written:


spk cf af gc
V V V V
  
,


where V
cf

is the cathode fall voltage, V
af

is the anode
fall voltage and V
gc

is the gas column voltage. T
he
anode fall voltage

is similar for the arc and glow
modes and equal to 18.75

V for Inconel (an alloy
ba
sed on Nickel, Chrome and iron). The cathode fall
voltage is 7.6

V during arc phase and 252

V during
glow phase for Inconel.
T
he gas column voltage

is
expressed by
:

0.32 0.51
40.46
gc spk s
V l i p





Figure

2
.

Schematic showing the voltage distribution
during
arc and glow phase.

3


At breakdown, about 60% of
the breakdown energy
-

function of the spark g
ap and of the breakdown
voltage
-

is released to the gas, providing the ignition
energy E
ign

before glow phase.


During the glow phase, the voltage fall is locali
sed in
the vicinity of the electrodes. Therefore it is assumed
that the energy released within these regions is lost to
the electrodes. Finally, the energy transferred to the
gas is deduced from the gas column voltage and the
intensity following:


( )
( ) ( )
ign
gc s
dE t
V t i t
dt



This energy E
ign
is used to determine if ignition is
successful or not.
Indeed, it is considered that a flame
kernel can be formed around the spark, and ignition
starts only if
( ) ( )
ign c
E t E t

, where


t
E
c

is a
critical ignition energy depending on local
thermodynamic properties in the vicinity of the spark.



In that case, an amount of burnt gas mass is deposited
at the spark, which corresponds to a cylinder of radius
2
L


and height

l
spk
:


2
spkplg
4
ign
b u spk L
m l
 
 


where
L


is the flame thickness.


3.

Flame kernel growth using ISSIM

3.1.

Flame surface density approach

It can be demonstrated [1] that the growth of a
spherical flame kernel stretched a
nd wrinkled by
turb
ulence (cf. F
igure 3) can be modelled by the
standard flame surface
density


equation already
available in th
e ECFM family combustion models
given below:




1 2 3
/
( )
i t
i i t i
u
P P P D
t x x Sc Sc x

 
 
 
 
  
        
 
 
 
   
 
 


Figure
3. F
lame kernel

wrinkled

by turbulence

In this equation, the only term provided by ISSIM is
the spark source term






described in section
3.3.1.

In addition, the laminar flame speed
L
S

is modified
to take into account the influe
nce of the energy
released by the spark plug.



Finally, t
he consumption rate of the fuel
u
F



presen
t
in the fresh gases is
computed as:


u u u
F F L
Y S
 
 



3.2.

Initial burned gases kernel

If the critical energy criterion is satis
fied, an initial
burned gases mass is deposited
.
This is achieved by
defining the target burned gases volume
fraction
ign
c
:


2
0
exp
0.7
spk
ign
ie
x x
c c
d
 
 

 
 
 
 
 
 
 
 


ign
c

is defined by imposing that constant c
0

satisfies


ign
b ign b
c dV m



.



In order to impose the value
(,)
ign
c x t
on the 3D
computational domain, the reaction
rate
of the
progress variable is written as follows:


( )
max(,)
b ign
c
u L
c c
S
dt

 

 


In
the above
expression, the

flame surfac
e density
(FSD)

of a possible pre
-
existing flame is also taken
into account. This allows
considering

the interaction
of flames coming from different
spark
ignitions.

The
main idea of ISSIM is to model the reaction rate of a
growing flame kernel thanks to t
he flame surface
density (FSD) equation from the very beginning of

spark

ignition. Consequently, at the instant of creation
of the initial burned gas kernel of
radius
ign
b
r
, the FSD
needs to be initialised. The following expression is
proposed:

3
max(,)
ign
ign
b
c
r
  


4


The expression
3
ign
ign
b
c
r

is chose
n

to recover the initial
total flame surface of a sphere of
radius
ign
b
r
:


3 2
3 3 3 4
( ) 4 ( )
3
ign ign
ign ign b b
ign ign ign
b b b
dV c dV c dV r r
r r r
 
    
  


3.3.

Source terms at the spark plug in the
pre
sence of a spark

As long as the spark exists (
0
s
E

), the ignition
criterion defined by
ign crit
E E


is calculated at the
spark plug. Once this criterion is satisfied, we
consider that a burned gases kernel correspondin
g to
the ignition burnt gases mass
ign
b
m
exists at the spark
plug. Without convection, the burnt gas mass is only
deposited at spark timing, and this condition is always
satisfied. When the flame is convected away from the
spark, it is

replaced by incoming fresh gases, which
ignite in the vicinity of the spark. If the ignition
criteria is satisfied, a target profile
(,)
ign
c x t

is
imposed at any instant .In the RANS approach, the
profile of
(,)
c x t

di
ffuses rapidly, so that
(,) (,)
ign
c x t c x t

, as shown in
Figure
4
. As a
consequence, the burnt gas mass deposit is
overestimated in the vicinity of the spark. A solution
to avoid this effect is to determine the right amount of
burnt gas mass
ign
b
dm

that is deposited around the
spark. This amount should be
non
-
zero

after spark
ignition only if the flame kernel is convected. It can be
estimated using a phenomenological approach, as
illustrated in
Figure

4
. The mass
ign
b
dm

corresponds
approximately to a parallelepiped with the height of
the spark gap (d
ie
), a depth of
2
L

and a width of
( )
ign
b b
d r r t

  

see
Figure

5
:


2
ign u
b L ie
dm d
  



where r
b
(t) is the evolution of the flame kernel radius
function of time. As the spark life is very short, we
neglect the flame wrinkling and the pressure variation
effect. Several tests have shown that t
hese
assumptions are reasonable. As for the initial burnt
gas mass, the target burnt gas volume fraction
ign
c

is
defined following by imposing that constant c
0

satisfies:




max ( ),0
ign
b b ign
dm c c dV

 


The spark source term in the ECFM

equation is
expressed following:

3
( ) max,0.0
ign
ign
b
c
r
 
   
 
 


This modelling choice has a consequence: if ignition
is successful at breakdown time and also afterwards, a
flame holder effect can be retrieved.



Figure
4.

Evolution of the progress variable

at spark,
along a 1D line.



Figure

5.

When the flame kernel is convected away
from the spark, a burnt gas mass
ign
b
dm
is deposited
at the spark



3.4.

Modification of the laminar flame speed
near spark plug

The energy
ign
E

transferred to the gas column leads to
an increase of the burned gases temperature in the
flame kernel. This temperature increase in turn leads to
an increase of the laminar flame speed, which can be
expressed as follow in the vicinity of spark:



5














spk
L
L
eff
L
l
S
S
0
0
4
1
5
.
0
*


with































b
b
p
ign
spk
L
spk
L
m
c
E
l
l
400
1
4
4
1
4
0
2
0




where
0
L
S

and

0
L


are the standard laminar flame
speed and thickness

respectively
.
b
p
c

is the

heat
capacity in the burnt gases.
spk
l

is the spark arc length.
3
1
( )
6
b b ie
m d
 


represents the total burned gases
mass.

4.

Validation of the flame kernel growth


The
experimental

configuration used is the one of the
Leeds Mk2 high
-
pressure / temperature spherical fan
-
stirred combustion bomb. An uniform isotropic
turbulence is generated by four symmetrical fans. The
corresponding integral len
gth scale
l
t

was found to be
20 mm. Available experiments

[3]

address various
turbulence intensities, fuels, equivalence ratios and
pressures. The measurement database was kindly
provided to IFP by Dr. R. Wooley and Pr. C.G.W.
Sheppard
.

The ignition system

is representative of an inductive
ignition system encountered in engines. The electrical
circuit parameters used in the computations were
deduced from the knowledge of the energy provided
to the spark (

23 mJ) and of the spark duration
(

1ms).

Figure 6
s
hows the 2D axi
-
symmetric computational
domain, of size 190

380mm in the x and z directions.
A uniform grid
of 0.5 mm
size
was used. The
turbulent kinetic energy and the integral length scales
are set constant during the computation. The
temperature of
the

walls
is set
to 360 K. The
coefficient of the turbulent stretch P
1

is set to 0.85.



Figure
6
. Computational domain for the Leeds
experiment.

4.1.

Results

Figure 7

shows

the temporal evolutions of the total
flame radius r versus time
for
ISSIM and AKTIM

ignit
ion models compared to the experiments
. The
numerical radius

were deduced from the flame surface
density as
/(4 )
r dV

 

. In the experiments, the
total flame radius is defined as the radius of an
equivalent circle with the same area as that e
nclosed
by the outer edges of the Schlieren images. Generally
5 ignitions were performed at each condition. The
individual measurements are plotted, showing the
variability of the flame radius evolution.


Considering the variability of the experimental res
ults,
both ISSIM and AKTIM provide good results, ISSIM
showing a faster growth than AKTIM on this case.



Figure
7
. Temporal evolution of the total flame radius
for
stoichiometric

iso
-
octane/air mixtures. The
symbols correspond

to the 5 experimental
measu
rements. The solid line corresponds to the
computations performed with ISSIM.


5.

Model verification and
assessment

under
engine conditions

5.1.

Engine configuration

The computed is a typical 2 liters SI Engine, under
production. Because of the importance of the
flow
structure, turbulence level and mean flow intensity at
Spark Timing, the full process of Intake, Injection,
Compression and Combustion is computed at each
simulation. Figure 8 shows the mesh used for a full
cycle simulation.


6




Figure 8:

View of computational grid: Complete
geometry (left) and combustion chamber (right)

5.2.


Model

validation



Full load @

2000
RPM

The computed and measured in
-
cylinder pressures and
corresponding rate of heat release
are represented on
figure
s

9

and
10

for the full load 2000 rpm. It is
shown that it is possible to achieve an overall good
agreement for both the simplified FI
-
ECFM model as
well as the ISSIM.


The main differences between the two models are how
easy to ge
t such good agreement. Obviously with the
FI
-
ECFM model some tuning were necessary, while
using the ISSIM model only the spark geometry and
the spark characteristics system were necessary. This
demonstrates the predictive capability of the ISSIM
model.


An
other difference between the FI
-
ECFM and ISSIM
appears in chimerical heat release history as show in
figure 9
. Th
e

sudden change in chemical heat release
observed in the FI
-
ECFM results is typical because
when the spark delay is reached an amount of flame
surface density is created during one time step leading
to this kind of discontinuity.

Thi
s

ISSIM chemical heat
releases

shows clearly to
smooth development of the flame
demonstrating

clearly

the transition
between

the initial kernel and the
main flame
pro
pagation
.



Figure 9. Chemical heat release history



Figure 10. In
-
cylinder pressure history



Figure

11.

Apparent Rate of heat release history



Figure

1
2
. Chemical heat re
lease history


This effect can b
e seen in Figure 13a and 13
b
. The
reaction rat
e contours are represented

by the flame
surface density.
The evolutions with both models are
significantly different: ISSIM predicts a more intense
combustion during ignition. The spark life is about
2°CA. The flame grows in the vicinity of the spark
and a
long the spray, propagating toward the opposite
side of the spray. With FI
-
ECFM, the initial flame
kernel created along the spark is convected towards
the spark which is not necessary consistent with the
local Eulerian field, as a result, the flame kernel
growth rate is underestimated.

7










Fig
ure 13
a
.
Flame density surface=30 at 341, 344, 346
°CA. Left : FIECFM, right : ISSIM
.











Fig
ure

13
b
.

Flame density surface=
50 at 344, 346, 348

°CA. Left : FIECFM, right : ISSIM



6.

CONCLUSION
S

A new

spark ig
nitio
n model based on an

Eulerian
approach of a flame density transport equation has
been developed

and implemented in STAR
-
CD. This

model
,

called ISSIM for
Imposed Stretch

Spark
Ignition Model
,

was originally developed at IFP [1].
The original main combus
tion model ECFM
-
3Z was
also modified to ensure the continuity of the flame
surface density transport equation. Several numeric
al
validations have been performed

to assess the right
implementation of the model. Validations were also
carried out in a constan
t volume chamber. Finally the
model is applied and validated against experimental
data under real engine configuration. Comparisons
with the simplified FI
-
ECFM ignition model are also
shown.















7.

Bibliography

[1]

O. Colin, Development of a spark ignition
model for LES based on the flame surface
density equation (ISSIM), D1.5a, IFP Report
60012, 2007.

[2]

J.M. Duclos and O. Col
in, Arc and kernel
tracking ignition model for 3D spark
-
ignition
engine calculations, COMODIA, pp. 343
-
350,
Nagoya, 2001.

[3]

M. Lawes et al. Variation of turbulent burning
rate of methane, methanol, and iso
-
octane air
mixtures with equivalence ratio at elevat
ed
pressures, Combust. Sci. and Tech. 177 (2005)
1273
-
1290.

[4]

S. Pischinger and J.B. Heywood, How Heat
Losses to the Spark Plug Electrodes Affect
Flame Kernel Development in an SI
-
Engine,
SAE transactions, 99(3) (1990) 53
-
73.

[5]

J. Kim and R.W. Anderson, Spark
Anemometry of Bulk Gas Velocity at the Plug
Gap of a Firing Engine, SAE transactions,
104(3) (1995) 2256
-
2266.

[6]

R. Maly and M. Vogel, Initiation and
propagation of flame fronts in lean CH
4
-
air
mixtures by the three modes of the ignition
spark, 17
th

Symp. (I
nt.) on Combust., pp.821
-
831, 1979.