47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
AIAA 2009-666
Modeling Diesel Spray Flame Lift-off using Detailed
Chemistry and a New Primary Breakup Model
Sibendu Som1 and Suresh K. Aggarwal2
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL 60607
Combustion in direct-injection diesel engines occurs in a lifted, turbulent diffusion flame
mode. Numerous studies indicate that the combustion and emission characteristics in such
engines are strongly influenced by the lifted flame behavior, which in turn is determined by
fuel and air mixing in the region upstream of the lifted flame, and consequently by the liquid
breakup and spray development processes. Thus primary jet breakup plays a key role in
engine processes, and is induced by cavitation and turbulence inside the injector nozzle, and
aerodynamic (Kelvin-Helmholtz) instability outside. In the present study, we examine the
effects of these three primary breakup processes in the flame liftoff behavior. A new primary
breakup model incorporating the inner nozzle flow (cavitation and turbulence) and
aerodynamic effects is developed and evaluated for predicting the flame liftoff
characteristics. The effects of various ambient and injection characteristics, and exhaust gas
recirculation on flame lift-off are simulated using a detailed chemistry, and validated against
data from Sandia National Laboratory. In general, very good agreement is observed under
all measured conditions. The effect of nozzle orifice geometry on flame lift-off is also
characterized.
Nomenclature
rKH
Λ KH , Ω KH
r
t
dt
τ KH
σ
ρ g ,l
radius of newly formed droplets
wavelength, maximum growth rate of the KH wave
radius of the parent droplet parcel
time
time-step size
KH model breakup time
Surface tension
Gas, Liquid density
Ur
νl
LT (t ) , τ T (t )
Relative velocity between the phases
TKE, TDR
SOI
K (t ) , ε (t )
Turbulent Kinetic Energy, Turbulent Dissipation rate
Start of Injection
Instantaneous TKE, TDR for a parcel
Cµ , Cε
k − ε turbulence model constants
K0 , ε 0
Initial TKE, TDR for a parcel
LCAV, τ CAV
Characteristic length and time-scale due for cavitation induced primary breakup model
τ Collapse
Bubble collapse time-scale
1
2
Liquid viscosity
Length, Time scale at any instant for turbulence induced primary breakup model
Graduate Research Assistant, Mechanical and Industrial Engineering, 2039 ERF, Student Member.
Professor, Mechanical and Industrial Engineering, 2039 ERF, Faculty Member.
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Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
τ Burst
Bubble burst time-scale
pv
Vapor pressure for fuel
rhole
Exit radius of the orifice
u 'turb
Turbulent velocity
CT ,CAV
Model constant for primary breakup model
LA ,τ A
Dominant length and time scales
U inj
Injection Velocity
L/d0
CT ,CAV
Ratio of length to nominal orifice diameter
Breakup law constant = 0.05
Din, Dout
Inlet and outlet diameters of nozzle orifice
I. Introduction
Diesel engine has been the preferred power train for heavy duty applications, especially in trucks due to its high
efficiency. High power output, good fuel economy, and significant reduction of engine noise are the main reasons
for its enormous popularity. During the last decade, the innovations in high pressure direct injection systems
combined with turbo charging have revolutionized the diesel engine technology. While the diesel engines are here to
stay, new challenges motivate the engine manufacturers to improve the existing technology. Heavy duty diesel
engines intrinsically generate high soot and NOx which need to be reduced in order to comply with the emission
legislations worldwide. While exhaust gas after-treatment techniques such as diesel particulate filters and Selective
Catalytic Reduction for NOx are lucrative options, there is significant interest in decreasing the engine’s raw
emissions and further improving fuel consumption. In order to reduce engine’s raw emissions several strategies need
to be combined and optimized together. Such strategies include enhancements in fuel injection systems (i.e.,
increased injection pressure, multiple injection, and rate shaping capability), efficient nozzle orifice design, and
combustion control strategies, exhaust gas recirculation (EGR), alternative fuels, optimized design of combustion
chamber and piston bowl etc.
Fuel injection characteristics, in particular the atomization and penetration of the fuel droplets, are known to
significantly affect the combustion and emission processes in diesel engines. Fuel atomization in the region near the
injector nozzle is governed by the primary breakup, which is known to be caused by three different mechanisms.
These include the turbulence induced jet disintegration [1,2], the cavitation-induced breakup [3] (as cavitation
structures developed inside the nozzle orifice can reach the exit, implode, and cause jet integration), and the
aerodynamic break-up due to Kelvin-Helmholtz (KH) instability, as high relative velocities between the liquid and
the gas phase induce aerodynamic shear force at the liquid-gas interphase [1,2,4]. While the above three jet breakup
mechanisms are well established, most of the current breakup models only consider aerodynamic jet breakup.
Although these aerodynamically induced breakup models perform well under certain conditions, they do not capture
the essential physics of the flow, especially near the injector. In a recent study by Som et al. [5] a primary breakup
model incorporating all the above three mechanisms for breakup was developed and statically linked with inner
nozzle flow simulations [6]. This lead to an improved spray prediction capability and the effects of inner nozzle flow
on spray characteristics were successfully captured [5].
The emission regulations for diesel engines are becoming increasingly more stringent. The US EPA’s current
requirements for heavy duty truck engines manufactured after 1st January 2008 are set at 0.01g/bhp-hr for
particulates and 0.2g/bhp-hr for NOx, both an order of magnitude lower than those a decade ago. This motivates the
diesel engine manufacturers to gain enhanced understanding of the NOx and soot (particulate matter, PM) formation
processes. Flame lift-off characteristics are known to play a central role in combustion and emission processes in
diesel engines [7,8,9,10,11]. The farthest upstream location of combustion on the spray axis locates the lift-off
length. Upstream of the lift-off length the fuel spray entrains ambient air allowing premixing prior to the combustion
zone. The product gases of this rich premixed fuel air mixture reaction at and beyond lift-off distance is ideal for
soot production. There have been several experimental studies [7,8,9,10] at Sandia National Laboratory
characterizing the effects of ambient temperature and density, injector orifice diameter, injection pressure, and
oxygen concentration on flame lift-off characteristics. Increase in ambient gas temperature or density was observed
to decrease lift-off length while increase in orifice diameter or injection pressure was seen to increase it. Lowering
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oxygen concentration in the air stream (representative of EGR) was seen to increase the flame lift-off length.
Another important length scale here is the liquid length, which is defined as the farthest penetration of liquid fuel in
terms of the axial location [12], and is established where total fuel evaporation rate equals the fuel injection rate. The
interplay between lift-off and liquid length is important for spray and combustion processes in diesel engines. It is
also important in the context of liquid spray impingement on cylinder walls and piston, which is an important source
for emissions. In case lift-off length is longer than liquid length, fuel evaporation is complete before combustion
process begins, however; when liquid length is higher than lift-off length the combustion process enhances fuel
evaporation while the relatively cooler fuel jet will decrease the flame temperature. A fundamental understanding of
the influence of various parameters on flame lift-off length in diesel sprays was developed based on atmospheric gas
jet diffusion flames [7,8]. Peters [13] developed scaling laws for flame lift-off length in gas jets as:
L f (Lift-off Length) ∝
where U inj ,
U inj Z st D
S L2 ( Z st )
(1)
D , Z st , S L ( Z st ) are the fuel injection velocity, thermal diffusivity, stoichiometric fuel mixture
fraction, and flame speed of stoichiometric fuel air mixture respectively. Peters [13] showed that the flame stabilizes
where the turbulent flame speed balances the mean convective flow. In spite of major differences between gas jets
and diesel sprays the above scaling law was successfully used by Siebers and Higgins [7] to explain the observed
experimental trends.
The above mentioned flame lift-off and soot data [14] was used for validation of detailed chemistry and
phenomenological soot model by Kong et al. [15]. Flame lift-off, heat release rate, and emission trends were well
predicted by the models. Senecal et al. [16,17] reported results for spray liquid length and flame lift-off by
employing KH instability based breakup model with detailed chemical kinetics. While the predicted liquid length
and flame lift-off trends showed agreement with the Sandia data [7,8], scopes of improvements were identified
while performing quantitative match. Specifically, lift-off and liquid lengths were overpredicted at high ambient gas
temperatures, while the lift-off length was underpredicted at lower ambient gas temperatures. Karrholm et al. [18]
compared the performance of OpenFOAM and KIVA-3V CFD codes in predicting flame lift-off [7,8] and flame
shape for a range of ambient temperature and EGR fractions. In general, KIVA-3V overpredicted flame lift-off
while OpenFOAM underpredicted it. The differences in prediction between the two codes were attributed to
computational mesh, sub-model implementation, and solution algorithms.
In the present study we investigate whether improved spray prediction capability [5] due to primary breakup
model development can improve flame lift-off and liquid length predictions. This forms a major motivation for this
study, i.e., to compare flame lift-off predictions by an aerodynamically induced breakup mechanism (KH) against a
primary breakup model incorporating the effects of cavitation, aerodynamics, and turbulence. This new primary
breakup model is extensively tested against the above mentioned flame lift-off data for a range of conditions.
Following this validation, a parametric study is performed to characterize the effect of nozzle orifice geometry on
spray and combustion processes. Modern nozzle orifices are usually hydroground and conical rather than being
cylindrical in nature. Hydrogrinding increases flow efficiency by removing flow abrasions due to sudden turning of
the flow while conical nozzles suppress cavitation.
Turbulence intensity at the nozzle exit also decreases
Injection System
Detroit Diesel, Common Rail
following these strategies. While the effect of nozzle
orifice geometry (orifice conicity and hydro-grinding)
Number of Orifices
1 - Cylindrical
on primary atomization characteristics and spray
100 to 500 µm
development has been studied previously [5], the
Orifice Diameter
L/D = 4.2
present study examines this influence on flame lift-off
and liquid lengths with an eye towards understanding
Injection Pressure [bar]
400 to 1900
combustion and emissions performance.
Mixture of N2, H2, O2, C2H2
Fill Gas
II. Overview of Flame lift-off experiments at
Sandia National Laboratory
Flame lift-off experiments have been performed at
Sandia National Laboratory [7,8,9,10] under diesel
engine like conditions. Lift-off length was determined
by acquiring time-averaged line-of-sight images of
light emission at 310 nm corresponding to the
Chamber Density [kg/m3]
3.3 to 60
Chamber Temperature [K]
700 to 1300
Oxygen concentration
15-21%
Table 1. Parameter ranges considered in experiments
[7,8]
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chemiluminescence emitted by the OH* [9,10]. A constant volume cubical combustion chamber of 108mm length
was used. Diesel conditions were simulated by filling the combustion vessel with a premixed mixture of nitrogen,
oxygen, hydrogen, and acetylene. Spark plugs were used to ignite the mixture resulting in high pressure, temperature
environment which cooled over time due to the heat transfer to the walls of combustion vessel. Fuel injection was
initiated once desired ambient conditions were attained in the vessel. A mixing fan was used to maintain uniform
temperature in the vessel. The range of conditions studied along with other experimental details are listed in Table 1.
III. Spray and Combustion Modeling Set-up
Simulations were performed using CFD code “CONVERGE” incorporating state-of-the-art models, based on
the Eulerian-Lagrangian modeling approach [16,17,19]. The Eulerian gas-phase flow field is described using the
Navier-Stokes equations in conjunction with the RNG k-ε turbulence model. These equations are solved using a
finite volume solver. The length and time scales for the spray are too small to be resolved; hence sub-grid scale
modeling is necessary to describe the spray physics. The spray is represented by a stochastic system of a discrete
number of parcels. These computational parcels are tracked using a Lagrangian formulation. The two phases are
coupled through the exchange of mass, momentum, and energy, represented by the appropriate source terms in the
gas phase conservation equations.
An innovative modified cut-cell Cartesian method for grid generation is used. The grid is generated internally to
the code at runtime. For all the cases the base grid size was fixed to 8mm. In order to resolve the flow near the
injector, a fixed grid embedding was employed such that the minimum grid size was 0.5mm. Apart from this region,
it is rather difficult to determine where a refined grid is desired. Hence four levels of adaptive mesh refinement were
employed for the velocity field such that the minimum grid size was 0.5mm. In order to match the spray chamber
geometry, a cube of 108mm was generated. Detailed kinetic modeling is performed using the SAGE chemical
kinetic solver [16,17] with n-heptane mechanism [20] developed at Chalmers University. This mechanism consists
of 42 species and 168 reactions for n-heptane combustion and NOx formation and was directly coupled with the gas
phase calculations using a well-stirred reactor model.
Spray phenomena that need to modeled include the following: jet atomization, droplet breakup, drop distortion
and drag, droplet interactions in terms of collision and coalescence, turbulent dispersion, drop vaporization, spray
wall interaction, etc. The models incorporated in CONVERGE to represent these phenomena are briefly described
here. The injection process is simulated using a blob injection model, which injects liquid droplet parcels with a
diameter equal to an effective nozzle diameter. The injection velocity is obtained form a top-hat injection profile
corresponding to experimental measurements [12,21]. Subsequent droplet breakup is predicted by KH and RT
(Rayleigh Taylor) aerodynamically induced breakup models. KH and RT are used as primary secondary breakup
mechanisms respectively. Droplet collisions are based on the NTC (No Time Counter) algorithm [22]. Once
collision occurs, the outcomes of the collision are predicted as bouncing stretching, reflexive separation, or
coalescence [23]. A single component droplet evaporation model [24] based on the Frossling correlation is used. A
dynamic drag model accounts for the effects of droplet distortion on drag [25]. The effects of turbulence on the
droplet is included using a standard turbulent dispersion model [24]. As discussed earlier, primary breakup of the
fuel spray in the region close to the injector nozzle is influenced by cavitation and turbulence generated inside the
nozzle as well as aerodynamic interactions between the liquid fuel and ambient gas outside. An improved primary
breakup model that incorporates these three processes was developed and implemented in CONVERGE. This model
is briefly described here. Further details can be found in Ref. [5].
TURBULENCE INDUCED BREAKUP MODEL: According to Huh and Gosman [26] the turbulent fluctuations in
a jet are responsible for the initial perturbations on the jet surface. The relevant length and timescales to be used for
turbulence induced breakup can be calculated as follows at any instant for any parcel:
(
1.5

,
K (t )
LT (t ) = Cµ  K (t )
 τ T (t ) = Cµ
ε (t )
ε
(
t
)


)
(2)
Assuming isotropic turbulence for the liquid phase and neglecting the diffusion, convection, and production terms in
the k − ε equation, the decay of turbulent kinetic energy for a parcel was estimated as:
C


K0 ) ε
(
K (t ) = 

 K 0 (1 + Cµ − Cµ Cε ) + ε 0t ( Cε − 1) 
where K0 and
ε0
1
(1−Cε )
Cε
 K (t ) 
, ε (t ) = ε 0 

 K0 
(3)
are the initial values at the nozzle exit at SOI, determined from nozzle flow simulations [6].
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CAVITATION INDUCED BREAKUP MODEL: Cavitation patterns generated inside the injector nozzle can reach
the nozzle exit, implosion of which enhances jet atomization. According to Bianchi and Pelloni [27] and
Arcoumanis and Gavaises [3], the characteristic time-scale of cavitation ( τ CAV ) is assumed to be the smaller of a
bubble collapse time and a bubble burst time:
τ CAV = min (τ Collapse : τ Burst ) .
The bubble collapse time is calculated from Rayleigh Plesset theory [28] as:
(4)
τ Collapse = 0.9145 RCAV
where RCAV is the effective radius of an equivalent bubble from the nozzle calculated as: RCAV = rhole
ρl
pv
(5)
(1 − Ca )
The area reduction coefficient (Ca) is calculated from the nozzle flow simulations [6] and rth is the exit radius of the
nozzle orifice. The average time required for a cavitation bubble to reach the periphery of the jet can be estimated
τ Burst =
as:
rhole − RCAV
u 'turb
(6)
2 K (t )
is obtained from inner nozzle flow simulations. The length scale for the cavitation induced
3
breakup is calculated as: LCAV = RCAV .
where
u 'turb =
AERODYNAMICALLY INDUCED BREAKUP MODEL: The KH model described by Reitz [29] is used to
calculate the instantaneous length and time scales for every parcel: LKH = r − rKH , τ KH =
3.276 B1r
ΩKH Λ KH
(7)
The ratio of length and time scales for each process is calculated. The largest ratio determines the dominant breakup
L
L
L (t ) 
= max  KH ; CAV ; T 
τA
 τ KH τ CAV τ T (t ) 
(8)
dr
L
= −CT ,CAV A
dt
τA
(9)
LA
process:
The following breakup law is used:
A value of 0.025 is used for CT ,CAV . The inner nozzle flow simulations provided the necessary boundary conditions
for the primary breakup model in terms of TKE, TDR, and extent of cavitation at the nozzle exit. In case nozzle
flow modeling/measurements were not feasible, analytical expressions were used [27] to calculate TKE and TDR:
K0 =
2
U inj
 1
2 
 2 − K C − (1 − S ) 
C
8 L

D  d
( )
The model constants used are [27]: KC=0.45,
,
ε 0 = Kε
3
U inj
 1
2 
 2 − K C − (1 − S ) 
2 L  Cd

(10)
K ε =0.27,
S=0.01. This primary breakup model is represented as
“New model,” the aerodynamically induced spray
breakup model is represented as “KH model” in
subsequent text.
IV. Results and Discussions
For all conditions studied, the start of simulations
corresponds to the time of fuel injection in the
experiments [7]. Each simulation was initialized with an
ambient gas density, temperature, and composition based
on experimental conditions [7]. The base case conditions
are tabulated in Table 2. Simulations were performed on
an 8-node Linux cluster with 2.8 GHz processors and
run times were between 90-110 hours.
Injection Pressure
142 MPa
Nozzle Geometry
Cylindrical, Non-hydroground
Orifice Parameters
180 µm, L/d0 = 4.2
Injection Duration
5 ms
Ambient Gas Composition
N2=0.693, O2=0.21,
CO =0.061, H O=0.036
2
Chamber Density
14.8 kg/m3
Chamber Temperature
1000 K
Table 2. Simulated base case conditions
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2
A. New Model vs. KH model in predicting flame lift-off data
Due to the axi-symmetric nature of spray and combustion process, visualization was possible on a cut-plane
through the center of the fuel jet. Figure 1 shows images from flame lift-off simulations using detailed chemistry and
the new model at 8 different times for the base case tabulated in Table 2. The field of view in both axial and radial
directions is 108 mm. Figure 1(a) shows penetration of the injected fuel (green color representing droplets) at
0.25ms after the start of injection (SOI). Processes such as atomization, collision, vaporization, and fuel-air mixing
occur simultaneously, however, ignition is not observed yet. Fig. 1(b) indicates for the set of ambient and upstream
conditions, ignition occurs at about 0.625ms after SOI with two symmetrically located flame kernels formed at the
tip of the spray. At this instant the fuel also seems to have reached its maximum penetration or “liquid length”
marked by the white dashed line. The most upstream ignition location (base of the flame) is seen to move upstream
in (c) while the flame-front develops and continues to propagate downstream. From Fig. 1(e) the base of the flame is
stabilized. The farthest upstream location of 2200 K contour on the spray axis locates the “lift-off” length marked by
the white solid line. Under the given conditions flame lift-off length was shorter than the liquid length. Both lift-off
length and liquid length agreed well with the experimental values (cf. Fig. 3). Flame-front reaches the downstream
wall of the combustion chamber at 2ms (cf. Fig. 1(f)) and is seen to propagate along the wall. It reaches the top and
bottom walls at 5ms (cf. Fig. 1(g)), which is also the end of injection event.
Temperature
(K)
Ignition
Locations
Sp
Spray Axis
y
x
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 1. Computed liquid fuel penetration and temperature contours for base case conditions at (a) 0.25, (b)
0.625, (c) 0.75, (d) 1.0, (e) 1.5, (f) 2.0, (g) 3.0, and (h) 5 ms after SOI.
Figure 2 presents a comparison of the computed flame images (including lift-off locations) obtained using the
new breakup model and the KH model for the base case conditions depicted in Table 2. Figures 2(a), (b), (c) show
the flame and lift-off location as measured by Siebers and Higgins [10], new model, and KH model respectively.
The field of view in axial and radial direction is about 80mm and 40mm respectively. The white solid line in
experiment and simulations mark the flame lift-off location. A zoomed view of the flame base region is shown to
emphasize the flame base stabilization location. The shape of the flame is accurately captured by both the models;
however, the flame lift-off length is better predicted by the new model. The KH model is seen to overpredict while
the new model is seen to marginally underpredict the flame lift-off length. The new model enhances droplet breakup
5
6 locally rich premixed
thus enhancing vaporization and improving fuel-air a.
mixing
prior to ignition. This leadsa.to
mixtures nearer to the fuel injector so that ignition locations are also further upstream. Hence the base of the flame is
stabilized close to the injector tip, which in turn leads to shortening
b. 2 of flame lift-off length for the new model
compared to that for the KH model. The decrease in flame lift-off length with the new model is also seen by
comparing Figs. (d), (e) with (f), (g) respectively. While the new model predicts liquid length (white dashed lines) to
exceed lift-off length, the KH model predicts otherwise. Under these conditions, experimental data also shows liquid
length to exceed flame lift-off length (cf. Fig. 4).
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(d)
(a)
Temperature
(K)
(f)
22.3 mm
(b)
New Model
KH Model
(e)
(g)
New Model
(c)
KH Model
New Model
KH Model
Figure 2: (a) Flame image, and computed fuel penetration and temperature contours for (b) new model, (c)
KH model under stabilized flame conditions, (d) new model at 1ms, (e) new model at 2.25ms, (f) KH model at
1ms, and KH model at 2.25ms after SOI. All the above illustrations are for base case conditions (cf. Table 2).
Solid and dashed white lines represent flame lift-off length and liquid length respectively.
is
ρ
−0.3
(based on thermal diffusivity scaling with
ρ −1 and laminar flame speed scaling with
−0.36
density as ρ
), that noted experimentally [7] and
−0.85
numerically from Fig. 3 is ρ
. Again the new
density as
model compares better with the data compared to the
KH model. Note that the predicted liquid length and
lift-off length are plotted at quasi-steady conditions
i.e., after liquid penetration and flame base
stabilization.
In this section we have established that the new
primary breakup model performs better than the KH
model in predicting flame lift-off under the conditions
simulated. The next section presents further validation
of this new model.
60
Ambient Gas Temperature = 1000K
50
Lift-off Length (mm)
Further comparison between the new breakup
model and KH model is presented in Fig. 3, which
compares the predicted and measured lift-off lengths
as a function of ambient gas density. The experimental
data is from Siebers and Higgins [7]. The dependence
of lift-off length on the ambient gas density seems to
be more pronounced for diesel sprays than that for gas
jets (cf. Eqn. 1). While from Eqn. 1, this dependence
40
Siebers Data
New Model
30
KH Model
20
10
0
0
10
20
30
40
50
60
3
Ambient Gas Density (kg/m )
Figure 3: Effect of ambient gas density on flame lift-off
length for an ambient gas temperature, orifice
diameter, and injection pressure of 1000 K, 180 µm,
and 142 MPa respectively.
B. Validation against flame lift-off data
Further validation is provided using experimental data characterizing the effects of ambient gas density, injection
pressure, and orifice diameter on the flame lift-off length. Figure 4 presents the effect of ambient gas temperature on
lift-off and liquid length for an ambient gas density, orifice diameter, and injection pressure of 14.8 kg/m3, 180 µm,
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Lengths (mm)
80
and 138 MPa respectively. The trend of decreasing liftoff and liquid length with increasing ambient gas
Ambient Gas Density = 14.8 kg/m3
temperature is well captured by the new model.
However, at 800 K the flame lift-off is underpredicted
Siebers data (Lift-off)
60
while at 1300 K it is overpredicted. In general, the
Siebers data (Liquid)
predicted flame lift-off and liquid lengths do not capture
New Model (Lift-off)
the temperature sensitivity especially at high
New Model (Liquid)
temperatures. It should be noted that the overpredictions
40
of liquid length at high temperatures has been observed
previously using the KH model [16,30]. The new model
improves the spray distribution and hence the liquid
20
lengths are better predicted than KH model. Siebers and
Higgins [7] observed that for low ambient temperatures,
Crossover
Engine Operating
the liquid length is shorter than the lift-off length. As the
point
Conditions
temperature is increased, the lift-off length decreases at a
0
faster rate than the liquid length until the two lengths
700 800 900 1000 1100 1200 1300 1400
become equal which was noted as the “crossover” point.
Ambient Gas Temperature (K)
For higher temperatures, the liquid length is higher than
the lift-off length. Under these conditions the new model Figure 4: Validation of the new model against liquid
predicts a crossover point at about 930 K while the length and lift-off length data for an ambient gas
measured value was 950 K approximately. The interplay density, orifice diameter, and injection pressure of
between lift-off and liquid length has important 14.8 kg/m3, 180 µm, and 142 MPa respectively.
implications for in-cylinder diesel engine processes
hence accurate prediction is essential. According to Siebers and Higgins [7] for conditions with lift-off length longer
than liquid length, fuel vaporization is complete prior to combustion zone. Hence no interaction occurs between the
fuel vaporization and combustion processes. However when lift-off length is shorter than liquid length, there is
interaction between fuel vaporization and combustion processes. Combustion will enhance fuel vaporization thus
decreasing liquid length; lower temperature fuel vapor will cool the ambient gases and thus increase lift-off length.
The expected part-load, quiescent engine operating conditions are also shown. It is clear that under engine operating
conditions, there is significant interaction between liquid and lift-off lengths.
60
40
Siebers Data (Lift-off)
Siebers Data (Liquid)
New Model (Lift-off)
New Model (Liquid)
40
30
Lengths (mm)
Lengths (mm)
50
30
20
20
10
10
Crossover point
Siebers Data (Lift-off)
(b)
(a)
New Model (Lift-off)
New Model (Liquid)
0
0
0
100
200
300
Orifice Diameter (microns)
400
0
40
80
120
160
200
Pressure drop across Injector Orifice (MPa)
Figure 5: Validation of the new model against liquid length and lift-off length data for various (a) orifice
diameters, (b) pressure drop across injector orifice, at an ambient gas density and temperature of 14.8 kg/m3,
and 1000 K respectively.
Similar interplay between liquid and lift-off lengths was also observed by Siebers and Higgins [7] while
characterizing the effect of nozzle orifice diameter. The lift-off length was observed (cf. Fig. 5a) to increase with
orifice diameter, a trend well captured by simulations. However, the lift-off length is slightly underpredicted by
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Lengths (mm)
simulations. The non-premixed gas jet theory (cf. Eqn. 1) fails to explain this dependence on orifice diameter since it
predicts flame lift-off to be independent of the orifice diameter. However, this trend can be explained by the fact that
the fuel injection rate and hence the total mass injected increases with increase in orifice diameter. Hence, to form a
conducive fuel-air mixture for ignition, the amount of air to be entrained also increases thus increasing the flame liftoff length. The liquid length is seen to increase linearly with orifice diameter. This is an important result since with a
smaller orifice; smaller liquid length can be achieved thus decreasing the chances of piston and wall impingements.
This behavior is also well captured by simulations. Under these ambient and upstream conditions the new model
predicts a crossover point at about 130 µm while the measured value was about 160 µm. Perhaps a more important
observation from Fig. 5a is that with decreasing orifice diameter beyond 130 µm the interaction between fuel
vaporization and combustion processes can be avoided. The effect of injection pressure on the lift-off and liquid
lengths is shown in Fig. 5b. As the pressure drop (difference between injection and ambient gas pressure) across the
orifice increases, the lift-off length also increases. The flame lift-off length is seen to vary linearly with injection
velocity from Eqn. 1, and since injection velocity increases with injection pressure, the monotonic increase in lift-off
length with injection pressure is understandable. This trend is well captured by simulations, however, the lift-off
length underpredicted by simulations. Siebers [12] has shown that higher injection pressures do not lead to liquid
impingement on piston bowls, since the liquid length was found to be insensitive to changes in injection pressure.
Simulations predict this trend fairly well; since as the orifice pressure drop changes from 40 to 180 MPa the liquid
length decreases by about 1.5mm only. The insensitivity of liquid length to injection pressure variation is due to the
fact that the corresponding fuel flow rate change balances the change in fuel evaporation rate [12].
Figure 6 presents the effect of oxygen concentration
40
(in the ambient gas) on the lift-off and liquid lengths for
an ambient gas density, ambient gas temperature, orifice
diameter, and injection pressure of 14.8 kg/m3, 1000 K,
180 µm, and 138 MPa respectively. A 21% ambient
30
oxygen concentration is indicative of a fresh air charge
(without any EGR). Decrease in oxygen concentration
indicates increase in EGR fraction. The experimental
data is from Siebers et al. [8,9]. Once sufficient air has
20
been entrained by the spray, ignition occurs when fuelair mixtures is conducive. With decrease in oxygen
concentration in ambient air, more air needs to be
Siebers Data (Lift-off)
10
entrained thus increasing the flame lift-off length. This
New Model (Lift-off)
trend is well captured by the simulations with minor
New Model (Liquid)
overprediction for lower oxygen concentrations. Liquid
length increases with increase in ambient oxygen
0
concentration, however, is less sensitive than decrease in
14
16
18
20
22
lift-off length. Flame temperatures were also seen to
% of O2 concentration in ambient gas
decrease with diminishing oxygen concentration in
Figure 6: Validation of the new model against lift-off
ambient air (not shown here).
In the preceding two sections, we have provided length data for an ambient gas density, temperature,
extensive assessment of the new primary breakup model orifice diameter, and injection pressure of 14.8 kg/m3,
in predicting liquid length and flame lift-off 1000 k, 180µm, and 138MPa respectively. Calculated
characteristics. The new model could capture all the liquid lengths are also plotted.
experimental trends for a range of ambient and injection
conditions. However, in general the flame lift-off length was slightly underpredicted.
C. Parametric Studies: Effect of Nozzle Orifice Geometry
Having performed extensive validation of the new primary breakup model in the previous sections, simulations
were performed to characterize the effects of nozzle orifice geometry (orifice conicity and hydro-grinding) on spray
and combustion processes. Figure 7a shows the geometric details of the injector nozzle orifice used in this study.
The nozzle conicity is represented in terms of Kfactor as: K factor =
( Din − Dout ) µ m
10
(10)
where Din and Dout represent the inlet and outlet diameters in microns respectively. Hence, a Kfactor=2 (conical
nozzle) represents an exit diameter of 160 µm as compared to 180 µm for Kfactor=0 (cylindrical nozzle). The extent
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of hydrogrinding (achieved by rounding-off the inlet to the orifice) is calculated based on the ratio of radius of
curvature at the inlet to the orifice (r) and orifice radius (R).
Figure 7b plots liquid penetration for different nozzle orifice geometries at an ambient gas density, temperature,
and injection pressure of 14.8 kg/m3, 1000 K, 142 MPa respectively. The injection duration was 5ms. However,
liquid penetration and a quasi-steady flame base were observed within the first 2ms. Hence, the subsequent plots
present results upto 3ms only. With increase in nozzle orifice conicity (at a fixed r/R=0) i.e., Kfactor=0 to Kfactor=2, the
liquid length decreases from 26.8mm to 25mm i.e., by about 2mm (Note: The Kfactor=0 is the base case tabulated in
Table 2). Similar trends have been observed by Paryi et al. [31] under evaporating conditions. This is an interesting
result since under non-evaporating spray conditions, increasing Kfactor lead to higher spray penetration [5].
Cylindrical nozzles (Kfactor=0) are characterized by higher extent of cavitation and turbulence [6]. These imploding
cavitation patterns and turbulence eddies from the nozzle destabilize the jet thus promoting faster atomization which
leads to lower spray penetration under non-evaporating conditions. For evaporating sprays, the liquid length is
stabilized where rate of injection balances the fuel vaporization rate [12]. Fuel atomization and vaporization rate are
higher for cylindrical nozzle due to increased atomization owing to higher cavitation and turbulence from the nozzle.
Increased atomization was seen with the decrease in sauter mean diameter (SMD) at each time-step. The cylindrical
nozzle also has a larger exit diameter compared to the conical. Thus for the same pressure drop, the fuel injection
rate is higher for the cylindrical nozzle. The fuel injection rate seems to be the dominating effect rather than the rate
of evaporation thus leading to higher liquid penetration and liquid length for the cylindrical nozzle. At a fixed
Kfactor=0, increasing r/R to 0.14 increases liquid penetration and liquid length (cf. Fig. 7b). Previous studies [6] have
shown that increase in hydrogrinding improves the nozzle flow efficiency (discharge coefficient) hence the fuel
injection rates are higher compared to r/R=0. Higher fuel injection rates lead to increase in liquid length for the
hydroground nozzle.
r
Din
Orifice
R=Din /2
Sac
Dout
Liquid Penetration (mm)
30
25
20
15
10
K_factor=0, r/R=0
K_factor=2, r/R=0
5
(a)
(b)
K_factor=0, r/R=0.14
0
0.0
0.5
1.0
1.5
2.0
Time (ms)
2.5
3.0
Figure 7: (a) Geometrical details of the nozzle orifice, (b) Effect of nozzle geometry on liquid penetration and
liquid length at an ambient gas density, temperature and injection pressure of 14.8 kg/m3, 1000 k, 142 MPa
respectively.
Figure 8 plots the effects of nozzle orifice geometry on liquid fuel penetration and temperature contours at 8
different times for the cases plotted in context of Fig. 7b. Due to the axisymmetric nature of spray and combustion
process, visualization was possible on a cut-plane through the center of the fuel jet. The field of view in both axial
and radial directions is 108 mm for all images. Some general observations about the three nozzles will be presented
first. The initial spray and combustion development process looks very similar for all the nozzles (upto 0.75ms).
Injected fuel is represented by green color droplets; temperature contour scales are also shown. The ignition occurs
between 0.5 and 0.75ms (not shown here). At 0.75ms the liquid fuel also seems to have reached its maximum
penetration or “liquid length”. After 0.75ms, the base of the flame is seen to move upstream, while the flame-front
develops and continues to propagate downstream. At about 1.5ms after SOI, the flame base is stabilized and the
flame-front reaches the downstream wall of the combustion chamber, and is seen to propagate along the wall
thereafter. Under the given conditions, the flame lift-off length is shorter than the liquid length for all the three
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nozzle cases, thus indicating significant interplay between the fuel vaporization and combustion processes. This also
shows that perhaps ambient conditions influences flame lift-off and liquid length more than nozzle geometry itself.
First we compare the effect of nozzle orifice conicity, i.e., cylindrical nozzle (images on the left) and conical
nozzle (images on the center), on spray and combustion characteristics for a non-hydroground nozzle (r/R=0).
Although difficult to observe from the images, the liquid length is higher for the cylindrical nozzle (cf. Fig. 7b). The
flame lift-off length for cylindrical nozzle is 19.3mm while for conical nozzle it is 17.9mm. The increase in liquid
length was attributed to higher fuel injection rates for cylindrical nozzle (cf. Fig. 7b) which results in more fuel
injected at any instant. Hence, the cylindrical nozzle would need to entrain more air to form a conducive fuel-air
mixture for ignition, which leads to the increased lift-off length. In addition, the flame front propagation speed is
also higher for cylindrical nozzle. At 1.25ms while the flame for the conical nozzle is about to hit the downstream
wall, the cylindrical nozzle flame is already propagating along the walls. Higher flame front propagation speed can
be attributed to higher flame temperatures (not shown here) for the cylindrical nozzle. Since the fuel injection rates
and hence the total fuel injected was higher for the cylindrical nozzle, flame temperatures were also greater
compared to the conical nozzle.
Kfactor=0, r/R=0
Kfactor=2, r/R=0
Kfactor=0, r/R=0.14
Temperature
(K)
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Temperature
(K)
Figure 8: Illustrations of fuel spray penetration and temperature contours for different nozzle orifice
geometries.
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The effect of hydrogrinding i.e., non-hydroground nozzle (Images on the left) and hydroground nozzle (Images
on the right), on spray and combustion characteristics for a cylindrical orifice is illustrated in Fig. 8. Although
difficult to observe from the images, the liquid length is higher for the hydroground nozzle. Flame lift-off length for
non-hydroground nozzle was 19.3mm while that for hydroground nozzle was about 20.6mm. The increase in liquid
length was attributed to higher fuel injection rates for hydroground nozzle (cf. Fig. 7b), which results in more fuel
injected at any instant. Hence, the hydroground nozzle would need to entrain more air to form a conducive fuel-air
mixture for ignition, which leads to the increased lift-off length. Negligible differences in flame propagation speeds
and flame shape were observed between these two cases.
V. Conclusion
A new primary breakup model which incorporates the effects of cavitation and turbulence in addition to
aerodynamic breakup has been implemented in an engine modeling software “CONVERGE”. Extensive validation
of this model under engine like conditions has been performed using measurements of liquid length and flame liftoff length [7,8,9,10]. The effect of nozzle orifice geometry on spray and combustion processes has been
characterized.
1. The new primary breakup model is seen to perform better than the KH model in predicting the flame lift-off
length, implying that the new model provides better prediction of spray characteristics. The new model is able
to reproduce the experimentally observed effects of various parameters, such as ambient density, temperature,
injector orifice diameter, injection pressure, etc., on the liquid length and liftoff length. Moreover, the
interplay between lift-off length and liquid length was also well captured in terms of the “crossover” point.
2. Results indicate similarities in flame development characteristics for the three nozzles simulated. For most
cases, the lift-off length is generally smaller than the liquid length, indicating interplay between fuel
vaporization and combustion processes.
3. The increase in nozzle conicity decreases both the liquid length and the flame lift-off length, while the effect
of hydrogrinding is to increase the liquid and lift-off lengths.
4. Future work will involve correlating the effects of nozzle orifice geometry changes on emissions. Also the
ability of this new primary breakup model in predicting engine characteristics under full cycle operations will
be assessed.
Acknowledgments
This work is supported by the U.S. Department of Energy Office of Vehicle Technology under the management
of Mr. Gurpreet Singh. Many useful discussions with Dr. Peter Kelly Senecal of Convergent Science Inc. are greatly
appreciated.
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