Post on 28-Jan-2023
ILASS – Europe 2010, 23rd Annual Conference on Liquid Atomization and Spray Systems, Brno, Czech Republic, September 2010
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URANS and SAS analysis of flow dynamics in a GDI nozzle
J.-M. Shi*, K. Wenzlawski*, J. Helie
†, H. Nuglisch
†, J. Cousin°
* Continental Automotive GmbH
Siemensstr. 12, 93055 Regensburg, Germany † Continental Automotive SAS
1 av. Paul Ourliac BP 1149, 31036 Toulouse Cedex 1, France
° Coria
INSA de Rouen, Campus du Madrillet - BP 8, 76801 Saint Etienne du Rouvray cedex, France
Abstract
URANS and SAS analysis of turbulent flow in a GDI nozzle was carried out. The vortex structures, velocity and
pressure distributions predicted based on the two different approaches were compared both for instant and statis-
tical values. FFT analysis was applied to the time series of mass flow rate, the velocity, pressure and turbulence
quantities at monitoring points. Only one dominant frequency was predicted by the URANS approach using the
SST turbulence model. A clear correlation was found among the frequency of the mass flow rate, pressure and
velocity at monitor points. In contrast, SAS predicted multiple frequencies. Though no simple correlation was
obtained, the frequency of big event in mass flow time series was found to be linked to the first dominant fre-
quency of the pressure monitors.
Introduction
The quality of spray and mixture formation in engine can be very different from fuel injection nozzle A to
nozzle B even under the same operating conditions. This indicates a strong effect of the in-nozzle flow on spray
formation. This work is an effort in pursuing understanding about the link between nozzle internal flow and
spray formation. For this purpose, high resolution zoomed spray visualization study in the proximity of the noz-
zle exit for a three-hole GDI injector were carried out at CORIA in cooperation with Continental Automotive.
The liquid ligaments in the process of primary breakup are clearly recognizable under an injection pressure up to
20bar. The obtained shot-to-shot spray images indicate that there exist multiple frequencies in the primary
breakup process. The simulation work reported here was to find the link between the in-nozzle flow and the pri-
mary breakup frequencies in order to obtain new understanding of atomization mechanism.
The flow in a fuel injection nozzle is characterized by high shear strain rate, high flow acceleration and de-
celeration, and high pressure gradient linked with throttle geometries. Therefore, vortex generation and their
dynamics in the nozzle is the key point to understand the flow dynamics. The simulation work was based on the
commercial CFD solver ANSYS-CFX12.0. The URANS approach based on the k-omega SST model [1] and the
Scale-Adaptive-Simulation (SAS) approach [2] were applied. The latter is also a RANS modelling approach but
with a DES-like capability, allowing to resolve the turbulence vortex structures in the region where the mesh size
is below the local physical turbulence scale. In this paper, we present a case study for the injection pressure
10 bar. The experience we made in house and also in literature [4] is that simulation of turbulent cavitating flow
in fuel injection nozzle is very sensitive to cavitation modelling. Here we restricted our study to deal with the
single-phase flow without considering cavitation. Best practice study for the mesh size and time step dependence
were carried out. Instant results and time average and RMS values of field variables and monitor quantities were
compared for 3 different computational grids. FFT analysis was applied to the time series of mass flow rate, the
velocity, pressure and turbulence quantities at monitoring points. Correlation or link between the mass flow rate,
pressure monitors, and the vortex motion was examined. The spray visualization study is still on going in order
to obtain a reliable statistics for the primary breakup frequencies. Here we mainly report the results from the
numerical study.
Simulation model and Numerical methods
The nozzle is axis-symmetrical with three injection holes. A 120°-sector geometrical model was adopted in
simulation and a cyclic period condition was applied at the sector boundaries (see Figure 1, left). Three monitor-
ing points were defined (see Figure 1, right) in order to get time series of the local velocity, pressure, and turbu-
lence variables. The fluid applied was n-heptane, with a density 680 kg/m3 and a viscosity 3.885e-4 Pa∙s. Ne-
glecting the cavitation model, a single phase turbulent flow problem of incompressible fluid was considered. The
Corresponding author: Junmei.Shi@continental-corporation.com
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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commercial flow solver ANSYS-CFX12.0 was applied to the investigation. Both URANS simulation based on
the k-ω SST two-equation model [1] and Scale-Resolved simulation based on the SST-SAS modelling [2] were
carried out. The SAS model is also based on the RANS two-equation modelling approach, but with a DES-like
capability. A detailed description of the CFX SST-SAS model could be found in [3]. This model differs from the
SST-RANS model by an additional SAS source term QSAS in the transport equation for the turbulence eddy fre-
quency ω,
0,,maxmax
2
2
2
2222
2 k
kk
LL
SAS CSQvK
(1)
Where S is the shear strain rate, k is the turbulence kinetic energy, 4/1/CkL is the length scale of the
modelled turbulence and 12 ,/max SvK CUSL is the von Karman length scale corresponding to a three
dimensional generalisation of the classic boundary layer thickness definition )(/)( yUyU . Here the coeffi-
cient 1SC times the local mesh size is introduced as the lower limiter for vKL to control damping of the finest
resolved turbulent fluctuations as in LES. This limiter was derived from the consideration of preventing the SAS
eddy viscosity SLC vKSASt 2)( from decreasing below the LES Smagorinsky subgrid-scale eddy viscos-
ity SCSLESt 2)( .
The CFX SAS implementation adopts a second order upwind scheme in RANS regions and a second order
central scheme in the LES region. Three meshes with about 0.9 M, 1.6 M and 3.0 M hexa cells (Figure 2) were
prepared for the analysis. Best Practice study for mesh size and time step were carried out. Vortex structure, ve-
locity and pressure distribution from the two approaches were compared each other in terms of instant, time av-
eraged values and the standard deviations. FFT analysis was applied to get frequencies of mass flow rate, veloc-
ity, pressure and turbulence quantities at various monitoring points as displayed in Figure 1. Correlation or link
between the mass flow rate, pressure monitors, and the vortex motion was examined.
Figure 1. Computational domain, boundary conditions (left) & monitoring points (right)
Figure 2. Computational meshes at injection hole outlet, the total mesh size is from left to right 0.9M, 1.6M,
3.0M cells, respectively
total pressure 11 bar at inlet
opening static pressure 1 bar at outlet
cyclic period cyclic
period
Sac center Injection hole
entrance center
Outlet center
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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Results and Discussion
Vortex visualization
Vortex structures and their dynamics are the key points to capture the flow dynamics. The instant vortex
cores in the nozzle from the SAS analysis using the 0.9M mesh are visualized in Figure 3 by applying the 2nd
invariant of the velocity gradient tensor, VVQ
2 . Three counter-rotating vortex pairs, which enter
the injection hole from the sac-volume, can be observed. The ring vortices mainly linked to the flow separation
due to the sudden expansion of the geometry in the sac. The sac vortex pairs are caused by flow acceleration
when the fluid is entering the injection hole from the sac volume. Strong vortices separating from the needle
surface in the region direct over the injection hole entrance were also predicted.
Figure 3. Vortex core visualization in the nozzle, Q=2.5e11 [s-2
], SST 0.9M mesh.
Figure 4 compares the instant vortices in sac volume for the SST and the SAS results of various meshes,
where the iso-surfaces are coloured by the pressure values from 0 to 10 bar. For the coarse mesh of 0.9 M cells
the SAS approach and the SST model predicted similar sac vortex structures to each other, with some smaller
vortices in the region direct over the injection hole entrance observed in the SAS results (Figure 4 a-b). With
increasing mesh refinement (Figure 4 c-d) the SAS approach predicted many fine-scale vortices instead of the
big ring vortices in the corresponding region as observed in Figure 3 or in Figure 4 a-b). The flow is relatively
inactive in the sac centre. Hence similar vortex structures were obtained for all cases.
A comparison of instant vortices in injection hole is presented in Figure 5, where the Q iso-surfaces are col-
oured by the pressure in the range from -2 bar (blue) to 2 bar (red). Negative pressure is predicted in the vortex
cores in injection hole, which is a consequence of neglecting cavitation in the present simulation model and can
be considered as an indication of cavitation occurrence. The results indicate strong vortex cavitation in the injec-
tion hole. With reference to these vortex structures it can be expected that the SAS and the URANS-SST ap-
proach are to predict very different vortex structures and thus different vortex cavitation behaviour and different
flow dynamics. Also, the results displayed in Figure 6 for the instant pressure distribution at the symmetrical
plane of the injection hole indicate that the vortex cavitation prediction is sensitive to the mesh resolution.
Figure 4. Vortices in sac-volume coloured by pressure in the range 0-10 bar
a) SST, 0.9M mesh
Q=0.81e12 [s-2
] b) SAS, 0.9M mesh
Q=1.44e12 [s-2
]
d) SAS, 3.0M mesh
Q=1.44e12 [s-2
]
c) SAS, 1.6M mesh
Q=1.44e12 [s-2
]
Needle shear vortices
Ring vortex sepa-rated from needle
sac vortex due to flow acceleration
needle separation
vortices linked to injection
hole
Ring vortex at sac wall
sac bottom vortex due to flow acceleration
sac vortex due to flow acceleration
Ring vortex sepa-rated from needle
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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Figure 5. Vortices in injection hole coloured by pressure in the range -2 bar to 2 bar
Figure 6. Instant pressure at symmetrical plane coloured by pressure values in the range -2 bar to 2 bar
The corresponding time averaged vortex structures are displayed in Figure 8, coloured according to the pres-
sure fluctuation. The time averaged vortex structures in the sac volume are alike to each other and the ring vor-
tices as observed in Figure 3 are again recognizable in the statistics sense of the SAS results (Figure 7, top). In
contrast, the time statistical vortex structures in injection hole are less similar between the SAS and SST results.
The time mean vortex cores in SST simulation are similar to the instant vortices in Figure 5, with long and
smooth Q iso-surfaces. Due to multiple scale vortices with higher fluctuations were resolved in SAS, the time
average of the vortex cores are much shorter and more irregular than in SST (Figure 7, bottom). This difference
is also reflected in the time averaged pressure distribution over the symmetrical plane of the injection hole pre-
sented in Figure 8. However, these averaged pressure distributions show very similar pattern in all cases, and are
similar to the instant SST results presented in Figure 6. That suggests, URANS simulation is sufficient to capture
the mean flow features in the statistical sense.
Figure 7. Time averaged vortex structures in sac-volume (top, coloured by standard pressure deviation 0-1.5
bar) and in injection hole (bottom, coloured by standard pressure deviation 0-4 bar), Q=0.81e12 [s-2
]
In comparison, the colour of the iso-surfaces in Figure 7 indicate that the SAS approach predicted much
higher fluctuations than the SST model both in the sac volume and in injection hole. The standard deviation of
pressure and velocity over the symmetrical plane, displayed in Figure 9 and Figure 10, also confirm this conclu-
sion. With a reference to Figure 5, Figure 7, Figure 8, Figure 9 and Figure 10 together, it can be concluded that
a) SST, 0.9M mesh
Q=0.81e12 [s-2
] b) SAS, 0.9M mesh
Q=2.5e12 [s-2
]
d) SAS, 3.0M mesh
Q=2.5e12 [s-2
]
c) SAS, 1.6M mesh
Q=2.5e12 [s-2
]
a) SST, 0.9M mesh b) SAS, 0.9M mesh d) SAS, 3.0M mesh c) SAS, 1.6M mesh
a) SST, 0.9M mesh b) SAS, 0.9M mesh d) SAS, 3.0M mesh c) SAS, 1.6M mesh
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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the strongest vortices in the injection hole and the strongest flow fluctuation as well occur in the centre region of
the injection hole.
Figure 8. Time averaged pressure at symmetrical plane
Figure 9. Standard deviation of pressure over symmetrical plane, 0 - 4bar
Figure 10. Standard deviation of velocity over symmetrical plane, 0 - 30 m/s
Time series of monitors
Time series were recorded for the local velocity, pressure, turbulence quantities at the monitor points (refer
to Figure 1) and for the mass flow rate weighted average of turbulence kinetic energy, eddy viscosity, and turbu-
lence length scale at the injection hole exit. As an example, a section of results for the mass flow rate and sac
centre pressure are demonstrated in Figure 11. The SST time series are quite regular and seem to correlate each
other. In comparison the SAS results are very irregular, show multiple frequencies. No simple correlation be-
tween the mass flow rate and the sac centre pressure can be observed in SAS.
Figure 11. Time series of monitored quantities
a) SST, 0.9M mesh b) SAS, 0.9M mesh d) SAS, 3.0M mesh c) SAS, 1.6M mesh
a) SST, 0.9M mesh b) SAS, 0.9M mesh d) SAS, 3.0M mesh c) SAS, 1.6M mesh
a) SST, 0.9M mesh b) SAS, 0.9M mesh d) SAS, 3.0M mesh c) SAS, 1.6M mesh
Mass flow rate
7170
7415
7730
7930
Sac center pressure
Time step a) SST, 0.9M mesh
10030
11110
12240
Time step b) SAS, 1.6M mesh
12750 Mass flow rate
Sac center pressure
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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The arithmetic mean value of the monitoring quantities and the corresponding relative fluctuations based on
the standard deviations are summarized in Table 1. The mean values from SAS show a convergence trend with
increasing mesh refinement. Especially, the average values of the modelled turbulence quantities at the nozzle
outlet in SAS 1.6M mesh and in SAS 3.0M mesh are almost identical. This indicates a sufficient grid resolution.
The standard deviation values also show the similar trend except for the value of pressure monitor at the injec-
tion hole entrance centre. Considering that turbulence eddies larger than the mesh size is direct resolved in SAS,
the predicted (modelled) turbulence kinetic energy in SAS is much lower than the corresponding SST results.
The eddy viscosity in the SST simulation is two orders higher than the molecular viscosity. The modelled eddy
viscosity in SAS is about one order lower than the value from SST. The average length scale of the modelled
turbulence is about 10 μm in SAS, which is about one fourth of the corresponding SST result. In addition, the
standard deviations are much higher in the SAS results, indicating higher fluctuations predicted by the SAS ap-
proach. That is consistent with those results shown in Figure 7, Figure 9 and Figure 10.
Table 1. Mean and standard deviation values of the monitors
Parameter
Time mean value
Standard deviation / Time mean
* 100%
SST
0.9M
SAS
0.9M
SAS
1.6M
SAS
3.0M
SST
0.9M
SAS
0.9M
SAS
1.6M
SAS
3.0M
Mass flow rate [g/s] 1.218 1.222 1.200 1.198 0.7 1.17 0.95
1.24
Average modelled turbulence
length scale @outlet [mm] 4.2e-2 1.2e-2 9.76e-3 9.74e-3 2.3 5.7 4.7 5.16
Average modelled turbulence
kinetic energy @outlet [J/kg] 60.8 22.5 20.6 20.3 6.6 12.9 10.7 11.3
Average modelled eddy viscosity
@outlet [Pa s] 3.4e-2 4.2e-3 3.3e-3 3.3e-3 11.6 28.8 29.2 35.5
Pressure @ Sac-center [bar] 11.01 10.99 10.91 10.85 1.3 1.6 1.8 1.9
Pressure @ injection hole
entrance center [bar] 2.58 2.34 2.39 2.37 13.8 49.7 57.5 48.1
Velocity w @outlet center [m/s] 22.2 19.6 20.5 21.0 12.9 41.1 37.2 39.0
Velocity u @outlet center [m/s] 20.1 27.0 27.7 28.1 34.7 41.1 36.1 38.1
FFT analysis of monitor time series
FFT analysis was applied to the time series of the monitor quantities. First, statistical convergence of the
power spectrum was examined. An example is demonstrated in Figure 12 for the time series of the mass flow
rate from the SST simulation. Here a main frequency of 21.6 kHz was obtained, corresponding to a time period
of 4.6e-5 [s]. The power spectrum can be considered as converged when the time reaches 5.55e-4 [s], corre-
sponding to 12 time period. Therefore, a time interval larger than 10 time periods is necessary in order to get a
converged FFT analysis result.
Figure 12. Convergence examination for FFT analysis of the mass flow rate time series from SST simulation
using 0.9M mesh. The results indicate that 10 periods of time is needed to get a converged power spectrum
Time = 0 to 5.55e-4 [s]
Time = 0 to 8.33e-4 [s]
Time = 0 to 11.11e-4 [s]
Time = 0 to 3.33e-4 [s]
Time = 0 to 4.44e-4 [s]
Frequency [kHz] 0 10 20 40 50 30
P
o
w
e
r
S
p
e
c
t
r
u
m
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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The results for the URANS simulation based SST model are presented in
Figure 13. A dominant frequency of 21.6 kHz is predicted for all the monitor quantities. This result is to ex-
pect in the RANS modelling, which can only resolve one scale. The interesting thing is the clear correlation
among all these monitors of different locations. A mono frequency for all the monitors as predicted by the SST
model was not predicted in SAS. It was found that the frequencies of the mass flow rate fluctuation are well cor-
related to the monitors located in the sac centre, as is displayed in Figure 14. Here two main frequencies, 12.5
kHz and 25 kHz, were predicted. In order to capture the main frequency of the flow, we evaluated the big events
in pressure fluctuation at the sac centre (shown in Figure 15). The results are shown in Figure 16. It was found
that the frequency 25 kHz is the dominant frequency in the pressure fluctuation and in the relatively stronger
vortex shedding from the needle. In addition, the vortex structures in the injection hole predicted by SAS are
shown in Figure 17. More fine scale vortices can generally be observed in the injection hole at the time points of
low mass flow rate.
It needs to point out that the above work was restricted to single phase flow model. The flow frequencies in
mass flow rate can be very different if the cavitation model is included. In addition, the spray visualization work
is still on going at Continental Automotive. A comparison between simulation and measurement is planned.
Conclusion
The present URANS and SAS analysis has revealed the vortex structures in a GDI nozzle. The results allow
draw the following conclusions:
The URANS approach based on the SST model can only resolve one scale, while the SAS model can resolve
multiple scales using mesh refinement.
The SST and SAS model predicted very different instant vortex structures in the nozzle. Thus it is to expect,
both model will produce very different results for vortex induced cavitation in injection hole.
The both models were found to produce similar time averaged vortex structures in the sac-volume, but the
SAS model predicted much higher fluctuations than the SST model.
A mono flow frequency and a clear correlation between the mass flow rate and all the monitors were pre-
dicted by the SST model. In comparison, multiple frequencies were obtained in SAS. The overall correlation
predicted by the SST model was not observed in SAS.
Acknowledgement
The authors would like to thank the internship students Mr. Ivan Krotow and Mr. Madhukar Kulkarni for the
assistance with the post-processing and FFT analysis.
The simulations were performed on the High Performance Computers at RRZE in the framework of coop-
eration with Prof. Dr.-Ing. Michael Wensing at University of Erlangen, which together with the support of Dr.-
Ing. Thomas Zeiser at RRZE and is gratefully acknowledged.
References
[1] Menter, F.R., Zonal two equation k-ω turbulence models for aerodynamic flows, AIAA Paper 93-2906
(1993).
[2] Menter, F.R., and Egorov, Y., A scale adaptive simulation model using two-equation models, AIAA Paper
2005-1095 (2006).
[3] Menter, F.R., and Egorov, Y., Development and application of SST-SAS turbulence model in the DESIDER
Project, Second Symposium on Hybrid RANS-LES Methods, 17/18 June 2007, Corfu, Greece.
[4] Giannadakis E., Papoulias D., Gavaises M., Arcoumanis C., Soteriou C. and Tang W., Evaluation of the
predictive capability of Diesel nozzle cavitation models, SAE 2007-01-0245.
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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Figure 13. FFT analysis results for the time series of monitors: SST 0.9M mesh
0 10 20 30 40 50
Frequency [kHz]
Outlet mass flow rate
Sac-center total pressure
Inj. hole entrance center
total pressure
Inj. hole entrance center velocity U
Inj. hole entrance center velocity V
Inj. hole entrance center velocity W
Inj. hole entrance center
turbulence kinetic energy
Inj. hole entrance center
eddy viscosity
Outlet center total pressure
Outlet center velocity U
Outlet center velocity W
Outlet center
turbulence kinetic energy
Outlet center eddy viscosity
Outlet center velocity V
21.6 kHz
50
ILASS – Europe 2010 URANS and SAS analysis of flow dynamics in a GDI nozzle
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Figure 14. Correlation between the frequency of mass flow rate and the monitor quantities at sac centre
Figure 15. Big events evaluation for the sac centre pressure fluctuation
Figure 16. Big events frequency distribution in sac centre pressure (left) and mass flow rate (right)
0 10 20 30 40 50 60 70 80 90 100
[kHz]
1 2 3
Turbulence kinetic
energy
Eddy viscosity
Turbulence length
scale
0 10 20 40 50 30
Mass flow rate 12.5 kHz 25 kHz
Frequency [kHz]
Power Spectru
m
0 5 10 15 20 25 30 35 40 45 50
[kHz]
1 2
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 [ms]