This document summarizes a simulation of internal fuel flow in a multi-hole diesel fuel injector nozzle. The study aims to validate CFD models of flow at low needle lifts without cavitation and perform a grid sensitivity analysis. Results show multiple vortexes forming in the nozzle sac and hole entrance. Grid independence is approached with finer grids, and predictions of mean axial velocity generally agree with experimental laser Doppler velocimetry data, though some discrepancies remain at low velocities near walls. The study enhances understanding of non-cavitating flow fields in these injectors.

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Single phase internal flow simulation in multi-hole(6) axisymmetric diesel
fuel injector
Aishvarya Kumar1
1: School of Engineering and Mathematical Sciences, City University London, UK
Background
• Cavitation has been identified as one of the major concern in
the fuel injector [1].
• Experimental studies on multi-hole injector revealed the
occurrence of cavitation on the upper edge of the injector hole
entrance which also occurs due to pressure reduction caused
by abrupt change in the flow passage [1][2].
§ In multi-hole injectors cavitation due formation of vortexes in
the sac volume have also been observed which can be
classified as: hole to hole connecting vortex cavitation, needle
cavitation or cavitating strings emerging from needle wall
opposing the injector hole and entering the nozzle hole [1][2].
§ In fuel injectors cavitation has advantages as well as
disadvantages: Cavitation is believed to enhance primary
break-up and subsequent atomization of liquid fuel jet due to
perceived enhancement in turbulence caused by cavitation [1]
[2]. Additionally cavitation bubbles in the injector holes are
believed to enhance fuel atomization through the generation
of smaller droplets, which vapourises rapidly, consequently
enhancing fuel/air mixing and reducing ignition delay [1][2].
§ Disadvantages of cavitation such as spray shape variation
due to the presence of cavitation string have been reported
[3]. Surface erosion has been associated with cavitation as
well [4][5].
Results Results
References
[1] Arcoumanis, Constantine, et al. Investigation of cavitation in a vertical multi-hole injector. No.
1999-01-0524. SAE Technical Paper, 1999.
[2] Roth, H., M. Gavaises, and C. Arcoumanis. Cavitation initiation, its development and link with
flow turbulence in diesel injector nozzles. No. 2002-01-0214. SAE Technical Paper, 2002.
[3] Mitroglou, N., et al. "Cavitation inside enlarged and real-size fully transparent injector nozzles
and its effect on near nozzle spray formation." Proceedings of the DIPSI Workshop 2011. Droplet
Impact Phenomena & Spray Investigations. Dip. Ingegneria industriale. Università degli studi di
Bergamo, 2011.
[4] Asi, Osman. "Failure of a diesel engine injector nozzle by cavitation damage."Engineering
Failure Analysis 13.7 (2006): 1126-1133.
[5] Gavaises, M., et al. Link between cavitation development and erosion damage in diesel injector
nozzles. No. 2007-01-0246. SAE Technical Paper, 2007.
[6] Arcoumanis, Constanti, et al. Analysis of the flow in the nozzle of a vertical multi-hole diesel
engine injector. No. 980811. SAE Technical Paper, 1998.
[7] Papoutsakis, A., et al. LES Predictions of the Vortical Flow Structures in Diesel Injector
Nozzles. No. 2009-01-0833. SAE Technical Paper, 2009.
[8] njectors (automobile), 2015. URL http://what-when-how.com/automobile/
injectors-automobile/.
Summary
Test case description
Research aims:
• Hence, it becomes important to gain understanding of the flow
field and identify such low-pressure regions at non-cavitating
conditions which can be identified as prerequisites for
cavitation occurrence.
• LDV (Laser Doppler Velocimetry) has been used [6][2] to
measure velocity field inside the enlarged model of the multi-
hole injector. The LDV results have allowed researchers to
gain understanding of flow field and also provided
opportunities to CFD modellers to validate CFD models to
further improve understanding [5][6].
• Nevertheless, CFD models have not been validated for lower
needle-lift (1.6 mm) at a non-cavitating condition and grid
sensitivity analysis has not been performed too.
• The objectives of present study are:
1. Perform CFD simulation of internal flow in an enlarged (20X)
multi-hole (6) fuel injector nozzle at lower lift non-cavitating
conditions. The experimental data from [2] would be used for
evaluation.
2. Perform grid sensitivity analysis
3. Evaluate model against experimental data
4. Enhance understanding of the flow field in post processing.
• The test case geometry represents 20 times magnification of
mini-sac type axisymmetric Bosch multi-hole (6) diesel fuel
injector nozzle. The test case (enlarged nozzle) was
manufactured of an acrylic material with refractive index of
1.49.
• LDV measurement for mean axial velocity and RMS velocity
were performed at a different position inside the injector hole.
• The working fluid was a mixture of 32% by volume of tetralin
and 68% by volume of turpentine oil. The mixture was
maintained at a temperature of 25 ±0.05 degree centigrade in
order to maintain a refractive index of 1.49.
• Two sets of experiments were performed, in the first series
cavitation number was varied and Reynolds number was kept
constant, in the second series of experiment, both cavitation
number and Reynolds number were varied.
Low needle lift (1.6 mm)
Series
CN
Re
Injection pressure
Back pressure
Injection
velocity
Flow rate
1
0.44
18000
2.55 bar
1.80 bar
8.43 m s-1
N/A
2
0.44
18000
2.55 bar
1.80 bar
8.43 m s-1
0.487 ls-1
• Grid sensitivity analysis indicates similar results have been
achieved for mean axial velocity with grids 6 and 7(Figure
4(a), (b), (c) and (d)), hence it can be said that grid
independence is being approached.
• On the plane x = 9.5 mm (Figure 4 (a)) experimental data for
mean axial velocity suggest recirculation zone at the upper
portion of the injection hole. Prediction results indicate slight
overprediction of recirculation zone. However, good
agreement has been achieved has been achieved in the
remaining section of the plane (x = 9.5 mm). Nevertheless,
discrepancies can be observed between first and second
series of experimental data at all axial positions.
• On the plane x = 10.5 mm (Figure 4(b)) experimental data
again indicate recirculation regime on the top section of the
injector hole. Mean axial velocity prediction indicates good
agreement with experimental data.
• On axial position x = 13.5 mm (Figure 4(c)) experimental data
for mean axial velocity indicate reattachment has been
achieved. Predictions also indicate reattachment; however,
indicate slightly lower velocity at the upper region of the
injector hole.
• On axial position x = 16.5 mm (Figure 4(d)) experimental data
indicate flow recovery after reattachment which has been
also predicted in simulation however the axial velocity is
lower predicted than an experiment at the upper region of the
injector hole.
Centre
of
Compressor
Technology
20th
Anniversary
Event
Modelling approach
• Incompressible steady-state Reynolds Averaged Navier-
Stokes equation has been solved. Realizable k-epsilon model
has been used have been used for turbulence modelling with
Enhanced Wall Treatment method to simulate turbulence in
the near wall region.
• One-sixth of flow domain with periodic boundary conditions
has been used. The flow domain has been discretised into the
semi-structured grid which consists of tetrahedral type cells
with five layers of prism type cells in the near wall region.
• The grids were successively refined to achieve grid
independence. Grids 5, 6, and 7 were also locally refined near
the injector hole and sac region.
• Boundary condition details can
be found in table 2.
Inlet
Outlet
Interface
Walls
Mass
flow
0.0726
kg
m-­‐3
Constant
pressure
78675
N
m-­‐2
Cyclic
No-­‐slip
walls
Figure 3) (A) One-sixth flow domain at low lift with
periodic (cyclic) boundary conditions. The numbers
represents boundaries of flow domains, (1) inlet (2)
outlet (3) walls (4) periodic (cyclic) interface, (B)
Mesh for one-sixth flow domain.
Grid
Control
Volumes
Refinement
factor
Maximum
y+
1
1,792,278 1
17.7
2
6,892, 758
3.84
10.44
3
11,049, 454
616
9.54
4
19,023, 384
10.61
7.5
5
16,410, 517
9.15
7.21
6
21,216,968
11.83
7.14
7
33, 446, 472
18.66
7.15
Figure 1) Real size injector unit [8]
Figure 2) Section view of fuel injector displaying positions
where LDV measurements were taken, (a) represents
Series 1 experiments and (b) Series 2 experiments.
Table 1: Boundary conditions.
Table 2: Grid refinement description
Figure 4 (a) Figure 4 (b)
Figure 4 (d)Figure 4 (c)
Figure 5
Figure 6 (a) Figure 6 (b)
Figure 6 (c)
Figure 6 (d)
• Multiple vortexes can be observed in the sac volume rotating
in anti-clockwise (yellow circle, Figure 6(a)) and clockwise
direction (blue circle, Figure 6(a)). Recirculation region can
be seen in the injector hole (orange circle, Figure 6(a)).
• Corresponding to recirculation region, lower pressure region
can be identified at the upper edge of hole entrance (Figure
6(b)).
• Vortex can also be seen (Figure 6(c)) at the injector cartridge
before the fluid enters the seat annulus.
• Velocity profiles at different planes in injector hole (Figure
6(d)).
• Grid independence is being approached with grid 6 and 7.
• Fairly good agreement achieved with experimental data for
mean axial velocity.
• Vortical structures observed inside the sac volume of the fuel
injector nozzle,
Contact info
Aishvarya Kumar
PhD Candidate, City University
Northampton Square
London, ECIV 0HB
Email: Aishvarya.kumar.2@city.ac.uk