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Citation: Andriotis, A., Gavaises, M. and Arcoumanis, C. (2008). Vortex flow and
cavitation in diesel injector nozzles. Journal of Fluid Mechanics, 610, pp. 195-215. doi:
10.1017/S0022112008002668
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J. Fluid Mech. (2008), vol. 610, pp. 195–215.
c
2008 Cambridge University Press
doi:10.1017/S0022112008002668 Printed in the United Kingdom
195
Vortex flow and cavitation in diesel
injector nozzles
A. ANDRIOTIS, M. GAVAISES† AND C. ARCOUMANIS
Research Centre for Energy and the Environment, School of Engineering and Mathematical Sciences,
City University, London, Northampton Square, EC1V 0HB London, UK
(Received 31 August 2007 and in revised form 29 May 2008)
Flow visualization as well as three-dimensional cavitating flow simulations have been
employed for characterizing the formation of cavitation inside transparent replicas
of fuel injector valves used in low-speed two-stroke diesel engines. The designs tested
have incorporated five-hole nozzles with cylindrical as well as tapered holes operating
at different fixed needle lift positions. High-speed images have revealed the formation
of an unsteady vapour structure upstream of the injection holes inside the nozzle
volume, which is referred to as ‘string-cavitation’. Computation of the flow distribution
and combination with three-dimensional reconstruction of the location of the strings
inside the nozzle volume has revealed that strings are found at the core of recirculation
zones; they originate either from pre-existing cavitation sites forming at sharp corners
inside the nozzle where the pressure falls below the vapour pressure of the flowing
liquid, or even from suction of outside air downstream of the hole exit. Processing of
the acquired images has allowed estimation of the mean location and probability
of appearance of the cavitating strings in the three-dimensional space as a function
of needle lift, cavitation and Reynolds number. The frequency of appearance of the
strings has been correlated with the Strouhal number of the vortices developing inside
the sac volume; the latter has been found to be a function of needle lift and hole
shape. The presence of strings has significantly affected the flow conditions at the
nozzle exit, influencing the injected spray. The cavitation structures formed inside
the injection holes are significantly altered by the presence of cavitation strings and
are jointly responsible for up to 10 % variation in the instantaneous fuel injection
quantity. Extrapolation using model predictions for real-size injectors operating at
realistic injection pressures indicates that cavitation strings are expected to appear
within the time scales of typical injection events, implying significant hole-to-hole and
cycle-to-cycle variations during the corresponding spray development.
1. Introduction
The realization that diesel injector nozzles may cavitate under typical operating
conditions inevitably adds a degree of complexity to the system design since, until
recently, it was not clear how and when cavitation is formed and most importantly
whether it has a beneficial influence on the exiting spray and the subsequent auto-
ignition process. Relevant publications on the subject of cavitation in real-size diesel
injectors are those of Chaves et al. (1995), Chaves & Obermeier (1998), Badock
et al. (1999), Arcoumanis et al. (2000), while a number of studies have examined
† Author to whom correspondence should be addressed: m.gavaises@city.ac.uk
196 A. Andriotis, M. Gavaises and C. Arcoumanis
the development of cavitation in simplified transparent nozzle replicas, for example
He & Ruiz (1995), Soteriou, Andrews & Smith (1995), Kim, Nishida & Hiroyasu
(1997), Soteriou et al. (2001). Despite the significant amount of work, there is still
uncertainty surrounding the advantages offered by the random formation of cavitation
in enhancing the two-phase flow mixture at the exit of the nozzle and the effect this
may have on possible wear of the nozzle metal body, as discussed by Gavaises et al.
(2007). One approach gaining some support tries to eliminate cavitation completely
through appropriate design of the hole entry and non-cylindrical shape of the holes
(Blessing et al. 2003; Soteriou et al. 2006). Irrespective of the prevailing trend in
nozzle design, thorough understanding of the nozzle internal flow is a prerequisite for
designing the next generation of diesel engines for passenger cars, commercial and
marine applications. Cavitation in such nozzles has been identified in two distinct
forms according to Arcoumanis & Gavaises (1998) and Roth, Gavaises & Arcoumanis
(2002). The geometric-induced cavitation is a relatively well-known phenomenon
initiating at sharp corners where the pressure may fall below the vapour pressure
of the flowing liquid. A second form of cavitation has been observed, and referred
to as ‘string’ or ‘vortex’ cavitation by Afzal et al. (1999) and Roth et al. (2002).
These two-phase flow structures are usually found in the bulk of the liquid, in the
areas where large-scale, relative to the nozzle geometry, vortices exist. Although more
recent studies have shown similar behaviour in various types of multi-hole nozzles, for
example Nouri et al. (2007), their formation process has been found to be relatively
irregular while their interaction with the mean flow remains poorly understood. Other
studies on cavitation performed in venturi-type nozzles, for example see Gopalan,
Katz & Knio (1999) and Gopalan & Katz (2000), have employed laser diagnostics to
provide insight into the mechanism of bubble entrapment into vortical flow structures,
but the complexity of the geometry of diesel injectors makes it difficul to obtain
such measurements. Furthermore, because of the difficulty in obtaining real-time
measurements during the injection process, most of the reported experimental studies
refer to experimental devices simulating operating conditions relevant to those of
diesel engines. Nevertheless, simplifications to the design of the nozzle itself or to the
transient operation of the needle are unavoidable, which has implications on the very
short injection durations and the very high liquid velocities, of the order of 400 m s
−1
in production injectors. Parallel to the continuing effort to obtain better experimental
information under as realistic conditions as possible, there is an increasing demand for
developing and validating computational fluid dynamics models to predict cavitation.
An increasing number of numerical models have appeared over the years in the
literature which allow the formation and development of cavitation inside the nozzle
to be simulated (Kubota, Kato & Yamaguchi 1992; Avva, Singhal & Gibson 1995;
Schmidt, Rutland & Corradini 1997; Alajbegovic, Grogger & Philipp 1999; Marcer
et al. 2000; Sauer, Winkler & Schnerr 2000; Singhal et al. 2001, 2002). Each model
is based on different assumptions while various numerical methodologies have been
used for implementation in commercial or in-house fluid-flow solvers. Most models
are based on the assumption that cavitation is a mechanically driven phenomenon
initiated by the presence of nuclei which grow to become bubbles and then form the
complex cavitation structures observed experimentally. Despite the effort devoted to
developing cavitation models applicable for fuel injectors, all of those applied so far
have focused on geometric-induced cavitation. It can be argued that there is no model
yet capable of predicting string cavitation in fuel-injection equipment. This is mainly
due to the lack of experimental data available for the relevant flow phenomena and,
thus, the incomplete physical understanding of the process. As it will be revealed later
Vortex flow and cavitation in diesel injector nozzles 197
in this paper, the aforementioned models are, in principle, incapable of simulating
string cavitation inside injector nozzles. Some studies on vortex cavitation, for example
Chahine & Duraiswami (1992) and Chahine & Kalumuck (2002), which represent
a promising theoretical background to this problem, have not yet been applied to
nozzle flows.
The present paper represents an extension to Gavaises & Andriotis (2006) and aims
to provide new experimental data for the origin, formation, development, lifetime and
influence on the nozzle hole flow of vortex-type or string cavitation. The designs
investigated include multi-hole injectors used in low-speed two-stroke diesel engines.
The specific design of these nozzles allows for clear optical access to all holes
and the nozzle sac volume to be obtained. In addition, their relatively large size
compared to that of automotive injectors offers the possibility of obtaining images
of cavitation in a 1:1 scale. This has been achieved by manufacturing a number of
fully transparent acrylic nozzle replicas, which have allowed optical access into the
nozzle volume upstream of the injection holes, inside them as well as into the sprays
formed at the nozzle exit. The designs tested include a number of cylindrical as well
as tapered (converging) holes; the latter greatly modify the pressure distribution at
the hole entry and may prevent formation of geometric cavitation, thus, providing
evidence about the origin of string cavitation in the absence of hole cavitation. Use
of two synchronised high-speed cameras has allowed reconstruction of the location
of the cavitation strings inside the three-dimensional nozzle sac volume as well as
characterization of the frequency of their appearance and development, as a function
of the needle lift, cavitation and Reynolds number. Use of computational fluid
dynamics (CFD) models has provided information about the local flow field at the
location where cavitation strings start developing. Image collection over long enough
times has provided information about their lifetime and an estimate of the mean
volume they occupy inside the nozzle tip. At the same time, measurements of the
flow rate both in the absence and in the presence of cavitation strings has provided
information about their effect on the flow-rate variation between individual injection
holes. These measurements have been combined with flow imaging of the cavitation
structures inside the injection holes. As expected, the hole flow is influenced by the
co-existence and interaction of the geometric-induced cavitation, which is normally
always present, and the relatively unsteady string cavitation. In turn, simultaneous
imaging of the flow inside the nozzle holes and the near nozzle spray formation
has shown that the atomization process of the injected liquid is greatly affected by
the cavitation strings. This results not only in uneven liquid dispersion within the
significantly increased spray cone angle, but also in hole-to-hole variations.
The next section of the paper describes the experimental set-up used, followed
by a brief description of the CFD model employed for simulating the single-phase
internal nozzle flow as well as the cavitation formation and development inside the
injection holes. Then the various results obtained are presented, followed by the most
important findings which are summarized at the end.
2. Experimental set-up and test cases
Various transparent five-hole nozzles were manufactured from a transparent acrylic
material; the nozzle geometry is shown in figure 1. All holes are concentrated on
one 90
◦
sector; this is because of the size of the engine they operate which has a
bore diameter of about 1.0 m. Three fuel valves are installed on the engine cylinder
head which inject the fuel circumferentially – rather than in the radial direction as
198 A. Andriotis, M. Gavaises and C. Arcoumanis
(a)(b)(c)
Fuel inlet
Hole 1
Hole 5
Expansion
tubes
Needle lift
Fuel exit
D
sac
Figure 1. Nozzle geometries investigated (a) 5-hole nozzle without expansion tubes, (b) 5-hole
nozzle with expansion tubes and (c) unstructured computational grid for the 5-hole nozzle
with local refinement upstream and at the entry to the injection holes.
in passenger car diesel engines. Another important characteristic of this nozzle is the
shape of the needle. As can be seen in figure 1, there is a hollow slide-type needle
which seals the injection holes directly, leaving almost zero sac volume when it closes.
When the needle opens, the slide uncovers the injection holes and fuel flows from the
fuel line in the inner part of the hollow needle, allowing fuel injection. The volume
below the needle and upstream of the injection holes will be referred to as ‘nozzle
volume’, and it is equivalent to the ‘sac volume’ of passenger car diesel injectors.
The transparent nozzle of figure 1(a) is manufactured on a 1:1 scale and it injects
liquid directly into ambient air under room temperature and atmospheric pressure;
the working fluid is water at 25
◦
C. This nozzle was used for visualization of the
liquid atomization process which also allowed at the same time visualization of the
cavitation strings. The nozzle of figure 1(b) was enlarged to a 2:1 scale and it was used
for investigating the internal nozzle flow in more detail; specially designed discharge
channels were manufactured for allowing injection into liquid without restricting the
nozzle hole flow upstream. In this way, splashing of the liquid on the outer surfaces
of the injector was prevented and thus, clear images of the internal nozzle flow have
been obtained. Two different versions of nozzles have been manufactured, one with
cylindrical and one with tapered holes. The nominal injection hole exit diameter for
both real-size nozzle designs is about 1.5 mm while the tapered holes incorporate a
4
◦
full cone angle; the needle lift at its full (stop) position is about 3.7 mm.
The test rig used has been used in a number of studies and it is described in
detail by Roth et al. (2002). The flow rate was controlled by a valve in the pipe
downstream of the feed pump and measured by an ultrasonic flow meter. The flow
rate from each of the injection holes was also measured simultaneously with the
incoming flow rate. Both the injection pressure and the pressure downstream of the
injection holes were adjusted by restricting the inflow and outflow of the injector,
respectively. In order to reach sub-atmospheric back pressures corresponding to
higher cavitation numbers, a suction pump was installed in addition to the main
feed pump. The Reynolds number has been defined on the basis of the mean flow
rate and the average hole diameter while the cavitation number is defined here as
