International Journal of Heat and Fluid Flow 44 (2013) 140–154
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International Journal of Heat and Fluid Flow
journal homepage: www.elsevier.com/locate/ijhff
Visualization and analysis of the characteristics of transitional
underexpanded jets
Jingzhou Yu ⇑, Ville Vuorinen, Ossi Kaario, Teemu Sarjovaara, Martti Larmi
Department of Energy Technology, Aalto University, Finland
a r t i c l e
i n f o
Article history:
Received 1 June 2012
Received in revised form 8 April 2013
Accepted 23 May 2013
Available online 25 June 2013
Keywords:
Transitional underexpanded jets
Shock waves
PLIF
LES
a b s t r a c t
Underexpanded jets can be formed when high-pressure gaseous fuel is injected directly into an engine
cylinder. In such conditions, shock waves are formed immediately near the nozzle exit. In the present
study, the flow structure and turbulent mixing of pulsed jets issuing from a circular nozzle is investigated
using acetone planar laser-induced fluorescence (PLIF). By monitoring axial and various radial cross-sections under different injection pressure conditions, different features of gaseous jets are visualized and
interpreted. The temporal development of the axial cross-sections reveals three typical jet flow patterns
(subsonic, moderately underexpanded, and highly underexpanded) during the injection. These stages are
(1) well described with the observed shock structures and (2) noted to take a considerably long portion of
the full injection process. The visualizations from the radial cross sections show how the nozzle inflow
conditions may influence the primary and the azimuthal (secondary) instability of the jet which influences the turbulence transition process and the mixing process. The results indicate the importance of
inner nozzle flow on the flow behavior. For example, systematic asymmetries in the mean concentration
fields are observed. In addition to PLIF data, numerical simulations can be used to support the experimental picture of the jet behavior. We give examples of large-eddy simulations (LESs) in order to further
explore the behavior of the underexpanded jets. Results show that LES is able to reproduce the basic
physics of underexpanded jets. LES and PLIF compare favorably in terms of the barrel shock structures
and the description of the normal shocks. LES also provides detailed flow field information including temperature, Mach number, concentration and scalar dissipation rate (SDR).
Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction
1.1. Motivation
Reducing air pollution and dependence on fossil fuels is crucial
for the sustainable development of the conventional internal combustion engines (ICEs). Natural gas (NG), a fuel abundant in nature,
is considered as one of the most promising alternative fuels for
ICEs (Korakianitis et al., 2011). Among fossil fuels, NG combustion
has the lowest level of greenhouse gas emissions along with negligible amounts of suspended particles and photochemical smog
promoters (Baratta et al., 2009). Recently, compressed natural
gas (CNG) port-injected spark-ignition (CNG-SI) engines have already reached the commercial production stage (e.g., city buses
and taxi cars). However, the power output and the emissions of unburned hydrocarbons are limited by the low volumetric efficiency
and a fuel short-circuit from inlet to exhaust. To further improve
the performance of CNG engine, many automotive engine
⇑ Corresponding author. Address: Puumiehenkuja 5 A, Espoo, FI-00076 Aalto,
Finland.
E-mail address: jingzhou.yu@hotmail.com (J. Yu).
0142-727X/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.ijheatfluidflow.2013.05.015
researchers believe that CNG direct-injection compression-ignition
(CNG-DICI) engine has a great potential to improve the thermal
efficiency and to meet the stringent emission regulation limits in
the near future (Kalam and Masjuki, 2011; Li et al., 2011; Yu
et al., 2013).
A major challenge of CNG-DICI engine is the poor ignition performance of NG due to its low cetane number. This problem could
be solved by the dual-fuel (DF) concept (Korakianitis et al., 2011;
McTaggart-Cowan et al., 2006). Conceptually, NG would be directly
injected into the cylinder as a primary fuel and mixed with air.
Subsequently, the fuel–air mixture would be ignited by a small
amount of pilot fuel with a high cetane number (e.g. diesel fuel).
In order to prevent methane slip and to extend the operation range
of the engine with high efficiency, it is necessary for CNG-DICI engine to operate with stratified charge by means of late injection
strategy. McTaggart-Cowan et al. (2006) reported that CNG-DICIDF engines not only maintain power output and thermal efficiency
levels compared to conventional pure diesel fueled engine, but
they also reach lower NOx and particle matter (PM) emissions. In
addition, it was stated that the improvement in CNG-DICI-DF engines can be obtained by varying the injection pressure of the
CNG fuel and diesel pilot fuel. They further investigated the effects
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
141
Nomenclature
D
L
Ma
Pe
Po
Pinj
P1
Reexit
Xfuel
Xdisk
Wdisk
r
a
c
diameter of the nozzle
axial distance of the jet
Mach number
in-nozzle pressure
upstream fuel-supply pressure of nozzle
gas injection pressure
back pressure
Reynolds number at the nozzle exit
gaseous fuel mole-fraction
Mach disk height
width of the Mach disk
radial distance from jet axial
shock reflection angle
passive scalar concentration
of injection pressure on the performance and emissions of a heavyduty dual-fuel engine using a diesel pilot ignition with late-cycle
direct-injection CNG from 210 to 300 bar (McTaggart-Cowan
et al., 2007). Based on the combustion parameters, such as the profiles of in-cylinder pressure and the rate of heat release, they concluded that the combustion process at all operation conditions is
restricted by the rate at which the fuel and oxidizer are mixing.
Increasing the injection pressure increases both the mass flux of
fuel into combustion chamber and the in-cylinder turbulence,
resulting in enhanced mixing, reducing combustion duration and
increasing peak combustion intensities. Moreover, they pointed
out that the effects of injection pressure may vary substantially
with the in-cylinder conditions because of the variation of the
injection pressure ratio (injection pressure to in-cylinder pressure).
Another main challenge of the CNG-DICI-DF engine is that there
is only a very short time for the mixture formation. Thereby, the
period of fuel injection can only take 5–10 ms. One of the key questions concerns improving and understanding the mixing efficiency
in a CNG engine. In general, when a gaseous fuel is directly injected
into the cylinder of an engine, it forms transient turbulent jets that
are typically underexpanded jets with strong shock waves near the
nozzle exit (Hill and Ouellette, 1999; Ouellette and Hill, 2000).
These shock waves can significantly influence the downstream
flow field.
In the context of DI gas engines, high-resolution imaging of
pulsed underexpanded jets has not, to our best knowledge, been
previously carried out using the PLIF technique. Thereby, the objective of this work is to gain an in-depth understanding on the characteristics of pulsed turbulent jets in CNG-engines, and to explore
the effects of shock waves on the downstream flow structures and
the turbulent mixing. This is accomplished by using a planar laserinduced fluorescence (PLIF) technique. Hiller and Hanson (1988),
Hiller and Hanson (1990) and Lemoine and Leporcq (1995) have
demonstrated the measurement of density and pressure fields of
underexpanded flow using the PLIF technique. However, they only
focused on the steady flow, and did not give high-resolution flow
field images including shock waves phenomena. In the case of high
pressure pulsed turbulent jets related to DI gas engine, previous
studies have used PLIF technique to study the characteristics of
high pressure gas jet in a constant chamber and in optical engines,
but they focused more on the macroscopic structures of the jet
(e.g., jet penetration), and they did not refer to the shock wave phenomena (Bruneaux, 2002; Bruneaux et al., 2011; Rubas et al., 1998;
Salazar and Kaiser, 2009, 2010). In addition to PLIF, we end the paper by showing high-resolution images from gas jet simulations in
order to complement the experimentally obtained picture. In particular, we demonstrate the power of large-eddy simulation (LES)
t
td
x, y, z
c
le
qe
q
Dc
Dref
Ve
v
vref
jet time
injection duration
position variables in jet
ratio of specific heat
dynamic viscosity
in-nozzle gas density
gas density
mixture fraction diffusivity
reference diffusivity
in-nozzle gas velocity
scalar dissipation
reference scalar dissipation
as a numerical diagnostic tool to give information on e.g. the jet
temperature and concentration fields as well as the scalar dissipation rates.
1.2. High-pressure jets in the DI gas engine
Theoretically, when a gas jet is injected through a circular converging nozzle into another gaseous medium, the maximum mass
flow occurs when the velocity at the nozzle exit equals the speed of
sound. Under such conditions, the inner nozzle exit pressure (Pe) is
always higher than the back pressure (P1), the flow is choked and
it becomes underexpanded. Assuming a choked flow and an ideal
gas that flows isentropically through the nozzle exit, the pressure
ratio between upstream fuel-supply pressure of nozzle exit (P0)
and the in-nozzle pressure (Pe), can be defined as (Heywood,
1988):
Pe
¼
P0
2
cþ1
c
c1
ð1Þ
For a polytropic gas, the ratio of specific heats (c) is constant
(c 1.4). The critical pressure ratio (Pe/P0) is approximately 0.528.
For a subsonic jet Pe always equals to P1, so Pe/P1 1.89. Thereby,
at high injection pressures the flow can become choked very easily
during the injection. At underexpanded conditions, the shock waves
can be formed immediately near the nozzle exit.
A vast amount of work has been done to investigate the characteristics of the underexpanded free jets in the past years. Most of
these studies are related to the aerospace applications, in particular jet aircraft and rocket propulsion systems (Crist et al., 1966;
Donaldson and Snedeker, 1971; Ewan and Moodie, 1986; Otobe
et al., 2008). According to the previous studies, a free jet usually
has three major variations of the flow pattern (subsonic, moderately underexpanded and highly underexpanded), mainly depending on P0/P1. In aerospace applications supersonic jets are usually
considered to be steady state jets since the injection periods are
very long (typically hours). In contrast, the high-pressure pulsed
jets in the engine related field are much more transient since the
injection period can be of the order of 1–10 ms. For pulsed jets in
the direct-injection (DI) gaseous fuel engine, due to the high compressibility of the gas and the variation of the in-cylinder pressure
(or back pressure P1), P0/P1 may also vary significantly during the
gas injection. Hence, the jet behavior is more complicated and
transient in engine applications than under steady state conditions.
Only a few studies have provided detailed information on high
pressure pulsed jets in gas engines. Hill and Ouellette (1999) investigated the effects of injection pressure ratio on the penetration in
142
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
a fixed volume chamber using the Schlieren technique, and they
developed an analytical relationship for jet tip penetration based
on self-similar characteristics of transient turbulent jets. Rubas
et al. (1998) examined the natural gas direct injection and mixing
in an optical engine using planar laser-induced fluorescence (PLIF)
technique. The injection pressure was 180 bar and cylinder pressure as high as 20 bar was used to match the in-cylinder density
during the injection in a firing engine. Recently Salazar and Kaiser
(2010) also used PLIF technique to study the mixing process in an
optically accessible DI hydrogen engine with high pressure injection (80–116 bar). They found that both the tumble flow and nozzle designs can influence the mixture formation and distribution.
Baert et al. (2010) visualized the transient jets using planar laser
sheet Mie scattering (PLMS) and measured the jet flow field using
particle image velocimetry (PIV). The jet penetration and jet angle
were investigated under different injection pressure ratios (15–
40 bar). More recently, the effects of the injection pressure on
the mixture formation were also reported by Roy et al. (2011)
and Bruneaux et al. (2011) using different optical techniques.
Nearly all of the previous studies focused only on the macroscopic
characteristics of the jets (e.g., jet penetration and jet cone angle).
In contrast, only little attention has been put on detailed investigations on the shock wave patterns and their connections to the mixture formation. Actually, the flow in the near-field region can
significantly influence the downstream flow structures and turbulent mixing, in particular for the underexpanded jet, since the jet
angle can be increased by the expansion shock waves, but also
the jet turbulence can be enhanced by the shock-induced instability. Therefore, the detailed information of the near-field region is
crucial for the complete understanding of jet mixing in a DI gas
engine.
has the ability to capture the characteristics of the high speed turbulent flow (Eckbreth, 1996). The basic principle of PLIF is based on
the excitation of tracer molecules within the laser sheet. Consequently, electromagnetic radiation is emitted when the molecule
returns back to a lower energy state. Almost all aliphatic hydrocarbons, forming also the major part of combustion fuels, are transparent within the spectral range of interest and therefore do not
give any fluorescence signal. Thereby, the tracer used in PLIF usually plays an important role in PLIF measurement system, in particular in the mixing process of non-reacting flows (Schulz and Sick,
2005). Acetone is a well-known and widely used fluorescent tracer.
Lozano et al. (1992) confirmed the linearity of acetone fluorescence
emission as a function of both incident laser intensity and acetone
partial pressure in the constant temperature and pressure nonreacting flow field. A detailed account of the photo-physics of laser
exited acetone fluorescence can be found in the reference (Thurber,
1999).
Here, we describe results from a 3-year project concentrating
on gaining an in-depth understanding on physics of fuel jets in natural gas engines. In particular, the project aimed at using the standard acetone PLIF technique and numerical simulations together as
complementary techniques supporting each other. Thereby, the
present paper has several objectives. First, we aim at analyzing
gaseous fuel jet characteristics in gas engine applications. In particular, this task is to be completed using a measurement system
based on the acetone PLIF technique. Second, we aim at providing
information on the transient stages and shock development times
of the gas jets. Third, the aim is to provide information to jet modelers on the practical matters (e.g. asymmetric features) present in
real jets. Fourth, the aim is to demonstrate the usage of LES as a
promising diagnostic tool to complement any experimental data
on underexpanded jets.
1.3. Laser-based diagnostics for high pressure jets
With the development of laser and imaging technology, a number of non-intrusive optical techniques, such as laser Doppler
velocimetry (LDV) and particle image velocimetry (PIV), planar laser sheet Mie scattering (PLMS) and phase Doppler particle anemometry (PDPA), have been used to investigate the flow field
(Eckbreth, 1996). These optical techniques rely on seeding the flow
with small particles (or droplets) and observing the motion of
those particles. Thereby, they are very suitable for liquid fuel
sprays which naturally contain small droplets in the flow field.
With particle seeding, these techniques can be suitable for investigating the low speed gas flows (for example, in-cylinder flow and
low pressure gas jets) as the seeding particles can follow the low
speed flows very well and represent the true fluid physics. However, the particle-based optical techniques are not efficient for
the high speed gas flow, especially for the highly underexpanded
jets. First, the particles may not follow such high speed and high
frequency containing flow because of the limitation of the response
of the seeding particles to the rapid changes of velocities across
shock waves. Second, particles cannot be used to observe smallscale structures, since the particle seeding density is limited by
secondary scattering, sampling ambiguities, and coherent scattering effects (Miles and Lempert, 1997).
In fact, there are two well-known non-intrusive and non-particle seeding flow-field image techniques, the Schlieren technique
and the shadowgraphy technique, to visualize the structure of
underexpanded jets (Settles, 2001). Based on the index-of-refraction effects, the general profile of shock waves can be observed
with these two optical techniques. However, the main limitation
of these two techniques is that the obtained two-dimensional
images are integrated across the whole flow field, which means
that the inner flow structure cannot be observed. As a non-intrusive non-particle seeding laser-sheet based optical technique, PLIF
2. Experimental setup
2.1. Experimental setup and conditions
The experimental setup is shown in Fig. 1. It consists of three
major parts: the gas supply and the tracer seeding system, the
gas injection system and the optical measurement system, as
shown in Fig. 1a. For safety reasons, the injected gas is nitrogen instead of natural gas. This approximation is considered to be adequate since the two gases have very similar properties in the
present conditions. A flow capacitor is connected to the injector
to weaken the fluctuations of injection pressure during the injection. The volume of the capacitor is approximately 1 l. The injection
pressure can be flexibly controlled and adjusted by a pressure regulator near the high-pressure nitrogen bottle. A photograph of the
experimental setup and the gas injector is shown in Fig. 1b. The
solenoid valve gas injector has a single nozzle hole with diameter
D = 1.4 mm. The typical needle fully opening time is about 0.4 ms.
As mentioned earlier, the jet behavior is mainly dependent on
the ratio P0/P1. However, it is very difficult to directly control P0/
P1 in high pressure pulsating gas jets for two reasons (1) the needle lift-off time is relatively long (0.4 ms) and (2) the pressure
losses inside the nozzle are significant (50%). Hence, in the present experimental study we focus on controlling the jets using Pinj/
P1 rather than P0/P1, since P0 has a close relationship with the initial injection pressure Pinj which can be flexibly adjusted by a gas
regulator. During the experiment, Pinj is adjusted from 5 bar up
to 40 bar while the chamber pressure (P1) remains constant as
ambient pressure (1 bar). Thereby, Pinj/P1 corresponds from 4 to
40 and it can cover almost the whole range of a high pressure DI
gas engine. In addition, the injection duration is fixed to td = 4.0 ms
for the all the experimental cases. This time is comparable to
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
143
Fig. 1. Experimental setup for the pulsed jets measurement using PLIF technique. (a) Schematic diagram of experimental setup. (b) Photograph of the experimental setup and
the gas injector tip (D = 1.4 mm).
typical injection durations in practical applications. During the
injection time the transient stages of the jets were captured and
all the jets were noted to reach eventually steady flow conditions.
2.2. Tracer seeding
As mentioned previously, acetone is a widely used as a tracer
for the PLIF measurement. Since acetone is liquid phase at room
conditions, it should be vaporized and homogeneously mixed with
the carrier gas before injection. A normal way for acetone seeding
is that the carrier gas is introduced at the bottom of the acetone
vessel through small holes, and the acetone vapor is formed as
the bubbles are rising through the liquid acetone. However, the
major disadvantage of this approach is that the acetone seeding
rate cannot be flexibly controlled. Since acetone has high volatility
and high vapor pressure, it can be evaporated rapidly into these
bubbles. Cody and Lester (2011) examined the evaporation of a
dual-stage acetone bubbling system, comprising two seeding vessels. It was found that essentially all evaporation takes place in
the first seeder for the lower flow rate, and only under high carrier
gas flow rate conditions the first seeder is insufficient to bring acetone to saturation pressure and some of the evaporation takes
place in the second seeder.
In this study, the acetone vapor can be kept at saturation in the
carrier gas nitrogen, which avoids the uncontrolled acetone seeding rate. Since the gas flow rate is very low due to the very short
jet duration (4 ms) and very long time interval between injections
(10–15 s), the acetone vapor could be efficiently saturated under
such conditions, although there is only one seeder in the present
experimental step-up. Actually, the saturated acetone vapor in
the carrier gas nitrogen has been also confirmed, because very little
condensed acetone can be observed in the flow capacitor after the
experiment.
It is worth to note that the concentration of fully saturated acetone vapor in the carrier gas nitrogen can be significantly varied
with the pressure of carrier gas. For example, under room temperature (25 °C), the concentration of acetone saturation vapor is
appropriately 30% (by volume) if the carrier gas pressure is room
pressure (1 bar). However, the acetone saturation concentration
is rapidly decreased (only 0.75% by volume) if the carrier gas pressure is 40 bar. It means that the acetone concentration in the high
pressure mixture is quite small, although the acetone vapor is saturated. Nevertheless, based on Dalton’s law, the mass flow rate of
acetone should be almost the same under the saturated condition.
Hence, the laser energy absorption could be little different under
different inlet conditions. Table 1 shows the estimation of the acetone saturation concentration based on Dalton’s law.
2.3. Imaging and data reduction
The fluorescence is excited by the 266 nm output of a frequency-quadrupled Quanta-Ray Lab-170-10 model Nd:YAG laser.
The laser pulse duration is 8–10 ns and the maximum laser energy
is approximately 90 mJ/pulse. Before entering the spray chamber,
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
Table 1
Acetone saturation concentration (by volume) under different conditions.
Mixture pressure
(bar)
Mixture
temperature (K)
Acetone saturation concentration
(by% volume)
1
5
10
20
30
40
295
295
295
295
295
295
30
6
3.3
1.5
1
0.75
the laser beam is expanded into a light sheet using a group of optical lens. The fluorescence signal is detected and recorded by an
intensified CCD camera. A Nikon 94 mm f/4.1 lens is associated
with the CCD camera. Spurious reflections of the incident laser
light are filtered out by an UV filter (300–450 nm) prior to imaging,
and the image intensifier gate (8 ns) is used to minimize the scattered light. For the axial flow structure visualization, the laser
sheet goes through the jet center line from jet tip to the nozzle
tip (Fig. 1) and the nominal resolution is 43 lm/pixel. For the radial
cross-sectional visualization, the laser sheet is perpendicular to the
jet axis and the nominal resolution is 25 lm/pixel. The camera is
always perpendicular to the laser sheet in both cases.
It is worth to mention that an unintensified CCDs can capture
finer flow structures (i.e. higher gradients) in mixing zone than
the intensified CCD, which is better suitable for quantitative scalar
measurement (Gordon et al., 2009). However, unintensified CCDs
have in general the major disadvantage that they rely on a (slow)
mechanical shutter to block unwanted light, and therefore the
shortest exposure times are several orders of magnitude longer
than for ICCDs, which routinely are gated for less than 100 ns (Salazar and Halter, 2009). In the present experimental setup, although
there is no combustion flame in the jet chamber, the laser sheet
lighting the inner wall of the chamber may lead to significant spurious scattered light for the PLIF images resulting from the big gate
of CCD. Therefore, it is better to use ICCD in the current PLIF detection system.
For the data reduction, the raw instantaneous PLIF images were
processed to correct for background scattered light. An average
background image which was obtained from 100 instantaneous
background images was used for background subtraction. Every
instantaneous background image was collected without gas injection but with the same intensification, aperture and laser sheet
emission. Then, the corrected images were filtered with a 5 5
Gaussian filter to reduce noise at a minimal cost to image resolution. Finally, these post-processing images which were shown in
the present study were individually normalized by their maximum
intensity.
2.4. Measurement uncertainty
In general, turning PLIF signal intensity into local mixture fraction is a delicate task, in particular for getting the quantitative mixing information, since there are quite many measurement
uncertainties in the PLIF measurement system. First, laser absorption along the laser sheet propagation in acetone seeded jet could
be an important measurement uncertainty. Gordon et al. (2009)
pointed out that the acetone seeding density (or concentration)
would significantly affect the laser energy absorption as high as
25% over 1 cm beam path. In order to reduce the laser energy
absorption, the acetone seeding densities below 10% was recommended in their study. In the present experiment, the acetone
seeding densities is much less than 10% under the mixture pres-
sure, as shown in Table 1. Hence, the laser absorption can be relatively low. In addition, according to the results of signal to noise
ratios, Gordon et al. (2009) recommended that an intensified relay
optics (IRO) intensifier is necessary under such conditions.
The second important measurement uncertainty would be from
the fluctuation of the shot-to-shot laser energy. A frequency-quadrupled Quanta-Ray Lab-170-10 model Nd:YAG laser is used in
the present experiment. The laser output energy (at 266 nm) is
set to approximately 90 mJ/shot. Under such conditions, the root
mean square (RMS) stability of the laser energy output is about
3.5% for every 50 laser pulses. The laser energy per shot is monitored by an advanced laser energy monitor. In our previous study,
the RMS stability was about 2.7% for every 50 laser shots when the
laser output energy (at 266 nm) was about 65 mJ/shot (Yu et al.,
2012). Although there are shot-to-shot laser energy fluctuations,
theoretically the time-averaged of the laser energy should not
change too much if there are enough snapshots. As mentioned earlier, previous studies have proven that the intensity of the fluorescence signal is proportional to the acetone concentration (Lozano
et al., 1992; Schulz and Sick, 2005; Thurber, 1999). In other words,
the total sum of fluorescence intensity (TSFI) should be linearly related to the total gas quantity under the same laser energy. Fig. 2
shows the normalized TSFI with injection time under Pinj/P1 = 10.
Results confirm the linear relationship between PLIF signal intensity and the injection gas quantity in the present experiment.
The TSFI is based on time-averaged PLIF images with injection
time. Every time-averaged image is obtained from 100 snapshots.
As can be seen that TSFI linearly increases with the injection time
(or injection quantity) after the solenoid valve is fully open when
t > 0.2 ms. This is due to that the mass flow rate is almost the same
during such a small period time (0.2 ms < t < 0.7 ms) when the flow
starts to be choked under Pinj/P1 = 10. Thus, the total injection
quantity of the gas is only linearly increased with time. The definition of the injection time t is after the start of injection (ASOI).
On the other hand, the mixture density, temperature and pressure fields of the underexpanded jets can vary widely in space and
time in the jet core region resulting from the strong shock waves.
This causes a very challenging environment to get quantitative
mixing information of the underexpanded jet, since the acetonePLIF signal is pressure-dependent and temperature dependent
(Narayanaswamy et al., 2010). For example, in the jet core region
of the underexpanded jet, the temperature and pressure can be
much lower than the ambient conditions. The pressure and temperature dependence of the acetone LIF signal for a 266 nm excitation was determined at low temperature and low pressure
Normalized TSFI
144
1.3
1.2
1.1
1.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Injection time t (ms)
Fig. 2. Normalized total sum of the fluorescence intensity (TSFI) with injection
time, Pinj/P1 = 10.
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
145
Fig. 3. Time evolution of the pulsed jet, left column shows instantaneous images and right column is the corresponding time-average images based on 100 instantaneous
images, (a) subsonic jet, (b) moderately underexpanded jet, and (c) highly underexpanded jet. (Pinj/P1 = 10 and td = 4.0 ms).
conditions by Bryant et al. (2000). The results showed that a 5%
variation of the relative acetone LIF signal intensity was observed
as the gas pressure increased from 0.1 to 1 bar and 6% as the gas
temperature was increased from 240 to 295 K. Therefore, considering these findings, we estimate the effect from the temperaturedependence and pressure-dependence to be relatively small in
the current study.
3. Results and discussion
3.1. Evolution of flow structures of the pulsed jet
The time evolution of PLIF images of gas jets under Pinj/P1 = 10
is shown in Fig. 3. The left column shows instantaneous images,
and the right column is the corresponding time-averaged images.
Each time-averaged image is obtained from 100 snapshots. Clearly,
the high-pressure pulsed jets cover three typical flow patterns
(subsonic, moderately underexpanded and highly underexpanded)
at different injection times. Before going any further, it is worth to
clarify that since the fluorescence signal is from the excited acetone molecules which are already homogeneously mixed with
the gas flow, the fluorescence intensity is proportional to the density of the jet. Moreover, due to the fact there is no fuel–air mixing
in the jet potential core region, the color bar only represents density distribution, which has been normalized by its maximum
intensity in every case.
In the beginning of the jet, the jet is characterized as subsonic,
as shown in Fig. 3a. In the subsonic jet (Pe/P1 = 1 and 1 < P0/
P1 < 1.89), a potential core region is quite evident and the length
of the potential core is usually very short, only several nozzle
diameters. It is surrounded by the turbulent shear layer mixing region which is induced by the Kelvin–Helmholtz instability. Due to
the spreading of this mixing region, the potential core no longer
exists when its two edges meet each other. Theoretically, there is
no viscous turbulent mixing and no mean velocity gradients in
the potential core region in the subsonic jet. It is very interesting
to notice, however, that the gas density field in the jet potential
core region seems to be disturbed when the flow is issuing from
the gas injector, as shown in Fig. 3a. Probably the main reason is
that the flow in the duct has been disturbed resulting from the
solenoid valve of the gas injector. These instability sources can
be further amplified during the flow issuing out of the nozzle,
which can significantly affect the jet potential core.
146
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
Fig. 4. Schematic of the near-field of a highly underexpanded jet (a is the shock
reflection angle).
Over time, once the upstream pressure is built-up enough (Pe/
P1 P 1.1 and (P0/P1 P 2.08), the jet flow is choked and becomes
underexpanded. When this choked flow is issuing into the ambient, it expands immediately downstream of the nozzle to equilibrate with ambient conditions. However, the flow may be
expanded too far causing the internal pressure to drop lower than
the ambient pressure. As a result, the jet flow is compressed or
squeezed inward by the surroundings to increase the flow pressure. The oblique shock waves and the ‘shock cell’ structure are
formed in this process, as shown in Fig. 3b. In general, the jet with
the ‘‘shock cell’’ structure is named moderately underexpanded jet
(Donaldson and Snedeker, 1971). Due to the friction and viscosity
existing in the actual gas flow, the difference between the internal
and external pressure is reduced each time when the flow passes
through one of these compression and expansion processes. As a
result, the dimension of the shock diamonds is decreased gradually
until the jet becomes subsonic. Although the profile of ‘shock cell’
is perfectly clear and smooth in the time-averaged images, it is
quite irregular in the instantaneous PLIF images. Probably the reason is that ‘shock cell’ structures are very sensitive, and they can be
easily disturbed by the turbulent instabilities in the actual high
speed compressible flow.
If the upstream fuel-supply pressure P0 is further increased (Pe/
P1 P 2 and P0/P1 P 3.85)), the moderately underexpanded jet will
change its characteristics and become the highly underexpanded.
Under such conditions, a barrel-shaped shock pattern is formed
closed to the nozzle exit, as shown in Fig. 3c. The barrel shock
structure is an axisymmetric curved shock produced by the merging of Prandtl–Meyer expansion waves. However, after the supersonic flow passes through the Mach disk, the gas jet becomes
chaotic along with the shock cell disappearing. One reason is that
the high energy loss causes the jet axial momentum flux to drop
sharply (Man et al., 1998). Another reason would be that the Richtmyer–Meshkov (RM) instability may lead to the formation of the
turbulent mixing zone after the Mach disk. This will be further discussed in Section 3.5.
3.2. Barrel shock structure and the Mach disk
Barrel shock structure plays an important role in downstream
flow structure and turbulent mixing. Fig. 4 illustrates the schematic of the barrel shock system in the highly underexpanded
jet. Due to the strong expansion and compression waves, the highly
underexpanded jet usually has three flow directions near the nozzle exit: outward expansion flow (yellow1 arrows), inward compression flow (green arrows) and parallel flow (blue arrows). The
1
For interpretation of color in Fig. 4, the reader is referred to the web version of
this article.
expansion waves (parallel flow) are capable of accelerating the flow
velocity and decaying the density distribution until to the Mach disk
in the jet axial direction. In addition, it is worth to clarify that in a gas
jet injection system several pressure levels can be defined, as shown
in Fig. 4. Similar as previous study (Donaldson and Snedeker, 1971),
three pressure levels P0, Pe and P1 are defined in present study,
where Pe depends on P0 and P1 based on Eq. (1). In a real fuel supply
system we further define the injection pressure Pinj which is the
pressure level provided by the regulator. It is important to note that
Pinj is not equal to P0 because of pressure losses inside the nozzle.
Fig. 5 shows the evolution of barrel shock structure with time at
Pinj/P1 = 17. As can be seen, the first barrel shock structure with
weak Mach disk is discerned at t = 0.5 ms. At the same time, the
first shock cell is split by the supersonic parallel flow. The barrel
shock grows slowly with time due to the increase of P0 while the
shock cells disappear almost completely after t = 1.0 ms. After
t = 2.5 ms, the barrel shock is fully developed, and the Mach disk
height Xdisk stays nearly stable.
Table 2 summarizes the evolutions of Xdisk/D, Wdisk/D and the
shock reflection angle a under Pinj/P1 = 17. As can be seen, the values of Xdisk and Wdisk are increased simultaneously with the jet
time, while the value of a is obviously decreased. This is mainly
attributed to the increase of P0/P1. For the pulsed jet, P0 always increases from a low starting to a high later value owing to the high
compressibility of the gas and the opening delay of the solenoid
valve. P0 can also be considered as the effective injection pressure,
which is one of important boundary parameters for gas jet simulation. Hence, it is desirable to obtain experimental information of P0.
However, a transducer that is mounted prior to the nozzle hole is
intrusive and may interfere with the nozzle flow, and then affect
the downstream flow field. Nonetheless, it is possible to effectively
estimate P0/P1 based on the information of barrel shock structures.
Previous studies show that the Mach disk is one of the most factors specifying highly underexpanded jets, and the Mach disk location is insensitive to the ratio of specific heat, condensation, solid
boundary geometry at the nozzle exit, and the absolute pressure
level, but it is strongly dependent on the pressure ratio between
P0 and P1 (Crist et al., 1966; Maté et al., 2001; White and Milton,
2008). Empirical Eq. (2) provides the relation between P0 and Xdisk
(Maté et al., 2001).
sffiffiffiffiffiffiffi
X disk
P0
¼ 0:67
D
P1
ð2Þ
Based on Eq. (2), P0/P1 was calculated for different injection pressures, as shown in Fig. 6. Apparently, it can be seen that P0/P1 is
much lower than Pinj/P1. Due to the high compressibility of gas
flow, P0/P1 is built-up gradually during the injection regardless of
the injection pressure levels. The peak value of P0/P1 increases with
the increase of Pinj/P1. It can also be seen that the lowest the pressure P0/P1 is about 4 for all the cases, which is very close to the theoretical critical value 3.85 when the jet character changes from
moderately under expanded to highly underexpanded conditions
(Donaldson and Snedeker, 1971). On the other hand, the Reynolds
number is an important parameter to predict whether the flow is
laminar or turbulent. For the pulsed jet, the nozzle exit Reynolds
number Reexit is always changing because of the variation of the upstream fuel-supply pressure. To calculate Reexit of underexpanded
jet, the isentropic and inviscid adiabatic flow in the nozzle was assumed. Reynolds number at nozzle exit can be calculated as:
Reexit ¼ qe V e D=le
ð3Þ
where D, qe, Ve and le are the nozzle exit diameter (m), the gas density (kg/m3), the velocity (m/s) and the dynamic viscosity (Pa s) at
the nozzle exit, respectively. The details of Reexit calculation at
underexpanded conditions can be found in some references
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J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
(Anderson, 2003; Wilkes et al., 2005). Fig. 7 shows the effects of Pinj/
P1 on Reexit of fully developed highly underexpanded jets (at
t = 3.5 ms). As can be seen that the effects of the injection pressure
on the Reexit is remarkable. The order of Reexit is as high as 105. High
Reynolds number would be very helpful to enhance the gaseous
fuel–air turbulent mixing and mixture formation in the engine cylinder. In other words, higher injection pressure is beneficial to the
jet turbulent mixing in CNG-DICI engine.
Table 2
Summary of results for highly underexpanded jets (Pinj/P1 = 17).
t (ms)
Xdisk/D
Wdisk/D
a (°)
0.5
1.0
1.5
2.0
2.5
3.0
1.36
1.51
1.66
1.71
1.76
1.78
0.29
0.49
0.61
0.69
0.8
0.84
42.4
37.1
35.5
34.5
31.1
28.4
3.3. Visualization of the radial cross-sections
For jets issuing from an axisymmetric nozzle, the perturbations
can be either axial (longitudinal) or azimuthal (Inman et al., 2008).
As a primary instability, Kelvin–Helmholtz waves, the axial perturbations, play an important role in initiating the transition process
of the turbulent jets. In general, the primary instability is evident
as a train of Kelvin–Helmholtz vortex rings at the sides of the jet
in the near-field region. As these vortex rings convect downstream,
they develop a secondary instability which manifest itself as azimuthal oscillations on each ring (Nichols et al., 2007). Zaman
(1996) pointed out that both the azimuthal and streamwise vortices, which are respectively corresponding to the secondary and
primary instability, are of equal importance to jet mixing process,
and they are not independent of each other. However, most of the
previous studies were focused on steady state flows.
Fig. 8 shows the evolution of the time-averaged radial crosssections of the highly underexpanded pulsed jet under different
conditions. Fig. 8 gives the cross-sectional visualization of a fully
developed highly underexpanded jet at different locations under
Pinj/P1 = 20. Obviously, the vortex ring is non-pertabative at the
location of L/D = 1, while the star-shaped patterns are clearly discerned at the locations of L/D = 2 and 3 due to the development
of the secondary instability. These star-shaped patterns are blurred
and become smooth when the jet becomes fully turbulent, for
example, at the locations of L/D = 4, 8 and 14. Interestingly, the
cross-sectional concentration filed of the jet exhibits rather asymmetric in the far-field region, even though the gas injector used in
this study has a round and straight single-hole nozzle. Probably
one main reason is that the drilled nozzle hole is not perfect round
which can considerably influence on the downstream flow
structure. This reasoning would also explain why the realistic jet
usually differs from their numerical counter parts.
Fig. 9 shows radial cross-sections of the highly underexpanded
pulsed jet with injection time at a fixed location (L/D = 3) under
Pinj/P1 = 40. It is notable that the star-shaped pattern can be
formed rapidly under higher injection pressure ratio. In particular,
the star-shaped pattern becomes quite clear after the barrel shock
structure is large enough (e.g. t 6 2.0 ms), since the gradual
increasing of P0/P1 results in the stronger primary instability and
azimuthal oscillations during the injection. Theoretically, the azimuthal oscillation is one of the typical characteristics of the high
speed gas flow.
Nonetheless, it should be pointed out that although each timeaveraged image is obtained from 100 instantaneous images, the
star-shaped pattern is still clearly visualized. It means that the
source of instability in every single jet is located in the same positions, regardless of the injection pressure ratio. One main reason
would be that surface roughness of the drilled nozzle hole exceeds
the boundary layer thickness (106 m), which contributes to the
initial perturbations at the same positions and then further similarly
affects the primary and the secondary instability during the injection process (e.g., the dashed elliptical region in Figs. 8 and 9).
Apparently, a careful design and manufacturing of the inner surface
structure of the nozzle hole is important for the gas jet performance.
3.4. Variation of the jet field
Due to the strong compression and expansion shock waves, the
density variations can be revealed by the fluorescence signal
Fig. 5. Evolution of time-averaged PLIF images of highly underexpanded jet in the near-field region (Pinj/P1 = 17 and td = 4.0 ms).
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region (e.g. L/D = 14), although it is not purely axisymmetric. It
indicates that the underexpanded jet has become turbulent and
subsonic in the far-field region.
25
20
3.5. Shock wave and turbulent mixing
15
10
5
0
1
2
3
4
5
Injection time t (ms)
Fig. 6. Calculated P0/P1 based on the Mach disk distance (Xdisk) under different
injection conditions (td = 4.0 ms).
7x105
Reexit
6x105
5x105
4x105
3x105
2x105
10
20
30
40
Fig. 7. Calculated Reynolds number at the nozzle exit (Reexit) at t = 3.5 ms.
intensity. Fig. 10a shows the normalized fluorescence intensity of
fully-developed underexpanded jets for different injection pressures. The y-coordinate, the fluorescence signal intensity, is nondimensionalized by the peak intensity value of each jet. As a result
of the expansion waves close to the nozzle exit, the fluorescence
intensity smoothly and rapidly decreases from the nozzle exit until
to the Mach disk or the first shock cell, and then rises suddenly
resulting from the compression waves. In the case of moderately
underexpanded (Pinj/P1 = 7), the oscillation of fluorescence intensity represents the consequence of the repeating expansion and
compression oblique shock structure in the jet. At the location of
L/D = 10, the jet becomes subsonic and fully turbulent. The decay
of the oscillation amplitude is due to the viscous dissipation and
the growth of the surrounding mixing layer. Under highly underexpanded conditions (Pinj/P1 = 20 50), when the flow passes
through the Mach disk, the fluorescence intensity keeps nearly
constant in the downstream field. On the other hand, despite the
fact that the variations of the temperature and pressure distribution can cause non-linear relation between fluorescence signal
intensity and tracer density, it is somewhat surprising to note that
the profiles of the centerline fluorescence intensity coincide with
each other very well near the nozzle tip regardless of the injection
pressure levels.
Fig. 10b presents to the normalized radial fluorescence intensity
at different locations under Pinj/P1 = 20. In the jet potential core region (e.g. L/D = 2 and 7), the density variation is high due to the
compression and expansion shock waves, while the general trend
of the density profiles exhibits almost self-similarity in the far-field
In general, for the subsonic flow the shear-induced turbulence
plays an important role in the turbulent mixing, while for the
underexpanded jet, in particular the highly underexpanded jet,
the flow structure and turbulent mixing are not only dependent
on the shear-induced turbulence, but also strongly affected by
shock-induced turbulence. The shock-induced instability is often
called the Richtmyer–Meshkov instability, which arises as a shock
wave interacts with an interface separating two fluids with different density. When two different fluids are impulsively accelerated
into each other by a shock wave, small perturbations at the interface grow first linearly and then evolve into non-linear structures
formed of ‘‘bubbles’’ and ‘‘spikes’’. Afterwards, it may lead to the
formation of a turbulent mixing zone (Bai, 2012), which can cause
the shock cells disappearing after Mach disk. Usually, both the
intersection point (red points) and the shock triple point (green
points) shown in Fig. 4 are considered as two main sources of
instabilities (Inman et al., 2008).
Fig. 11 shows the effects of shock waves on the flow structure
and turbulent mixing in highly underexpanded jet under different
conditions. Clearly, under higher pressure ratio (e.g. Pinj/P1 P 20),
the turbulence takes place immediately after the Mach disk due to
the strong Richtmyer–Meshkov instability, and then leads to the
turbulent mixing zone. On the other hand, the growth of barrel
shock leads to the increase in the jet cone angle in the near-field
region, which is very important for improvement of the fuel–air
mixing efficiency and mixture spatial distribution.
According to the results and discussions in the above sections,
the characteristics of the main structures in underexpanded jets
can be captured quite well by means of acetone-PLIF technology.
However, it is very challenging to quantitatively measure the local
mixture fraction in the underexpanded jet due to the wide variation of temperature and pressure in space and time. In order to
gain an in-depth understanding in the underexpanded jets which
is beyond the capability of the current optical technology, LES is
used to further explore the underexpanded jet in the next section.
The aim of the next section is to demonstrate the use LES as a diagnostic tool to support PLIF and other experimental techniques in
supersonic flow research.
3.6. Large-eddy simulation of underexpanded gas jets
3.6.1. Brief introduction to the present large-eddy simulation
Using LES, turbulent flow may be simulated by solving the Navier–Stokes equations with high spatial and temporal resolution
(Garnier et al., 2009). Thereby, LES may offer a complete transient
3D visualization of the flow field. In supersonic flows LES potentially resolves the shock structures, acoustic waves, thermodynamic fields and mixing. In fact, LES of supersonic flows is a
relatively new research topic which has achieved more attention
only recently. During the past 3 years several groups in the field
of aeroacoustics have adopted LES as a computational diagnostic
tool to support different experimental techniques (Dauptain
et al., 2010; Gieseking et al., 2011; Kawai and Lele, 2010; Munday
et al., 2011; Vuorinen et al., 2013). The recent studies have mostly
focused on moderately underexpanded jets exhibiting oblique
shocks in various nozzle geometries (Dauptain et al., 2010; Kawai
and Lele, 2010; Munday et al., 2011) or overexpanded conditions
(Gieseking et al., 2011). Very recently, highly underexpanded jets
were studied using LES in a setup emulating the present experimental conditions (Vuorinen et al., 2013).
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Pinj P∞ = 20
X fuel
Fig. 8. Visualization of the cross-section of the pulsed jet (time-averaged) at different locations. (Pinj/P1 = 20, t = 3.5 ms, and td = 4.0 ms).
Pinj P∞ = 40
(a)
1.0
Normalized fluorescence intensity
Normalized fluorescence intensity
Fig. 9. The evolution of the cross-section of the pulsed jet (time-averaged) at the fixed location L/D = 3 (Pinj/P1 = 40, and td = 4.0 ms).
0.8
0.6
0.4
0.2
0.0
0
2
4
6
L/D
8
10
12
(b)
1.2
Nozzle
0.8
0.4
0.0
-4
-2
0
2
4
r/D
Fig. 10. Variation of normalized fluorescence intensity for different injection pressures, (a) normalized centerline fluorescence intensity, and (b) normalized radial
fluorescence intensity at different location. Every profile is based on the time-averaged PLIF image at t = 3.5 ms and td = 4.0 ms.
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In the present LES we discretize the detailed information concerning the numerical methods and setup of the present LES can
be found in the recent study focusing on the computational modeling of highly underexpanded gas jets (Vuorinen et al., 2013).
Here, we briefly summarize some of the most important numerical
details. In the present LES, a gas jet is formed by modeling a
smooth and converging nozzle. The upstream pressure of the nozzle is simulated by taking into account a very large pressure reservoir which forces the jet through the nozzle into the ambient
conditions. The Navier–Stokes equations are solved using an explicit, density based Runge–Kutta method with fourth order temporal
accuracy. The grid resolution is D/70 in the radial and D/35 in the
axial direction offering a good spatial resolution comparable to
previous studies in similar flows (Dauptain et al., 2010; Munday
et al., 2011; Vuorinen et al., 2013). LES of supersonic flows aims
at simultaneous capturing of shock waves and turbulence. These
objectives are particularly challenging as resolving the discontinuous shock waves requires robust numerics (typically reduction of
the spatial accuracy to first order) with high level of dissipation
whereas turbulence should be treated with non-dissipative discretization schemes (at least second order spatial accuracy) (Grinstein et al., 2007). In the present LES we discretize the convection
terms using a second order accurate scale-selective filtering procedure that was recently developed, tested and validated for LES by
Vuorinen et al. (2012). The third order diffusive error of the
scale-selective discretization (SSD) scheme acts as a stand-alone
turbulence model similar to implicit LES (ILES) and thereby we
do not apply an explicit turbulent viscosity (Grinstein et al.,
2007). A detailed spectral analysis of the SSD scheme has been given by Vuorinen et al. (2012). In fact, it should be noted that in LES
of supersonic jets the ILES approach seems to be the most com-
monly used approach as it has been noted to favorably capture
the turbulence transition process (Kawai and Lele, 2009). Also
the shock capturing needs to be accounted for with a separate
model and in the present LES the shock waves are treated with
the bulk-viscosity method by Cook and Cabot (2005) which only
influences the dilational part of the viscous stress tensor. This approach has become one of the state-of-the-art methods in LES of
supersonic flows as the dilational part of the stress tensor is typically assumed to be small in comparison to the symmetric part
of the stress tensor (Cook and Cabot, 2005; Dauptain et al., 2010;
Kawai and Lele, 2009). To summarize, the present LES has been tailored to involve minimal numerical dissipation while still capturing the supersonic features involving high gradients. Next, we
further discuss the present PLIF measurements in the light of present LES. The capability of LES at two different nozzle pressure ratios (P0/P1) is investigated using a simulation model detailed
earlier by Vuorinen et al. (2013) who used the model in highly
underexpanded conditions. Here, we carry out two simulations:
one at moderately underexpanded conditions (P0/P1 = 3) and one
at highly underexpanded conditions (P0/P1 = 5.5).
3.6.2. Comparison of PLIF and LES near the nozzle exit
It should be noted that Pinj in experiments and P0 in the present
LES are not equal due to pressure losses in the injector. Thereby, P0
in experiments is not known whereas in LES it can be controlled by
the boundary condition in the pressure reservoir. One way to compare PLIF and LES with each other is to use the empirical Eq. (2). For
a PLIF case with injection pressure Pinj/P1 = 15 the Mach disk
height is noted to be about 2.39 mm for which Eq. (2) gives P0/
P1 = 6.5. The PLIF image is captured under a quasi-steady jet
(t = 9 ms, td = 10 ms) with constant Pinj/P1 = 15. Under such
Pinj P∞ = 5
Pinj P∞ = 10
Pinj P∞ = 10
Pinj P∞ = 20
Pinj P∞ = 20
Pinj P∞ = 30
Pinj P∞ = 30
Pinj P∞ = 40
Pinj P∞ = 40
X fuel
Pinj P∞ = 5
Fig. 11. Effects of injection pressure on the jet structures and turbulent mixing process in highly underexpanded jets at t = 3.5 ms. td = 4.0 ms.
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J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
conditions, the underexpanded jet is fully developed and the upstream pressure of the gas supply P0 can be considered as steady
state. Thereby, in order to compare LES and PLIF we need to compare the experimental case Pinj/P1 = 15 and LES case P0/P1 = 6.5
with one another. Fig. 12 shows the comparison between timeaveraged LES (upper half) and time-averaged PLIF (lower half) in
the near nozzle region. It is noted that the basic aspects of the
underexpanded jet are well reproduced by LES including (1) the
location of the Mach disk and (2) the angle and shape of shock
reflection. However, a meaningful quantitative comparison is not
possible as there are several differences between the two results.
For example, in reality the inner nozzle boundary layers are very
thin and thereby they are left unmodeled in LES. Thus, the inflow
condition in LES is laminar whereas in PLIF it is likely to be transitional which results in obvious differences already at the inlet.
However, as shown previously, a very good agreement between
LES and PLIF may be observed for the number of shock cells and
general flow topology (Vuorinen et al., 2013).
3.6.3. Effects of injection pressure ratio on the underexpanded jet
Fig. 13 shows the temperature field of the fully developed
underexpanded jets. The left side shows a jet under moderately
underexpanded at nozzle pressure ratio P0/P1 = 3 and the right
side shows a highly underexpanded jet at P0/P1 = 5.5. As was mentioned previously, the temperature varies widely in the underexpanded jet in time and space due to the strong expansion of the
supersonic flow. This phenomenon can be clearly captured in the
temperature field in Fig. 13a. With the increase of P0/P1 from 3
to 5.5, the variation of the temperature field is obviously increased,
as shown in Fig. 13b. The minimum temperature is of the order
160 K, which is observed in the intersection point of the oblique
shocks at P0/P1 = 3, and the temperature fluctuations have almost
disappeared after 10D. At P0/P1 = 5.5, the minimum temperature
decreases rapidly to 100 K, and visible temperature fluctuations
exist even as far as 20D. The position of the minimum temperature
is pointed by the white arrow in Fig. 13a and b, respectively.
The Mach number (Ma) is a very important parameter of the
supersonic jet flow field. However, it is not possible to measure
Ma in the flow field using PLIF technology. Furthermore, such complicated velocity flow field cannot be accurately measured even by
PIV either (Miles and Lempert, 1997). Based on LES, Ma can be efficiently captured. Fig. 14a and b display the velocity field (indicated
by Ma) of the underexpanded jet under different inlet conditions.
Due to the intensive expansion and compression shock waves,
the velocity varies strongly between supersonic and subsonic values in the near field of the jet. The maximum Ma is approximately
2 when P0/P1 = 3, while Ma is increased to 3 under P0/P1 = 5.5. The
position of the maximum Ma is pointed by the white arrows in
Fig. 14a and b, respectively. Additionally, it is noted how the stagnation conditions are approximately met inside the shock cells as
expected.
Fig. 14c and d demonstrate the concentration (qc) normalized
with the inlet value in the underexpanded jets at P0/P1 = 3 and
5.5, respectively. Here, c is a passive scalar that is used to visualize
and study mixing similar to acetone concentration in PLIF (Vuorinen et al., 2013). In addition to temperature and Mach number
fields, the passive scalar field reveals additional details concerning
the mixing. For example, the fine resolution LES captures vortex
instabilities resembling the classical Kelvin–Helmholtz waves in
the shear layers of the jets. There are clear differences in the formation of the vortex structures. For example, the moderately underexpanded jet exhibits a symmetric vortex pattern whereas an
antisymmetric, helical vortex structure forms for the highly underexpanded jet (Vuorinen et al., 2013). It is important to (1) note the
ability of LES to capture the presence of these structures and (2)
note that the structures were not seen as clearly for PLIF. These
Fig. 12. Comparison between time-averaged LES (upper half) and time-averaged
PLIF (lower half) of the underexpanded jet.
examples provide evidence on the ability of LES to capture fine
scale details of moderately and highly underexpanded jets thereby
supporting the experimentally obtained picture.
We note that, despite the obvious similarities, the LES and PLIF
results differ to some extent. In LES, the transition to turbulence
begins visibly after the Mach disk in the form of the shear layer
instability. In contrast, in PLIF some flow exists already outside
the barrel shock which can be explained by the flow being turbulent/transitional in the experiments already at the nozzle exit. In
LES the nozzle exit condition is laminar which explains the differences. The observed asymmetries in the experiments (see e.g.
Fig. 11) also imply that the scalar fields may be even asymmetric
in practice. A possible explanation to this anomaly could be the inner nozzle surface roughness. In other words, the boundary conditions are crucial for LES of underexpanded jets to obtain results
close to the experiments.
3.6.4. Scalar dissipation rate of underexpanded jets
Scalar dissipation rate (SDR) is typically used to estimate high
concentration gradients and estimate the local mixing activity of
the flow field. It is particularly important in combustion applications because it is fundamentally related to the structure of turbulent non-premixed flames and appears directly or indirectly in
most turbulent combustion models (Frank and Kaiser, 2007; Gordon et al., 2009; Wang and Barlow, 2007). The scalar dissipation
is defined as v (Pope, 2000)
v ¼ 2Dc
"
@c
ax
2
@c
þ
@y
2
2 #
@c
þ
az
ð4Þ
where Dc is the mixture fraction diffusivity; c is the passive scalar
concentration; x, y, z are the position variables of the jet. It is noted
from Eq. (4) that the definition of scalar dissipation is 3d and thereby it can be directly evaluated from the instantaneous LES data as
further discussed below.
Previous experimental studies on subsonic jets have indicated
that SDR exhibits narrow string-like structures where the mixing
rate is high (Gordon et al., 2009; Karpetis and Barlow, 2005; Wang
et al., 2007a; Wang et al., 2007b). In addition, the previous studies
have also indicated that compared to intensified CCDs, unintensified CCDs offer better quantitative scalar measurements because
of the lower level of noise (Frank and Kaiser, 2010; Frank and Kaiser, 2007; Kaiser and Frank, 2009). However, the PLIF image captured from intensified CCD can be heavily obscured by the
intensifier noise. Therefore, the current experimental PLIF data
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J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
Fig. 13. Temperature field of LES instantaneous snapshots of quasi-steady underexpanded jets under different inlet conditions. (a) P0/P1 = 3 and (b) P0/P1 = 5.5.
Fig. 14. LES of instantaneous snapshots of quasi-steady underexpanded jets under different inlet conditions. Left (a and b) P0/P1 = 3, and right (c and d) P0/P1 = 5.5.
may not be suitable for SDR analysis. Here, we use the 3d LES data
for visualizing how the dissipation rate structures based on the resolved quantities appear in LES of supersonic jets.
Fig. 15a and b shows SDR (log10(v/vref)) of underexpanded jets
under P0/P1 = 3 and 5.5 at jet time t = 0.5 ms. Here, v is made nondimensional using the integral scales to define a reference quantity
vref = 2Dref(cmax/D)2, where cmax = 1, and Dref is the reference diffusivity in the far-field. Clearly, in the near-field of the jet, the turbulence transition process results in the onset of intense mixing and
high-level of SDR. In contrast, in the far field, the SDR decreases as
the turbulence has further evolved and mixed the flow. Fig. 15c
and d are the corresponding areas of the dashed yellow box in
Fig. 15a and b, respectively. The left and right sides of the dashed
yellow box are 6D and 13D away from the nozzle exit, respectively.
It is noted that the differences between the two underexpanded
jets are relatively small. The SDR exhibits narrow, string-like structures which mostly highlight the edges between high and low concentration regions. According to the definition of SDR, high values
of SDR indicate that mixing is still incomplete as high gradients exist. As seen from Fig. 15, it should be noted that SDR varies over
roughly 2–3 orders of magnitude. Higher SDR values are seen in
the lower pressure ratio case implying stronger concentration gradients which have high potential for further mixing. On the other
hand, the higher pressure ratio case exhibits reduced SDR compared to the lower pressure ratio case indicating reduced concentration gradients due to mixing that has already taken place. In
general low SDR would imply good mixing as the gradients have
dissipated away. Hence, these results point to the direction where
a higher P0/P1 would imply a better mixing. It is a highly interesting question how to really use this kind of detailed data for mixture
quality analysis. For example, future studies could involve tailoring
the objectives for good mixture quality in DI CNG engines based on
LES data such as that presented in Fig. 15.
Last, it is noted that any LES may only offer an approximation of
SDR based on the resolved scalar fields. For example, as the scalar
gradients are eventually determined by the Batchelor scales, the
quantitative value of SDR is likely to depend to some extent on
the grid resolution in any practical LES. Similar problems occur also
in experiments as capturing the smallest flow scales depends on
the pixel size in addition to background noise and other measurement errors. One of the advantages of the present LES is that the
simulations are carried out on a relatively fine grid where the
scale-selective implicit filtering acts as a stand-alone turbulence
model similar to ILES (Grinstein et al., 2007). Using the ILES approach has been common in previous literature for supersonic
flows (Kawai and Lele, 2009; Munday et al., 2011). Thereby, we
note that the results of Fig. 15 are not influenced by an explicit subgrid scale turbulence model. Instead, as previously explained, the
turbulence is modeled by the higher order dissipative terms of
the truncation error of the SSD scheme (Vuorinen et al., 2012).
We note the similarity between the relatively clear string-like
structures of SDR for supersonic jets as has been previously noted
for reacting flows in the literature (Frank and Kaiser, 2010; Kaiser
and Frank, 2011). In addition, to our best knowledge, such SDR
structures of supersonic jets have not been previously reported
in the literature.
4. Conclusions
This work has been motivated by our attempt to develop CNG
direct-injection compression-ignition (CNG-DICI) dual-fuel engines with high efficiency and low emissions. In general, shock
waves can be formed immediately when the gaseous fuel with high
pressure ratio is injected into the cylinder. It is highly important to
gain an in-depth understanding of the jet mixing to develop such
kind of CNG engine. For this purpose, the experimental study of
high-pressure pulsed jets based on planar laser-induced fluorescence (PLIF) was carried out in a constant-volume vessel under different injection pressure ratios. In order to better understand the
characteristics of underexpanded jets, LES was further used in
the present study.
The main findings of this work are summarized as follows. First,
the standard acetone PLIF visualization could be used to capture
J. Yu et al. / International Journal of Heat and Fluid Flow 44 (2013) 140–154
153
Fig. 15. The effect of inlet conditions on the scalar dissipation rate of underexpanded jets at t = 0.5 ms. (a) P0/P1 = 3.0, (b) P0/P1 = 5.5, and (c) and (d) are the enlarge area of
the yellow box in (a) and (b), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the average concentration fields in jets which can already reveal
very useful information on the transient and average features of
the jets. Second, the results revealed that pulsed jet in DI CNG type
applications at high pressure ratios contain three typical flow patterns: subsonic, moderately underexpanded and highly underexpanded in the jet core region. Importantly, all these stages are
long-lasting in comparison to the duration of injection and thereby
the present jets are also highly transient. Third, the results indicate
that realistic gas jets in DI CNG type engines may involve asymmetric features. The visualizations of the radial cross-section identify that the azimuthal instability which is the development of the
primary instability exists in the highly underexpanded jet. Surprisingly, the star shaped pattern can still be clearly discerned in the
time-averaged images, although the gas injector is circular. The
main reason would be the surface roughness of the drilled hole
which exceeds the boundary layer thickness (106 m), which
contributes to the initial perturbations at the same positions and
then further similarly affects the primary and azimuthal instability
in the realistic gas jet. Hence, the careful design and manufacturing
of the nozzle would be important for the physical characteristics of
the jets. Considering this together with the transient nature of the
jets poses a significant challenge to modelers since the observations point to the direction where also the flow inside the injector
needs to be modeled. Fourth, we demonstrated the capability of
LES to capture flow features of transient underexpanded jets which
are out of the reach of any experimental configuration. We note
that LES may strongly complement the PLIF technique in future
studies on underexpanded jets. In particular, detailed tailoring of
mixture quality indicators for premixed/partially premixed combustion at various injection conditions could be conveniently designed based on LES.
Acknowledgments
Financial support from Finnish Technology Foundation (TEKES)
and Aalto University in the Future Combustion Engine Power Plant
(FCEP) research program is gratefully acknowledged.
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