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We report a comprehensive speed of sound database for multi-component mixing of underexpanded fuel jets with real gas expansion. The paper presents several reference test cases with well-defined experimental conditions providing quantitative data for validation of computational simulations. Two injectant fluids, fundamentally different with respect to their critical properties, are brought to supercritical state and discharged into cold nitrogen at different pressures. The database features a wide range of nozzle pressure ratios covering the regimes that are generally classified as highly and extremely highly underexpanded jets. Further variation is introduced by investigating different injection temperatures. Measurements are obtained along the centerline at different axial positions. In addition, an adiabatic mixing model based on non-ideal thermodynamic mixture properties is used to extract mixture compositions from the experimental speed of sound data. The concentration data obtained are complemented by existing experimental data and represented by an empirical fit.
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Experiments in Fluids (2018) 59:44
https://doi.org/10.1007/s00348-018-2488-1
RESEARCH ARTICLE
Mixing characterization ofhighly underexpanded fluid jets withreal
gas expansion
FelixJ.Förster1· SteenBaab2· ChristophSteinhausen2· GraziaLamanna2· PaulEwart1· BernhardWeigand2
Received: 19 October 2017 / Revised: 18 December 2017 / Accepted: 2 January 2018 / Published online: 9 February 2018
© The Author(s) 2018. This article is an open access publication
Abstract
We report a comprehensive speed of sound database for multi-component mixing of underexpanded fuel jets with real gas
expansion. The paper presents several reference test cases with well-defined experimental conditions providing quantitative
data for validation of computational simulations. Two injectant fluids, fundamentally different with respect to their critical
properties, are brought to supercritical state and discharged into cold nitrogen at different pressures. The database features a
wide range of nozzle pressure ratios covering the regimes that are generally classified as highly and extremely highly under-
expanded jets. Further variation is introduced by investigating different injection temperatures. Measurements are obtained
along the centerline at different axial positions. In addition, an adiabatic mixing model based on non-ideal thermodynamic
mixture properties is used to extract mixture compositions from the experimental speed of sound data. The concentration
data obtained are complemented by existing experimental data and represented by an empirical fit.
1 Introduction
The injection strategies and resulting mixing processes in
engines strongly influence the combustion performance, and,
ultimately, the achievable efficiency and pollutant emission
(Idicheria and Pickett 2007). Naturally, there is an ecological
and economic incentive to make advances in this area which
is further encouraged by recent political focus. Therefore,
characterization of the fuel injection process is a crucial ele-
ment of virtually all combustion-based energy conversion
systems.
In this context, high system pressures are typically used
to facilitate efficient mixing and to provide sufficiently
high fuel mass flows. Examples in the automotive industry
include the potential benefits for direct injection engines (De
Boer etal. 2013), especially with respect to natural gas or
hydrogen injection (Hamzehloo and Aleiferis 2014). Fur-
thermore, high injection pressures are an inherent feature of
efficient fuel/oxidizer preparation in the conventional direct
injection engines (Idicheria and Pickett 2007). For the latter,
a pre-heating of the fuel to supercritical temperatures was
also found to yield higher engine efficiencies and a simul-
taneous decrease in emissions (Tavlarides and Antiescu
2009; Anitescu etal. 2012; Whitaker etal. 2011). Similar to
hydrogen and natural gas, the fuel, then, features consider-
able compressibility. Consequently, choked flow conditions
are easily reached resulting in the formation of an underex-
panded jet downstream of the nozzle. The expansion char-
acteristics are determined by the ratio of reservoir
pinj
to
chamber pressure
pch
, typically expressed as nozzle pressure
ratio (NPR). Depending on the NPR, the jets are classified as
subsonic, moderately, and highly underexpanded.
For highly underexpanded jets, the flow adapts to
pch
through a single, barrel-shaped shock structure. A common
criterion for this classification is the NPR, which is typical
four and above (Donaldson and Snedeker 1971) such gases
like air, nitrogen, or hydrogen. Furthermore, the flow field
and shock system, especially the distance of the normal
shock from the nozzle exit, is strongly affected by the NPR
(Franquet etal. 2015).
Supercritical fluids are highly compressible and can show
significant variation in their thermodynamic properties dur-
ing the relaxation process to the, often, subcritical
pch
. This,
consequently, even influences the mixing process in the far-
field zone (Banholzer etal. 2017; Baab etal. 2017).
* Felix J. Förster
felix.foerster@physics.ox.ac.uk
Steffen Baab
sba@itlr.uni-stuttgart.de
1 Department ofPhysics, Clarendon Laboratory, University
ofOxford, Parks Road, OxfordOX13PU, UK
2 Institute ofAerospace Thermodynamics (ITLR), University
ofStuttgart, Pfaffenwaldring 31, 70569Stuttgart, Germany
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Experiments in Fluids (2018) 59:44
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44 Page 2 of 10
This complex coupling between thermo- and aerody-
namic behavior is challenging for numerical simulations
which emerged as an essential design tool for future combus-
tion systems. Consequently, considerable efforts have been
made in recent years to develop reliable numerical frame-
works (e.g., Banholzer etal. 2017; Hamzehloo and Aleiferis
2016a; Velikorodny and Kudriakov 2012; Vuorinen etal.
2013; Mohamed and Paraschivoiu 2005; Bonelli etal. 2013;
Khaksarfard etal. 2010).
Suitable experimental data sets and test cases for valida-
tion of such numerical predictions are, however, limited as
stated, for instance, in Hamzehloo and Aleiferis (2016a, b).
Existing studies usually focus on a particular application,
e.g., leakage studies for high-pressure hydrogen storage,
e.g., Molkov (2012) or aerospace applications involving
very large nozzle diameters (as discussed in Hamzehloo
and Aleiferis (2016a)), which do not allow for an univer-
sal assessment of the mixing phenomena across the entire
range of applications. This study is designed to increase the
fundamental understanding of such processes and proposes
detailed reference cases for numerical simulations.
In a previous study, we demonstrated that laser-induced
thermal acoustics (LITA), also referred to as laser-induced
grating spectroscopy (LIGS) is capable of acquiring quantita-
tive data for such applications. It was shown that measure-
ments of small-scale jet mixing processes are feasible despite
the turbulent mixing flow and harsh flow field properties.
This qualifies the technique as an excellent method to over-
come the general lack of experimental data. A full discussion
of the advantages of this technique, a comparison to alterna-
tive diagnostic tools as well as an overview of existing exper-
imental studies in literature are given in Baab etal. (2016).
The purpose of this study is to apply the technique to
generate a comprehensive experimental database. Specifi-
cally, it features
1. a wide range of NPRs to alter the shock/expansion system,
2. injection conditions, such that real gas treatment is man-
datory,
3. flow and nozzle geometry in the order of
(100 μm)
as
typically found for internal combustion engines, and
4. an application-near surrogate fuel as well as an academi-
cally interesting fluid.
The experimental conditions were selected, such that
the treatment of real gas effects in the expansion process
becomes mandatory.
To the best of our knowledge, this is the first study to pro-
vide such extensive and quantitative speed of sound data in
this context. This database can be used for the validation of
numerical simulations, as it is not biased by any assumption
on the mixing mechanism or by the choice of a thermody-
namic model. In addition, mixture composition is extracted
from the experimental speed of sound data using a mixing
model with non-ideal thermodynamic properties. The dis-
tinct separation between directly measured data (i.e. speed
of sound) and thermodynamically derived quantities (i.e.
species concentration) represents, in our opinion, one of the
main advantages of the LIGS database. This is particularly
relevant for supercritical fluid injection, where the develop-
ment of accurate EoS and associated mixing rules is still an
open field of research.
Ultimately, the obtained mixture compositions lead to
an empirical fit for the entire range of injection conditions
investigated in this study.
2 Measurement conditions
The injectant is initially stored at supercritical temperature
and pressure and discharged into cold nitrogen at ambient
pressure. We use two different injectants, an alkane, namely
n-hexane (n-
C6H14
, purity
>99%
), and a fluoroketone (FK-
5-1-12,
3MTM
Novec 649). Table1 summarizes the critical
properties of the two injectant fluids.
The choice of the injectant fluids had to fulfil several cri-
teria. Firstly, it was decided to use single-component inject-
ant fluids to avoid additional complexity in the description
of the thermal properties. Secondly, one alkane injectant was
desired as a typical component of gasoline fuel. For alkanes,
thermal decomposition (’cracking’) into lower order hydro-
carbons is a general concern in the heating process. This
may occur prior to
Tc
for alkanes longer than 10 C-atoms
(Smith etal. 1987). On the other hand, the critical pressure
increases with decreasing chain length of the alkane.
C6H14
,
hence, represents a good compromise for laboratory tests at
near- and supercritical conditions as it possesses a compa-
rably low
and
Tc
(Baab etal. 2017). Furthermore, Isbarn
etal. (1981) showed that cracking is negligible for
C6H14
for
the selected temperature range which, therefore, justifies the
single-component constraint.
In addition, we performed injection experiments with
FK at similar conditions with respect to the fluid’s critical
properties. As the critical point of
C6H14
and FK is different,
this leads to significantly different reservoir/chamber condi-
tions. For FK, this allows nozzle pressure ratios two orders
of magnitude below that for
C6H14
. The thermodynamic
Table 1 Critical properties of the injectant fluids taken from NIST
database (Lemmon etal. 2013)
Fluid
pc(MPa)
Tc(K)
𝜌c
(kg m
3)
n-hexane 3.03 507.8 233.2
Fluoroketone 1.87 441.8 606.8
Nitrogen 3.40 126.8 313.3
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Experiments in Fluids (2018) 59:44
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similarities become apparent by comparison of the expan-
sion process and the vapor-liquid saturation lines illustrated
in
p,T
phase diagrams in Fig.1. The data for saturation
line (solid), isopycnic lines (dashed), and critical point were
taken from the NIST database (Lemmon etal. 2013).
The expansion process starts at the reservoir conditions
labelled with index inj. Looking at the
p,T
phase diagram,
the reservoir conditions are left of the Widom line, which
separates the phase space into a region of liquid- and gas-
like properties (Gorelli etal. 2006). Hence, a fluid with liq-
uid-like density, but considerable compressibility expands
within the nozzle. During the relaxation process, the fluid
transforms from a high-density fluid with liquid-like proper-
ties towards a gas-like fluid of significantly lower density.
The expansion process may be separated into parts, namely
the expansion within the nozzle and the relaxation to ambi-
ent pressure downstream of the nozzle exit.
For the first part, we estimated the nozzle exit condi-
tions with a one-dimensional code that assumes isentropic
flow through the nozzle as detailed in Baab etal. (2014).
The nozzle exit conditions are indicated with e. In case of
underexpanded jets, the flow chokes within the nozzle and is
discharged with sonic velocity (Anderson 1990). This leads
to further expansion downstream of the nozzle exit and the
formation of a shock system within a distance of a few noz-
zle diameters, as shown in Fig.2. This barrel-shaped shock
system prevents the entrainment of
N2
(Harstad and Bellan
2006), which allows for a single-component treatment of the
flow up of the normal shock (Mach disk). For the present
injection conditions, it can be assumed, furthermore, that the
post-shock (index PS) pressure behind the Mach disk is equal
to the chamber pressure
pch
and that the immediate post-
shock temperature is approximately equal to
Tinj
(Harstad and
Bellan 2006; Ewan and Moodie 1986; Birch etal. 1987).
In general, the expansion process is characterized by real
gas effects due to the crossing of the region of transition
from liquid to gas-like properties. To illustrate the impli-
cations regarding the thermodynamic fluid properties, the
ratio of specific heats
𝛾
is plotted over the static pressure
during a virtual expansion process from reservoir to chamber
pressure in Fig.3. Here, highly non-linear behavior of
𝛾
can
be observed with a distinct maximum at the Widom line,
which marks the transition in the thermodynamic behavior.
Likewise, it is seen that the extent of non-ideal behavior is
quite sensitive to the individual injection conditions used.
For comparison, the
𝛾
evolution for the injection condi-
tions of Wu etal. (1999) is included in the diagram. Their
data set comprises supercritical ethylene injections
C2H4
into
low-pressure
N2
and represents a rare example of quantita-
tive data for such conditions. Despite the fact that similar
injection conditions with respect to the critical properties
were used, it can be seen that a nearly ideal expansion is
given in their experiments as the Widom line is not crossed in
the expansion process. Consequently, real gas effects may be
negligible for the presented
C2H4
experiments in contrast to
the present configurations. This demonstrates that a detailed
analysis of the thermodynamic regime for the expansion is
mandatory to characterize the injection conditions, especially
350 400 450 500 550 600
-2
-1
0
1
black Reservoir(pin j )
gray Nozzle exit (pe)
white Post-shock state (pch )
2 kg m
3
5 kg m
3
10 kg m
3
20 kg m
3
50 kg m
3
100 kg m
3
400 kg m
3
500 kg m
3
T(K)
log (p) (MPa)
Sat. line
Widom line
ρ
const
Critical point
pch 10MPa
pch 05MPa
pch 02MPa
pch 0 05 MPa
C
6
H
14
:T
in j
577 K
300 350 400 450 500 550
black Reservoir(pin j )
gray Nozzle exit (pe)
white Post-shock state(pch )
20 kg m
3
50 kg m
3
100 kg m
3
200 kg m
3
400 kg m
3
1000 kg m
3
1400 kg m
3
T(K)
Sat. line
Widomline
ρ
const
Critical point
pch 15MPa
pch 05MPa
FK: T
in j
500 K
Fig. 1 p,T-phase diagrams for
C6H14
and FK illustrating reservoir, nozzle exit, and post-shock conditions
Mixingzone
Potential core
pps =pch
p<<p
ch
pe>p
ch
pinj
Fig. 2 Schematic illustration of an highly underexpanded jet and its
shock/expansion system
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Experiments in Fluids (2018) 59:44
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in terms of non-ideal behavior. The data presented here serve
as a validation basis for CFD tools that are capable of mod-
elling real gas effects of expanding flows, particularly rel-
evant for the simulation of underexpanded jets resulting from
supercritical reservoir conditions. The experimental condi-
tions covered in this study are summarized in Table2.
3 Experimental facility andmeasurement
technique
3.1 Test chamber andinjection system
The jet experiments were performed in a cylindrical con-
stant-volume chamber. The chamber design and experimen-
tal strategy are the same as in Baab etal. (2016). Chamber
pressure and temperature are measured with a piezoresistive
pressure sensor (Keller PA-21Y) and two K-type thermocou-
ples, respectively.
The injection system is integrated into the front side end
wall, so that the axis of injector nozzle and cylinder coincide.
All
C6H14
injections use a classical common rail system pro-
viding injection pressures in the order of hundreds of bars.
For the low injection pressures used for the FK, a custom-
made injection system is used consisting of a sealed metal
container that is pressurized externally with nitrogen. The
injector is based on a magnetic-valve type commercially sold
by Robert Bosch GmbH fitted with a costume-made straight-
hole nozzle with a diameter of
D=0.236 mm
and length
of
L=1 mm
(i.e.
L
D
4.2
). Two temperature-controlled
heater cartridges surround the injector body and tip to heat
the fluid to the desired injection temperature. The tempera-
ture calibration of the injection system has been performed
inStotz (2011) and was verified prior to this campaign. The
uncertainty of injection temperature is considered to be
within
±2
K.
3.2 Laser‑induced thermal acoustics (LITA)
Laser-induced thermal acoustics (LITA), or more generally
referred to as laser-induced gratings (LIGS), is discussed to
more detail in the literature: Baab etal. (2016) with respect
to its application for fuel jets or, for instance (Kiefer and
Ewart 2011) for a full treatment of the theory. The discus-
sion of underlying principles shall, therefore, be limited to
the following brief outline. Two beams of a short-pulse laser
source (excitation laser) are crossed to modulate the density
of the test medium within the measurement volume. The
resulting spatially periodic perturbation with fringe spacing
𝛬
scatters light of a third input wave originating from a sec-
ond laser source (interrogation laser) into the coherent LITA
signal beam, the temporal evolution of which is a func-
tion of the gas properties. In this case, the LITA signal is
observed as damped oscillation with frequency
𝛺0
, which is
proportional to the local speed of sound in the test medium.
It is crucial to realize that the speed of sound is directly
obtained from signal frequency involving only a proportion-
ality constant (namely the grating spacing). The speed of
sound is, therefore, measured without the use of an equation
of state or other thermodynamic modelling assumptions.
Fig. 3 Evolution of the ratio of
specific heats
𝛾
in the expansion
process: a
C6H14
; b FK and
C2H4
0510 15 20 25 30
1
1.25
1.5
1.75
2
2.25
2.5(a) (b)
p(MPa)
γ
C
6
H
14
:
Tinj
= 577 K,
pch
=0
.
05 MPa
C6H14:Tinj = 600 K, pch =0.05 MPa
C6H14:Tinj = 630 K, pch =0.05 MPa
123456
p(MPa)
FK:
Tinj
= 500 K,
pch
=0
.
5MPa
C2H4:Tinj = 310 K, pch =0.2MPa (Wuetal.)
C2H4:Tinj = 358 K, pch =0.2MPa (Wuetal.)
Table 2 Overview of the experimental conditions for the investigated injections
Fluid/Gas
Tinj (K)
pinj (MPa)
Te(K)
pe(MPa)
NPR (−) Pos. CL (x/D) Figure
FK/
N2
500 6 490 3.77 4;12 55;80;110 8
C6H14
/
N2
553;577;600;630 30 534;559;582;612 8.16;9.77;11.08;12.47 150;600 110 6
C6H14
/
N2
600;630 30 582;612 11.08;12.46 60;150;600 110 9
C6H14
/
N2
577 30 559 9.77 30;60;150;600 173 7
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Experiments in Fluids (2018) 59:44
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This makes the technique particular feasible for the use in
fluids with non-ideal thermodynamic behavior for which the
development of accurate EoS is a difficult task.
3.2.1 Optical setup
The optical arrangement is illustrated in Fig.4. Note again
that it is adapted from earlier versions of the setup described
in Förster etal. (2015) and Baab etal. (2016). The descrip-
tion here is, therefore, limited to the essentials like the wave-
lengths of the excitation (
𝜆=1064 nm
) and interrogation
beams (
𝜆=532 nm
). All beams are focused by a lens with
a focal length of
700 mm
, which results in a
3
crossing
angle of the excitation beams. This results in an ellipsoi-
dally shaped interaction region of the excitation beams with
a diameter of approximately
200 μm
and less than 8 mm in
length. Note that this represents the worst-case approxima-
tion of the measurement volume as the interrogation beam
only partially overlaps the excited region. The same con-
figuration was used in Baab etal. (2016) that allowed reso-
lution of the radial profiles of the jets whose characteristic
dimensions typically comprise several nozzle diameters
(
D=236 μm
). To ensure that the optical alignment for this
study has the same accuracy in probing the centerline as the
previous study, the same alignment approach is used, i.e. the
visualization of the laser beam paths via a CCD chip.
3.2.2 Post‑processing
The LITA signal is characterized by a frequency propor-
tional to speed of sound in the medium. The corresponding
constant of proportionality is found in a calibration experi-
ment using a system with known thermodynamic properties.
The calibration procedure is identical to the one in Förster
etal. (2015), where the effect of uncertainties from the
calibration is found to be within 1.3%. One of the important
features of LITA is that this characteristic frequency is also
found if the LITA is heavily deteriorated by scattering events
caused for instance by inhomogeneous density fields along
the beam path lengths and turbulence. This advantage makes
LITA especially desirable for the present application. Two
post-processing algorithms are used here. For chamber pres-
sures at 0.2 MPa and below, the signal frequency is derived
from an individual detection of the oscillation periods. This
approach is found superior to an FFT due to the small num-
ber of signal oscillations found under these conditions. It is
based on determining the intersection of tangents on rising
and falling edge defined by a gradient criterion and was vali-
dated in Baab etal. (2016). For all chamber pressures above
0.2 MPa, LITA signals were post-processed using a FFT.
Although both approaches yield identical results, the FFT
was selected as being the more conventional analysis tool.
While the speed of sound is directly measured by extract-
ing the signal frequency, it is possible to derive further fluid
properties through a thermodynamic interpretation of this
parameter. For a mixture of gases in local thermodynamic
equilibrium, the speed of sound
amix
is generally a function
of species concentration, temperature and pressure, that is
where
cmix
contains the mass fractions of the mixing com-
ponents. Hence, for an isobaric mixing process at known
pressure,
amix
is defined by the local mixture composition
and temperature. On the basis of a measured speed of sound
ameas
, either T can be determined for known
cmix
or vice
versa. In its simplest form, this relation may be given by the
ideal gas law,
amix
(c
mix
,T,p)=
𝛾
mix
R
mix
T with
𝛾mix
as the
ratio of specific heats and
Rmix
the specific gas constant for
the ideal gas mixture.
However, if one or more mixture components cannot be
approximated as ideal gases, this simple relation for
amix
is not valid. Especially for fluids close to their saturation
state (e.g., dew-point line) and at high pressures (particu-
larly near the critical pressure), incorporation of real fluid
behavior is mandatory. High-order equations of state (EoS)
in combination with non-linear mixing rules are then neces-
sary to calculate thermodynamic properties. Considering the
thermodynamic regimes for the presented injection case as
discussed in Sect.2, these effects have to be considered here.
Again, this approach was developed in Baab etal. (2016)
and the inclined reader is referred to this publication for a
more rigorous treatment of the underlying thermodynamics.
To provide a brief description of the principle, it can be
said that the ambiguity of
ameas
with respect to
cmix
and T
is overcome by assuming an adiabatic mixing of injectant
and ambient gas. This is justified as the mixing process is
dominated by advection, while diffusion plays a negligible
role in the mass and energy transport.
(1)
amix =amix(cmix ,T,p),
50%50%
10%
90%
Excitation-
laser:
1064 nm
pulsed
Interrogation-
laser:
532 nm
continuous
Alignment
beam Lens
x
z
DAQ
Flash lamp
Q-Switch PTU Trigger
Fluid Injector
Detector
Test chamber
y
Fig. 4 Experimental setup of LITA measurements in fuel jets
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Experiments in Fluids (2018) 59:44
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The specific enthalpy of a real mixture consists of
the enthalpy of the ideal mixing process as well as an
excess contribution from non-ideal mixing process. Here,
hmix(cmix ,Tmix,pch )
of the real mixture at an adiabatic mixing
temperature
Tmix
can then be expressed as follows:
Here,
hid
is the specific enthalpy that originates from ideal
mixing of fluid and
N2
, while
hexcess
accounts for the non-
ideality of the binary system. As discussed in Baab etal.
(2016), the pressure and temperature of both the injected
fluid and the environment are known prior to mixing. In the
calculation procedure,
amix
and all
hi
(including the excess
contribution) have been tabulated from REFPROP for the
relevant t and p range. An iterative scheme optimizes for
cmix
and
Tmix
, so that
while at the same time
Although this approach yields an approximation of
cmix
and
Tmix
, it should be stressed that it is possible to account
for real fluid behavior using the NIST database. Hence, the
developed approach is generally valid for non-ideal mixing
provided that energy transfer through diffusion (of heat or
mass) within the mixing zone is negligible. The general rela-
tion between
amix
,
Tmix
and
cmix
is illustrated in Fig.5. For
C6H14
, this relationship is non-monotonic for small concen-
trations. However, all measured speeds of sound were found
below
350 m s1
, which assures a distinct determination. For
FK, on the other hand, this ambiguity does not exist at the
investigated conditions.
4 Results
The results are presented in two parts. Experimental speed
of sound data sets is provided at different positions and vary-
ing injection temperature. Based on these measurements,
centerline concentrations are estimated using an adiabatic
mixing model based on non-ideal fluid properties.
4.1 Experimental speed ofsound data
In a first step, the range of the speed of sound values for the
particular binary system (fluid/gas) are evaluated. Under the
assumption of a fully adiabatic mixing process of injectant
(2)
h
mix
(c
mix
,T
mix
,p
ch
)=…
hexcess(cmix,Tmix ,pch )+hid(cmix ,Tmix,pch ).
(3)
amix
(c
mix
,T
mix
,p
ch
)
!
=a
meas,
(4)
h
mix(cmix ,Tmix,pch )−hexcess(cmix,Tmix,pch )
!
=…
c
fluid
h
fluid
(T
ps
,p
ch
)+(1c
fluid
)h
N2
(T
ch
,p
ch
)
.
and ambient gas, this range is determined by the pure inject-
ant at
Tinj
and
N2
at
Tch
. The pressure within the far-field mix-
ing domain is equal to the corresponding chamber pressure
pch
as the injected jet has fully adapted at this stage. However,
variations in speed of sound due to the different chamber
pressures are small and so this first assessment is done as an
example for
pch =0.5 MPa
as for Fig.5. Table3 lists the rel-
evant speed of sound data for both injectants and the ambient
gas. All data are taken from NIST database (Lemmon etal.
2013). It is evident that the initial speed of the sound of the
pure injectant defines the possible range for the mixture and,
ultimately, the sensitivity of
amix
towards the mixture prop-
erties. In the case of
C6H14
, this spread is beyond
100 m s1
,
which proved to be sufficient in preceding studies (Baab etal.
2016). For the FK/
N2
, this spread increases to
240 m s1
as
a result of the very low speed of sound of FK, which makes
the fluid an interesting choice both from scientific point of
view and the diagnostic technique itself.
Figure6 shows centerline measurements for two different
NPRs at varying
Tinj
. Here, and for all following figures, error
bars represent the standard error of the mean (i.e. one sample
standard deviation divided by the square root of the sample
size). As detailed in Baab etal. (2016), an approximately
linear relationship was found between
ameas
and
Tinj
for fixed
x/D. The data in Fig.6 show that this trend is preserved even
when the expansion ratio is four times larger (600 instead of
150). Likewise, the difference in measured speed of sound for
the different NPR is approximately constant, i.e. same gradi-
ent, for all injection temperatures. Note that the existing data
set in Baab etal. (2016) only contains one NPR of 150 and
the axial range is limited to
xD=55, 80
, and 110. Because
a deviation from this trend is expected for a position further
downstream of the injection point, Fig.7 provides
ameas
in the
far-field at
x
D
=173
for various NPRs. It is seen that the
00.20.40.60.
81
100
150
200
250
300
350
400
c
mix
(kgkg
1)
amix (m s1)
C6H14:Tinj = 630 K
FK: Tinj = 500 K
Fig. 5 Speed of sound for adiabatic mixing of n-hexane and FK with
N2
at p
ch
=
0.5 MPa
:
cfluid
refers to the concentration of
C6H14
and
FK, respectively
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Experiments in Fluids (2018) 59:44
1 3
Page 7 of 10 44
linear slope is maintained for NPRs down to 60, but deviates
for lower NPRs, i.e.
NPR =30
.
This behavior is most likely explained by the lower
injectant concentrations due to the lower NPR and the
resulting higher entrainment of
N2
. In addition, the low
injectant concentrations approach the non-linear region
in the speed of sound dependence, as shown in Fig.5.
Hence, for the following experiments, the measurement
position was set closer to the nozzle again. Furthermore,
it is seen that as fuel concentration reduces, the measured
speed of sound approaches the value of nitrogen at cham-
ber conditions. To vary the nozzle pressure ratio further,
an injectant with lower initial speed of sound is required,
so that low concentrations result in a significant change of
amix
compared to nitrogen.
Following these considerations, we used FK as an inject-
ant for the very low NPR. Figure8 shows the obtained
ameas
for FK at
Tinj =500 K
for different x/D along with the data
acquired for
C6H14
in Baab etal. (2016). However, instead
of varying
Tinj
, Fig.8 focuses on the axial evolution for dif-
ferent NPRs. Similar trends as previously for both the injec-
tion temperature and axial position are found for the much
lower NPRs. Given that NPRs as low as 4 are realized for
the FK jets, the jets approach the limit for underexpansion
and, hence, conclude the highly underexpanded flow regime.
Figure9 shows the evolution of
ameas
along the center-
line for decreasing NPR at
xD=110
. For the
C6H14
jets,
it is seen that a change in injection temperature results in an
approximately constant offset of the linear trend, while, for
FK, the gradient of the linear slope changes. This is due to
the lower
aFK (Tinj,pch )
. In addition to the graphic illustra-
tions, Table4 in the appendix provides a detailed listing of
the acquired experimental data. Furthermore, radial profiles
at fixed axial positions were published in Baab etal. (2016)
for
C6H14
at
NPR =150
.
4.2 Mixing characterization
The adiabatic mixing approach was used for all conditions
in Table2. Figure10 summarizes the values of the center-
line concentrations obtained in this work. The results are
plotted over a non-dimensional parameter that originates
Table 3 Speed of sound of pure
n-hexane, FK and
N2
at relevant
temperatures and constant
pressure of
pch =0.5 MPa
T (K) 295 500 554 577 600 630
ahexane
(m/s) 226.1 232.3 237.9 244.9
aFK
(m/s) 109.7
aN2
(m/s) 350.8
550 570 590 610 630
270
290
310
330 x/D = 110
y/D=0
T
inj
(K)
ameas (m s1)
C6H14:NPR= 150 (Baabet al.)
C6H14:NPR= 600
Fig. 6
C6H14
injections with nozzle pressure ratio of 150 and 600
101102103
290
310
330
350 x/D =173
y/D=0
NPR
(
-
)
ameas (m s1)
Fig. 7
C6H14
: influence of different chamber pressures
55 80 110
250
270
290
310
x
/
D
ameas (m s1)
C6H14:NPR= 150 (Baab et al.)
FK: NPR=12
FK: NPR=4
Fig. 8 Comparison
C6H14
and FK at different axial positions x/D
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Experiments in Fluids (2018) 59:44
1 3
44 Page 8 of 10
from a similarity analysis initially proposed by Chen and
Rodi (1980) and used in Baab etal. (2016) to describe the
axial concentration decay for momentum-controlled mixing.
The dotted line in Fig.10 represent this similarity parameter
given by the following:
Here, A is an empirical scaling constant (set to
A=5.4
),
𝜌e
the injectant density at the nozzle exit plane, and
𝜌ch
the
ambient gas density. While this equation was successful in
condensing experimental concentration data for the n-hex-
ane jet injected into nitrogen at
pch =0.2 MPa
as well as for
the data published by Wu etal. (1999), noticeable deviations
are found for the present data that feature higher chamber
pressures. This was initially surprising as Molkov (2012)
(5)
c
cl =A
𝜌e
𝜌
ch 0.5
x
D
1
.
used Eq.5 with
A=5.4
as well to condense experimental
concentration data for both expanded and underexpanded,
non-ideal hydrogen jets at high pressures – and, hence, for
a wide range of expansion ratios and other experimental
conditions (i.e., pressure ratio, nozzle diameter, and axial
distance).
However, it is explained due to the fact that experimental
data featured in Molkov (2012) focus on safety aspects of
hydrogen storage. Therefore, it exclusively considers leakage
of high-pressure storage and, hence, an expansion to ambient
pressure. While a chamber pressure of
pch =0.2 MPa
, as
used for our previous experiments published in Baab etal.
(2016) as well as for the work of Wu etal. (1999), seems
acceptably close to this value, higher chamber pressures of
up to
1.5 MPa
are not described accurately. Looking at Eq.5
again, it is seen that the correlation includes only a relative
factor for the injectant/chamber conditions, but makes no
statement about the absolute level of the nozzle flow. There-
fore, we chose to include a non-dimensional parameter that
relates to the nozzle exit conditions, namely the exit Reyn-
olds number
Re
e=
𝜌
e
v
e
D
𝜂
e
. This leads to an empirical fitting
function in the form:
By fitting all data points, included those published in Baab
etal. (2016) and Wu etal. (1999), a new empirical correla-
tion is found for the constants
A=75
,
n=0.6
,
m=−1.2
and
C=1
. As seen in Fig.11, this relationship provides
a better representation of the complete data set. Note that
these constants, in this study and in Molkov (2012), are
empirical, obtained by the best fit to the data, and do not
represent a physical property. At this stage, it is, hence, not
applicable for the entirety of possible injection conditions
but optimized for the data in the present and cited studies.
5 Conclusions
In this study, we investigated the mixing characteristics of
underexpanded fluid jets with supercritical reservoir con-
ditions discharged into a cold nitrogen atmosphere at sub-
critical pressure (with respect to the injectant). By applying
laser-induced thermal acoustics, a technique previously sug-
gested and successfully demonstrated for the present flow
fields, a quantitative speed of sound data set is generated for
a wide range of experimental conditions. The need for such
experimental database is frequently stated in the literature
and the main intention of this paper is to present reference
test cases for evaluating numerical tools. To our knowledge,
(6)
1
ccl
=
x
D
A
𝜌e
𝜌
ch n
Ree
10
5
m1
+C
.
101102
270
290
310
330
350 x/D = 110
y/D=0
NPR(-)
ameas (m s1)
C6H14:Tinj = 630 K
C6H14:Tinj = 600 K
FK: Tinj = 500 K
Fig. 9 Comparison
C6H14
and FK for varying nozzle pressure ratios
0246810
0
0.2
0.4
0.6
0.8
1
x
D5.4ρe
ρch
0.51
ccl (kg/kg)
FK
C6H14
Wu et al.
Similaritylaw
Fig. 10 Similarity analysis of
ccl
for
C6H14
, FK, and
C2H4
injections
using the approach in Baab etal. (2016)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
Experiments in Fluids (2018) 59:44
1 3
Page 9 of 10 44
it is the first study to provide quantitative data for validation
to this extent.
In this study, two injectants, different in respect to their
critical properties, viz., n-hexane and Novec 649, are studied
for nozzle pressure ratios from 4 to 600, hence covering a
wide range from highly to extremely highly underexpanded
jets. Simultaneously, the injection temperature is varied to
resolve characteristic trends in the resulting speed of sound
distribution along different axial positions on the centerline.
In addition to the measured speed of sound, an adiabatic
mixing model based on non-ideal fluid properties is used to
estimate local mixture compositions. All concentration data
are expressed by an empirical fit based on the injectant prop-
erties at the nozzle exit. For the presented data, it states that
the far-field mixing is well characterized using the calculated
exit density, the injected mass flux, and the density of the
gas atmosphere in which the jet is injected into. Hence, the
proposed fit allows to estimate the mixing characteristics of
underexpanded fluid jets without the requirement to charac-
terize the complex thermodynamic process of the expansion
from the nozzle exit to chamber conditions.
Acknowledgements This work was performed within the Collabo-
rative Research Center “Technological foundations for the design of
thermally and mechanically highly loaded components of future space
transportation systems (SFB-TRR40)”. The authors would like to thank
the German Research Foundation (Deutsche Forschungsgemeinschaft
DFG) for the financial support of this work.
Open Access This article is distributed under the terms of the Crea-
tive Commons Attribution 4.0 International License (http://creat iveco
mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribu-
tion, and reproduction in any medium, provided you give appropriate
credit to the original author(s) and the source, provide a link to the
Creative Commons license, and indicate if changes were made.
0246
81
0
0
0.2
0.4
0.6
0.8
1
x
D75 ρe
ρch
0.6Ree
105
1.21
+1
ccl (kg/kg)
FK
C6H14
Wu et al.
f(x)=1/x
Fig. 11 Empirical fit proposed on basis of the experimental data to
include both exit density ratio and Reynolds number
Table 4 Summary of the experimental data set: all measurements refer to
yD=0
Fluid NPR
pinj (MPa)
pe(MPa)
pch (MPa)
Tinj (K)
Te(K)
Tch (K)
Ree
x/D
ameas
(ms
1)
cad(kg kg1)
FK 12 6.1 3.77 0.5 500 490 295 3.26e+05 80
247.6 ±4.0
0.63 ±0.015
FK 12 6.2 3.77 0.5 500 490 295 3.26e+05 110
273.6 ±5.7
0.53 ±0.024
FK 4 6.2 3.77 1.5 500 490 295 3.26e+05 55
261.0 ±6.5
0.60 ±0.023
FK 4 6.1 3.77 1.5 500 490 295 3.26e+05 80
273.6 ±3.2
0.56 ±0.013
FK 4 6.2 3.77 1.5 500 490 295 3.26e+05 110
295.5 ±9.1
0.46 ±0.048
C6H14
600 30 8.15 0.05 553 534 295 4.87e+05 110
270.2 ±6.4
0.84 ±0.032
C6H14
600 30 9.76 0.05 577 559 295 4.87e+05 110
282.0 ±3.7
0.78 ±0.020
C6H14
600 30 11.08 0.05 600 582 295 4.87e+05 110
292.4 ±5.4
0.76 ±0.017
C6H14
600 30 12.47 0.05 630 612 295 4.86e+05 110
303.8 ±4.8
0.73 ±0.016
C6H14
150 30 8.16 0.2 553 534 295 4.88e+05 110
296.5 ±10.4
0.69 ±0.118
C6H14
150 30 9.77 0.2 577 559 295 4.88e+05 110
307.1 ±3.9
0.66 ±0.047
C6H14
150 30 11.08 0.2 600 582 295 4.88e+05 110
320.6 ±5.9
0.61 ±0.073
C6H14
150 30 12.46 0.2 630 612 295 4.87e+05 110
326.9 ±5.2
0.62 ±0.067
C6H14
600 30 9.76 0.05 577 559 295 4.87e+05 173
295.5 ±4.8
0.73 ±0.027
C6H14
150 30 9.77 0.2 577 559 295 4.88e+05 173
317.8 ±3.1
0.60 ±0.020
C6H14
60 30 9.79 0.5 577 559 295 4.90e+05 173
340.8 ±4.9
0.43 ±0.043
C6H14
30 30 9.76 1.0 577 559 295 4.97e+05 173
345.4 ±3.2
0.39 ±0.023
C6H14
60 30 11.09 0.5 600 582 295 4.90e+05 110
341.3 ±3.0
0.47 ±0.025
C6H14
150 30 11.08 0.2 600 582 295 4.88e+05 110
320.6 ±5.9
0.62 ±0.035
C6H14
600 30 11.08 0.05 600 582 295 4.87e+05 110
292.4 ±3.2
0.77 ±0.017
C6H14
60 30 12.46 0.5 630 612 295 4.91e+05 110
346.6 ±2.4
0.49 ±0.019
C6H14
150 30 12.46 0.2 630 612 295 4.87e+05 110
326.9 ±5.2
0.62 ±0.031
C6H14
600 30 12.47 0.05 630 612 295 4.86e+05 110
303.8 ±3.0
0.75 ±0.016
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Experiments in Fluids (2018) 59:44
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44 Page 10 of 10
Appendix
In addition to Figs.6, 7, 8, 9, 10, 11, all data are summarized
in Table4 for easy access. Parameters measured in the indi-
vidual experiments include
pinj
,
pch
,
Tch
, x/D, and
ameas
.
Tinj
is based on measured data, but ultimately results from the
calibration procedure described in Stotz (2011).
The parameter
pe
and
Te
are calculated based on the isen-
tropic nozzle flow approach detailed in Baab etal. (2014),
cad
using
ameas
and the adiabatic mixing model. Both
ameas
and
cad
are stated plus/minus the standard error of the mean.
All data are obtained at the centerline. Note that radial
profiles for
C6H14
and
NPR =150
are published in Baab
etal. (2016).
References
Anderson JD (1990) Modern compressible flow: with historical per-
spective, vol 12. McGraw-Hill, New York
Anitescu G, Bruno TJ, Tavlarides LL (2012) Dieseline for supercritical
injection and combustion in compression-ignition engines: vola-
tility, phase transitions, spray/jet structure, and thermal stability.
Energy Fuels 26(10):6247
Baab S, Förster F, Lamanna G, Weigand B (2016) Speed of sound
measurements and mixing characterization of underexpanded fuel
jets with supercritical reservoir condition using laser-induced ther-
mal acoustics. Exp Fluids 57(11):172
Baab S, Lamanna G, Weigand B (2014) Combined elastic light scatter-
ing and two-scale shadowgraphy of near-critical fuel jets. ILASS
Americas 26th annual conference on liquid atomization and spray
systems, Portland, OR, May 2014
Baab S, Lamanna G, Weigand B (2017) Two-phase disintegration of
high-pressure retrograde fluid jets at near-critical injection tem-
perature discharged into a subcritical pressure atmosphere. J Mul-
tiph Flow (under review)
Banholzer M, Müller H, Pfitzner M (2017) Numerical investigation
of the flow structure of underexpanded jets in quiescent air using
real-gas thermodynamics. 23rd AIAA computational fluid dynam-
ics conference
Birch AD, Hughes DJ, Swaffield F (1987) Velocity decay of high pres-
sure jets. Combust Sci Technol 52(1–3):161
Bonelli F, Viggiano A, Magi V (2013) A numerical analysis of hydro-
gen underexpanded jets under real gas assumption. J Fluids Eng
135(12):121101
Chen CJ, Rodi W (1980) Vertical turbulent buoyant jets: a review of
experimental data. Pergamon Press, Oxford
De Boer C, Bonar G, Sasaki S, Shetty S (2013) Application of super-
critical gasoline injection to a direct injection spark ignition
engine for particulate reduction. Tech. rep., SAE Technical Paper
Donaldson C, Snedeker RS (1971) A study of free jet impingement.
Part 1. Mean properties of free and impinging jets. J Fluid Mech
45(2):281
Ewan BCR, Moodie K (1986) Structure and velocity measurements in
underexpanded jets. Combust Sci Technol 45(5–6):275
Franquet E, Perrier V, Gibout S, Bruel P (2015) Free underexpanded
jets in a quiescent medium: a review. Prog Aerosp Sci 77:25
Förster FJ, Baab S, Lamanna G, Weigand B (2015) Temperature and
velocity determination of shock-heated flows with non-reso-
nant heterodyne laser-induced thermal acoustics. Appl Phys B
121(3):235
Gorelli F, Santoro M, Scopigno T, Krisch M, Ruocco G (2006) Liquid-
like behavior of supercritical fluids. Phys Rev Lett 97(24):245702
Hamzehloo A, Aleiferis P (2016) Numerical modelling of transient
under-expanded jets under different ambient thermodynamic
conditions with adaptive mesh refinement. Int J Heat Fluid
Flow 61(Part B):711. https ://doi.org/10.1016/j.ijhea tflui dflow
.2016.07.015
Hamzehloo A, Aleiferis P (2016) Gas dynamics and flow character-
istics of highly turbulent under-expanded hydrogen and methane
jets under various nozzle pressure ratios and ambient pressures.
Int J Hydrog Energy 41(15):6544
Hamzehloo A, Aleiferis P (2014) Numerical modelling of mixture
formation and combustion in disi hydrogen engines with various
injection strategies. Tech. rep., SAE Technical Paper
Harstad K, Bellan J (2006) Global analysis and parametric depend-
encies for potential unintended hydrogen-fuel releases. Combust
Flame 144(1):89
Idicheria CA, Pickett LM (2007) Quantitative mixing measurements
in a vaporizing diesel spray by rayleigh imaging. Tech. rep., SAE
Technical Paper
Isbarn G, Ederer H, Ebert K (1981) Modelling of chemical reaction
systems. Springer, New York, pp 235–248
Khaksarfard R, Kameshki M, Paraschivoiu M (2010) Numerical simu-
lation of high pressure release and dispersion of hydrogen into air
with real gas model. Shock Waves 20(3):205
Kiefer J, Ewart P (2011) Laser diagnostics and minor species detec-
tion in combustion using resonant four-wave mixing. Prog Energy
Combust Sci 37(5):525
Lemmon EW, Huber ML, McLinden MO (2013) NIST Standard Ref-
erence Database 23: reference fluid thermodynamic and trans-
port properties—REFPROP version 9.1. National Institute of
Standards and Technology, Standard Reference Data Program,
Gaithersburg
Mohamed K, Paraschivoiu M (2005) Real gas simulation of hydro-
gen release from a high-pressure chamber. Int J Hydrog Energy
30(8):903
Molkov V (2012) Hydrogen safety engineering: the state-of-the-art and
future progress. Elsevier, Oxford
Smith RL, Teja A, Kay W (1987) Measurement of critical temperatures
of thermally unstable n-Alkanes. AIChE J 33(2):232
Stotz I (2011) Shock tube study on the disintegration of fuel jets at
elevated pressures and temperatures. Ph.D. Thesis, University of
Stuttgart
Tavlarides LL, Antiescu G (2009) Supercritical diesel fuel composi-
tion, combustion process and fuel system. US Patent 7,488,357
Velikorodny A, Kudriakov S (2012) Numerical study of the near-field
of highly underexpanded turbulent gas jets. Int J Hydrog Energy
37(22):17390
Vuorinen V, Yu J, Tirunagari S, Kaario O, Larmi M, Duwig C,
Boersma B (2013) Large-eddy simulation of highly underex-
panded transient gas jets. Phys Fluids 25(1):016101
Whitaker P, Kapus P, Ogris M, Hollerer P (2011) Measures to reduce
particulate emissions from gasoline DI engines. SAE Int J Engines
4(2011–01–1219):1498
Wu PK, Shahnam M, Kirkendall KA, Carter CD, Nejad AS (1999)
Expansion and mixing processes of underexpanded supercritical
fuel jets injected into superheated conditions. J Propuls Power
15(5):642
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1.
2.
3.
4.
5.
6.
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... The evaluation is conducted for n-hexane at three different pressures, namely 300 115 6.19 Comparison of the centerline concentration for the investigated n-hexane jets. Experimental speed of sound data were taken from Baab et al. [14] and Förster et al. [80] and have been post-processed using the adiabatic mixture concept. . . . . . 116 6.20 Pressure-temperature diagram of argon together with an approximated isentropic expansion path for a perfect gas (Ar: γ = 1.67) from reservoir to chamber conditions.118 ...
... Optical access is provided by three quartz windows. Recently, Baab et al. [14] and Förster et al. [80] used laser-induced thermal acoustics (LITA) to investigate the mixing process of highly underexpanded jets within this chamber. The speed of sound can be directly measured by extracting the frequency of the LITA signal and post-processing it using, for instance, the Fast Fourier transformation. ...
... The speed of sound can be directly measured by extracting the frequency of the LITA signal and post-processing it using, for instance, the Fast Fourier transformation. From these two recent measurement campaigns [14,80] a total of 14 injection experiments have been reported. The results of these experimental investigations [14,80] are summarized in Tab. ...
Thesis
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Injection, mixing and combustion under high-pressure conditions are key processes in modern energy conversion machines. Driven by the demand for higher efficiency and reduction of pollutants, intensive investments are made in recent years in the further development of especially two types of fuel-fired engines: liquid-propellant rocket engines (LREs) and gas engines (GEs). This arises from the fact, that LREs will remain an essential component for payload launchers in the foreseeable future and that GEs fired with hydrogen or natural gas are a possible solution to gradually diversify towards cleaner energy conversion machines. Computational fluid dynamics (CFD) can contribute to a better understanding of the injection, mixing and combustion processes within these types of engines. Here, especially one thermodynamic topic is of paramount interest within recent years: phase separation processes under initially supercritical conditions. This work presents a CFD tool that enables the thorough investigation of these processes. Both a pressure- and a density-based solver framework are introduced. The first comprises different formulations of the pressure equation to cover a wide range of Mach numbers. A double-flux scheme specifically tailored for real-gas flows is the core of the density-based solver. The thermodynamic framework relies on a rigorous and fully conservative description of the thermodynamic state. Cubic equations of state and the departure function concept form the basis of the thermal and caloric closure. Consequently, real-gas effects are included inherently. Multicomponent phase separation processes are considered by means of a minimization of the Gibbs energy. For the investigation of the non-premixed combustion process, a tabulated combustion model based on the flamelet concept is employed. Overall, measurement data from five different experimental test campaigns are used to validate the numerical framework. Both Large-Eddy Simulations and Reynolds-Averaged Navier-Stokes simulations are performed. Most of the simulations are conducted with the pressure-based framework. In the first step, real-gas effects in underexpanded jets are investigated. Very good agreement with experimental speed of sound measurements is found. Further investigations demonstrate the importance of the consideration of real-gas effects to correctly capture the jet mixing process. Next, the phase separation process in an underexpanded argon jet is studied. In the fully developed jet, the single-phase instabilities are found downstream of the nozzle exit and upstream of the Mach disk. This is in excellent agreement with experimental Mie scattering measurements. Next, the possibility of phase separation under GE-like operating conditions is investigated. Two different fuels - hydrogen- and methane-based - are considered. For the latter, pronounced phase separation processes are found which are triggered by a strong expansion and a mixing with the ambient gas. No two-phase effects occur in the hydrogen-based fuel as the critical temperature of the less volatile component is dramatically lower as in the methane-based fuel. For the investigation of phase separation processes under LRE-like operating conditions a combined experimental and numerical study together with the University of Stuttgart is conducted. Three different test cases are defined. The characteristics of the phase formation process agree well between experiments and simulations. The single-phase instability is caused solely by a mixing process of the injected fuel with the ambient gas. Next, the prediction capabilities of the pressure- and the density-based solver are assessed in detail. For the pressure-based approach a very good agreement with three experimental test cases is found. The density-based method, in contrast, yields possibly nonphysical states indicated by a strong entrainment into the two-phase region. Finally, phase separation effects in a hydrogen and a methane flame under LRE-typical operating conditions are studied. Single-phase instabilities are found on both sides of the flamelet caused by the low temperatures and the presence of water. For the methane flame, a Large-Eddy Simulation for a reference experiment is conducted. The results show that the region of phase separation is mostly restricted to the oxygen core. The OH* emission images indicate that both flame length and shape are in good agreement with the experimental results.
... In order to gain a better understanding of high-pressure fluid mixing with respect to the interplay between large scale dynamics and micro scale diffusion, in this paper we present a critical evaluation of speed of sound measurements in binary mixtures, performed by means of Laser Induced Thermal Acoustic (LITA). The experiments have been performed exclusively in regime III in both underexpanded [36,41] and subsonic high-pressure jets [42]. The advantage of fluid injection experiments in regime III is twofold. ...
... We used laser-induced thermal acoustics (LITA) to obtain quantitative jet mixing data along the centerline in binary mixtures. Several experimental studies [36,41,42] demonstrated the applicability of the technique to turbulent, mixing jets and provided a comprehensive speed of sound database. ...
... In the following sections, the already existing LITA speed of sound databases [42,41] for underexpanded and submerged turbulent jets are critically evaluated. As clarified in Section 1, the objective is twofold. ...
Article
The present work provides an overview on the possible phase transitions associated with supercritical fluid injection and a detailed evaluation of the mixing process between injectant fluid and quiescent ambience. The experiments cover superheated liquid disintegration, pseudo-boiling transition and single-phase jets under different nozzle pressure ratios. Pseudo-boiling effects emerge when rapid, subsequent changes in pressure/temperature interact with the non-linear behavior of thermodynamic response functions across the Widom line. The associated density fluctuations cause a significant increase in the scattering cross section and may lead to thermo-convective instabilities. Our analysis of the mixing process demonstrates the limited applicability of the adiabatic mixing model, which is often restricted to short residence times even in highly turbulent jets (Re=O(105)). Specifically, our findings show the importance of considering all coupled transport processes in the analysis of mixing problems at high pressures, in particular in presence of large mass concentration and temperature gradients.
... In this context, Baab et al. [8,9] and Förster et al. [10] performed supercritical injection studies in order to deliver quantitative jet mixing data. Using laser-induced thermal acoustics (LITA), they measured the local speed of sound in high-pressure injection with varying temperature and ambient pressure. ...
... Considering this, an extended analysis of the mixing data with regard to the applicability of the adiabatic mixing model is carried out. In the studies of Baab et al. [8] and Förster et al. [10], underexpanded jets followed the adiabatic mixing model quite accurately for axial distances of / below 110. However, in dense single-phase jets, deviations are expected in comparison to an analytical solution. ...
... Baab et al. [8] and Förster et al. [10] showed adiabatic and self-similar characteristics within underexpanded jets for axial distances of / < 110. Underexpansion implies high exit velocities and an eruptive discharge of the fluid. ...
Chapter
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Mixing characteristics of supercritical injection studies were analyzed with regard to the necessity to include diffusive fluxes. Therefore, speed of sound data from mixing jets were investigated using an adiabatic mixing model and compared to an analytic solution. In this work, we show that the generalized application of the adiabatic mixing model may become inappropriate for subsonic submerged jets at high-pressure conditions. Two cases are discussed where thermal and concentration driven fluxes are seen to have significant influence. To which extent the adiabatic mixing model is valid depends on the relative importance of local diffusive fluxes, namely Fourier, Fick and Dufour diffusion. This is inter alia influenced by different time and length scales. The experimental data from a high-pressure n-hexane/nitrogen jet injection were investigated numerically. Finally, based on recent numerical findings, the plausibility of different thermodynamic mixing models for binary mixtures under high pressure conditions is analyzed.
... High-pressure gaseous fuel injection generates an underexpanded jet that exhibits highly complex physics including turbulence, mixing layers, strong Prandtl-Meyer expansion fans and shock waves, as well as nonlinearly changing fluid properties at varying pressures and temperatures [5][6][7] . The jet characteristics depend on the nozzle pressure ratio, NPR, that is defined as the ratio between the upstream nozzle injection pres-sure and the ambient back pressure, NPR = P o /P ∞ 8 . ...
Article
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The flow field of an impulsively started round, confined nitrogen jet was investigated using combined high speed schlieren imaging and particle velocimetry (PIV) measurements. PIV measurements were carried out at five different, normalized times (55 ≤ t * ≤ 392) relative to jet intrusion into a constant volume chamber. Between 100 < t * < 250, the NPR linearly increased to that for a moderately underexpanded jet (NPR ≈ 3.5). Distributions of the mean flow and Reynolds normal and shear stresses revealed two different stages in jet development. In stage I (t * = 55 to 103), prior to clear shock cell appearance, the jet was characterized by a leading, toroidal vortex whose induced recirculatory motion inhibited the growth of the trailing jet's shear layer instabilities and radial spreading. In stage II (t * = 196 and 392), the jet became moderately underexpanded (NPR ≥ 2) and close to the nozzle exit, flow characteristics resembled those of a "co-annular" jet. The "co-annular" region did not extend beyond 15D. An analysis of instantaneous vortex numbers and strengths further supported the two identified stages in jet development and their connection to shear layer instability growth. Based on the distributions of mean flow and Reynolds stresses, it was shown that the static pressure gradient along the jet's centerline is mainly governed by the dynamic pressure gradient. Gradients of the Reynolds normal and shear stresses play a minor role. Important for gaseous fuel injection at high injection pressures, results point at limited mixing during stage I and enhanced mixing during stage II.
... To utilize LITA as a reliable tool for experimental investigation in jet disintegration or droplet evaporation studies, a high spatial resolution is imperative. Studies by Baab et al. (2016), Baab et al. (2018), andFörster et al. (2018) already showed the capability of acquiring quantitative speed of sound data in jet disintegration. Especially to be emphasised are the investigations by Baab et al. (2018), which demonstrated the potential of acquiring speed of sound data for multi-component jet mixing at high pressures in the near nozzle region. ...
Article
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Mixing and evaporation processes play an important role in fluid injection and disintegration. Laser-induced thermal acoustics (LITA) also known as laser-induced grating spectroscopy (LIGS) is a promising four-wave mixing technique capable to acquire speed of sound and transport properties of fluids. Since the signal intensity scales with pressure, LITA is effective in high-pressure environments. By analysing the frequency of LITA signals using a direct Fourier analysis, speed of sound data can be directly determined using only geometrical parameters of the optical arrangement no equation of state or additional modelling is needed at this point. Furthermore, transport properties, like acoustic damping rate and thermal diffusivity, are acquired using an analytical expression for LITA signals with finite beam sizes. By combining both evaluations in one LITA signal, we can estimate mixing parameters, such as the mixture temperature and composition, using suitable models for speed of sound and the acquired transport properties. Finally, direct measurements of the acoustic damping rate can provide important insights on the physics of supercritical fluid behaviour. Graphic Abstract
... The technique has also been successfully applied to calibration of Two-Colour Planar Laser Induced Fluorescence imaging of temperature distributions in a firing engine [10] . Recent developments have also included applications in shock tubes and high-speed fuel injection jets and mixing [11,12] . ...
Article
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Crank angle-resolved temperatures have been measured using laser induced grating spectroscopy (LIGS) in a motored reciprocating compression machine to simulate diesel engine operating conditions. A portable LIGS system based on a pulsed Nd:YAG laser, fundamental emission at 1064 nm and the fourth harmonic at 266 nm, was used with a c.w. diode-pumped solid state laser as probe at 660 nm. Laser induced thermal grating scattering (LITGS) using resonant absorption by 1-methylnaphthalene, as a substitute fuel, of the 266 nm pump-radiation was used for temperature measurements during non-combusting cycles. Laser induced electrostrictive grating scattering (LIEGS) using 1064 nm pump-radiation was used to measure temperatures in both combusting and non-combusting cycles with good agreement with the results of LITGS measurements which had a single-shot precision of ± 15 K and standard error of ± 1.5 K. The accuracy was estimated to be ± 3 K based on the uncertainty involved in the modified equation of state used in the derivation from the LIGS measurements of sound speed in the gas. Differences in the in-cylinder bulk gas temperature between combusting and non-combusting cycles were unambiguously resolved and temperatures of 2300 ± 100 K, typical of flames, were recorded in individual cycles. The results confirm the potential for LIGS-based thermometry for high-precision thermometry of combustion under compression-ignition conditions.
... There is a large body of literature on experimental investigations of underexpanded jets. Many studies have focused on the compressible features of free jets, mostly using Schlieren imaging as in the seminal article by Crist andco-workers in 1966 (Crist et al. 1966), or later using advanced laser techniques to measure temperature, velocity, pressure and recently the speed of sound (Paul et al. 1989;Naik et al. 2009;Förster et al. 2018). From a heat transfer standpoint, measurements of fluid-to-wall heat transfer rates were reported on underexpanded jets impinging on plane (Rahimi et al. 2003) or cylindrical surfaces (Vinze et al. 2017). ...
Article
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This article describes experiments to investigate the fluid-to-wall interaction downstream of a highly underexpanded jet, with a pressure ratio of 120, confined in a channel. Heat transfer induced by Joule-Thomson cooling, which is a real gas effect in such a configuration, has critical implications on the safety of pressurised gas components. This phenomenon is challenging to model numerically due to the requirement to implement a real gas equation of state, the large range of (subsonic and supersonic) velocities, the high turbulence levels and the near-wall behaviour. An experimental setup with simple geometry and boundary conditions, and with a wide optical access was designed and implemented. It consisted of a high-pressure gas reservoir at controlled temperature and pressure, discharging argon through a nozzle into a square channel. This facility was designed to allow for a steady-state expansion from over 120 bar to atmospheric pressure for over 1 min. The choice of fluid, pressure and temperature regulation system, and the implementation of a high pressure particle seeding system are discussed. The gas dynamics of this flow was then investigated by two separate optical techniques. Schlieren measurements were used to locate the position of the Mach disk, and planar particle image velocimetry (PIV) was used to measure the turbulent velocity field in the regions of lower velocity downstream. Mie scattering images also indicated the presence of a condensed argon phase in the supersonic region as expected from previous studies on nucleation. The observed location of the sharp interface at the Mach disk was found to be in excellent agreement with the Crist correlation. Rapid statistics were derived from the PIV measurements at 3 kHz. The recirculation zone was found to extend about 4 channel heights downstream, and in the region between 2 and 3 channel heights downstream, a continuous deceleration on the centerline velocity was observed in line with the narrowing of the recirculation zone. The first and second velocity moments as well as Reynold stresses were quantified, including pdf distributions. In addition, a sensitivity and repeatability analysis, an evaluation of the PIV random uncertainty, as well as an estimation of errors induced by particle inertia were performed to allow for a full quantitative comparison with numerical simulations. Graphical abstract Open image in new window
Article
The mixing process of extremely underexpanded supercritical jets into a gaseous environment is studied. The focus lies on the influence of the nonideal fluid behavior on the mixing process. Numerical simulations are conducted for eight different injection conditions where experimental sound speed measurements are available. Overall, a very good agreement between simulations and experiments is found. A comparison of the real-gas and the ideal-gas closures shows the necessity to account for nonideal fluid behavior. The application of the ideal-gas law results in an incorrect energetic state which most prominently leads to an overestimation of the post-shock temperature by 70 K. The wrong energetic state yields erroneous thermodynamic properties in the mixing region. Finally, a mixture model is deduced enabling the prediction of mixture properties. As independent measurements of mass/mole fractions are not available, this evaluation procedure is a first attempt to numerically predict the mixture composition in underexpanded jets.
Article
High-resolution direct numerical simulations are conducted for under-expanded cryogenic hydrogen gas jets to characterize the nearfield flow physics. The basic flow features and jet dynamics are analyzed in detail, revealing the existence of four stages during early jet development, namely, (a) initial penetration, (b) establishment of near-nozzle expansion, (c) formation of downstream compression, and (d) wave propagation. Complex acoustic waves are formed around the under-expanded jets. The jet expansion can also lead to conditions for local liquefaction from the pressurized cryogenic hydrogen gas release. A series of simulations are conducted with systematically varied nozzle pressure ratios and systematically changed exit diameters. The acoustic waves around the jets are found to waken with the decrease in the nozzle pressure ratio. The increase in the nozzle pressure ratio is found to accelerate hydrogen dispersion and widen the regions with hydrogen liquefaction potential. The increase in the nozzle exit diameter also widens the region with hydrogen liquefaction potential but slows down the evolution of the flow structures.
Article
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The four-wave mixing technique laser-induced thermal acoustics was used to measure the local speed of sound in the farfield zone of extremely underexpanded jets. N-hexane at supercritical injection temperature and pressure (supercritical reservoir condition) was injected into quiescent subcritical nitrogen (with respect to the injectant). The technique’s capability to quantify the nonisothermal, turbulent mixing zone of small-scale jets is demonstrated for the first time. Consistent radially resolved speed of sound profiles are presented for different axial positions and varying injection temperatures. Furthermore, an adiabatic mixing model based on nonideal thermodynamic properties is presented to extract mixture composition and temperature from the experimental speed of sound data. High fuel mass fractions of up to 94 % are found for the centerline at an axial distance of 55 diameters from the nozzle followed by a rapid decay in axial direction. This is attributed to a supercritical fuel state at the nozzle exit resulting in the injection of a high-density fluid. The obtained concentration data are complemented by existing measurements and collapsed in a similarity law. It allows for mixture prediction of underexpanded jets with supercritical reservoir condition provided that nonideal thermodynamic behavior is considered for the nozzle flow. Specifically, it is shown that the fuel concentration in the farfield zone is very sensitive to the thermodynamic state at the nozzle exit. Here, a transition from supercritical fluid to subcritical vapor state results in strongly varying fuel concentrations, which implies high impact on the mixture formation and, consequently, on the combustion characteristics.
Article
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Non-resonant laser-induced thermal acoustics (LITA), a four-wave mixing technique, was applied to post-shock flows within a shock tube. Simultaneous single-shot determination of temperature, speed of sound and flow velocity behind incident and reflected shock waves at different pressure and temperature levels are presented. Measurements were performed non-intrusively and without any seeding. The paper describes the technique and outlines its advantages compared to more established laser-based methods with respect to the challenges of shock tube experiments. The experiments include argon and nitrogen as test gas at temperatures of up to 1000 K and pressures of up to 43 bar. The experimental data are compared to calculated values based on inviscid one-dimensional shock wave theory. The single-shot uncertainty of the technique is investigated for worst-case test conditions resulting in relative standard deviations of 1, 1.7 and 3.4 % for Mach number, speed of sound and temperature, respectively. For all further experimental conditions, calculated values stay well within the 95 % confidence intervals of the LITA measurement.
Article
In this study, n-hexane was compressed beyond six times its critical pressure and discharged into argon at subcritical pressure (with respect to the injectant). The injection temperature systematically varied from sub- to supercritical values to investigate near-critical disintegration phenomena of retrograde jets. Here, the ratio of the pressure in the nozzle reservoir and chamber was always above 14 leading to highly-expanded injections. We analyzed the breakup process in terms of combined shadowgraphy and light scattering measurements. Close to the critical point, different physical mechanisms have been observed. Their occurrence is predominantly determined by the expansion process resulting from the thermodynamic conditions in nozzle reservoir and chamber in combination with thermodynamic properties of the injectant. The experimental images for near- but subcritical injection temperatures imply that a fluid in liquid state expands in the nozzle and atomizes downstream of it. For sufficiently low backpressures, high liquid superheats trigger rapid vapor formation across a thin transition layer inside the nozzle that leads to a choked two-phase flow. A thermodynamic model that assumes a discontinuous phase transition layer and uses metastable fluid properties provides a physical explanation of the resulting underexpanded two-phase disintegration downstream of the nozzle exit. An increase to supercritical injection temperatures increases the compressibility of the fluid within the nozzle. An isentropic flow analysis showed that this triggers choking at thermodynamic states in the supercritical pressure regime resulting in the discharge of a sonic single-phase fluid. The expansion within the Mach barrel can lead to a supersaturated fluid state at near-critical temperature. In this case, a sharp phase transition front established approximately half a nozzle diameter downstream of the exit. We defined a dimensionless parameter to characterize the two-phase extent in underexpanded jets with near-critical phase transition based on initial injection conditions and retrograde fluid properties. We deduced the axial extent of the two-phase region from light scattering signals for a wide parameter range and demonstrate that it features a clear dependency upon the proposed parameter, which demonstrates its feasibility.
Article
The current study used large eddy simulations to investigate the sonic and mixing characteristics of turbulent under-expanded hydrogen and methane jets with various nozzle pressure ratios issued into various ambient pressures including elevated conditions relevant to applications in direct injection gaseous-fuelled internal combustion engines. Due to the relatively low density of most gaseous fuels such as hydrogen and methane, DI requires high injection pressures to achieve suitable mass flow rates for fast in-cylinder fuel delivery and rapid fuel-air mixing. Such pressures typically form an under-expanded fuel jet past the nozzle exit. Test cases of hydrogen injection with nozzle pressure ratio (NPR) of 10 issued into quiescent air with pressure P∞ ≈ 1, 5 and 10 bar were simulated. Direct comparison between hydrogen and methane jets with NPR = 8.5 and P∞ ≈ 1 was also made. The effect of ambient pressure on features of transient development of the near-nozzle shock structure and tip vortices (vortex ring) was investigated. It was observed that at constant NPR, higher ambient pressure resulted in slightly faster formation of the Mach reflection and shorter Mach disk settlement time. Different mechanisms were observed between hydrogen and methane with regards to transient formation of their initial tip vortex rings. It was found that the initial transient tip vortices of hydrogen jets may also contribute to the flow instabilities at the boundary of the intercepting shock and, unlike for methane, promote fuel-air mixing before the Mach reflection. It was also shown that the near-nozzle shock structure was only affected by NPR regardless of the ambient pressure. Furthermore, no flow recirculation zone was found just downstream of the Mach disk, a finding comparable to all previous experimental investigations. Also, it was observed that a locally richer mixture was created for jets with higher NPR or with higher ambient pressure at constant NPR. Based on the results of the current study, correlations were proposed for the shock cell spacing and jet tip penetration of highly under-expanded jets issued from millimetre-size circular nozzles.
Article
Investigations using novel fuel injection equipment, which allows fuel injection at highly elevated temperatures, were made to demonstrate the potential for improved mixture formation and exhaust particulate emission mitigation. Tests were carried out on a single cylinder gasoline spark ignition engine with direct fuel injection and operating in both homogeneous and stratified charge modes. Detailed measurements of the combustion characteristics, thermal efficiency and exhaust emissions were made. Particular attention was paid to particulate emission; measurements including smoke (FSN), particulate mass and particle count were made. Tests were carried out over a wide range of engine speed and load conditions to demonstrate that combustion performance is generally maintained. Particulate mass reduction in excess of 50% and particle count reduction of more than 90% were measured. Additional tests were carried out to characterize the performance of heated sprays using an optical pressure vessel under engine operating conditions over a range of fuel temperatures. The optical data was used to map spray geometry, dynamics and quality.
Article
This paper details the development and application of a Rayleigh imaging technique for quantitative mixing measurements in a vaporizing diesel spray under engine conditions. Experiments were performed in an optically accessible constant-volume combustion vessel that simulated the ambient conditions in a diesel engine. Two-dimensional imaging of Rayleigh scattering from a diesel spray of n-heptane and well-characterized ambient was accomplished by using a 532 nm Nd:YAG laser sheet and a low-noise back-illuminated CCD camera. Methods to minimize interference from unwanted elastic scattering sources (e.g. windows, particles) were investigated and are discussed in detail. The simultaneous measurement of Rayleigh scattering signal from the ambient and from the diesel spray provides important benefits towards making the technique quantitative and accurate. The Rayleigh scattering signal from the uniform ambient provides an in-situ calibration for the spatial non-uniformity in laser sheet intensity on a shot-to-shot basis caused by energy variation in the delivery beam as well as beam steering in the high-pressure combustion vessel. The diagnostic technique was validated by investigating the effect of equivalence ratio on soot formation in diesel jets. Consistent with previous studies, the diesel jet becomes non-sooting when the equivalence ratio distribution in the premixed-burn region is less than two.
Chapter
The kinetics and the mechanism of the thermal decomposition on n-hexane have been investigated in a static apparatus in the temperature range from 650 to 840 K. Based on the kinetic results and the experimental product distributions, a reaction mechanism is proposed which fits the experimental results reasonably well up to medium extents of the reaction. Problems arising in simulation are briefly discussed.
Article
High-priority research directions for the hydrogen economy include safety as not only a technological issue but as also a psychological and sociological issue. This chapter provides an overview of the state-of-the-art in hydrogen safety as a technological issue only. Progress in closing knowledge gaps in hydrogen safety engineering is described including the similarity law for hydrogen concentration decay in unignited underexpanded jets; the universal correlation for hydrogen jet flame length; and pressure effects of unscheduled releases of hydrogen, jet fires, deflagrations and detonations, and so on. Regulations, codes, and standards are presented, and the framework is introduced for carrying out the hydrogen safety engineering, which is defined as an application of scientific and engineering principles to the protection of life, property, and environment from the adverse effects of incidents involving hydrogen. Safety strategies and accident prevention and mitigation techniques are overviewed. The most important topics of future hydrogen safety research are identified.