Conference PaperPDF Available

# Comparison of the Primary Atomization Model PAMELA with Drop Size Distributions of an Industrial Preﬁlming Airblast Nozzle

Authors:

## Abstract and Figures

The spray of an annular preﬁlmling airblast nozzle was investigated at ambient conditions with the shadowgraphy technique. The measured volume probability densities of the droplets and Sauter mean diameters conﬁrm the trends of previous investigations performed at planar preﬁlmers, where the gas velocity was found to have much stronger effect on the atomization process compared to the ﬁlm ﬂow rate. Furthermore, the experimental results were compared to the Primary Atomization Model for prEﬁlming airBLast injectors (PAMELA) in terms of drop size distribution and Sauter Mean Diameter (SMD). It was observed that the PAMELA model is capable to predict the SMD of an annular preﬁlming airblast nozzle adequately, without further adjustment of the constants derived from previous experimental investigations at planar geometries.
Content may be subject to copyright.
ILASS – Europe 2016, 27th Annual Conference on Liquid Atomization and Spray Systems, 4-7 September 2016, Brighton, UK
Comparison of the Primary Atomization Model PAMELA
with Drop Size Distributions
of an Industrial Preﬁlming Airblast Nozzle
Simon Holz, Geoffroy Chaussonnet, Sebastian Gepperth, Rainer Koch, Hans-Jörg Bauer
Institut für Thermische Strömungsmaschinen, Karlsruhe Institute of Technology, Germany
*Corresponding author: simon.holz@kit.edu
Abstract
The spray of an annular preﬁlmling airblast nozzle was investigated at ambient conditions with the shadowgraphy
technique. The measured volume probability densities of the droplets and Sauter mean diameters conﬁrm the
trends of previous investigations performed at planar preﬁlmers, where the gas velocity was found to have much
stronger effect on the atomization process compared to the ﬁlm ﬂow rate. Furthermore, the experimental results
were compared to the Primary Atomization Model for prEﬁlming airBLast injectors (PAMELA) in terms of drop size
distribution and Sauter Mean Diameter (SMD). It was observed that the PAMELA model is capable to predict the
SMD of an annular preﬁlming airblast nozzle adequately, without further adjustment of the constants derived from
previous experimental investigations at planar geometries.
Introduction
In the near future gas turbines used for aircraft propulsion will have to fulﬁl more stringent emission regulations.
To meet these requirements an understanding of the combustion itself and its inﬂuencing parameters is essential.
One of these parameters is the fuel injection which is mostly performed by preﬁlming airblast atomizers.
Preﬁlming airblast atomizers have a number of advantages including ﬁne atomization, comparatively little change
of the spray quantities over a wide range of fuel ﬂow rates and low pressure losses [1]. The spray generation itself
can be split up into the following mechanisms: formation of bags and ligaments with subsequent breakup (so called
primary breakup) and the breakup of large droplets (so called secondary breakup). The secondary breakup of
droplets is widely understood, but the primary atomization is still a topic of active research.
For the investigation of the atomization process, phase Doppler techniques like PDA and direct imaging techniques
like shadowgraphy are widely used. The PDA captures only spherical droplets within a small punctual measure-
ment volume, whereas by the shadowgraphy technique liquid structures of any shape can be recorded within a large
measurement volume spanned by the focal plane and the depth of ﬁeld [2]. Hence for studying the primary breakup,
where a large number of non-spherical droplets occurs, the shadowgraphy technique is better suited than the PDA.
Planar preﬁlmers have been investigated with PDA [3], Fraunhofer diffraction measurements [4] and shadowgraphy
measurements [5, 6, 7]. However, annular preﬁlming airblast nozzles have been studied only by PDA [8, 9, 10, 11].
Thus to the knowledge of the authors, no data about the drop size distribution in the primary breakup zone of an
annular preﬁlming airblast nozzles is available.
For the design of atomizers and combustion chambers CFD simulations are widely used. Although there are sev-
eral approaches based on ﬁrst principles for simulating the atomization process like SPH [12] or eDNS [13], these
methods are far away to be used for a full combustion chamber simulation including atomization. The reasons are
the small scales in time and space which have to be resolved for capturing the atomization process. Thus, the CPU
and memory consumption for a full combustion chamber prediction would exceed today’s computation capacities
by far. To overcome this shortage, mostly Euler-Lagrangian CFD techniques with primary atomization models are
used. The main purpose of these models is to estimate the spray’s initial drop size distribution and velocity. These
models are based on experimental data and analytical models which use assumptions regarding the physics of
primary breakup.
For preﬁlming airblast atomizers different modelling strategies for describing the primary breakup have been pro-
posed. Gepperth et al. [6] proposed a model which for the ﬁrst time did not depend on the ﬁlm thickness but on the
boundary layer thickness and other ﬂow quantities. An approach depending on the ﬁlm thickness was presented by
Inamura et al. [4]. Eckel et al. [14] proposed a model which is based on the same assumptions like the model of
Inamura et al. [4]: Longitudinal and transversal waves are built up at the preﬁlmer, but neither their frequency nor
their amplitude does depend on the ﬁlm thickness. Later Gepperth et al. [15] demonstrated by experimental results
that the atomizing edge thickness has a strong inﬂuence on the SMD, whereas an inﬂuence of the mean ﬁlm thick-
ness could not be observed. Based on these observations Andreini et al. [16] presented a modiﬁed Senecal model
[17] which takes into account the atomizing edge thickness instead of the ﬁlm thickness. In this context Chausson-
net et al. [18, 19] developed the Primary Atomization Model for prEﬁling airbLAst injectors, named PAMELA. This
model provides a drop size distribution based on the gas velocity and the atomizing edge thickness. PAMELA was
calibrated with experimental data of Gepperth et al. [5, 15, 20] obtained from planar preﬁlmers.
1
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Although the same breakup mechanism was observed in a planar and an annular swirled nozzle [21], PAMELA
up to now was not compared to experimental results of an annular conﬁguration. To overcome this shortage, the
drop size distributions at an annular preﬁlmling airblast nozzle investigated at ambient conditions by Gepperth et al.
[21] are extracted at locations near the atomizing edge using the shadowgraphy technique [5, 6, 7]. Three different
analytical distribution functions are ﬁtted to the measured drop size distributions and compared in terms of sum of
squared errors (SSE). Furthermore, the measured SMDs are compared to SMDs as predicted by PAMELA.
Experimental setup
Gepperth et al. [21, 22] investigated the preﬁlming airblast nozzle to be discussed in this paper at atmospheric
conditions. In this paper, the experimental data of Gepperth is analysed with focus on the droplet size distribution
resulting from the primary breakup process near the atomizing edge.
Preﬁlming airblast nozzle
The investigated annular preﬁlming airblast nozzle, as depicted in Figure 1, is identical to that investigated by
Gepperth et al. [21] previously. The nozzle consists of a two co-rotating swirler systems, the preﬁlmer being the
separataring wall.
Figure 1. Sketch of nozzle, adapted from [21].
liquid ﬁlm on the preﬁlmer. The outer swirler has a shorter exit
length, so that the preﬁlming edge juts out of the nozzle for better
optical access (Figure 1) [22]. The liquid is supplied by 42 injection
holes on the preﬁlmer surface. The diameter of the preﬁlmer DP F
is 15 mm, the distance from the injection holes to the preﬁlmer’s tip
LP F is 8 mm and the length of the surface overﬂown by the gas
from the primary swirler outlet to preﬁlmer’s tip Lsurf is 24 mm.
The perimeter bof the preﬁlmer is 47 mm. The swirl number Sis
equal to one for both swirlers. More detailed information about the
geometry of the swirl generators can be found in [21].
A substitute fuel is injected on the inner side of the preﬁlmer and
forms a liquid ﬁlm. Due to momentum transfer from the swirling
gas ﬂow, the liquid ﬁlm is driven to the preﬁlmer tip and breaks
up forming bags, ligaments and droplets downstream the pre-
ﬁlmer.
Operating conditions
The air and liquid mass ﬂow ˙mgand ˙mlare independently varied over 4 operating points each (Table 1), leading
to 16 cases which correspond to nominal conditions in real gas turbines. The air is at ambient pressure and
temperature, so that air density ρgand dynamic viscosity µgare 1.21 kg/m3and 1.815 105kg/(m s), respectively.
As substitute fuel Shellsol D70 is used with density ρl= 770 kg/m3, surface tension σ= 0.0275 kg/s2and dynamic
viscosity µl= 1.56 103kg/(m s).
Table 1. Flowing conditions
Gas mass ﬂow rate ˙mg[g/s] 10 15 20 25
Gas bulk velocity ubulk [m/s] 23 35 47 58
Liquid mass ﬂow rate ˙ml[g/s] 0.5 1 2 4
Volumetric liquid ﬁlm ﬂow rate ˙
V /b [mm2/s] 14 28 55 110
Measurement technique
The atomization process was captured using high speed shadowgraphy. The recorded data was further post pro-
cessed by a Particle and Ligament Tracking Velocimetry (PLTV) algorithm previously developed at the Institut für
Thermische Strömungsmaschinen (ITS) by Müller et al. [7, 23].
The high speed images analysed for this publication have been recorded previously by Gepperth et al. [21], using
a LaVision HighSpeedStar8 high speed camera at a frequency of 50 kHz and a spatial resolution of 27.6 µm per
pixel. For each operating point 15.000 images are recorded during a period of 300 ms. The measurement volume is
illuminated using a 1 kW halogen spotlight which is mounted opposite of the camera. For a more detailed description
2
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Particle Ligament Tracking Velocimetry (PLTV)
For postprocessing of the images recorded by shadowgraphy, the particle and ligament tracking velocimetry (PLTV)
algorithm was developed by Müller et al. [7, 23]. It is used to extract the droplet diameter and velocity. The algorithm
performs the following four steps to extract drop sizes. First, the image brightness and contrast are normalized by
two special calibration images called dark image and white image. Second, a contouring algorithm detects the
closed surface of potential liquid structures. Third, an ellipsoid is ﬁtted to each pixel array. Fourth, the droplet’s
diameter is estimated under the assumption that the area of the ellipsoid is equivalent to the area of a circle.
Subsequently the diameters are corrected with a calibration curve similar to the approach of Müller [7]. The calibra-
tion curve was generated by analysing a image of a calibration plate from La Vision with the same PLTV algorithm
and settings as used to extract the droplet diameters. Therefore the corrected diameters are in a range of 80 to
1025 µm.
Measurement uncertainty
Gepperth et al. [5] estimated the uncertainty for setting the liquid and gas mass ﬂow at the atmospheric atomization
rig below 3.5 %. Müller [24] studied the uncertainty of the drop size as determined by PLTV and estimated the
error to be 5 % for diameters within a range of 50 to 600 µm. Therefore, droplets with an uncorrected diameter
below 2 px = 55.2 µm are not taken into account. For droplets larger than 600 µm, Müller mentioned that the error is
unpredictable high because the droplet’s shape is getting more and more non-spherical due to high Weber numbers.
Therefore, droplets with an uncorrected diameter larger than 1000 µm are neglected. These considerations lead to
an over all measurement uncertainty of 6.1 % for the diameter range of 50 to 600 µm.
Description of the breakup mode
Snapshots of the breakup process occurring at the atomizing edge are displayed in Figure 2. The images have
a size of 144 x 360 pixels which corresponds to 4 x 10 mm. Here z = 0 mm corresponds to the position of the
atomizing edge. The gas and liquid phase ﬂow is from top to bottom of the images. Due to the swirl, a deﬂection
of the liquid to the right can be observed. The breakup process shows the same features like the planar preﬁlmer
[5, 15]: the liquid ﬁlm is accumulated at the tip of the preﬁlmer and forms a reservoir which is torn apart by the air
stream, forming bags and ligaments. From Figure 2, it is obvious that the inﬂuence of liquid and gas mass ﬂow rate
is qualitatively identical to that observed by Gepperth et al. [5] at the planar geometry . When the liquid mass ﬂow
rate increases, the number of liquid structures (or breakup events) is increased, but the dimension of the ligaments
remains almost the same (Figures 2(a) and 2(b)). When the gas velocity is increased, the size of the ligaments is
signiﬁcantly reduced (Figures 2(a) and 2(c)).
x in mm
-5 -4 -3 -2 -1 0 1 2 3 4 5
z in mm
0
0.5
1
1.5
2
2.5
3
3.5
4
(a) ubulk = 35 m/s and
˙
V /b = 28 mm2/s
x in mm
-5 -4 -3 -2 -1 0 1 2 3 4 5
z in mm
0
0.5
1
1.5
2
2.5
3
3.5
4
(b) ubulk = 35 m/s and
˙
V /b = 55 mm2/s
x in mm
-5 -4 -3 -2 -1 0 1 2 3 4 5
z in mm
0
0.5
1
1.5
2
2.5
3
3.5
4
(c) ubulk = 58 m/s and
˙
V /b = 28 mm2/s
x in mm
-5 -4 -3 -2 -1 0 1 2 3 4 5
z in mm
0
0.5
1
1.5
2
2.5
3
3.5
4
(d) ubulk = 58 m/s and
˙
V /b = 55 mm2/s
Figure 2. Snapshot of the breakup process, for different operating points
3
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
The PAMELA model
A primary atomization model, named PAMELA for Primary Atomization Model for prEﬁling airbLAst injectors, was
developed previously [18, 19] in order to provide instantaneous and local boundary conditions for the simulation of
reacting ﬂows inside the combustion chamber. The model does not include details of the dynamics of the liquid
accumulation and the attached ligament, but focuses on the drop size distribution of the spray generated directly
downstream the atomizing edge. It relies on the relevant parameters identiﬁed by Gepperth et al. [5], namely the
atomizing edge thickness ha, the surface tension σand the momentum ﬂux of the gas M=ρgu2
g.
Figure 3. Sketch of the breakup mechanism, adapted from [19].
The model is based on experimental observa-
tions and proposes the scenario as depicted in
Figure 3. The ﬁlm ﬂow feeds the liquid reser-
voir (i) which is partly immersed into the high-
speed gas ﬂow (ii). Due to the high velocity
difference, the surface of the liquid reservoir is
sheared and strongly accelerated (iii) in the lon-
gitudinal direction, leading to a Rayleigh-Taylor
instability that develops in the transverse direc-
tion (iv). This instability generates crests on the
liquid surface that are blown up by the high-
speed gas (v), and ﬁnally disrupt into bags and
ligaments (vi).
It is assumed that the SMD of the generated
spray is proportional to the theoretical wave-
length λRT of the transverse instability, and that
the number drop size distribution of the spray
follows the Rosin-Rammler function deﬁned by:
f0(d) = q mqdq1exp d
mq(1)
where mand qare the scale and shape parameters, respectively. The former has the dimension of a length and
determines the characteristic size of the droplets while the latter reﬂects the width of the droplet size distribution.
For determining λRT , it is assumed that the amount of liquid, which is accelerated by the gas stream, is proportional
to the atomizing edge thickness ha, leading to the expression of λha
RT :
λha
RT =2π
rρu
gs6C1haσ
ρg
with rρ=ρl
ρl+ρg
(2)
where C1is a constant, and the term u
grepresents the mean gas velocity at the location where the breakup occurs.
Assuming that the SMD of the spray is proportional to λha
RT and expressing the SMD of a spray according to a
Rosin-Rammler distribution, one can link the scale parameter mto the transverse wavelength by:
m=C2λha
RT
Γ(2/q + 1)
Γ(3/q + 1) (3)
where C2and Γare a constant and the gamma function, respectively. The shape parameter qcontrols the width
of the distribution. It is assumed to depend on the aerodynamic effects and the atomizing edge thickness only. It is
thus expressed as a function of the aerodynamics Weber number Weδ=ρgδu2
gwhere δis the thickness of the
boundary layer on the preﬁlmer just upstream of the atomizing edge. It yields:
q(Weδ, ha) = C3
Weδ
+ha
C42
+C5(4)
where C3to C5are the last constants of the model. The Sauter mean diameter D32 estimated by the model is
related to the transverse wavelength by:
D32 =C2λha
RT (5)
The overview of the model is depicted in Figure 4 and highlights the main steps for obtaining the spray drop size
distribution.
The constants C1to C5were determined using the experimental results from Gepperth et al. [5, 15, 20]. They are
essentially independent of the liquid properties or the geometry. Hence they are kept constant for the whole study.
C1was found by comparing the transverse wavelength of water and ethyl-alcohol ﬁlms atomized by air ﬂowing at
a velocity between 20 and 90 m/s. C2was set by comparing the SMD of the spray just directly downstream the
4
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
b) Intermediate values
Density parameter:
Transverse wavelength:
(Rayleigh-Taylor instability)
a) Inputs
Liquid surface tension:
Liquid density:
Gas density:
Atomizing edge thickness:
Local gas velocity:
Boundary layer thickness:
c) Rosin-Rammler parameters
Shape parameter:
Scale parameter:
with
d) Diameter distribution
Figure 4. Overview of the PAMELA model
atomizing edge with Eq. 2. The constants C3to C5were derived by matching the experimental drop size distribution
to a Rosin-Rammler function and by ﬁtting the shape qparameter. For C2to C5, the investigated liquids were
Shellsol D70 and a volume mixture of 50% Propanediol and 50% of water. Their values can be found in Table 2.
Table 2. Constants of the PAMELA model, adapted from [19].
C1[-] C2[-] C3[-] C4[mm] C5[-]
0.67 0.112 6.82 5.99 0.0177
The PAMELA model can be used for two purposes, depending on the type of input parameters. The ﬁrst scenario,
referred to the local mode, is to embed the model into a CFD code, where it is used to provide local and instanta-
neous spray conditions. In this case, the model relies on local input provided by the ﬂow solver. More details about
the local mode can be found in [19]. The second scenario would be a global mode where the input values are deter-
mined from the global operating conditions. In this study, the model is used in global mode, and the determination
of the global input parameters is discussed in the following.
Application of the PAMELA model to the annular nozzle
The ﬁrst set of input parameters are the physical properties of the gas and the liquid (ρl,ρgand σ), and they are
easily determined from the operating conditions. The second set of inputs are the geometrical features of the nozzle,
i.e. the thickness of the atomizing edge haand the total length of the preﬁlmer Lsurf . Due to a complex shape of
the preﬁlmer lip (Figure 5), the determination of hais not obvious and, therefore, it is necessary to clarify its purpose
in the model: It is used to quantify the amount of liquid which is accelerated by the high speed gas ﬂow, and, in
a given range, it is equal to the thickness of the liquid accumulation. At ﬁrst, it is expected from Figure 5 that the
liquid accumulation covers the atomizing edge until the tip of the preﬁlmer, leading to an atomizing edge thickness
of 300 µm. However, SPH (Smooth Particle Hydrodynamics) numerical simulations of a similar geometry [25]
showed that the liquid goes beyond the tip and spills to the outer side of the preﬁlmer. Therefore the size of the
atomizing edge might be 330 µm. In addition, this spilling effect might be enhanced by the conjunction gap on
the secondary gas ﬂow side depicted in Figure 5. This gap can be seen as a tiny backward facing step which might
induce a recirculation zone and would allow the liquid to be trapped in this zone. For these conditions, the atomizing
edge thickness is taken to 650 µm.
To determine the thickness of the boundary layer δthe total length of the preﬁlmer Lsurf = 24 mm has to be
considered. Due to the swirl number Sequal to one the length over ﬂown by the gas is 2Lsurf , as depicted in
Figure 6. The boundary layer is expressed as proposed by [5] as:
δ= 0.16 2Lsurf
Re1/7with Re =ug2Lsurf
νg
(6)
Finally, the local velocity u
gis the most sensitive input parameter due to its large exponent of -1 in Eq. 2. In the
planar preﬁlmer conﬁguration, the bulk velocity is parallel to the local velocity seen by the liquid accumulation, and
it was observed by [19] that due to the boundary layer, the local velocity magnitude u
gcorresponds to 70% of the
bulk velocity:
u
g= 0.7ubulk (7)
5
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Figure 5. left: sketch of nozzle, adapted from [21]; right: sketch of the atomizing edge.
Equation 7 was determined by the observation of the mean turbulent velocity proﬁle downstream a backward facing
step, and it is assumed to be valid for any type of conﬁguration where a turbulent boundary layer is established on
the preﬁlmer. Therefore, Equation 7 is a part of the model and it is not modiﬁed here.
However, the present conﬁguration is an annular swirling ﬂow, implying that the bulk velocity is not representative of
the mean velocity magnitude at the tip of the preﬁlmer. As the swirl number Sis equal to one, the circumferential
component uθis equal to the axial component ubulk, so that the mean velocity magnitude, i.e. the global velocity ug
to be used in the model, should be equal to 2ubulk (Figure 6).
prefilmer perimeter b
Lsurf 2Lsurf
ubulk
uθ
2ubulk
Injection holes
Figure 6. Planar view of the preﬁlmer
Additionally, due to centrifugal effects, the axial velocity proﬁle across the nozzle is also modiﬁed in comparison
to the planar conﬁguration, as it shows a larger value close to the inner side of the preﬁlmer, where the liquid
accumulation is fragmented. The SPH simulation of a similar nozzle [25] showed a velocity magnitude in the vicinity
of the preﬁlmer 43% larger than the mean axial velocity. Therefore, the bulk velocity should multiplied by 1.43.
The superposition of the two above-mentioned effects leads to the input velocity ugor local velocity magnitude u
g:
ug= 1.43 ×2×ubulk u
g0.7
|{z}
boundary
layer
×1.43
|{z}
centrifugal
effect
×2
|{z}
circumferential
velocity
×ubulk (8)
In the section dedicated to the results analysis, the importance of the swirl effect in the input velocity ugis illustrated
by setting it to ubulk (no swirl effects accounted) or to 2 ubulk (swirl effects accounted).
Results and Discussion
First measured volume probability densities (vpds) and SMDs will be shown. Second three analytical distribution
functions will be tested to ﬁt the measured vpds. Third the measurements are compared to PAMELA in terms of
volume pdf and SMD.
6
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Measured drop size distributions
The measured volume probability densities for four operating points are depicted in Figure 7. An increase in gas
velocity increases the volume probability density at diameters around 100µm. Decreasing volumetric liquid ﬁlm ﬂow
rates ˙
V /b seem to slightly support this trend. This behaviour coincidences with the observations of Gepperth et al.
[5] who described that the gas velocity has a major effect on the atomization process whereas the volumetric liquid
ﬁlm ﬂow rate has only a minor effect.
(a) ubulk = 35 m/s and
˙
V /b = 28 mm2/s (b) ubulk = 35 m/s and
˙
V /b = 55 mm2/s
(c) ubulk = 58 m/s and
˙
V /b = 28 mm2/s (d) ubulk = 58 m/s and
˙
V /b = 55 mm2/s
Figure 7. Measured volume probability densities of selected operating points.
In Figure 8 the measured Sauter Mean Diameter (SMD) over the bulk velocity of the gaseous phase is depicted for
different volumetric liquid ﬁlm ﬂow rates ˙
V /b.
Figure 8. Inﬂuence of air and liquid mass ﬂow on the SMD extracted from the Experiment.
7
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
As expected, the SMD decreases with increasing gas velocity. At medium and high gas velocities (35, 47, 58 m/s)
only a slight decrease in SMD can be observed. This behaviour might be explained by the low resolution of the high
speed images: the diameters that can be detected are in a range of about 80 to 1025µm. Droplets smaller than
80 µm are not captured. As droplet diameters decrease with increasing gas velocity, it means that more smaller
droplets are disgorged at large velocities, leading to an overestimated SMD. For the different volumetric liquid ﬁlm
ﬂow rates ˙
V /b only a slight trend to higher SMDs with increasing liquid mass ﬂow can be noticed at high gas
velocities.
Fit of several distributions to the measured drop size distributions
One of the most relevant distribution in the context of spray generation is the Rosin-Rammler distribution, originally
established as cumulative volume distribution function F3,RR(D)for powders by Rosin and Rammler [26]. The
derivative of F3,RR(D)leads to the volume probability density function (vpdf) f3,RR(D).
F3,RR(D) = 1 e(D
m)q
f3,RR(D) = Dq1mqq e(D
m)q
(9)
Chaussonnet et al. [18, 19] used Rosin and Rammler’s distribution (Eq. 9) to describe the cumulative number
distribution function F0(D), leading to the volume PDF:
f3,ChRR (D) = Dq+2 mqq e(D
m)q
V1
tot (10)
where the exponent of D changes from q-1 to q+2.
Rizk and Lefebvre modiﬁed Rosin’s and Rammler’s deﬁnition (Eq. 9) to obtain a better ﬁt for large droplets [26]:
F3,modRR(D) = 1 eln(D)
ln(m)q
f3,modRR(D) = D1ln(D)q1ln(m)qq eln(D)
ln(m)q
(11)
In order to quantify the error between the measured volume probability densities q3(D)and the volume probability
density functions f3(D)the sum of squared errors (SSE) is used as indicator.
SSE =
n
X
i=1
(q3(D)f3(D))2(12)
In terms of SSE at low to medium liquid mass ﬂows (0.5 to 2.0 g/s) Chaussonnet’s Rosin-Rammler vpdf f3,ChRR
(Eq. 10) is slightly better than the modiﬁed Rosin-Rammler vpdf f3,modRR (Eq. 11). At high liquid mass ﬂows
(4.0 g/s) the modiﬁed Rosin-Rammler vpdf f3,modRR shows a slightly better match with the measured vpd q3. The
Rosin-Rammler vpdf f3,RR (Eq. 9) has the worst concurrence of all three vpdfs. Nevertheless all volume probability
density functions follow the measured volume probability densities quite well, as depicted in Figure 9.
(a) ubulk = 35 m/s and
˙
V /b = 28 mm2/s (b) ubulk = 35 m/s and
˙
V /b = 55 mm2/s
(c) ubulk = 58 m/s and
˙
V /b = 28 mm2/s (d) ubulk = 58 m/s and
˙
V /b = 55 mm2/s
Figure 9. Measured volume probability densities and ﬁts with analytical distributions for selected operating points.
8
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Comparison of the PAMELA model to the measured drop size distributions
The main input parameters of the PAMELA model (Figure 4) are the velocity of the gaseous phase ugand the
thickness of the atomizing edge ha. As discussed in the section application of the PAMELA model to the annular
nozzle and documented in Table 3, the effects of swirl have to be taken into account (set 2) and compared to a
situation with no swirl (set 1). Furthermore the thickness of the atomizing edge hais considered with 650 µm.
Table 3. Different sets of PAMELA
set no ug
1ubulk
22ubulk
The volume pdfs estimated by PAMELA are depicted for two different conﬁgurations (sets 1 and 2) and selected
operating points in Figure 10. For comparison, the measured volume probability densities q3are also shown.
(a) ubulk = 35 m/s and
˙
V /b = 28 mm2/s (b) ubulk = 35 m/s and
˙
V /b = 55 mm2/s
(c) ubulk = 58 m/s and
˙
V /b = 28 mm2/s (d) ubulk = 58 m/s and
˙
V /b = 55 mm2/s
Figure 10. Measured volume probability densities and volume pdfs estimated by the PAMELA model.
As expected, PAMELA set 1 estimates larger droplets than PAMELA set 2. For Figures 10(c) and 10(d) the peak
locations of the vpdf estimated by PAMELA set 1 are in good agreement with the measurements. The increase in
bulk velocity shifts the peaks of the vpdf estimated by PAMELA to smaller diameters and for PAMELA set 2 and high
bulk velocities (Figures 10(c) and 10(d)) even below the lower limit of the spatial resolution of 80 µm. Hence, the vpd
of small to medium droplets is highly overestimated by model set 2. Furthermore, droplets larger than 500 µm are
not taken into account by the model’s vpdfs. According to Figure 2, spherical droplets with a diameter in the order
of 500 µm are quite unrealistic. Most of the structures with a size in that order of magnitude seem to be stretched
and non-spherical. This might lead to a signiﬁcant overestimation of large droplet’s volume by the experiment.
The Sauter mean diameters (SMDs) measured with the shadowgraphy technique and the SMDs estimated by
PAMELA sets 1 and 2 are depicted in Figure 11(a) over the bulk velocity of the gaseous phase and for different
volumetric liquid ﬁlm ﬂow rates ˙
V /b. Note that the SMDs of PAMELA in Figure 11(a) are determined from minimal
to maximal measured diameter to ensure comparability (SMD cut).
9
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Bulk velocity of gaseous phase [m/s]
20 30 40 50 60
Sauter mean diameter [µm]
50
100
150
200
250
300
350
Experiment, ˙
V /b = 14 mm2/s
Experiment, ˙
V /b = 28 mm2/s
Experiment, ˙
V /b = 55 mm2/s
Experiment, ˙
V /b = 110 mm2/s
PAMELA, set 1, SMD cut
PAMELA, set 2, SMD cut
(a) SMD determined from measured Dmin to Dmax
Bulk velocity of gaseous phase [m/s]
20 30 40 50 60
Sauter mean diameter [µm]
50
100
150
200
250
300
350
Experiment, ˙
V /b = 14 mm2/s
Experiment, ˙
V /b = 28 mm2/s
Experiment, ˙
V /b = 55 mm2/s
Experiment, ˙
V /b = 110 mm2/s
PAMELA set 1
PAMELA set 2
(b) SMD determined from zero to inﬁnity
Figure 11. Comparison of the measured SMDs with the SMDs estimated by PAMELA.
For PAMELA set 1, SMD cut (no swirl effects accounted) the SMD is overestimated for low to medium gas velocities
and is in good agreement with the measurements at medium and high gas velocities. However the slight decrease
of the SMD at medium to high gas velocities is not captured by PAMELA set 1. With PAMELA set 2, SMD cut
(swirl effects accounted) the estimated SMDs are smaller than the measured SMDs. Therefore the over all trend is
satisfactorily captured by PAMELA set 2.
In Figure 11(b) again the measured and estimated SMDs over the bulk velocity is depicted, but this time the esti-
mated SMDs are determined from zero to inﬁnity. Taking into account droplets below 80µm results in a substantial
steeper decrease of the SMDs estimated by the model with increasing gas velocity. The signiﬁcant deviations be-
tween the measurements and the model in Figure 11(b) may can be explained with the following effects.
First, the experimental settings of the measurements used to calibrate PAMELA and the measurements presented
in this paper are different. While the model was calibrated using measurements of a planar preﬁlmer with a deﬁned
sharp atomizing edge, in the present case an annular nozzle with a curved geometry at the tip and a swirl ﬂow is
explored. As shown in Figure 10 this has a tremendous effect on the vpdf estimated by the model.
Second a lot of small droplets might be missed due to the low spatial resolution of the high speed images. This
may leads to an overestimation of the SMD at high gas velocities where signiﬁcantly more small droplets occur as
compared to low gas velocities. This hypothesis is supported by the trends of the model in Figures 11(a) and 11(b)
where the SMDs determined within the diameter range of the measurements show signiﬁcantly better coincidence
with the measurements than the SMDs determined from zero to inﬁnity.
Summary and Conclusions
The spray near the atomizing edge of an annular preﬁlmling airblast nozzle was investigated at ambient condi-
tions with the shadowgraphy technique. Three different analytical distributions were ﬁtted to the measured volume
probability densities and the error was compared in terms of sum of squared errors (SSE). In addition, the mea-
sured SMDs were compared to SMDs estimated by the Primary Atomization Model for prEﬁlming airBLast injectors
(PAMELA).
The measured volume probability densities and SMDs conﬁrm the trends of previous investigations at planar pre-
ﬁlmers, where the gas velocity was found to have a major effect on the atomization process compared to the liquid
mass ﬂow. At medium and high air mass ﬂows only a slight decrease in SMD was be observed, which may be
attributed to the spatial resolution of the shadowgraphy technique. All three analytical drop size distributions were
found to follow the measured volume probability densities quite well. The SMDs estimated by PAMELA show sat-
isfactory coincidence with the experiments when swirl as well as the limited spatial resolution of the measurement
technique are taken into account.
It was observed that PAMELA is capable to predict the SMD of an annular preﬁlming airblast nozzle adequately,
without further adjustment of the constants derived from previous experimental investigations at planar geometries.
10
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
Acknowledgements
The present research was particularly founded by the European Union’s Seventh Framework Programme (FP7/2007-
2013) of the Clean Sky Joint Technology Initiative under project DREAMCODE grant n620143.
The authors gratefully acknowledge the work of Lukas Hagmanns during his diploma thesis at the ITS. Further-
more the authors thank Enrico Bärow, Thilo Dauch and Christian Lieber for the fruitful discussions on the topic.
Nomenclature
Abbreviations
eDNS embedded Direct Numercial Simulation
ITS Institut für Thermische Strömungsmaschinen
english: Institute of Thermal Turbomachinery
npd number probability density
npdf number probability density function
pdf probability density function
PAMELA Primary Atomization Model
for prEﬁling airbLAst injectors
PDA Phase Doppler Anemometry
PLTV Particle and Ligament Tracking Velocimetry
SMD Sauter Mean Diameter
SPH Smoothed Particle Hydrodynamics
SSE Sum of Squared Errors
vpd volume probability density
vpdf volume probability density function
Latin Symbols
Ddroplet diameter [m]
Dxy diameter of xy [m]
fprobability density function [m1]
Fcumulative distribution function [m1]
hheight [m]
Llength [m]
mscale factor [m]
˙mmass ﬂow [kg/s]
Mmomentum ﬂux of the gas [kg/(m s2)]
qshape factor []
qmeasured probability density [m1]
Sswirl number []
SSE sum of squared errors [m2]
Vtot total droplet volume [m3]
˙
V /b volumetric liquid ﬁlm ﬂow rate [m2/s]
Greek Symbols
µdynamic viscosity [kg/(m s)]
ρdensity [kg/m3]
σsurface tension [kg/s2]
θcircumferential component
Subscripts
0number
3volume
aatomizing edge
bulk bulk
ggaseous phase
ChRR Chaussonnet’s Rosin-Rammler distribution
lliquid phase
modRR modiﬁed Rosin-Rammler distribution
P F preﬁlmer
RR Rosin-Rammler distribution
surf surface overﬂown by the gas ﬂow
References
[1] Lefebvre, A. H., Atomization and Sprays, 10:251–276 (2000).
[2] Tropea, C., Annual Review of Fluid Mechanics, 43:399–426 (2011).
[3] Bhayaraju, U. and Hassa, C., ICLASS, 10th Triennial International Conference on Liquid Atomization and Spray
System, Kyoto, Japan (2006).
[4] Inamura, T.; Shirota, M.; Tsushima, M.; Kato, M.; Hamajima, S. and Sato, A., ICLASS, 12th Triennial Inter-
national Annual Conference on Liquid Atomization and Spray Systems, Heidelberg, Germany, Heidelberg,
Germany (2012).
[5] Gepperth, S.; Müller, A.; Koch, R. and Bauer, H.-J., ICLASS, 12th Triennial International Annual Conference on
Liquid Atomization and Spray Systems, Heidelberg, Germany (2012).
[6] Gepperth, S.; Guildenbecher, D.; Koch, R. and Bauer, H.-J., ILASS Europe, 23rd Annual Conference on Liquid
Atomization and Spray Systems, Brno, Czech Republic (2010).
[7] Müller, A.; Koch, R.; Bauer, H.-J.; Hehle, M. and Schäfer, O., ASME Turbo Expo: Power for Land, Sea and Air,
GT2006-90432, Barcelona, Spain (2006).
[8] Opfer, L.; Roisman, I. V. and Tropea, C., Fluid Mechanics and Its Applications, pp. 3–27 (2012).
[9] Schober, P.; Meier, R.; Schäfer, O. and Wittig, S., International Symposium on Visualization and Imaging in
Transport Phenomena, Antalya, Turkey (2002).
[10] Meier, R.; Merkle, K.; Maier, G.; Zarzalis, N.; Leuckel, W. and Wittig, S., ILASS Europe, 15th Annual Confer-
ence on Liquid Atomization and Spray Systems, Toulouse, France (1999).
[11] Carvalho, I. S. and Heitor, M. V., Experiments in Fluids, 24:408–415 (1998).
[12] Braun, S.; Wieth, L.; Koch, R. and Bauer, H.-J., ICLASS, 13 th Triennial International Conference on Liquid
Atomization and Spray System, Tainan, Taiwan (2015).
[13] Sauer, B.; Sadiki, A. and Janicka, J., Journal of Computational Multiphase Flows, 6(3):179–192 (2014).
[14] Eckel, G.; Rachner, M.; Clercq, P. L. and Aigner, M., 8th International Conference on Multiphase Flow, Jeju,
Korea (2013).
11
ILASS – Europe 2016, 4-7 Sep. 2016, Brighton, UK
[15] Gepperth, S.; Koch, R. and Bauer, H.-J., ASME Turbo Expo: Turbine Technical Conference and Exposition,
GT2013-94033, San Antonio, Texas (2013).
[16] Andreini, A.; Bianchini, C.; Caciolli, G.; Facchini, B.; Giusti, A. and Turrini, F., ASME Turbo Expo: Turbine
Technical Conference and Exposition, Düsseldorf, Germany (2014).
[17] Senecal, P.; Schmidt, D.; Nouar, I.; Rutland, C.; Reitz, R. and Corradini, M., International Journal of Multiphase
Flow, 25(6-7):1073 – 1097 (1999).
[18] Chaussonnet, G.; Riber, E.; Vermorel, O.; Cuenot, B.; Gepperth, S. and Koch, R., ILASS, 25th European
Conference on Liquid Atomization and Spray Systems, Chania, Crete (2013).
[19] Chaussonnet, G.; Vermorel, O.; Riber, E. and Cuenot, B., International Journal of Multiphase Flow, 80:29–42
(2016).
[20] Müller, A.; Meier, R.; Schäfer, O. and Wittig, S., DFG-Tagung - Atomization and Spray Processes, Dortmund,
Germany (2004).
[21] Gepperth, S.; Baerow, E.; Koch, R. and Bauer, H.-J., ILASS Europe, 26th Annual Conference on Liquid Atom-
ization and Spray Systems, Bremen, Germany (2014).
[22] Bärow, E.; Gepperth, S.; Koch, R. and Bauer, H.-J., Zeitschrift für Physikalische Chemie, 229(6):909–929
(2015).
[23] Kapulla, R.; Tuchtenhagen, J.; Müller, A.; Dullenkopf, K. and Bauer, H.-J., GALA Fachtagung Lasermethoden
in der Strömungsmesstechnik, Karlsruhe, Germany (2008).
[24] Müller, A., Experimentelle Untersuchung des Zerstäubungsverhaltens luftgestützter Brennstoffdüsen bei oszil-
lierenden Strömungen, Ph.D. thesis, Institut für Thermische Strömungsmaschinen (ITS), Karlsruhe Institute of
Technology (KIT) (2015).
[25] Dauch, T.; Braun, S.; Wieth, L.; Chaussonnet, G.; Keller, M.; Koch, R. and Bauer, H.-J., ASME Turbo Expo:
Turbine Technical Conference and Exposition, Seoul, South Korea (2016).
[26] Lefebvre, A. H. and Ballal, D. R., Gas Turbine Combustion: Alternative Fuels and Emissions, Third Edition,
CRC Press (2012).
12
... On the other hand, the planar configuration of airblast atomization has different breakup physics compared to its cylindrical counterpart. Many experimental [9,19,20,21] and numerical [22,23,24,25] works have investigated this configuration to understand the breakup physics and the atomization characteristics such as drop size distribution (DSD) and drop velocity distributions (DVD). Many of the past experimental studies have found that the aerodynamic forces play a significant and key role in the droplet sizes; specifically, the increase in the mean air velocities resulted in reduction in the droplet sizes [26,27,28,29] while a reduction in the Sauter Mean Diameter (SMD) has been observed with the increase in the surface tension of the liquid fuel [26,27]. ...
... Many of the previous studies on experimental [19,20,9,21] and numerical [22,23,24,25] investigations of airblast atomization of liquid sheet have focused entirely on the primary atomization. However, it is physically and statistically possible that the atomized drops produced from various breakup mechanisms can undergo secondary atomization within the computational domain. ...
Article
Full-text available
This paper investigates the primary atomization of airblasted liquid sheet using detailed numerical simulations.The atomization of liquid sheet under airblasting conditions involve complex mechanisms and a thorough understanding is necessary. A planar pre-filming airblast atomization configuration have been chosen to study the breakup of liquid sheet/film injected on a solid flat plate. We have investigated an operating point directlyrelevant for high altitude relight condition of the aircraft. This configuration has been chosen based onthe experimental investigation of Gepperth et al. [S. Gepperth, A. Müller, R. Koch, H.-J. Bauer, Ligament and droplet characteristics in pre-filming airblast atomization, Proceedings of the ICLASS, 12th Triennial International Conference on Liquid Atomization and Spray Systems, September 2-6, Heidelberg, Germany,2012] for the airblast atomization. The numerical simulations have been performed using in-house Navier–Stokes solver that uses consistent mass and momentum flux computation technique. The purpose of this work is to provide a comprehensive database and analyses of the airblast atomization of liquid sheet. This include studies on the effect of velocity profile on the atomization characteristics, occurrence of secondary atomization and drop coalescence, and extraction of near-field atomization characteristics. The qualitative analyses of the results from the simulations showed that there are two major atomization mechanisms of liquid film breakup— sheet/bag breakup and ligament breakup. The drop diameter and velocity distributions computed from the simulations was found to be of the same order of magnitude although under-predicting the experimental data.Based on the atomized drop data, both the secondary atomization and drop coalescence have been observed to occur in the simulations. The quantitative analyses of the near-field liquid ligaments results revealed the lengths of these ligaments are of the same order of magnitude as the experimental data while an under-prediction in the ligament velocity has been observed. Finally, an excellent agreement between simulations and experimental data has been found for the Sauter Mean Diameter (SMD) of the atomized droplets.
... Nevertheless, the annular configuration of the airblast atomizer poses a multi-scale nature problem and presents some geometrical complexity, importantly hindering its study. In this sense, many researchers have focused their efforts on planar configurations, which are much simpler but allow extrapolating conclusions to the actual annular configurations due to an analogy by similarity, as pointed out by Berthoumieu and Lavergne [8] and confirmed by Holz et al. [9]. ...
Preprint
Full-text available
Prefilming airblast atomization is widely used in aero engines. Fundamental studies on the annular configuration of airblast atomizers are difficult to realize. For this reason, researchers focused on planar configurations. In this regard, the Karlsruhe Institute of Technology (KIT) developed a test rig to conduct experimental activities, conforming a large database with results for different conditions. Such data allow validation of two-phase flow calculations concerning primary atomization on these devices. The present investigation proposes a Direct Numerical Simulation (DNS) on the KIT planar configuration through the Volume of Fluid (VOF) method within the PARIS code. The novelty compared to DNS reported in the literature resides in the use of a boundary condition that accounts not only for the gas inflow turbulence but also for the spatio-temporal evolution of the liquid film thickness at the DNS inlet and its effect on turbulence. The proposed methodology requires computing precursor single-phase and two-phase flow Large-Eddy Simulations. Results are compared to DNS that only account for a constant (both timewise and spanwise) liquid film thickness at the domain inlet, validating the workflow. The proposed methodology improves the qualitative description of the breakup mechanism, as its different stages (liquid accumulation behind the prefilmer edge, bag formation, bag breakup, ligament formation and ligament breakup) coexist spanwise for a given temporal snapshot. This implies more continuous atomization than the one predicted by the constant film thickness case, which showed the same breakup stage to be present along the prefilmer span for a given instant and led to a more discretized set of atomization events. The proposed workflow allows quantifying the influence of the liquid film flow evolution above the prefilmer on primary breakup frequency and atomization features.
... Furthermore, for reasons of numerical stability, droplets larger than D max = 600 μm are not generated. The selected diameter range represents a typical characteristic drop size distribution for the planar prefilmer at the operating point considered [22,34]. Based on the underlying drop size distribution calculated by the PAMELA model, only few parcels ( 7% ) assigned with a diameter larger than 100 μm are injected. ...
Article
Full-text available
The pollutant emissions of aircraft engines are strongly affected by the fuel injection into the combustion chamber. Hence, the precise description of the fuel spray is required in order to predict these emissions more reliably. The characteristics of a spray is determined during the atomization process, especially during primary breakup in the vicinity of the atomizer nozzle. Currently, Euler-Lagrangian approaches are used to predict the droplet trajectories in combustor simulations along with reaction and pollutant formation models. To be able to reliably predict pollutant emissions in the future, well-defined starting conditions of the liquid fuel droplets close to the atomizer nozzle are necessary. In the present work, Euler-Lagrangian simulations of a generic airblast atomizer are presented. The starting conditions of the droplets are varied in the simulations by means of a primary breakup model, which takes into account the local gas velocity when predicting the droplet diameter. The objective of this work is to determine the optimal parameters of the probability density functions for the starting position and the starting velocity of the droplets. Spray properties observed in the simulations are used to qualitatively evaluate the major effects of the distribution parameters on the spray and the suitability of the primary breakup model being applied. Hence, the spatial distribution of an experimental spray can be reproduced using a statistical model for the droplet starting conditions.
... For example, Chiodi et al.[161], Chiodi and Desjardins[162,163] was able to reproduce the breakup physics through numerical simulations using geometric liquid volume fraction transport method[61] and accurate conservative level set (ACLS) method.On the other hand, the planar configuration of Airblast atomization has different breakup physics than the cylindrical configuration. Hence, there have been many experimental works[2,38,164,165] and numerical works[4,[166][167][168] that investigated into understanding the breakup physics and the atomization characteristics such as drop size distribution (DSD) and drop velocity distributions (DVD). Many of the past experimental studies have found that the aerodynamic forces play a significant and key role in the droplet sizes; specifically, the increase in the mean air velocities resulted in reduction in the droplet sizes[36,[169][170][171] while a reduction in the Sauter Mean Diameter(SMD) has been observed with the increase in the surface tension of the liquid fuel[169,170].Multiple works using numerical simulations have been performed in the past years, for example, Fuster et al.[64] studied the instability frequency of the primary break up of planar coflowing sheets of water and air at dynamic pressure ratios of 0.5 to 32. ...
Thesis
Full-text available
With the increase in the passenger air travel, it has become necessary to design fuel efficient engines for long-haul and ultra-long-haul flights. Because of the continuous progress in the supercomputing power and advances in the computational fluid dynamics (CFD) methods, numerical simulations have been sought after as the choice for investigating the physical processes occurring inside the aircraft engines. Of the many processess, atomization of the liquid fuel, i.e., the process by which the injected liquid fuel breaks up into droplets remains imperative to be completely understood. Since atomization processgoverns the size of the fuel droplets produced, it has a direct influence on the evaporation rate, completeness of combustion, and even pollutant formation. However, due to the multiscale, multiphysical, and multiphase aspect of this process, it has become a challenge to numerically simulate it. Most often, the simulations run into under-resolution limitation when capturing the droplets. To mitigate this shortcoming and to make the simulations numerically tractable, this work presents two numerical methods of liquid/gas interface reconstruction to capture the liquid droplets {moment of fluid (MOF) method and hybrid moment of fluid{level set (HyMOFLS) method. These methods are coupled with consistent mass and momentum flux computation as well as ghost fluid method (GFM) for handling discontinuities in density and jump in pressure across the interface. The MOF method uses liquid volume fraction as well as liquid and gas phase centroids for interface reconstruction in each computational cell in the simulations. The advantage in using the phase centroids is that the neighbor cell data are not required in the interface reconstruction process resulting in a uniform treatment of interior and boundary cells in the computational domain. This method improves the liquid/gas interface orientation and reconstruction in the underresolved regions of the domain. The HyMOFLS method combines the MOF method and CLSVOF method such that MOF method is employed to capture under-resolved regions and CLSVOF method for resolved regions of the interface. The switch between the choice of these methods in the computational domain is made according to local mesh spacing and curvature of the interface. This method strikes a good balance between the reconstruction accuracy and modest computational cost requirement compared to MOF method. Hence, it is a natural choice for performing simulations of primary atomization at aircraft engine operating conditions. The HyMOFLS method is employed in to simulate primary atomization of liquid for two injection con_gurations used in aircraft engines under relevant operating conditions. First, a planar pre-filming Airblast atomization configuration is simulated using two gridresolutions and inlet velocity profile to investigate and analyze their effect on the atomization characteristics, i.e., droplet and ligament properties. Results suggest that the simulations are matching satisfactorily with the experiments and are of the same order of magnitude as the experimental data. Next, primary atomization of a turbulent liquid jet in gaseous crossow configuration is simulated under three di_erent (low, moderate,and high) density ratio operating conditions using three different mesh resolutions. The analyses of the results yielded that there is low probability of occurrence of secondary atomization due to aerodynamic forces, the jet bending and penetration decrease with increase in density ratio, and the wavelength of the instability waves formed on the windward side of the liquid jet decreases from low to moderate density ratio and increases from moderate to high density ratio.
... Sketch of annular prefilming airblast nozzle illustrating common droplet starting positions and initial velocity vector in magenta, adapted from[10]. ...
Article
Full-text available
The formation of pollutant emissions in jet engines is closely related to the fuel distribution inside the combustor. Hence, the characteristics of the spray formed during primary breakup are of major importance for an accurate prediction of the pollutant emissions. Currently, an Euler–Lagrangian approach for droplet transport in combination with combustion and pollutant formation models is used to predict the pollutant emissions. The missing element for predicting these emissions more accurately is well defined starting conditions for the liquid fuel droplets as they emerge from the fuel nozzle. Recently, it was demonstrated that the primary breakup can be predicted from first principles by the Lagrangian, mesh-free, Smoothed Particle Hydrodynamics (SPH) method. In the present work, 2D Direct Numerical Simulations (DNS) of a planar prefilming airblast atomizer using the SPH method are presented, which capture most of the breakup phenomena known from experiments. Strong links between the ligament breakup and the resulting spray in terms of droplet size, trajectory and velocity are demonstrated. The SPH predictions at elevated pressure conditions resemble quite well the effects observed in experiments. Significant interdependencies between droplet diameter, position and velocity are observed. This encourages to employ such multidimensional interdependence relations as a base for the development of primary atomization models.
... It is a planar prefilming airblast atomizer and can be considered as a 2D abstraction of a realistic annular atomizer. It has the advantage to feature the same breakup mechanism like in annular atomizers (Gepperth et al. 2012;Holz et al. 2016) in a deterministic plane that simplifies optical measurements. The geometry consists of a wing-shaped prefilmer located at the center of a rectangular channel. ...
Preprint
Full-text available
The influence of the ambient pressure on the breakup process is investigated by means of PIV and shadowgraphy in the configuration of a planar prefilming airblast atomizer. Other investigated parameters are the gas velocity and the film loading. It is found that the gas velocity in the vicinity of the prefilmer partly matches the analytical profile from the near-wake theory. The shadowgraphy images of the liquid phase allow to extract characteristic quantities of the liquid accumulation at the atomizing edge. Two different characteristic lengths, the ligament velocity and a breakup frequency are determined. In addition, the spray Sauter Mean Diameter (SMD) and the mean droplet velocity are given for each operating point. A scaling law of these quantities with regard to ambient pressure is derived. A correlation is observed between the characteristic length of the accumulation and the SMD, thus promoting the idea that the liquid accumulation determines the primary spray characteristics. An threshold to distinguish the zones between primary and secondary breakup is proposed based on an objective criterion. It is also shown that taking non-spherical droplets into account significantly modifies the shape of the dropsize distribution, thus stressing the need to use shadowgraphy when investigating primary breakup. The ambient pressure and the velocity are varied accordingly to keep the aerodynamic stress $\rho_g U_g^2$ constant. This leads to almost identical liquid accumulation and spray characteristics, confirming that the aerodynamic stress is a key parameter to characterize prefilming airblast breakup. Finally, SMD correlations from the literature are compared to the present experiment. Most of the correlations calibrated with LDA/LDT measurement underestimate the SMD. This highlights the need to use shadrowgraphy for calibrating primary breakup models.
... Both time scales are found to be proportional to the capillarity time as τ RT ≈ 10 τ c and τ bu ≈ 1.8 τ c [21] so that τ tot = C τ τ c with C τ ≈ 11.8. Constants C 1 to C 5 in Eqs. 8 are essentially independent of the liquid properties or the geometry, and although they were calibrated for a planar geometry, they showed a good agreement when predicting an annular nozzle [22]. Their values are 0.67, 0.112, 6.82, 5.99 [m], 0.0177, respectively. ...
Article
The present study investigates the response of recent primary breakup models in the presence of an oscillating air flow, and compares them to an experiment realized by Müller and coworkers in 2008. The experiment showed that the oscillating flow field has a significant influence on the Sauter Mean Diameter (SMD) up to a given frequency. This observation highlights the low-pass filter character of the prefilming airblast atomization phenomenon, which also introduces a significant phase shift on the dynamics of SMD of the generated spray. The models are tested in their original formulations without any calibration in order to assess their robustness versus different experiments in terms of SMD and time-response to an oscillating flow field. Special emphasis is put to identify the advantages and weaknesses of theses models, in order to facilitate their future implementation in CFD codes. It is observed that some models need an additional calibration of the time constant in order to match the time shift observed in the experiment, whereas some others show a good agreement with the experiment without any modification. Finally, it is demonstrated that the low-pass filter character of the breakup phenomenon can be retrieved by considering the history of the local gas velocity, instead of the instantaneous velocity. This might result in a higher simulation fidelity within CFD codes.
Article
The influence of the ambient pressure on the breakup process is investigated by means of PIV and shadowgraphy in the configuration of a planar prefilming airblast atomizer. The ambient pressure is varied from 1 to 8 bar. Other investigated parameters are the gas velocity and the film loading. From single-phase PIV measurements, it is found that the gas velocity in the vicinity of the prefilmer partly matches the analytical profile from the near-wake theory. As done in previous publications, the characteristics of the liquid accumulation are extracted from the shadowgraphy images of the liquid phase directly downstream of the prefilmer. Two different characteristic lengths, as well as the ligament velocity and a breakup frequency are determined. In addition, the droplets generated directly downstream of the liquid accumulation are captured. Hence, the spray Sauter Mean Diameter (SMD) and the mean droplet velocity are given for each operating point. The novelty of this study is that a scaling law of these quantities with regard to ambient pressure is derived. A correlation is observed between the characteristic length of the accumulation and the SMD, thus reinforcing the idea that the liquid accumulation determines the primary spray characteristics. In this paper, a threshold to distinguish the zones between primary and secondary breakup is proposed based on an objective criterion. It is also shown that taking non-spherical droplets into account significantly modifies the shape of the dropsize distribution, thus stressing the need to use shadowgraphy when investigating primary breakup. Additionally, the ambient pressure and the velocity are varied accordingly to keep the aerodynamic stress ρgUg2 constant. This leads to almost identical liquid accumulation and spray characteristics. Hence, it is confirmed that the aerodynamic stress is a more appropriate parameter than the gas velocity or the ambient pressure to characterize prefilming airblast breakup. Finally, SMD correlations from the literature are compared to the present experiment. Most of the correlations calibrated with LDA/LDT measurement underestimate the SMD. This highlights the need to use shadrowgraphy for calibrating primary breakup models.
Chapter
An understanding of the fundamental mechanisms involved in the interaction between bubbles and vortices is relevant to many important engineering applications. Classical assumptions of bubble sphericity and decoupling between bubble and flow behavior prevent one from capturing some essential elements of the interaction. Bubble motion and deformation are seen to be of great importance for most bubbles in the size spectrum. In this chapter, studies on bubble capture by a vortex, bubble motion and deformation during that capture, and bubble behavior once the bubble is on the vortex axis are described. Flow field modifications once the bubble is on the vortex axis are also briefly considered. The most promising approach appears to consist of a coupling between a boundary element method to describe the bubble behavior, and a viscous flow solver to describe the basic flow.
Article
Particle characterization in dispersed multiphase flows is important in quantifying transport processes both in fundamental and applied research: Examples include atomization and spray processes, cavitation and bubbly flows, and solid particle transport in gas and liquid carrier phases. Optical techniques of particle characterization are preferred owing to their nonintrusiveness, and they can yield information about size, velocity, composition, and to some extent the shape of individual particles. This review focuses on recent advances for measuring size, temperature, and the composition of particles, including several planar methods, various imaging techniques, laser-induced fluorescence, and the more recent use of femtosecond pulsed light sources. It emphasizes the main sources of uncertainty, the achievable accuracy, and the outlook for improvement of specific techniques and for specific applications. Some remarks are also directed toward the computational tools used to design and investigate the perfo...
Article
The paper describes the atomisation process of a liquid in an axissymmetric shear layer formed through the interaction of turbulent coaxial jets (respectively, inner and outer jets), with and without swirl, in a model airblast prefilming atomiser. The atomisation process and spray quality was studied using different visualisation techniques, namely laser shadowgraphy and digital image acquisition. The experiments were conducted for different liquid flow rates, Reynolds numbers ranging from 6600 to 66000 and 27300 to 92900 for the inner and outer air flows, respectively, for different outer flow swirl levels, and two liquid film thicknesses −0.2 and 0.7 mm. All the tests were carried out at atmospheric pressure and using water. The results include the analysis of the film structure at break-up and of the break-up length, and suggest that the deterioration of the liquid film close to the atomising edge exhibits a periodic behaviour and is mainly dependent on the inner air velocity. Film thickness strongly affects the time and length scales of the break-up process for the lower range of air velocities. For higher inner air velocities, the break-up length and time become less dependent on liquid flow rate and initial film thickness.
Article
A linear stability analysis is presented for a liquid sheet that includes the effects of the surrounding gas, surface tension and the liquid viscosity on the wave growth process. An inviscid dispersion relation is used to identify the transition from a long wavelength regime to a short wavelength regime, analogous to the first and second wind induced breakup regimes of cylindrical liquid jets. This transition, which is found to occur at a gas Weber number of 27/16, is used to simplify the viscous dispersion relation for use in multi-dimensional simulations of sheet breakup. The resulting dispersion relation is used to predict the maximum unstable growth rate and wave length, the sheet breakup length and the resulting drop size for pressure-swirl atomizers. The predicted drop size is used as a boundary condition in a multi-dimensional spray model. The results show that the model is able to accurately predict liquid spray penetration, local Sauter mean diameter and overall spray shape.
• A H Lefebvre
Lefebvre, A. H., Atomization and Sprays, 10:251-276 (2000).
• B Sauer