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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.

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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].

The nozzle is made out of perspex for better optical access to the

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 10−5kg/(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 10−3kg/(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].

High speed shadowgraphy

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

of the shadowgraphy setup the reader is referred to [7].

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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

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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 m−qdq−1exp −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

g/σ where 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

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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 =ug√2Lsurf

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)

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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∗

g≈0.7

|{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.

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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.

Bulk velocity of gaseous phase [m/s]

20 30 40 50 60

Sauter mean diameter [µm]

150

175

200

225

250

275

Experiment, ˙

V /b = 14 mm2/s

Experiment, ˙

V /b = 28 mm2/s

Experiment, ˙

V /b = 55 mm2/s

Experiment, ˙

V /b = 110 mm2/s

Figure 8. Inﬂuence of air and liquid mass ﬂow on the SMD extracted from the Experiment.

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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) = Dq−1m−qq 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 m−qq e−(D

m)q

V−1

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 −e−ln(D)

ln(m)q

⇔f3,modRR(D) = D−1ln(D)q−1ln(m)−qq e−ln(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.

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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).

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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.

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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 n◦620143.

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 [m−1]

Fcumulative distribution function [m−1]

hheight [m]

Llength [m]

mscale factor [m]

˙mmass ﬂow [kg/s]

Mmomentum ﬂux of the gas [kg/(m s2)]

qshape factor []

qmeasured probability density [m−1]

Sswirl number []

SSE sum of squared errors [m−2]

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

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