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:
[email protected]
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 measurement 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 several 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 proposed. 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 thickness 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 Chaussonnet 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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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. 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 b of the prefilmer is 47 mm. The swirl number S is 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 Figure 1. Sketch of nozzle, adapted from [21]. up forming bags, ligaments and droplets downstream the prefilmer.
Operating conditions The air and liquid mass flow m ˙ g and m ˙ l are 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 ρg and dynamic viscosity µg are 1.21 kg/m3 and 1.815 10−5 kg/(m s), respectively. As substitute fuel Shellsol D70 is used with density ρl = 770 kg/m3 , surface tension σ = 0.0275 kg/s2 and dynamic viscosity µl = 1.56 10−3 kg/(m s).
Table 1. Flowing conditions
Gas mass flow rate Gas bulk velocity Liquid mass flow rate Volumetric liquid film flow rate
m ˙g ubulk m ˙l V˙ /b
[g/s] [m/s] [g/s] [mm2 /s]
10 23 0.5 14
15 35 1 28
20 47 2 55
25 58 4 110
Measurement technique The atomization process was captured using high speed shadowgraphy. The recorded data was further post processed 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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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 calibration 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.
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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)).
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Figure 2. Snapshot of the breakup process, for different operating points
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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 σ and the momentum flux of the gas M = ρg u2g . The model is based on experimental observations and proposes the scenario as depicted in Figure 3. The film flow feeds the liquid reservoir (i) which is partly immersed into the highspeed gas flow (ii). Due to the high velocity difference, the surface of the liquid reservoir is sheared and strongly accelerated (iii) in the longitudinal direction, leading to a Rayleigh-Taylor instability that develops in the transverse direction (iv). This instability generates crests on the liquid surface that are blown up by the highspeed 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 wavelength λRT of the transverse instability, and that the number drop size distribution of the spray Figure 3. Sketch of the breakup mechanism, adapted from [19]. follows the Rosin-Rammler function defined by:
f0 (d) = q m
−q
q−1
d
q d exp − m
(1)
where m and q are 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 a : to the atomizing edge thickness ha , leading to the expression of λhRT s √ ρl 2π 6 C 1 ha σ a = λhRT with rρ = √ (2) √ rρ u∗g ρg ρl + ρ g where C1 is a constant, and the term u∗g represents the mean gas velocity at the location where the breakup occurs. a Assuming that the SMD of the spray is proportional to λhRT and expressing the SMD of a spray according to a Rosin-Rammler distribution, one can link the scale parameter m to the transverse wavelength by: a m = C2 λhRT
Γ(2/q + 1) Γ(3/q + 1)
(3)
where C2 and Γ are a constant and the gamma function, respectively. The shape parameter q controls 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 = ρg δu2g /σ where δ is the thickness of the boundary layer on the prefilmer just upstream of the atomizing edge. It yields: 2 C3 ha q(Weδ , ha ) = √ + + C5 (4) C4 Weδ where C3 to C5 are the last constants of the model. The Sauter mean diameter D32 estimated by the model is related to the transverse wavelength by: ha D32 = C2 λRT
(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 C1 to C5 were 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. C1 was 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. C2 was 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
a) Inputs
Density parameter:
Transverse wavelength: (Rayleigh-Taylor instability)
c) Rosin-Rammler parameters Liquid surface tension: Shape parameter:
Liquid density:
with
Gas density: Scale parameter:
Atomizing edge thickness: Local gas velocity: Boundary layer thickness:
d) Diameter distribution
Figure 4. Overview of the PAMELA model
atomizing edge with Eq. 2. The constants C3 to C5 were derived by matching the experimental drop size distribution to a Rosin-Rammler function and by fitting the shape q parameter. For C2 to 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 [-] 0.67
C2 [-] 0.112
C3 [-] 6.82
C4 [mm] 5.99
C5 [-] 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 instantaneous 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 determined 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 , ρg and 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 ha and the total length of the prefilmer Lsurf . Due to a complex shape of the prefilmer lip (Figure 5), the determination of ha is 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 δ the total length of the prefilmer Lsurf √ = 24 mm has to be considered. Due to the swirl number S equal to one the length over flown by the gas is 2 Lsurf , as depicted in Figure 6. The boundary layer is expressed as proposed by [5] as: √ √ 2 Lsurf ug 2 Lsurf δ = 0.16 with Re = (6) νg Re1/7 Finally, the local velocity u∗g is 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∗g corresponds to 70% of the bulk velocity: u∗g = 0.7 ubulk
(7) 5
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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 S is equal to one, the circumferential component uθ is 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 2 ubulk (Figure 6).
prefilmer perimeter b
Injection holes
Lsurf
2 Lsurf
2 ubulk
ubulk uθ
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 ug or local velocity magnitude u∗g : √ √ ug = 1.43 × 2 × ubulk ⇔ u∗g ≈ |{z} 0.7 × 1.43 2 × ubulk (8) |{z} × |{z} boundary layer
centrifugal effect
circumferential velocity
In the section dedicated to the results analysis, the importance of the swirl effect in the input velocity ug is 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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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 100 µm. 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.
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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. 275 Experiment, Experiment, Experiment, Experiment,
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Figure 8. Influence of air and liquid mass flow on the SMD extracted from the Experiment.
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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 1025 µm. 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). D
F3,RR (D) = 1 − e−( m )
q
⇔
D
f3,RR (D) = Dq−1 m−q q e−( 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: D
q
−1 f3,ChRR (D) = Dq+2 m−q q e−( m ) Vtot
(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]: ln(D) q − ln(m)
F3,modRR (D) = 1 − e
⇔
ln(D) q − ln(m)
f3,modRR (D) = D−1 ln(D)q−1 ln(m)−q q e
(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
(q3 (D) − f3 (D))2
(12)
i=1
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.
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Figure 9. Measured volume probability densities and fits with analytical distributions for selected operating points.
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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 ug and 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 ha is considered with 650 µm. Table 3. Different sets of PAMELA
set no 1 2
ug ubulk 2 ubulk
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 q3 are also shown.
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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
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(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 estimated SMDs are determined from zero to infinity. Taking into account droplets below 80 µm results in a substantial steeper decrease of the SMDs estimated by the model with increasing gas velocity. The significant deviations between 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 conditions 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 measured 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 prefilmers, 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 satisfactory 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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Acknowledgements The present research was particularly founded by the European Union’s Seventh Framework Programme (FP7/20072013) 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. Furthermore 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 D droplet diameter [m] Dxy diameter of xy [m] f probability density function [m−1 ] F cumulative distribution function [m−1 ] h height [m] L length [m] m scale factor [m] m ˙ mass flow [kg/s] M momentum flux of the gas [kg/(m s2 )]
q q S SSE Vtot V˙ /b
shape factor [] measured probability density [m−1 ] swirl number [] sum of squared errors [m−2 ] total droplet volume [m3 ] volumetric liquid film flow rate [m2 /s]
Greek Symbols µ dynamic viscosity [kg/(m s)] ρ density [kg/m3 ] σ surface tension [kg/s2 ] θ circumferential component Subscripts number 0 volume 3 atomizing edge a bulk bulk gaseous phase g Chaussonnet’s Rosin-Rammler distribution ChRR liquid phase l modified Rosin-Rammler distribution modRR prefilmer PF Rosin-Rammler distribution RR surface overflown by the gas flow surf
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