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Analysis by droplet size classes of the liquid flow structure in a pressure swirl hollow cone spray
Chemical Engineering and Processing 49 (2010) 125–131
Contents lists available at ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Analysis by droplet size classes of the liquid flow structure in a pressure swirl hollow cone spray J.L. Santolaya ∗ , L.A. Aísa, E. Calvo, I. García, J.A. García Fluid Mechanics Area, Zaragoza University, María de Luna 3, 50015 Zaragoza, Spain
a r t i c l e
i n f o
Article history: Received 7 June 2009 Received in revised form 22 November 2009 Accepted 11 December 2009 Available online 21 December 2009 Keywords: Two-phase flow Droplet size classes Volume flux Droplet collisions Coalescence
a b s t r a c t In this work the structure of a spray resulting from the break-up of a conical liquid sheet was investigated through experimental techniques. The disperse and continuous phase velocities and the size of droplets were measured using a phase Doppler particle analyzer. A data post-processing, applying the generalized integral method, was used to evaluate liquid volume fluxes for different droplet size classes. The spatial distribution of the liquid flow was characterized by the radial mean spread and spatial dispersion parameters. It was found to be mainly influenced by the differences in droplet inertia and by the droplet collision phenomena. A high dispersion of droplet velocity module was measured at the spray densest region predicting high droplet collision rates. As a consequence of the coalescing collisions, a liquid flow rate transfer between size classes was detected as the spray developed. This process favoured the large size classes and caused the progressive increase of the droplet mean diameter. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The performance of many industrial processes depends on the mixing between the spray droplets and its surrounding gas. Applications as agriculture, combustion, air and water pollution or numerous manufacturing processes involve the formation and development of droplets. As well as the liquid disintegration process [1–3], other phenomena as the two-way coupling between the phases [4–6] and the interaction between droplets [7,8] take decisive part in the two-phase flow configuration. Among the wide variety of devices used to achieve the disintegration of a liquid volume, pressure swirl nozzles are satisfactory for producing well-atomized sprays through the break-up of thin conical sheets [9,10]. The high angular momentum that acquires the fluid inside this kind of nozzle, forces it to emerge in the form of a hollow conical sheet that soon becomes unstable and disintegrates because of different mechanisms [11]. The interaction of the atomized liquid with the gas flow field redistributes spatially the spray droplets due to the differences in droplet inertia, momentum and drag. Velocity and droplet size measurements, obtained by non-intrusive optical measurement techniques such as phase Doppler anemometry, showed that, for pressure swirl atomizers, in the absence of any significant external air flow field, large droplets tend to maintain the high velocity of the
∗ Corresponding author. Tel.: +34 976761881; fax: +34 976761882. E-mail address: [email protected] (J.L. Santolaya). 0255-2701/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2009.12.003
liquid sheet whereas small droplets couple to the local-induced air flow [12,13]. The droplet number concentration increases almost continuously from the edge towards the core region of the spray because of the preferential accumulation of small droplets which are transported by the continuous phase. Nevertheless, axial volume fluxes present initially local maxima at the edge of the spray [14]. It is also known that the air flow rate, which is drawn into the spray has a decisive influence on the heat and mass transfer between phases, however entrained airflow rate measurements are relatively small [6]. On the other hand, droplet collision is expected to be a frequent event immediately downstream of the sheet break-up, promoted by the high concentrations and by the relative velocities between droplets. The collision phenomena cause a droplet velocity exchange and can intimately affect the droplet size distribution. Experimental investigations of the droplet collision dynamics [15], establish five distinct regimes of collision outcomes that depends mainly on the ratio of the inertia force to the surface tension force, the droplet size ratio and the geometrical orientation of the interacting droplets. The different collision outcomes were named: slow coalescence, bouncing, coalescence after substantial deformation, reflexive or near head-on separation and stretching or off-centre separation. Stable coalescence causes an increase of the droplet mean size as spray develops [16] and, therefore, affects critically spray mixing and subsequent processes. Most spray investigations analyze the effects of collision phenomena from the evolution of the integral mean diameter along the spray or from the behaviour of the droplet size distributions
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J.L. Santolaya et al. / Chemical Engineering and Processing 49 (2010) 125–131 Table 1 Oil properties at T = 95 ◦ C.
Density (kg/m3 ) Dynamic viscosity (kg/ms) Surface tension (N/m) Vapour pressure (pa) Refractive index
847 0.0166 0.032 98.13 1.483 + 0.00072i
obtained by systems based on Mie scattering, not providing droplet velocity information. The present work approaches the spray study via the analysis of the correlations between droplet size and velocities and via the examination of the overall volume droplet size distribution across the spray, which should elucidate the transfer process of the liquid flow rate between droplet size classes as spray develops. A comprehensive study about the relevance of this process could not be found until now. With this objective, emphasis is laid on the determination of droplet volume fluxes and total liquid flow rates by droplet size classes at different axial stations along the spray. 2. Experimental setup Experiments were performed at a specially designed facility for spray generation under controlled conditions. The test liquid was oil of industrial origin, used previously in lubrication and refrigeration applications. The oil properties, measured at the injection temperature, are listed in Table 1. The liquid was driven from the tank to the nozzle through a pumping line (Fig. 1), then was filtered to eliminate the undesirable solid particles and was heated by an electrical resistance in order to decrease its high viscosity and to improve atomization performance. A commercial pressure swirl nozzle (Danfoss 0.5 80◦ H) of low flow rate, cone angle of 80◦ and exit orifice diameter of 0.2 mm was used in this research. The pressure and temperature of the injected liquid were fixed in experiments at 16 bar and 95 ◦ C, respectively.
Under those specific test conditions, the oil volumetric flow rate injected through the atomizer was 0.77 cm3 /s and the nozzle discharge coefficient [17] was 0.4. Sprays developed inside a transparent chamber 340 mm square. An exhaust system provided a surrounding airflow into the chamber (co-flow) with a mean velocity of the 0.15 m/s. An auxiliary equipment was used to generate a very fine aerosol of water–glycerin mixture (D10 = 3.4 m), which was added to the coflow allowing the continuous phase measurements by the PDPA technique. After atomization, the injected liquid was recovered for recycling. A low noise CCD and a stroboscopic light source of 0.5 s pulse time were used to visualize the instantaneous disintegration of the emerging liquid film. The spray measurements were carried out by means of a TSI-Aerometrics 3100 PDPA system which allowed us to simultaneously measure the drop size and two components of velocity. The receiving optics was placed to collect scattered light at 70◦ from the forward direction. At this angle the light scattering is dominated by first order of refraction and that due to reflection is a minimum. Thus, errors associated with trajectory ambiguities due to the Gaussian beam effect were reduced [13]. Other geometrical settings were also tested but a nonlinear relationship between phase shift and droplet diameter was detected. The beam separation was 40 mm and a transmission lens with 500 mm of focal length was used. The focal length of the receiving optics was 300 mm, which is very much bigger than the size of the spray droplets. Thus, the measurements were considered not affected by changes in the optical path length of the refracted beams. Both, emitter and receiver were mounted on a traversing system controlled by computer. 3. Flow study method Spray measurements were carried out at four axial stations located at 9, 18, 36 and 72 mm from the atomizer exit. The droplet diameter and both, the axial and radial velocities, were measured every 2 mm in radial direction at each axial station using the PDPA system. A typical validation rate along a generic radius in the spray field was 85–95% for velocities and 65–85% for drop sizes. It should be noted that the PDPA rejects signals from non-spherical droplets and those due to multiple droplets in the probe volume. The mean velocities were determined by averaging overall droplet size distribution at the respective locations. The Sauter mean diameter, SMD or D32 , which is inversely proportional to the interfacial area per unit volume, was taken as characteristic parameter of the local droplet size distribution. The droplet number concentration and the liquid volume flux were determined by the method based on the transit time of the droplet at the probe volume [18,19]. This method, which avoids errors due to the droplet trajectory through the probe volume, can be formulated as a particular case of the General Integral Method (GIM), such as proposed by Aísa et al., [20]. Nevertheless, the accuracy of droplet volume flux measurements depends on a perfect signal detection and size evaluation of all droplets crossing the probe volume and on the determination of the probe volume size itself. The liquid volume flux corresponding to each droplet size class was obtained by the following expression: fVi
Fig. 1. Experimental setup.
1 = t
∀kj ttkj · VDj
Voli
·
Di3 6
(1)
where t is the measurement time at each location, Voli is the PDPA detection volume for each droplet size class, VDj is the velocity vector for each droplet velocity module class and ttkj is the transit time
J.L. Santolaya et al. / Chemical Engineering and Processing 49 (2010) 125–131
127
Fig. 2. Two-phase flow structure.
though the detection volume for droplets corresponding to each velocity direction class and each velocity module class. The liquid volume flux for all droplets was calculated as:
Spray analysis was carried out under the hypothesis of axisymmetry, plotting variables evolution profiles on the dimensionless radial coordinate r*. This coordinate was obtained as:
fV =
r∗ =
fVi
(2)
∀i
Droplet volume fluxes were evaluated in axial direction. The total liquid flow rates at each measurement axial station, for each droplet size class and for all droplets, were calculated respectively as:
FTi =
fVxi · ds
(3)
fVx · ds
(4)
ST
FT = ST
where ST is the spray cross-transversal area. The spray boundary at each axial station was located from PDPA measurements as the radial position where the data rate was less than 10 droplets per minute. The percentage of total liquid flow rate not measured was calculated as:
def = 100 · 1 −
FT Q
(5)
where Q is the liquid volumetric flow rate injected through the atomizer.
r R50
(6)
where R50 is the radial position that contains 50% of the total liquid volumetric flow rate measured at each axial station. In a similar way, the radii R10 and R90 , which are the radial positions including, respectively, 10 and 90% of the collected liquid flow rate at each axial station, were defined. Hence, the spray spatial dispersion parameter was calculated as follows: R = R90 − R10
(7)
The analysis of dispersed phase included the detailed study of three droplet size classes that were named small, medium and large. The small class integrated droplet diameters from 5 to 10 m; the medium class, diameters from 20 to 30 m, and the large class, diameters from 50 to 60 m. The characterization of the continuous phase, and subsequent determination of the air velocity fields, was performed analyzing the signals of the smallest droplets (smaller than 5 m) which supposedly follow the instantaneous changes in gas velocity. As mentioned before, a very fine aerosol was added to the co-flow allowing gas phase measurements by the PDPA.
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The entrained air flow rate was calculated by integrating the local axial air velocities across the spray, as shown in the following expression:
FTa =
Vax · ds
(8)
ST
Air mass flow rate balances were checked in several cylindrical control volumes in order to validate the continuous phase measurements. Average errors of 8% were obtained between incoming and outgoing air flow rates. 4. Two-phase flow structure The liquid emerges from the nozzle in the form of a diverging conical-shaped sheet of angle 80◦ which breaks up via a wave growth process according to the regime 2 of sheet disrupting mechanisms [11]. An image of the sheet instantaneous disintegration, the mean velocity fields of both phases (droplets and air) and the profiles of droplet axial volume flux, fVx , at each axial measurement station are represented in Fig. 2. It is also shown the axial evolution of the R50 and R parameters, which represent the spray radial mean spread and the spray zone where the liquid flow rate is mainly concentrated, respectively. The hollow cone structure of the spray is remarked by the axial volume flux profile at the nearest axial location to the sheet break-up point. The liquid flow rate is initially concentrated in a small region of annular cross-section shape (densest spray region), with the highest volume flux around the R50 position. As spray develops, the droplets are transported into the spray core by the incoming air. The droplet inertial classification causes the spatial redistribution of the liquid flow rate and, consequently, more uniform profiles of the axial volume flux. A progressive increase of R50 and R was also obtained due to the droplet spatial dispersion. Values at each measurement axial station are listed in Table 2. The total liquid flow rates and the liquid flow rate deficits were calculated at each axial station from Eqs. (4) and (5), respectively. Results are presented in Table 2. It can be noticed that the injected liquid volumetric flow rate was not completely captured by the measurements. With the exception of x = 9 mm, deficits about 20% were obtained. The results are similar to those obtained by other researchers [21]. Usual explanations for no droplets validation by PDPA technique are the presence of multiple droplets in the probe volume or non-spherical droplets produced in the first sheet break-up. Here, non-spherical droplets generated by the collision phenomena are believed to be a very likely cause of data reject. As discussed below, droplet collisions will be a particularly important phenomenon in the densest zone of the spray and as previous experiments showed [15], the temporal formation of a mass of deforming liquid is produced in the most droplet collision events. The mean velocity map of the continuous phase, plotted in Fig. 2, shows that the surrounding air flows into the spray near field causing a high velocity jet at the central zone. The interaction between the incoming air and the disperse phase gives rise to the transport
Fig. 3. Profiles of the Sauter mean diameter.
of the smallest droplets towards the spray core and the consequent coupling of the velocities of both phases in this region. The entrained airflow rate at each axial station was obtained from Eq. (8). Its values, summarized in Table 2, show a progressive increase as the spray develops due to the significant incoming air flow rate and the radial spread of the spray. Although the velocities of the two phases are coupled at the spray core, high relative velocities between phases can be detected around the densest spray region and towards the spray periphery. Nevertheless, droplets quickly decelerate downstream by the strong momentum exchange with the slower moving air and droplet velocities approach those of the continuous phase in the spray far field. The D32 profiles, plotted in Fig. 3 using the dimensionless radial coordinate, show a progressive growing in radial direction something that is typical of hollow cone sprays. The smaller droplets are held in the spray core transported by the continuous phase, whereas the larger droplets move to the spray edge, relatively unperturbed, according to a process of droplet inertial classification. In addition, the use of the r* coordinate allow us to detect the significant axial growth of the D32 values, which is a consequence of the droplet collision–coalescence phenomena that occur along the spray. 5. Liquid flow structure: analysis of three different droplet size classes The resulting axial volume flux profiles, denoted as fVxs for the small, fVxm for the medium and fVxl for the large size class, were plotted in Fig. 4 at each axial measurement station. R50 parameter was also calculated for each droplet size class. In Fig. 4, the axial evolution of the radial mean spreads of size class, designated as R50s , R50m and R50l , respectively, were compared with the radial mean spread of the spray. The initial spray hollow cone structure can be perceived from the fVxm and fVxl profiles at the nearest axial location to the sheet break-up. As spray develops a radial redistribution of the liquid flow rate of the different size classes is produced. A very distinct behaviour has been observed in the classes: the peak of the fVxm profile moves progressively to the spray centre, while the fVxl peak
Table 2 Spray experimental data at each axial measurement station. x (mm)
R50 (mm)
R (mm)
FT (cm3 /s)
def (%)
FTa (l/s)
9 18 36 72
9.13 12.11 16.31 18.49
6.84 12.39 20.88 24.70
0.509 0.619 0.638 0.606
34.4 20.3 17.8 22
1.52 2.33 3.57 4.70
J.L. Santolaya et al. / Chemical Engineering and Processing 49 (2010) 125–131
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Fig. 4. Liquid flow structure. Study of three different droplet size classes: small, medium and large.
moves to the periphery. This trend is also observed for R50m and R50l that evolve, respectively, to the core and to the edge of the spray. On the other hand, the small size class, with low axial volume fluxes, is concentrated at the spray core. The axial evolution of the fVxm profile must be analyzed taking into account the axial variation of the total liquid flow rate of a size class, see Fig. 6. A progressive transfer of liquid flow rate from the medium droplet size class to other size classes was produced along the spray, which specifically affected their spatial distribution. This liquid transfer between droplet size classes is the result of droplet coalescing collisions. The mean velocity maps of the three droplet size classes are also plotted in Fig. 4. At the spray near field a behaviour clearly dominated by the aerodynamic effects can be noted for the mean velocity vectors at the densest spray region. The significant initial discrepancies between the velocities of different size classes are reduced downstream and a progressive coupling of the velocity fields appears. An analysis of the correlation between axial and radial droplet velocity components was carried out for the R50 location at x = 9 mm. The vertexes of the velocity vectors for a number of droplets of the small, medium, large and all size classes were represented in Fig. 5a–d, respectively. Strong correlation between velocity components and elevated dispersion of velocity modules can be observed in all cases. Accord-
ing to the classic kinetic theory of gases the collision rate between droplets can be related to their own relative velocity. Therefore, high droplet collision rates are expected at the densest spray region, even within each droplet size class. 6. Overall droplet size distributions In order to elucidate the incidence of the droplet collision–coalescence phenomena on the spray development, the axial evolution of the overall droplet size distribution across the spray was analyzed. By means of Eq. (3), the total liquid flow rates for 10 droplet size classes were calculated at each measurement axial station of the spray. The resulting distributions of the total liquid flow rate by droplet size classes are represented in Fig. 6. If the medium and large droplet size classes are examined, a substantial variation of the total liquid flow rate percentages can be detected along the spray. %FT of the medium size class reduces from 22.1% at x = 9 mm to 9.1% at x = 72 mm, while %FT of the large size class increases from 11.1 to 21.6%. Data for all stations and the corresponding mean diameters and typical deviations of the overall droplet size distributions across the spray are summarized in Table 3. Statistical moments show that spray evolution leads to coarser and wider volume droplet size distributions. The axial increase of
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J.L. Santolaya et al. / Chemical Engineering and Processing 49 (2010) 125–131
Fig. 5. Vertexes of the droplet velocity vectors: (a) small class; (b) medium class; (c) large class; (d) all droplets. Axial station: x = 9 mm. Radial position: r* = 1.
Table 3 Data of the overall droplet size distributions at different axial stations. x (mm)
%FT (medium class)
%FT (large class)
D43 ()
rmsF (m)
9 18 36 72
22.1 17.1 13.3 9.1
11.1 13.8 20.3 21.6
37.89 39.95 42.71 49.67
14.92 15.01 16.30 17.93
the droplet mean diameter is often a result reported in numerous spray research works, but not sufficiently analyzed trough experiments, which were mainly based on the study of the numeric droplet size distributions. Here, the analysis of the total liquid flow rate distribution by droplet size classes allows us to discover the progressive liquid flow rate transfer between size classes as spray develops. This process, which favoured the large size classes, is the
result of the droplet collision–coalescence phenomena along the spray. More investigations, including calculations of droplet collision rates according to kinetic theory of gases and the subsequent estimation of the overall droplet size distribution using suitable criteria of collision outcome, are in progress. 7. Conclusions
Fig. 6. Axial evolution of the overall droplet size distribution across the spray.
The structure of an oil spray generated by a pressure swirl nozzle and developing into a surrounding airflow of low velocity was analyzed by means of a PDPA system. The study included the determination of the two phases mean velocity fields and an exhaustive evaluation of liquid volume fluxes and total flow rates, for all droplets and size classes. Measurements in the spray near field showed that the liquid flow rate was concentrated in a small region where droplets presented a high dispersion of sizes. Nevertheless, the smallest droplets were transported to the spray core by the incoming air flow rate. The velocities of both phases were coupled at this region. High dispersion of velocity modules and strong directional correlation were also detected for the droplets of the spray densest region, even within each droplet size class.
J.L. Santolaya et al. / Chemical Engineering and Processing 49 (2010) 125–131
The relative velocities between droplets promoted high collision rates, which decisively contributed to the redistribution of the liquid flow rate along the spray. The coalescing collisions caused the liquid flow rate of the larger size classes to increase as spray developed and as a consequence, coarser and wider overall droplet size distributions. Appendix A. Nomenclature D D32 D43 def FT FTi FTa fV fVx P Q R50 r r* rmsF ST Va VD VDr VDx x R
droplet diameter (m) Sauter mean diameter (m) droplet mean diameter of the volume size distribution (m) liquid flow rate deficit (%) total liquid volumetric flow rate (cm3 /s) total liquid volumetric flow rate for each droplet size class (cm3 /s) total air volumetric flow rate (l/s) droplet volume flux (cm3 /cm2 s) axial droplet volume flux (cm3 /cm2 s) injection pressure injected liquid volumetric flow rate (cm3 /s) radial mean spread of the spray (mm) radial coordinate (mm) dimensionless radial coordinate typical deviation of the volume size distribution (m) spray cross-transversal area air velocity (m/s) droplet velocity (m/s) radial component of the droplet velocity (m/s) axial component of the droplet velocity (m/s) axial coordinate (mm) radial dispersion of the spray (mm)
References [1] H. Lefebvre, Atomization and Sprays, Hemisphere, New York, 1989. [2] P.K. Senecal, D.P. Schmidt, I. Nouar, C.J. Rutland, R.D. Reitz, M.L. Corradini, Modelling high-speed viscous liquid sheet atomization, Int. J. Multiphase Flow 25 (1999) 1073–1097. [3] S. Nonnenmacher, M. Piesche, Design of hollow cone pressure swirl nozzles to atomize Newtonian fluids, Chem. Eng. Sci. 55 (2000) 4339–4348.
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[4] W.H. Lai, M.R. Wang, D.Y. Huang, Turbulence Modulation in a Simplex Spray, ICLASS 97, Seoul, 1997, pp. 409–416. [5] M. Sommerfeld, Analysis of isothermal and evaporating turbulent sprays by phase-doppler anemometry and numerical calculations, Int. J. Heat Fluid Flow 19 (1998) 1173–1186. [6] J. Schelling, L. Reh, Influence of atomiser design and coaxial gas velocity on gas entrainment into sprays, Chem. Eng. Proc. 38 (1999) 383–393. [7] M. Sommerfeld, Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence, Int. J. Multiphase Flow 27 (2001) 1829–1858. [8] L.P. Scott, J. Abraham, Modelling the outcome of drop–drop collisions in Diesel sprays, Int. J. Multiphase Flow 28 (2002) 997–1019. [9] J.M. Ballester, C. Dopazo, Drop size measurements in heavy oil sprays for pressure swirl nozzles, Atomization Sprays 6 (1996) 377–408. [10] I.P. Chung, C. Presser, Fuel property effects on sheet disintegration of a simplex pressure-swirl atomizer, AIAA J. Prop. Power 17 (1) (2001) 212–216. [11] J.L. Santolaya, L.A. Aísa, E. Calvo, I. García, L.M. Cerecedo, Experimental study of near-field flow structure in hollow cone pressure swirl sprays, AIAA J. Prop. Power 23 (2) (2007) 382–389. [12] C.J. Bates, The Effect of Aperture Setting on Pressure Atomizer Phase Doppler Anemometry Measurements, ICLASS 94, Rouen, 1994, pp. 429–436. [13] W.D. Bachalo, Spray diagnostics for the twenty-first century, Atomization Sprays 10 (2000) 439–474. [14] D.A. Feikema, R. Eskridge, J.J. Hutt, Structure of a nonevaporating swirl injector spray, Atomization Sprays 7 (1997) 77–95. [15] J. Qian, C.K. Law, Regimes of coalescence and separation in droplet collision, J. Fluid Mech. 331 (1997) 59–80. [16] M. Rüger, S. Hohmann, M. Sommerfeld, G. Kohnen, Euler/Lagrange calculations of turbulent sprays: the effect of droplet collisions and coalescence, Atomization Sprays 10 (2000) 47–81. [17] D. Dupoy, B. Florès, D. Lisiecki, C. Dumouchel, Behaviour of Swirl Atomizers of Small Dimensions, ICLASS 94, Rouen, 1994, pp. 374–381. [18] W.D. Bachalo, R.C. Rudoff, A. Brena de la Rosa, Mass flux measurements of a high number density spray system using the phase Doppler particle analyzer, in: AIAA 26th Aerospace Science Meeting, Reno NV 11–14 January, 1988. [19] H.H. Qiu, M. Sommerfeld, A reliable method for determining the measurement volume size and particle mass fluxes using phase-Doppler anemometry, Exp. Fluids 13 (1992) 393–404. [20] L.A. Aísa, J.A. García, L.M. Cerecedo, J.I. García, E. Calvo, Particle concentration and local mass flux measurements in two-phase flows with PDA. Application to a study on the dispersion of spherical particles in a turbulent air jet, Int. J. Multiphase Flow 28 (2002) 301–324. [21] J. Domnick, Some Comments Concerning the State-of-the-art of Phase Doppler Anemometry Applied to Liquid Sprays, ILASS 97, Florence, 1997, pp. 366–374.
Contents lists available at ScienceDirect
Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep
Analysis by droplet size classes of the liquid flow structure in a pressure swirl hollow cone spray J.L. Santolaya ∗ , L.A. Aísa, E. Calvo, I. García, J.A. García Fluid Mechanics Area, Zaragoza University, María de Luna 3, 50015 Zaragoza, Spain
a r t i c l e
i n f o
Article history: Received 7 June 2009 Received in revised form 22 November 2009 Accepted 11 December 2009 Available online 21 December 2009 Keywords: Two-phase flow Droplet size classes Volume flux Droplet collisions Coalescence
a b s t r a c t In this work the structure of a spray resulting from the break-up of a conical liquid sheet was investigated through experimental techniques. The disperse and continuous phase velocities and the size of droplets were measured using a phase Doppler particle analyzer. A data post-processing, applying the generalized integral method, was used to evaluate liquid volume fluxes for different droplet size classes. The spatial distribution of the liquid flow was characterized by the radial mean spread and spatial dispersion parameters. It was found to be mainly influenced by the differences in droplet inertia and by the droplet collision phenomena. A high dispersion of droplet velocity module was measured at the spray densest region predicting high droplet collision rates. As a consequence of the coalescing collisions, a liquid flow rate transfer between size classes was detected as the spray developed. This process favoured the large size classes and caused the progressive increase of the droplet mean diameter. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The performance of many industrial processes depends on the mixing between the spray droplets and its surrounding gas. Applications as agriculture, combustion, air and water pollution or numerous manufacturing processes involve the formation and development of droplets. As well as the liquid disintegration process [1–3], other phenomena as the two-way coupling between the phases [4–6] and the interaction between droplets [7,8] take decisive part in the two-phase flow configuration. Among the wide variety of devices used to achieve the disintegration of a liquid volume, pressure swirl nozzles are satisfactory for producing well-atomized sprays through the break-up of thin conical sheets [9,10]. The high angular momentum that acquires the fluid inside this kind of nozzle, forces it to emerge in the form of a hollow conical sheet that soon becomes unstable and disintegrates because of different mechanisms [11]. The interaction of the atomized liquid with the gas flow field redistributes spatially the spray droplets due to the differences in droplet inertia, momentum and drag. Velocity and droplet size measurements, obtained by non-intrusive optical measurement techniques such as phase Doppler anemometry, showed that, for pressure swirl atomizers, in the absence of any significant external air flow field, large droplets tend to maintain the high velocity of the
∗ Corresponding author. Tel.: +34 976761881; fax: +34 976761882. E-mail address: [email protected] (J.L. Santolaya). 0255-2701/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2009.12.003
liquid sheet whereas small droplets couple to the local-induced air flow [12,13]. The droplet number concentration increases almost continuously from the edge towards the core region of the spray because of the preferential accumulation of small droplets which are transported by the continuous phase. Nevertheless, axial volume fluxes present initially local maxima at the edge of the spray [14]. It is also known that the air flow rate, which is drawn into the spray has a decisive influence on the heat and mass transfer between phases, however entrained airflow rate measurements are relatively small [6]. On the other hand, droplet collision is expected to be a frequent event immediately downstream of the sheet break-up, promoted by the high concentrations and by the relative velocities between droplets. The collision phenomena cause a droplet velocity exchange and can intimately affect the droplet size distribution. Experimental investigations of the droplet collision dynamics [15], establish five distinct regimes of collision outcomes that depends mainly on the ratio of the inertia force to the surface tension force, the droplet size ratio and the geometrical orientation of the interacting droplets. The different collision outcomes were named: slow coalescence, bouncing, coalescence after substantial deformation, reflexive or near head-on separation and stretching or off-centre separation. Stable coalescence causes an increase of the droplet mean size as spray develops [16] and, therefore, affects critically spray mixing and subsequent processes. Most spray investigations analyze the effects of collision phenomena from the evolution of the integral mean diameter along the spray or from the behaviour of the droplet size distributions
126
J.L. Santolaya et al. / Chemical Engineering and Processing 49 (2010) 125–131 Table 1 Oil properties at T = 95 ◦ C.
Density (kg/m3 ) Dynamic viscosity (kg/ms) Surface tension (N/m) Vapour pressure (pa) Refractive index
847 0.0166 0.032 98.13 1.483 + 0.00072i
obtained by systems based on Mie scattering, not providing droplet velocity information. The present work approaches the spray study via the analysis of the correlations between droplet size and velocities and via the examination of the overall volume droplet size distribution across the spray, which should elucidate the transfer process of the liquid flow rate between droplet size classes as spray develops. A comprehensive study about the relevance of this process could not be found until now. With this objective, emphasis is laid on the determination of droplet volume fluxes and total liquid flow rates by droplet size classes at different axial stations along the spray. 2. Experimental setup Experiments were performed at a specially designed facility for spray generation under controlled conditions. The test liquid was oil of industrial origin, used previously in lubrication and refrigeration applications. The oil properties, measured at the injection temperature, are listed in Table 1. The liquid was driven from the tank to the nozzle through a pumping line (Fig. 1), then was filtered to eliminate the undesirable solid particles and was heated by an electrical resistance in order to decrease its high viscosity and to improve atomization performance. A commercial pressure swirl nozzle (Danfoss 0.5 80◦ H) of low flow rate, cone angle of 80◦ and exit orifice diameter of 0.2 mm was used in this research. The pressure and temperature of the injected liquid were fixed in experiments at 16 bar and 95 ◦ C, respectively.
Under those specific test conditions, the oil volumetric flow rate injected through the atomizer was 0.77 cm3 /s and the nozzle discharge coefficient [17] was 0.4. Sprays developed inside a transparent chamber 340 mm square. An exhaust system provided a surrounding airflow into the chamber (co-flow) with a mean velocity of the 0.15 m/s. An auxiliary equipment was used to generate a very fine aerosol of water–glycerin mixture (D10 = 3.4 m), which was added to the coflow allowing the continuous phase measurements by the PDPA technique. After atomization, the injected liquid was recovered for recycling. A low noise CCD and a stroboscopic light source of 0.5 s pulse time were used to visualize the instantaneous disintegration of the emerging liquid film. The spray measurements were carried out by means of a TSI-Aerometrics 3100 PDPA system which allowed us to simultaneously measure the drop size and two components of velocity. The receiving optics was placed to collect scattered light at 70◦ from the forward direction. At this angle the light scattering is dominated by first order of refraction and that due to reflection is a minimum. Thus, errors associated with trajectory ambiguities due to the Gaussian beam effect were reduced [13]. Other geometrical settings were also tested but a nonlinear relationship between phase shift and droplet diameter was detected. The beam separation was 40 mm and a transmission lens with 500 mm of focal length was used. The focal length of the receiving optics was 300 mm, which is very much bigger than the size of the spray droplets. Thus, the measurements were considered not affected by changes in the optical path length of the refracted beams. Both, emitter and receiver were mounted on a traversing system controlled by computer. 3. Flow study method Spray measurements were carried out at four axial stations located at 9, 18, 36 and 72 mm from the atomizer exit. The droplet diameter and both, the axial and radial velocities, were measured every 2 mm in radial direction at each axial station using the PDPA system. A typical validation rate along a generic radius in the spray field was 85–95% for velocities and 65–85% for drop sizes. It should be noted that the PDPA rejects signals from non-spherical droplets and those due to multiple droplets in the probe volume. The mean velocities were determined by averaging overall droplet size distribution at the respective locations. The Sauter mean diameter, SMD or D32 , which is inversely proportional to the interfacial area per unit volume, was taken as characteristic parameter of the local droplet size distribution. The droplet number concentration and the liquid volume flux were determined by the method based on the transit time of the droplet at the probe volume [18,19]. This method, which avoids errors due to the droplet trajectory through the probe volume, can be formulated as a particular case of the General Integral Method (GIM), such as proposed by Aísa et al., [20]. Nevertheless, the accuracy of droplet volume flux measurements depends on a perfect signal detection and size evaluation of all droplets crossing the probe volume and on the determination of the probe volume size itself. The liquid volume flux corresponding to each droplet size class was obtained by the following expression: fVi
Fig. 1. Experimental setup.
1 = t
∀kj ttkj · VDj
Voli
·
Di3 6
(1)
where t is the measurement time at each location, Voli is the PDPA detection volume for each droplet size class, VDj is the velocity vector for each droplet velocity module class and ttkj is the transit time
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127
Fig. 2. Two-phase flow structure.
though the detection volume for droplets corresponding to each velocity direction class and each velocity module class. The liquid volume flux for all droplets was calculated as:
Spray analysis was carried out under the hypothesis of axisymmetry, plotting variables evolution profiles on the dimensionless radial coordinate r*. This coordinate was obtained as:
fV =
r∗ =
fVi
(2)
∀i
Droplet volume fluxes were evaluated in axial direction. The total liquid flow rates at each measurement axial station, for each droplet size class and for all droplets, were calculated respectively as:
FTi =
fVxi · ds
(3)
fVx · ds
(4)
ST
FT = ST
where ST is the spray cross-transversal area. The spray boundary at each axial station was located from PDPA measurements as the radial position where the data rate was less than 10 droplets per minute. The percentage of total liquid flow rate not measured was calculated as:
def = 100 · 1 −
FT Q
(5)
where Q is the liquid volumetric flow rate injected through the atomizer.
r R50
(6)
where R50 is the radial position that contains 50% of the total liquid volumetric flow rate measured at each axial station. In a similar way, the radii R10 and R90 , which are the radial positions including, respectively, 10 and 90% of the collected liquid flow rate at each axial station, were defined. Hence, the spray spatial dispersion parameter was calculated as follows: R = R90 − R10
(7)
The analysis of dispersed phase included the detailed study of three droplet size classes that were named small, medium and large. The small class integrated droplet diameters from 5 to 10 m; the medium class, diameters from 20 to 30 m, and the large class, diameters from 50 to 60 m. The characterization of the continuous phase, and subsequent determination of the air velocity fields, was performed analyzing the signals of the smallest droplets (smaller than 5 m) which supposedly follow the instantaneous changes in gas velocity. As mentioned before, a very fine aerosol was added to the co-flow allowing gas phase measurements by the PDPA.
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The entrained air flow rate was calculated by integrating the local axial air velocities across the spray, as shown in the following expression:
FTa =
Vax · ds
(8)
ST
Air mass flow rate balances were checked in several cylindrical control volumes in order to validate the continuous phase measurements. Average errors of 8% were obtained between incoming and outgoing air flow rates. 4. Two-phase flow structure The liquid emerges from the nozzle in the form of a diverging conical-shaped sheet of angle 80◦ which breaks up via a wave growth process according to the regime 2 of sheet disrupting mechanisms [11]. An image of the sheet instantaneous disintegration, the mean velocity fields of both phases (droplets and air) and the profiles of droplet axial volume flux, fVx , at each axial measurement station are represented in Fig. 2. It is also shown the axial evolution of the R50 and R parameters, which represent the spray radial mean spread and the spray zone where the liquid flow rate is mainly concentrated, respectively. The hollow cone structure of the spray is remarked by the axial volume flux profile at the nearest axial location to the sheet break-up point. The liquid flow rate is initially concentrated in a small region of annular cross-section shape (densest spray region), with the highest volume flux around the R50 position. As spray develops, the droplets are transported into the spray core by the incoming air. The droplet inertial classification causes the spatial redistribution of the liquid flow rate and, consequently, more uniform profiles of the axial volume flux. A progressive increase of R50 and R was also obtained due to the droplet spatial dispersion. Values at each measurement axial station are listed in Table 2. The total liquid flow rates and the liquid flow rate deficits were calculated at each axial station from Eqs. (4) and (5), respectively. Results are presented in Table 2. It can be noticed that the injected liquid volumetric flow rate was not completely captured by the measurements. With the exception of x = 9 mm, deficits about 20% were obtained. The results are similar to those obtained by other researchers [21]. Usual explanations for no droplets validation by PDPA technique are the presence of multiple droplets in the probe volume or non-spherical droplets produced in the first sheet break-up. Here, non-spherical droplets generated by the collision phenomena are believed to be a very likely cause of data reject. As discussed below, droplet collisions will be a particularly important phenomenon in the densest zone of the spray and as previous experiments showed [15], the temporal formation of a mass of deforming liquid is produced in the most droplet collision events. The mean velocity map of the continuous phase, plotted in Fig. 2, shows that the surrounding air flows into the spray near field causing a high velocity jet at the central zone. The interaction between the incoming air and the disperse phase gives rise to the transport
Fig. 3. Profiles of the Sauter mean diameter.
of the smallest droplets towards the spray core and the consequent coupling of the velocities of both phases in this region. The entrained airflow rate at each axial station was obtained from Eq. (8). Its values, summarized in Table 2, show a progressive increase as the spray develops due to the significant incoming air flow rate and the radial spread of the spray. Although the velocities of the two phases are coupled at the spray core, high relative velocities between phases can be detected around the densest spray region and towards the spray periphery. Nevertheless, droplets quickly decelerate downstream by the strong momentum exchange with the slower moving air and droplet velocities approach those of the continuous phase in the spray far field. The D32 profiles, plotted in Fig. 3 using the dimensionless radial coordinate, show a progressive growing in radial direction something that is typical of hollow cone sprays. The smaller droplets are held in the spray core transported by the continuous phase, whereas the larger droplets move to the spray edge, relatively unperturbed, according to a process of droplet inertial classification. In addition, the use of the r* coordinate allow us to detect the significant axial growth of the D32 values, which is a consequence of the droplet collision–coalescence phenomena that occur along the spray. 5. Liquid flow structure: analysis of three different droplet size classes The resulting axial volume flux profiles, denoted as fVxs for the small, fVxm for the medium and fVxl for the large size class, were plotted in Fig. 4 at each axial measurement station. R50 parameter was also calculated for each droplet size class. In Fig. 4, the axial evolution of the radial mean spreads of size class, designated as R50s , R50m and R50l , respectively, were compared with the radial mean spread of the spray. The initial spray hollow cone structure can be perceived from the fVxm and fVxl profiles at the nearest axial location to the sheet break-up. As spray develops a radial redistribution of the liquid flow rate of the different size classes is produced. A very distinct behaviour has been observed in the classes: the peak of the fVxm profile moves progressively to the spray centre, while the fVxl peak
Table 2 Spray experimental data at each axial measurement station. x (mm)
R50 (mm)
R (mm)
FT (cm3 /s)
def (%)
FTa (l/s)
9 18 36 72
9.13 12.11 16.31 18.49
6.84 12.39 20.88 24.70
0.509 0.619 0.638 0.606
34.4 20.3 17.8 22
1.52 2.33 3.57 4.70
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Fig. 4. Liquid flow structure. Study of three different droplet size classes: small, medium and large.
moves to the periphery. This trend is also observed for R50m and R50l that evolve, respectively, to the core and to the edge of the spray. On the other hand, the small size class, with low axial volume fluxes, is concentrated at the spray core. The axial evolution of the fVxm profile must be analyzed taking into account the axial variation of the total liquid flow rate of a size class, see Fig. 6. A progressive transfer of liquid flow rate from the medium droplet size class to other size classes was produced along the spray, which specifically affected their spatial distribution. This liquid transfer between droplet size classes is the result of droplet coalescing collisions. The mean velocity maps of the three droplet size classes are also plotted in Fig. 4. At the spray near field a behaviour clearly dominated by the aerodynamic effects can be noted for the mean velocity vectors at the densest spray region. The significant initial discrepancies between the velocities of different size classes are reduced downstream and a progressive coupling of the velocity fields appears. An analysis of the correlation between axial and radial droplet velocity components was carried out for the R50 location at x = 9 mm. The vertexes of the velocity vectors for a number of droplets of the small, medium, large and all size classes were represented in Fig. 5a–d, respectively. Strong correlation between velocity components and elevated dispersion of velocity modules can be observed in all cases. Accord-
ing to the classic kinetic theory of gases the collision rate between droplets can be related to their own relative velocity. Therefore, high droplet collision rates are expected at the densest spray region, even within each droplet size class. 6. Overall droplet size distributions In order to elucidate the incidence of the droplet collision–coalescence phenomena on the spray development, the axial evolution of the overall droplet size distribution across the spray was analyzed. By means of Eq. (3), the total liquid flow rates for 10 droplet size classes were calculated at each measurement axial station of the spray. The resulting distributions of the total liquid flow rate by droplet size classes are represented in Fig. 6. If the medium and large droplet size classes are examined, a substantial variation of the total liquid flow rate percentages can be detected along the spray. %FT of the medium size class reduces from 22.1% at x = 9 mm to 9.1% at x = 72 mm, while %FT of the large size class increases from 11.1 to 21.6%. Data for all stations and the corresponding mean diameters and typical deviations of the overall droplet size distributions across the spray are summarized in Table 3. Statistical moments show that spray evolution leads to coarser and wider volume droplet size distributions. The axial increase of
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Fig. 5. Vertexes of the droplet velocity vectors: (a) small class; (b) medium class; (c) large class; (d) all droplets. Axial station: x = 9 mm. Radial position: r* = 1.
Table 3 Data of the overall droplet size distributions at different axial stations. x (mm)
%FT (medium class)
%FT (large class)
D43 ()
rmsF (m)
9 18 36 72
22.1 17.1 13.3 9.1
11.1 13.8 20.3 21.6
37.89 39.95 42.71 49.67
14.92 15.01 16.30 17.93
the droplet mean diameter is often a result reported in numerous spray research works, but not sufficiently analyzed trough experiments, which were mainly based on the study of the numeric droplet size distributions. Here, the analysis of the total liquid flow rate distribution by droplet size classes allows us to discover the progressive liquid flow rate transfer between size classes as spray develops. This process, which favoured the large size classes, is the
result of the droplet collision–coalescence phenomena along the spray. More investigations, including calculations of droplet collision rates according to kinetic theory of gases and the subsequent estimation of the overall droplet size distribution using suitable criteria of collision outcome, are in progress. 7. Conclusions
Fig. 6. Axial evolution of the overall droplet size distribution across the spray.
The structure of an oil spray generated by a pressure swirl nozzle and developing into a surrounding airflow of low velocity was analyzed by means of a PDPA system. The study included the determination of the two phases mean velocity fields and an exhaustive evaluation of liquid volume fluxes and total flow rates, for all droplets and size classes. Measurements in the spray near field showed that the liquid flow rate was concentrated in a small region where droplets presented a high dispersion of sizes. Nevertheless, the smallest droplets were transported to the spray core by the incoming air flow rate. The velocities of both phases were coupled at this region. High dispersion of velocity modules and strong directional correlation were also detected for the droplets of the spray densest region, even within each droplet size class.
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The relative velocities between droplets promoted high collision rates, which decisively contributed to the redistribution of the liquid flow rate along the spray. The coalescing collisions caused the liquid flow rate of the larger size classes to increase as spray developed and as a consequence, coarser and wider overall droplet size distributions. Appendix A. Nomenclature D D32 D43 def FT FTi FTa fV fVx P Q R50 r r* rmsF ST Va VD VDr VDx x R
droplet diameter (m) Sauter mean diameter (m) droplet mean diameter of the volume size distribution (m) liquid flow rate deficit (%) total liquid volumetric flow rate (cm3 /s) total liquid volumetric flow rate for each droplet size class (cm3 /s) total air volumetric flow rate (l/s) droplet volume flux (cm3 /cm2 s) axial droplet volume flux (cm3 /cm2 s) injection pressure injected liquid volumetric flow rate (cm3 /s) radial mean spread of the spray (mm) radial coordinate (mm) dimensionless radial coordinate typical deviation of the volume size distribution (m) spray cross-transversal area air velocity (m/s) droplet velocity (m/s) radial component of the droplet velocity (m/s) axial component of the droplet velocity (m/s) axial coordinate (mm) radial dispersion of the spray (mm)
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