Published 12 issues per year
ISSN Print: 1044-5110
ISSN Online: 1936-2684
Indexed in
ANALYSIS OF THE EFFECT OF THE 2D PROJECTION ON DROPLET SHAPE PARAMETERS
ABSTRACT
The characterization of the shape of liquid elements in a spray is a good way to analyze atomization processes. Experimental approaches based on common imaging techniques suffer from partial information given by 2D images to characterize intrinsically 3D objects such as liquid droplets. In this paper, we address the question, To what extent can the shape parameters measured on 2D images reveal the 3D content of the droplet shape? An analytical approach is first adopted to determine relationships between 2D and 3D shape parameters for two families of objects, the oblate and prolate spheroids. Two numerical databases obtained from direct numerical simulation of two-phase flows are then explored for their ability to give complete 3D shape information and extrapolate 2D parameter values from projections on planes selected according to flow characteristics. Focus is put on one shape parameter particularly sensitive to 3D to 2D projection effects, namely the uniformity parameter introduced by Blaisot and Yon (2005). Statistics obtained from the numerical databases are used to guide the analysis of results extracted from experimental images. It is shown that statistics on a 3D shape parameter could be induced from the ones for the 2D parameters. Two conditions are necessary: (1) the 2D projection is performed perpendicularly to the main flow direction, which is always the case in experiments; and (2) a particular care must be put on the determination of the statistics of orientations of the main axis of the liquid elements. This last point should be tackled in future experimental analyzes to estimate 3D shape parameter statistics from 2D images.
Figures
-
Adrian, R.J., Particle-Imaging Techniques for Experimental Fluid Mechanics, Ann. Rev. Fluid. Mech., vol. 23, no. 1, pp. 261-304, 1991.
-
Adrian, R.J., Twenty Years of Particle Image Velocimetry, Exper. Fluids, vol. 39, no. 2, pp. 159-169, 2005.
-
Bachalo,W. and Houser,M., Phase/Doppler Spray Analyzer for Simultaneous Measurements of Drop Size and Velocity Distributions, Optical Eng., vol. 23, no. 5, p. 235583, 1984.
-
Baert, L., Fanara, D., Remon, J.P., and Massart, D., Correlation of Extrusion Forces, Raw Materials and Sphere Characteristics, J. Pharm. Pharm., vol. 44, no. 8, pp. 676-678, 1992.
-
Blaisot, J. and Yon, J., Droplet Size and Morphology Characterization for Dense Sprays by Image Processing: Application to the Diesel Spray, Exper. Fluids, vol. 39, no. 6, pp. 977-994, 2005.
-
Blott, S.J. and Pye, K., Particle Shape: A Review and New Methods of Characterization and Classification, Sedimentol., vol. 55, no. 1, pp. 31-63, 2008.
-
Bothell, J.K., Machicoane, N., Li, D., Morgan, T.B., Aliseda, A., Kastengren, A.L., and Heindel, T.J., Comparison of X-Ray and Optical Measurements in the Near-Field of an Optically Dense Coaxial Air-Assisted Atomizer, Int. J. Multif. Flow, vol. 125, p. 103219, 2020.
-
Chan, W.H.R., Dodd, M.S., Johnson, P.L., and Moin, P., Identifying and Tracking Bubbles and Drops in Simulations: A Toolbox for Obtaining Sizes, Lineages, and Breakup and Coalescence Statistics, J. Comput. Phys., vol. 432, p. 110156, 2021.
-
Charpentier, J.B., Brandle de Motta, J., and Menard, T., Capillary Phenomena in Assemblies of Parallel Cylindrical Fibers: From Statics to Dynamics, Int. J. Multif. Flow, vol. 129, p. 103304, 2020.
-
Chen, T., Cheron, V., Guo, Z., Brandle De Motta, J.C., Menard, T., and Wang, L.P., Simulation of Immiscible Two-Phase Flows Based on a Kinetic Diffuse Interface Approach, 10th Int. Conf. Multiphase Flow, Rio de Janeiro, Brazil, May 19-24, 2019.
-
Cheron, V., Brandle de Motta, J.C., Vaudor, G., Menard, T., and Berlemont, A., From Droplets to Particles: Transformation Criteria, 29th European Conf. on Liquid Atomization and Spray Systems, Paris, France, September 2-4, 2019.
-
Clift, R., Grace, J.R., and Weber, M., Bubbles, Drops and Particles, New York, NY: Academic Press, 1978.
-
Dodd,M.S. and Ferrante, A., On the Interaction of Taylor Length Scale Size Droplets and Isotropic Turbulence, J. Fluid. Mech., vol. 806, pp. 356-412, 2016.
-
Dumouchel, C. and Blaisot, J.B., Multi-Scale Analysis of Liquid Atomization Processes and Sprays, 25th European Conf. on Liquid Atomization and Spray Systems, Chania, Greece, September 1-4, 2013.
-
Dumouchel, C. and Blaisot, J.B., Laser Diffraction Measurement of Nonspherical Drop Sprays, Atomization Sprays, vol. 24, no. 3, pp. 223-249, 2014.
-
Dumouchel, C., Blaisot, J.B., Bouche, E., Menard, T., and Vu, T.T., Multi-Scale Analysis of Atomizing Liquid Ligaments, Int. J. Multif. Flow, vol. 73, pp. 251-263, 2015.
-
Duret, B., Luret, G., Reveillon, J., Menard, T., Berlemont, A., and Demoulin, F.X., DNS Analysis of Turbulent Mixing in Two-Phase Flows, Int. J. Multif. Flow, vol. 40, pp. 93-105, 2012.
-
Eriksson, M., Alderborn, G., Nystrom, C., Podczeck, F., and Newton, J., Comparison between and Evaluation of Some Methods for the Assessment of the Sphericity of Pellets, Int. J. Pharmaceutics, vol. 148, no. 2, pp. 149-154, 1997.
-
Fdida, N. and Blaisot, J., Morphological Characterization of Droplets. Application to Atomization of Sprays, Proc. 13th Int. Symp. on Flow Visualization, Nice, France, July 1-4, 2008.
-
Fdida, N., Blaisot, J.B., Floch, A., and Dechaume, D., Drop-Size Measurement Techniques Applied to Gasoline Sprays, Atomization Sprays, vol. 20, no. 2, 2010.
-
Fedkiw, R.P., Aslam, T., Merriman, B., and Osher, S., A Non-Oscillatory Eulerian Approach to Interfaces inMultimaterial Flows (The Ghost Fluid Method), J. Comput. Phys., vol. 152, no. 2, pp. 457-492, 1999.
-
Ficuciello, A., Blaisot, J., Richard, C., and Baillot, F., Investigation of Air-Assisted Sprays Submitted to High Frequency Transverse Acoustic Fields: Droplet Clustering, Phys. Fluids, vol. 29, no. 6, p. 067103, 2017.
-
Ghaemi, S., Rahimi, P., and Nobes, D., Measurement of Droplet Centricity and Velocity in the Spray Field of an Effervescent Atomizer, 14th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 7-10, 2008.
-
Ghaemi, S., Rahimi, P., and Nobes, D.S., Assessment of Parameters for Distinguishing Droplet Shape in a Spray Field Using Image-Based Techniques, Atomization Sprays, vol. 19, no. 9, 2009.
-
Gonzalez, H. and Garcia, F., The Measurement of Growth Rates in Capillary Jets, J. Fluid.Mech., vol. 619, p. 179, 2009.
-
Green, A., An Approximation for the Shapes of Large Raindrops, J. Appl. Meteorol., vol. 14, no. 8, pp. 1578-1583, 1975.
-
Han, L., Luo, H., and Liu, Y., A Theoretical Model for Droplet Breakup in Turbulent Dispersions, Chem. Eng. Sci., vol. 66, no. 4, pp. 766-776, 2011.
-
Herrmann, M., Detailed Numerical Simulations of the Primary Atomization of a Turbulent Liquid Jet in Crossflow, J. Eng. Gas Turbin. Power, vol. 132, no. 6, 2010a.
-
Herrmann,M., A Parallel Eulerian Interface Tracking/Lagrangian Point ParticleMulti-Scale Coupling Procedure, J. Comput. Phys., vol. 229, no. 3, pp. 745-759, 2010b.
-
Lamb, H., On the Vibrations of an Elastic Sphere, Proc. London Math. Soc., vol. s1-13, no. 1, pp. 189-212, 1881.
-
Lebas, R., Menard, T., Beau, P.A., Berlemont, A., and Demoulin, F.X., Numerical Simulation of Primary Break-Up and Atomization: DNS and Modelling Study, Int. J. Multif. Flow, vol. 35, no. 3, pp. 247-260, 2009.
-
Lohse, D., Fundamental Fluid Dynamics Challenges in Inkjet Printing, Ann. Rev. Fluid. Mech., vol. 54, pp. 349-382, 2022.
-
Lopez, J. and Hernandez, J., Analytical and Geometrical Tools for 3D Volume of Fluid Methods in General Grids, J. Comput. Phys., vol. 227, no. 12, pp. 5939-5948, 2008.
-
Malot, H. and Blaisot, J.B., Droplet Size Distribution and Sphericity Measurements of Low-Density Sprays through Image Analysis, Part. Part. Sys. Charact., vol. 17, no. 4, pp. 146-158, 2000.
-
Masuk, A.U.M., Salibindla, A., and Ni, R., A Robust Virtual-Camera 3D Shape Reconstruction of Deforming Bubbles/Droplets with Additional Physical Constraints, Int. J. Multif. Flow, vol. 120, p. 103088, 2019.
-
Mayor, L., Silva, M., and Sereno, A., Microstructural Changes during Drying of Apple Slices, Drying Technol., vol. 23, nos. 9-11, pp. 2261-2276, 2005.
-
Menard, T., Tanguy, S., and Berlemont, A., Coupling Level Set/VOF/Ghost Fluid Methods: Validation and Application to 3D Simulation of the Primary Break-Up of a Liquid Jet, Int. J. Multif. Flow, vol. 33, no. 5, pp. 510-524, 2007.
-
Moallemi, N., Li, R., and Mehravaran, K., Breakup of Capillary Jets with Different Disturbances, Phys. Fluids, vol. 28, no. 1, p. 012101, 2016.
-
Mukherjee, S., Safdari, A., Shardt, O., Kenjeres, S., and Van den Akker, H.E.A., Droplet-Turbulence Interactions and Quasi-Equilibrium Dynamics in Turbulent Emulsions, J. Fluid. Mech., vol. 878, 2019.
-
Mukundan, A.A., Menard, T., Berlemont, A., de Motta, J.C.B., and Eggels, R., Validation and Analysis of 3D DNS of Planar Pre-Filming Airblast Atomization Simulations, in Proc. of ILASS Americas, 30th Annual Conf. on Liquid Atomization and Spray Systems, Tempe, AZ, USA, May 12-15, 2019.
-
Mukundan, A.A., Tretola, G., Menard, T., Herrmann, M., Navarro-Martinez, S., Vogiatzaki, K., de Motta, J.C.B., and Berlemont, A., DNS and LES of Primary Atomization of Turbulent Liquid Jet Injection into a Gaseous Crossflow Environment, Proc. Combust. Inst., vol. 38, no. 2, pp. 3233-3241, 2021.
-
Peano, G., Applicazioni Geometriche Del Calcolo Infinitesimale, Turin, Italy: Fratelli Bocca Editori, 1887.
-
Perlekar, P., Biferale, L., Sbragaglia,M., Srivastava, S., and Toschi, F., Droplet Size Distribution in Homogeneous Isotropic Turbulence, Phys. Fluids, vol. 24, no. 6, p. 065101, 2012.
-
Perrard, S., Riviere, A., Mostert, W., and Deike, L., Bubble Deformation by a Turbulent Flow, J. Fluid. Mech., vol. 920, 2021.
-
Podczeck, F., Rahman, S., and Newton, J., Evaluation of a Standardised Procedure to Assess the Shape of Pellets Using Image Analysis, Int. J. Pharm., vol. 192, no. 2, pp. 123-138, 1999.
-
Pope, S.B., Turbulent Flows, Cambridge, UK: Cambridge University Press, 2000.
-
Ravelet, F., Colin, C., and Risso, F., On the Dynamics and Breakup of a Bubble Rising in a Turbulent Flow, Phys. Fluids, vol. 23, no. 10, p. 103301, 2011.
-
Rorato, R., Arroyo, M., Ando, E., and Gens, A., Sphericity Measures of Sand Grains, Eng. Geology, vol. 254, pp. 43-53, 2019.
-
Rosales, C. and Meneveau, C., Linear Forcing in Numerical Simulations of Isotropic Turbulence: Physical Space Implementations and Convergence Properties, Phys. Fluids, vol. 17, no. 9, p. 095106, 2005.
-
Schober, P.,Meier, R., Schafer, O., and Wittig, S., Visualization and Phase Doppler Particle Analysis Measurements of Oscillating Spray Propagation of an Airblast Atomizer under Typical Engine Conditions, Ann. New York Acad. Sci., vol. 972, no. 1, pp. 277-284, 2002.
-
Sussman, M., Fatemi, E., Smereka, P., and Osher, S., An Improved Level Set Method for Incompressible Two-Phase Flows, Comput. Fluids, vol. 27, nos. 5-6, pp. 663-680, 1998.
-
Tanguy, S. and Berlemont, A., Application of a Level Set Method for Simulation of Droplet Collisions, Int. J. Multif. Flow, vol. 31, no. 9, pp. 1015-1035, 2005.
-
Trontin, P., Vincent, S., Estivalezes, J.L., and Caltagirone, J.P., Direct Numerical Simulation of a Freely Decaying Turbulent Interfacial Flow, Int. J. Multif. Flow, vol. 36, nos. 11-12, pp. 891-907, 2010.
-
van Beeck, J. and Riethmuller, M., Rainbow Phenomena Applied to the Measurement of Droplet Size and Velocity and to the Detection of Nonsphericity, Appl. Optics, vol. 35, no. 13, pp. 2259-2266, 1996.
-
Vaudor, G., Menard, T., Aniszewski, W., Doring, M., and Berlemont, A., A Consistent Mass and Momentum Flux Computation Method for Two Phase Flows. Application to Atomization Process, Comput. Fluids, vol. 152, pp. 204-216, 2017.
-
Warncke, K., Gepperth, S., Sauer, B., Sadiki, A., Janicka, J., Koch, R., and Bauer, H.J., Experimental and Numerical Investigation of the Primary Breakup of an Airblasted Liquid Sheet, Int. J. Multif. Flow, vol. 91, pp. 208-224, 2017.