Skip to main content Accessibility help
×
Home

On the dynamics of vortex–droplet interactions, dispersion and breakup in a coaxial swirling flow

  • Kuppuraj Rajamanickam (a1) and Saptarshi Basu (a1)

Abstract

This paper discusses the fundamental mechanisms of vortex–droplet interactions leading to flow distortion, droplet dispersion and breakup in a complex swirling gas flow field. In particular, the way in which the location of droplet injection determines the degree of inhomogeneous dispersion and breakup modes has been elucidated in detail using high-fidelity laser diagnostics. The droplets are injected as monodispersed streams at various spatial locations such as the vortex breakdown bubble and the shear layers (inner and outer) exhibited by the swirling flow. Simultaneous time-resolved particle image velocimetry ( $3500~\text{frames}~\text{s}^{-1}$ ) and high-speed shadowgraphy measurements are employed to delineate the two-phase interaction dynamics. These measurements have been used to evaluate the fluctuations in instantaneous circulation strength $\unicode[STIX]{x1D6E4}^{\prime }$ caused by the flow field eddies and the resultant angular dispersion in the droplet trajectories $\unicode[STIX]{x1D703}^{\prime }$ . The droplet–flow interactions show two-way coupling at low momentum ratios ( $MR$ ) and strong one-way coupling at high momentum ratios. The gas phase flow field is globally altered at low airflow rates (low $MR$ ) due to impact of droplets with the vortex core. The flow perturbation is found to be minimal and mainly local at high airflow rates (high $MR$ ). Spectral coherence analysis is carried out to understand the correlation between eddy circulation strength $\unicode[STIX]{x1D6E4}^{\prime }$ and droplet dispersion $\unicode[STIX]{x1D703}^{\prime }$ . The droplet dispersion shows strong coherence with the flow in certain frequency bands. Subsequently, proper orthogonal decomposition (POD) is implemented to elucidate the governing instability mechanism and frequency signatures associated with the turbulent coherent structures. The POD results suggest dominance of the Kelvin–Helmholtz (KH) instability mode (axial and azimuthal shear). The frequency range pertaining to high coherence between dispersion and circulation shows good agreement with KH instability quantified from POD analysis. The droplets injected at the inner shear layer (ISL) and outer shear layer (OSL) show different interaction dynamics. For instance, droplet dispersion at the OSL exhibits secondary frequency (shedding mode) coupling in addition to the KH mode, whereas ISL injection couples only in a single narrow frequency band (i.e. KH mode). Further, high-speed shadow imaging ( $7500~\text{frames}~\text{s}^{-1}$ ) is employed to visualize the breakup dynamics of the droplets. The effect of coherent structures on the droplet breakup modes is shown as a function of the Weber number ( $We$ ) defined based on the circulation strength. The wide fluctuations caused in the instantaneous circulation strength lead to different breakup modes (bag, multimodal, shear thinning, catastrophic) even for fixed airflow rates. These fluctuations also lead to inhomogeneous spatial dispersion of the droplets in the swirling gas flow field. We are able to present the dispersion contours in terms of the Stokes number and a spatial homogeneity parameter. In essence, the dispersion inhomogeneity is found to be a strong function of the injection location, the phase relationship with the eddies and the momentum ratio ( $MR$ ).

Copyright

Corresponding author

Email address for correspondence: sbasu@mecheng.iisc.ernet.in

References

Hide All
Adrian, R. J. 1991 Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech. 23, 261304.
Aggarwal, S. K. 1994 Relationship between Stokes number and intrinsic frequencies in particle-laden flows. AIAA J. 32, 13221325.
Aggarwal, S. K. & Park, T. W. 1999 Dispersion of evaporating droplets in a swirling axisymmetric jet. AIAA J. 37, 15781587.
Al Taweel, A. M. & Landau, J. 1977 Turbulence modulation in two-phase jets. Intl J. Multiphase Flow 3, 341351.
Albrecht, H.-E., Damaschke, N., Borys, M. & Tropea, C. 2013 Laser Doppler and Phase Doppler Measurement Techniques. Springer.
Balachandar, S. & Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annu. Rev. Fluid Mech. 42, 111133.
Beér, J. M. & Chigier, N. A. 1972 Combustion Aerodynamics. Applied Science Publishers Ltd.
Bendat, J. S. & Piersol, A. G. 1980 Engineering Applications of Correlation and Spectral Analysis. Wiley-Interscience.
Benjamin, T. B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14, 593629.
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539575.
Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183219.
Boileau, M., Pascaud, S., Riber, E., Cuenot, B., Gicquel, L. Y. M., Poinsot, T. J. & Cazalens, M. 2008 Investigation of two-fluid methods for large eddy simulation of spray combustion in gas turbines. Flow Turbul. Combust. 80, 291321.
Cebeci, T. & Bradshaw, P. 1977 Momentum Transfer in Boundary Layers. McGraw-Hill.
Champagne, F. H. & Kromat, S. 2000 Experiments on the formation of a recirculation zone in swirling coaxial jets. Exp. Fluids 29, 494504.
Chandrasekhar, S. 2013 Hydrodynamic and Hydromagnetic Stability. Courier Corporation.
Chigier, N. A. & Chervinsky, A. 1967 Experimental investigation of swirling vortex motion in jets. Trans. ASME J. Appl. Mech. 34, 443451.
Chou, W.-H., Hsiang, L.-P. & Faeth, G. M. 1997 Temporal properties of drop breakup in the shear breakup regime. Intl J. Multiphase Flow 23, 651669.
Chung, J. N. & Troutt, T. R. 1988 Simulation of particle dispersion in an axisymmetric jet. J. Fluid Mech. 186, 199222.
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385425.
Crowe, C. T., Chung, J. N. & Troutt, T. R. 1988 Particle mixing in free shear flows. Prog. Energy Combust. Sci. 14, 171194.
Crowe, C. T., Sommerfeld, M. & Tsuji, Y. 1998 Fundamentals of Gas–Particle and Gas–Droplet Flows. CRC.
Crowe, C. T., Troutt, T. R. & Chung, J. N. 1996 Numerical models for two-phase turbulent flows. Annu. Rev. Fluid Mech. 28, 1143.
Czainski, A., Garncarek, Z. & Piasecki, R. 1994 Quantitative characterization of inhomogeneity in thin metallic films using Garncarek’s method. J. Phys. D: Appl. Phys. 27 (3), 616622.
Dai, Z. & Faeth, G. M. 2001 Temporal properties of secondary drop breakup in the multimode breakup regime. Intl J. Multiphase Flow 27, 217236.
Danon, H., Wolfshtein, M. & Hetsroni, G. 1977 Numerical calculations of two-phase turbulent round jet. Intl J. Multiphase Flow 3, 223234.
Dimotakis, P. E. 1986 Two-dimensional shear-layer entrainment. AIAA J. 24, 17911796.
Elghobashi, S. E. & Abou-Arab, T. W. 1983 A two-equation turbulence model for two-phase flows. Phys. Fluids 26, 931938.
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids Fluid Dyn. 5, 17901801.
Engelbert, C., Hardalupas, Y. & Whitelaw, J. H. 1995 Breakup phenomena in coaxial airblast atomizers. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, pp. 189229. The Royal Society.
Faeth, G. M., Hsiang, L.-P. & Wu, P.-K. 1995 Structure and breakup properties of sprays. Intl J. Multiphase Flow 21, 99127.
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 37423749.
Flock, A. K., Guildenbecher, D. R., Chen, J., Sojka, P. E. & Bauer, H.-J. 2012 Experimental statistics of droplet trajectory and air flow during aerodynamic fragmentation of liquid drops. Intl J. Multiphase Flow 47, 3749.
Gallaire, F. & Chomaz, J.-M. 2003 Instability mechanisms in swirling flows. Phys. Fluids 15, 26222639.
Garncarek, Z.1993 Constructions of the measures of distribution features for finite point sets with examples of applications in natural and technical sciences. ZN WSP Opole Stud. Monogr. NR 203, 1–114.
Gillandt, I., Fritsching, U. & Bauckhage, K. 2001 Measurement of phase interaction in dispersed gas/particle two-phase flow. Intl J. Multiphase Flow 27, 13131332.
Gu, X., Basu, S. & Kumar, R. 2012 Dispersion and vaporization of biofuels and conventional fuels in a crossflow pre-mixer. Intl J. Heat Mass Transfer 55, 336346.
Guildenbecher, D. R., López-Rivera, C. & Sojka, P. E. 2009 Secondary atomization. Exp. Fluids 46, 371402.
Hall, M. G. 1967 A new approach to vortex breakdown. In 14th Atmospheric Flight Mechanics Conference, pp. 319340. AIAA Paper 1987-2495.
Han, J. & Tryggvason, G. 1999 Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Phys. Fluids 11, 36503667.
Hanson, A. R., Domich, E. G. & Adams, H. S. 1963 Shock tube investigation of the breakup of drops by air blasts. Phys. Fluids 6, 10701080.
Hayakawa, S., Okajima, S. & Tokuoka, N. 2008 The study of spray structure by numerical simulation – the effect of interaction between droplets on spatial inhomogeneity. In 22nd European Conference on Liquid Atomization and Spray Systems 8–10 September 2008, Como Lake, Italy, ILASS-Europe.
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289295.
Hishida, K., Ando, A. & Maeda, M. 1992 Experiments on particle dispersion in a turbulent mixing layer. Intl J. Multiphase Flow 18, 181194.
Hopfinger, E. J. & Lasheras, J. C. 1996 Explosive breakup of a liquid jet by a swirling coaxial gas jet. Phys. Fluids 8, 16961698.
Hsiang, L.-P. & Faeth, G. M. 1992 Near-limit drop deformation and secondary breakup. Intl J. Multiphase Flow 18, 635652.
Keane, R. D. & Adrian, R. J. 1990 Optimization of particle image velocimeters. I. Double pulsed systems. Meas. Sci. Technol. 1, 1202.
Khalitov, D. A. & Longmire, E. K. 2002 Simultaneous two-phase PIV by two-parameter phase discrimination. Exp. Fluids 32, 252268.
Khalitov, D. A. & Longmire, E. K. 2003 Effect of particle size on velocity correlations in turbulent channel flow. In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference, pp. 445453. American Society of Mechanical Engineers.
Kosiwczuk, W., Cessou, A., Trinite, M. & Lecordier, B. 2005 Simultaneous velocity field measurements in two-phase flows for turbulent mixing of sprays by means of two-phase PIV. Exp. Fluids 39, 895908.
Kulick, J. D., Fessler, J. R. & Eaton, J. K. 1994 Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109134.
Lasheras, J. C. & Hopfinger, E. J. 2000 Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32, 275308.
Lasheras, J. C., Villermaux, E. & Hopfinger, E. J. 1998 Break-up and atomization of a round water jet by a high-speed annular air jet. J. Fluid Mech. 357, 351379.
Lazaro, B. J. & Lasheras, J. C. 1992 Particle dispersion in the developing free shear layer. Part 1. Unforced flow. J. Fluid Mech. 235, 143178.
Lefebvre, A. H. 2010 Gas Turbine Combustion. CRC.
Liang, H. & Maxworthy, T. 2005 An experimental investigation of swirling jets. J. Fluid Mech. 525, 115159.
Lilley, D. G. 1977 Swirl flows in combustion: a review. AIAA J. 15, 10631078.
Liu, A. B., Mather, D. & Reitz, R. D.1993 Modeling the effects of drop drag and breakup on fuel sprays. DTIC Document.
Longmire, E. K. & Eaton, J. K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217257.
Loth, E., Tryggvason, G., Tsuji, Y., Elghobashi, S. E., Crowe, C. T., Berlemont, A., Reeks, M., Simonin, O., Frank, T., Onishi, Y. et al. 2006 Multiphase Flow Handbook. CRC.
Lozano, A., Barreras, F., Siegler, C. & Löw, D. 2005 The effects of sheet thickness on the oscillation of an air-blasted liquid sheet. Exp. Fluids 39, 127139.
Lucca-Negro, O. & O’doherty, T. 2001 Vortex breakdown: a review. Prog. Energy Combust. Sci. 27, 431481.
Marmottant, P. & Villermaux, E. 2004 On spray formation. J. Fluid Mech. 498, 73111.
Martinelli, F., Olivani, A. & Coghe, A. 2007 Experimental analysis of the precessing vortex core in a free swirling jet. Exp. Fluids 42, 827839.
Mashayek, F. 1998 Droplet–turbulence interactions in low-Mach-number homogeneous shear two-phase flows. J. Fluid Mech. 367, 163203.
Moin, P. & Apte, S. V. 2006 Large-eddy simulation of realistic gas turbine combustors. AIAA J. 44, 698708.
Nicholls, J. A. & Ranger, A. A. 1969 Aerodynamic shattering of liquid drops. AIAA J. 7, 285290.
Oweis, G. F., Van der Hout, I. E., Iyer, C., Tryggvason, G. & Ceccio, S. L. 2005 Capture and inception of bubbles near line vortices. Phys. Fluids 17, 022105.
Park, T. W., Katta, V. R. & Aggarwal, S. K. 1998 On the dynamics of a two-phase, nonevaporating swirling jet. Intl J. Multiphase Flow 24, 295317.
Raffel, M., Willert, C. E., Wereley, S. & Kompenhans, J. 2013 Particle Image Velocimetry: A Practical Guide. Springer.
Rajamanickam, K. & Basu, S. 2017 Insights into the dynamics of spray–swirl interactions. J. Fluid Mech. 810, 82126.
Ribeiro, M. M. & Whitelaw, J. H. 1980 Coaxial jets with and without swirl. J. Fluid Mech. 96, 769795.
Saha, A., Lee, J. D., Basu, S. & Kumar, R. 2012 Breakup and coalescence characteristics of a hollow cone swirling spray. Phys. Fluids 24, 124103.
Sahu, S., Hardalupas, Y. & Taylor, A. 2014 Droplet–turbulence interaction in a confined polydispersed spray: effect of droplet size and flow length scales on spatial droplet–gas velocity correlations. J. Fluid Mech. 741, 98138.
Sakakibara, J., Wicker, R. B. & Eaton, J. K. 1996 Measurements of the particle–fluid velocity correlation and the extra dissipation in a round jet. Intl J. Multiphase Flow 22, 863881.
Sanadi, D., Rajamanickam, K. & Basu, S. 2017 Analysis of hollow cone spray injected in an unconfined, isothermal, co-annular swirling jet environment. Atomization and Sprays 27, 729.
Sankaran, V. & Menon, S. 2002 LES of spray combustion in swirling flows. J. Turbul. 3, 123.
Santhosh, R., Miglani, A. & Basu, S. 2014 Transition in vortex breakdown modes in a coaxial isothermal unconfined swirling jet. Phys. Fluids 26, 043601.
Sarpkaya, T. 1971 On stationary and travelling vortex breakdowns. J. Fluid Mech. 45, 545559.
Schröder, A., Geisler, R., Staack, K., Elsinga, G. E., Scarano, F., Wieneke, B., Henning, A., Poelma, C. & Westerweel, J. 2011 Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV. Exp. Fluids 50, 10711091.
Sciacchitano, A., Wieneke, B. & Scarano, F. 2013 PIV uncertainty quantification by image matching. Meas. Sci. Technol. 24, 045302.
Shirolkar, J. S., Coimbra, C. F. M. & McQuay, M. Q. 1996 Fundamental aspects of modeling turbulent particle dispersion in dilute flows. Prog. Energy Combust. Sci. 22, 363399.
Simpkins, P. G. & Bales, E. L. 1972 Water-drop response to sudden accelerations. J. Fluid Mech. 55, 629639.
Sirignano, W. A. 1999 Fluid Dynamics and Transport of Droplets and Sprays. Cambridge University Press.
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Part I: coherent structures. Q. Appl. Maths 45, 561571.
Squire, H. B. 1953 Investigation of the instability of a moving liquid film. Brit. J. Appl. Phys. 4, 167.
Sung, J. & Yoo, J. Y. 2001 Three-dimensional phase averaging of time-resolved PIV measurement data. Meas. Sci. Technol. 12, 655.
Syred, N. 2006 A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems. Prog. Energy Combust. Sci. 32, 93161.
Taylor, G. I. 1963 The shape and acceleration of a drop in a high speed air stream. In Scientific Papers of G. I. Taylor (ed. Batchelor, G. K.), vol. 3, pp. 457464. Cambridge University Press.
Tropea, C., Yarin, A. L. & Foss, J. F. 2007 Springer Handbook of Experimental Fluid Mechanics. Springer.
Wang, H. Y., McDonell, V. G. & Samuelsen, S. 1993 Influence of hardware design on the flow field structures and the patterns of droplet dispersion: Part I – mean quantities. In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition, p. V03AT15A050. American Society of Mechanical Engineers.
Wang, S., Yang, V., Hsiao, G., Hsieh, S.-Y. & Mongia, H. C. 2007 Large-eddy simulations of gas-turbine swirl injector flow dynamics. J. Fluid Mech. 583, 110.
Wieneke, B. 2015 PIV uncertainty quantification from correlation statistics. Meas. Sci. Technol. 26, 074002.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Type Description Title
VIDEO
Movies

Rajamanickam supplementary movie 1
Flow field at Re=5089 and Re=33888

 Video (20.8 MB)
20.8 MB
VIDEO
Movies

Rajamanickam supplementary movie 2
Droplet dispersion at MR=184 for ISL and OSL injections

 Video (13.3 MB)
13.3 MB
VIDEO
Movies

Rajamanickam supplementary movie 3
Droplet dispersion at MR=450 for ISL and OSL injections

 Video (13.1 MB)
13.1 MB
VIDEO
Movies

Rajamanickam supplementary movie 4
Droplet dispersion at MR=8164 for ISL and OSL injections

 Video (16.4 MB)
16.4 MB
VIDEO
Movies

Rajamanickam supplementary movie 5
Droplet dispersion and corresponding flowfield streamlines at MR=8164 for ISL and OSL injections

 Video (19.9 MB)
19.9 MB
VIDEO
Movies

Rajamanickam supplementary movie 6
Droplet breakup(Regime I) for MR=184, We=57

 Video (6.0 MB)
6.0 MB
VIDEO
Movies

Rajamanickam supplementary movie 7
Droplet breakup(Regime II) for MR=450, We=100

 Video (3.7 MB)
3.7 MB
VIDEO
Movies

Rajamanickam supplementary movie 8
Droplet breakup(Regime II) for MR=8164, We=500

 Video (6.1 MB)
6.1 MB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed