Break-up dynamics and drop size distributions created from spiralling liquid jets (original) (raw)

Abstract

The dynamics of the break-up of spiralling jets of Newtonian liquids were visualised. The jets were created from orifices at the bottom of a 0.085-m-diameter can rotating about its vertical axis and imaged using a high-speed camera. The effects of liquid dynamic viscosity (0.001–0.09 Pa s), rotation rate (5–31 rad s−1) and orifice size (0.001 and 0.003 m) upon the jet break-up and drop size distributions produced in the Rayleigh regime were investigated. The ranges of dimensionless parameters were 1<Re<103, 0.2<Rb<4, 0.5<We<25 and 5×10−3<Oh<4×10−1. Four generic break-up modes identified were a strong function of dynamic viscosity and jet exit velocity. A flow pattern map of Ohnesorge number against Weber number enabled prediction of these modes. Increasing the can rotation rate increases jet exit velocity due to centrifugal forces and the trajectory of the jet becomes more curved. The break-up dynamics of the jets were non-linear, although some agreement between measured break-up lengths with the linear stability analysis developed previously was noted at low Reynolds numbers. A non-linear theoretical analysis is required to elucidate the important features.

Figures (24)

Fig. 1. Spiralling jet experimental set-up.

Fig. 1. Spiralling jet experimental set-up.

Summary of test conditions Table 1

Summary of test conditions Table 1

D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520 Fig. 2. Features of Mode 1 break-up with increasing rotational speed with a 0.001-m orifice: (a) Rb = co (0 rpm), U = 0.764 ms"; (b) Rb = 3.53 (50 rpm), U = 0.785 ms~!; (c) Rb = 1.81 (100 rpm), U = 0.806 ms™!; (d) Rb = 1.00 (200 rpm), U = 0.891 ms~!. Oh = 0.005 (y = 0.0001 Pas; » = 998.1 kgm~%); (e) sketch of Mode 1 break-up.

D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520 Fig. 2. Features of Mode 1 break-up with increasing rotational speed with a 0.001-m orifice: (a) Rb = co (0 rpm), U = 0.764 ms"; (b) Rb = 3.53 (50 rpm), U = 0.785 ms~!; (c) Rb = 1.81 (100 rpm), U = 0.806 ms™!; (d) Rb = 1.00 (200 rpm), U = 0.891 ms~!. Oh = 0.005 (y = 0.0001 Pas; » = 998.1 kgm~%); (e) sketch of Mode 1 break-up.

tig. 3. Sequence (1-3) of Mode 2 break-up with a 0.001-m orifice at Rb = 1.06 (200 rpm): U =0.944 ms7!; Dh = 0.0095 (y = 0.00181 Pas; p = 1054.2 kgm~3); (4) sketch of Mode 2 break-up. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

tig. 3. Sequence (1-3) of Mode 2 break-up with a 0.001-m orifice at Rb = 1.06 (200 rpm): U =0.944 ms7!; Dh = 0.0095 (y = 0.00181 Pas; p = 1054.2 kgm~3); (4) sketch of Mode 2 break-up. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 4. Sequence (1-3) of Mode 3 break-up with a 0.003-m orifice which resembles a Rayleigh type mode: Rb = 0.80 (200 rpm); U = 0.642 ms~!; Oh = 0.241 (7 = 0.0817 Pas; p = 1215.5 kgm~?); (4) sketch of Mode 3 break-up. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 4. Sequence (1-3) of Mode 3 break-up with a 0.003-m orifice which resembles a Rayleigh type mode: Rb = 0.80 (200 rpm); U = 0.642 ms~!; Oh = 0.241 (7 = 0.0817 Pas; p = 1215.5 kgm~?); (4) sketch of Mode 3 break-up. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 5. Sequence (1-4) showing dynamics of Mode 4 break-up and recoiling phenomenon with a 0.001-m orifice: Rb = 0.32 (250 rpm); U = 0.352 ms7!; Oh = 0.233 (y = 0.0451 Pas; p = 1202.6 kg m~°); (5) sketch of Mode 4 break-up.

Fig. 5. Sequence (1-4) showing dynamics of Mode 4 break-up and recoiling phenomenon with a 0.001-m orifice: Rb = 0.32 (250 rpm); U = 0.352 ms7!; Oh = 0.233 (y = 0.0451 Pas; p = 1202.6 kg m~°); (5) sketch of Mode 4 break-up.

D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520 Fig. 6. Break-up regime maps: (a) OA versus We, (b) Oh versus Rb and (c) Oh versus Fr/Rb.

D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520 Fig. 6. Break-up regime maps: (a) OA versus We, (b) Oh versus Rb and (c) Oh versus Fr/Rb.

Fig. 7. Absence of coherent jet when We <1: Rb = 0.43 (200 rpm); U = 0.384 ms~!; Oh = 0.005 (y = 0.001 Pas; p = 998.1 kgm™3); ¢ = 0.0724 Nm}. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 7. Absence of coherent jet when We <1: Rb = 0.43 (200 rpm); U = 0.384 ms~!; Oh = 0.005 (y = 0.001 Pas; p = 998.1 kgm™3); ¢ = 0.0724 Nm}. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Table of normalised break-up lengths for experiments using 0.001-m orifice and predictions from the linear instability model

Table of normalised break-up lengths for experiments using 0.001-m orifice and predictions from the linear instability model

Fig. 8. Influence of rotation rate upon exit velocity of jet for different viscosity fluids (0.0029 < Oh < 0.24). D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 8. Influence of rotation rate upon exit velocity of jet for different viscosity fluids (0.0029 < Oh < 0.24). D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 10. Exit angle in relation to Rossby number for water—glycerol solutions. Sees eS! Se See ees Les Sees eee ee eee Se Se Sees | eee Fig. 10 shows that upon decreasing the Rossby number (i.e., increasing the rotation rate) the jet exit angle, « (i.e., the angle between the centre line of the jet and the tangent at the orifice) is no longer orthogonal. This was taken as an assumption in the theoretical work by Wallwork et al. (2002) and Decent et al. (2002), together with the assumption of solid body rotation of fluid in the rotating can. A series of controlled experiments carried out using particle image velocimetry (PIV) showed that the assumption of solid-body rotation of fluid in the can was valid. A likely expla- nation for the changing jet exit angle is deviation caused by the creation of a thin viscous boundary layer at the can surface created from the action of the air close to the spinning can. This boundary layer only influences the jet very close to the can surface since the Reynolds number of the air is of the order of several thousand and the diffusion of vorticity from this boundary layer is very slow. The observed jet trajectories and break-up modes are not dependent upon a long timescale, as might be expected if the airflow was important because this diffusion of vorticity

Fig. 10. Exit angle in relation to Rossby number for water—glycerol solutions. Sees eS! Se See ees Les Sees eee ee eee Se Se Sees | eee Fig. 10 shows that upon decreasing the Rossby number (i.e., increasing the rotation rate) the jet exit angle, « (i.e., the angle between the centre line of the jet and the tangent at the orifice) is no longer orthogonal. This was taken as an assumption in the theoretical work by Wallwork et al. (2002) and Decent et al. (2002), together with the assumption of solid body rotation of fluid in the rotating can. A series of controlled experiments carried out using particle image velocimetry (PIV) showed that the assumption of solid-body rotation of fluid in the can was valid. A likely expla- nation for the changing jet exit angle is deviation caused by the creation of a thin viscous boundary layer at the can surface created from the action of the air close to the spinning can. This boundary layer only influences the jet very close to the can surface since the Reynolds number of the air is of the order of several thousand and the diffusion of vorticity from this boundary layer is very slow. The observed jet trajectories and break-up modes are not dependent upon a long timescale, as might be expected if the airflow was important because this diffusion of vorticity

Fig. 9. Influence of rotation rate and exit velocity upon break-up length of the spiralling jet in Modes 1 and 2 for different viscosity fluids (0.0029 < Oh < 0.023). D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 9. Influence of rotation rate and exit velocity upon break-up length of the spiralling jet in Modes 1 and 2 for different viscosity fluids (0.0029 < Oh < 0.023). D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

where the break-up occurs at s = s* and s is the non-dimensionalised arclength along the jet. Here R is the non-dimensionalised radius of the jet, ¢ is the ratio of the orifice to the radius of the can and uw is the non-dimensionalised jet velocity at its centreline. The equations for uo(s) and Ro(s) are given by the following differential equations and initial conditions:

where the break-up occurs at s = s* and s is the non-dimensionalised arclength along the jet. Here R is the non-dimensionalised radius of the jet, ¢ is the ratio of the orifice to the radius of the can and uw is the non-dimensionalised jet velocity at its centreline. The equations for uo(s) and Ro(s) are given by the following differential equations and initial conditions:

Fig. 11. Comparison of experimental and theoretical break-up lengths for various Reynolds numbers. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-52(

Fig. 11. Comparison of experimental and theoretical break-up lengths for various Reynolds numbers. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-52(

Effect of sample size on mean drop diameter Fig. 12. Effect of the sample size on volume density function. For size classes based on a geometric series ratio of 1.142:0.001 m orifice: Rb = 0.98 (200 rpm); Oh = 0.0036 (7 = 0.001 Pas, p = 998.1 kgm~3). Table 3

Effect of sample size on mean drop diameter Fig. 12. Effect of the sample size on volume density function. For size classes based on a geometric series ratio of 1.142:0.001 m orifice: Rb = 0.98 (200 rpm); Oh = 0.0036 (7 = 0.001 Pas, p = 998.1 kgm~3). Table 3

Fig. 13. Drop size distribution for three rotational rates: Rb = 3.53, 1.81, 0.98 (50, 100, 200 rpm) in break-up Mode 1 (400 < Re < 500; We < 10; Oh = 0.005 (y = 0.001 Pas, p = 998.1 kgm~%)). D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 13. Drop size distribution for three rotational rates: Rb = 3.53, 1.81, 0.98 (50, 100, 200 rpm) in break-up Mode 1 (400 < Re < 500; We < 10; Oh = 0.005 (y = 0.001 Pas, p = 998.1 kgm~%)). D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

ig. 14. Drop size distributions for three rotational rates: Rb = 3.94, 2.01, 1.07 (50, 100, 200 rpm) in break-up Mode 2 ve > 1,000; 15 < We < 20; Oh = 0.0029 (y = 0.001 Pas, p = 998.1 kgm™~)).

ig. 14. Drop size distributions for three rotational rates: Rb = 3.94, 2.01, 1.07 (50, 100, 200 rpm) in break-up Mode 2 ve > 1,000; 15 < We < 20; Oh = 0.0029 (y = 0.001 Pas, p = 998.1 kgm™~)).

Fig. 16. Drop size distributions for two rotational rates: (a) Rb = 0.67, 0.62 (250, 300 rpm) in break-up Mode 3 with a 0.003-m orifice (20 < Re < 25; 15 < We < 20; Oh = 0.178 (y = 0.061 Pas, p = 1215.5 kgm~*)); (b) Rb = 0.26, 0.37 (255, 300 rpm) in break-up Mode 4 with a 0.001-m orifice (Re < 5; We < 3; Oh = 0.352 (y = 0.071 Pas, p = 1215.5 kgm~)). Fig. 15. Drop size distributions for three rotational rates: Rb = 4.31, 2.20, 1.17 (20, 100, 200 rpm) in break-up Mode 3 (120 < Re < 150; 20 < We < 30; Oh = 0.038 (n = 0.0129 Pas, p = 1164.6 kgm™°)).

Fig. 16. Drop size distributions for two rotational rates: (a) Rb = 0.67, 0.62 (250, 300 rpm) in break-up Mode 3 with a 0.003-m orifice (20 < Re < 25; 15 < We < 20; Oh = 0.178 (y = 0.061 Pas, p = 1215.5 kgm~*)); (b) Rb = 0.26, 0.37 (255, 300 rpm) in break-up Mode 4 with a 0.001-m orifice (Re < 5; We < 3; Oh = 0.352 (y = 0.071 Pas, p = 1215.5 kgm~)). Fig. 15. Drop size distributions for three rotational rates: Rb = 4.31, 2.20, 1.17 (20, 100, 200 rpm) in break-up Mode 3 (120 < Re < 150; 20 < We < 30; Oh = 0.038 (n = 0.0129 Pas, p = 1164.6 kgm™°)).

D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Drop sizes for each mode of break-up D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Drop sizes for each mode of break-up D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 17. Effect of Ohnesorge number on primary and corresponding satellite drop sizes. An increase in the rotation rate always results in an increase of jet exit velocity and a more curved jet trajectory, which also causes a thinning of the jet as seen by Wong et al. (2003). Jets that are rotating at a high rotation rate produce smaller droplets. This rotation increased the growth rate to such an extent that it significantly reduced the length of break-up, which means that the

Fig. 17. Effect of Ohnesorge number on primary and corresponding satellite drop sizes. An increase in the rotation rate always results in an increase of jet exit velocity and a more curved jet trajectory, which also causes a thinning of the jet as seen by Wong et al. (2003). Jets that are rotating at a high rotation rate produce smaller droplets. This rotation increased the growth rate to such an extent that it significantly reduced the length of break-up, which means that the

[Fig. 19. Effect of average jet exit velocity on primary and corresponding satellite drop sizes. aN ig Fig. 19 shows the effect of jet exit velocity on both primary and satellite drop sizes. There is n nonotonic relationship between drop size and exit velocity from the results obtained in this work [he primary drop sizes generally increase as the exit velocity increases between 0.3 and 0.9 ms~ tTowever, the trend then reverses for exit velocities between 0.9 and 1.05 ms~!. The satellit lroplets appear to reduce in size slightly. Based on the data available at present, a qualitativ xplanation is given here. For low exit velocities (small Reynolds numbers), the growth rate | letermined by a balance of surface tension and viscous forces alone, while inertial forces ar nsignificant. As the exit velocity increases, the inertial forces become increasingly important an ict to promote the growth rate of the disturbance. As the disturbance is convected by the mea low, a further increase of jet exit velocity can result in the convection becoming fast enough t weep disturbances away before they can grow, hence produce smaller droplets (Eggers, 1997). ](https://figures.academia-assets.com/50612154/figure_020.jpg)

Fig. 19. Effect of average jet exit velocity on primary and corresponding satellite drop sizes. aN ig Fig. 19 shows the effect of jet exit velocity on both primary and satellite drop sizes. There is n nonotonic relationship between drop size and exit velocity from the results obtained in this work [he primary drop sizes generally increase as the exit velocity increases between 0.3 and 0.9 ms~ tTowever, the trend then reverses for exit velocities between 0.9 and 1.05 ms~!. The satellit lroplets appear to reduce in size slightly. Based on the data available at present, a qualitativ xplanation is given here. For low exit velocities (small Reynolds numbers), the growth rate | letermined by a balance of surface tension and viscous forces alone, while inertial forces ar nsignificant. As the exit velocity increases, the inertial forces become increasingly important an ict to promote the growth rate of the disturbance. As the disturbance is convected by the mea low, a further increase of jet exit velocity can result in the convection becoming fast enough t weep disturbances away before they can grow, hence produce smaller droplets (Eggers, 1997).

Fig. 18. Effect of Rossby number on primary and corresponding satellite drop sizes. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

Fig. 18. Effect of Rossby number on primary and corresponding satellite drop sizes. D.C.Y. Wong et al. | International Journal of Multiphase Flow 30 (2004) 499-520

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References (35)

  1. Baird, M.H.I., Davidson, J.F., 1962. Annular jets--I. Fluid dynamics. Chem. Eng. Sci. 17, 467-472.
  2. Blaisot, J.B., Adeline, S., 2003. Instabilities on a free falling jet under an internal flow breakup mode regime. Int. J. Multiphase Flow 29, 629-653.
  3. Bousfield, D.W., Denn, M.M., 1987. Jet break-up enhanced by an initial pulse. Chem. Eng. Comm. 53, 61-68.
  4. Bousfield, D.W., Keunigs, G., Marrucci, G., Denn, M.M., 1986. Nonlinear-analysis of the surface-tension driven breakup of viscoelastic filaments. J. Non-Newton. Fluid Mech. 21, 79-97.
  5. Camelot, D.M.A., Hartman, R.P.A., Marijnissen, J.C.M., Scarlett, B., Brunner, D., 1999. Experimental study of the jet break up for electrohydrodynamics atomisation of liquids in the cone-jet mode. J. Aerosol Sci. 30, 976-977.
  6. Chaudhary, K.C., Redekopp, L., 1980. The nonlinear capillary instability of a liquid jet, Part I & II. J. Fluid Mech. 96, 263-286.
  7. Chigier, N., Reitz, R.D., 1995. Regimes of jet breakup and breakup mechanisms--physical aspects. Prog. Astronaut. Aeronaut. 1, 109-135.
  8. Decent, S.P., King, A.C., Wallwork, I.M., 2002. Free jets spun from a prilling tower. J. Eng. Math. 42, 265-282.
  9. Donnelly, R.J., Glaberson, W., 1965. Experiments on the capillary instability of a liquid jet. Proc. R. Soc. Lond. 290, 547-556.
  10. Eggers, J., 1997. Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865-929.
  11. Finnicum, D.S., Weinstein, S.J., Ruschak, K.J., 1993. The effect of applied pressure on the shape of a two-dimensional liquid curtain falling under the influence of gravity. J. Fluid Mech. 255, 647-665.
  12. Goedde, E.F., Yuen, M.C., 1970. Experiments on liquid jet instability. J. Fluid Mech. 40, 495-511.
  13. Hilbing, J.H., Heister, S.D., 1996. Droplet size control in liquid jet break-up. Phys. Fluids 8, 1574-1581.
  14. Keller, J.B., Rubinow, S.I., Tu, Y.O., 1973. Spatial instability of a jet. Phys. Fluids 16, 2052-2055.
  15. Lin, S.P., Reitz, R.D., 1998. Drop and spray formation from a liquid jet. Ann. Rev. Fluid Mech. 30, 85-105.
  16. Lindblad, N.R., Schneider, J.M., 1965. Production of uniform-sized droplets. J. Sci. Instrum. 42, 635-642.
  17. McCreery, G.E., Stoots, C.M., 1996. Drop formation mechanism and size distributions for spray plate orifices. Int. J. Multiphase Flow 22, 431-452.
  18. Meessen, J.H., Petersen, H., 1996. Urea. Ullmann's Encyc. Ind. Chem. A 27, 333-363.
  19. Middleman, S., 1995. Modelling Axisymmetric Flows: Dynamics of Films, Jets and Drops. Academic Press, New York. pp. 94-123.
  20. Moses, M.P., 1995. Visualization of liquid jet break-up and droplet formation. M.Sc. Thesis, Purdue University.
  21. Ohnesorge, W., 1936. Formation of drops by nozzles and the breakup of liquid jets. Z. Angew. Math. Mech. 16, 355- 358.
  22. Parau, E., Decent, S.P., King, A.C., Simmons, M.J.H., Wong, D.C.Y., 2003. Nonlinear travelling waves on a spiralling liquid jet. J. Eng. Math., submitted.
  23. Ramos, J.I., 1996. Upward and downward annular liquid jets: conservation properties, singularities, and numerical errors. Appl. Math. Model. 20, 44-458.
  24. Rayleigh, L., 1878. On the stability of jets. Proc. Lond. Math. Soc. 10, 4-13.
  25. Rutland, D.F., Jameson, G.J., 1971. A non-linear effect in the capillary instability of liquid jets. J. Fluid Mech. 46, 267- 275.
  26. Savart, F., 1833. Memoire sur la Constitution des Veines Liquides lancees par des orifices circulaires en mince paroi. Ann. Chim. Phys. 53, 337-386.
  27. Shield, T.W., Bogy, D.B., Denn, M.M., 1987. Drop formation by DOD ink-jet orifices: a comparison of experimental and numerical simulation. IBM J. Res. Dev. 31, 96-110.
  28. Taub, H.H., 1976. Investigation of nonlinear waves on liquid jets. Phys. Fluids 46, 1124-1129.
  29. Teng, H., Kinoshita, C.M., Masutani, S.M., 1995. Prediction of droplet size from the breakup of cylindrical liquid jets. Int. J. Multiphase Flow 21, 129-136.
  30. Torpey, P.A., 1989. A nonlinear theory for describing the propagation of disturbances on a capillary jet. Phys. Fluids 1, 66-71.
  31. Wallwork, I.M., 2002. The trajectory and stability of a spiralling liquid jet. Ph.D. Thesis, The University of Birmingham, UK.
  32. Wallwork, I.M., Decent, S.P., King, A.C., Schulkes, R.M.S.M., 2002. The trajectory and stability of a spiralling liquid jet: Part 1. Inviscid theory. J. Fluid Mech. 459, 43-65.
  33. Weber, C., 1931. Zum zerfall eines flussigkeitsstrahles. Z. Angew. Math. Mech. 11, 136-141.
  34. Wong, D.C.Y, Simmons, M.J.H., King, A.C., Decent, S.P., Parau, E., 2003. Dynamic break-up and drop formation from a liquid jet spun from a rotating orifice. Part 1: Experimental. In: Proc. FEDSM'03, IBSN 0-7918-3673-8, FEDSM2003-45148.
  35. Wu, P.K., Miranda, R.F., Faeth, G.M., 1995. Effects of initial flow conditions on primary break-up of non turbulent and turbulent round liquid jets. Atom. Sprays 5, 175-196.