Dynamics of Particle-Laden Wake Flow in a Karman Vortex Street Considering the Droplet-Vortex Interactions

Document Type : Regular Article


1 College of Electronic Information and Automation, Civil Aviation University of China, Tianjin, 300300, China

2 School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China



To investigate the dynamics of droplet-vortex interactions in particle-laden Karman vortex street flows, the simulations were carried out by using Euler-Lagrange approach, which was validated by the available experiments and numerical results. Then, the particle dispersion and the dimensionless frequency (Strouhal number) of the wake flow were analyzed to evaluate the particle-vortex interactions. The particle dispersion was statistically analyzed from both time and space dimensions and the different instantaneous dispersion patterns were explained by the relative slip velocity. Two independent scaling parameters, Stokes number StL and particle-fluid mass loading ratio Φ were revealed, and the particle mean square displacement and the Strouhal number were modelled by using these two scaling parameters, respectively. Finally, the characteristic lengths of the particle-laden wake flow were researched, and the Strouhal number physical model was developed based on the oscillating fishtail model. The results indicated that, firstly, StL and Φ, which constitute a dominant scaling group, can characterize the dynamics of droplet-vortex interactions in wake flow. Particles gradually separate from the vortex with the increase of StL due to the centrifugal effect, and the vortex intensity and regularity get worse with the increase of Φ, which further disperses the droplets for their momentum exchange with irregular vortex structures. Secondly, the length of the formation region and the width of the free shear layer diffuse are the two simultaneous characteristic lengths of the Strouhal number in oscillating wake. The proposed Strouhal number model gives a physical basis for the frequency determination, and the predicted errors are within ±1.5% error bands with mean absolute percentage error of 0.67%.


Aggarwal, S. K., T. W. Park and V. R. Katta (1996). Unsteady spray behavior in a heated jet shear-layer: droplet-vortex interactions. Combustion Science & Technology 113(1), 429−449.##
Armenio, V. and V. Fiorotto (2001). The importance of the forces acting on particles in turbulent flows. Physics of Fluids 13(8), 2437–2440.##
Birkhoff, G. (1953). Formation vortex street. Journal of Applied Physics 24(1), 98–103.##
Bloor, M. S. (1964). The transition to turbulence in the wake of a circular cylinder. Journal of Fluid Mechanics 19(2), 290–304.##
Bordás, R., V. John, E. Schmeyer and D. Thévenin (2013). Numerical methods for the simulation of a coalescence-driven droplet size distribution. Theoretical & Computational Fluid Dynamics 27(3−4), 253−271.##
Burger, M., R. Schmehl, R. Koch, S. Witting and H. J. Bauer (2006). DNS of droplet–vortex interaction with a Karman vortex street. International Journal of Heat & Fluid Flow 27(2), 181−191.##
Crowe, C. T., M. P. Sharma and D. E. Stock (1975). The particle-source-in cell (PSI-CELL) model for gas-droplet flow. Journal of Fluids Engineering 99(2), 325–332.##
Crowe, C. T., R. A. Gore and T. R. Troutt (1985). Particle dispersion by coherent structures in free shear flows. Particulate Science and Technology 3(3-4), 149–158.##
Crowe, C. T. (1991). The state-of-the-art in the development of numerical models for dispersed phase flows. In Proceedings of International Conference on Multiphase Flows, Tsukuba, Japan, 3, 49–60.##
Dougherty, N., J. Holt, B. Liu and J. O' Farrell (2006). Time-accurate Navier-Stokes computations of unsteady flows - The Karman vortex street. In Conference: 27th Aerospace Sciences Meeting.##
Eaton, J. K. and J. R. Fessler (1994). Preferential concentration of particles by turbulence. International Journal of Multiphase Flow 20(1), 169–209.##
Fan, J., K. Luo, M. Y. Ha and K. Cen (2004). Direct numerical simulation of a near-field particle-laden plane turbulent jet. Physical Review E 70(2), 026303.##
Fleckhaus, D., K. Hishida and M. Maeda (1987). Effect of laden solid particles on the turbulent flow structure of a round free jet. Experiments in Fluids 5(5), 323–333.##
Funakawa, M. (1969). The Vibration of a Cylinder Caused by Wake Force in a Flow. Bulletin of JSME 12(53), 1003–1010.##
Gerrard, J. H. (1966). The mechanics of the formation region of vortices behind bluff bodies. Journal of Fluid Mechanics 25(2), 401.##
Goldburg, A, W. K. Washburn and B. H. Florsheim (1965). Strouhal numbers for the hypersonic wakes of spheres and cones. AIAA Journal 3(7), 1332–1333.##
Henderson, R. D. (1995). Details of the drag curve near the onset of vortex shedding. Physics of Fluids 7(9), 2102–2104.##
Lazaro, B.J. and J.C. Lasheras (2006). Particle dispersion in the developing free shear-layer. I - Unforced flow. II - Forced flow. Journal of Fluid Mechanics 235, 179–221.##
Li, J., C. Wang, H. Ding, Z. Zhang and H. Sun (2018). EMD and spectrum-centrobaric-correction-based analysis of vortex street characteristics in annular mist flow of wet gas. IEEE Transactions on Instrumentation and Measurement 37(5), 1150–1160.##
Monkewitz, P. A. and L. N. Nguyen (1987). Absolute instability in the near-wake of two-dimensional bluff bodies. Journal of Fluids & Structures 1(2), 165–184.##
Norberg, C. (1994). Experimental investigation of the flow around a circular cylinder: Influence of aspect ratio. Journal of Fluid Mechanics 258, 287–316.##
Park, T. W., S. K. Aggarwal and V. R. Katta (1996). A numerical study of droplet-vortex interactions in an evaporating spray. International Journal of Heat & Mass Transfer 39(11), 2205−2219.##
Park, J., K. Kwon and H. Choi (1998). Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME International Journal 12(6), 1200–1205.##
Posdziech, O. and R. Grundmann (2007). A systematic approach to the numerical calculation of fundamental quantities of the two-dimensional flow over a circular cylinder. Journal of Fluids & Structures 23(3), 479–499.##
Qiao, J., R. Deng and C. H. Wang (2015). Particle motion in a Taylor vortex. International Journal of Multiphase Flow 77, 120–130.##
Qu, L., C. Norberg, L. Davidson, S. H. Peng and F. Wang (2013). Quantitative numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200. Journal of Fluids & Structures 39(5), 347–370.##
Roshko, A. (1954). On the wake and drag of bluff bodies. Journal of the Aeronautical Sciences 22, 124–132.##
Schmeyer, E., R. Bordás, D. Thévenin and V. John  (2014). Numerical simulations and measurements of a droplet size distribution in a turbulent vortex street. Meteorologische Zeitschrift 23(4), 387−396.##
Takahiko, B., H. Yosuke and T. Katsuroku (2009). Spontaneous motion of a droplet evolved by resonant oscillation of a vortex pair. Physical Review E 79(1), 031602.##
Tang, L., C. T. Crowe, J. N.  Chung and T. R. Troutt (1969). Effect of momentum coupling on the development of shear-layers in gas-particle mixtures. In Proceedings of International Conference on the Mecnics of Two-phase Flows, Taipei, Taiwan, 387–391.##
Tomohiko, T. and J. K. Eaton (2008). Classification of turbulence modification by dispersed spheres using a novel dimensionless number. Journal of Fluids Engineering 101(11), 6037–6040.##
Williamson, C. H. K. and A. Roshko (1990). A. Measurements of base pressure in the wake of a cylinder at low Reynolds numbers. Zeitschrift fur Flugwissenschaften und Weltraumforschung 14(1), 38–46.##
Williamson, C. H. K. (1995). Vortex dynamics in the wake of a cylinder. In: Green, S.I. (Ed.), Fluid Vortices. Kluwer Academic Publishers, Amsterdam, Holland, 155–234.##
Williamson, C. H. K. and G. L. Brown (1998). A series in 1/√Re to represent the Strouhal–Reynolds number relationship of the cylinder wake. Journal of Fluids & Structures 12(8), 1073–1085.##
Yang, X., N. H. Thomas and L. J. Guo (2000). Particle dispersion in organized vortex structures within turbulent free shear flow. Chemical Engineering Science 55(7), 1305–1324.##
Yang, Y., J. N. Chung, T. R. Troutt and C. T. Crowe (1993). The effects of particles on the stability of a two-phase wake flow. International Journal of Multiphase Flow 19(1), 137–149.##