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

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%.