Instabilities of a freely moving spherical particle in a Newtonian fluid: Direct Numerical Simulation

Abstract

Abstract Direct Numerical Simulations (DNS) were carried out for a freely falling/rising rigid particle in an otherwise quiescent fluid, using a non-Lagrangian multiplier based fictitious domain (FD) method. Validation studies showed that the proposed FD based DNS are in good agreement with the existing experimental results in the transition regime of falling/rising spheres. Simulations done in the transitional regime (50 < Reynolds number (Re) < 1800 and solid-to-fluid density ratios Γ = ρ p / ρ f ${\Gamma}={\rho }_{p}/{\rho }_{f}$ from 0.08 to 4), confirmed that (i) a falling spherical particle (Γ = 4) exhibits a helical trajectory in the range 270 < Re < 320, and (ii) a rising particle (Γ = 0.5) shows a zig-zagging trajectory in the same range of Re. This finding closes the uncertainty to the question as to whether or not rising/falling particles exhibit a helical and a zig-zagging trajectory. In addition to this, a total of seven distinctive flow regimes were identified, which are as follows: (I) vertical straight path (II) steady oblique path (III) Wavy oblique path (IV) zig-zagging path (for 0.08 < Γ < 1) (V) helical path (for 1 < Γ < 4) (VI) early transition to chaos and (VII) chaotic regime. Regime IV occurs only for light particles (Γ < 1), whereas Regime V occurs only for heavy particles (Γ > 1). Fast Fourier Transform (FFT) analysis characterized the presence of a bimodal frequency similar to that exhibited by flow past an isolated stationary bluff body.