Wake-Driven Dynamics of Finite-Sized Buoyant Spheres in Turbulence

Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle’s density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace this reversed trend back to the growing contribution from wake-induced forces, unaccounted for in current particle models in turbulence. Our findings highlight the need for improved multiphysics based models that account for particle wake effects for a faithful representation of buoyant-sphere dynamics in turbulence.

Figure 1

Parameter space of density ratio ($\mathrm{\Gamma }$) vs size ratio ($\mathrm{\Xi }$) for particles in turbulence. Data points from literature: triangle -Voth et al. [9]; left side triangle -Volk et al. [13]; star -Gibert et al. [24]; diamond -Brown et al. [1]; circle -Qureshi et al. [10]; sum symbol -Volk et al. [14]; downward triangle-Mercado et al. [25]; filled circle -Prakash et al. [16]; and present experiments: blue square -marginally light, green square -moderately light and red square -very buoyant particle.

Figure 2

Acceleration statistics for buoyant particles in turbulence at ${\mathrm{Re}}_{\lambda }\approx 180$. (a) Acceleration PDF for marginally buoyant spheres. Inset shows ${⟨a^2⟩}^{1/2}$ ($\mathrm{mm}/s^2$) vs $\mathrm{\Xi }\equiv d_p/\eta$. The dash-dotted line (in blue) with slope $\approx -1/3$ shows the prediction based on classical inertial scaling arguments [10]. (b) Normalized acceleration variance from experiments (EXP) compared to the results from Faxén-corrected (FC) simulations at ${\mathrm{Re}}_{\lambda }=180$ [2]. The horizontal dashed and dash-dotted lines (in black) are lines marking the tracer particle acceleration ($⟨a^2⟩/⟨a_f^2⟩=1$) and the upper bound of FC simulations ($⟨a^2⟩/⟨a_f^2⟩=9$) respectively. Here, $a_f$ is the fluid tracer acceleration.

Figure 3

(a) Lagrangian acceleration autocorrelation function $C_a(\tau )$ for marginally buoyant (MB, $\mathrm{\Gamma }\approx 0.92$) and neutrally buoyant (NB, $\mathrm{\Gamma }\approx 1$) spheres with low $\mathrm{Ga}(\le 30)$, along with fully resolved DNS predictions from Ref. [11] for NB particles at ${\mathrm{Re}}_{\lambda }=32$. (b) $C_a(\tau )$ for MB particles ($\mathrm{\Gamma }\approx 0.92$) with moderately large $\mathrm{Ga}(225\le \mathrm{Ga}\le 900)$ at ${\mathrm{Re}}_{\lambda }$ $\approx 180$.

Figure 4

PDFs of (a) horizontal and (b) vertical components of velocity and acceleration for a very buoyant ($\mathrm{\Gamma }\approx 0.02$) finite-sized sphere at $\mathrm{Ga}\approx 3000$. Blue, green, and red colors correspond to ${\mathrm{Re}}_{\lambda }\approx 180$, 250, and 300, respectively. The variable $X$ corresponds to $v_h$, $a_h$, $v_y$, and $a_y$ in their respective PDFs. The PDFs have been shifted vertically for clarity in viewing. A Gaussian profile (thin black line) is overlaid for comparison. (c)–(f) Show time traces of velocity and acceleration components of a representative trajectory at ${\mathrm{Re}}_{\lambda }\approx 300$. (g)–(j) Show the trajectory corresponding to the time traces in (c)–(f), projected on a vertical plane and color-coded with instantaneous quantities.