Buoyant finite-size particles in turbulent duct flow

Particle image velocimetry and particle tracking velocimetry have been employed to investigate the dynamics of finite-size spherical particles, slightly heavier than the carrier fluid, in a horizontal turbulent square duct flow. Interface resolved direct numerical simulations (DNSs) have also been performed with the immersed boundary method at the same experimental conditions, bulk Reynolds number ${\text{Re}}_{2H}=5600$, duct height to particle-size ratio $2H/d_p=14.5$, particle volume fraction $\mathrm{\Phi }=1\%$, and particle to fluid density ratio ${\rho }_p/{\rho }_f=1.0035$. Good agreement has been observed between experiments and simulations in terms of the overall pressure drop, concentration distribution, and turbulent statistics of the two phases. Additional experimental results considering two particle sizes $2H/d_p=14.5$ and 9 and multiple $\mathrm{\Phi }=1\%$, 2%, 3%, 4%, and 5% are reported at the same ${\text{Re}}_{2H}$. The pressure drop monotonically increases with the volume fraction, almost linearly and nearly independently of the particle size for the above parameters. However, despite the similar pressure drop, the microscopic picture in terms of fluid velocity statistics differs significantly with the particle size. This one-to-one comparison between simulations and experiments extends the validity of interface resolved DNS in complex turbulent multiphase flows and highlights the ability of experiments to investigate such flows in considerable detail, even in regions where the local volume fraction is relatively high.

Figure 1

(a) Schematic of the flow loop. (b) Photo of the section where PIV is performed.

Figure 2

(a) Raw image for PIV, (b) enhanced image for particle tracking velocimetry (PTV), and (c) resultant PIV (green, in fluid phase) plus PTV (red, in particle phase) velocity vectors. The above example corresponds to large particles at $\mathrm{\Phi }=3\%$. Note that the particle region is encircled with a solid black line in (b).

Figure 3

Instantaneous snapshot of the magnitude of the near-wall fluid streamwise velocity together with the particles. The solid volume fraction $\mathrm{\Phi }=1\%$.

Figure 4

Single-phase velocity statistics: (a) mean streamwise velocity, (b) primary Reynolds shear stress scaled in bulk units $(U_{\mathrm{bulk}}$ and $2H)$, and (c) mean streamwise velocity scaled in inner units $(u_{\tau }$ and $\nu /u_{\tau })$. In (c), the plots for successive spanwise planes are shifted upward by $5U^{+}$ units for better visualization).

Figure 5

Simulation and experimental results for SPs at $\mathrm{\Phi }=1\%$: (a)–(c) mean particle concentration, (d)–(f) mean streamwise velocity, and (g)–(i) primary Reynolds shear stress for three spanwise planes, namely, (a), (d), and (g) $z/H=0$, (b), (e), and (h) $z/H=0.4$, and (c), (f), and (i) $z/H=0.8$.

Figure 6

(a) Particle concentration distribution (in percent) and (b) mean secondary fluid velocity $\sqrt{V^2+W^2}/U_{\mathrm{bulk}}$ from simulations. In (b), the left panel corresponds to single-phase flow $\mathrm{\Phi }=0\%$ and the right panel corresponds to $\mathrm{\Phi }=1\%$.

Figure 7

Friction Reynolds number at bulk ${\text{Re}}_{2H}=5600$ as a function of the particle size and volume fraction.

Figure 8

Particle concentration and mean velocity at $z/H=0$: (a) and (d) mean particle concentration, (b) and (e) mean fluid streamwise velocity, and (c) and (f) mean particle streamwise velocity for (a)–(c) smaller particles and (d)–(f) larger particles. The relative size and distribution of the particles are illustrated by the cartoon in the corresponding inset in (a) and (d).

Figure 9

Fluid velocity fluctuation statistics at $z/H=0$: (a) and (d) primary Reynolds shear stress, (b) and (e) rms of the streamwise fluctuating velocity, and (c) and (f) rms of the wall-normal fluctuating velocity for results for (a)–(c) smaller particles and (d)–(f) larger particles.

Figure 10

Concentration and relative velocity distribution around a reference particle at $\mathrm{\Phi }=1\%$ for both SPs and LPs. The three rows corresponds to three layers of particles: (a)–(d) bottom near-wall layer, (e)–(h) second layer above the wall, and (i)–(l) third layer above the wall for the (a), (e), and (i) particle-centered concentration distribution for SPs, (b), (f), and (j) relative streamwise velocity for SPs, (c), (g), and (k) particle distribution for LPs, and (d), (h), and (l) relative streamwise velocity for LPs. The white arrows in the second and fourth columns represent the net relative velocity $U_{\mathrm{rel}}\widehat{x}+V_{\mathrm{rel}}\widehat{y}$.

Figure 11

Particle-centered distribution and relative velocity field at $\mathrm{\Phi }=5\%$. The details are the same as in Fig. 10.

Figure 12

(a) Particles occasionally moving in a trainlike cluster and (b) particles moving with nearly constant relative spacing. These instances correspond to LPs at $\mathrm{\Phi }=3\%$.

Figure 13

Probability distribution function of the center-to-center separation distance between neighboring particles in the bottom near-wall layer for (a) smaller particles and (b) larger particles. The vertical lines (the same color corresponds to the same volume fraction) correspond to the average spacing denoting a scenario where the particles would move with a constant relative spacing. The black vertical line corresponds to a separation distance of one particle diameter corresponding to the scenario where all neighboring particles are in contact and move as a continuous train.