Flow-induced separation in wall turbulence

One of the defining characteristics of turbulence is its ability to promote mixing. We present here a case where the opposite happens—simulation results indicate that particles can separate near the wall of a turbulent channel flow, when they have sufficiently different Schmidt numbers without use of any other means. The physical mechanism of the separation is understood when the interplay between convection and diffusion, as expressed by their characteristic time scales, is considered, leading to the determination of the necessary conditions for a successful separation between particles. Practical applications of these results can be found when very small particles need to be separated or removed from a fluid.

Figure 1

Locations of markers with $\mathrm{Sc}=0.1$ (green) and 500 (crimson) at different times from their simultaneous release: (a) $t=50$; (b) $t=100$; (c) $t=220$. Clear separation between the two clouds is observed in panel (b), while a thin overlap region is observed at $x\approx 1000–1200$ in panel (c). Only the bottom half of the channel is shown, from $y=0$ to 300 (see Supplemental Material [42]).

Figure 2

Number of markers in the overlap region, $N_{\mathrm{ov}}$, when markers with $\mathrm{Sc}=0.1$ are released simultaneously with markers of different Sc. (a) Number of markers from the leading cloud, $\mathrm{Sc}=0.1$. (b) Number of markers from the higher Sc trailing cloud.

Figure 3

Number of markers in the overlap region when markers with $\mathrm{Sc}=0.1$ and 2400 are simultaneously released at different initial vertical positions: (a) markers of the leading cloud; (b) markers of the trailing cloud.

Figure 4

Separation time as a function of the ratio $R_t$ of the ${\tau }_{\mathrm{III}}$ of the low Sc over the ${\tau }_{\mathrm{I}}$ of the high Sc. The solid line is Eq. (4).

Figure 5

Mean displacement of particles with different Sc in (a) streamwise direction; (b) vertical direction. Data obtained from LST simulations.

Figure 6

Prediction of vertical displacement in zone I: comparison between the model of Eq. (9) (lines marked with open circles) and LST results (lines without any markings).

Figure 7

Mean vertical displacement of particles in the log layer. Data obtained from LST simulation.

Figure 8

Mean vertical displacement of different Sc. Results obtained from the LST data (lines without markers) and with our model based on Eqs. (8)–(10) are presented (lines marked with open circles).

Figure 9

Mean streamwise displacement of different Sc: (a) $\mathrm{Sc}=0.1$, (b) $\mathrm{Sc}=6$, (c) $\mathrm{Sc}=100$. Results are obtained from LST data (lined without markers) and Batchelor's model (lines marked with open circles).

Figure 10

Front and back boundaries of 99% of population of clouds in the streamwise direction, using mean displacement and normal distribution to predict the concentration distribution. (a) Prediction for clouds with Sc = 0.7 and 30000 and (b) prediction for clouds with Sc = 6 and 7500.