Fluid flow in low aspect-ratio curved channels: from small to moderate Dean numbers

Abstract

We investigated the pressure-driven flow in curved channels at low aspect ratio, the latter being the ratio between the channel height (along the axial direction) and width (along the radial direction). The dynamics was studied numerically, as a function of the characteristic Dean number, $\mathrm{De}=\mathrm{Re}\sqrtδ$, by varying independently the Reynolds number $\mathrm{Re}$ and the curvature ratio $δ$, the ratio between the hydraulic diameter and the radius of curvature. We considered the flow within a wide range of dimensionless numbers: $\mathrm{De}\lesssim200$ and $0.005\leqδ\leq0.15$. For $\mathrm{De}\lesssim 100$, the flow remained stable in time, whereas at larger Dean numbers, the flow was stable while traveling several turns before transient structures developed. While investigating the flow features in the stable regime, only one pair of counter-rotating vortices was observed. At small $\mathrm{De}$ and large $δ$, the peak of the streamwise velocity and the center of the vortices were located near the inner channel wall. They both shifted toward the outer wall as $\mathrm{De}$ was increased and/or $δ$ was decreased. This phenomenon is expected to have considerable impact on the interpretation of the transport of dispersed phase in multiphase flows in curved channels. Based on a dimensional analysis, the primary and secondary flow profiles, the friction coefficient of the flow as well as the flow development angle were all rationalized in terms of both $\mathrm{Re}$ and $δ$.

Figures (10)

• Figure 1: Schematic representation of the flow geometry and the coordinate system.
• Figure 2: Contours of the azimuthal velocity $\overline{v}_\theta$ for various Dean numbers and curvature ratios. The streamlines indicate secondary vortices in the cross-section. Note that the aspect ratio of the channel cross-section is $\lambda=0.17$.
• Figure 3: Profiles of the dimensionless tangential velocity $\overline{v}_\theta$ along the mid-plane $\overline{x} = 0.5$ for various $\mathrm{Re}$ and curvature ratios. Solid and dashed lines correspond to $\delta_4$ and $\delta_5$, respectively.
• Figure 4: Axial profiles of the radial velocity $\overline{v}_r$ along the mid-plane $\overline{r} =0$ for various curvature ratios at (a) low De and (b) moderate De.
• Figure 5: Secondary flow intensity as a function of the Dean number.