Vortical cleaning of oil-impregnated porous surfaces

We investigate the cleaning mechanism of an oil-impregnated porous surface by utilizing a method of vortex ring interaction. The kinetic energy of a vortex ring is exploited to expunge the trapped oil from the spherical-bead-based porous surface. Qualitative and quantitative measurements were made using high-speed shadowgraphy imaging, planar laser-induced fluorescence (PLIF) imaging, and particle image velocimetry (PIV) techniques. The interaction phenomenon is explored from the perspective of vortex ring dynamics followed by oil sheet dynamics. Five different strengths of a vortex ring [characterized by the circulation ($\mathrm{\Gamma }$) -based Reynolds number (${\mathrm{Re}}_{\mathrm{\Gamma }}=2550$–14 260: ${\mathrm{Re}}_{\mathrm{\Gamma }}=\mathrm{\Gamma }/\nu$, where $\nu$ is the kinematic viscosity)] and two types of surface porosity ($\varphi$) (open area ratio, 0.21 and 0.41) are considered for parametric analysis. The interaction process with oil is divided into three regimes: (i) penetration, (ii) bag formation, and (iii) bag breakup. Depending on the strength of the vortex ring, it is observed that surface cleaning takes place from both upstream and downstream regions of the porous surface. The vortex rings with higher ${\mathrm{Re}}_{\mathrm{\Gamma }}$ can expunge more oil through a complicated interaction process involving Rayleigh-Taylor- and Rayleigh-Plateau-type instabilities. However, along with ${\mathrm{Re}}_{\mathrm{\Gamma }}$, the interaction dynamics depend strongly on the shape and $\varphi$ value. The interaction process is characterized by vorticity cancellation, Kelvin-Helmholtz (KH) instabilities, and three-dimensional interactions.

Figure 1

(a) A typical experimental setup used in the present study. (b) Setup for PIV and PLIF measurements. (c) Setup for shadowgraphy and top view imaging. (d) A nonuniform porous surface placed inside an acrylic water tank. (e) A vortex ring illuminated using a PIV laser just before interacting with a porous surface.

Figure 2

(a) Schematic showing the important features of a vortex ring. (b) Cross section of the uniform porous surface. (c) Cross section of the nonuniform porous surface used in the present study.

Figure 3

Evolution of free vortex rings at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at different time instances. The initial row depicts the flow structures at the time of ejection, and the final row shows the vortex ring structure near the location of interaction ($\mathit{x}\sim 0.85\mathit{D}$). The scale bar represents 5 mm.

Figure 4

Vorticity contours at the time of ejection and before interacting at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$. The occurrence of shear-layer vortices can be visualized from the first row especially at higher values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$. The scale bar represents 5 mm.

Figure 5

$\varphi =0$. (a) PLIF, (b) PIV images at ${\mathrm{Re}}_{\mathrm{\Gamma }}=2550$. The scale bars represent 5 mm. As the vortex ring approaches the solid surface, a series of phenomena including vortex stretching and rebounding can be seen.

Figure 6

(a) PLIF, (b) PIV images at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$ after interaction for $\varphi =0$. The scale bars represent 5 mm. The three-dimensional affects become prominent with an increase in the value of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ as can be seen from both PLIF and PIV images.

Figure 7

PLIF images for $\varphi =0.21$ with no oil at different values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale represents 5 mm for each ${\mathrm{Re}}_{\mathrm{\Gamma }}$ value.

Figure 8

PIV images for $\varphi =0.21$ with no oil at different values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale bar represents 5 mm.

Figure 9

PLIF images of vortex reformation in the downstream region for $\varphi =0.21$ with no oil at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$. The scale bar represents 5 mm.

Figure 10

PLIF images for $\varphi =0.41$ with no oil at different values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale represents 5 mm for each ${\mathrm{Re}}_{\mathrm{\Gamma }}$ value.

Figure 11

PIV images for $\varphi =0.41$ with no oil at different values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale bar represents 5 mm.

Figure 12

PLIF images of vortex reformation in the downstream region for $\varphi =0.41$ with no oil at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$. The scale bar represents 5 mm.

Figure 13

(a) Kinetic energy (inset shows the $KE/\rho$ values for ${\mathrm{Re}}_{\mathrm{\Gamma }}=2550$). (b) Enstrophy of the upstream vortex ring at $\mathit{x}\sim 1.5\mathit{D}$.

Figure 14

Vortex core trajectory for (a) $\varphi =0$, (b) uniform ($\varphi =0.21$) no oil, (c) nonuniform ($\varphi =0.41$) no oil, (d) uniform ($\varphi =0.21$) oil, and (e) nonuniform ($\varphi =0.41$) oil at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$ values.

Figure 15

Upstream energy dissipation at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$ for different types of porous surfaces with and without oil. The kinetic energy shown here is normalized by the initial kinetic energy of the vortex ring.

Figure 16

PLIF images for $\varphi =0.21$ with oil at different values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale bar represents 5 mm.

Figure 17

PLIF images for $\varphi =0.41$ with oil at different values of ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale bar represents 5 mm.

Figure 18

Variation of $h$ with time at (a) ${\mathrm{Re}}_{\mathrm{\Gamma }}=6300$, (b) ${\mathrm{Re}}_{\mathrm{\Gamma }}=10640$, (c) ${\mathrm{Re}}_{\mathrm{\Gamma }}=12150$, (d) ${\mathrm{Re}}_{\mathrm{\Gamma }}=14260$, and (e) actual and predicted coefficient of ${\mathit{t}}^2$.

Figure 19

Shadowgraphy images for $\varphi =0.21$ with oil at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale represents 5 mm. The marked zone for ${\mathrm{Re}}_{\mathrm{\Gamma }}=10640$ shows the occurrence of a hole at the head of the cylindrical oil bag. For ${\mathrm{Re}}_{\mathrm{\Gamma }}=12150$ and 14 260, it highlights the formation of oil ligaments.

Figure 20

Different forms of ligaments and droplet formation in the upstream region for $\varphi =0.21$ at ${\mathrm{Re}}_{\mathrm{\Gamma }}=12150$ shown at two different instances. The scale bar represents 5 mm.

Figure 21

Shadowgraphy images for $\varphi =0.41$ with oil at different ${\mathrm{Re}}_{\mathrm{\Gamma }}$ shown at various $t^{*}$. The scale bar represents 5 mm. The marked zone for ${\mathrm{Re}}_{\mathrm{\Gamma }}=10640$ at $t^{*}=13.5$ shows the initiation of the first hole. For ${\mathrm{Re}}_{\mathrm{\Gamma }}=10640$ at $t^{*}=14.4, {\mathrm{Re}}_{\mathrm{\Gamma }}=12150$ at $t^{*}=16.4$ and ${\mathrm{Re}}_{\mathrm{\Gamma }}=14260$ at $t^{*}=14.5$, the marked area shows the accumulation of oil at the heads in the upstream region.

Figure 22

Oil bag formation for (a) ${\mathrm{Re}}_{\mathrm{\Gamma }}=10640$ (b) Oil bag formation for ${\mathrm{Re}}_{\mathrm{\Gamma }}=12150$. The dashed blue curve is fitted in the shape of a semi-ellipsoid as shown in (c) for $\varphi =0.41$.

Figure 23

Thickness of the oil bag just before rupturing for $\varphi =0.41$.

Figure 24

Time of rupture calculated using (a) Lubrication theory estimation using Eq. (8), (b) kinematic arguments using Eq. (11).