Vortex ring impingement on a wall with a coaxial aperture

The interaction of a vortex ring impinging on a rigid wall with a coaxial aperture is examined experimentally with various aperture sizes and vortex ring Reynolds numbers. Flow visualization and particle image velocimetry are utilized to investigate the dynamics of the impact interaction. For large aperture-to–ring radius ratios, the vortex ring passes through the aperture relatively unabated, while for smaller ratios, the incoming ring can be partially or completely blocked. For cases where the vortex ring is slightly smaller than the aperture, the vortex ring passes through, but suffers a significant loss in energy because of the influence of the wall. For apertures smaller than the ring, the vortex ring–wall interaction is similar to the dynamics of a vortex ring impacting a full wall; that is, the vortex ring-induced boundary layer separates and rolls up into a secondary vortex ring. Flow through the aperture, however, causes the formation of a new vortex ring. A semianalytical model is introduced to predict the strength of the newly formed vortex ring for small aperture-to-ring radius cases.

Figure 1

Schematic of a vortex ring impinging on a rigid wall with a coaxially aligned aperture. The vortex ring on the left is the incoming vortex ring, while the vortex ring on the right is the postimpact vortex ring.

Figure 2

Experimental setup.

Figure 3

Vorticity evolution of the high-Reynolds-number full wall collision scenario, increasing in time from (a) $t\approx 15$ to (e) $t\approx 27$ at an interval of $t\approx 3$. The wall is immediately to the right of each frame.

Figure 4

Time series of the primary vortex ring during a full wall collision at $\mathrm{Re}\approx 4600$ (black line) and $\mathrm{Re}\approx 1850$ (gray line): (a) distance to the wall, (b) ring radius, (c) circulation, (d) impulse, and (e) energy.

Figure 5

Flow visualization snapshots for the high-Reynolds-number case for the (a)–(c) small-, (d)–(f) medium-, and (g)–(i) large-aperture cases. Snapshots at dimensional time $t=3.33$, 3.75, and $4.08\mathrm{s}$ are shown in each column from left to right, respectively.

Figure 6

Vorticity field snapshots of the high-Reynolds-number case for the (a)–(c) small-, (d)–(f) medium-, and (g)–(i) large-aperture cases. Snapshots of $t=15$, 20, and 25 s are shown in each column from left to right, respectively. Gray and black areas are masked regions for the aperture and the wall, respectively.

Figure 7

Time series of vortex ring properties during the interactions. The small-, medium-, and large-aperture cases are presented in columns from left to right, respectively. The mean vortex ring $x$ position, ring radius, circulation, impulse, and energy are organized into rows from top to bottom, respectively. Black and gray lines represent high- and low-Reynolds-number cases, respectively, while solid and dashed lines denote preimpact and postimpact vortex ring properties.

Figure 8

Ratios of the post- to preimpact vortex ring properties versus aperture size for both Reynolds numbers: (a) ring radius $R_2/R_{\text{e}}$, (b) circulation ${\mathrm{\Gamma }}_2/{\mathrm{\Gamma }}_{\text{e}}$, (c) impulse $I_2/I_{\text{e}}$, and (d) energy $E_2/E_{\text{e}}$. High- and low-Reynolds-number cases are shown with black and gray symbols, respectively. Spline fit trend lines are also included.

Figure 9

Flow across the aperture induced by the impinging vortex ring for the (a) small-, (b) medium-, and (c) large-aperture cases; black and gray lines represent high- and low-Reynolds-number cases, respectively.

Figure 10

Axial velocity profile behind the aperture ($x=0.22R_1^{\mathrm{i}}$) when the induced flow through the aperture reaches its peak for the high-Reynolds-number case. Solid, dashed, and dotted lines represent the small, medium, and large apertures, respectively.

Figure 11

Comparison of analytical and experimental results for the (a)–(c) low- and (d)–(f) high-Reynolds-number cases. The analytical results are displayed as black lines, while the experimental results with their $95\%$ confidence intervals are represented with gray bands. The incoming vortex ring's (a) and (d) $x$ position, (b) and (e) circulation, and (c) and (f) aperture flow rate are shown.