Effects of wind on the dynamics of the central jet during drop impact onto a deep-water surface

The cavity and central jet generated by the impact of a single water drop on a deep-water surface in a wind field are experimentally studied. Different experiments are performed by varying the impacting drop diameter and wind speed. The contour profile histories of the cavity (also called crater) and central jet (also called stalk) are measured in detail with a backlit cinematic shadowgraph technique. The results show that shortly after the drop hits the water surface an asymmetrical cavity appears along the wind direction, with a train of capillary waves on the cavity wall. This is followed by the formation of an inclined central jet at the location of the drop impact. It is found that the wind has little effect on the penetration depth of the cavity at the early stage of the cavity expansion, but markedly changes the capillary waves during the retraction of the cavity. The capillary waves in turn shift the position of the central jet formation leeward. The dynamics of the central jet are dominated by two mechanisms: (i) the oblique drop impact produced by the wind and (ii) the wind drag force directly acting on the jet. The maximum height of the central jet, called the stalk height, is drastically affected by the wind, and the nondimensional stalk height $H/D$ decreases with increasing $\theta {\text{Re}}^{-1}$, where $D$ is the drop diameter, $\theta$ is the impingement angle of drop impact, and $\text{Re}={\rho }_a{U}_{w}D/{\mu }_a$ is the Reynolds number with air density ${\rho }_a$, wind speed $U_w$, and air viscosity ${\mu }_a$.

Figure 1

Schematic showing (a) the facility for single-drop impact experiments and (b) the setup of the high-speed camera and light in the lateral perspective (end view).

Figure 2

Wind velocities versus the height above the water surface $\left(z=0\right)$ at the locations of drop impacts in the test section of the wind tunnel.

Figure 3

(a) Horizontal and (b) vertical impact velocities of primary drops versus the drop diameter with various wind speeds. The three solid lines in (a) correspond to three different size needles, while the dashed line refers to $U_w=6.0$ m/s.

Figure 4

Images from a high-speed movie of the normal impact of a single drop on the deep-water surface in the lateral perspective. Each image shows a $48.2\times 30.1{\mathrm{mm}}^2$ section. The diameter of the primary drop $D=3.5$ mm, the impact velocity $U=2.0$ m/s, $\text{We}=192$, and $\text{Fr}=117$. (a) The drop is about to collide with the water surface $(t=0$ ms); (b) a crown forms above the water surface while a cavity with a flat base appears underneath the water surface in a short time $(t=4$ ms) after the drop impact and secondary droplets are generated from the crown top; (c) the cavity expands outward and downward to a maximum depth $(t=18$ ms); (d) the crater retreats upward and forms a cone shape with a bubble generation underneath the bottom of the crater $(t=31$ ms); (e) the crater vanishes $(t=36$ ms); (f) a stalk (central jet) forms at the center of the impact site $(t=40$ ms); (g) the stalk rises to its maximum height with a droplet forming on the tip $(t=60$ ms); and (h) a large secondary droplet is ejected from the tip of the stalk and moves upward until the maximum height $(t=80$ ms).

Figure 5

Images from the high-speed movie of the oblique impact of a single drop on the deep-water surface with a wind speed of 4.5 m/s. Each image shows a $28.6\times 21.4{\mathrm{mm}}^2$ section and the wind is blowing from left to right. The time in milliseconds refers to the frame just before the drop impact $(t=0$ ms). The diameter of the primary drop is $D=3.3$ mm, the impact angle is $\theta =13.3^{\circ }$, the vertical and horizontal impact velocities are $v=2.0$ and $u=0.45$ m/s, respectively, and $\text{We}=171$.

Figure 6

Contour profile histories of the cavity and stalk from the same movie as the images shown in Fig. 5. (a) Growth phase of the cavity from the moment 4 ms prior to the drop impact to the maximum depth, $t=18$ ms (red line), and (b) collapse phase of the cavity from the moment of maximum depth (red line) and the growth phase of the stalk until the maximum height (green line). Here $x=0$ is the impact center and $y=0$ corresponds to the free water surface. The time between profiles is 2 ms. The horizontal line portions of the cavity and stalk contours are the bottom and top of the meniscus on the tank wall, respectively.

Figure 7

Images from the high-speed movie of the oblique impact of a single drop on the deep-water surface with a wind speed of 6.0 m/s. Each image shows a $28.6\times 21.4{\mathrm{mm}}^2$ section and the wind is blowing from left to right. The time in milliseconds refers to the frame just before the drop impact $(t=0$ ms). The diameter of the primary drop is $D=3.1$ mm, the impact angle is $\theta =25.3^{\circ }$, the vertical and horizontal impact velocities are $v=1.9$ m/s and $u=0.9$ m/s, respectively, and $\text{We}=183$.

Figure 8

Contour profile histories of the cavity and stalk from the same high-speed movie as the images shown in Fig. 7, for the oblique impact of a single drop on the deep-water surface with a wind speed of 6.0 m/s. (a) Downward movement of the cavity, from the moment 4 ms prior to the drop impact to the maximum depth, $t=18$ ms (red line), and (b) retreat of the cavity from the moment of maximum depth (red line) and upward movement of the stalk until the maximum height (green line). Here $x=0$ is the impact center and $y=0$ corresponds to the free water surface. The time between profiles is 2 ms. The horizontal line portions of the cavity and stalk contours are the bottom and top of the meniscus on the tank wall, respectively.

Figure 9

(a) Cavity depth $h_{\mathrm{cavt}}$ and (b) displacement $d_{\mathrm{cavt}}$ as a function of time under various wind conditions. Here $t=0$ corresponds to the moment of the drop impact, $v$ is the vertical impact velocity of the primary drop, and the diameters $D$ of the primary drops corresponding to $U_w=0$, 4.5, and 6.0 m/s are 3.5, 3.3, and 3.1 mm, respectively.

Figure 10

Maximum crater depth $h_m$ as a function of the impact angle of the primary drop under various wind conditions.

Figure 11

Shape profile history of the crater during its retraction $(U_w=4.5$ m/s and $D=3.3$ mm). The profile data are from Fig. 6. The bottom red curve is the crater contour at the moment the crater reaches the maximum depth, defined as the first image of the time sequence $\left(j=1\right)$, while the dashed curve is a semiellipse for normal impact, as described in [23]. Each successive profile is plotted 1/2 mm above the previous profile for clarity and the time between profiles is 1 ms. The top profile shows the central jet formed on the water surface and the big gap between the last two profiles is due to the meniscus on the tank wall.

Figure 12

Contours of the stalk at the moment they reach the maximum heights. The case of $U_w=0$ corresponds to the normal impact (without wind) and the origin is the impact center at the free water surface. The horizontal line portions of the stalk contours are the top of the meniscus. The diameters of the primary drops corresponding to $U_w=0$, 4.5, and 6.0 m/s are 3.5, 3.3, and 3.1 mm, respectively.

Figure 13

Nondimensional maximum stalk height $H/D$ versus the impact angle $\theta$ of the primary drop. The data points for the case of no wind $\left(\theta =0\right)$ are divided into two groups, corresponding to different types of jets [23]: $⊲$, a slow thick (Worthington) jet; $◂$, a fast thin jet. Three closed circles connected by a green line are the experimental data of normal impacts on horizontally moving films estimated from [39]. The data points around the two vertical bars show that $H/D$ increases with increasing wind speed.

Figure 14

Schematic showing the growing stalk in the wind field.

Figure 15

Nondimensional stalk height $H/D$ varying with $\theta {\text{Re}}^{-1}$ with the experimental data shown in Fig. 13. For clarity, only slow thick (Worthington) jets for the case of no wind are included in this figure. The solid curve is Eq. (4) and $\theta$ is in degrees.

Figure 16

Drop impact angle $\theta$ varying with the Froude number ${\text{Fr}}_w=U_w^2/gD$. The solid curve is Eq. (A6): $\theta =0.022{\text{Fr}}_w$.