Solid obstacles can reduce hydrodynamic loading during water entry

The notion of sympathetic interactions between solids immersed in fluids is ubiquitous in applied physics, and the complexity of these interactions often results in unexpected outcomes. In this paper, we study the water entry of a rigid wedge in the presence of a neutrally buoyant solid cylinder below the water surface. We combine particle image velocimetry and direct measurements to elucidate the fluid-structure interaction. While the fluid confinement from the cylinder elicits a predictable increase in the pressure close to the keel, it is also responsible for a surprising reduction in the pressure toward the pileup. Through a detailed solution based on potential flow theory, we offer an explanation for this phenomenon. Our results may find application in the study of marine vessels that maneuver in occluded waters and seabirds that plunge and dive close to rocks or ice.

Figure 1

Schematics of the problem and definition of significant quantities. (a) Experimental apparatus and data acquisition system. The wedge, fluid, and cylinder are shown at (b) the onset of the impact (red markers label the location of the pressure sensors) and (c) a few milliseconds into the entry.

Figure 2

(a) Entry depth $\xi$, (b) velocity $\dot{\xi }$, and (c) acceleration $\ddot{\xi }$ of the wedge from experiments in the presence (solid black line) and in the absence (dashed blue line) of the cylinder (results reproduced from [28]) as functions of time. The time instant of the contact between the wedge and the cylinder is highlighted by a vertical red line. Results are averaged across repetitions and presented with their corresponding standard deviations.

Figure 3

(a) Particle image velocimetry images overlaid with velocity vectors and contour plot of the velocity magnitude in m/s at $7.5\mathrm{ms}$; the blue markers identify the location of the pressure sensors on the right-hand side of the wedge. (b) Pressure time histories at the locations of the pressure sensors at $L_{\mathrm{s}}=22\mathrm{mm}$ (bottom) and $47\mathrm{mm}$ (top). (Pressure measurements should be considered valid only after the sensor touches the water surface. The initial difference in the pressure readings is likely due to the combination of measurement uncertainty and variations in the installation process. Similar results were in fact noted in [28], without the presence of a cylinder.) The time instant of the contact between the wedge and the cylinder is highlighted by a vertical red line. Note that the results in (b) are averaged across the repetitions and presented with their corresponding standard deviations.

Figure 4

(a) Horizontal $x_{\mathrm{c}}$ and vertical $y_{\mathrm{c}}$ coordinates of the cylinder (top) and time histories of the left $c_1$ and right $c_2$ wetted widths (bottom). (b) Rotation of the cylinder during impact. Note that the results in (a) and (b) are averaged across the repetitions and presented with their corresponding standard deviations.

Figure 5

Experimental results for the horizontal $l_x$ and vertical $l_y$ cylinder displacements versus $\chi$, together with their corresponding linear fits.

Figure 6

(a) Time histories of the left $c_1$ and right $c_2$ wetted widths (top) and their derivatives ${\dot{c}}_1$ and ${\dot{c}}_2$ (bottom) from the MLM. (b) Pressure profile on the wedge wetted surface from the MLM; the location of the keel and the pressure sensors are highlighted by $*$ (keel), + (sensors at $L_{\mathrm{s}}=22\mathrm{mm}$), and $\times$ (sensors at $L_{\mathrm{s}}=47\mathrm{mm}$). (c) Pressure time histories at $L_{\mathrm{s}}=22\mathrm{mm}$ (blue) and $L_{\mathrm{s}}=47\mathrm{mm}$ (black) on the left- (solid line) and right- (dashed line) hand sides of the wedge from the MLM.