Drag Moderation by the Melting of an Ice Surface in Contact with Water

We report measurements of the effects of a melting ice surface on the hydrodynamic drag of ice-shell-metal-core spheres free falling in water at a Reynolds of number $\mathrm{Re}\sim 2\times {10}^4–3\times {10}^5$ and demonstrate that the melting surface induces the early onset of the drag crisis, thus reducing the hydrodynamic drag by more than 50%. Direct visualization of the flow pattern demonstrates the key role of surface melting. Our observations support the hypothesis that the drag reduction is due to the disturbance of the viscous boundary layer by the mass transfer from the melting ice surface.

Figure 1

Images of a 60 mm diameter ice-shell sphere with a 40 mm diameter spherical steel core. (a) Image of the sphere before immersion in water. After the sphere is released from the mold, the ice surface starts to melt slowly and a thin water layer wets the surface, resulting in a glossy appearance. (b) Image of the ice sphere immersed in water. See other examples in Figs. S3 and S8 in the Supplemental Material [21].

Figure 2

Fall velocities versus time for a 60 mm diameter ice-covered tungsten carbide sphere and a 60 mm diameter solid steel sphere of the same average density, ${\rho }_s=7.8\mathrm{g}/{\mathrm{cm}}^3$, during free fall in room temperature ($22°\mathrm{C}$) water. Each data series is fitted with the extrapolation function [13] $U(t)=U_T(1-e^{-t/\tau })$ (lines). An upper bound estimate based on the maximum measured velocity gives $C_D=0.23$ for the ice sphere and $C_D=0.50$ for the solid sphere. See Video 1 of the Supplemental Material [21].

Figure 3

Drag coefficient dependence on the Reynolds number for ice surface spheres and smooth solid surface spheres free falling in room temperature ($22°\mathrm{C}$) water: solid squares (red) are for ice-shell sphere, open circles (blue) are for solid steel spheres, and open triangles (blue) are for solid surface composite spheres matching the weight and the size of the ice-shell spheres [21]. Open squares (red) are drag coefficients for ice-shell spheres calculated using the extrapolated values for the terminal velocity. Solid diamonds (red) are drag coefficients for ice-shell spheres falling in $6\pm 1°\mathrm{C}$ water. Literature values for smooth solid surface spheres falling in an infinite tank measured by White [11] are shown as blue crosses.

Figure 4

High-speed camera snapshots of 60 mm diameter dyed-ice ice-covered metal sphere falling in water (a) at a low speed of about $0.8\mathrm{m}/\mathrm{s}$ corresponding to $\mathrm{Re}\approx 5\times {10}^4$ and (b) at a higher speed of about 2.4 m/s corresponding to $\mathrm{Re}\approx 1.5\times {10}^5$. Arrows indicate the approximate position at which flow separation occurs. See Video 2 of the Supplemental Material [21].