Simulation Parameters

Simulation Parameters

Simulate a water droplet hitting a flat water surface.

Measurements taken from this recording setup. Note that water droplets are only truly spherical when moving slowly or when they are so small that surface tension dominates. The terminal velocity for these sized droplets is around 12 m/s, which requires a free falling distance of about 40 m. Several papers have looked at droplet impact at terminal velocity, because that is how rain strikes water. The recordings that this is based on have much slower impact velocities.

Droplet diameter6 mm
Droplet shapeSpherical
Droplet speed5.5 m/s (downward)

The domain should be something like a square box half filled with water. The physical configuration should start the drop a moment before impact with the surface, or even just touching the surface. The impact is quite energetic, so ideally the walls should allow outgoing waves and drops to leave. As for resolution, the initial droplet must be resolved to a reasonable level, but the box must also be fairly large so as to not chop off anything too important.

Here's a horrible little ASCII drawing to make it clear:

|-----------------------|
|                       |
|                       |
|           -           |
|         /   \         |
|         \   /         |
|           -           |
|-----------------------|
|                       |
|                       |
|                       |
|                       |
|                       |
|-----------------------|

Notes on the impact velocity

I did not have a record of the velocity at which the droplet hit, so I used the standard formula for the drag force experienced by a sphere to calculate the velocity. i.e. F_drag = 1/(2*mass) * C * rho * S * v^2 where C is the coefficient of drag (0.5 for a sphere), rho is the density of air, S is the projected area (pi * r^2), and v is the velocity. The parameters I used here were:

Radius r3mm (6mm diameter)
Gravitational acceleration g9.81 m/s^2
Density of air rho_air1.21 kg/m^3
Density of water rho_water998 kg/m^3

That's fresh water at 20 degrees Celsius.