heave oscillation floating body

Hey there,

I'm running a CFD simulation of a small body which falls vertically in a watertank. The acceleration, velocity and translating (in Z direction -> heavemotion) are calculated and also the resulting wavepattern (it's a closed testtank). The exact particulars of the body and the simulation details are not important but the body can roughly be described as a cone shape so the waterline section is always a circular area.

While running the CFD simulation I noticed a oscillation time period of about ~0.57 s. I just had an idea how to calculate the harmonic heave frequency of a floating body, assuming an mass spring system (not damped) F = -k *x :
F = restoring spring force, in this case the buoyant force acting on the body at it's specified weight
k = spring coefficient
x = draught (distance between body just touching the watersurface and body in equilibrium at it's specified weight)

As F and x are known now k can be calculated. With k the the time period can be calculated:
T = 2 * pi * (m / k)^0.5

For my body I calculated this:
F = 0.2087 kg * 9.81 m/s^2 = 2.047 N
x = 0.079 m

-> k = 25.91

-> T = 2 * pi * (0.2087 / 25.91)^0.5 = 0.56 s

This pretty matches the time period I noticed in the CFD simulation.

Has anybody thoughts on this? Could this be used as a preliminary, simplified assumption of the heavemotion of ships or is this just a ******** idea which matches nearly perfectly by accident?

Yes I had a course ship motion at university but I don't remember too much of this quiet complex subject.

 

Hi,
I don't think this will be more than an lucky accident. In a mass spring system the elongation of the spring is related linear to the spring force, the bouyancy of a cone is not. A heave motion of a solid in a fluid is influenced by the viscosity of the fluid (think of a heave motion in oil or honey).

 

So far the motion amplitude is small (which means the waterline area remains constant), and the body is not moved otherwise (no additional hydrodynanic effects) your assumption is right. In pracitize your heaving frequency will be a bit lower because the damping throug viscosity and waves.

This is not right because they describe the change of the water section area with the excursion from the equilibrium - your "spring constant" is not really a constant. For a cone shape you get F ~ - (k1*x + k2*x^2 ...). If you transform your cfd results in the frequency domain you will see higher harmonics of the basic heave frequency.