Oscillating Water Column Scaling Issues
As described in the 'Scaling' section of the website, oscillating water columns, can approximately be scaled according to the Froude number, disregarding other scaling factors such as the Reynolds number. This type of scaling - for all intents and purposes - is a good starting point and a fairly accurate representation of the full scale device. Below is a table of Froude scaling laws for various quantities where s is the geometric scale:
Issues in scaling oscillating water columns come about because the process is driven by both hydrodynamic and aerodynamic effects - hydrodynamic for the displacement of water and aerodynamic for the power take-off as air is pushed in and out of the chamber. The hydrodynamics are dominated - as mentioned before - by inertial and gravitational forces while the aerodynamics are dominated by a compression force, Fc. yna Assuming volume deformation of the chamber in one dimension and reversible adiabatic conditions:
Where P0 is initial pressure, k the isentropic exponent and l the characteristic length [2]. The inertial and pressure forces both act as restoring forces in the motion of the water column, this means keeping a balance between these forces at both scales is important:
Fc taken from above and Fi taken from the 'Scaling' section. Keeping the Froude number AND the Fi/Fc ratio constant means the ratio:
must be kept constant, a difficult task in practice. Maunsell and Murphy have tried to get around the problem by designing the model to different scales above and below the waterline while keeping the horizontal scale the same[3].