This section details general scaling for wave tank testing. For more specific information on OWC scaling please click on the following link:
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Scaling
The mechanical interactions between fluids and solids are generally dominated by three types of forces: inertia, gravity and viscosity i.e.:
Where Fi, Fg and Fv are inertial, gravitational and viscosity forces respectively. U is the fluid velocity, g the gravitational acceleration, l the characteristic length of the solid/fluid interaction, ρ ('ro') the density and μ the dynamic viscosity.
As mentioned previously in the "Physical Modelling" section, the relative importance of each of these forces will vary depending on problem being investigated. The two non-dimensional numbers most commonly used for scaling in this context are the Froude number Fr and the Reynolds number Re.
As mentioned previously in the "Physical Modelling" section, the relative importance of each of these forces will vary depending on problem being investigated. The two non-dimensional numbers most commonly used for scaling in this context are the Froude number Fr and the Reynolds number Re.
where ν is the kinematic viscosity (ν = μ/ρ).
A perfect scale model would keep the same balance between Fi, Fg and Fv thas the full scale device which means the Froude and Reynolds numbers would be the same for both but this is often unachievable, especially at the smaller scales. For example:
In a 1:100 scale model of an object moving through a fluid, assuming g is constant in both models, keeping the Froude number constant - Equation (4) - requires the velocity of the model, to be 1/10th of full scale. Assuming the same fluid is used for both models - ν is held constant - and Re from Equation (5) is to be the same for both models, U at the model scale would have to be 100 times that of the full scale device. These problems can be overcome by changing some of the other variables in the equation such as increasing the gravity, g, by carrying out the experiments in a centrifuge or decreasing ν by using a less viscous fluid. Changing these variables in tank tests for wave energy devices is not practical because of the size of the tank and the tanks being filled with water.
The relative influence of viscous forces is usually strongest at the boundary layer, near where the fluid and the body are in contact. This entails that the relative influence of viscous forces increases with 'wetted surface area to submerged volume' ratio. OWC's have large volumes and low wetted surface areas so viscous effects are assumed to be negligible, an assumption that often leads to conservative predictions for full scale devices
A perfect scale model would keep the same balance between Fi, Fg and Fv thas the full scale device which means the Froude and Reynolds numbers would be the same for both but this is often unachievable, especially at the smaller scales. For example:
In a 1:100 scale model of an object moving through a fluid, assuming g is constant in both models, keeping the Froude number constant - Equation (4) - requires the velocity of the model, to be 1/10th of full scale. Assuming the same fluid is used for both models - ν is held constant - and Re from Equation (5) is to be the same for both models, U at the model scale would have to be 100 times that of the full scale device. These problems can be overcome by changing some of the other variables in the equation such as increasing the gravity, g, by carrying out the experiments in a centrifuge or decreasing ν by using a less viscous fluid. Changing these variables in tank tests for wave energy devices is not practical because of the size of the tank and the tanks being filled with water.
The relative influence of viscous forces is usually strongest at the boundary layer, near where the fluid and the body are in contact. This entails that the relative influence of viscous forces increases with 'wetted surface area to submerged volume' ratio. OWC's have large volumes and low wetted surface areas so viscous effects are assumed to be negligible, an assumption that often leads to conservative predictions for full scale devices