4. Offshore oil drilling model: The large portion of an offshore oil drill is a

Question

4. Offshore oil drilling model: The large portion of an offshore oil drill is a long cylinder (diameter D and length L) that lowers the drill head to the ocean bed. The water flow (velocity V) over the cylinder creates vortex shedding (eddies), which create an oscillatory force on the cylinder (FL). If the frequency of the oscillatory force and the vortex shedding (fy) is in resonance with the natural frequency of the structure (fs), large amplitude oscillations of the cylinder will occur that can destabilize and even damage the drilling equipment. Such large amplitude oscillations are called vortex-induced vibrations (VIV). A team of engineers are required to examine the VIV of their new drill design before building the full-scale prototype. How can they achieve full similarity between their model and the full-scale drilling prototype

Explanation / Answer

Full similarity between model and full-scale drilling prototype can be achieved if all relevant dimensionless parameters have the same corresponding values for model and prototype.

The dimesionless parameters here mentions the PI number calculated for both model and prototype. It mentions that model and prototype should have the same PI number.

The system can have one or more PI numbers, if so all the PI numbers should be same.

Equation for PI number is calculated for the problem based on the depending factors. In this case the given factors are Flow velocity (v), Oscillatory force on the cylinder (FL), Dimensions of cylinder (D,L), vortex shedding frequency (fv).

Using the equation calculated PI number for vortex induced vibrations in the model is calculated.

As per the theorem the prototype should have the same PI number so using the same, vortex induced vibrations for the full-scale prototype is calculated.   

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