ESRU

Channel Model Results and Analysis

Effective Channel Area

It was decided by the group to adopt a rule of ½ when considering the surface area actually experiencing the full magnitude of our rated velocity. This decision was made to account for losses at the edge and bottom roughness etc. The group concedes that it is a fairly crude approximation. However, given the lack of availability of sea bed topography and detailed channel geometry, it was decided to approximate for the losses and slower moving regions of water near the edges and bottom of the channel.

So, Effective Channel Area= ½ x Idealised Channel Area

Apparent “Knee Point” on Power Curves

The most striking result from our channel model for both the Pentland Firth and Kyle Rhea channels was the development of a “knee point” in the power flux curves. Clearly the gradient of the curve begins to decrease significantly at a certain point becoming almost horizontal at large numbers of KT.

Pentland Firth Results:

Kyle Rhea Results:

This would seem to suggest that as the value of KT (loss coefficient due to turbine in channel) increases from zero, the power per turbine (gradient of the curve) will remain constant until an optimum point, after which it rapidly drops off.

Thus it seems that there will be a point at which it ceases to be beneficial to continue increasing KT. What this implies is that as the site developer continues to add MCT’s to the channel, a point will be reached whereupon the power per turbine will at its maximum, thereafter decreasing rapidly. This will coincide with the maximum turning point or “peak” of the curve.

However, this group feels that in reality the developer should stop adding turbines well before reaching that peak because as the gradient drops off, it will rapidly cease to be financially viable to further increase the number of MCT’s, as each additional turbine added will experience a progressively lower and lower power take-off. Passing beyond this peak will undoubtedly increase the cost/ KWh of overall generation for the site unless major economies of scale are in effect.

Therefore it is this group’s belief that there will be a point occurring before the peak is reached at which the “optimum” K value will occur.

Our group performed a sensitivity analysis of the slope of the 6

time-incremental power curves and found the following results for each channel:

Pentland Firth -

The group arrived at a value of KT=0.6 which coincided with a 40% drop off in the gradient (power per turbine)

Kyle Rhea

The group reached a value of KT=0.74 which coincided with a 40% drop off in the gradient (power per turbine) This value of Kt when compared to the value for the same drop off in the Pentland Firth is higher, perhaps due to the much narrower geometry of the Kyle Rhea channel. It may be that there is more of a venturi effect in operation here and so it takes a larger number of turbines (larger KT value) to reach the same drop off point. This theory is back up by looking at the graph for KT against actual velocity, where the velocity drop off seen in Kyle Rhea is smaller than that for the same time period in the Pentland Firth channel.

Basic Assumptions

The values for “number of turbines” are based on first and second generation MCT’s and assume 500 kW and 1 MW generators respectively. In the case of Kyle Rhea where we have less channel depth and so smaller rotor blades, the first and second generation refer to 250 kW and 500 kW units respectively.

The use of the arbitrary value of 60% of the initial power flux curve gradient was based on a conservative or more pessimistic estimate of where the increase in power from additional turbines will cease to be financially viable. This number could be pushed up to 80-90% (i.e 10-20% drop off) but our initial aim was to estimate it conservatively. Further work could look into carrying out a more in depth sensitivity analysis of this value.

The depth of the channel in Kyle Rhea is notably less than is the case in the Pentland Firth (around 22m compared with 50-70 meters). This would mean any MCT’s installed in Kyle Rhea would have to be of a much smaller rotor blade diameter. For our purposes we have used 7m as our rotor diameter and this is reflected in the channel model (see channel model for details).