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Object To determine the optimum Tip Speed Ratio for the model tidal turbine.
Theory The speed of the blade tip is given by the circumference of the blade tip circle (pD) divided by the time taken for the blade to rotate once (60/RPM). Thus
The turbine efficiency depends on the Tip Speed Ratio (Andrews and Jelley, 2013. Yaakob et al., 2013). The Tip Speed Ratio is the ratio of the speed of the blade tip to the flow speed:
In the experiments, we measure the output voltage, V, for a load, R and the output power is given by
The power coefficient Cp is defined as the ratio of the output power from the generator, PO, to the input power from the flow, PI = ½ r A U3. Substituting A = D2 we have the Power Coefficient as:
Where vtip is the speed of the blade tip (m/s) turning at RPM Revolutions Per Minute
D is the diameter of the turbine (m)
l is the Tip Speed Ratio
U is the flow speed (m/s)
V is the output voltage (V) against load resistance (R) ohms
PO is the output power from the generator (W)
PI is the input power from the wind (W)
Cp is the power coefficient or efficiency of the device
r is the density of water, taken as 1,000 kg
Turbine Diameter D m
DETAIL INSTRUCTIONS OR FORMAT OF THE REPORT
750 word reports should follow the OTMRAC structure:
Object 10 Broadly introduce the topic and derive the objective
Theory 10 A referenced derivation of the appropriate theoretical equation(s)
Method 10 Describe the experimental procedure or data gathering exercises using the past tense. Examples of calculations etc. The test of the methodology is that it should be written in a manner so that your work could be replicated by another and produce the same results.
Results 10 List and plot the data as they were measured but do not undertake any secondary calculations
Analysis 20 Calculate, tabulate, plot and describe any derived parameters and test the theory
D&C 40 Draw appropriate conclusions making reference back to the objective(s) and to the theory being tested. Is the theory supported, if not, why not? Discuss the errors.