Frog Investigation – Dr. Bob Cattley

Investigation of Losses from Drag on Ballast of 1/100th scale model PS Frog

Dr. Bob Cattley.

Contents

	Summary
Definitions and test model details
Method
Results	Vertical plate
	Torpedo
	Disk
	Original design
	Cylinder
Discussion
Conclusions
Further Work
Appendix 1	Specification for investigation of losses from drag on ballast of PS Frog
Appendix 2	Calibration of wave gauge
Appendix 3	Calibration of wave generator.
Appendix 4	Tuning PS Frog and power take off
Appendix 5	Q as a measure of the performance of wave energy converters
Appendix 6	Impulse tests on the wave tank Conclusions drawn from tank impulse tests
Appendix 7	Bretschneider forcing spectrum tests
Appendix 8	Examination of the time series and spectra of the vertical plane design
Appendix 9	Natural modes of the tank

References.

Summary:

This report examines the performance of a 100th scale model of PS Frog in Lancaster University’s wave tank with various arrangements of ballast in monochromatic seas in accordance with the specification in appendix 1.

At the request of Black and Veach simulation of real seas using the Bretschneider spectrum was attempted also, the results are in appendix 7. Unfortunately, there was not enough time allowed by Black and Veach to satisfactorily complete the tests.

The arrangement that produced the highest power output in monochromatic sea was the vertical plate design shown in figure 1. The cylindrical design of figure 5 was a close second. These both had a power output more than 3 dB greater than the original design.

It is shown in appendix 6 that the tank interacts with the model and produces misleading results. Appendix 9 shows the tank natural modes and it is hypothesised that the tank second natural mode is coincident with the 005 mode of the fluid in the tank. Appendix 8 shows that the tank resonance does not enhance the power output of the model under test.

Further work required has been highlighted.
Definitions and Test Model Details

Definition of directions:

X (100) in the direction of the incident wave, along the wave tank
Y (010) in the vertical direction
Z (001) in direction transverse to the incident wave (across the tank)

Ballast shapes:

1. Vertical plate, square edges
X = 12.0 mm
Y = 75.0 mm
Z = 310.0 mm

Figure 1, Vertical plate test shape.

2. Torpedo, cylinder with approximately spherical ends
X = φ 45.1 mm
Y = 186.4 mm
Z = φ 45.1 mm

Figure 2, torpedo test shape

3. Disk, flat ends
X = φ 118.2 mm
Y = φ 118.2 mm
Z = 25.5 mm

Figure 3, disk test shape.

4. Original plate, rounded leading edges
X = 89.1 mm
Y = 10.4 mm
Z = 312.9 mm

Figure 4, original design

5. Cylinder, approximately spherical ends
X = φ 45.1 mm
Y = φ 45.1 mm
Z = 186.4 mm

Figure 5, Cylinder test shape.

Table 1: Ballast leading dimensions.

Abbreviations
PTO power take off dB decibel
f0 resonant frequency BW bandwidth

Method

The 100th scale model of PS Frog was fitted with each test ballast weight shown in figures 1 – 5 and held in the dynamometer in the wave tank. The dynamometer only allows movement in pitch and surge. The forcing frequency that produced the maximum power with arbitrary damping was determined. The model was excited at this frequency and the damping factor altered to determine the value for maximum power output. The model was then excited with the previously determined damping factor by a range of frequencies to determine the spectral properties of the arrangement. The model was excited by monochromatic waves at discrete frequencies controlled by the uncalibrated wave generator data files. The wave height was not controlled to a standard value by the wave generator. This means that the power measurements whilst believed to be correct in absolute terms could not be directly related to measurements made at other frequencies. All power measurements were normalised as follows:
1    The wave height (peak value) was averaged and recorded over 20 seconds at the position which the model would have occupied as a voltage at each waveform used
2   The wave gauge was calibrated against a length standard of 20.00 mm
3   The wave gauge constant was calculated (see appendix 2) 13.995 mm / volt
4   The actual wave height was calculated from the above constant
5   A power correction factor was calculated by taking the square of the reciprocal of the gauge voltage.

Measurements of power normalised as above are believed to be comparable to each other.

Measurements were made and recorded in the standard way used by the wave energy group. Time steps are 32 milliseconds. There is a time record of each measurement summarised in the results section full details are stored in the wave tank computer under C:\logged records\carbon trust ballast exps\… in various subdirectories identifying the test configuration. The files total 142 containing over 7.5 M bytes of data. File names contain unambiguous information about the wave source file, hull loading, wave frequency and damping. The data is organised in eight columns as follows.