This is an individual exercise aimed at assessing your ability to use mathematical analysis and computational tools to arrive at a preliminary aerodynamic design of a wind turbine rotor.

Overview of the assignment

You will be allocated a rated wind speed, power output and tip speed ratio for a single 3-bladed wind turbine. The objective is to use the theory covered in the Maths lectures, along with the XFLR5 computational tool, to develop a wing turbine rotor geometry which will deliver your assigned power output for your assigned wind speed and tip speed ratio. You will then evaluate that rotor using the slightly more complete aerodynamic theory which includes wake swirl effects.

Learning outcomes

This exercise will contribute to the two module learning outcomes listed below:

• Apply the science of fluid dynamics to model the effectiveness of wind, marine and hydro energy extraction using fluidic devices.
• Evaluate the factors influencing the design and operation of fluid energy devices, including energy policy, the planning process, economic considerations and the data required to support these.

Analysis and reporting

You must submit a short report, including equations and graphical results as necessary, outlining your progress through the following steps of a rotor design process. The report should not exceed 4500 words (excluding captions, equations, references, title pages, etc) and should contain no more than 20 figures. You may expect the main body of your report to be around 20 pages (excluding title pages and references). Pay attention to the specification below in respect of section headings, figures and tables.

1. Your report should commence with a one-page introduction to the wind turbine market in your segment. To prepare for this, you need to research existing (or planned) wind turbines with rated wind speed and power outputs which are within 25% of your allocated parameters. Hopefully you can find 2-3 competitors within this range, but don’t dig into detail for more than 5-6. These competitors should be summarised in a table. In the process of acquiring this data, you should also try to get a feeling for the market opportunities for a new turbine of your specified rating. Extensive data from the US Wind Turbine Database¹ and wind turbine and power curve data from TheWindPower.net² are available on Blackboard to help with this initial task.
2. The next section involves getting a ‘feel’ for the important but unknown dimensionless parameters by extracting the following data on your competitor turbines, so far as it is available:
   1. the efficiency 𝜂 of a typical wind turbine power transmission (gearbox and generator)
   1. the power curve, 𝑃 = 𝑓(𝑈), which can be used to determine the power coefficient of the rotor, 𝐶P = 𝑓(𝑈), using the rated wind speed, the rotor disk area and – don’t forget – the transmission efficiency above
   1. approximate chord width, 𝑐, of the turbine blades at 20% and 90% of rotor disk radius, 𝑅, expressed in dimensionless form, 𝑐⁄𝑅

The use of dimensionless parameters stops you from simply copying an existing design: they characterise how the physical parameters of a wind turbine scale with the available power density and required output power. This section should include explanation of your values of transmission efficiency, plots of power curves and power coefficient with one or two supporting equations explaining how you derived 𝐶P, and some figures justifying your dimensionless chord widths.

• Based on the preceding analysis, and your understanding of the limiting Betz efficiency for a rotor, decide upon a credible, but improved, design power coefficient which will be the performance objective for your design. With this value of power coefficient, and a representative transmission efficiency, you can then determine your required rotor disk area. This will be a very short section with one or two supporting equations.

1 Data | USWTDB (usgs.gov)

2 Wind energy database (thewindpower.net)

Having predicted an expected value of power coefficient, from this point on you can assume that your rotor will actually operate at the Betz limit of 𝐶P = 16⁄27 (so 𝑎 = 1⁄3 as per the Sasha’s notes).

• From disk area you can obtain the rotor radius (blade length) and, again referring to preceding analysis, estimate the likely chord lengths at 20% and 90% of rotor disk radius. Use these two locations on the blade, along with your design tip speed ratio, rated wind speed and a velocity triangle analysis, to estimate the range of blade chord Reynolds numbers for which you will need to analyse the performance of the blade aerofoil sections. Remember to assume Betz flow angles for this calculation. Again, a brief section with supporting diagrams and equations.
• Visiting the UIUC aerofoil database, sources if you wish, select a range (10-15) of candidate wind turbine aerofoil shapes for 2D aerodynamic analysis. Some example geometry image (GIF) files, available from this source, are shown at Appendix A. Download the geometry co-ordinate files (ideally in a format compatible with XFLR5 – see notes at Appendix B) and, following the process outlined on the XFLR5 worksheet, analyse each section over suitable ranges of incidence (0° to 20° should be plenty) and Reynolds number, as determined earlier. You are particularly interested in the best L/D ratio and the angle of incidence at which it occurs. Care is required in reporting this work: do not overload the report with figures but do make sure that the important aspects of aerofoil performance are presented graphically.

• Down-select a set of different aerofoil sections for different parts of the blade. Bear in mind the following points:
  • Different aerofoils may perform better at different Reynolds numbers, but the aerofoil shape should not change abruptly as you move from hub to tip.
  • You will require thicker sections nearer the hub, for structural reasons.

You can exercise the option (see marks below) to define your own aerofoil sections. Typically, you would decompose each geometry into camber (centreline) and thickness (distance between surface and centreline) distributions and ‘blend’ these independently of each other. The actual performance should be tested before adoption of your new aerofoil section.

This section must contain an explanation of your decision-making and a summary of the chosen sections.

• Apply the 1D (no swirl) theory covered in sections 7-8 of Sasha’s lectures, equations 62 and 63, to determine the ‘optimum’ chord width and pitch angle (defined in section 9) for your chosen blade sections at each of

0.2  r/R  1.0 in steps of 0.1 r/R. This analysis is at your design conditions (rated power output, wind speed, tip speed ratio) and you can again assume that you are operating at the Betz limit when calculating your flow angles. Notes:

1. Don’t worry about radii r less than 20% of tip radius R (but you should explain why).
2. There is no need to force a linear trend to either chord or twist.

You should present sufficient equations to demonstrate the main steps in the analysis without overloading this section with equations. At the end you should tabulate the section, chord width, blade pitch and resulting angle of incidence for 0.2  r/R  1.0 in r/R steps of 0.1, leaving space for later additions to this table.

• Next, analyse the predicted performance your design including the effects of swirl downstream of the rotor and the effects of tip loss, sections 10-11 of Sasha’s lectures. This is best done numerically using e.g. Excel.
  • First you need to determine the effect of the rotor wake on the flow angles at the blades. The relevant equation in Sasha’s notes is 72, which relates the lift generated by the blades to the swirl in the wake. This equation, with different coefficients at each r/R, must be consistent with the lift curve 𝑐L(𝛼) calculated by XFLR5 at the same radius: effectively you are looking for the intersection point between the wake condition, equation 72, and the aerofoil performance 𝑐L(𝛼): it is recommended that you first carry out an additional XFLR5 analysis for your selected aerofoils with a finer resolution of angle of incidence (say 0.1°) but only in the vicinity of maximum L/D.

Then, for each section, plot the curve defined by equation 72 on the same axes as the lift curve from XFLR5 to determine where they intersect: this defines the actual operating angle of attack and section lift coefficient at each radius.

(8a continued)

Your graphs can be put in an appendix, but your operating angle of attack and section lift coefficient at each radius should be added to the rotor geometry table presented at the end of section 7. The values should correspond clearly to the intersection points shown in your graphs.

• Once you have tabulated the actual lift coefficient distribution across the blade, integrate this numerically (using equations 74 – 76 in Sasha’s notes and the trapezium rule) to determine the predicted power coefficient, 𝐶P, of your rotor design.

Section 8 should demonstrate that you understand the analysis, again without overloading the report with equations, while presenting (in the main report and the appendix) sufficient results to validate your analysis. Comment on the predicted 𝐶P and the values you determined for your competitor turbines.

• Conclude your report with a reflective discussion on the design process and what you imagine the next steps might be, before your design is committed to production.
• Make sure your report has a notation section and a list of references.

Effort and mark breakdown

This assessment is worth 35% of the module mark and should require typically 30-40 hours of effort. The indicative mark breakdown, across the mandatory components (not italicised) above, is as follows:

• Up to 10% for the introduction (section 1)
• Up to 15% for the research and analysis of competitor turbine(s) (2 – 4)
• Up to 20% for the aerofoil analysis and down-selection (5 & 6)
• Up to 10% for the blade design using 1D theory (7)
• Up to 15% for the rotor performance verification (8)
• Up to 10% for the reflective discussion (9). Additional marks are available for:
• The scope of your competitor dataset, i.e. number of turbines (1) considered in (2): up to 5%
• The scope of your aerofoil analysis and discussion (5): up to 5%
• Any aerofoil ‘design’ work (6): up to 10%

Untidy or badly laid-out reports, poorly resolved figures, and any deficiencies in item 10 will be penalised by up to 15%.

Submission arrangements

The report must be submitted as a PDF via Blackboard using the link provided on the module page. Learning support needs

Please make sure that the Module Organiser is aware of any agreed support needs relevant to this assessment.

Appendix A: example wing sections from the UIUC aerofoil database.

Appendix B: important points when downloading geometries for analysis by XFLR5:

• XFLR5 only accepts one layout for co-ordinate data: the file must have an initial title line, followed by two columns of co-ordinates starting and finishing at the trailing edge of the aerofoil (so: 1.00 0.00). The file should have a .dat extension.
  • The UIUC database contains files in two different formats, intermingled (shocker). The above format (great), and the old XFOIL format which is
    • title line
    • two integers (number of upper surface points, number of lower surface points) sometimes entered as reals (ugh)
    • blank line
    • two columns of upper surface co-ordinates starting at the leading edge (0.00 0.00) and finishing at the trailing edge (1.00 0.00) of the aerofoil
    • another blank line
    • two columns of lower surface co-ordinates starting at the leading edge (0.00 0.00) and finishing at the trailing edge (1.00 0.00) of the aerofoil
  • If your data is in format (2), you need to:
    • import into Excel and shuffle stuff around so that the co-ordinates are in adjacent columns
    • select the upper-surface co-ordinates (both x and y) and sort them by x co-ordinate in reverse order (so the list starts with 1.00 0.00)
    • delete the blank rows and the row containing the numbers of co-ordinates
    • format the columns so that there is a clear space between the co-ordinates and the LH margin of the cells containing them
    • re-export in text format with a .dat extension
    • open in something like WordPad to check that it looks OK
  • To import into XFLR5, open the programe, select File -> Open and locate your saved geometry file (with a .dat extension). Select the File -> Direct Foil Design menu option and have a look at your aerofoil geometry – there should be no line down the middle, and no weird lines heading off to (48 48) or (61 61). You can then Save your Project, which will result in a file with the .xfl extension.

• Any problems or weird-looking results from XFLR5, contact Chris.

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