Module 5.2 Wind Turbine Design (Continued)

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Module 5.2Wind Turbine Design (Continued)

• Lakshmi N Sankar
• lsankar_at_ae.gatech.edu

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OVERVIEW

• In Module 5.1, we gave preliminary comments about
  rotor design.
• We reviewed the possible approaches to rotor
  design (parametric sweep, optimization, inverse
  design, genetic algorithm).
• These may be combined.
• For example, a response surface (or a carpet
  plot) of the power production as a function of
  design variables may be curve fitted, and
  searched for an optimum combination.
• While increasing the rotor radius is a good way
  of increasing power (since power varies as swept
  area) this greatly increases the weight and
  ultimately the cost of the system.
• Other parameters should also be optimized.
• In Module 5.1, we also looked at some available
  airfoils and their characteristics.

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Selection of Planform

• Once the airfoils are chosen, and the best lift
  coefficient (yielding highest Cl/Cd)at which the
  airfoil will operate are known, we can determine
  how chord c should vary with r.
• The idea is to set the axial induction factor to
  be equal to 1/3 equal to the Betz limit- from
  root to tip.
• This value of induction factor yields the highest
  possible power from actuator disk model studies
  in Module 2.
• Optimum planforms are possible for a given tip
  speed ratio, but not for all tip speed ratios.

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Recall Thrust Produced by an Annulus of the Rotor
Disk
Area 2prdr Mass flow rate 2prr(U8
-v)dr Change in induced velocity 2v Thrust
produced over this annulus dT dT (Mass flow
rate) (2v, i.e. Twice the induced
velocity at the annulus) 4prr(U8
-v)vdr dT 4prr U82(1-a)adr (1)
dr
r
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Blade Elements Captured by the Annulus
Thrust generated by these blade elements
dr
Some blade sections near the root and tip may not
behave like 2-D sections. This is due to a loss
of lift as pressure Tends to equalize between
upper and lower sides of the rot and tip. We
correct this with a loss factor F
r
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Optimum variation of Chord with r

• Equate 1 and 2 (neglecting drag effects, which
  are small)

small
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Optimal Variation of Chord vs r
Local solidity
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Variation of Chord with r for Optimum Rotors

• The previous slide states that chord should vary
  as 1/r , large near the root and small near the
  tip.
• In practice, linear tapered blades are easier to
  manufacture.
• The design variables root and tip chord- are
  parametrically varied, with a linear taper, to
  find optimum combinations.

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Optimum Number of Blades

• In the previous derivation of optimum variation
  of chord with radius, Bc/pR is a non-dimensional
  combination, where B is the number of blades.
• This quantity is called local solidity.
• If solidity is high, Cl can be low and the rotor
  can operate away from stall.
• On the other hand, if solidity is too high,
  blades are subject to extreme wind loads.
• This equation says we can have a large number of
  blades (B) with small c, or vice versa.
• In practice fewer number of blades (2 or 3 at
  most) with a large chord is preferred, both from
  a cost and strength perspective
• Blades and appendages are costly!)
• Larger chord, implies thicker blades that are
  structurally stronger.

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Optimum Variation of Twist with r
Twist
Angle of attack For best L/D
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Selection of Tip Speed Ratio

• Best tip speed ratio WR/U? may be found by a
  parametric sweep, using a computer code such as
  WT_PERF or a spreadsheet based analysis.
• Initially, as tip speed increases, for a fixed
  wind speed, f increases increasing the propulsive
  force.
• Power increases, but optimum induced velocity has
  not been realized yet. Efficiency is low.
• As tip speed further rises, efficiency rises and
  peaks.
• At higher tip speeds, the airfoil sections begin
  to operate at non-optimum angles of attack, and
  propulsive force decreases.
• Power decreases.

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Variation of Power Coefficient with Tip Speed
Ratio for a Representative RotorNREL Phase VI
RotorRecall 16/27 is the maximum Power
Coefficient (Betz Limit)
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In summary..

• Keep number of blades small (2 or 3).
• Keep solidity sufficiently high to avoid stall,
  but small enough to avoid extreme airloads as
  well.
• Use linear taper ratio for simplicity in
  manufacturing.
• Consider nonlinear twist to keep induction factor
  close to 1/3 over most of the rotor.
• Nonlinear twist is easily accommodated in modern
  wind turbines.
• Operate, if possible, at optimum speed ratios
  where power production peaks.