Core: Energy 210

Master’s Programme: ENERGY TECHNOLOGY

‘Energy Physics and Energy Technology’

LECTURE: Aerodynamics of Wind Turbines

Thomas Hansen Email: thomas.h.hansen@ntnu.no

Objective

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• Aerodynamics of horizontal-axis wind turbines

• Airfoil theory

• Numerical tools

• BEM method

• Navier-Stokes simulations

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• Danish type – traditional three bladed turbine normally used

• Structurally balanced

• Rotational velocity and noise considerations

Number of blades

Aerodynamics of HAWT`s

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• Some fundamental definitions for a HAWT are the;

• Swept area

• Solidity

• And the tip speed ratio, lambda

Increasing power

5

• The swept area, A is the parameter used to increase the power production from wind turbines

• Density is constant

• Wind speed is difficult to change, but cubed

• Cp (efficiency of turbine) is close to maximum possible

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Rotor blade and airfoils

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Rotor blade and airfoils

• Due to structural requirements thicker airfoilsare needed towards the root

• The blades are twisted to compensate for the reduced rotational velocity (and flow angle) towards the root

• Aerodynamic airfoil data is normally needed to design or analyse a wind turbine rotor blade

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• Fundamental definitions for airfoilgeometries

• Zero camber means symmetrical airfoil

• Position and value for maximum thickness is important for wind turbines

Airfoil geometry definitions

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• Lift is perpendicular to the free-stream wind

• Drag is parallell to the free-stream wind

• Moment is positive nose-up

• All forces with respect to 25% of the chord

Airfoil theory

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• The conversion of the free stream wind into tangential force occurs due to the shape of the rotor blade airfoils

• Most of the tangential force is produced in the tip region of the blade

• Ct is maximized when the ratio Cl/Cd for the airfoil is maximized

• Cn is normal to plane of rotation, and bends the blade

Force coefficients on wind turbine

Wind tunnel experiments

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• To obtain high quality airfoildata, wind tunnel experimentsare often performed

• Experiments are expensive and time consuming

• Quality and accuracy of thetest model, effect themeasured data

XFOIL – 2D numerical wind tunnel

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• Panel method with fully-coupled viscous/inviscid interaction

• Developed by Professor Mark Drela at MIT

• Most used tool for creatingairfoil data for the design ofrotor blades

• Predicts airfoil performancewell for attached flow

http://web.mit.edu/drela/Public/web/xfoil/

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• XFOIL calculates the pressure and the boundary layer flow around the airfoil

• Predicts steady aerodynamic derivatives such as Cl, Cd and Cm

• Very fast and accurate tool

Pressure coefficient

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XFOIL calculations

• Constant Re (shown is Re = 3 million)

• Sweep in angle of attack alpha, like on a wind turbine

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XFOIL calculations

• Important characteristics for wind turbine airfoils, especially in tip region of rotor blades are;

• High Cl/Cd ratio

• Reasonable span in alpha between design-Cl and stall-Cl

• Soft stall

• Limited drop in Cl after stall to avoid excessive forces on turbine in case of wind gust or slow working pitch system

Stall

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• More details about flow and wake

• Time consuming

• Mesh dependent

• Normal CFD does not capture laminar part of the flow

• Transition modelling difficult

Navier-Stokes CFD simulations - 2D

Normal turbulent CFD simulation

CFD simulation with transition model

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• Blade element momentum method, used for design and analysis

• Navier- Stokes simulations, mostly used for analysis

Numerical tools for predicting wind

turbine rotor blade performance

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• Fast and accurate method to calculate the performance of wind turbine rotor blades

• Most used design/analysis tool in the wind energy industry, almost all turbines are designed using BEM

• Combines momentum theory and aerodynamic airfoil data (at finite blade elements) to predict performance of rotor blades

Blade element momentum method

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• One dimensional stream tube model for an ideal rotor

• No turbine present, rotor blades modelled as permeable, actuator disc

• No friction on disk

• No rotational velocity component in wake

1-D momentum theory

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• Can be used to derive relationship between the velocity V0, u1 and u, the thrust T, and the absorbed shaft power P

• The thrust is the force in the stream-wise direction due the pressure drop over the rotor, that reduce the wind speed from V0 to u1

1-D momentum theory

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• The axial induction factor a, is a measure for how much power is extracted at the actuator disc

• It can be visualized by how much the wake expands behind the disk

• In the figure, a increases according to the increase in Ct

1-D momentum theory

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• The power and thrust coefficients for an ideal 1-D wind turbine can be expressed as a function of the axial induction factor, a

• Betz limit = 0.5926, for a = 1/3

• What is wrong in the figure? Hint, Ct at high values of a…

1-D momentum theory

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• Combines momentum theory with the local event at the actual blade

• Uses the deflected flow as calculated with momentum theory and adds the influence due to the aerodynamic airfoil forces

• The stream tube model is discretized into N annular elements of height dr

• At each element the actual airfoildata is used to compute the rotor performance

Blade element theory

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• No radial dependency – what happens at one annular element tube is not felt by the others

• The force on the blade is constant in each annular element tube

• Prandtl`s tip loss correction used to compute rotor with finite number of blades

Blade element theory

Glauert correction used to correct Ct for large axial induction factors, where thesimple momentum theory brakes down

a’ : rotational speed in the wake

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1. Initialize a and a’

2. Compute the flow angle, phi

3. Compute the local angle of attack alpha

4. Read lift and drag coefficient airfoil data from table

5. Compute Cn and Ct

6. Calculate a and a’

7. If a and a’ has changed more than given tolerance, go to step 2, else stop

8. Compute the local loads on the element

BEM algorithm2.

3.

5.

6.

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• Corrects the assumption of having infinite number of blades in the blade element momentum method

• The tip loss correction effects step 6 in the BEM algorithm

Prandtl`s tip loss factor

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• Corrects the un-physical thrust coefficient at high values of a, predicted with momentum theory

• Drag coefficient of circular flat plate is about 2, hence Ct of 2 when a = 1 makes sense

• The Glauert correction only effects the calculation of Ct at step 5 in the BEM algorithm

Glauert correction for high values of a

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• Example of BEM simulation using the NTNU model wind turbine

• Diameter 0.944m

• S826 airfoil on full blade

• Simulation time is seconds

BEM – simulation, same as task

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BEM – simulation, same as task

• Cp well predicted using BEM

• In the shown example the airfoil data is computed using the correct Re at each element for the different TSR

• Ct underpredicted slightly

• Possible reason for theunderprediction might be that thetransition part at the root is not included in the BEM calculations

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Example of Reynolds-Averaged-Navier-Stokes

(RANS) CFD simulation of wind turbine in 3D

Navier-Stokes Simulations

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• Experiment performed for validation of numerical tools

• Large database ofaerodynamic and aeroelastic measurements

• 10m in diameter - stall regulated

• Use single airfoil

• NASA Ames wind tunnel

NREL Ames Phase VI Experiments

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• STAR CCM+, commercialNavier-Stokes solver

• Built-in tools from CAD design to post-processing

• Automated meshing

• Large amount ofturbulence models

• RANS LES

The Navier-Stokes solver

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• One blade is instrumented

• Pressure orifices at five span-wisepositions

• Normal force coefficients comparedto validate the CFD predictions

Validation in 3D

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• The surface model is the starting point for creating the CFD mesh

• To reproduce thegeometry of the windturbine correctly a goodsurface model is needed

• Surface model createdusing ProEngineer

3D - surface model

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• Two bladed turbine -only half domain neededdue to symmetry

• Periodic conditions

• Moving reference framemodel used for rotation

• Simulations performedsteady state

• k-omega SST turbulencemodel used

Boundary conditions

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Surface mesh

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Volume mesh

• Mesh created using STAR CCM+

• Trimmed hexahedral mesh

Refinement blocks used to bettercapture the flow in the wake

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7 m/s - constrained streamlines

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Pressure coefficients - 7 m/s

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10 m/s – constrained streamlines

Slide 41 / 26-Apr-16

RANS Wake

Slide 42 / 26-Apr-16

Large Eddy Simulation - Wake

• Detailedinformation aboutthe flow in the wakepossible using LES

• Very time consuming

• Requires largecomputer, 1000 CPU cluster used to calculate the shownexample

• Industry is startingto use LES to studydifferent types ofwind turbine flows

43

Questions?

Vertical axis

Wind Turbines

Energy210

Thomas Hansen

thomas.h.hansen@ntnu.no

Introduction

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• Objective: Aerodynamics of Vertical-axiswind turbines

• VAWT exist in many shapes and configurations – mostly small in size

• They all follow the same aerodynamicprinciples

• At the start of the wind turbine age some 30 years ago, VAWT wasinvestigated, but lost to the HAWT

• Recent interest in VAWT is based onpossible benefits for offshore application

Aerodynamics of VAWT`s

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• The geometry of a VAWT can be defined by:

• Swept area

• Solidity

• Beta

• For a given solidity the chord length is a function of Beta

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• The conversion of the free stream wind into torque occurs due to the aerodynamic shape of the rotor blades

• The torque is maximized when the ratio Cl/Cd is maximized

• The better the efficiency of the airfoil, the higher the torque

Force coefficients

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Single blade, full rotation

• The ratio of the rotational velocity compared to the free-stream wind is called the TSR or lambda

• The TSR defines the flow conditions on the rotor blades

• Due to the rotation the relative velocity of the flow and the angle of attack on the blades changes

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Lambda sweep, geometrical relation

• Pure geometrical relation

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Induction on VAWT

• For a given solidity the VAWT system will converge towards some state

• For increased values of TSR, the velocity field will be reduced, in the downwind region

• To produce maximum power the VAWT needs to operate at its optimum TSR

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Angle of attack on airfoil

• When extractingenergy from the freestream wind thevelocity in thedownwind half of therotation is reduced

• The reduction in velocity also leads to reduced angles ofattack on the airfoils

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Torque coefficient

• Semi-analytic methodused to investigate thegeneration of torque for the single blade

• Lift and drag coefficientsare generated using XFOIL

• Less torque is produced in the downwind sector due to the lower wind speed

Simulating a vertical axis wind turbine

using Navier-Stokes CFD

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NORCOWE VAWT concept

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• Design a floating VAWT that is more cost-effective than the traditional designs

• Maintain the benefits of the simple VAWT design

• Lower the weights and C.G.

• Smaller floater than for the equivalent sizedHywind HAWT?

• Generator in protected environment

• Easy maintenance

2.3 MW VAWT

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• Maintain constant tip speed ratio on blades by increasingthe diameter of the turbine

• Length of blades about 100 m

• Mean diameter about 55 m

• Uses 21 % thick symmetricalNACA airfoil

• Solidity = 0.3

Navier-Stokes simulation

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• Navier-Stokes simulations on a two dimensional mesh

• Mesh created using a hybrid structured/unstructured mesh

• K-omega SST turbulence model

Two dimensional hybrid mesh

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• Hyperbolic extruded prism layer around airfoil

• Rotation modelled using movingmesh region

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Tip speed ratio = 1=> The turbine blades are stalled for most of the rotation, induction factor is low.

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Tip speed ratio = 3=> Fully attached flow on the blades, the turbine is only mildly affected by the wake, close to optimum energy capture.

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Tip speed ratio = 5=> The turbine blades operate in its own wake, induction factor is increased

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Tip speed ratio = 7=> Turbine blades operate totally in wake, induction is further increased. At higher tip speed ratios the turbine will start to act as propeller

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Power coefficient

• A three bladed VAWT with solidity 0.3 have best performance at a tip speed ratio of 3-4 (HAWT 8-9)

• The turbine should be operated at its design tip speed ratio for increased wind speeds up to rated condition

• At wind speeds higher than rated the tip speed ratio should be decreased to reduce the loading

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TSR = 3.5, turbulence

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TSR = 3.5, velocity and streamlines

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Power production

• The cyclicaerodynamic nature ofthe VAWT makes thepower produced cyclicduring a full rotation

• For TSR above theoptimum, theamplitude of thepower grows in size

• This cyclic powerproduction introduces large unsteady forcesto the VAWT system

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Forces

• Forces in the direction ofthe wind

• Forces normal to the wind

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NORCOWE VAWT summary

• The dynamic forces produced by theblades of a VAWT are significant and grow in size for increased TSR

• The large and dynamic forces cancel outmost of the benifits from using a largesize VAWT compared to a HAWT

• Startup difficult, stopping the turbine at high wind speeds difficult

• Not easy to design MW class offshore VAWT that will last for 20 years

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Questions?

TASK – BEM

using QBlade

Energy210

Thomas Hansen

thomas.h.hansen@ntnu.no

Objective

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• Simulate theperformance of a wind turbine usingBEM

• Compare BEM resultsto experimental windtunnel data

• Know about QBladefor future projects

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Link to QBlade video: https://www.youtube.com/watch?v=T9laLMswJrw