Matteo Pregrasso – matteo.pregrasso@gmail.com – Master degree in Mechanical Engineering
updated on November, 2016

## Introduction

Fig. 1 – 50 kW 3 blades wind turbine

This project is about the dynamics and mechanical response  of a 50kW wind turbine blade. The first part of the project is the fluid-dynamics study and design of the blade, where forces and geometry are calculated with BEM (Blade Element Momentum theory) approach. The second part is about building the flexible model of a single blade which is rotating and force loaded (by the wind). The blade is monitored in terms of stress and translation displacement in different key points and with different wind velocities profile.

## Objectives

The objectives of this project are modeling the dynamics and mechanical behavior of the blade in standard conditions, in critical conditions and different wind velocity. After this preliminary study we can modify the structural geometry, choose the appropriate material and verify the fatigue stress life.

## The modelling problem

### Fluid-dynamics and design study

Fig. 3 – Chord distributions

Fig. 4 – Twist distributions

The fluid-dynamics study was made with BEM (Blade element momentum theory) approach [1]. Blade element momentum theory is a theory that combines both blade element theory and momentum theory. It is used to calculate the local forces on a propeller or wind-turbine blade. Blade element theory is combined with momentum theory to alleviate some of the difficulties in calculating the induced velocities at the rotor. In matlab I performed an optimized simulation, with genetic algorithm, varying chord, pitch, twist and the span distribution of the S81* airfoil series of the blade [2].  The algorithm reached the best individual with the lowest weight and the target power generation of 50 kW at 12 m/s wind speed and 65 rpm rotor velocity.  After, matlab outputs 10 scaled and rotated profile (S812, S813, S814 airfoil) along the 7.5m span. These sections are imported in Solid Works were the loft was made. After that I export, in parsolid extension, the connection between the blade to the hub and the blade.

Fig. 4 – Pareto front

### Connection and flex bodies in Adams

In Adams view I made the hub with a rigid cylinder and I import the parasolid file of the hub connection and the blade. I put a revolute joint between the hub and the ground and a fixed joint between the hub and the connection to the blade.

Now I want to make the blade flexible and before doing that I need to put some fixed joints between the blade and the connection. I make 6 fixed joints along the perimeter of first profile section (0.5 m span). Now I can make the blade flexible. In the bodies panel I select rigid to flex box and I create a new .MNF file. So now I need the blade’s material proprieties. I use carbon –epoxy composite (61% fiber) whit 140 GPa of Young’s module, 1600 kg/m^3 density and 0.26 Poisson ratio. I make a new material whit this character.

Fig. 6 – Mesh properties

I select 12 numbers of modes and in the geometry window I tick advanced setting and I select shell elements with triangle and curved shape.  I choose 10 mm shell thickness and middle stress layers and Y normal direction of the shell. Now I go to the attachments window and I wait for the meshing preview. I press find attachments (fixed joints between connection and blade) and after they are loaded I select one by one and I choose on the right ‘selection type: spherical, ‘attachment method: rigid’, ‘10 mm radius’ and I press ‘transfer IDs’. These actions converge the meshing points in the sphere volume to the fixed joint, which simulate the rigid attachment to the hub. Now I press ok and the final mesh is generated.

Fig. 7 – Attachements

### Forces and motions

Fig. 8 – Lift and drag forces

Firstly I make a state variable in elements-> state variable algebraic equation called ‘v’ and this is the wind speed variable. BEM program gives also the distribution along the span of the tangential and normal forces acting on the blade. For 3 different wind speed (6, 12, 16 m/s) I cumulate the front and normal forces in 5 points (1.172, 2.586, 4, 5.414, 6.811 m of span). I assume the forces acting points of all the 5 span sections are in this location ( X:0 , Y:0,  Z:* ).

Fig. 9 – Force distributions

In excel, for every span, I obtain a 3rd order regression trend line for the 3 different wind speeds. Now in Adams I make the 5 markers fixed to the blade and in plane orientation. For every marker I put X and Y single forces where I select body moving and custom characteristic. Now I modify the forces putting the function obtained in excel, changing the variable name ‘x’ in VARVAL (.pala_fissa_adams.v). So the forces are a function of wind speed ‘v’. The wind turbine is built for running at 65 rpm, so I apply a motion of (-390d * time) in the center revolute joint.

Fig. 10 – Force to wind speed interpolation

### Vibration and modes

Fig. 11 – First natural mode

In modify flex body we see a window where we can visualize the modes of the blade. The first 6 modes are the rigid modes. The other modes are flexional and torsional mode combined each other. The first natural frequency is about 34 rad/s (5.4 Hz), and consists of the the first flap-wise mode. The first edge-wise mode has a frequency of 126 rad/s (19.74 Hz) and the first torsion mode a frequency of 216 rad/s (34 Hz).

### Measures

Fig. 12 – Stress points

For better understand the flexional and torsional behavior of the blade I measure translational displacement Y of the 5 markers where the forces are placed. I also measure the Von Mises stress of 6 markers spaced 10mm in span from the connection fixed joints (this because in proximity of the attached nodes there are higher stress level from the reality).

## Simulations and analysis of results

I perform many simulations in the time domain varying the wind speed. The simulations are performed in the gravity field, lasting 50s and 10000 steps.

First simulation is performed with no wind (v=0)

Plot – 1 Translational displacements Y wind 0 m/s

Plot – 2 Von Mises stresses wind 0 m/s

In the displacement and stress plots we can see the sinusoid shape (with frequency 65rpm) of the measures due to the blade’s rotation and gravity interaction, after a transient of about 1-2s (indeed the simulation do not start from an equilibrium condition). The largest mean stress and amplitude of the stress fluctuation at the measured points are 75 MPa (centrifugal effect) and ±7 MPa (gravity effect) respectively. This is only a preliminary test: the blade can’t rotate without wind in the reality.

Fig.13 – Eigen values

After the simulation I linearized the vibrational modes from the rotating domain: in the interactive simulation control I generate the linear modes with ‘PSTATE’ from the revolute joint of the hub.

Plot 3 – Eigen values

Fig. 14 – First mode

Now I animate the modes: The first mode is about 6.20 Hz, for every wind shape simulation (like the others modes), and it’s a flex deformation about the minor inertial axis of the section (first flap-wise mode).

Fig. 15 – Second mode

The second mode is about 21.75 Hz and it’s a flection deformation about the major inertial axis of the section (first edge-wise mode).

Fig. 16 – Third mode

The third mode is about 32.33 Hz and it’s a flection deformation of second order about the minor inertial axis (second flap-wise mode).

Second simulation is performed with constant wind speed of 12m/s (design speed)

Plot 4 – Translational displacement Y wind 12 m/s

Plot 5 – Von Mises stresses wind 12 m/s

In the stress and displacements plots we can see the vibrations decrease slowly because the blade have a low damping ratio; after about 50s a stable equilibrium is reached. The largest mean stress and amplitude of the stress fluctuation at the measured points are 482 MPa and ±13 MPa respectively after 50s.

Plot 6 – Translational displacement Y wind 12 m/s zoom

Plot 7 – Von Mises stresses wind 12 m/s zoom

Third simulation is performed with a 12m/s constant speed plus 5 m/s cosinusoidal wind pulsing at 5 rad/s (0.8 Hz). I use this frequency and variation because in the normal duty days the wind gusts have approximated this shape [3].

Plot 8 – Translational displacement Y wind 12+5*cos(5*time)

Plot 9 – Von Mises stresses wind 12+5*cos(5*time)

In the displacement and stress plots we can see, after a transient phase, the sinusoidal shape of the measures due to the pulsing wind gust.  The largest mean stress and amplitude of the stress fluctuation at the measured points are 464 MPa and 121 MPa respectively after 50s.

Fourth simulation is performed with 12m/s constant speed plus 5 m/s cosinusoidal wind pulsing at 39 rad/s (6.2 Hz). I use this frequency because I want to simulate the resonance response of the blade. This is an unusual but severe condition for the material and we can verify the peak stress.

Plot 10 – Translational displacement Y wind 12+5*cos(39*time)

Plot 11 – Von Mises stresses wind 12+5*cos(39*time)

Plot 12 – Translational displacement Y wind 12+5*cos(39*time) zoom

Plot 13 – Von Mises stresses wind 12+5*cos(39*time) zoom

In the displacement and stress plots we can see, after a transient, the sinusoidal shape of the measures due to the pulsing wind gust. The amplitude is limited by the small damping of the blade only. The largest mean stress and amplitude of the stress fluctuation at the measured points are 436 MPa and 512 MPa respectively after 50s.

Fifth simulation is performed with step shape wind from 5 m/s to 20 m/s and from 15 s to 15.1 s ramp. This is a common situation of a sharp wind gust that invests the running blade.

Plot 14 – Translational displacement Y wind 5 to 20 m/s

Plot 15 – Von Mises stresses wind 5 to 20 m/s

We can focus around the step time and we can measure the peak stress and translation.  The largest mean stress and amplitude of the stress fluctuation at the measured points are 630 MPa and 315 MPa respectively.

Plot 16 – Translational displacement Y wind 5 to 20 m/s zoom

Plot 17 – Von Mises stresses wind 5 to 20 m/s zoom

Animations

The animations are made around the wind’s step moment: we can see the hot spot (most stressed node) with its value and frame and also the colored Von Mises stress nodes.

Blade vibration with following camera isometric view:  https://youtu.be/GPh6jL8mIcU

## Conclusion

A flexible model of a single wind turbine blade has been analyzed. The design has been performed based on the BEM theory. The resulting model has been generated in SolidWork, then imported in Adams, where it was meshed and simulated. A basic wind model has been considered. The system has been analysed in terms of vibration modes and time domain response. The deflection and stress have been computed in different wind scenarios, namely no wind, constant wind, constant wind plus fluctuating wind, wind gust step.

## References

[1] BEM Theory for HAWT design – Andrea Dal Monte https://elearning.unipd.it/dii/pluginfile.php/36365/mod_resource/content/1/L1_BEM.pdf

[2] NREL’s S-Series Airfoils https://wind.nrel.gov/airfoils/shapes/S812_Shape.html

[3] Guidelines for converting between varius wind averaging periods in tropical cyclone condition – B. A. Harper  J. D. Kepert J. D. Ginger https://www.wmo.int/pages/prog/www/tcp/Meetings/HC31/documents/Doc.3.part2.pdf