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Dynamic stall modelling for wind turbines
- 1. 1 Dynamic Stall Modeling for Wind Turbines Muhammad Arsalan Khan European Wind Energy Master Rotor Design – Aerodynamics Supervisor ECN: Dr. Gerard J. Schepers Supervisor TUD: Dr. Carlos S. Ferreira Supervisor DTU: Prof. Niels N. Sorensen
- 2. 2 Outline • Motivation • Objective • Methodology • Code Description • Results – New MEXICO – Standstill Conditions – Improvement of Models – Rotating Yawed Conditions – AVATAR Case Study • Conclusions
- 3. 3 What is Dynamic Stall ? U∞ U∞ Angle of Attack Lift Stall Disclaimer: Animations are exaggerated
- 4. 4 Motivation • Dynamic Stall (DS) • Relevance for Wind Turbines – High Freq. DS • Turbulent environment • Storm Conditions – 1P DS • Yaw misalignment • Wind shear • Implications: • Fatigue • Instabilities – Aero. Damping • Cost of Energy Graphics adapted from Leishman, “Principle of Helicopter Aerodynamics”
- 5. 5 Objective • Comparing the performance of different dynamic stall models in yawed and standstill conditions by using New MEXICO experimental data for validation. • Dynamic Stall Models used: – Snel Model – Beddoes Leishman Model – ONERA Model
- 6. 6 Methodology New MEXICO Data Analysis • Data Quality Assessment • 3D Airfoil Polars Standstill Conditions • Validation of BEM + DS Models • Cross-Flow Principle • AVATAR Case Study Yawed Flow Conditions • Stall delay models • Validation of BEM + DS Model • Optimum BL Model Parameters ECN Aero-Module
- 7. 7 Code Description Graphics taken from Boorsma, “ECN Aero-Module User’s Manual v238” • ECN Aero-Module – Aero-BEM • Classical BEM Theory • Annulas Average Approach • Based on implementation in PHATAS – Aero-AWSM • Lifting Line Model • Vortex Wake Model
- 8. 8 Code Description • Dynamic Stall Models – Snel’s Model • 1st Order Model • 2nd Order Model – Beddoes-Leishman Model • Attached Flow Module • Separated Flow Module • Leading Edge Separation Module • Vortex Lift Module – ONERA Model • Linear attached flow • Non-linear separated flow
- 9. 9 Results – New MEXICO • DS in Yaw 24 m/s -30o
- 10. 10 Results – New MEXICO • DS in Yaw 24 m/s -30o 12 9 3 6
- 11. 11 Results – New MEXICO • DS in Standstill – Self-Induced
- 12. 12 Results – New MEXICO • Strouhal Number Structured Vortex Shedding x - Tip to Root flow - Root to Tip flow - no span-flow Low Strouhal Freq. , where
- 13. 13 Results – New MEXICO • 3D Steady Airfoil Polars Lift Drag
- 14. 14 Results – New MEXICO • 3D Steady Airfoil Polars – Comparison with Flat Plate Theory in Deep Stall
- 15. 15 Results – Standstill Conditions (New MEXICO) Axial Flow AOA Range Pitch Range Observation Low , ~ -15o to +15o ~ 75o to 90o Good Agreement High , ~ 45o to 90o ~30o to ~-2.3o Bad Agreement Pitch = 30o Wind Speed = 30 m/s Yaw = 0o
- 16. 16 Results – Standstill Conditions (New MEXICO) Yawed Flow AOA Range Yaw Angles Observation Low 15o & 30o Good Agreement High -30o, -45o, -60o, & -90o Bad Agreement Pitch = 90o Wind Speed = 30 m/s Yaw = -45o Non-axisymmetric Flow
- 17. 17 Results – Improvement of Models • Beddoes-Leishman Flow Separation Model
- 18. 18 Results – Improvement of Models • Beddoes-Leishman Flow Separation Model – Øye Model – FFA (Bjørck) Model – Larsen Model Graphics taken from Larsen et al., Journal of Fluids and Structures 2007.
- 19. 19 Results – Improvement of Models • Beddoes-Leishman Flow Separation Model
- 20. 20 Results – Improvement of Models • ONERA Model D. Petot “Differential equation modeling of dynamic stall” 1989.
- 21. 21 Results – Improvement of Models • ONERA Model
- 22. 22 Results – Rotating Yawed Conditions • Azimuthal Load Variation 24 m/s 45o Azimuth [deg.]
- 23. 23 Results – Rotating Yawed Conditions • Error Analysis
- 24. 24 Results – AVATAR Case Study • Case Study Definition – Pitch Sweep • 0o 125o (2.5o step) – Blade Stiffness DOFs • Flap, Edge, & Torsion – DOFs Switched Off • Tower Dynamics • Drive-train torsion • Gravity – Wind Speed • 42 m/s Pitch Sweep 90o Azimuth AVATAR Aeroelastic Workout at Polimi, Technical Report, 2015.
- 25. 25 Results – AVATAR Case Study • Effect of Time Step Size Pitch [deg.] Pitch [deg.]
- 26. 26 Results – AVATAR Case Study • Damping Ratio StallDeep Stall Pitch [deg.]
- 27. 27 Results – AVATAR Case Study • Hysteresis Loops at Pitch = 30o
- 28. 28 Results – AVATAR Case Study • Hysteresis Loops at Pitch = 50o
- 29. 29 Conclusions • Limited Bluff Body Vortex Shedding for Finite Aspect Ratio Blade in Deep Stall • Improvement of DS Models in Aero-Module – Snel relocation of fader function – B-L Larsen Separation Model + Effect of Varying Incoming Velocity – ONERA Piece-wise function for Stiffness Term • Typically, a 10% reduction in Error with DS models in yawed conditions • Edgewise Instability effected by shape and rotation of DS hysteresis loop
- 30. 30 Thank You
- 31. 31 Questions?
- 32. 32 Backup – New MEXICO (Yaw) 30 deg.
- 33. 33 Backup – New MEXICO (Standstill) Yaw = 30 deg.Pitch = 90 deg.
- 34. 34 Backup – Kirchoff Model • Problems at Large AoA
- 35. 35 Backup – Kirchoff Model • Problems at Large AoA (without fader2)
- 36. 36 Backup – Cross Flow Model • Cross-Flow Error Ratio* * Cross-Flow Model by Gaunaa et al., Journal of Physics, 2016. θcf = +60 deg. θcf = -60 deg. TE LE
- 37. 37 Backup – Cross Flow Model • Cross-Flow Model* * Cross-Flow Model by Gaunaa et al., Journal of Physics, 2016. Yaw = -60o Pitch = 90o
- 38. 38 Backup – Standstill in Yaw Yaw = -90o Yaw = -45o
- 39. 39 Backup – Optimizing B-L Model Parameters • Mapping of B-L Model Parameters
- 40. 40 Backup – Optimizing B-L Model Parameters • Improved B-L Parameters
- 41. 41 Backup – Effect of Varying Inflow Velocity U∞ U∞
- 42. 42
- 43. 43 Backup – AVATAR Case Study • Hysteresis Loops at Pitch = 30o
- 44. 44 Backup – New MEXICO • Frequency Domain Analysis – Signal Conditioning
- 45. 45 Backup – New MEXICO • Frequency Domain Analysis – Signal Conditioning – Erroneous Freq. DP = 371 ; Span = 35% ; U∞ = 0 m/s
- 46. 46 Backup – Improvement of ONERA
- 47. 47 Results – AVATAR Case Study • Peak-to-Peak Tip Displacement
- 48. 48 Results – AVATAR Case Study • Tip Displacement PSD
- 49. 49 Results – Standstill Conditions (New MEXICO) • Mean of Standard Deviation of Normal Force Axial Flow Yawed Flow Pitch: 90o -2.3o Yaw: -90o 30o
- 50. 50 Results – AVATAR Case Study • Determination of Damping Ratio
- 51. 51 Results – Standalone DS Models • OSU Database – Pitch Oscillations • Light DS • Deep DS
- 52. 52 Results – Yawed Conditions • Rotational Augmentation 25% span
- 53. 53 Results – Yawed Conditions • Error Analysis
- 54. 54 Results – New MEXICO • Frequency Domain Analysis x - Tip to Root flow - Root to Tip flow - no span-flow
Editor's Notes
- What is Dynamic Stall? Before we try to answer this question lets look at what is stall. Lets say we have an airfoil and we slowly increase the AoA of this airfoil and observe the lift response. What we see is the lift starts decreasing after a certain AoA, which we call as the stall angle of the airfoil. Now, imagine we have another similar airfoil. We repeat the process for this airfoil But this time instead of doing it slowly we do it really fast. What happens is that not only do we see an increase in lift but also a delay in stall angle. This behavior is what is known as dynamic stall. The reason why it happen is because flow over the airfoil is unable to react to changes in AoA instantaneously.
- What is Dynamic Stall? The classical definition of dynamic stall characterizes it into 5 distinct stages from lag in separation to development of LEV to lag in re-attachment of flow. Principally, dynamic stall is an unsteady aerodynamic phenomenon characterized by five distinct stages. Stage 1 Airfoil exceed static stall angle and flow reversal starts taking place in the boundary near the TE Stage 2 Onset of formation of LE vortex Stage 3 Convection of LE vortex Stage 4 LEV has crossed TE and complete separation happens Stage 5 Flow re-attachment at lower AoA than static stall AoA Turbulence can be from the general atmospheric conditions or due to operation in the wake of another wind turbine in a wind farm High AoA in storm operation when the turbine has no control and wind can hit it at high speed from any direction. Wind turbine operating in deep stall …. Where the stall is extremely dynamic in nature. Yaw misalignment is very common on wind turbines. The response of yaw system is not fast enough for changing wind directions Horizontal or vertical wind shear introduced as fluctuation in AoA causing DS Turbulent Environment High Freq. DS Storm Conditions High Freq. DS Yaw Misalignment 1P DS Wind Shear 1P DS IN the end it all boils down to reducing the cost of energy by accurately predicting dynamic stall
- Behavior of stall at very large AoA b/c that is still a big unknown in the scientific community due to lack of experimental data.
- Model are semi-empirical and require back-bone curves and parameters Three different dynamic stall models are implemented in Aero-Module Of these models only Snel’s first order model has been extensively validated before. Dynamic Stall Models Snel’s Model 1st Order Model 2nd Order Model Beddoes-Leishman Model Attached Flow Module (A1,A2,b1,b2,TI) Separated Flow Module (Tp and Tf) Leading Edge Separation Module (Cn1) Vortex Lift Module ( Tv and Tvl) ONERA Model Flat plate parameters Mean airfoil parameters
- A nice animation showing the dynamic stall phenomenon in action. -Sharp rise in leading edge suction pressure due to creation of LEV. The suction peaks drops abruptly but the lift coefficient still increases b/c LEV is convecting over upper surface The lift coefficient suffers an abrupt stall once the LEV has passed the trailing edge.
- A nice animation showing the dynamic stall phenomenon in action. -Sharp rise in leading edge suction pressure due to creation of LEV. The suction peaks drops abruptly but the lift coefficient still increases b/c LEV is convecting over upper surface The lift coefficient suffers an abrupt stall once the LEV has passed the trailing edge.
- What sort of dynamic phenomenon is observed in deep stall conditions. Is there any structured vortex shedding? Self-induced dynamic stall/turbulence
- Two cluster of points were identified. One of them corresponding to bluff body vortex shedding Stourhal Numbers While the other corresponded to low Strouhal Freq. shedding that was also observed in NREL UAE experiment in NASA Ames Wind tunnel. The cause of these low freq. strouhal number has been associated to periodic switching between attached and separated flow near the leading edge. What was surprising to see was that no structured vortex shedding freq. was observed at very large AoA beyond 50 degrees. Lindenburg had postulated that finite aspect ratio blades can only have partially structured vortex shedding. Early break-up of shed vorticity due to suction of air into the vortex core.
- Mainly large difference b/w 2D and 3D polars in deep stall. Mainly because of base drag as 2D profile has higher base drag. But also according to Linderburg due to absence of structured vortex shedding in 3D blade of finite aspect ratio the drag will be lower than 2D blade sections because 2D blade sections have structured vortex shedding. The reason for this is the fact ‘’’’mention’’’ the experiment with and without end blades on airfoils.
- The Standstill conditions for Rigid New MEXICO rotor were validated with Simulations and It was found that simulations show good agreement with measurements at Low AoA. While show bad agreement at Large AoA. One example case of bad agreement is presented in the figure below. Particularly important to note is the strange behavior predicted by B-L and ONERA model for this case.
- Now looking at standstill conditions but with yawed flow. Again good agreement was seen for test cases with low AoA. An example test case of bad agreement between simulations and experiments is shown in the figure below. Here again ONERA model and B-L model were seen to give strange results. Therefore, the cause of this discrepancy was investigated and three major causes were found: Implementation of fader functions in both models Kirchoff Flow separation model in B-L model One of the forcing terms in non-linear second order differential equation of the ONERA model
- Before proceeding with further validation the model were improved. Firstly the B-L model was improved. This model is based on Kirchoff flow separation model which itself is based on small angle approximation. Therefore, this model was giving problems in re-constructing the static polar at very large AoA as shown in the figure. Also, by default Aero-Module was using fader functions to circumvent this problem but they did not seem to remedy the problem.
- To fix the problem the following three different flow separation model were programmed in Aero-Module The Oye Model and FFA model used a different formulations of same Kirchoff model to fix the problems at large AoA. While Larsen used a conformal mapping approach by mapping the f parameter onto a circle in the complex plane. The main advantage of this model is that it avoids an intrinsic singularity in the kirchoff model.
- Here you can see a comparison between the default model in Aero-Module and the improved model. The results show simulated hysteresis loops at different mean AoAs. The default model gives unrealistic results at large AoA which was also why the standstill validation cases with New MEXICO data were showing bad results. Airfoil: DU 91-W2-250
- In case of ONERA model two main improvement were made. Firstly, the second forcing term on RHS of second order equation was replaced with alpha dot instead of rate of change of delta Cl, based on the recommendation from Petot. Secondly, a piece-wise function was introduced to model the stiffness term in the second order equation. This function increase the stiffness term for a downstroke cycle resulting in better comparison with experimental results during the re-attachment phase of dynamic stall. The reason why alpha dot (pitch rate) was used is because the lift coefficient was found to be more sensitive to alpha dot in comparison to rate of change of delta Cl
- This figure shows a comparison between default model and the improved ONERA model. It was seen that even with the corrections the model showed increasing size of hystersis loops at large AoA. Hence a fader function called “cdelPot” from PHATAS was applied to the dynamic lift coefficient to switch off the ONERA model at very large AOA to prevent queer results. Airfoil: DU 91-W2-250
- A through error analysis was performed for different yaw angles and different spanwise sections. Dynamics stall models did not show any reduction in error for outboard blade sections in comparison to quasi-steady model For the inboard sections all the model showed large improvement in error except the ONERA model which was having trouble in modeling the re-attachment phase.
- In simple words this case study is as simple as taking a blade and hitting with a hammer to see how the vibrations are damped over time In simple words the purpose of this case study was to excite one of the blades and see how the vibrations on the blade decay over time with and without using Dynamic Stall Models The last part of the research involved an aero-elastic case study of the AVATAR rotor. This case study mainly follows the work of test case no. 2 from Aeroelastic Workout in Polimi in 2015. Simulation time = 120 seconds For the aeroelastic simulations Aero-Module was coupled with PHATAS using windows command line. The case study mainly involved analyzing the tip displacements response and root bending moments.
- ** flapwise results independent of time step size. ** Edgewise results dependent on time step size A time step sensitivity was performed. The figures show peak to peak tip displacements for in-plane and out-of-plane deformations for different time step sizes with quasi-steady aerodynamic model No monotonic trend was observed with reducing time step size. However, the range of pitch angles for which very large peak to peak response was observed, possibly due to instability, was consistent for different time step sizes.
- This slide shows the variation of damping ratio versus pitch angle for different dynamic stall models. It can be clearly seen from figure that dynamic stall model are adding aerodynamic damping to the system in comparison to quasi-steady aerodynamic model in the stall regime. ONERA model shows a positive damping ratio for the complete range of AoA While BL and Snel model show negative damping for a small range of AoA. This behavior of these two model was further investigated to identify the cause.
- First we look at Snel model at 30 deg. pitch setting In this animation the top row of figures present the tip trace while the bottom row presents the hysteresis loops. On observing hysteresis loop for Snel model a counter-clockwise hysteresis loop was observed in stark contrast to typically observed clockwise hysteresis loop that give positive damping. It was found that a fader function called “cdelPot” in Aero-Module was causing this problem. If this fader function is removed then the Snel model gives positive aerodynamic damping over the entire range of pitch settings
- For the test case where B-L model shows instability a different reason was identified. Observing the hysteresis loop for B-L model a sort of half hysteresis loop was identified causing positive damping in upstroke while negative damping similar to quasi-steady aerodynamic model in downstroke. The reason why B-L model gives this hysteresis loop behavior in deep stall is due to the fact that flow is completely separated over the upper surface and only Vortex Lift Module is causing the hysteresis effects.
- Now I present a few results from the New MEXICO measurements. As an example here the pressure distributions for 30 degree yaw case are shown. Large STD in pressure for Low TSR cases as AoA is higher and so is the advancing and retreating blade effect regime at Low TSR - Low TSR has higher AoA Stagnation point indicated by -1 further aft than High TSR curve Low TSR has more STD than High TSR cases large hyteresis in normal force. dynamic stall Kinks in pressure data at inboard stations was normally seen for High TSR
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- The cross-flow error ratio was determined based on CFD measurements on DTU 10 MW reference turbine. A first order correction was fitted to the obtained error ratios to obtain the cross flow model to be used as an add-on on the regular cross-flow principle. Lift and drag error ratios were identical therefore a the same error ratio was used for both
- Testing this model does not directly have to do anything with dynamic stall. However, the main purpose of testing this model was to see if it improves the overall prediction of loads in standstill condition. It seems to accurately predict results for the 8 o’clock blade. The model completely misrepresents the trend for the 4 o’ clock blade. Model still needs development and validation to be used in standstill conditions. Hence, it was not pursued further as it was out of the scope of the current research.
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- 2 problems with optimization: Explores unrealistic solution space. Does not give any knowledge about the domain
- Snels and Lindenburg model are very similar. Lindenburg infact builds on Snels model by adding a local speed ratio dependency. Schepers mode is a tuned version of Hansens model.
- The mean was subtracted from the time series to remove energy from the DC component of the time signal as it contains the most energy and could potentially mask any dominant vortex shedding frequencies. Additionally, signals were divided by their standard deviation to standardize the spectrum output and facilitate comparison between normal and tangential force on the same plot. PSD Welch’s Method MATLAB Windowing function applied to mitigate spectral noise by averaging segments of time series. Hanning Window --- 50% overlap
- Testing this model does not directly have to do anything with dynamic stall. However, the main purpose of testing this model was to see if it improves the overall prediction of loads in standstill condition. It seems to accurately predict results for the 8 o’clock blade. The model completely misrepresents the trend for the 4 o’ clock blade. Model still needs development and validation to be used in standstill conditions. Hence, it was not pursued further as it was out of the scope of the current research.
- Snels and Lindenburg model are very similar. Lindenburg infact builds on Snels model by adding a local speed ratio dependency. Schepers mode is a tuned version of Hansens model.
- Snels and Lindenburg model are very similar. Lindenburg infact builds on Snels model by adding a local speed ratio dependency. Schepers mode is a tuned version of Hansens model.
- A FFT of the non-linear time response from all simulation revealed that the edgewise mode was causing instability. Therefore, to determine damping ratio a bandpass filter was developed to isolate the edgewise frequency component in the time signal. Once isolating the signal peaks were extracted and plotted against number of cycles between amplitudes to fit a linear regression line. The slope of this line gave the logarithmic decrement From which damping ratio was computed using a simple formula.
- Before simulating dynamic stall in standstill and yawed conditions, standalone dynamic stall models were validated using OSU wind tunnel experiments. S814 airfoil profile, which is a wind turbine specific airfoil with relative thickness comparable to DU91 profile on the MEXICO blade.
- Snels and Lindenburg model are very similar. Lindenburg infact builds on Snels model by adding a local speed ratio dependency. Schepers mode is a tuned version of Hansens model.
- A through error analysis was performed for different yaw angles and different spanwise sections. Dynamics stall models did not show any reduction in error for outboard blade sections. For the inboard sections all the model showed large improvement in error except the ONERA model which was having trouble in modeling the re-attachment phase.
- The frequencies below the dashed line will not be considered for calculating Strouhal number for two main reasons: The frequencies below the – – line give very low Strouhal Numbers All the erroneous frequencies were observed to lie below this level For 25% section dominant frequencies seen even in the attached flow AoA ranges. However, on observing the standard deviation of pressure distribution no large transients could be identified at these low AoA. Hence these frequencies were not considered for computing the Strouhal numbers.