Computational Studies of Horizontal Axis Wind Turbines Ph.D. Oral Defense Presented By Guanpeng Xu Advisor: Dr. L Sankar School of Aerospace Engineering Georgia Institute of Technology This work was supported by NREL Monitor: Dr. Scott Schreck Georgia Tech School of Aerospace Engineering

Outline of the Presentation Importance of wind energy Overview of the present research Methodology and numerical procedure Results and discussions Conclusions and recommendations Georgia Tech School of Aerospace Engineering

Importance of Wind Energy Wind Energy is a clean source of energy. Wind Energy is renewable. It may be used to augment to other forms of energy, e.g. fossil fuel. Many parts of US and other countries have sites with high wind, making wind energy based power generation feasible. Georgia Tech School of Aerospace Engineering

Existing Approaches for Wind Turbine Performance Blade Element Methods –2-D strip theory –Analytical inflow –Fast and is in routine use –Require table look up for airfoil data –Modeling tip losses and 3-D stall effects remain unsolved issues Navier-Stokes Simulations –Can capture all the physics from first principles –Can provide high-quality details of the flow field –Require large computer time Hybrid Methods Georgia Tech School of Aerospace Engineering

Hybrid Methodology The flow field is made of –a viscous region near the blade(s) –A potential flow region that propagates the blade circulation and thickness effects to the far field –A Lagrangean representation of the tip vortex, and concentrated vorticity shed from nearby bluff bodies such as the tower This method is unsteady, compressible, and does not have singularities near separation lines N-S zone Potential Flow Zone Tip Vortex Georgia Tech School of Aerospace Engineering

A hybrid technique offers the following capabilities: It can capture viscous phenomena efficiently. Tip vortex is modeled accurately. There is no need for analytical inflow models. It is applicable to steady and unsteady HAWT applications. High order accuracy solutions are obtained with small CPU time. Hybrid Solver Versus Others Georgia Tech School of Aerospace Engineering

Georgia Tech School of Aerospace Engineering Incorporation of Tower Effects –Body-fitted grids are used for rotating blades and tower. –Each grid block is simulated using either a Navier-Stokes or hybrid method. –The flow fields among the grid sets are linked by 3-D interpolation. Inclusion of tower effects requires modeling non- rotating and rotating components. Georgia Tech CHIMERA methodology has been modified for tower shadow effects of HAWT :

Mathematical Formulation Reynolds Averaged Navier-Stokes Equations in Finite Volume Representation:    t q  dV  E ˆ i  F ˆ j  G ˆ k     ndS  R ˆ i  S ˆ j  T ˆ k     ndS Where q is the state vector. E, F, and G are the inviscid fluxes, and R, S, and T are the viscous fluxes A finite volume formulation using Roe’s scheme is used. The scheme is third order or fifth order accurate in space and second order accurate in time. Georgia Tech School of Aerospace Engineering

Full Potential Region Procedure The velocity is decomposed into three parts: PDE for velocity potential:  Georgia Tech School of Aerospace Engineering

Navier-Stokes/Full Potential Coupling The flow field around reference blade is divided into two blocks. For each block, there are three interfaces separate Navier-Stokes and FPE zones. From FPE to Viscous Zone From Viscous to FPE Zone Velocity Components Speed of sound Temperature Energy Equation  and P Neumann Boundary Condition Georgia Tech School of Aerospace Engineering

Tip Vortex Model Wake shed from the blade is captured inside the Navier- Stokes zone. Once the tip vortex leaves the Navier-Stokes zone, it is modeled by a series of piecewise linear elements. The induced velocity field due to these vortex filaments is calculated by Biot-Savart law where needed. Georgia Tech School of Aerospace Engineering NS

Turbulence Model Used Georgia Tech School of Aerospace Engineering Algebraic, Prandtl’s mixing-length like model called Baldwin-Lomax model –Simple –fast –is not valid in massively separated flows One equation transport model called Spalart- Allmaras model for an eddy-viscosity like quantity –robust –more time consuming –in wide use for separated and unsteady flows

Spalart-Allmaras Turbulence Model The following transport equation is solved: The Reynolds Stresses are given by: The eddy viscosity is given by: where Georgia Tech School of Aerospace Engineering

Eppler’s Transition Model Transition occurs when where r is a roughness parameter. H 32 is the ratio of the energy thickness to the momentum thickness . Georgia Tech School of Aerospace Engineering

Michel’s Model This model is in wide use in fixed wing aircraft industry. Reynolds No. based on momentum thickness Reynolds Number based on distance from leading edge=u  x/ Transition Region is simulated by: Georgia Tech School of Aerospace Engineering Local impinging velocities are used.

Yaw Effects The analysis must now address –Velocity component in the plane of rotor disk –Skewness of tip vortex wake –Deformation of the wind blades, teetering and flapping The rotor tested by NREL uses rigid blades Georgia Tech School of Aerospace Engineering

Validation Studies Axial Wind Conditions Yaw Conditions Tower Interaction Effects Georgia Tech School of Aerospace Engineering Extraction of Physics Examination of flow field, transition lines and blade loads Examination of wake state Examination and improvement of tip loss models using CFD results as a guide Examination of stall delay models using CFD results as a guide

Validation Studies (I) NREL has collected extensive performance data for three rotor configurations: –A rotor with rectangular planform, untwisted blade and S- 809 airfoil sections, called the Phase II Rotor –A twisted rotor, with rectangular planform and S-809 sections, called the Phase III Rotor –A two bladed, tapered and twisted rotor, called the Phase VI Rotor. Best quality measurements (wind tunnel) are available. Georgia Tech School of Aerospace Engineering

Results and Discussion -- Sample Grid Body fitted grid on Phase II rotor Size 110  43  40  2(380,000) Viscous zone 60  43  20  2 (100,000) Georgia Tech School of Aerospace Engineering

Results for the Phase II Rotor Georgia Tech School of Aerospace Engineering

RESULTS for the Phase III Rotor Georgia Tech School of Aerospace Engineering

The Hybrid Code Converges Rapidly (7 seconds/iteration on a SGI Octane 2 Workstation) Georgia Tech School of Aerospace Engineering

The Upper Surface of the Phase II Rotor at 20 m/s Georgia Tech School of Aerospace Engineering Flow Field May be Examined for Interesting Features

Upper Surface Transition Lines for the Phase III Rotor at 6m/s Georgia Tech School of Aerospace Engineering

Lower Surface Transition Lines for the Phase III Rotor at 6m/s Georgia Tech School of Aerospace Engineering

Performance of Transition and Turbulence Models Eppler’s model predicts a transition location that is slightly upstream of Michel’s predictions, unless if there is a laminar separation bubble. On the lower surface, the pressure gradients tend to be more favorable than on the upper side. This leads to a thinner boundary layer and transition aft of the 40% chord. The Reynolds number near the root is less than Both models predict that the lower surface flow will remain laminar all the way to the trailing edge, near the root region. Transition line location appears insensitive to the turbulence model used. Georgia Tech School of Aerospace Engineering

Georgia Tech School of Aerospace Engineering The NREL Blind Run Comparison The Phase VI Rotor Full Scale Wind Tunnel Tests at NASA Ames Chordwise pressure tap at 0.3, 0.47, 0.63, 0.8, 0.95R

Georgia Tech School of Aerospace Engineering Blind Run Comparison (I) The 95%R Normal Force Coefficients

Georgia Tech School of Aerospace Engineering Blind Run Comparison (II) Flap Bending Moment for One Blade

Georgia Tech School of Aerospace Engineering Blind Run Comparison (II)

Georgia Tech School of Aerospace Engineering Blind Run Comparison (III) 95% Span Local Dynamic Pressure

Validation Studies Axial Wind Conditions Yaw Conditions Tower Interaction Effects Georgia Tech School of Aerospace Engineering Extraction of Physics Examination of flow field, transition lines and blade loads Examination of wake state Examination and improvement of tip loss models using CFD results as a guide Examination of stall delay models using CFD results as a guide

Yaw Simulations Georgia Tech School of Aerospace Engineering Field data is often unreliable because of constantly shifting wind conditions. Phase VI data is highly reliable, but unfortunately was not available till towards the end of this research. For these reasons, the present simulations have not been validated in the strictest sense, but do give useful insight into yaw effects.

Typical Natural 10m/s Inflow Wind Georgia Tech School of Aerospace Engineering

Measured Power v.s. Time at 20 degree Yaw Georgia Tech School of Aerospace Engineering Average values well predicted Higher harmonics are not captured well, because we only model the first harmonic of the wind.

Validation Studies Axial Wind Conditions Yaw Conditions Tower Interaction Effects Georgia Tech School of Aerospace Engineering Extraction of Physics Examination of flow field, transition lines and blade loads Examination of wake state Examination and improvement of tip loss models using CFD results as a guide Examination of stall delay models using CFD results as a guide

OVERSET GRID A very coarse grid was used for Proof of Concept Georgia Tech School of Aerospace Engineering

Portion of the Rotor Disk exposed to the tower wake Tower Shadow Causes 15% Variation in Wind Speed Georgia Tech School of Aerospace Engineering 10m/s ~8.5m/s Code predicted this loss in dynamic pressure, but not the vortex shedding effects due to the sparse grid employed.

Tower Shadow Effects toward Pressure Distribution Georgia Tech School of Aerospace Engineering Scatters in field measurements due to wind fluctions

Validation Studies Axial Wind Conditions Yaw Conditions Tower Interaction Effects Georgia Tech School of Aerospace Engineering Extraction of Physics Examination of flow field, transition lines and blade loads Examination of wake state Examination and improvement of tip loss models using CFD results as a guide Examination of stall delay models using CFD results as a guide

Study of Wind Turbine States Wind Turbine States includes: Propeller, zero-slip,windmill, turbulent windmill, vortex ring, and propeller brake states. The present method models all these states well. Ignoring transition from one state to another will lead to incorrect performance predictions. Georgia Tech School of Aerospace Engineering

Study of Wind Turbine States This break is due to transition from wind mill state to turbulent wind mill state If proper transition is not modeled, an incorrect result will occur Georgia Tech School of Aerospace Engineering

Validation Studies Axial Wind Conditions Yaw Conditions Tower Interaction Effects Georgia Tech School of Aerospace Engineering Extraction of Physics Examination of flow field, transition lines and blade loads Examination of wake state Examination and improvement of tip loss models using CFD results as a guide Examination of stall delay models using CFD results as a guide

Validation for the Prandtl’s Tip Losses Model The Prandtl’s Tip Loss Model: –Tip Loss Factor: Georgia Tech School of Aerospace Engineering

Characteristics of the Prandtl’s Tip Loss Model Georgia Tech School of Aerospace Engineering

Extraction of the tip loss factor from CFD Focuses on tip region only; r/R from 0.8 to 1 Extract Lift L(r), Local impinging angle  (r), and local dynamic pressure Q(r) r = 0.8 ~ 1 Normalize by F(r) max to eliminate stall delay effects Constant Stall delay of 1  (Stall delay is explained later) Georgia Tech School of Aerospace Engineering

CFD v.s. Strip Theory for a Post- Stall Condition Georgia Tech School of Aerospace Engineering

CFD v.s. Strip Theory for Pre-Stall Condition (I) Georgia Tech School of Aerospace Engineering

Reasons for Discrepancies in Prandtl’s Tip Loss Model Prandtl’s model is based on rotor in hover, where a closely spaced wake immediately under the disk exists. Wind turbines operate in large axial velocity environment, which increases the vortex ring placement. A new empirical tip loss model has been developed using Phase VI data, and tested with Phase III data. Prandtl’s model was tailored for helicopter rotors Georgia Tech School of Aerospace Engineering

BEM Theory Predictions with the New and Old Tip Loss Model Torque vs. Wind Speed for the Phase VI Rotor There are still some discrepancies if stall delay is not modeled. Georgia Tech School of Aerospace Engineering

Development of New Tip Loss Model Power vs. Wind Speed for the Phase III Rotor Discrepancy due to lack of stall delay effect Georgia Tech School of Aerospace Engineering

Validation of Corrigan’s Stall Delay Model Stall delay occurs because of radial flow by Coriolis force and radial pressure gradient. Tip Low Pressure Key factors for stall delay are (c/r) and Re Georgia Tech School of Aerospace Engineering

Validation of Corrigan’s Stall Delay Model Corrigan’s model: Corrigan suggested that n varies from 0.8~1.6, and suggested n = 1 for most conditions. Corrigan’s model with n=1 is widely used. Georgia Tech School of Aerospace Engineering

Corrigan’s model vs. CFD The value of n in Corrigan’s model should be ~1.8 to 1.9 according to CFD results Georgia Tech School of Aerospace Engineering

BEM Theory Predictions Using the Corrigan’s Model with n= 1.8 Effects of Corrigan’s Model with Different values of n Georgia Tech School of Aerospace Engineering

Conclusions (I) The Hybrid methodology is an efficient means of studying the HAWT flow phenomena for both axial and yaw conditions. The Spalart-Allmaras model, a one-equation turbulence model, predicts higher turbulence viscosity than the Baldwin-Lomax turbulence model. As a consequence the Spalart-Allmaras model predicts slightly lower power values. Nevertheless, both models yield power predictions that are well within the uncertainties associated with the measurements. Georgia Tech School of Aerospace Engineering

Conclusions(II) The Eppler’s transition model and the Michel’s transition model in the present methodology both give comparable transition locations. The Eppler’s model assumes that transition will occur if there is a laminar separation bubble at the leading edge. Based on this physical consideration, Eppler’s model is considered to be superior to Michel’s model. Wind turbine states profoundly affects the power estimates. Proper transition of the wake geometry from one state to the next, as the wind speed increases, is found to be essential to accurately predicting the generated power. Georgia Tech School of Aerospace Engineering

Conclusions(III) The present simulations for rotors operating in yaw conditions reveal that presence of N b -per revolution, 2N b -per-rev, and higher harmonic fluctuations in the loads, where N b is the number of blades. Accurate prediction of these higher harmonics is important for fatigue life estimates. The present simulations suggest a very small reduction in power due to tower shadow effects. If one is interested in power estimates, it is not necessary to include tower effects. However, the tower wake can trigger dynamic stall, which will persist over a larger potion of the rotor disk. Tower effects must be studied if these factors, which contribute to fatigue, are important. Georgia Tech School of Aerospace Engineering

Recommendation(I) The present method is quite efficient ( ~ 4 hours on a Linux system). Further efficiency gains are possible using multigrid, local time stepping, parallel/distributed computing, etc. These options must be explored. Further validation of the present method using the high quality Phase VI Rotor data is recommended. The proposed wake state models can and should be implemented in industry methods such as YawDyn, to correctly model the breaks in the Power vs. Wind Speed Curve. Georgia Tech School of Aerospace Engineering

Recommendation(II) The proposed tip loss model (based on curve-fit of Phase III rotor results), and the stall delay model (n = 1.8) should be further tested, using Phase VI and other wind tunnel data. The present study relied on power measurement, a global quantity. Flow details such as velocity, vorticity, turbulence load etc, must be studied and improving using Phase VI data. Georgia Tech School of Aerospace Engineering