BEM-Codes Validation Tables

7/31/2019 BEM-Codes Validation Tables

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Ricardo Santos Pereira nr 1371282 November 2009

Validation of BEM-codes

Objective:

In the following pages a comparative study will be performed between two Blade-Element-

Momentum codes and the pressure measurements from the MEXICO obtained at yawed flow

conditions, with the objective of validating these calculation methods so that posteriorly dynamic stall

models are included in the computation.

Motivation:

One of the main goals of this master thesis is to compare the performance of different Dynamic

Stall models in the prediction of the loads wind turbines under yawed flow conditions will experience,

and as discussed before, usually these semi-empirical dynamic stall models require the angle of attack

history as an input, i.e., Cl=f( ), with =f(t).

However it is firstly necessary to understand exactly what 'angle of attack' signifies; the 'angle of

attack' is defined as the angle an airfoil's chord is at with the stream velocity, however, in the wind

turbine environment the local velocity greatly varies when different rotor positions are considered,since the blades indeed slow down the incoming wind, and especially in yawed conditions this

makes the 'angle of attack' concept rather unclear.

Still, it is possible to compute the angle of attack at different spanwise stations and azimuthal

positions of a wind turbine using both BEM and lifting-line codes. In his work, Micallef [ref to

document with IFW] used an inverse free wake code to compute the local angles of attack throughout

the rotor of the MEXICO. Inverse free wake codes use loads as input, and considering the influence of

bound, shed and trailed vortices they compute, locally, what should be the bound circulation such that

the Kutta-condition is met with. From this circulation, the angle of attack is then calculated, and based

on its method of computation, let us call this value the 'circulatory' angle of attack.

However, in Dynamic Stall modeling, the angle of attack, which as mentioned above is usually

the input for the unsteady load computation, is taken simply as the angle the airfoil's chord is instantly

at with the stream velocity. Based upon how it is defined, let us call this value the ' geometric' angle of

attack. The direction of the stream velocity is well defined in wind tunnel testing where most of the data

used to derive the semi-empirical Dynamic stall models was taken from, leaving no room for ambiguity.

Naturally, if there is some shed vorticity in wind tunnel tests, the local velocity at the airfoil will be

influenced by it, and the bound circulation necessary to meet with the Kutta condition will be

associated with an instantaneous 'circulatory' angle of attack which is different from the usually taken


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'geometric' angle of attack.

Thus it is understood that using the angle of attack history, =f(t), computed with an inverse

free wake method, as an input to Dynamic Stall models is not expected to yield good predictions of the

aerodynamic loads, since we are indeed in presence of two different ways to tackle and simulate the

problem at hands.

On the other hand, it is also possible to use a BEM code to compute =f(t) and use the angle of

attack history as an input to Dynamic Stall models and thus obtain the unsteady loads, to compare with

the MEXICO measurements. However, in a BEM code, at each time instant the momentum loss of the

incoming air stream is equated with the forces on the blades, iterating on the induction factors; since in

a standard BEM code these forces are calculated by static Cl vs functions, it is easy to understand that

if the reduced frequency is high enough, this will lead to an inaccurate computation of the

instantaneous induction factors and thus to an erroneous alpha history.

From the stated above, one is lead to conclude that the dynamic stall models must be

implemented inside the BEM code, that is to say the instantaneous loads must be calculated

considering the angle of attack history, =f(t), so that the momentum balance yields a more accurate estimation of the induction factors in the following time instant.

It is important to state that the BEM models will be validated against MEXICO measurements

obtained at moderatewind speeds; this is justified by the fact that at low wind speeds it is likely that

the turbine is working in the turbulent wake state, which means that the trailed vortices will have a

major influence in the flow field and consequentially in the observed loading. Bearing in mind that the

goal is to use the BEM codes to simulate Dynamic Stall, which will naturally occur at high wind

speeds, it is understandable that the validation at low wind speeds is not very relevant.

When high wind speeds are considered, it is expectable that the airfoil stalls, at least in someportion of the blades, and as discussed before this stall will have a dynamic nature. Since the BEM

codes under consideration use static Cl vs functions, it is not expectable that good agreement is

found between calculations and measurements at these high wind speeds, and so it makes little sense to

compare such results.

Finally, one should also keep in mind that at high wind speeds, i.e. at low tip speed ratios, the

induction factors will have a smaller magnitude[include reference that explains this], which means that

the advance retreating blade effect will be dominant. As mentioned before, BEM codes iterate on the

induction factors, but since these factors will have a smaller magnitude their contribution to the angle of

attack 'seen' by the blade will also be small compared to the geometric effect, and consequentially the

accurate computation of these induction factors becomes less important in the prediction of theunsteady loads the wind turbine blades will experience.


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Considered Models:

Two distinct Blade Element Momentum models will be considered, which from now on will be

referred to as 'Classical' BEM and 'Empirical' BEM:

Classical BEM

This designation refers to the algorithm for BEM code in yawed flow suggested in [reference to

the 'Wind Energy Handbook'], and was mainly adapted from the previous work by Micallef [ reference

to Daniel's BEM code].

This model assumes the induced velocity to be given by:

u=uavg1K F sin

, where Kdepends on the wake shape, F is a flow expansion function where is the fraction radiusand is the azimuth angle. This codes iterates the induction factors at each radial position by averagingover the azimuth, using vortex cylinder theory for the thrust forces, and computes both azimuthally

averaged axial and tangential induction factors.

In this model the flow expansion is also included, as well as both tip and root loss factors, andalso the wake rotation, computed assuming a single vortex being trailed from the center of rotation.

Once the azimuthally averaged inductions are computed this model calculates the load variations, and

the azimuthal variations can be found by using the thrust and torque gradients. A more detailed

description is given in [reference to Daniel's BEM code].

The normal and tangential force coefficients illustrated below are derived from the computed lift

and drag coefficients, using also the calculated angles of attack, according to

Cn=Cl .cosCd .sin Ct=Cl .sin Cd. sin


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Empirical BEM

This method of computation uses the empirical model from Schepers [reference to Gerard's

model] of the axially induced velocities in a yawed flow wind turbine; it was derived from an

experiment performed at TUDelft, where the velocity distribution was measured at several spanwiseand azimuthal positions and fit with a second harmonic Fourier series, taking the form:

u=uavg 1A1cos P1A2cos 2P2

where A1 , A2, P1 and P2 are functions of the relative radius, of the azimuth and of the empirically

derived constants.

It should be noted that this axial induction velocities empirical model was derived only for the

design condition , and that measurements only covered spanwise stations up to 80%. For positions

closer to the tip the results were simply extrapolated from the azimuthally averaged induction, which

means that the tip-loss was not taken into account.

As explained in [reference to Gerard's model], this empirical model has been previously

extensively validated, from the output forces, with measurements, performing very often better than

other models, and never worse.

Now regarding the BEM model implemented, the inplane velocities simply consider the skewed

inflow, which can be derived from geometric considerations; in this approach the induced tangential

velocities are neglected, however it is not expected that this will greatly affect the force's calculation

since their magnitude is very small when compared with the inplane velocities due to the blade's

rotation.

From both the inplane and axial velocities, the angle of attack at each spanwise position is

calculated, and using static Cl vs and Cd vs functions, the forces on each blade element are

calculated. Finally integrating over the span and summing the contribution of all blades we get the total

Thrust, and iterate on the average axial induction coefficient according to

CT=T

0.5 .UWind. cos2

. Aand CT=4a 1a

Once the process converges, the normal and tangential force coefficients are computed in an

identical way has was done for the 'Classical' BEM.


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Processing of the results from the MEXICO

Since they are plotted for comparison and took as a reference to compute the associated error, it

is necessary to explain how the results from the MEXICO experiment were processed.

For the normal and tangential forces, acubic interpolation

of thepressure

measured by eachsensor was taken, and integrated over a cubic interpolation of the airfoil surface. To obtain the force

coefficients, these computed forces were divided by the maximum pressure occurring over the airfoil,

taken as the maximum of the cubic interpolation of the pressure sensors.

CnMEXICO=FnInterp

PmaxInterp

From the followed approach the computed forces and force coefficients can be expected to yield

results which are accurate enough to compare models against.

Viscous Contribution

It should also be stated that by simply integrating the pressures over the airfoil one does not

actually compute the Drag force, since obviously there is also a viscous contribution. However, the

magnitude of this contribution is quite small, and the associated error can be computed[reference to

viscous/pressure drag computation] resulting in:

Cn0.0005 and Ct0.08

Being so this discrepancy will, for the moment, not be taken into account.


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Results:

The normal and tangential forcecoefficients will now be plotted, versus the azimuth angle, for

each of the spanwise stations and considering different yaw angles and incoming wind speeds of 15 and

18 m/s. We should also bare in mind that the first wind speed corresponds to the design condition.

In the plots, we should observe the following legend:

Blue, for the tangential force coefficient from the MEXICO measurements

Turquoise, for tangential force coefficient from the Empirical BEM

Green, for the tangential force coefficient from the Classical BEM

Red, for the normal force coefficient from the MEXICO measurements

Pink, for the normal force coefficient from the Empirical BEM

Black, for the normal force coefficient from the Classical BEM

Moreover, for each spanwise station the average and maximum relative error is shown in a table,

including comparisons for normal and tangential force and normal and tangential force coefficient, for

both BEM models.

25% Span

Illustration 1: U=15m/s, Beta=15 deg


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Illustration 2: U=15 m/s, beta=30 deg

Illustration 3: U=15,beta=45

Illustration 4: U=18 m/s, Beta=15 deg


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Illustration 6: U=18 m/s, Beta= 45


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From the results shown above there are several things to observe; firstly, it is clear that the

empirical BEM is capable of predicting the trends which the force coefficients display, throughout a

whole revolution; one can also see that the magnitude of the calculated values with the empirical BEM

is in agreement with the measured values. As for the classical BEM one can say that its load prediction

is somewhat poorer.

One must bare in mind that the axial velocity, and thus the angle of attack, will be directly

related with the product UWind. cos .It is thus understandable that both models cannot really

predict the loads at U=18 m/s and =15 deg, since then the airfoil will be (dynamically) stalled over alarge portion of the revolution, and as mentioned before, no unsteady effects are taken into account in

the models under consideration.

Also, since 25% is the span closest to the root, the rotational effects will be very strong and it is

natural that stall delay and thus increased lift is present, as can be seen in fig 6; since the implemented

models are based on 2D static data, one can understand the poor agreement often found at 0 deg

azimuth, i.e. where the angles of attack will be larger. Better results are likely to be met with if some

rotational correction is included, or if a specific software is used to obtain the force coefficients, such as

Xfoil.

35 % Span



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Illustration 8: U=15, Beta=30 deg




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In the results above, the trials corresponding to U=18 m/s, =15 deg and U=18 m/s and =30

deg were not displayed since the pressure distribution over the airfoil was extremely incoherent, and soit is assumed that a pressure sensor malfunction has occurred meaning the results should be discarded.

It is possible to observe similar trends are found at this spanwise section from what was found at

the 25% position, which is understandable since these are indeed stations under a considerable

influence of the root, and thus the models should show a similar level of agreement.

60% Span

Illustration 11: U=15 ms, Beta=15 deg


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Illustration 12: U=15 m/s, Beta=30




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At this spanwise station it is again possible to see that the empirical BEM model closely follows

the trends observed in the empirical results, while the classical BEM generally performs not so well.

One also gets the impression that the magnitude of the predicted loads are somewhat closer than at the

more inboard sections, which can be confirmed by analyzing the error tables; this better agreement can

be explained by the fact that, at this mid span position, the airfoil is less likely to stall, and thus the

(unaccounted for) unsteady effects will have a smaller influence, and also because the rotational effects

too will have a less noticeable impact on the loading.

82% Span




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Minding the results above one can see that for this outboard section the empirical BEM again is

able to follow the trends the empirical results show, usually in a better fashion than the classical BEM

model. Regarding the magnitude of the loading predictions, it is possible to observe that, at small yaw

angles, some over estimation of the aerodynamic forces seems to take place, which can perhaps be

caused by the fact that tip-losses are not taken into account in the empirical BEM model. When large

yaw angles are considered, however, one can see there is very good agreement between the empirical

BEM model and the measured loading.



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92% Span




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BEM-Codes Validation Tables

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