valid-Three sub-objectives, elaborated on in the remainder, can be distinguished inthis thesis: 1 the assessment of experimental unsteady load determination, 2 aone degree of freedom aer
Motivation
Dynamic interactions between a fluid flow and a structure play a pronounced role in current designs Amongst others reasons are that in many applications engineers are deemed to create designs which are as light as possible or to design structures where (static) interaction is intentionally part of the design philosophy An example of the latter can be found in the field of mechanical engineering, where passively deformable spoilers are applied on race cars, see Heinze [2007] In aeronautics aeroelasticity plays a major role in e.g micro air vehicle wings, see Wootton [1981], Shyy et al [2010], and in helicopter blades as discussed by e.g Friedmann and Hodges [2003], Lim and Lee
[2009] But also in civil engineering the understanding and prediction of interactions between constructions like buildings and bridges is of utmost importance to prevent occasions like the well-known Tacoma Narrows bridge disaster of 1940 In the field of bio mechanics fluid-structure interactions cannot be ignored in for example arterial blood flows and the lungs, see Bertram Fung [1997], Fern´andez [2011].
In the wind turbine industry there is much interest in fluid-structure interactions. Firstly, in the past aeroelastic unstable situations have been reported for wind turbines and for the next generation of turbines this must be prevented Hereto, proper pre- dictions of aeroelastic responses are required as discussed by amongst others Hansen
[2007] Secondly, there is still a trend to increase rotor diameters in order to make wind turbines economically more attractive One of the drawbacks of larger rotors is the larger susceptibility to aeroelastic effects, see e.g Hansen et al [2006] Thirdly, a promising option is to use smart wind turbine blades, see van Wingerden et al [2008], which are tailored to reduce the aerodynamic loading based on e.g measured wind fields, blade root moments or the blade bending Hereby, especially for slender, long blades the aeroelastic response to the instantaneously changing loads is important to consider.
Numerical models can be used to simulate and predict fluid-structure interactions for wind turbines, as reported by e.g Chaviaropoulos et al [2003a] In general nu- merical fluid-structure interaction modelling is widely explored, see e.g Garcia [2005],
Gardner et al [2008] or Riziotis et al [2004] Despite the fact that many engineers rely on these simulations, the validation of the numerical fluid-structure interaction models with measurement data is limited and relatively unexplored This is certainly true for fluid-structure interactions for wind turbines yielding high Reynolds numbers. Main cause is the limited availability of good experimental data, amongst others due to the complexity of aeroelastic wind tunnel experiments An example of such a com- plexity is unsteady wind tunnel interference Furthermore, there is a restriction on the available data in the sense it has a limited applicability due to specific combina- tions of Reynolds numbers and structure types Examples of such experiments are for instance work of Gerontakos and Lee [2008] who assessed the unsteady aerodynamics around a prescribed oscillatory aerofoil with trailing edge flap or aeroelastic flutter ex- periments performed by Rivera et al [1991] with the aim to obtain experimental data for validation purposes In the latter research for a large range of Mach numbers from low subsonic to transonic, pitch and plunge magnitudes and phases are determined as well as unsteady surface pressure measurements are performed Reynolds numbers are approximately in the order of a few million Although not all flow parameters are known, together with the structural parameters this is a valuable data set that can be used in the development of aeroelastic codes.
The lack of experimental validation material for fluid-structure interaction prob- lems for wind turbine applications is the main motivation for this doctoral research work Within the INNWIND project where this thesis is part of, research activities are defined to improve the aeroelastic modelling One of the main tasks in this is to obtain validation data for aeroelastic simulations, where for wind turbines typ- ical Reynolds numbers of > 500 000 are considered and the structural shape is a good representation of a wind turbine section Furthermore, in the framework of act- ive control strategies it is beneficial to integrate a controllable flap in the structure. Therefore, the main target of this research is defined to obtain validation material for fluid-structure problems for wind turbine related Reynolds numbers and structures.
A numerical benchmark study is part of the research to obtain amongst others more insight in possible issues in modelling the validation experiment.
Literature review of present state
Fluid-structure interactions (FSI) of wind turbines can be investigated by performing field measurements, conducting numerical assessments or by doing controlled labor- atory experiments The incentive of this thesis and the used approach is based on existing research and common practices on the numerical and experimental side A short overview of this background information is presented before the approach is discussed.
Fluid-structure interaction is about the interaction between a fluid flow and a de- forming or moving structure Depending on the fluid and structural properties, the interaction can be qualified as weak or strong In general weakly coupled problems most often deal with stiff structures which are with respect to the fluid heavy Strongly coupled problems deal typically with flexible, more light-weight structures.
Fluid-structure interaction problems can be solved in a monolithic (see e.g H¨ubner et al [2004], Michler et al [2004], Ryzhakov et al [2010]) or a partitioned manner (see e.g Felippa and Geers [1988], Piperno et al [1995]) In the monolithic approach, a dedicated solver is needed where the flow and the structure are combined in one physical model Advantage is that no spatial and temporal coupling interface exists between the flow and the structure Drawback is the fact a dedicated solver needs to be developed, maintained and updated which is relatively expensive Furthermore, monolithic solvers are often limited to a class of problems for which it is specifically designed.
The drawbacks of monolithic solvers are such that most often one relies on par- titioned solvers, where (commercially available) separate flow and structure solvers are coupled For partitioned codes a coupling interface is needed where the spatial and temporal discretisations of the flow and structure solver are linked The spatial coupling consists of an interpolation technique needed for non-matching fluid and structure computational meshes The temporal coupling is needed to take care of the communication of structure and flow solutions when the simulation advances in time. For weakly coupled problems it is often sufficient to evaluate the coupling terms only once per time step leaving a temporal coupling error For strongly coupled problems multiple evaluations are required to obtain a converged solution and an acceptable temporal coupling error Strong interactions can impose numerical instabilities and require stability enhancing measures like relaxation techniques (see K¨uttler and Wall [2008]) Reduction of the computational effort for strongly coupled problems can be achieved by application of e.g the Newton-Krylov solving strategy as discussed by Michler et al [2005] or multigrid algorithms as laid down by van Zuijlen and Bijl [2009].
For both the monolithic and partitioned approaches validation is required to assess the accuracy of the model Besides implementation errors, for monolithic solvers the validation covers flow and structure modelling errors and discretisation errors For partitioned solvers, the solvers are usually validated separately for a wide range of test problems and validation is at least required to assess the implementation of the spatial and temporal coupling between the flow and structure solvers.
Due to the lack of experimental data, academic test problems or benchmark stud- ies are often used to assess fluid-structure interaction solvers Disadvantage is that in general only analytical solutions exist of physically simple test problems For more challenging, real physical problems one has to fall back on experiments Numerical benchmark studies, where solutions of different codes are compared, provide a good means of a first analysis of the code, however the check with reality still lacks.
Experiments are performed to check numerical results or directly assess fluid-structure interaction cases As mentioned, for validation purposes not much data is available and the available data is mostly confined to specific combinations of Reynolds numbers and structure types Examples of aeroelastic experiments are e.g work by Dietz et al [2004], Tang and Dowell [2011] about flutter and Neumann and Mai [2013] on an aeroelastic gust response of a wing.
In setting up a fluid-structure interaction experiment for validation purposes, amongst others the following considerations need to be addressed before a detailed experimental design can be made:
• Conformability level of numerical modelling wrt experiment
• Structure type and degrees of freedom
With validation purpose is meant whether a specific part(s) of a numerical algorithm or the complete solver is to be validated and roughly for which boundary conditions this should be enabled The conformability level of the numerical modelling determ- ines how much effort it takes to model the experiment in the numerical setup: keep in mind that in case an experiment is designed that is very complex to model in a numerical solver, it is not particular suited for general validation purposes Based on the set incentives the experiment can be designed in detail, whereby the guidelines described in the next section should be taken into consideration.
Validation experiments need to comply to certain requirements as thoroughly ex- plained in e.g Oberkampf [2001], Oberkampf and Trucano [2002], Oberkampf and Barone [2006] Six guidelines are defined by Oberkampf [2001] for designing and conducting validation experiments, which are:
• Guideline I: A validation experiment should be jointly designed by experiment- alists and code developers or analysts working closely together throughout the program, from inception to documentation, with complete candor about the strengths and weaknesses of each approach.
• Guideline II:A validation experiment should be designed to capture the essential physics of interest, including all relevant physical modelling data and initial and boundary conditions required by the code.
• Guideline III:A validation experiment should strive to emphasize the inherent synergism between computational and experimental approaches.
• Guideline IV: Although the experimental design should be developed cooper- atively, independence must be maintained in obtaining both the computational and experimental results.
• Guideline V:A hierarchy of experimental measurements of increasing computa- tional difficulty and specificity should be made.
• Guideline VI: The experimental design should be constructed to analyze and estimate the components of random (precision) and bias (systematic) experi- mental errors.
For a more in depth discussion of these guidelines the reader is referred to the specified source In this work it is aimed for to adhere to all guidelines, whereby guideline V is considered to be partly beyond the scope of this work Mind these guidelines do not specify strict requirements in terms of the desired accuracy levels and acceptable uncertainties Furthermore, for validation it is clear that there must be an undis- puted confidence in the experimental data meaning among others no ambiguities are observed.
A wide variety of qualitative and quantitative aerodynamic measurement techniques have been developed Qualitative techniques can be of added value in the comprehen- sion of flow features, but are not sufficient for the validation purposes foreseen with this work The intrusiveness of measurement techniques is also important to consider when a suitable measurement technique is selected.
Non-intrusive and accurate load measurements on objects that can deform or move are often not trivial For these experiments, as long as e.g electric wires or pressure tubes are no obstruction to (free) motions, unsteady forces can be measured directly with high accuracy by using e.g load cells or strain gauges, see Hillenherms et al.
[2004] When using load cells or strain gauges special attention should be given to the possible contamination of measured forces with e.g structural responses of the sup- porting structure The unsteady loads can also be indirectly derived from measured flow-field quantities Examples of the latter are for example wake rake measure- ments, measurements with pressure sensitive paint (McLachlan and Bell [1995] and Klein et al [2005]) and pressure taps For unsteady flow, pressure orifices based measurements require relatively expensive sensors that are prone to drift when sub- jected to multiple pressure cycles This means the accuracy reduces over time unless frequent calibrations are performed, which is undesired Pressure sensitive paint is non-intrusive and can be applied to unsteady flows, although the sensitivity deterior- ates with decreasing Mach number For velocities beyond the low-subsonic range this method can be applied with enough accuracy However in this work the low-subsonic range is covered and pressure sensitive paint lacks accuracy Surface stress-sensitive film is also suited for low-subsonic flows and additionally measures skin friction forces, see e.g Fonov et al [2005] Problem is that even the smallest vibration in the camera setup deteriorates the accuracy of the measurement of the applied film layer thickness and cameras must be focused on the moving surface when recording.
In previous research mainly strain gauges and pressure sensors are used to determ- ine loads and/or deflections for an aerofoil with moving flap This includes work of Frederick et al [2008], van Wingerden et al [2008], Bak et al [2010] and Heinz et al.
Approach
The main incentive of this research is to conduct an aeroelastic experiment that com- plements the available, limited database with aeroelastic experimental data Focus is on data that can be used for wind turbine applications Hereby one can think of validation of e.g high fidelity aeroelastic solvers, but also structurally coupled BEM codes including its input databases.
Relevant aeroelastic motions for wind turbines are flapwise, edgewise and pitching motions, see e.g Petersen et al [1998] and Chaviaropoulos et al [2003b] Further- more, wind turbines operate at moderate to large angles of attack whereby dynamic stall can occur In order to capture most of these relevant aspects, an experimental setup is designed with which plunging and pitching motions can be investigated, either combined or isolated Based on the authors experience level, it is decided to commence in this research with the assessment of an isolated plunging or pitching structure and the combined motion is left as next step There is no strong preference to start with either pitching motions or plunging motions, although plunging motions are expected to be more challenging regarding the PIV measurements It is simply decided to start with plunging motions.
Starting point is to achieve a low complexity level of the experiment to: 1) limit the amount of possible error sources in the experimental data, 2) enable in valida- tion processes a better pinpointing of the origin of deviations in the numerical data compared to the experimental data, and 3) make sure the emphasis can be put on the coupling of the flow and structure solvers Reduction of the complexity level can be arranged on the aerodynamic part by amongst others moderate angles of attack to prevent dynamic flow attachments and detachments On the structure part the number of degrees of freedom can be reduced to cancel higher order mode shapes In this context, the decision is made to use a rigid wing with one degree of freedom and a controllable flap to generate time varying forces The setup is intended to result in quasi-2-D flow, the Reynolds number is chosen such that it complements on the Reynolds regimes of other aeroelastic data Next to aeroelastic data, also existing measurement data for the same wing shape are taken into consideration: for the tar- get Reynolds number other steady measurement data are available that can serve as reference.
The measurement techniques which are used are well-known, except for the applic- ation and implementation of Noca’s method for moving and/or deformable structures. Therefore it is decided to prior to the fluid-structure interaction experimental cam- paign assess Noca’s method for a deformable structure: a wing (similar as used in the fluid-structure interaction campaign) with a moving trailing edge flap.
For the application of PIV with moving objects, a decision must be made upon the part of the flow field that must be captured for each location of the structure.
In combination with the desired flow field resolution this determines eventually the number of cameras that is needed or how many separate camera setups are needed in case of repeatable experiments Initial knowledge about the expected structural displacements is hereby needed Hereto, a numerical model based on Theodorsens model is applied to roughly estimate the structural properties and the accompanying structural responses.
The aeroelastic experiment is designed using Theodorsens model: the measure- ments to conduct and the structural properties are determined from simulations. Hereby, a trade-off for the structural parameters is made keeping in mind the amount of camera setups for PIV, the frequency limits of the flap, the desired frequency range to cover (0.5/ ω/ ω n /1.5) and the aim to have only low to moderate induced angles of attack due to the structural velocities The experiment is conducted in the open jet facility to have the best optical access to the structure and since wing blockage effects might be influential in the closed tunnel.
Finally, in this thesis the fluid-structure interaction cases under consideration are simulated with three levels of fidelity numerical models: Theodorsens model, a panel code and an URANS solver The emphasis is on the possibility of modelling the quasi- 2-D experiment as a 2-D case with corrections for the wind tunnel influences, in order to reduce the computational time The impact of the modelling choices is assessed based on a comparison with the experimental data and the other computations.
Outline
The outline of this thesis follows roughly the setup as described in the approach.
In Chapter 2 first some fundamental concepts, implementations and post-processing techniques are described The first experiment treating the application of Noca’s method to deformable structures is treated in Chapter 3 Chapter 4 discusses the fluid-structure interaction experiment followed by the numerical simulations of the experiment in Chapter 5 Conclusions and recommendations are finally presented inChapters 6 and 7.
Terminology, wind tunnel models and methodologies
In this chapter background information is provided about used terminology, existing methodologies and the wind tunnel model Background information that is specific for topics treated in the various chapters, is discussed in those chapters separately.
In this chapter first some general terminology is explained and averaging and data reduction methods are discussed Background information is provided about the wind tunnel model and the 2-D numerical representation of this model Measurements are conducted in a closed wind tunnel and an open jet tunnel, as elaborated on in Sections3.1 and 4.1 For both tunnels a discussion about wind tunnel corrections is provided.Next the load determination using particle image velocimetry (PIV) is discussed.Regarding the post-processing next to the data reduction the uncertainty analysis is treated Parts of this chapter are based on two papers: Sterenborg et al [2014a] andSterenborg et al [2014b] Section 2.2 is based on work done by Boon et al [2012].
Terminology
Characteristic (non-)dimensional numbers
First consider a quasi-steady or unsteady periodic flow Classification of these types of flows can be arranged using non-dimensional numbers In fluid dynamics the residence time tr can be expressed as a function of a characteristic length scale L and the undisturbed flow velocityuas follows: tr= L u (2.1)
For unsteady flows with some periodic flow feature, the residence time can be related to some periodic time scale ω − 1 The resulting quantity is known as the Strouhal number:
In this relation f is the frequency of the oscillating flow mechanism In case of periodic motions an important parameter is the non-dimensional reduced frequency that relates the velocity of the motion to the undisturbed flow velocityuaccording to k=πf c u , (2.3) where in this workf is the flap frequency andc is the chord The reduced frequency is a measure for the degree to which unsteady phenomena are occurring.
Flap phase angle
The attitude of the flap of the wing model used is controlled using two servo engines. Besides static flap deflections, in this thesis harmonic flap deflections are prescribed. This means that the flap deflectionδ can be written according to δ=δmean+δampãsin
In this equationφis the flap phase angle in degrees,δmeanis the mean flap deflection andδamp is the amplitude of the deflection around the mean By definition the phase angleθδ = 0 and can therefore be omitted.
The flap phase angle is used as reference signal in the experiments, but also as a reference signal in the post-processing of the measurement data and the numerical solutions.
Averaging methods
Based on the harmonic flap oscillations, the fact that attached flow is promoted and displacements are kept small, periodic flow phenomena and structural responses are expected Consequently the data can be post-processed using phase averaging, where the flap deflection determines the phase angleφ Hussain and Reynolds [1972] proposed a decomposition of an arbitrary fluctuating quantityf(~x, t) in three com- ponents, namely the classical time average ¯f(~x), a coherent fluctuation ˜f(~x, t) and an incoherent or random fluctuationf ′ (~x, t): f(~x, t) = ¯f(~x) + ˜f(~x, t) +f ′ (~x, t) =hf(~x, t)i+f ′ (~x, t) (2.5)
Phase averaging will result in the sum of the time average and the coherent fluctu- ations, hf(~x, t)iby the elimination of the incoherent or random fluctuations f ′ (~x, t) from the input signalf(~x, t) Phase averaging is based on ensemble averaging, where the instance of evaluation is in this case based on the instantaneous flap phase angle φ(t): hf(~x, φ(t))i= 1
In this relationT is the period belonging to the flap oscillation.
Prior to the described phase averaging, moving averaging is employed to reduce noise in the various quantities of interest Mind that in this process the random fluctuationsf ′ (~x, t) are modified as well as the resolution of the quantities of interest.
In a mathematical formulation the simple moving averaging process is described by f(~x, φ(tint)) = 1
X tǫ[t 1 ,t 2 ] f(~x, φ(t)), (2.7) wheretint is the discretized time at which the simple moving average for the interval t1 ≤t≤t2 is assigned and t1 ≤tint ≤t2 The number of samples found within the interval equalsN.
Data reduction
After averaging of the data, for each quantity the data is reduced to one full period of the flap phase angleφ In the data reduction process it is investigated whether the periodic signal is harmonic In case a harmonic signal is found, the quantity is fully determined by a mean value, an amplitude and a phase angleθ It turns out that all quantities of interest are harmonic, except for the drag that deviates from a harmonic signal Despite a small error is made, also for the drag the same characteristic values are used to represent the signal.
Wind tunnel model
Model description
The used wind tunnel model is a wing based on the 18% thick DU96-W-180 wind turbine aerofoil Reason for this choice is the amount of available data for this aerofoil, mainly measured in the same facility, see Timmer and van Rooij [2003], Timmer [2010] and Appendix H The wing is untwisted and untapered and has a chord of 0.5 m, a span of 1.8 m and a 0.2cflap Except for the wing span, which is based on wind tunnel dimensions, the wing size is driven by the desired Reynolds numbers and the fact that flap engines must be housed inside the wing In Chapter 1 it was elaborated that a rigid wing with a controllable flap is used such that the flow topology and the structure dynamics can adequately be controlled This will help to bound the overall complexity and more straightforward validations are foreseen To achieve a good rigidity and a low mass, the wing is made of carbon fibre The flap is hinged at the lower surface of the carbon fibre wing using continuous hinges This suspension allows the flap to move in upward and downward directions over a range of at least ±25 ◦ Gap flow between the wing and flap as reported by Liggett and Smith [2013] is prevented by seals covering the gaps on both the suction and pressure side The manufacturing tolerance is about 1 mm, meaning the actual shape differs from the DU96-W-180 The wing span has a manufacturing tolerance of 5 mm In the following section (2.2.2) this is more elaborated on.
The Reynolds number for the tests is around Rep0 000, for which in steady flow natural transition is expected somewhere mid/aft of the chord of the model In the majority of the experiments the flap is oscillating and for the aeroelastic experiments the wing plunges, which might affect the transition location In the end the transition location is not known and it is helpful to force transition with tripping wires This to reduce uncertainty in e.g calculated force coefficients since also in simulations the transition location is difficult to predict For each experiment, details about the tripping wire setup are presented in the experimental setup descriptions, see Section3.1.2 and Section 4.1.2.
Wing model derived with co-kriging
For modelling purposes, the actual geometry including seals has been measured using two different approaches Using these two measurement data sets as input for co- kriging, the wing model shape is determined as described by Boon et al [2012] In this section a summary is given of the results presented by Boon et al [2012]. For the first measurement approach at seven spanwise stations the cross-sectional shape is measured with a coordinate measuring machine (CMM) The resulting 2-D profiles are subjected to a measurement uncertainty of about 0.25 mm The second measurement has been conducted with an optical technique called photogrammetry, see e.g Li [1993] With this technique 3-D coordinates of the wing are determined. This technique is based on images taken with calibrated cameras from various ob- servation locations with respect to the wing The wing is marked with yellow labels to identify specific locations, as can be seen in appendix D A computer algorithm extracts the location of the marks from the pictures and computes the belonging coordinates of the three-dimensional object The accuracy of the photogrammetry measurements is determined to be 0.10 mm.
With co-kriging the low-fidelity CMM measurement data and the high-fidelity, but low resolution 3-D photogrammetry measurement data can be combined to obtain a high fidelity wing model Co-kriging is explained by Kennedy and O’Hagan [2000,
2001] as a method that interpolates outputs by combining multiple data sources, considering also the uncertainty and the smoothness of the data Based on kriging, this technique uses the assumption of Gaussian processes A more detailed description of co-kriging is given in appendix C.
In the high fidelity shape determination, the variances used in co-kriging for the input data are based on the accuracy of the measurements: 0.25 mm for the low fidelity data and 0.10 mm for the high fidelity data Figure 2.1 shows the measurements of the geometry and the high fidelity wing representation obtained using co-kriging. From the data presented in Figures 2.1 and D.2 it can be concluded that the wing planform is not two-dimensional as it is supposed to be In general, this implies that in 3-D simulations this determined shape should be modelled accordingly In the 2-D numerical simulations in this research a 2-D cross-sectional shape is used by taking the mean of the 35 reconstructed aerofoils along the span displayed in Figure 2.1b.
In appendix D this geometry is tabulated and the variance on the mean shape with respect to the 35 sections is presented Although not further reported here, Boon et al.
[2012] investigated the propagated uncertainty of amongst others the use of this mean geometry in the computed force and moment coefficients for steady flow Mind also that due to the reported shape deviations, a fair comparison with the DU96-W-180 data measured by Timmer [2010] and presented in Appendix H is not possible. x [m] y [m ] z [m]
Figure 2.1: CMM measurements (blue dots) and photogrammetry measurements (red dots) of the 3-D wing geometry are shown in Figure 2.1a The 3-D wing model resulting from co-kriging of the CMM and photogrammetry data is shown in Figure 2.1b Source: Boon et al [2012]
Standard wind tunnel corrections for steady flow
Steady corrections closed wind tunnels
For steady flows Havelock [1938] presented a set of relations for the 2-D lift interference correction for a centrally positioned wind tunnel model The relations correct the angle of attack and the lift and moment coefficients as follows:
In these equations the subscript t denotes a tunnel recorded value, his the tunnel height,c the chord andβ the Prandtl-Glauert compressibility factor given by β =p
1−M 2 , (2.9) where M is the Mach number The solid blockage and wake blockage can be corrected using correction formulations presented by Krynytzky et al [1998] For solid blockage and wake blockage the interferences can be determined using ǫsb=π 6
(2.10) where the solid blockage is indicated by the subscript sb and the wake blockage by wb In the solid blockage relationAis the effective cross-sectional area of the model, the other variables are according to the previous definitions These relations can be used to apply a linear correction to amongst others the flow velocity and the Reynolds number: u=ut(1 +ǫsb+ǫwb),
The presented corrections are applied in numerical simulations The steady balance measurements in the closed wind tunnel, see Chapter 3, are corrected by embedded correction models in the wind tunnel control systems, as presented in A These cor- rection formulations differ from the corrections presented here, but the underlying principles are similar Furthermore, a quick check using both correction methods on steady balance measurements in the closed wind tunnel learned that the corrected results are very similar.
Steady corrections for open jet wind tunnels
The open jet wind tunnel corrections are taken from work presented by Brooks et al.
[1984] The wind tunnel corrections are valid for an aerofoil in a steady, open jet flow and given by the relations: α=αt−
√3σ π cl,t−2σ πcl,t−σ π4cm,t, cl =cl,t, cd=cd,t+
(2.12) where the tunnel blockage factorσis a parameter based on the wind tunnel geometry: σ=π 2 48 c h 2
In the equations the subscript t again denotes the measured quantity in the wind tunnel,his the wind tunnel height andcthe wing chord These corrections are used in the various numerical simulations of the aeroelastic experiment to take into account the wind tunnel influences.
Wind tunnel measurements and FSI
The wind tunnel corrections presented in the former section are an example of widely accepted and used correction methods by the community Drawback is that the cor- rections are intrinsically valid for steady measurements For unsteady measurements corrections are less straightforward and an assessment of each problem can be done to quantify the influence of the wind tunnel on the measured unsteady quantities. This influence will be a combination of level shifts, similar to steady flows, and time delays In this work two different wind tunnels are used and for each of these tunnels an investigation is done on the wind tunnel corrections This will be presented more in depth including results in Section 3.3 for a closed wind tunnel and in Sections 4.2.6 and 5.1.2 for an open jet wind tunnel.
For fluid-structure interaction wind tunnel experiments the influence of the wind tunnel is not only visible in the forces, but also in the structural responses Depend- ing on the reduced frequency or unsteadiness level, mainly quantitative level shifts are expected or a combination of quantity level shifts and phase changes In the numerical modelling this means that the wind tunnel influences must be modelled as well to capture the correct flow and structure states Two possible options are: 1) full modelling of the setup including wind tunnel, or 2) a modelling of wind tunnel corrections on the forces used to compute the new structure state.
The second approach is based on a correction procedure that can be summarised as follows for a certain (subiteration within a) time step, starting with the structural state:
1 Update the structure state Structural displacements and velocities are com- puted for aerodynamic loading in the open jet or closed wind tunnel.
2 Update the flow state in freestream conditions for the structural state (in the open jet or closed tunnel) computed in step 1.
3 Determine the free stream aerodynamic loads on the structure using the flow state computed in step 2.
4 Correct the calculated aerodynamic loads using wind tunnel corrections and pass these open jet or closed tunnel loads to the structural solver Proceed to step 1.
The solution consists of the corrected aerodynamic loads and the structure state.
In case the flow state is first treated instead of the structure state, the approach is similar with the difference one starts at point 2 and ends with 1 each time level or subiteration.
The drawback of this second correction approach is that there is an inconsistency in the calculation of the flow state for freestream conditions, since it uses displacements that are based on wind tunnel conditions For displacements with a considerable in- fluence on the effective angle of attack (several degrees) and/or flow conditions outside the linear part of the lift curve, this used approach is likely to cause non-negligible errors However, for the flow and structure states considered in this work this method can be used without any significant error due to this mentioned inconsistency.
Particle Image Velocimetry
Principles of PIV
Particle image velocimetry (PIV) is a measurement technique based on images of scattered light from tracer particles submerged in a fluid flow The measurement technique is extensively described in literature, see e.g Westerweel [1997], Raffel et al [2007] PIV is considered to be a non-intrusive measurement technique and can be applied to a 2-D plane or a 3-D area For 2-D measurements a laser combined with optics is used to illuminate a thin planar area where the tracer particles pass through With one or more cameras the tracer particle locations are recorded and the velocity field is reconstructed from two consecutive images by post-processing The post-processing is based on cross-correlation for individual, small image regions called interrogation windows The resolution of the resulting velocity field depends on this subdivision of the images in interrogation windows.
When two cameras are used to observe a specific 2-D area, the out-of-plane velocity component can also be reconstructed (stereoscopic PIV) For 3-D tomo-PIV laser with optics illuminate a 3-D area observed by multiple cameras Following the work of Elsinga et al [2006] from the recordings a 3-D flow field can be reconstructed using optical tomography In this work planar PIV is applied in the experiments Only a few stereoscopic PIV images are recorded for flow three-dimensionality checks. The area which is captured with the camera(s) is called the field of view (FOV).
In the ideal case the FOV covers the flow domain of interest, which means that one camera setup suffices In case the FOV is smaller than the region of interest, cameras must observe different parts of the flow domain This can be accomplished in one or multiple experimental runs.
In case the PIV images are recorded using multiple camera/laser setups also the experimental repeatability must be assured For the various runs the flow properties(viz undisturbed velocity, temperature, density, pressure) might differ slightly Small variations in the undisturbed flow velocity for the various runs can be dealt with by making each velocity field non-dimensional using the corresponding undisturbed velo- city After combining the various velocity fields into one velocity field for each phase angle, the resulting velocity field is dimensionalised using the average undisturbed velocity.
Phase-locked PIV
For periodical flows PIV can be applied in a phase-locked approach This is convenient when e.g the frequency of the periodical flow pattern is too large to capture the full cycle with the desired temporal resolution with the PIV system or when the flow field cannot be captured with the available camera(s) at once For phase-locked measurements a fixed reference signal is needed for timing and using user specified time delays with respect to this trigger signal the full cycle can be resolved with a desired temporal resolution It is evident that phase-locked PIV is only allowed when the periodicity of the flow is guaranteed.
Methods to derive (un)steady forces
Kutta-Joukowski’s circulatory approach
For inviscid, incompressible (un)steady flow the lift of a thin aerofoil can be determ- ined using Kutta-Joukowski’s method, see Katz and Plotkin [2001] The lift can be written as a combination of the instantaneous circulation bounding the aerofoil Γ(t) (first term, equivalent to the steady-state circulation) and a time dependent con- tribution dealing with pressure changes due to the acceleration of the fluid (second term):
∂tΓ(x, t)dx, (2.14) wherexis the chordwise distance and the circulation Γ is given by Γ(t) Z Z
According to Kelvin’s theorem a change in bound circulation leads to vortex shedding in the wake of equal, opposite strength This implies that for steady flow the location of the contourC is not important, as long as it surrounds the aerofoil For unsteady flow, vorticity is shed in the wake and the location of the contour C in the wake determines the extent of time history or delay in the captured circulation Hereby the contourC must intersect the wake more or less perpendicular with respect to the direction of convection The time delay equals the time it takes for particles to travel from the aerofoil’s trailing edge to contourC in the wake An exact determination of the time delay from experimental data is not always straightforward.
Since all unsteady lift forces are expected to be periodic, it is chosen to not de- termine the phase and use Relation (2.14) for steady flow in this work by neglecting the second term Only the lift variation and mean value are considered The occurring time delay will not be regarded Furthermore, the disregard of viscosity introduces a small offset with respect to determined forces including viscosity effects (e.g balance measurements).
Noca’s momentum flux equation
Noca’s method allows for the determination of (un)steady loads acting on a submerged object from the velocity field and its derivatives in space and time The formulation is a rewritten version of the Navier Stokes momentum equation and is valid for in- compressible flows (∇ ãu= 0) A complete description can be found in the work of Noca et al [1999] The final relation in tensor form is given by Equation (2.16) and the corresponding contours and sign conventions can be found in Figure 2.2, where a sample domain of integration is given.
In Equation (2.16) all bold printed variables are tensors and N is the dimension of the problem In this research planar PIV is used and consequentlyN = 2 The term γfluxis a short notation for γflux=1
As can be seen in Equation (2.16) the forceF is composed of a surface integral along a finite contourS(t) enclosing the object(s) of interest and two surface integrals along the circumference of the object(s), denoted by Sb(t) Steady and unsteady loads predicted with Noca’s method are for incompressible flows in theory indifferent to the location of the body enclosing contour The strength of the relation is that only the velocity field u, its time derivatives ∂ ∂t u and the spatial variablex are needed Also the spatial derivatives of the velocity field must be known to compute the vorticity ω and the viscous stress tensorT, for which a Newtonian fluid assumption is used.Other variables present in Equations (2.16) and (2.17) are: the normal vectornˆand the body wall velocityus in tensor form. ˆ n ˆ n
Figure 2.2: Domain of integration momentum flux equation Included is the orientation of boundaries S(t) and S b (t) and of the normal vectors ˆ n Based on an image presented in Noca et al [1999].
The second term of Equation (2.16) evaluates the velocity normal component at the surface of the object(s) In case no boundary layer suction or blowing is applied, just like in this thesis, the term vanishes The third integral will be non-zero in case accelerations of the object(s) occur In this work a wing with oscillating trailing edge flap is considered and for the fluid-structure interactions the wing additionally moves in space Therefore this term will contribute for all unsteady cases to the aerodynamic loading This term is discretized similar to the determination of the time derivatives of the velocity: central differences or forward differences are applied to the exact flap positions in time.
In order to evaluate unsteady forces using the momentum flux equation it is re- quired to have velocity fields at multiple instants Since the time derivative of the velocity is needed, at least two pairs of snapshots within a short time interval are needed to determine the unsteady loads at a certain time Depending on the time scale of the problem, an estimate can be made of the desired temporal resolution with which the unsteady loads are determined.
The third and fourth terms in Noca’s formulation (2.17) are based on the first moment of vorticity In case of spatial coarseness of experimental data in thin wakes, the spatial velocity derivatives and thus the vorticity are not captured properly The influence of a poorly determined vorticity field on the predicted loads can be minimised by a reduction of the distance tensorx, according to a coordinate transformation as proposed by Sim˜ao Ferreira et al [2008] Although in this thesis the spatial resolution is sufficient, the coordinate transformation is performed preventively.
Velocity fields acquired with phase-locked PIV are averaged velocity fields This means that quadratic terms in the velocity of the wake result in Reynolds stress like terms This introduces another error that is not quantified in this research, but deserves attention in the future For thin wakes as is the case in this work, the impact is expected to be small.
Implementation of Noca’s method
A post-processor is written to extract the loads from the various velocity fields using Noca’s method A validation of this implementation of Noca’s method is presented using only numerical velocity fields and when applicable the structural motions Fur- thermore, an examination is presented on the influence of the contour location along which Noca’s formulation is evaluated.
Consider first a viscous steady velocity field obtained with a RANS solver, Hex- stream of NUMECA International [2007] A wind tunnel and the DU96-W-180 aero- foil, as described in Section 3.1, are modelled in 2-D with slip walls for the wind tunnel using an unstructured, body conformal mesh of 258k cells The inlet is 6 chord lengths upstream and the outlet is 20 chord lengths downstream Closure model is Spalart Allmaras’ turbulence model The angle of attack isα= 0 ◦ , the flap is not deflected and the Reynolds number is Re = 700 000 For post-processing the RANS solution is mapped onto a new, equally spaced computational mesh using linear interpolation. Elliptic contours are chosen, since the change in shortest distance with respect to the aerofoil surface along the contour is small This latter is indicative for the influence of viscous effects outside the wake Drawback of this choice is the solution needs to be interpolated to the contour control points The distance d of the contours with respect to the aerofoil varies between d = 0.08c and d = c The presented results are obtained for a mapping onto a mesh with 0.2%c grid spacing and 750 contour elements Part of the computational domain, the aerofoil and the used contours are plotted along with the mapped velocity field and vorticity field in Figures 2.3a and 2.3b respectively. x / c [-] y / c [- ]
(a) Dimensionless velocity field and 45 con- tours. x / c [-] y / c [- ] ωãc / u [-]
(b) Dimensionless vorticity field and 45 contours.
Figure 2.3: Part of dimensionless velocity and vorticity fields, along with 45 contours. Mapped 2-D RANS solution, α = 0 ◦ and δ = 0 ◦ , grid spacing is 0.2%c and 750 con- tour elements Velocity U scaled with free stream velocity u, vorticity ω scaled with chord c and free stream velocity u.
In Figure 2.4 the lift coefficient as a function of the non-dimensional contour distance d / c with respect to the aerofoil is plotted for Noca’s approach along with the numerical solution Also the contribution of the first four terms of Relation (2.17) are given The first two momentum terms are approximating the numerical solution with increasing contour distance The vorticity related third and fourth term, are supposed to drop significantly with increasing contour distance This trend is also found in Figure 2.4, as well as small variations.
RANS solution Noca (258k) Noca, term 1,2 (258k) Noca, term 3,4 (258k)
Figure 2.4: Lift coefficient c l as a function of the distance d divided by the chord c Obtained with Noca’s approach for 45 contours applied to a 258k viscous RANS simulation Included is the contribution of the first four terms of Relation (2.17) and the numerical solution.
For the current implementation the main conclusions are: 1) for contours with a distance less than 0.1cfrom the aerofoil, the forces are more than 10% off from the forces determined with the solver, and 2) the solutions within one chord distance from the object on different contours fluctuates around the target solution with an error of about 2% Since Noca’s formulation is exact, the errors are due to the implementation.
In particular the numerical determination of gradients and linear interpolations, which are applied for mapping the solution onto the new computational mesh and onto the contour of evaluation, are error sources Verification of the numerical methods is executed by using finite difference schemes of different order, by changing the grid spacing and the number of contour elements.
The errors can be reduced by e.g applying the contours of evaluation in regions with relatively small gradients in the solution, using sufficient contour elements and/or by using higher order finite difference schemes to compute gradients Numerical errors will also reduce significantly by using a higher resolution data set Furthermore, in general the numerical errors are not constant for different contours and a statistical assessment using multiple contours is advised For this particular case taking an average of the forces evaluated on contours ranging from 0.1< d /c0.05, see Mathew and Philip [2011], and 2) the effect of changing flap deflection and unsteadiness level is identifiable in the response.
The first test case consists of steady measurements with the balance system without flap deflection, so δmean = 0 ◦ An angle of attack sweep is made from α=−5 ◦ up toα= 25 ◦ , see Appendix H This test case serves as a reference for thePIV measurements The second test case, is a sequence of four steady PIV experi- ments with flap deflections ofδmean = 0 ◦ ,2 ◦ ,4 ◦ ,6 ◦ forα= 0 ◦ The unsteady test cases, all PIV measurements, are characterised by a harmonically actuated flap with reduced frequencies ofk = 0.1 and k = 0.2, where the reduced frequency is defined
Figure 3.4: Parker PRA25 flap actuation system attached to the flap, with the wind tunnel side wall partially opened up. according to Equation (2.3) Fork= 0.1 the flap mean deflectionδmeanand the amp- litudeδamp are set to 3 ◦ and 3 ◦ respectively Fork= 0.2, next to these settings also a mean deflection of 1 ◦ and an amplitude of 1 ◦ are used Standard sign conventions apply, meaning downward flap deflections have a positive sign The angle of attackα is for all unsteady casesα= 0 ◦
Test case α a δmean b δamp c k d Reynolds number
5 0 ◦ 3 ◦ 3 ◦ 0.2 a angle of attack [ ◦ ]. b flap mean deflection, downward positive [ ◦ ]. c flap deflection amplitude [ ◦ ]. d Reduced frequency [].
PIV setup and apparatus
Details about the PIV setup and settings are presented in this section In Section 2.5 a concise explanation of PIV is provided, for more details about the used terminology and concepts the work of Raffel et al [2007] can be consulted Each velocity field that is acquired with PIV covers a cross-sectional plane mid-span of the wing The captured area ranges in all directions maximum half a chord length and is built up from 16 different separate image pair recordings or fields of view (FOV), which each have an overlap with respect to each other, see Figure 3.5 Each constructed velocity field is normalised with the undisturbed flow velocity, such that all separate fields of view can be stitched to end up with one body enclosing velocity field The overlapping regions are a source of unwanted noise in the total velocity field With an increasing number of FOV’s the quality of the data is likely to deteriorate compared to one FOV with the same resolution Possible causes are: alignment errors of the laser sheet, calibration errors and timing errors Stitching is performed by taking the mean value in the overlap region In some overlap regions the data of one FOV is used, since the lack of quality in the other FOV Judgement of quality is based on either visual inspection of the velocity field and/or the PIV peak ratio In some regions, smaller than 5%c, use is made of data interpolation, to prevent jumps in the solution due to erroneous data. x/ c [-] y/c[-]
Figure 3.5: The domain of interest and the 16 field of views.
Two CCD cameras of 1.4 megapixel are used in a co-planar orientation with lenses of 180 mm to record the FOV’s The cameras are mounted in a fixed position on a traversing system such that one calibration is sufficient for all images The laser sheet, with an approximate thickness of 3 mm is generated with a Nd:YAG double pulse laser with a power of 200mJ/pulse and a variable interval between two consecutive pulses. The used particles are 1àm droplets generated by a fog machine, having its outlet directly downstream of the test section.
Since the motion of the flap is periodic, all the images can be recorded in a phase- locked approach, see Section 2.5.2 Hereto, at a fixed flap deflection a trigger signal is sent to the PIV-computer Predetermined time intervals with respect to this trigger signal are applied to prescribe the desired flap phase anglesφat which the images are taken At each phase angle 100 image pairs are recorded and averaged The number of image pairs is based on the convergence of the resulting velocity field with respect to the number of image pairs A converged solution was found for about 40 image pairs, so the recorded 100 image pairs are more than sufficient The phase angleφis related to the flap angleδaccording to Relation (2.4) withθδ = 0 ◦ andδamp =δmean: δ=δmean
The temporal resolution is defined by two sequences of images: one is recorded for φ =m×45 ◦ , another sequence of images is obtained for φ= 5 ◦ +m×45 ◦ , with
0 ◦ ≤ φ < 360 ◦ and m a positive integer Using the phase difference ∆φms = 5 ◦ between both sequences, the velocity derivatives with respect to time (needed for Noca’s approach, see 2.6.2) can be approximated using forward differences (first order accurate) Hereby, according to the work of Jensen and Pedersen [2004], it is aimed for that the phase difference between the first and second sequence is chosen just large enough This should lead to time derivatives with a good signal to noise ratio, without loosing the instantaneous character For comparison, also central differences (second order accurate) are applied with ∆φms = 45 ◦ for the determination of the time derivatives of the velocity.
Images are post-processed by multipass sequential cross correlation with Whit- taker reconstruction, see Whittaker [1915] The first pass is performed using an interrogation window size of 64×64 pixels with zero overlap followed by a second pass with interrogation windows of 32×32 pixels and 50% overlap Each FOV has a standard size of 225 mm×170 mm, leading to about one vector per 1% chord length for a window size of 32×32 pixels The actual vector resolution is even more dense, since overlap is used.
For the steady measurements the same settings apply for the post-processing The only difference is that a trigger signal is not necessary, since the 100 image pairs can be recorded at any time after steady flow settlement.
In reality the flow is three-dimensional and therefore not fully captured by planar, two-dimensional PIV The applicability of planar PIV to the current setup is assessed by observing the amount of flow three-dimensionality Hereto, for steady flow multiple drag measurements are conducted around mid-span in span direction, covering at least50% of the span The three-dimensionality is not dominant for α= 0 ◦ : a standard deviation of the drag of 0.71 drag counts is found Wool tuft measurements for both the steady and unsteady cases also showed no dominant three-dimensionality of the flow.