Wakes behind wind turbines - Studies on tip vortex evolution and stability. Ylva Odemark

Transcription

1 Wakes behind wind turbines - Studies on tip vortex evolution and stability by Ylva Odemark May 22 Technical Reports from Royal Institute of Technology KTH Mechanics SE- 44 Stockholm, Sweden

2 Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie licentiatexamen tisdagen den 22:a maj 22 kl :5 i sal E33, Lindstedtsvägen 3, Kungliga Tekniska Högskolan, Stockholm. cylva Odemark 22 Universitetsservice US AB, Stockholm 22

3 Ylva Odemark 22, Wakes behind wind turbines - Studies on tip vortex evolution and stability Linné Flow Centre, KTH Mechanics, SE- 44 Stockholm, Sweden Abstract The increased fatigue loads and decreased power output of a wind turbine placed in the wake of another turbine is a well-known problem when building new wind power farms. In order to better estimate the total power output of a wind power farm, knowledge about the development and stability of wind turbine wakes is crucial. In the present thesis, the wake behind a small-scale model turbine was investigated experimentally in a wind tunnel. The velocity in the wake was measured with hot-wire anemometry, for different free stream velocities and tip speed ratios. To characterize the behaviour of the model turbine, the power output, thrust force and rotational frequency of the model were also measured. These results were then compared to calculations using the Blade Element Momentum (BEM) method. New turbine blades for the model were constructed using the same method, in order to get an estimate of the distribution of the lift and drag forces along the blades. This information is needed for comparisons with certain numerical simulations, which however remains to be performed. By placing the turbine at different heights in a turbulent boundary layer, the effects of forest turbulence on wind turbine outputs (power and thrust) could also be investigated. The evolution of the tip vortices shed from the turbine blades was studied by performing velocity measurements around the location of the tip vortex breakdown. The vortices receptivity to disturbances was then studied by introducing a disturbance in the form of two pulsed jets, located in the rear part of the nacelle. In order to introduce a well-defined disturbance and perform phase-locked measurements, a new experimental setup was constructed and successfully tested for two different disturbance frequencies. The mean streamwise velocity and the streamwise turbulence intensity was found to scale well with the free stream velocity and the spreading of the wake was found to be proportional to the square root of the downstream distance. The comparison for power and thrust between measurements and BEM calculations showed good agreement in some cases but worse agreement when the pitch angle of the blades was small. The velocity measurements showed that the tip vortices can be susceptible to disturbances and an earlier breakdown could be detected. However, more measurements need to be made to fully investigate the dependance on disturbance frequency and amplitude. iii

4 Preface This licentiate thesis within fluid mechanics deals with the evolution and stability of wakes behind wind turbines, with special focus on the development and breakdown of the tip vortices that are shed from the turbine blades. This was studied experimentally in a wind tunnel by performing velocity measurements with hot-wire anemometry in the wake behind a small-scale model turbine. The thesis is divided into two parts, where the first part consists of a description of the measurements and a summary of the present work. The second part consists of two papers. In chapter 6 of the first part, the authors contributions to the papers are stated. April 22, Stockholm Ylva Odemark iv

5 Contents Abstract Preface iii iv Part I. Overview and summary Chapter. Introduction Chapter 2. Wakes behind wind turbines Basic definitions Theory of wind turbine wakes D momentum and mass conservation for an ideal wind turbine The Blade Element Momentum method Chapter 3. Experimental design and setup Wind tunnel Measurement techniques Disturbance generation Turbine models Turbine blade design 27 Chapter 4. Results Comparison between measurements and the BEM method Wake development Tip vortex instabilities 56 Chapter 5. Summary and conclusions 69 Chapter 6. Papers and the authors contributions 72 Acknowledgements 74 v

6 References 76 Part II. Paper. Papers Phase-locked hot-wire measurements on the breakdown of wind turbine tip vortices 83 Paper 2. Effect of forest turbulence on wind turbine outputs 5 vi

7 Part I Overview and summary

8

9 CHAPTER Introduction For several years, there has been an increasing demand for energy. The world s resources are limited, and the need for renewable energy sources are evident for creating a sustainable society. Wind energy is currently a fast growing source of renewable energy, as can be seen in Fig.., where the installed capacity as a function of time is shown. By building multiple wind power plants in farms, the production cost per kwh can be decreased. Fig..2 shows the number of wind power sites in Sweden as a function of time. In 2, there were 37 sites, corresponding to 66 wind power plants. When building wind power farms, the key parameter to optimize is the total production of the farm as a whole. This is a quite difficult problem, and it is not obvious that maximum energy should be extracted from the first turbine, i. e. the turbine that sees the undisturbed wind. The placement of the turbines inside farms is a complex problem with many parameters. The wind conditions on the specific site has to be considered (wind speed, wind directions and turbulence levels), but also the loadings on the individual turbines, maintenance costs and the cost for building the farm. The production losses and additional loads on turbines placed in the wake of another turbine is a well-known problem when building new wind power farms, and a subject of intensive research. An important tool in wind farm design is different types of numerical simulations. These can be quite simple and fast, or more advanced, which in general means that they require more computer resources. A simulation of a farm where the flow is completely resolved everywhere is not possible today, and the flow and the turbines need to be modelled in some way. In order for a model to give reliable results for different types of cases with different boundary conditions, it needs to model, or at least describe, the physics of the problem in an adequate way. There is a need for these models to be validated, which can be done with either controlled laboratory experiments or with field measurements. There is to current date only a limited amount of idealized, controlled studies available for comparison with the numerical models. There is a need for more measurements for comparison, which will also help to enhance the understanding of the physics of wind turbine wakes, which is crucial when developing new models.

10 2. INTRODUCTION Installed capacity in the world, [GW] Installed capacity in Sweden, [GW] year Figure.. Installed capacity of wind energy 996-2, in the world (grey) and in Sweden (black). Data from the Global Wind Energy Council (22), the World Wind Energy Association (22) and the Swedish Energy Agency (22). Number of wind power sites year Figure.2. Number of wind power sites in Sweden Data from the Swedish Energy Agency (22).

11 CHAPTER 2 Wakes behind wind turbines 2.. Basic definitions The Reynolds number, which can be seen as inertial forces divided by viscous forces, is defined as: Re = U D, (2.) ν where U is the free stream velocity, D is the turbine diameter and ν is the viscosity. The chord Reynolds number is defined in the same way, but with the blade chord length c as the characteristic length scale: Re c = U c ν. (2.2) To scale the frequency f of a periodic phenomenon, the dimensionless Strouhal number St can be used: St = fd U. (2.3) In this study, the added secondary disturbances with frequency f are scaled to non-dimensional frequencies f d according to: f d = 2πfν U 2 6. (2.4) The tip speed ratio λ is the ratio between the rotational velocity at the tip (ωr) and the free stream velocity: λ = ωr U, (2.5) where ω is the angular velocity and R is the blade radius. The axial induction factor a and the tangential induction factor a are defined as: a = u U, a = u θ 2ωr, (2.6) where u is the streamwise velocity at the rotor plane, u θ is the tangential velocity in the wake and r is the radial coordinate. 3

12 4 2. WAKES BEHIND WIND TURBINES The thrust and power coefficients are defined as: T C T = 2 ρu A, (2.7) 2 P C P = 2 ρu A, (2.8) 3 where T is the thrust force, P is the power output from the turbine, ρ is the air density and A is the rotor area. The lift and drag coefficients, based on the lift L and drag D per unit length, are defined as: L C L = 2 ρu rel 2 c, (2.9) D C D = 2 ρu rel 2 c, (2.) where U rel is the relative velocity seen by the blade and c is the chord length. The solidity σ of a turbine at a radial position r is: σ(r) = c(r)b, (2.) 2πr where B is the number of blades. The total solidity can then be found by integrating Eq. 2. along the radius Theory of wind turbine wakes Basic features of wakes behind wind turbines The wake behind a wind turbine can be divided into the near wake region and the far wake region (Vermeer et al. 23). The near wake is strongly effected by the rotor shape, the number of blades, blade aerodynamics (attached or stalled flows) and 3D-effects (Hu et al. 2). Another strong feature of the near wake is the helical system of tip vortices, which are shed from the blades. These vortices have been found to significantly affect the turbulent flow structures in the wake (Hu et al. 2) and they also have a strong influence on the behaviour of the wind turbine rotor as a whole (Vermeer et al. 23). The vortices have also been found to be a source of noise generation and blade vibrations (Massouh & Dobrev 27). The far wake is the part of the wake where the actual rotor shape is less important. When studying wind turbine wakes, among the most interesting properties are the wake expansion, defined by the tip vortex path, vortex spiral twist angle and vortex strength. For wind power farms, the stability of the wakes is also very important, since the velocity deficit has a direct influence on the power output from the subsequent turbine, and because the increased turbulence levels in the wake cause increased loadings for the next turbine. The yaw angle (angle between the rotor plane and the incoming wind, where a 9 degree angle

13 2.2. THEORY OF WIND TURBINE WAKES 5 corresponds to zero yaw) also has a strong effect on the turbine performance. In a wind tunnel experiment, Krogstad & Adaramola (2) showed that a yaw angle larger than decreased the power output significantly. The same results were also shown in a wind tunnel study by Medici (25), where C P decreased by 4% for a yaw angle of and with 2% for a yaw angle of 2. The main advantage of wind tunnel experiments (as opposed to field measurements) is the controlled conditions. There is the possibility to control both the temperature, the incoming velocity profile and the turbulence intensity. A number of different parameter studies can thus be made. The main drawback is the much lower Reynolds numbers as compared to a real turbine or farm. A typical example of a real wind turbine, with a free stream velocity of about m/s, a rotor diameter of m and a viscosity of ν=.5 5, would give a Reynolds number of For the present work, the model turbine that was mostly used has a diameter of.78 m, and the free stream velocity is varied between 6. and.5 m/s. This gives a Reynolds number between 7 and 4, and the actual size of the model is thus about 5 times smaller than in reality. The chord Reynolds number Re c is also smaller in wind tunnel experiments, as compared to real turbines. For a typical wind power turbine in operation, Re c 5, and in the present experiments.4 4 <Re c < The chord Reynolds number has previously been found to have a significant effect on the characteristics of wind turbine performance (Alfredsson et al. 982) and the maximum power coefficient is also lower for a turbine operating at lower Reynolds numbers. However, the behaviour of the vortex structures and turbulent flow structures are less dependent of the chord Reynolds number (Medici & Alfredsson 26). Despite a difference in Reynolds number, parameter studies and validations with computations can therefore still be made. Some typical Reynolds numbers, free stream velocities, diameters and tip speed ratios are summarized in Tab.. Re Re c U, [m/s] D, [m] λ Field Exp Table. Comparison between typical Reynolds number Re, chord Reynolds number Re c, free stream velocity U,turbine diameter D and tip speed ratio λ for a real wind turbine (Field) and the present experimental model (Exp.). Another important parameter which has gained attention recently is the influence of the atmospheric boundary layer. Experiments with model wind turbines placed in an atmospheric boundary layer flow has been performed by for example Chamorro & Porté-Agel (29) and Zhang et al. (2), where

14 6 2. WAKES BEHIND WIND TURBINES it was shown that the wake had a non-axisymmetric distribution of both the mean velocity and the turbulence intensity. The evolution and stability of the tip vortices have been studied both experimentally (Grant et al. (2), Grant & Parkin (2), Yang et al. (22)) and numerically (Okulov & Sørensen (27), Walther et al. (27)). In a numerical study by Ivanell et al. (2), the stability was investigated by introducing a harmonic disturbance to the flow, and disturbance growth was detected for some specific frequencies and types of modes. However, very few attempts have been made to do the same experimentally Comparison between turbines and discs In numerical studies, turbines are often modelled as porous discs with a certain drag distribution. Experimentally, this can be achieved by substituting a rotor with a perforated plate. The rotor can thus be seen as a permeable disc, and as the tip speed ratio increases, the rotor acts more like a solid disc. Due to viscosity, the flow around a solid disc separates at the disc s edge, causing a low static pressure in the wake. In order to achieve atmospheric pressure in the far wake, the air must gain energy from the turbulent mixing processes in the wake. There is a stagnation point at the center of the disc, and thus very high pressure in front of the disc, causing a high pressure drag. The drag coefficient for a solid plate is.7 at sufficiently high Reynolds numbers (Hoerner 965). For a rotating disc (a rotor with an axial induction factor of ), the drag is even higher (Burton et al. 2). The reason is the thicker rotating boundary layer created on the upstream surface of the disc, which causes an even lower pressure on the downstream side. Small-scale model turbines get a higher chord-to-radius-ratio c/r as compared to a full-scale turbine. This is a Reynolds number effect and can be seen clearly when designing a turbine blade according to the Blade Element Momentum (BEM) method, which will be described later in this chapter. The longer chord together with a higher angular velocity give the small models a higher solidity than larger turbines, which also make them behave more as porous (or solid) discs. A disc with porosity high enough does not experience vortex shedding, whereas a solid disc does. The solidity of many turbine models do indeed become large enough to give rise to vortex shedding (see e. g. Medici & Alfredsson (26) and Medici & Alfredsson (28)), which is a feature not present in the wakes of large-scale turbines. For a porous disc, the shedding depends on the solidity. Cannon et al. (993) did visualizations of the flow behind porous discs with 5%, 6% and 85% solidity and for a solid disc. The shedding was very clear for the disc and the 85% case. Treating the model used in this study as a disc gives a Reynolds number based on the turbine diameter and the free stream velocity of 4 5. The shedding frequency at U =6.5 m/s was 6 Hz, which gives a Strouhal number

15 2.3. D MOMENTUM AND MASS CONSERVATION FOR AN IDEAL WIND TURBINE 7 of.6, which is in accordance with that of a disc. Miau et al. (997) measured the shedding frequency behind discs at Re between 3 and 5. The Strouhal number was found to be rather constant around.4 and slightly increasing with Re. It was concluded that the anti-phase characteristics of positions located 8 apart was preserved, but that the shedding also had a random nature. For the perforated plate, the interaction between the separated shear layers is disturbed by the flow through the disc, causing a delayed formation of vortices and an increased pressure behind the plate. This gives the perforated plate a lower drag and a higher Strouhal number as compared to the solid disc, as shown by Castro (97) for perforated plates of varying porosity at Re 4. The drag force naturally increase with an increasing solidity. Another interesting phenomena present in wind turbine wakes is a highly unsteady flow characterized by random horizontal oscillations (España et al. (2), Larsen et al. (28)).This wake meandering is due to large turbulent structures, with length scales larger than the wake width. España et al. (2) compared porous discs placed in an atmospheric boundary layer (ABL) as well as in conditions of homogeneous isotropic turbulence and found meandering in the first case, but not in the latter where the size of the largest scales were considerably smaller. The horizontal displacements of the wake were also found to be larger than the vertical ones in the ABL case D momentum and mass conservation for an ideal wind turbine For an ideal wind turbine, the flow is assumed to be frictionless and the rotational velocity component in the wake is assumed to be zero. For the cylindrical control volume with a circular cross section shown in Fig. 2., conservation of momentum (Eq. 2.2) and mass (Eq. 2.3) are written as: and ρu 2 A + ρu 2 (A A )+ṁ side U ρu 2 A = T (2.2) ρu A + ρu (A A )+ṁ side = ρu A ṁ side = ρa (U u ). (2.3) Mass conservation also gives: Combining Eqs gives: ṁ = ρua = ρu A. (2.4) T = ρua(u u )=ṁ(u u ). (2.5) The flow can be considered stationary, frictionless and incompressible everywhere except for the region around the rotor. Bernoulli s equation can therefore be applied from far upstream (pressure p,velocityu )tojustin

16 8 2. WAKES BEHIND WIND TURBINES!" m side " U! " A " u" T" A" u " U! " A " Figure 2.. Cross section of a cylindrical control volume around a wind turbine. The cylindrical control volume has a circular cross-sectional area and ṁ side is the total mass flow out of the surface area (not including the two circular cross sections). front of the rotor (pressure p, velocityu) and from just behind the rotor (pressure p p, velocityu) to far downstream (pressure p,velocityu ) according to: p + 2 ρu 2 = p + 2 ρu2, (2.6) Combining these two equations yields: p p + 2 ρu2 = p + 2 ρu2. (2.7) p = 2 ρ(u 2 u 2 ). (2.8) This equation together with T = pa and Eq. 2.5 yield the simple result: u = 2 (U + u ), (2.9) saying that the velocity at the rotor plane is the mean between the velocity far upstream and downstream The Betz limit By defining a control volume following the streamlines and applying conservation of energy, the following expression for the power P is found: P = ṁ( 2 U 2 + p ρ 2 u2 p ρ ) P = 2 ρua(u 2 u 2 ). (2.2) For this control volume, the expression for the thrust force becomes: T = ρua(u u )+F pressure. By comparing this equation to the equation derived earlier (Eq. 2.5), it can be concluded that the pressure on the surfaces

17 2.3. D MOMENTUM AND MASS CONSERVATION FOR AN IDEAL WIND TURBINE 9 F pressure must be zero. By introducing the axial induction factor a and using Eq. 2.9, the power and the thrust force can be written as: and P =2ρU 3 a( a) 2 A (2.2) T =2ρU 2 a( a)a, (2.22) respectively. The dimensionless power and thrust coefficients thus become: P C P = 2 ρu A =4a( 3 a)2, (2.23) T C T = 2 ρu =4a( a). (2.24) A 2 These two equations are plotted in Fig By differentiating C P with respect to a, it can be found that the maximum value for C P is 6/27, for a=/3. This is known as the Betz limit, which is the maximum energy that can be extracted from the wind for an ideal wind turbine..9.8 C P C T Betz limit.7.6 C P, C T a Figure 2.2. Power coefficient C P and thrust coefficient C T as functions of the axial induction factor a according to D momentum theory for an ideal wind turbine.

18 2. WAKES BEHIND WIND TURBINES 2.4. The Blade Element Momentum method For the design of wind turbine blades, the most common method is the Blade Element Momentum (BEM) method. In this method, the streamtube covering the turbine is divided into N annular elements, as can be seen in Fig Two assumptions are made for the annular elements: There is no radial dependency, implying that each element can be treated separately from the others. The force from the blades on the flow is constant in each element, which corresponds to the case of a turbine with infinitely many blades. dr! r! R! Figure 2.3. The annular control volume of thickness dr used in the BEM model. Fig. 2.4 shows a 2D section of the turbine blade at position r. The axial velocity at the rotor plane is u = U ( a) and the tangential velocity is ωr( + a )=ωr + u θ 2, where the tangential velocity is assumed to be zero upstream and u θ in the wake. For an annular element at radial distance r, the equation for the thrust force from D momentum theory (Eq. 2.5), becomes: dt =(U u )dṁ =2πrρu(U u )dr. (2.25) The torque dm at position r can be written as: dm = ru θ dṁ =2πr 2 ρuu θ dr, (2.26) where u θ is the rotational velocity in the wake and the power contribution is dp = ωdm. In terms of induction factors (Eq. 2.6), these equations become: and dt =4πrρU 2 a( a)dr (2.27) dm =4πr 3 ρu ω( a)a dr. (2.28) The assumption of an infinite number of blades can be corrected using Prandtl s tip loss correction factor F, which is simply multiplied with Eqs and 2.28: dt =4πrρU 2 a( a)fdr, (2.29)

19 2.4. THE BLADE ELEMENT MOMENTUM METHOD!r(+a )" U rel" $" &" %" Plane of rotation" U # (-a)" U # " Figure 2.4. Sketch of the velocity components as seen by a 2D section of a wind turbine blade. U rel and α are the relative velocity and the angle of attack, respectively. θ is the pitch angle and φ is the angle between the plane of rotation (rotor plane) and the relative velocity. where dm =4πr 3 ρu ω( a)a Fdr, (2.3) F = 2 π arccos(e f ), f = B 2 R r r sin(φ(r)). (2.3) Here, B is the number of blades, R is the rotor radius, r is the local radius and φ is the local flow angle (angle between the rotor plane and the relative velocity). If the 2D lift and drag coefficients (C L and C D ) for the airfoil are known, the lift and drag forces (L and D) on each radial element can be computed

20 2 2. WAKES BEHIND WIND TURBINES according to: L = 2 ρu 2 relc C L, (2.32) D = 2 ρu 2 relc C D. (2.33) As can be seen in Fig. 2.5, these forces can be projected on the normal and tangential directions according to: F N = L cos φ + D sin φ, C n = F N 2 ρu 2 rel c (2.34) F T = L sin φ D cos φ, C t = F T 2 ρu 2 rel c (2.35) #/2-$! L! U rel! $! F T! R! #/2-$! F N! U "! D! Plane of rotation! Figure 2.5. Lift L and drag D forces on a cross section of a wind turbine blade. R is here the resulting force and F N and F T are the normal (streamwise) and tangential (vertical) components, respectively. The thrust and torque on each annular element can be written as: dt = BF N dr, (2.36) dm = rbf T dr. (2.37)

21 From Fig. 2.4 it can be seen that: and 2.4. THE BLADE ELEMENT MOMENTUM METHOD 3 U rel sin φ = U ( a) (2.38) U rel cos φ = ωr( + a ). (2.39) Combining Eqs yield two new expressions for dt and dm: dt = 2 ρb U ( 2 a) 2 sin 2 cc n dr, (2.4) φ dm = 2 ρb U ( a)ωr( + a ) cc t rdr. (2.4) sin φ cos φ These two expressions can be equalized with Eqs and 2.3, which together with the definition of solidity σ (Eq. 2.) give two equations for the induction factors a and a : a = 4sin 2 φ σc n +, (2.42) a = 4sinφcos φ σc t. (2.43) In Fig. 2.4 it can also be seen that: and tan φ = ( a)u ( + a )ωr (2.44) α = φ θ. (2.45) Eqs constitute the equations for blade design using the Blade Element Momentum method. The theory thus relies on the availability of 2D airfoil data, i. e. C L (α, Re c ) and C D (α, Re c ), to be able to compute C n and C t Glauert optimum By multiplying Eq with ω, the equation for the power contribution dp at radial distance r becomes: dp = ωdm =4πr 3 ρu ω 2 ( a)a dr. (2.46) The power coefficient is found by integrating this expression over the radius and dividing by the total available power in the wind ( 2 ρu A): 3 r 3 r C P =8λ 2 a ( a) d. (2.47) R R The maximum C P is found by optimizing the expression a ( a). However, a and a are not independent. In Fig. 2.6 it can be seen that:

22 4 2. WAKES BEHIND WIND TURBINES tan φ = ωra U a. (2.48)!r(+a )" U rel" U # " $" $" U # a"!ra " U # (-a)" Figure 2.6. Sketch of the velocity components as seen by a 2D section of a wind turbine blade. By equalizing Eq with Eq. 2.44, the relationship between a and a is found: 2 ωr a( a) =a ( + a ). (2.49) U By now optimizing the expression a ( a) (under the condition that Eq still holds) it is found that the maximum C P occurs for: a = 3a 4a, (2.5) which is known as the Glauert optimum. Using the BEM method with the Glauert optimum predicts a C P that increases with an increasing tip speed ratio and goes asymptotically towards the Betz limit, as can be seen in Fig As will be shown later with experimental C P -curves, this is not the case. The validity of the BEM theory breaks down for high values of a. A rule of thumb is that it is only valid up to approximately a=.4.

23 2.4. THE BLADE ELEMENT MOMENTUM METHOD C P λ Figure 2.7. Power coefficient C P as a function of tip speed ratio λ (solid line) together with the Betz limit (dotted line).

24 CHAPTER 3 Experimental design and setup 3.. Wind tunnel The experiments were performed in the Minimum Turbulence Level (MTL) wind tunnel located at The Royal Institute of Technology (KTH) in Stockholm. It has a 7 m long test section with a cross sectional area of.2.8 m (width height). The tunnel is a closed circuit tunnel with a cooling system that can keep the temperature within ±.5 C at the nominal free stream velocity of 25 m/s. The contraction ratio is 9: and the height of the ceiling can be adjusted to ensure zero pressure gradient along the test section. The tunnel is driven by a 85 kw axial fan and can run up to 7 m/s. Due to 5 screens, a honeycomb, and specially designed guiding vanes, the turbulence intensity in the test section can be kept very low. For the present experiments, which were performed with a free stream velocity between 6 and m/s, the streamwise turbulence intensity was.5%. This was based on two profiles (one horizontal and one vertical) at the beginning of the test section. The signals were filtered using a highpass filter with a cut-off frequency based on the free stream velocity and a characteristic length scale of 2 m (width + height of the cross section of the tunnel), (Lindgren & Johansson 22). A sketch of the wind tunnel is shown in Fig m test section honeycomb+ 5 screens fan noise absorber heat exchanger Figure 3.. Schematic sketch of the MTL wind tunnel, which was used for the present experiments. 6

25 3.2. Measurement techniques 3.2. MEASUREMENT TECHNIQUES Hot-wire anemometry Hot-wire anemometry is a technique for measuring fluid velocity, based on the heat transfer from a thin, heated wire to the surrounding fluid. In this study, Constant Temperature Anemometry (CTA) was used, where the temperature of the wire is kept constant and the wire is the fourth arm of a Wheatstone bridge. When the velocity changes, the cooling of the wire and hence also its resistance changes, causing the bridge to get out of balance. In order to get the bridge in balance again, the current through it will change, and the changed voltage can be measured. The relationship between velocity and voltage can be described by different calibration functions. In this study, the modified King s law (Johansson & Alfredsson 982) was used: U = k (E 2 E 2 ) /n + k 2 (E E ) /2, (3.) where U is the fluid velocity, E is the measured voltage, E is the voltage at zero velocity, and k, k 2 and n are calibration constants. A typical curve with the velocity as a function of voltage can be seen in Fig The hot-wire probes used were self-manufactured and had a platinum wire with a diameter of 5 µm and a length of mm. The sampling frequency was khz. One of the hot-wire probes can be seen in Fig a)! 2 b) Hot wire Modified King, s law cm! U, [m/s] E, [V] Figure 3.2. An in-house made hot-wire probe (a) and a typical velocity versus voltage curve (b) Measurements on the turbine model In order to get the thrust (C T ) and power coefficients (C P ) of the model, the thrust T on the model, the rotational frequency f and the current I from the generator were measured. The thrust was measured with a strain gauge attached to the support of the model. The deformation of the strain gauge changes its resistance, and the output voltage has a linear relation to the force

26 8 3. EXPERIMENTAL DESIGN AND SETUP applied, as can be seen in the calibration curve in Fig The 24 V DC generator was connected to 23 diods, which can be seen in the circuit scheme in Fig This made it possible to apply different breaking torques, and hence change the rotational frequency of the model and obtain different tip speed ratios λ. As a result, the voltage over the generator changes when the resistance is varied. By measuring the voltage over a known resistance in the circuit, the current can be calculated. The power P was then calculated as torque times angular frequency (P = M ω), where the torque can be obtained from the current as: M = k I + k 2. (3.2) Here, k and k 2 are calibration constants. The power could also be calculated by P = I 2 R (where R is the resistance), but by instead calibrating the generator and get the torque from the current, the internal losses in the generator are not taken into account. In order to reduce the sampling time, a low pass filter was applied on the signal from the generator, with a cut-off frequency of.3 Hz (f cut off =/(2πRC)). Here, R is the resistance of the resistors and C is the capacitance of the capacitor, as can be seen in Fig The rotational frequency was measured by a photomicrosensor, which gave a pulse at the passage of a pre-marked blade. The thrust, rotational frequency and current from the generator were measured both before and after each hot-wire measurement. The average errors between the measurements before and after was.4% for the thrust,.% for the rotational frequency and.7% for the current Thrust, [N] Voltage, [V] Figure 3.3. Calibration curve for the strain gauge.

27 3.2. MEASUREMENT TECHNIQUES 9 Generator.66! V adjustable number of diodes Figure 3.4. Electrical circuit for the generator. A variable number of diods (between and 23) can be connected to the circuit (here illustrated by the dashed lines), making it possible to apply different breaking torques and therefore also different tip speed ratios. R V in C V out R Figure 3.5. Electrical circuit for the RC-filter used for the signal from the generator. The resistances were 5 kω and the capacitance was µf Phase-locking The velocity in the wake of the model was measured with a hot-wire probe which could be traversed in the x-, y- and z-directions. Detailed hot-wire measurements on any flow instability requires an experimental setup where the event of interest can be repeated accurately. In order to capture the same event, the measurements in this case needed to be triggered on both the blade passage and the added disturbance frequency (which will be described in the next section). Since the blades are not exactly identical, the triggering also needed to be on one pre-marked blade. The flow around this model turbine has previously been seen to show evidence of vortex shedding (Medici & Alfredsson 26). The measurements therefore needed to be triggered on this shedding frequency as well. To monitor the shedding frequency, a fixed hot-wire probe was installed in the wind tunnel, as can be seen in Fig All measurements on wake instabilities were phase-locked based on these three signals: the passage of one of the blades, the added disturbance frequency and the vortex shedding

28 2 3. EXPERIMENTAL DESIGN AND SETUP around the model. The voltage outputs from these three signals were added, and the measurements were triggered on this sum according to: V trigger level = V blade passage + V disturbance + V vortex shedding. (3.3) The signals were added using a non-inverting adder according to the circuit scheme in Fig The trigger signal thus consists of one hot-wire signal and two square wave signals, as can be seen in Fig Figure 3.6. Sketch of the setup with the model and the fixed hot-wire probe. R R 2 V in, V in,2!! V out V in,3 Figure 3.7. Circuit scheme for the non-inverting adder used for creating the trigger signal.

29 3.3. DISTURBANCE GENERATION 2 Voltage time, [s] Figure 3.8. Trigger signal for instability measurements. The trigger signal is the sum of three signals corresponding to the blade passage, the added disturbance and the vortex shedding behind the model. The dashed line is the chosen trigger level Disturbance generation The applied periodic disturbances were in the form of pulsed jets, and in Fig. 3.9, a schematic picture of the setup and the disturbance generation is shown. A compressor was used to generate a high pressure in a large accumulator tank (tank ), which was connected to a smaller accumulator tank (tank 2) through a precision regulator. The pressure in tank 2 was kept constant at p 2 =8 kpa throughout the measurements, and it was measured before and after each hot-wire measurement with an average difference of 2%. Tank 2 was connected to two fast-switching valves (FESTO MHE2 solenoid valves), which in turn were connected to the model through flexible tubes (inner diameter 4 mm) attached at the back of the support, ending in a small attachment at the rear end of the nacelle. The orifices of the pulsed jets were rectangular in shape (approximately 2 mm wide and mm long), and directed perpendicular to the main flow. The valves were driven by a 3 A power supply and regulated by

30 22 3. EXPERIMENTAL DESIGN AND SETUP square waves generated by a signal generator via a computer-controlled amplifier. The valves could be controlled individually, in order to be able to trigger both varicose and sinusoidal modes. This feature has however not been used, and all measurements have been made with sinusoidal disturbances. U!! 7 cm! orifice location! power supply! fast-switching valve! precision regulator!! accumulator tank 2!! computer! accumulator tank!! compressor!! pressure sensor! Figure 3.9. Schematic sketch of the experimental setup with the generation of the disturbance. Two different disturbance frequencies f were tested: 42 and 7 Hz. With U = 6.5 m/s and ν =.5 5 m2 /s, these frequencies correspond to scaled ν frequencies fd = 2πf 6 of 9 and 6. In order to characterize the distur2 U bances, the velocity from the pulsed jets were measured cm and 2 cm behind the orifices, with the wind tunnel turned off. To carry out accurate hot-wire measurements, it is important to keep the temperature constant at the value where the calibration was performed. Since the tunnel was turned off, and the temperature of the air coming form the tank could not be controlled, the accuracy of these velocity measurements are not as good as for the wake measurements. However, the purpose of these measurements was only to ensure that the pulsed jet had the right frequency and the same amplitude in both cases, and for this purpose, a possible offset in the absolute velocity does not have an effect. The velocity and corresponding power spectral density cm from the orifices are shown in Figs. 3. and 3. for the two cases.

31 3.3. DISTURBANCE GENERATION 23 6 Velocity, [m/s] time, [s] PSD frequency, [Hz] Figure 3.. Velocity and power spectral density for the added disturbance with the frequency f =42 Hz. 6 Velocity, [m/s] time, [s] PSD frequency, [Hz] Figure 3.. Velocity and power spectral density for the added disturbance with the frequency f =7 Hz.

32 24 3. EXPERIMENTAL DESIGN AND SETUP The mass flow through the orifice for the case of f=42 Hz was calculated by measuring the velocity in a plane perpendicular to the flow, cm from the orifice. The mass flow was calculated as ṁ = ρau bulk,whereρ is the density, A is the area and U bulk is the bulk velocity. With ρ=.2 kg/m 3, A = m 2 and U bulk =2.76 m/s, the mass flow was ṁ =.42 g/s Turbine models Turbine model Model was a three-bladed wind turbine model that can be seen in Fig The model diameter was.78 m, and the solidity was 2.9%. The area blockage ratio (area of the rotor divided by the cross sectional area of the wind tunnel) was.26. The first measurements were made with a rather short support, which gave the model a hub height of.22 m. To be able to measure the wake further downstream without interaction with the wind tunnel floor, a new support was made with a hub height of.37 m, which placed the turbine model axis in the middle of the test section. To further reduce the influence of the support, a third support was constructed with a smaller diameter. For this design, the strain gauge had to be removed, and in order to make the model stable, it had to be supported by two steel wires. The three supports are summarized in Tab.. The tip speed ratio was changed by applying different electrical loads to the generator. The rotational frequency was changed from 2 to 3 rpm, corresponding to a change in tip speed ratio from.3 to 4.6. Support number height, [m] minimum diameter, [mm] maximum diameter, [mm] Table. Heights and diameters of the three different supports that were used. The blade consisted of a non-twisted cambered plate with a pitch angle of 2. The airfoil profile was Göttingen 47a (Goe47a). To check the model airfoil and compare it to the theoretical profile, gypsum casts were made at three different radial positions along the blade. The casts were then photographed and the profile was calculated based on the darkness of each pixel. Photographs of a blade and the cast can be seen in Fig The Göttingen 47a profile from the literature (Selig et al. 989) together with the measured one are shown in Fig An interpolation was made from the three profiles to construct the full 3D geometry of the blade, which can be seen in Fig The power

33 3.4. TURBINE MODELS m!.22 m! strain gauge! Figure 3.2. The wind turbine model used in the experiments. Three different supports were tested (see Tab. ), of which this is support. output of this model was fairly insensitive to the pitch angle of the blade, indicating that the flow is probably separated on a large part of the blade. A Blade Element Momentum analysis was made on this profile, and the results of the analysis are summarized in Chapter 4. 3 mm Figure 3.3. Photographs of a model blade (left) and the gypsum cast showing the profile (right). The diameter of the model was.78 m and the length of the blade was.79 m.

34 26 3. EXPERIMENTAL DESIGN AND SETUP. y/c theoretical. measured x/c Figure 3.4. Blade profile of airfoil Göttingen 47a. Theoretical profile data from Selig et al. (989) and the measured profile, as described above Figure 3.5. Drawing of one of the blades for the first model (profile Göttingen 47a). The axes are in mm Turbine model 2 Model 2 had the same generator as model, with support number 2. The difference was that new blades were constructed using the Blade Element Momentum (BEM) method, which will be described in the next section. These

35 3.5. TURBINE BLADE DESIGN 27 blades had the airfoil profile SD73, with a pitch angle of 3.3 and a total twist from root to tip of 3. The twist is here defined as being zero at the tip. A photograph of one of the blades can be seen in Fig Figure 3.6. Photograph showing the blade for model 2 with airfoil profile SD73. The diameter of the model was.226 m, and the length of the blade was. m Turbine blade design There has been several wind tunnel experiments with small-scale model turbines, see e. g. Whale et al. (2), Grant et al. (2), Ebert & Wood (22), Medici & Alfredsson (26), Sicot et al. (26), Chamorro & Porte Agel (29). (Note that this is not a comprehensive list.) In many cases, the blades are non-twisted, thin airfoils, mainly due to construction issues. There is also the possibility to use a small-scale propeller, but turning it in the opposite direction. In a study by Krogstad & Adaramola (2), the blades for the model turbine were constructed using an in-house made Blade Element Momentum method. In the present thesis, two types of blades were used, one with a non-twisted Go ttingen 47a profile, and one with a SD73 profile, which was constructed using the BEM method with the Glauert optimization, which is described in Chapter 2. This effort was done in order to acquire an estimate of the lift and drag distribution along the blade, which is needed for comparison with numerical simulations. A more aerodynamically shaped blade would also hopefully produce a wake more similar to that behind a full-scale turbine. The SD73 profile were chosen based on a previous study by Nielsen (27), where four low-reynolds number airfoils were compared with regard to maximum CP -value and the broadness of the peak in the CP -curve. Among the investigated profiles, the optimal one was found to be SD73. The profile, which has a maximum thickness of 8.5% of the chord, can be seen in Fig Airfoil data (lift and drag) is needed for designing a blade according to the BEM method. Data for Re=6, 2, 23 and 35 was taken from Selig et al. (989), see Figs. 3.8 and 3.9 for blade data of the Goe47a and SD73 profiles, respectively. For Reynolds numbers outside this range, the data was extrapolated to get lift and drag for Re=5 and Re=6.

36 28 3. EXPERIMENTAL DESIGN AND SETUP. SD73 y/c x/c Figure 3.7. The profile SD73, which was used in the design..5.5 C L.5.5 C L.5.5 Re c =6 Re c = Re c =2 Re c = α C D Figure 3.8. Lift and drag coefficients for the profile Goe47a. Data from Selig et al. (997).

37 3.5. TURBINE BLADE DESIGN C L.5.5 C L.5.5 Re c =6 Re c = Re c =2 Re c = α C D Figure 3.9. Lift and drag coefficients for the profile SD73. Data from Selig et al. (989). The input parameters for the design are the rotor radius, the free stream velocity and the lift distribution in the radial direction. The optimal chord length and twist distributions are then computed for different tip speed ratios. The design was made for a rotor radius of. m, which gave an area blockage ratio A rotor /A wind tunnel of less than.4. The free stream velocity was set to 6 m/s and the lift distribution was given a linear dependency of the radius according to C L (k) =.9.3k, wherek is the radial coordinate scaled with the rotor radius k = r/r. This gave a more even Reynolds number distribution over the radius, as compared to giving C L a fixed value. The equations for a, a, φ and c were solved according to Eqs a( a) =λ 2 k 2 a ( + a ), k = r/r, (3.4) a = 3a 4a, (3.5) tan φ = ( a) λk( + a ), (3.6)

38 3 3. EXPERIMENTAL DESIGN AND SETUP c R C L = 8πa k cos φ B( + a ). (3.7) The relative velocity U rel (see Fig. 2.4) and the Reynolds number Re c, based on relative velocity and chord length, were then computed from Eqs. 3.8 and 3.9. U rel = (( + a )ωr) 2 +(( a)u ) 2 (3.8) Re c = U relc (3.9) ν The local angle of attack α and the drag coefficient C D were then interpolated from tabulated airfoil data. The scaled normal and tangential forces F n and F t were then computed according to: C n = C L cos φ + C D sin φ, (3.) C t = C L sin φ C D cos φ, (3.) F n = C n 2 ρu 2 relc, (3.2) F t = C t 2 ρu relc 2, (3.3) where φ is the local flow angle introduced in Chapter 2. The thrust force and torque can now be computed, and finally the thrust and power coefficients: T = N b M = N b F n Rdk, (3.4) krf t Rdk, (3.5) T C T = 2 ρu A, (3.6) 2 C P = Mω 2 ρu A, (3.7) 3 where A = πr 2 is the rotor area. Note that the power coefficient can also be calculated from a and a according to C P =8λ 2 a ( a)k 3 dk. (3.8) However, in this case the drag is not taken into account, resulting in a C P curve that increases with λ and goes asymptotically to the Betz limit as λ

39 3.5. TURBINE BLADE DESIGN 3 goes to infinity. This can be seen in Fig. 3.2, where the power coefficient from both computations are included. The results for the optimal chord and twist distribution, as well as the Reynolds number and angle of attack along the blade, are shown in Figs. 3.2 and It can be seen that the chord length, twist angle and Reynolds number are decreasing with increasing tip speed ratio, while the angle of attack is slightly increasing. Prandtl s tip loss correction factor was used in all cases, as described in Chapter C P, C T C T C P, C. P,2 Betz limit λ Figure 3.2. Power and thrust coefficients from Glauert optimization for SD73 with U =6 m/s. C P is calculated both from the torque ( ), Eq. 3.7, and from the induced velocities ( ), Eq. 3.8.

40 32 3. EXPERIMENTAL DESIGN AND SETUP.5 increasing tip speed ratio.4 c/r r/r β increasing tip speed ratio r/r Figure 3.2. Optimal chord (c) and twist (β) distribution for airfoil profile SD73 according to the Glauert optimization, with U =6 m/s. The tip speed ratio λ is ranging from 3 to 4 and the chosen design with λ=5 is shown in red. x 4 increasing tip speed ratio 7.5 Re c r/r 8 7 α 6 5 increasing tip speed ratio r/r Figure Reynolds number and angle of attack along the blade, with tip speed ratio λ ranging from 3 to 4 and the chosen design with λ=5 shown in red.

41 3.5. TURBINE BLADE DESIGN 33 In order to maximize the power output, a tip speed ratio of 5 was chosen. The twist and chord distribution for this tip speed ratio was computed in the range.7 <k<.98. For the inner most part and the outer most part, a spline interpolation was done from the computed chord distribution to c =. A BEM algorithm from Hansen (2) was used to check how the design (optimized for λ = 5) would behave at different tip speed ratios. In these computations, the twist and chord were fixed, starting values for a and a were provided, and all variables (α, U rel, Re, C L, C D ) were then computed through an iterative procedure. In this algorithm, it is the Reynolds number and the angle of attack that are computed, whereas the lift is interpolated from tabulated data. A BEM computation was also done for the first airfoil, which was Goe47a. The rotor diameter was.78 m, the free stream velocity 9 m/s, and the lift distribution was set to a constant value of C L =.8. The results can be seen in Figs C P, C T C T C P,. C P,2 Betz limit λ Figure Power and thrust coefficients from Glauert optimization for Goe47a, with U =9 m/s. C P is calculated both from the torque ( ), Eq. 3.7, and from the induced velocities ( ), Eq. 3.8.

42 34 3. EXPERIMENTAL DESIGN AND SETUP.5 increasing tip speed ratio.4 c/r r/r β increasing tip speed ratio r/r Figure Optimal chord and twist distribution for airfoil profile Goe47a according to the Glauert optimization, with U =9 m/s. The tip speed ratio λ is ranging from 3 to 4. 6 x 4 increasing tip speed ratio 4 Re c r/r 5.5 α 5 increasing tip speed ratio r/r Figure Reynolds number and angle of attack along the blade, with tip speed ratio λ ranging from 3 to 4.

43 3.5. TURBINE BLADE DESIGN 35 Fig shows BEM computations for the experimental conditions (λ = 3.5) for both profiles. Here, the optimal twist and chord distributions for λ =3.5 have been chosen, and computations have been made for other tip speed ratios than the optimal one. It can be noted that the maximum C P for Goe47a is slightly higher than for SD73, but the decrease in power output when operating at a different tip speed ratio than the optimal one is also much larger. The data in this figure is based on k-values in the range.7 <k< SD73 Goe47a.4.35 C P λ Figure Power coefficient for both profiles. Both are here optimized for the experimental case, with D=.78 m, U =9 m/s and λ=3.5.

44 CHAPTER 4 Results 4.. Comparison between measurements and the BEM method 4... Model For model (airfoil profile Goe47a), the power curve (power coefficient C P as a function of tip speed ratio λ) was measured for different free stream velocities and different pitch angles of the blades. BEM computations for these cases were also performed, and the comparison can be seen in Figs In Fig. 4., it can be seen that the agreement between BEM and the measurements are good in all cases except for high tip speed ratios at the two lowest pitch angles (θ=6 and θ= ). Low pitch angles give higher angles of attack, and thus separation over a larger part of the blade. High tip speed ratios on the other hand, corresponds to lower angles of attack. A possible explanation for the discrepancies in this region (low pitch angles and high tip speed ratios), is that the flow in reality has separated over a larger part of the blade, as compared to the predictions from the BEM analysis. The experimental results for all pitch angles at the same free stream velocity (U = 6 m/s) are summarized in Fig It can be seen that the difference in power output between pitch angles from to 4 are minor. Only the case with the lowest pitch angle (6 ) stands out with lower C P -values. The tip speed ratio giving the maximum power output is the same in all cases. Fig. 4.3 shows BEM calculations for the same cases. Here, there is a week trend indicating that the maximum C P -value is shifted towards higher tip speed ratios for lower pitch angles. There is also a larger difference between the maximum values, with θ= and θ=2 giving the largest maximum values. Based on the results from the power measurements, a pitch angle of θ=2 was chosen for the remaining measurements with model. With U = 6 m/s, this case gave a measured power coefficient of C P =.28. From the computations, the result was C P =.3, with a thrust coefficient of C T =.63. The thrust can also be computed from the velocity deficit in the wake by doing a control volume analysis, which in this case resulted in C T =.59, based on streamwise velocity data at 6 diameters downstream (shown in Fig. 4. in Section 4.2.3). The results varied however heavily with the downstream distance, which can be 36

45 4.. COMPARISON BETWEEN MEASUREMENTS AND THE BEM METHOD U =6 m/s θ=6 o BEM Exp..4.3 U =6 m/s θ= o C P U =6 m/s θ=2 o.4.3 U =6 m/s θ=4 o C P U =8 m/s θ=2 o.4.3 U = m/s θ=2 o C P λ λ Figure 4.. Power coefficient C P as a function of tip speed ratio λ. Results from BEM computations (-) and measurements ( ). The first four figures have a constant free stream velocity of 6 m/s, and the last two have a constant pitch angle of 2. due to several factors. The normal stresses can give a contribution to the total force (Townsend 976), which has not been taken into account in this case. For a circular cylinder, this contribution has been shown not to be negligible until 3 diameters downstream (Antonia & Rajagopalan 99). It is also assumed that the pressure is fully recovered, which might not be the case.

46 38 4. RESULTS.4.3 θ C P, max 6 λ=2.9 λ=2.9 2 λ=3. 4 λ=3. θ=6 o θ= o θ=2 o θ=4 o C P λ Figure 4.2. Power coefficient C P ratio λ from the measurements. as a function of tip speed.4.3 θ C P, max 6 λ=3.2 λ=3.2 2 λ=3. 4 λ=2.8 θ=6 o θ= o θ=2 o θ=4 o C P λ Figure 4.3. BEM calculations of power coefficient C P as a function of tip speed ratio λ. Same cases as in Figure 4.2.

47 4.. COMPARISON BETWEEN MEASUREMENTS AND THE BEM METHOD 39 C P and C T can be computed both from the induced velocities a and a using Eqs (which does not take drag into account), or from the computed lift and drag forces according to Eqs The latter is the most common, since it includes drag. The measured and computed data for the case with U = 6 m/s and θ=2 are summarized in Tab.. The total discrepancy between BEM computations and measurements of about % is to be expected. Airfoil data was only available down to Re c =6, and for the experimental case, the chord Reynolds number were between and 2. Hence, the data had to be extrapolated to be able to perform the computations. C P =8λ 2 dt =4a( a) 2 ρu 2 2πrdr, T = dt =4a ( + a ) 2 ρω2 r 2 2πrdr, T = r 3 r a ( a) d R R R R T dt, C T = 2 ρu A 2 T dt, C T = 2 ρu A 2 (4.) (4.2) (4.3) Goe47a C P C T Measurements.28 BEM, with drag, from Eqs BEM, without drag, from Eq BEM, without drag, from Eq BEM, without drag, from Eq From velocity deficit.59 Table. Power and thrust coefficients from measurements and computed in two different ways. BEM, without drag means computations from the induced velocities a and a. BEM, with drag means computations from the integrated loads. Velocity deficit means that the thrust force is computed with a control volume analysis Model 2 For model 2 (profile SD73), the BEM design for the new rotor blades was made for U =6 m/s and λ=5. Due to generator constraints, the highest possible velocity was 4.5 m/s. For this case, with λ=5.5, C P and C T were.4 and.92, respectively. The corresponding values from the BEM analysis were.43 and.8, which gave a discrepancy of 7% for C P and 4% for C T.

48 4 4. RESULTS Figs show comparisons between measurements and BEM analysis for model 2. By comparing these results to the power curves for model, it can be concluded that the blades designed with the BEM method was more sensitive to a change in pitch angle as compared to the non-twisted blades with profile Goe47a (model ). The tip speed ratio corresponding to the maximum C P -value was independent of the pitch angle for model, but for model 2 it decreased with an increasing pitch angle. This is in accordance with the BEM results, where C P,max is also shifted towards lower λ for an increasing pitch angle, both for Goe47a and SD73 (not shown here). It could also be worth mentioning that the standard deviation of the power output was 4.3% of the mean value for model, but only.3% for model 2, at similar tip speed ratios. The overall agreement with the BEM method is however better for model. One possible explanation is that the behaviour of the non-twisted blades are more dependent of the global geometry, and less dependent on Re c.thebem method uses extrapolated airfoil data in both cases, but the uncertainty of the extrapolated data remains to be determined. The lift and drag of the SD73 profile might be more Re c - dependent in this range of Reynolds numbers. C P C T BEM Exp Figure 4.4. Comparison of C P and C T between BEM and measurements for the case with profile SD73, θ=3.3 and U =6.5 m/s.

49 4.. COMPARISON BETWEEN MEASUREMENTS AND THE BEM METHOD θ C P, max 6 λ=5.5 7 λ=5.2 8 λ=5. 9 λ=4.8 λ=4.5 θ=6 o θ=7 o θ=8 o θ=9 o θ= o C P λ Figure 4.5. Measurements of C P for the case with profile SD73, U =6.5 m/s and θ ranging from 6 to degrees..8 θ=6 o θ=7 o θ=8 o θ=9 o θ= o C T λ Figure 4.6. Measurements of C T for the case with profile SD73, U =6.5 m/s and θ ranging from 6 to degrees.

50 42 4. RESULTS 4.2. Wake development Inlet conditions The inlet streamwise velocity profiles were measured two and four diameters upstream of the model. The results for two diameters upstream can be seen in Fig The origin is at the centre of rotor plane, with x as the streamwise coordinate (positive downstream), y as the vertical coordinate (positive upwards) and z as the spanwise coordinate in a right-handed coordinate system. There seems to be a small trend of decreased U from below to above the centre line in the vertical direction. In the spanwise direction, the velocity distribution is close to homogeneous. The streamwise turbulence intensity was.5%. The sampling time for all measurements regarding wake development was 2 s. This ensured that the mean values were converged within.7% and the standard deviations within %, based on the case with U =6.5 m/s and λ=5 for model 2. The convergence was calculated as the relative difference between the values after 9 and 2 s. In the free stream the relative errors for the standard deviations are larger than in the wake, since the standard deviations are very small. By not taking the points in the free stream into account and only looking at points in the wake, the standard deviation was converged within.4%..5.5 y/d U/U.98.2 U/U Figure 4.7. The vertical and horizontal inlet profiles at the centre line, two diameters upstream of the model. The spatial coordinates are scaled with the model diameter D and the velocity is scaled with the velocity measured by a Prandtl tube placed at the beginning of the test section.

51 4.2. WAKE DEVELOPMENT Influence of thickness and height of the model support Three different supports were used, as summarize in Tab. in Section 3.4. It was noticed that the wake started to interact with the wall rather fast, and the wake from the support could also clearly be seen. In order to perform a case with minimum influence of the walls and the support, the hub height need to be in the middle of the test section, and the support need to be as thin as possible without making the model unstable. Support 3 was therefore used for most measurements, since it was thin and had a hub height which placed it in the middle of the test section. In Fig. 4.8, vertical profiles at the centre of the model are compared between all three supports at four diameters downstream. The shapes for all three supports are similar. The only difference between support 2 and 3 is the thickness, but an effect of this can not be seen in this figure. There could however be visible effects closer to the wall. The dashed and the dashed-dotted lines are the respective hub heights. The streamwise velocity in vertical planes at different downstream positions were measured for support and 2, with heights of 22 and 37 cm, respectively. The results for the mean velocity and the standard deviation of the velocity for support 2 can be seen in Fig. 4.9 (the results for support looks similar)..5 Support Support 2 Support 3 Model axis location, support Model axis location, support 2 and 3 y/d U/U Figure 4.8. Vertical streamwise velocity profiles for the three different supports at x/d=4. Here, y= corresponds to hub height for support 2 and 3.

52 44 4. RESULTS U/U urms/u y/d y/d y/d y/d y/d y/d Figure 4.9. The development of the mean streamwise velocity (left column) and velocity fluctuations (right column) for support 2. The locations are from top to bottom: x/d=4, 8 and 4. The floor is located at y/d=-2..

53 4.2. WAKE DEVELOPMENT Variation of the free stream velocity and tip speed ratio Spanwise velocity profiles at hub height (y/d=) were measured for model (airfoil profile Goe47a, support 3) and model 2 (airfoil profile SD73, support 2). The results for the mean velocity (U) and the standard deviation of the velocity (u rms ) scale well with the free stream velocity, as can be seen in Figs The u rms -profiles follow naturally their corresponding mean velocity distributions, with peaks at the inflection points of the mean profiles. The rather different mean velocity profiles, particularly in the near wake (.5- diameter downstream), cause quite different u rms -profiles (see Figs. 4. and 4.3). In the far wake (where the actual geometry of the blades are less important), the u rms -profiles look more alike due to a better agreement between their corresponding mean velocity profiles. By comparing Figs. 4. and 4.2, it can be concluded that, for model 2, the wake of the nacelle can be seen more clearly and the recovery of the wake is slower. The overall lower turbulence levels for model 2 is a possible explanation for the slower recovery of the wake in this case, as compared to model. The last two profiles for model, at 6 and 8 diameters downstream, are not perfectly symmetrical around = (Fig. 4.). This is probably due to a small yaw angle of the model in the negative direction around the y-axis, which causes the wake on the positive spanwise side to be a bit more developed than on the negative side. Model 2 shows an even larger asymmetry in the last two u rms -profiles in Fig Although some of the asymmetry might be referred to the corresponding asymmetry of the mean profiles, this can not be the whole explanation. Figs show mean velocity and standard deviation of the velocity for model and 2 for three different tip speed ratios. The free stream velocities in these cases were 9. m/s for model and 6.5 m/s for model 2. The tip speed ratios and the corresponding power coefficients are summarized in Tab. 2. Despite large differences in power outputs, the wakes do not seem to show corresponding differences. Model Model 2 λ=2.5, C P =.29 λ=3, C P =.4 λ=3.5, C P =.29 λ=5, C P =.32 λ=4.5, C P =. λ=7, C P =.22 Table 2. Power coefficients for different tip speed ratios, where the corresponding spanwise velocity profiles are shown in Figs

54 46 4. RESULTS.8 x/d=.5.8 x/d= U/U.6.4 U/U x/d=2.8 x/d=4 U/U.6.4 U/U x/d=6.8 U =6. m/s U =7.6 m/s x/d=8 U/U.6.4 U/U.6.4 U =9. m/s U =. m/s Figure 4.. Model. Mean streamwise velocity at the centre line at different downstream positions, for four different free stream velocities at λ=3.5.

55 4.2. WAKE DEVELOPMENT x/d= x/d= u rms /U.5. u rms /U x/d= x/d=4 u rms /U.5. u rms /U u rms /U x/d=6 2 2 u rms /U U =6. m/s U =7.6 m/s U =9. m/s U =. m/s x/d=8 2 2 Figure 4.. Model. Streamwise velocity fluctuations at the centre line at different downstream positions, for four different free stream velocities at λ=3.5.

56 48 4. RESULTS.8 x/d=.5.8 x/d= U/U.6.4 U/U x/d=2.8 x/d=4 U/U.6.4 U/U x/d=6.8 U =6.5 m/s U =9. m/s x/d=8 U/U.6.4 U/U Figure 4.2. Model 2. Mean streamwise velocity at the centre line at different downstream positions, for two different free stream velocities at λ=5.

57 4.2. WAKE DEVELOPMENT x/d= x/d= u rms /U.5. u rms /U x/d= x/d=4 u rms /U.5. u rms /U x/d= U =6.5 m/s U =9. m/s x/d=8 u rms /U.5. u rms /U Figure 4.3. Model 2. Streamwise velocity fluctuations at the centre line at different downstream positions, for two different free stream velocities at λ=5.

58 5 4. RESULTS.8 x/d=.5.8 x/d= U/U.6.4 U/U x/d=2.8 x/d=4 U/U.6.4 U/U U/U x/d=6 U/U λ=2.5 λ=3.5 λ=4.5 x/d= Figure 4.4. Model. Mean streamwise velocity at the centre line at different downstream positions, for three different tip speed ratios with U =9 m/s.

59 4.2. WAKE DEVELOPMENT x/d= x/d= u rms /U.5. u rms /U x/d= x/d=4 u rms /U.5. u rms /U u rms /U x/d=6 u rms /U λ=2.5 λ=3.5 λ=4.5 x/d= Figure 4.5. Model. Streamwise velocity fluctuations at the centre line at different downstream positions, for three different tip speed ratios with U =9 m/s.

60 52 4. RESULTS.8 x/d=.5.8 x/d= U/U.6.4 U/U x/d=2.8 x/d=4 U/U.6.4 U/U U/U x/d=6 U/U x/d=8 λ=3 λ=5 λ= Figure 4.6. Model 2. Mean streamwise velocity at the centre line at different downstream positions, for three different tip speed ratios with U =6.5 m/s.

61 4.2. WAKE DEVELOPMENT x/d= x/d= u rms /U.5. u rms /U x/d= x/d=4 u rms /U.5. u rms /U u rms /U x/d=6 u rms /U x/d=8 λ=3 λ=5 λ= Figure 4.7. Model 2. Streamwise velocity fluctuations at the centre line at different downstream positions, for three different tip speed ratios with U =6.5 m/s. Despite the differences in mean velocity profiles and standard deviations, the most prominent difference between model and 2 is the absence of vortex shedding around model 2. This can clearly be seen by looking at the time series and spectra shown in Figs. 4.8 and 4.9. The time series show the same locations in positions scaled by the model diameter D. The point shown in Fig. 4.8 is almost in the free stream, but the tip vortices are still detectable. Fig. 4.9 show a point at the location of a tip vortex, where the effect of the shedding is most evident. In this position, the shedding enhances the amplitude

62 54 4. RESULTS of the tip vortices by shifting the vortex position and thus makes the velocity alternate between very high and very low..2 Goe47a SD73 U/U time, [s] P Goe47a SD frequency, [Hz] Figure 4.8. Comparison between the time series for model and 2 at (x/d,y/d,)=(,,-.75). U/U Goe47a SD time, [s] P Goe47a SD frequency, [Hz] Figure 4.9. Comparison between the time series for model and 2 at (x/d,y/d,)=(,,-.58).

63 Wake spreading 4.2. WAKE DEVELOPMENT 55 In order to characterize the spreading of the wake, the edge of the wake is here defined as the spanwise location where the velocity has reached 95% of the free stream velocity, denoted z 95. To make a comparison with the wake behind a bluff body, z 95 is plotted as a function of downstream distance (Fig. 4.2), together with a function of the form: z 95 D = C x D + C 2, which was fitted in a least square sense to the data. The resulting mean difference between the data and the fitted curve was: (z 95,data z 95,fit ) 2 =.8, or.9% of z 95,data. The data is from model and shows the results for four different free stream velocities. Included in the figure is also the location of the maximum value of the flatness (averaged over all four cases). The flatness is an intermittency measure, well-suited in determining a fixed point in the interface between any laminar-turbulent flow. It however requires spatially well resolved data. 2.5 z 95, U =6 m/s z 95, U =8 m/s z 95, U =9 m/s z 95, U = m/s z 95, fit <u 4 > max x/d Figure 4.2. Model. Wake width as a function of downstream distance, scaled with the model diameter D. z 95 is the position where the velocity has reached 95% of the free stream velocity and z 95,fit is a least squares fit, proportional to the square root of x/d. Included in the figure is also the position of the maximum of the flatness (< u 4 > max ).

64 56 4. RESULTS 4.3. Tip vortex instabilities Cases and phase-locking Two cases with different disturbance frequencies are compared to the reference case without disturbance. The cases are summarized in Tab. 3. All measurements were done with model and a free stream velocity of 6.5 m/s. The measurement planes were 5 5cm 2 and located between.76 < <.48,.4 < y/d <.4, which corresponded to the location of a tip vortex. The measurements were performed between.65 and.55 diameters downstream and for each measurement plane, 2 sets with sampling time 2 s were measured in points. In the contour plots presented, the data has been linearly interpolated to a finer grid in order to get smoother images. Case Disturbance frequency f, [Hz] Scaled disturbance frequency f d,[-] no dist. - - f d =9 42 Hz 9 f d =6 7 Hz 6 Table 3. Disturbance frequencies f d that were used in the measurements. The scaling of the frequencies were made according to f d = 2πfν U 6. 2 In order to elucidate the performance of the triggering mechanism and the results from the phase-locked measurements, examples of the time series are shown in Figs. 4.2 and The figures clearly show both the tip vortices (high frequency) and the vortex shedding (low frequency) behind the model (all measurements in this chapter are from model, where the vortex shedding was always present). Triggering the measurements on the blade passage and the disturbance frequency is straight forward, whereas the triggering on the vortex shedding in the wake is more complicated, partly because its a hot-wire signal and partly because the shedding is a physical phenomenon and not a computer-generated square wave. Therefore, the different sets are clearly in phase with regard to the blade passage and the disturbance frequency, whereas some discrepancies can be seen with regard to the shedding. The problem is the low frequency, which gives a relatively broad peak of the time signal. One way to get around this would have been to add a fourth signal (S 4 )tothefull triggering signal. S 4 should have been a computer-generated square wave with the same frequency as the shedding frequency, where the width of the square wave specified the tolerance of the phase triggering. It should be noted that the triggering problem can be solved a posteriori in a post-processing algorithm, in which one would use the first set in each measurement as a reference and then phase shift the following sets using standard numerical fast Fourier transforms

65 4.3. TIP VORTEX INSTABILITIES 57 based on the shedding frequency. Custom would be to low pass filter the sets just above the shedding frequency before calculating the corresponding phase shift. Non of the above solutions to the triggering problem has so far been tested. U/U time, [s] Figure 4.2. Time series for five different sets at the point (x/d, y/d, )=(.8,-.2,-.57). The results when calculating a set average over 2 sets are shown in Figs for the undisturbed reference case (Fig. 4.23) and with added secondary disturbances of f d =9 and 6 (Figs and 4.25). The figures show the first.65 seconds of the measurements, for downstream distances between.65d to.55d. With the presence of external disturbances it is seen that the tip vortices appear less distinct and hence are less visible, which is the result of having advanced the onset of breakdown to turbulence of the tip vortices.

66 58 4. RESULTS U/U time, [s] Figure Time series for five different sets at the point (x/d, y/d, )=(.8,-.2,-.57)..4.2 U/U time, [s].2.8 x/d Figure Phase averaged time series for the case without disturbance, following a tip vortex.

67 4.3. TIP VORTEX INSTABILITIES U/U time, [s].2.8 x/d Figure Phase averaged time series for the case with a disturbance f d = 9, following a tip vortex..4.2 U/U time, [s].2.8 x/d Figure Phase averaged time series for the case with a disturbance f d = 6, following a tip vortex.

68 6 4. RESULTS Visualization of vortices Since all measurements were phase-locked, instantaneous planes can also be plotted, even though only one-point measurements were performed. One way of visualizing the vortices is by plotting U(t) Ūlocal, i.e. the instantaneous streamwise velocity minus the mean value in each point. The vortices can then clearly be seen as regions with high velocity next to low velocity, since the vortices are rotating in the negative direction around the y-axis on the negative spanwise side, where the measurements were taken. This way of visualizing the vortex is shown in Figs (visualization in space) and 4.27 (visualization in time), for the undisturbed case. For each plane (downstream position) in Fig. 4.26, the time step was chosen as to give the strongest possible vortex. The strength of the vortex was in this case defined as the sum of the maximum velocity difference for each y/d-value. Fig shows five different time steps for x/d=.65, corresponding to five different phases (, π/2, π, 3π/2 and 2π). U Ūlocal U Figure Phase averaged instantaneous streamwise velocity for the case without disturbance. Three different downstream positions, x/d=.65,.95 and.25.

69 4.3. TIP VORTEX INSTABILITIES 6 U Ūlocal U Figure Phase averaged instantaneous streamwise velocity for the case without disturbance at x/d=.65. The four planes correspond to different phases γ between and 2π. Figs show the standard deviation between the sets for each point for the three cases: no disturbance, f d =9 and f d =6, respectively. This is a visualization in space, and the four planes correspond to x = D=.65,.95,.25 and.55. The time steps for each plane have been selected to capture the strongest possible vortex, which here was defined as the sum of the maximum values for each y/d-position. It can be seen that the vortex in the undisturbed case is more defined, especially in the most upstream plane. This gives an indication that the added secondary disturbances do have an effect on the vortices and that an earlier breakdown is likely to happen.