Lift Measurements in Unsteady Flow Conditions Jörge Schneemann∗
Pascal Knebel†
Patrick Milan‡
Joachim Peinke§
ForWind - Center for Wind Energy Research, Institute of Physics, Carl-von-Ossietzky University of Oldenburg D-26111 Oldenburg, Germany
Abstract
1 Introduction
In this contribution lift measurements on a Wortmann FX 79-W-151A airfoil under laminar and turbulent inflow are presented. A Reynolds number of Re ≈ 700, 000 has been achieved. To investigate the impact of turbulence on this airfoil, different grids were put into the flow in front of it. One of the grids had a fractal square geometry. Two different experimental methods of lift measurements were performed simultaneously: measuring the pressure distribution on the wind tunnel walls (wall pressure method) and measuring lift forces directly on the mounting of the airfoil (force method). It turns out that the wall pressure method gives also correct time averaged lift curves in turbulent inflow. Lift curves measured in turbulent inflow for the FX 79-W-151A airfoil show different behavior than those measured in laminar flow. The maximum lift coefficient CA,max increases with growing turbulence intensity and is shifted to higher angles of attack. Furthermore a different behavior for different inflow is found. The fluctuations in lift, shown by the standard deviation of the lift, are much higher in the wake of the fractal square grid, than in the wake of a ’classical grid’, even though the turbulence intensity of the fractal grid was lower. This result is discussed in the background of higher order statistics. Intermittent PDFs (probability density functions) of the velocity increments were measured for time steps up to τ = 10 s in the wake of the fractal grid. A new dynamical approach based on the Langevin equation was applied to the measured lift data to quantify the observed behavior in terms of stochastic equations. Keywords: lift measurements, airfoil, turbulence, fractal grid, Langevin equation
The airfoils selected for application on a wind turbine blade have big influence on the whole wind energy converter. These airfoils are commonly characterized by static lift and drag curves. They contain information about lift (and drag) for a fixed angle of attack (AoA) with laminar inflow for the given Reynolds number Re. In practice, a wind turbine hardly sees laminar inflow conditions. The incoming wind field is turbulent due to surface roughness of the ground and the rotor experiences fast changing AoA’s e.g. due to the increasing wind speed with increasing height [1]. In both cases dynamic effects on the airfoil appear. The changes in the AoA cause an increased maximum lift coefficient CL,max and formation of an hysteresis loop in the dynamic lift curve (dynamic stall). Turbulent inflow can cause increased and delayed maximum lift coefficients. This leads to higher and fast changing loads on the airfoil. Dynamic effects on airfoils were first studied for application in helicopters, where the rotor blades are pitched on every turn (i.e. [2, 3]). In the 1990’s the importance for wind turbines was realized. Some groups studied different airfoils periodically pitched in laminar flow [4–7]. Dynamic lift in turbulent inflow was investigated by [8–10]. Increasing maximum lift coefficients CL,max with increasing turbulence intensity for a NACA 634− 421 airfoil was found by [8]. An increased performance of a small wind turbine in turbulent flow compared to laminar inflow was measured by [11]. Computation or model studies about dynamic stall are reported in [12–16]. The influence of turbulence on the loads acting on wind turbines was studied by [17]. There are different ways to measure dynamic lift forces. A standard method for measuring dynamic stall is using pressure sensors placed in the airfoil [4, 7, 8]. An alternative and noninvasive approach introduced by [18] and used by [5] and [6] is to measure the pressure distribution on the wind tunnel walls. This method works
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well using laminar inflow. But it is not proven to work with turbulent flow conditions. The most straightforward method is to measure lift forces directly via a balance or a force sensor. In this contribution we present results from studies in which we compare the wall pressure measurements with balance measurements and show that surprisingly the pressure measurements work quite well even for the turbulent case. Based on these experimental results we are able to extract from the measurements a new approach to characterize the dynamics of the stall effect, based on the stochastic formalism of the Langevin equation, cf. section 2.1. Such an approach will help to improve the modeling of load forces on a wind turbine. To generate turbulent inflow, different grids were installed on the nozzle of the wind tunnel. This allows to compare the two different methods for lift measurement in laminar and turbulent inflow conditions. The sampling frequency of fs = 1 kHz and measurements for up to 300 s give the opportunity to calculate lift curves not just by averaging time series, but to use a dynamical approach based on the Langevin equation (Langevin approach). One of the grids in use had a fractal square geometry like described in [19]. The fractal generated turbulence showed different statistical characteristics than turbulence generated by classical square grids. A different behavior of the airfoil in this type of turbulence was measured. In applications, it is common to describe turbulent flows by the turbulence intensity. Our measurements encourage the statement, that the turbulence intensity is insufficient to characterize turbulent flows.
Figure 1: Photograph from the inside of the closed test section in upstream direction to the nozzle with the mounted fractal grid. The airfoil with its end plates can be seen in front. On the right side of the picture the small boxes containing the wall pressure sensors can be seen. The force sensors are not visible, they are covered by the end plates the airfoil is mounted on.
p(uτ) / a.u.
ratory turbulence generated by a classical square grid, shows an intermittent shape. This intermittency differs from the Gaussian distribution as it shows much higher probability of extreme events. For bigger values of τ , the PDF of increments of laboratory turbulence converges towards a Gaussian, while atmospheric turbu2 Methods lence shows intermittent distributions of velocity increMeasurements were performed in the closed test sec- ments even for large values of τ [21]. In contrast to the tion of the closed loop wind tunnel of Oldenburg Univer- results of the classical grid, we measured intermittent sity (1.0 m × 0.8 m, 2.0 m long). Reynolds numbers of distributions of velocity increments even for τ = 10 s Re ≈ 700.000 were reached (chord length of the verti- in turbulent flow generated by the fractal square grid. cally mounted aluminum milled airfoil c = 0.2 m, wind PDFs of velocity increments for a classical grid and the speed u ≈ 50 m/s). To generate turbulent inflow condi- fractal square grid are shown in figure 2. tions, four different grids were installed on the nozzle of the wind tunnel, one of them with a square fractal geometry generating even intermittent inflows for time steps up to 10 s (see figure 1 and [20]). The three square grids had mesh widths of a: 25 mm, b: 50 mm and c: 100 mm. The blockage ratio of all grids was 25%. Turbulence intensities σu (1) Ti = u −10 0 10 −10 0 10 (u: mean wind speed, σu : standard deviation.) of uτ / στ uτ / στ < 1.0% (without grid), a: 2.2%, b: 3.6%, c: 6.7% and 4.6% (fractal grid), were generated. (a) Grid b: (b) Fractal square grid Additional features of turbulent flows can be characterFigure 2: PDFs of the velocity increments for time steps ized by statistics of the velocity increments uτ := u(t + τ ) − u(t).
(2)
For small values of the time step τ , the probability density function (PDF) of the velocity increments of labo-
τ = [0.033, 0.1, 1, 10, 102 , 103 , 104 ] ms in a half logarithmic view (τ increasing from top to bottom). uτ is normalized by its standard deviation. The mean velocity was ub ≈ 42 m/s and uf ractal ≈ 48 m/s.
3 Results
• The pressure distribution on the wind tunnel walls was measured using 80 pressure sensors, 40 opposite of the suction side and 40 opposite of the pressure side of the airfoil. The interval between the sensors was 5 cm. Lift was calculated according to pp − ps L CL,p = · (3) q c·η where pp − ps is the difference between the overall pressure of the pressure- and suction side of the airfoil, q = ρ2 u2 the dynamic pressure of the inflow, L the length of the wind tunnel walls (the space between 40 pressure sensors of one wall) and η = 0.94 the so-called Althaus factor correcting the finite length the pressure distribution is measured on [18], see also [6]. • The airfoil was mounted between two strain gauge based force sensors measuring lift and drag forces (perpendicular and parallel to the inflow). The lift coefficient CL was obtained from CL,F =
FL . q·A
(4)
Hereby FL is the lift force and A is the area of the used airfoil.
For laminar inflow conditions the time averaged steady lift curves obtained from force measurement and wall pressure measurement fit the reference data provided by [25] well (see figure 3). The higher lift coefficient of the reference in the region of stall onset (α ∈ [7; 12]) can be explained by small differences in the used airfoils and the finish of their surface. The curves measured with the wall pressure method and the force method fit each other quite good. Thus we can conclude that both methods perform well and measure the same effect.
1.2 1 Lift coefficient CL
Lift was obtained in two different ways:
0.8 0.6 0.4 0.2 0
CL,p wall pressure method CL,F force method C reference Althaus
L The data was measured for fixed angles of attack on a −0.2 −5 0 5 10 15 20 25 FX 79-W-151A airfoil for time intervals of 30 s to 300 s AoA / ° with a sampling frequency of fs = 1 kHz. The pressure signals were calibrated and CL (t) time series were Figure 3: Static lift coefficients obtained from wall prescalculated. The lift data obtained from force measuresure and force measurement. Turbulence intensity T i < ments was calibrated using the mean lift data calculated 1% (no grid installed). Re ≈ 700, 000. Reference data by the wall pressure for the laminar case. Time series of by [25] for Re = 700, 000. the flow against the airfoil generated by the grids were measured using a hot wire probe to obtain statistical inFigure 4 shows an averaged lift curve for low turbulence formation of the inflow and the turbulence intensity. intensity and the lift curves for both measuring techniques with grid c: installed (T i = 6.7%). The shape of the curves under highly turbulent conditions is the 2.1 Langevin approach to blade static lift same. There is only a small offset between them. The measurements force measurement is expected to give correct results, The time series of the static lift CL (t) appear to be highly because it measures the lift force directly. In contrast dynamical. Whether driven by a laminar or a turbulent to that, the wall pressure method is not obvious to inflow, CL (t) can display information on the mechanical work in turbulent inflow conditions, since it could be lift effect, even when embedded in turbulent, noise-like disturbed by vortices passing the pressure sensors. signals. A Langevin approach was applied to this com- Now that both measurements have been shown to plex, turbulence-driven system, so as to extract the un- provide comparable results, the wall pressure method derlying dynamics [22–24]. The Langevin approach is can be accepted for averaged measurements under based on the drift field of CL (t), which is defined as turbulent inflow conditions. hCL (t + τ ) − CL (t)i D(CL ; α) = lim (5) τ →0 τ CL (t)=CL ;α
and is computed for every angle of attack α and for discretized values of CL . D(CL ; α) gives the (first-order) time evolution of CL (t) for the values CL and α. The corresponding Langevin equation is an evolution equation for CL (t). We limit our analysis to the drift field that gives the local dynamics of the system.
in case of the fractal grid: even though the turbulence intensity and the CL,max is smaller than in case of grid c, fluctuations in CL (t) are up to twice as big. This suggests that other characteristics of turbulence, like the statistics of the velocity increments, have to be considered.
1.4
1 0.8
1.4 CL,p Ti=6.7%
0.6
1.3
CL,F Ti=6.7% 0.4 0
CL,F laminar 5
10 15 AoA / °
20
25
Figure 4: Static lift coefficients obtained from wall pressure and force measurement. Turbulence intensity T i < 1% for wall pressure method, T i = 6.7% for wall pressure and force measurement.
Lift coefficient CL
Lift coefficient CL
1.2
1.2 1.1 1
CL,F Ti=6.7% CL,F Ti=4.6% fractal
0.9
CL,F laminar
An increasing maximum lift coefficient with increasing turbulence intensity is shown in figure 5. The delay to higher angles of attack with increased turbulence intensity can also be seen. Both effects were measured on a NACA 634− 421 airfoil by [8]. The FX 79-W-151A airfoil shows a similar behavior.
Lift coefficient CL
1.3 1.2 1.1 1 CL,p Ti=6.7%
0.9
CL,p Ti=3.6% CL,p Ti=2.2%
0.8 0.7 5
CL,p laminar 10
15 AoA / °
20
25
Figure 5: Static lift coefficients obtained from wall pressure measurements. Data for turbulence intensities of < 1.0% (without grid), grid a: 2.2%, grid b: 3.6% and grid c: 6.7% is shown. Maximum lift coefficients for the curves are marked by open circles.
Fluctuations in the lift coefficient, represented by the standard deviation of the time series of CL (t), are shown in figure 6 for the laminar case, the fractal grid and grid c. In all cases, the standard deviation is low in the range of linear increase of lift and rises in the stall range of the airfoil. A remarkable result can be seen
0.8 5
10
15 AoA / °
20
25
Figure 6: Static lift coefficients obtained from force measurements. Data for turbulence intensities of < 1.0% (without grid), 4.6% (fractal grid) and 6.7% (grid c) is shown. The dashed lines mark the standard deviation of the lift coefficient.
Figure 7 illustrates the insights provided by the Langevin approach. The stable fixed points of the drift field represent the attractive regions of the dynamics, where D(CL ; α) = 0. They match almost perfectly with the mean lift coefficient here as we study a laminar inflow. Also, the drift field D(CL ; α) gives additional insight as it models the local dynamics of the lift process. The drift field gives the short-time dynamics of the lift process at every value {CL ; α}, unlike the mean value that averages out this information. For a turbulent inflow, the dynamics become more complex and the Langevin approach is expected to provide more information than the mean lift coefficient. Also, turbulence induces asymmetry that spoils the result given by the mean lift coefficient, so that the Langevin approach might give more accurate results. Developments are being made in this direction, including hysteresis situations induced by stall effects.
1.2
φ(CL, AoA=23o)
Lift coefficient CL 0.6 0.8 1.0
0.9
CL
1
1.1
0.4
^ 5
10
15 AoA / o
20
sd(CL(t)) D(CL;α) D(CL;α)=0 25
Figure 7: Static lift curve for a laminar inflow for AoA α ∈ [1◦ ; 25◦ ] (force measurement). The blue full line represents the mean lift coefficient CL , with corresponding standard deviation (blue dashed lines). The black arrows represent the drift field D(CL ; α) both in direction and magnitude. The stable fixed points D(CL ; α) = 0 of the drift field are represented by red crosses. To clarify the meaning of the drift field, the inset shows RC a potential φ(CL ; α) = − 0 L D(C˜L ; α)dC˜L for α = 23◦ which gives the local dynamics of the (in this case stalled) airfoil.
4 Conclusions In this study we measured lift on a FX 79-W-151A airfoil in laminar and turbulent inflow conditions with two different methods. Their comparison shows, that the wall pressure method obtains good time averaged results in turbulent flow. Up to now very little experimental lift data have been measured in turbulent flow. Here we added another airfoil, showing an analog behavior to other studies. The maximum of the lift coefficient CL,max increases with the turbulence intensity and shifts to higher angles of attack. A new kind of laboratory turbulence, generated by a fractal square grid [19, 20], was also used as inflow. In view of the statistics of the velocity increments of the flow, this kind of turbulence is more similar to atmospheric conditions. The airfoil used showed highly increased fluctuations (standard deviation) of the lift coefficient for AoA’s in the stall range using this turbulence as inflow, compared to its behavior in turbulence generated by a classical grid. These results justify the conclusion that the turbulence intensity is an important quantity to describe turbulence, but it is insufficient to describe fundamental effects even in applications. Thus additional quantities are needed to describe turbulent flows. An advanced characterization of wind turbulence by higher order statistics is discussed in [26]. The design and the modeling of wind turbine blades
and the choice of the right airfoils is still a difficult task. With the Langevin approach, a new method to calculate lift curves was introduced. It allows to extract the local dynamics of the turbulence driven system from the measured data. This dynamics may be used i.e. for future simulations of wind turbine blades in turbulent flow. The approach should allow to identify multi-stable flow situations like double stall [27] by the output of multiple fixed points. This can lead to a much better understanding and modeling of the airfoils used in applications like wind turbine blades.
5 Acknowledgments We would like to thank René Grüneberger, Thomas Bohlen and Gerrit Wolken-Möhlmann for their work on the topic and the experimental setup. Furthermore we thank the unknown reviewers for their helpful suggestions.
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