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CFD and experimental database of flow devices, comparison Marinos Manolesos, John Prospathopoulos NTUA 18 February 2015
Agreement n.: Duration: Coordinator:
FP7-ENERGY-2013-1/ n° 608396 November 2013 to November 2017 ECN Wind Energy, Petten, The Netherlands Supported by:
This project has received funding from the European Union’s Seventh Programme for research, technological development and demonstration under grant agreement No FP7-ENERGY-2013-1/
n° 608396
Document information Document Name:
CFD and experimental database of flow devices, comparison
Confidentiality Class
PU
Document Number:
D3.1
Editor:
NTUA Marinos Manolesos, John Prospathopoulos
Contributing authors:
CENER Gonzalez, A., Aparicio, M., Méndez, B., Gómez-Iradi, S., Munduate. X. CRES Chaviaropoulos, T. DTU Barlas, A., Garcia N. R., Sorensen, N. N. University of Liverpool Barakos, G., Wang, Y. University of Stuttgart Jost, E. NTUA Chasapogiannhs, P., Diakakis, K., Papadakis, G, Voutsinas, S. TU DELFT Baldacchino, D.
Review:
TU DELFT Simao Ferreira, C.
Date:
18/02/15
WP:
WP 3
Task:
Task 3.1
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Table of contents 1.
Introduction
5
2.
Scope and content
6
3.
The experimental data base
7
3.1 3.1.1 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.2 3.4.3 3.4.4 3.5 3.5.1 3.5.2 3.6 3.6.1 3.6.2 3.6.3
Vortex generator tests (TU DELFT) Wind tunnel and experimental set up Pressure Measurements Vortex generator tests (NTUA) Wind tunnel and experimental set up Pressure Measurements Stereo Particle Image Velocimetry Vortex Generators on a flat plate (TU DELFT) Experimental Set up and Conditions Flow measurement results and discussion Static flap tests (University of Stuttgart) Wind tunnel and experimental set up Test matrix Polar measurement Transition position Transient response flap tests (DTU WIND) Wind-Tunnel and experimental set-up Results Unsteady measurements of the DU95W180 airfoil with oscillating flap Wind-Tunnel and experimental set-up Results Conclusions
7 7 7 8 8 10 11 13 13 19 23 23 26 26 26 26 27 29 31 31 34 34
4.
Description of CFD codes
41
4.1 4.2 4.3 4.3.1 4.3.2 4.4 4.4.1 4.4.2 4.4.3 4.5
CENER CRES DTU EllipSys Q3UIC NTUA MaPFlow GENUVP FoiL2W ULIV
41 42 42 42 43 44 44 45 46 46
5.
Description of the test matrix of control devices
49
6.
Validation and cross-checking
54
6.1 6.1.1 6.1.2 6.2 6.2.1
Part A – Comparison with experimental data Vortex Generators Trailing edge flap static cases with experimental data Part B Vortex generators
54 54 58 63 63
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6.2.2 6.2.3 6.3 6.3.1
Dynamic TE flap cases Dynamic LE flap cases Part C: 3D rotor cases Dynamic TE flap cases
66 80 84 84
7.
Discussion
89
7.1 7.2 7.2.1 7.2.2
Vortex generators Trailing Edge flap – Leading Edge Slat Static TE flap cases - Comparison with experimental data 2D dynamic TE and LE flap cases - Comparison among predictions
89 92 92 95
8.
Conclusions
References
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100 104
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1. Introduction The present document reports on the activities carried out within WP3 under Task 3.1. WP3 as a whole aims at the development and assessment of models for add-on flow devices and flow control on large wind turbine blades. As a first step to this aim, the creation of a CFD and experimental database has been defined. Participants to this task include CENER, CRES, DTUWIND, NTUA, ULIV who provided CFD data, TU Delft who provided new experimental data and GE and LM who provided their industrial insight and ECN who provided supporting analysis. The Task was structured as follows: 1. Inquiry and collection of existing experimental data that could be made available to the project as in-kind contribution, 2. Definition and conduction of new experiments, 3. Definition of a matrix of CFD computations for LE/TE flaps and vortex generators including some cases from the experimental data base, 4. Collection and compilation of the CFD computations into a data base, 5. Formulation of an evaluation/assessment procedure for code-to-code and code-to-test comparisons 6. Reporting on the comparison study In the next section the scope and content of the present report are outlined. In sections 3 and 4 the experimental database and the codes used to produce the numerical results are described, respectively. In section 5 the test matrix is given, while in section 6 the comparison between simulation and experimental results is performed. Next, a quantitative discussion of the results is given in section 7 and the report closes with section 8, where the concluding remarks are given.
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2. Scope and content The objective of Task 3.1 was to assess the current state of knowledge and modelling capabilities on flow control devices that have been proposed or used on wind turbine blades. To this end, tests and simulations have been combined and analysed. The objective was to analyse the underlying flow mechanisms and assess the accuracy of intermediate and high level models with respect to experimental data. The end product was defined to be a CFD and experimental data base that would help the forthcoming tasks within WP3. To serve that, out of the analysis of the data collected, confidence levels for the different models and quantification of the deviations have been defined. In terms of content, two main types of devices have been considered: LE/TE flaps and VGs. Flaps aim at controlling/reducing loads while VGs aim at improving the performance mainly over the inboard part of the blades. For both types of devices, existing experiments concern only generic set-ups configured on wing models placed in wind tunnel facilities. There are no detailed aerodynamic measurements on rotating blades for either of the two types of devices while for LE flaps the community lacks any experimental test. Tests on wing models aim at providing data for validation of 2D simulations. In certain tests, however, the nominally 2D flow becomes three-dimensional and eventually unsteady, as in the case of Stall Cell onset. This is even more challenging for unsteady flows as in the case of dynamic LE/TE flaps, which were selected as test cases. For the CFD data base, the approach was to large extent determined by the current practice in design, which is linked to 2D polars for BEM codes. This justifies the selection of a considerable number of 2D cases, despite the three-dimensional challenges previously described. In order to get a better overview and comparison between the different models, 3D (rotor) simulations have been also included which were then correlated to 2D polars. In the majority of test cases, (U)RANS CFD tools were used which are regarded to be of the highest available fidelity nowadays for engineering applications. However, in view of the forthcoming tasks, tools based on vortex or integral (of the viscous-inviscid type) methods have been also applied. These methods are less expensive to run and therefore they can span large design spaces at lower cost compared to (U)RANS.
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3. The experimental data base The experimental database contains six (6) tests in total. One concerns the flow past a VG on a flat plate (TU DELFT), two concern airfoil models equipped with VGs (provided by TU DELFT and NTUA), and three concern airfoil models with TE flap (provided by the University of Stuttgart, DTU WIND and TU DELFT). In this section a description of the experimental tests is given and the available data are outlined. A comparison of the experimental results with numerical ones is given in Section 6.
3.1
Vortex generator tests (TU DELFT)
The tests reported here were performed in the low-speed, low-turbulence wind tunnel of the Faculty of Aerospace Engineering of Delft University [1]. The experimental results are provided as in - kind contribution to the AVATAR project for validation purposes. 3.1.1 Wind tunnel and experimental set up The wind tunnel (Figure 1 – a) is of the closed single-return type with a total circuit length of 72.7m. The circuit has a contraction ratio of 17.8 to 1. The free-stream turbulence level, in the 2.6 m long, 1.25 m high, and 1.80 m wide octagonal test section, ranges from 0.02% at a wind speed of 25 m/s to 0.07% at 75 m/s. The chord Reynolds numbers range from 1.0e6 to 3.0e6. The airfoil selected for comparison was the DU 97-W-300 with and without VGs. The VGs (Figure 1 – b) were tested at two different locations, at 20% and 30% chord. Force and moment polars are provided at a Reynolds number of 2.0e6.
(a)
(b)
Figure 1: (a) The model of airfoil DU 97-W-300 in the wind tunnel test section seen from inside the contraction; (b) Sketch of the vortex generators used during most wind tunnel tests. Dimensions in mm. [1]
3.1.2 Pressure Measurements The composite model had a chord of 0.65 m and completely spanned the height of the test section (Aspect Ratio of 2.08). Around 90 to 100 pressure orifices with a diameter of 0.4 mm. were installed in staggered formation. The model static pressures and the wake rake static and total pressures were fed either to an electronically read 200 tube liquid multi-manometer with fibre optic cells or an electronic pressure scanner system. Data were recorded using an electronic data acquisition system and were on line processed using the laboratory computer. Page 7 of 106
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During the years, a variety of wake rakes has been used ranging from a device with 50 total tubes and 12 static tubes with a width of 219 mm to the present one having 67 total pressure tubes and 16 static pressure tubes over a length of 504 mm. The testing of each new model configuration started with a number of wake rake traverse measurements in span wise direction at various angles-of-attack and Reynolds numbers to confirm the two-dimensionality and to establish the wake rake position, giving an average drag value representative for the model. The model pressure distributions were integrated to obtain normal force and tangential force coefficients Cn and Ct and moment coefficients Cm. Lift coefficients were computed using Cn and the wake rake drag according to Eqn. (1). In the post stall region the pressure drag was used, computed from the pressure distributions. 𝐶𝑙 =
𝐶𝑛 − 𝐶𝑑 ∗ tan 𝛼 cos 𝛼
(1)
The measured data were corrected for the presence of the wind tunnel walls with the standard correction method for lift-interference and model solid and wake blockage [2]. Corrections have also been made for the effect of solid blockage of the wake rake on the test section velocity and the effect of the wake rake self-blockage on the values of the static pressures (and consequently the dynamic pressure) measured by the wake rake. The standard position of the wake rake was about 60% chord length downstream from the model trailing edge.
3.2
Vortex generator tests (NTUA)
The data reported here were collected prior to the AVATAR project1 and are provided as in kind contribution. 3.2.1 Wind tunnel and experimental set up All experiments were carried out at the small test section (1.4mx1.8m) of the National Technical University of Athens (NTUA) wind tunnel. The wind tunnel is of the closed single-return type with a total circuit length of 68.81 m. The circuit has a contraction ratio of 6.45 to 1. The free-stream turbulence level in the 3.75 m long octagonal test section is 0.2% with a maximum test section velocity of about 60 m/s. The 18% thick airfoil profile was designed at the NTUA [3] and was optimized for use on variable pitch and variable speed multi MW wind turbine rotors. Shape optimization was based on evolution algorithms and XFOIL was used as flow solver. The profile belongs to the flat-top type experiencing trailing edge (TE) separation leading to gradual lift built-up and smooth post stall behaviour. Under separated flow conditions the flow becomes highly three-dimensional and a single or more Stall Cells (SCs) appear. The inherently unstable SC flow was stabilized by placing a zigzag tape (see Figure 2b) at x/c=0.02 and for only 10% of the span [4-6].
1
The study was financially supported by the NTUA and the Onassis foundation and through the G ZF 032 / 20092010 PhD scholarship grant. Page 8 of 106
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The wing model had a chord of 0.6m and spanned the test section vertically in order to minimize blockage. The solid blockage of the model was 6.9% of the tunnel section at 12° angle of attack and reached a maximum of 9.2% at the highest measured angle, 16°. Plexiglas fences (see Figure 2a) were used to minimize the wind tunnel wall boundary layer effect and the wing aspect ratio was 2.0. The vortex generators were constructed by a 0.2mm thick aluminium strip so that they have adequate rigidity and impose minimum distortion to the boundary layer. Counter rotating triangular vanes with common flow up were used in all measurements with VGs. The VG shape and positioning parameters are shown in Figure 3 and their values are given in Table 1. (b)
(a)
Figure 2: (a) The fences dimensions; (b) The zigzag tape dimensions.
Table 1: Vortex generator configuration parameters
x = 0.3c: β = 20°: δ = 6mm: h = δ: l = 3h: D = 11.7h: d = 3.7h:
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Chordwise position of the VG array, where c is the wing chord VG angle to the free stream flow Boundary layer height at the location of the VG array VG height VG length Distance between two VG pairs Spanwise distance between the LE of two VGs of the same pair
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Figure 3: Triangular vane vortex generator parameters. (Top left) Wing side view: global positioning parameter, (top right) VG side view: VG shape parameters, (bottom) Top view: relative positioning parameters.
3.2.2 Pressure Measurements The model had 60 pressure taps located at the centre of the wing span. In the chordwise direction, they extended from the leading edge to 88.8% of the chord. The wake rake used is 39.1cm wide and consists of 45 total pressure tubes and two static pressure tubes, located on a different plane from that of the rake. For attached flow conditions the drag coefficient (Cd) was computed from the wake pressure distribution according to [7]. For separated flow conditions the pressure drag was used instead. The lift coefficient (Cl) was computed from the pressure distribution around the airfoil. For the case with VGs the drag varied significantly even under attached flow conditions due to the presence of the streamwise vortices shed by the actuators, as expected. The drag was hence measured in four positions downstream of a VG pair and the average value is reported here. The central VG pair was selected, which was downstream of the ZZ tape. The four drag measurement positions are shown in Figure 4. Wind tunnel corrections were applied to the measured data according to [7] for the case of a wing spanning the tunnel height. In particular the corrections allowed for the model's solid blockage, the wake blockage and the tunnel walls. The horizontal buoyancy is considered insignificant for 2D airfoil models. All experiments were conducted at a chord Reynolds number of 0.87e6 and Mach = 0.07 and the angle of attack range was from -5° to 16°. Pressure measurements are available for four flow cases: Page 10 of 106
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1. 2. 3. 4.
Case without VGs Case with VGs at x=0.3c Case with VGs at x=0.4c - increasing α Case with VGs at x=0.4c - decreasing α
Figure 4: Drag measurement positions. Position 0 was between the two VGs of the central VG pair, Position 3 was between two consecutive VG pairs and Positions 1 and 2 were in equal distance between Positions 0 and 3.
3.2.3 Stereo Particle Image Velocimetry A schematic side view of the test set up is given in Figure 5, where the measurement planes for the case without VGs are also shown. The cameras were located inside the test section 1.2c downstream of the wing TE. Their vibration was found to have negligible effect on the results, see [8]. All processing is done using TSI Insight 4G software and in-house tools. All experiments were conducted at α = 10° at a chord Reynolds number of 0.87e6 and Mach = 0.07. There are data for three cases, without VGs, with VGs at 30% chord and with VGs at 40% chord. The measurement planes for each case are given below. 1. Case without VGs o Measurements on 3 planes normal to the flow x=0.6 - plane A in Figure 6 x=0.8 - plane B in Figure 6 x=1.06 - plane C in Figure 6 o Measurements on 5 planes normal to the flow (planes α to ε in Figure 6, z=±0.133, z=±0.067, z=0.0)
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WING
Tunnel
A B Zigzag tape Fences
C α β γ δ ε
Cameras
U∞
Tunnel Floor Figure 5: Schematic planform view of the test set up. The wing, the fences, the zigzag tape and the cameras are shown along with the measurement planes. The measurement planes for the case without VGs are also shown. Planes normal to the flow (A, B and C) are indicated by vertical green lines, while planes normal to the wing span (α, β, γ, δ and ε) are shown with red horizontal lines.
𝑈∞
Figure 6: Stereo PIV measurement planes for no VGs case. Planes normal to the flow are shown with solid green line. The red dotted line shows the planes normal to the wing span.
2. Case with VGs at x=0.3c o Measurements on 3 planes normal to the flow x = 0.6 or Δx = 27.2h - plane A in Figure 7 x = 0.7 or Δx = 37.2h - plane B in Figure 7 x = 0.8 or Δx = 47.2h - plane C in Figure 7
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𝑈∞
Figure 7: Stereo PIV measurement planes for the VG cases. Planes A, B and C are shown with solid green line. The axes are shown twice, once non-dimensionalized with the wing chord (c) and once with the VG height (h). In the latter case the x axis starts at the VG TE.
3. Case with VGs at x=0.4c (no bifurcation was observed at α=10° when increasing or decreasing the angle of attack) o Measurements on 2 planes normal to the flow x=0.6 or Δx= 17.2h - plane A in Figure 7 x=0.8 or Δx= 37.2h - plane C in Figure 7
3.3
Vortex Generators on a flat plate (TU DELFT)
3.3.1 Experimental Set up and Conditions Wind Tunnel Facility The Boundary Layer Wind Tunnel of the TU Delft was used for this study, the schematic of which is shown in Figure 8. The tunnel can attain a maximum speed of 38𝑚/𝑠 in the widewalled test section of 1.5 × 0.25𝑚2. The large separation of the side walls (1.5𝑚) minimizes end effects on the flow region of interest along the centreline zone. Air flows around the circuit in a counter-clockwise fashion, passing through the diffuser section immediately after the fan, followed by a large settling chamber and into the testing section with a contraction ratio of 16.7. The latter is highlighted on said diagram and is further illustrated in Figures 2 and 4. An adjustable back wall allows adjustment of the pressure gradient, ensuring a truly null pressure gradient when desired, as well as the prescription of an arbitrary pressure distribution. Additional wind tunnel details are listed in Table 2. The choice for such a tunnel enabled the generation of relatively thick attached boundary layers (see for e.g. boundary layer profiles in Figure 15). This facilitated flow characterization and flow resolution. It was not the aim of this experimental campaign to quantify separating flows, and thus it will be seen that all data provided pertains to attached boundary layer flow. This also Page 13 of 106
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allows the near wake vortex evolution to be studied since the flow is attached and well defined at the location of VG induced vorticity generation. Due to the supporting skeleton (red frame) of the flat plate (see Figure 9), optical access for the tunnel was not straightforward and this limited the measurement planes downstream of the VGs to 50 device heights, or 250mm.
Figure 8: Boundary Layer Wind Tunnel schematic highlighting the test section.
Table 2: Wind Tunnel detailed specifications
Feature Settling Chamber
Value 2.5 × 2.5 𝑚2
Test Section
1.5 × 0.25 𝑚2
Test Section Length
5.6𝑚
Contraction Ratio
16.7
Two successive 2D contractions
Motor
11 𝑘𝑊 DC
Electric Motor
Fan Turbulence level (in freestream) Maximum Speed
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Remarks Seven straightening screens included
9-bladed fan 0.5%
At maximum free stream velocity
38.4 𝑚/𝑠
At test section entrance
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Pressure taps
Figure 9: Wind tunnel test section; (left) Pneumatically traversable test wall equipped with pressure taps; (right) Internal view of the deformable wall, blackened to minimise laser reflections.
Mixing devices and flow conditions The rectangular and triangular vane type vortex generators used in this study are described in Table 3 and Figure 10. The devices were 3D-printed with a surface layering precision of 0.05mm and the resulting vanes have a material thickness of 0.5mm. The design of the VGs is partly based on recommendations of Godard and Stanislas [9]. Their work covered a wide parameter sensitivity study in which different configurations were assessed for their ability to delay separation (increase skin friction) and reduce backflow in separating flows. The low-profile nature of the VGs examined here means that profile drag is significantly reduced whilst still energising the boundary layer where is it most required [10]. In this study, direct drag measurements were not possible and skin friction may only be deduced indirectly from Clausertype fitting routines, taking advantage of the high wall resolution. Table 3: Vortex Generator Geometry
VG property
Symbol
Value [mm]
Device height Trailing edge separation Vane chord length Distance between VG pairs Angle with respect to the free stream VG trailing edge location relative to plate leading edge
h d l D ∅
5.0 12.5 12.5 30.0 18°
Size in h units [-] 1 2,5 2,5 6 -
xVG
985
197
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Rectangular/triangular vortex generator models
Vortex generator array layout
Vortex generator array - yawed layout Figure 10: Vortex generator lay outs.
The placement of the VGs is such that flow impinges on the vanes in a divergent manner, producing counter-rotating, common down-flow embedded vortices. For each test case, 25 VG pairs were mounted in array configuration (side by side as shown in Figure 10, covering a spanwise distance of 0.75m, centred on the tunnel centreline. This was done in order to minimize end-effects from the finite array. The streamwise position of the VGs relative to the start of the flat plate is at 985mm, measured to the trailing edge of the vanes and indicated in Figure 13. For the case of the yawed VGs [see Figure 10], the devices are yawed about the intersection between the VG leading edge connector and the meridional planes (pivot indicated on Figure 13 with black dots) and a positive yaw angle as used in these tests is indicated as counter-clockwise in Figure 10 (c). The relative placement of VGs is shown schematically in Figure 2. An issue to contend with is the fact that upon changing the pressure gradient (more adverse), the boundary layer will tend to thicken at a given streamwise location, changing the relative height of the device. This complicates absolute cross-comparisons. In the current experiment, the vortex generator to Page 16 of 106
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boundary layer height ratio (hvg /δ) was approximately 0.35 for the case of zero pressure gradient (ZPG). As a consequence of the thicker boundary layer obtained with an adverse pressure gradient (APG), the actual device height ratio would tend to reduce.
Figure 11: Test section Plan View schematic (as viewed from the top)
For this reason it is useful to define a typical airfoil as a reference, with which experimental flow parameters and results can be cross-checked. We consider the wind turbine DU-97-W300 airfoil. This airfoil is considered a moderately thick airfoil, representative of root and mid-board profiles of wind turbine rotor blades [1]. Table 4: Test parameters
Parameters Value Ue Reθ TI BL state (turbulent)
Remarks 15𝑚/𝑠 3 − 6 × 103 0.05 − 0.2%
DU-300 airfoil @ 𝑅𝑒 ≈ 2 − 5 × 106 (𝛼~10°)
Tripped, equilibrium TBL Tripped at 150mm from LE; Carborundum 0.8𝑚𝑚
Boundary layer transition was fixed at 150mm from the leading edge of the flat plate (whose origin is shown in Figure 11) using carborundum roughness particles of 0.8mm. The free stream velocity is measured using a wall mounted pitot probe, the intake of which is aligned with the start of the flat plate. The experiments were subsequently conducted at a freestream velocity of 15m/s (measured at the same fixed location x=0). The pressure distribution is measured using a differential pressure logger, reading off the static wall pressure of the flat plate which was prefitted with taps at 100mm intervals. The boundary layer is fully developed at the position of the VGs and is well within the attached operating regime. Data acquisition and post-processing The stereo-PIV setup consisted of an Nd:Yag double pulsed Evergreen laser which was used to illuminate the seeding particles circulating within the wind tunnel. Relatively high seeding input had to be maintained in order to attain sufficient particle density within the retardant boundary layer. Two 16Mpix LaVision cameras were used to capture the illuminated particles with 500 realisations per scanning plane which were then post-processed using LaVision Davis 8.1.4. The physical PIV setup is shown in Figure 12. Measurements were performed on planes normal to the flow at different streamwise locations downstream of the VGs, sized to capture the full height of the boundary layer. In order to assess the spatial (spanwise) periodicity of the induced vortex flow field, the field of view was centred over the meridional plane of a VG pair, and Page 17 of 106
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spanned approximately ±25𝑚𝑚 on either side. This gave a field of view of 50 × 40𝑚𝑚 with 570 × 385 vectors.
Figure 12: Experimental setup mounted on traverse system; (left) laser and camera setup; (right) laser sheet orientation relative to the cameras and test section
The entire setup was mounted on a high precision, three degree-of-freedom traversing mechanism, able to traverse in the streamwise direction with an accuracy of 0.01mm. The laser sheet was aligned with the trailing edge of the VGs and a local coordinate system established from this plane. Thus, all plane indications in terms of device heights are measured from this plane. Figure 13 indicates spanwise positions at which the spanwise uniformity of the flow was examined. Due to the manner of acquisition, the measured streamwise velocity appears to exit the laser sheet and thus appears with a negative sign in the streamwise velocity data. The flow direction is in the positive 𝑥 − direction. Moreover, the data acquired at the planes located between the VG trailing edge and the 5ℎ streamwise location are not reliable due to the presence of the VG projection on the image plane. Thus data considered is after the 5ℎ location.
Aligned Laser Sheet
Figure 13: Alignment and measurement planes
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Test matrix Four test cases are made available for the experimental database and summarized in Table 5. The baseline flow (without VGs) and the pressure distributions for both pressure gradients are provided. Table 5: Test cases
Case
Pressure Gradient
Yaw
Shape
Planes
1 2 3 4
ZPG ZPG ZPG APG
0° 10° 0° 0°
Recta. Recta. Delta Recta.
5-10,15,25,50 5-10,15,25,50 5,15,25 5-10,15,25,50
3.3.2 Flow measurement results and discussion Flow measurement results are presented for Case 1, for the zero pressure gradient flow with axially oriented VGs. Figure 14 shows the out-of-plane velocity contours on spanwise planes at three different locations downstream of the vortex generators. The roll-up process largely occurs even before the 𝑥/ℎ = 10 location. The wake-like evolution is typical of the induced flow field where the velocity deficit is visibly greatest near the core of the vortex. In Figure 15, streamwise velocity profiles are shown for the case of the zero pressure gradient for the rectangular VGs. Different spanwise locations are shown (±𝐷/2, ±𝐷/3, ±𝑇𝐸, 𝐷 = 0, see Figure 13). The typical s-shaped inflexion and wake-like profiles of the VG induced flow field are clearly visible and qualitatively corroborate well with the results from previous studies [11, 12]. At 𝑧/𝐷 = 0, the actuated flow exhibits a fuller profile, directly under the influence of the combined vortex downwash. These figures are a stark reminder that the flow is by no means uniform in the spanwise sense, even at 50 device heights downstream, and highlights the limitations of inherently 2D flow models. Spanwise velocity profiles are shown in Figure 16 for the same locations as for the streamwise velocity. The action of the vortices is perhaps more lucid from these profiles. Although the first profiles on either side of the centreline are extracted at the trailing edge of the VG (±𝑇𝐸), the uplifting motion of the vortices is visible. This occurs due to the growth of the vortex core with downstream evolution and the action of ground proximity in convecting vortices away from each other and from the wall. Non-idealities in the spanwise uniformity are visible and can arise easily due to mixing device misalignment and errors in alignment the field of view with the flat plate surface, causing uncertainty in the exact location of the wall position.
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(a) 𝒙/𝒉 = 𝟏𝟎
(b) 𝒙/𝒉 = 𝟐𝟓
(c) 𝒙/𝒉 = 𝟓𝟎
Figure 14: Contours of out-of-plane velocity (𝑼𝒙 ); in-plane flow indicated with overlaid quiver plot
As a means of quantifying the velocity profiles, the spanwise varying integral boundary properties are shown in Figure 17. These are defined as ∞ ∗
𝛿 = ∫ (1 − 0 ∞
𝜃=∫ 0
𝑢 ) 𝑑𝑦 𝑈𝑒
𝑢 𝑢 (1 − ) 𝑑𝑦 𝑈𝑒 𝑈𝑒 𝐻=
𝛿∗ 𝜃
(2)
(3)
(4)
Due to the common downflow configuration, the boundary layer shape factor is reduced (hence improved) most in the centre of the VG vanes. It takes here a value of approximately 1.3, typical of a fully developed turbulent boundary layer with a zero pressure gradient. The figure shows also the evolution of the boundary layer parameters in the downstream direction.
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Figure 15: Controlled (grey) and baseline (black) streamwise velocity (𝑼𝒙 ) profiles at different spanwise locations for (top) 𝟏𝟎𝒉 (middle) 𝟐𝟓𝒉 (bottom) 𝟓𝟎𝒉 device height positions behind the VGs
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Figure 16: Controlled (grey) and baseline (black) spanwise velocity (𝑼𝒛 ) profiles at different spanwise locations for (top) 𝟏𝟎𝒉 (middle) 𝟐𝟓𝒉 (bottom) 𝟓𝟎𝒉 device height positions behind the VGs
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Figure 17: Illustration of the spanwise-periodic distribution of the boundary layer integral parameters for three streamwise locations aft of the scanned VG pair (dash-dot:𝟏𝟎𝒉; dash-dash:𝟐𝟓𝒉; solid:𝟓𝟎𝒉)
3.4
Static flap tests (University of Stuttgart)
Wind tunnel tests of an airfoil with trailing edge flap have been performed in the course of the European UPWIND project at the Institute of Aerodynamics and Gas Dynamics (IAG), University of Stuttgart. The results have been made available to the AVATAR project for code validation purposes. The analysed airfoil was the TL-190-82 which is of 18% thickness and specifically designed for load alleviation purposes by active trailing edge flaps. It was equipped with 10 % trailing edge flap (TEF). Static TEF deflections in the range from -10 to 10 degree have been examined in clean and tripped conditions at three different Reynolds numbers (Re = 1.5e6, 2.5e6, 3.3e6). Full polar measurements are available for -10, -5, 0, 5 and 10 degree TEF deflection. The results have been published in [13] and documented in [14]. 3.4.1 Wind tunnel and experimental set up The measurements were performed in the institute’s Laminar Wind Tunnel (LWT) [14]. The LWT is an open return tunnel with a closed test section (Figure 18). The rectangular test section measures 0.732.73 m2 and is 3.15 m long.
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Figure 18: Sketch of the Laminar Wind Tunnel, total length 46m [14]
The high contraction ratio of 100:1 as well as five screens and filters results in a very low turbulence level of less than Tu = 210-4 for a frequency range of 20-5000 Hz and a flow velocity of 30 m/s. A maximum speed of 90 m/s can be achieved which allows testing up to a Reynolds number of 4.5106. The lift is determined by experimental integration of the pressure distribution along the opposite two tunnel walls while the drag is determined by an integrating wake rake, which is positioned approximately 0.45 chord length behind the model trailing edge. The rake automatically travels into the centre of the wake and is traversed in spanwise direction to obtain a mean value for the drag. Standard wind tunnel corrections are applied for the aerodynamic coefficients. The data acquisition system is controlled by a PC and carefully calibrated before each set of measurements. More information about the wind tunnel corrections is documented in [15] and in reports to be downloaded from the Laminar Wind Tunnel homepage [16, 17]. Blowing air tangential in the corners between the model and the mounting plates is used as a boundary layer control to ensure two-dimensional conditions. The nozzles were placed on the tunnel wall at 0.6 x/c of the upper surface of the airfoil, which is the standard position. The influence of the blowing system on the measured lift data is studied in each measuring campaign for a few representative test cases. In general the lift is slightly enhanced, with a stronger effect for positive flap setting. The order of magnitude is in the usually observed range and can be attributed to local corner effects. Therefore, no additional investigations were performed. An infra-red camera system was used to check the transition position during the speed-up of the wind tunnel in order to check for the two-dimensionality of the flow. This method takes advantage from the fact that the heat transfer from the surface is different in a laminar boundary layer in comparison to a turbulent one. Therefore, only a small temperature difference (approximately 2° C) between model and free stream is sufficient to provide a picture of the boundary layer state without any disturbances to the flow field. The measurement of the transition position as function of the angle of attack was performed with the help of a stethoscope. A small microphone inside the stethoscope reads the pressure fluctuations in the boundary layer. The signal is amplified and transmitted to an earphone. The turbulent boundary layer can be clearly distinguished from the laminar one by a typical loud broadband noise. In the laminar boundary layer nearly nothing can be heard. The ‘onset’ of transition is characterized by a strong increase in loudness. Comparison to other transition detection methods show that the determined transition ‘position’ is similar to the position where the skin friction starts to increase. Therefore the detected positions are equivalent to those obtained from visualizations with surface oil-film methods. Page 24 of 106
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Several measurements were performed with artificial roughness at the leading edge to simulate contamination. A 2D tape with a width of 2mm was selected as turbulator to be consistent with previous measurements on wind turbine airfoils. The wind tunnel model of TL-190-82 was manufactured at the IAG workshop in CNC-milled negative moulds to ensure maximum contour accuracy (Figure 19). A chord length of 0.6m was chosen. The shell of the model was built as a symmetrical carbon-fibre / glass-fibre / carbonfibre sandwich with 6 mm wall thickness. After finishing the remaining roughness heights of the wind tunnel model are in the order of 1.5 μm RMS measured with a high precision surface measuring instrument. For acoustic measurements the trailing edge thickness is an important parameter. It must be kept very thin to avoid blunt trailing edge noise which would otherwise spoil the measurements. The design coordinates of the airfoil were modified by rotation of the upper surface around the leading edge to provide thin trailing edges of 0.3 mm thickness. During the whole manufacturing process great care is taken to achieve a trailing edge thickness as close as possible to the nominal value.
Figure 19: Negative mould and side view of the TL 190-82 wind tunnel model [14].
Figure 20: Details of the flap conjunction [14].
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The flap was cut from the main part of the wind tunnel model. The nose of the flap was built from SIKA SLABS M600 as a positive part. This piece is exactly circular around the flap hinge and fits tangential to the surface contour on the upper and lower side of the model. The gap between flap and main part has a width of 1mm and allows flap deflections of = 20°. An internal sealing made of V-seal tapes provides air tightness of the flap. Figure 20 gives an overview of the flap mounting. 3.4.2 Test matrix Polar measurements were performed for three different Reynolds numbers (1.5e6, 2.5e6 and 3.3e6) and five flap positions (−10, −5, 0, +5, +10). Flap is defined as positive when lift is increased. All cases are investigated for clean and tripped configurations. For the latter case a trip is placed on upper and lower side of the airfoil at 5% chord. To achieve turbulent flow on the lower side at all angles of attack the trip height is doubled (0.36 mm) compared to the upper side (0.18 mm). This procedure was the same for all tripped measurements. The polar measurements were performed with activated wall blowing to reduce the influence of the wind tunnel walls on the flow. Finally the transition position was detected for a Reynolds number of 2.5e6 and different flap deflections (−10, −5, 0, +5, +10) and angles of attack (−6 till +10 in 1 degree steps). 3.4.3 Polar measurement The standard procedure for polar measurements was applied. With this procedure the evaluation of lift and drag starts with the lowest angle of attack. The angle of attack is increased until Clmax is exceeded. Then the angle of attack is reduced and additional points were collected if a hysteresis of the Cl- curve is visible. Hysteresis effects are always carefully checked. The same procedure was done in a similar way for the negative part of the Cl- curve. Drag measurements were performed, if possible. 3.4.4 Transition position The transition position was detected for a Reynolds number of 2.5e6 and different flap deflections (−10, −5, 0, +5, +10) and angles of attack (−6 till +10 in 1 degree steps). The results can be found on the AVATAR website.
3.5
Transient response flap tests (DTU WIND)
Wind tunnel tests of an airfoil with a flexible trailing edge flap have been performed at RisøDTU. The results have been made available to the AVATAR project for code validation purposes. The analysed airfoil is NACA 0015 which is a 15% thickness symmetric airfoil. It is equipped with 15% controllable rubber trailing edge flap (CRTEF), which is actuated using a controlled pneumatic system. Static CRTEF deflections in the range from -8° to 2.4° have been examined at two different Reynolds numbers (Re = 1.6e6, 2.6e6). Polar measurements are available for -8° and 2.4° CRTEF deflection for a range of angles of attack of -5° to 20°. Dynamic flap cases are also performed, where the flap angle is following a step input signal towards its max/min values. Part of the results has been documented in [18].
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3.5.1 Wind-Tunnel and experimental set-up The measurements were performed in the VELUX wind tunnel in 2009, which is of the closed return type with an open test section having a cross section of 7.5mx7.5m and a length of 10.5m. The cross section of the quadratic jet blowing into the test section is 3.4x3.4 m (Figure 21). The maximum flow velocity is U=42 m/s giving a Reynolds number of 2.6e6 for the airfoil. A NACA 0015 airfoil section model with a chord of 1 m and a spanwise length of 1.9 m was manufactured and instrumented with 64 pressure taps. Six of the prototype CRTEFs were glued together and mounted on the airfoil section model where 15% of the original trailing edge part of the model was cut away (Figure 22). The airfoil section model with the flap was afterwards mounted in a test rig 3.2 m from the nozzle outlet and 1.6m from the floor as seen in Figure 23. The turbulence intensity at the test section has been estimated to be 1%. The flow conditions at the position of the test stand have been determined in [19] and measurement corrections for most relevant effects have been utilized.
Figure 21: Sketch of the experimental setup at the Velux wind tunnel.
Pressure distributions were measured for a number of step activations of the flap at different mean angles of attack. The CRTEF was controlled using proportional pressure valves which could regulate the pressure from zero and up to nine bars. To assess the aerodynamic response the pressure distribution was measured using 64 pressure taps drilled on the suction and pressure side of the airfoil. Unfortunately, it was not possible to install pressure taps in the rubber material which would have enabled measurement of the full aerodynamic response including the pressure near the trailing edge. In all cases the exact CRTEF deflection as defined from the target (straight) flap angle has been estimated from lab testing (Figure 24) and found to be practically independent of the aerodynamic loading [18]. The flap angle command and response signals are measured using strain gauges and input pressures on the flap which are calibrated using a laser position sensor.
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Figure 22: The 1.9 m wide NACA0015 airfoil section model with a chord length of 1 m. Six of the flap prototypes are glued together and then attached to the airfoil section model.
Figure 23: Left: test rig with the 1.9m long test section. Right: test rig with pitot tubes for measuring the airfoil drag.
Figure 24 - CRTEF deformation camber line (for 1 degree 'straight' flap angle).
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For the dynamic flap cases, the actual CRTEF response to an input flap angle has been determined from step input cases during wind tunnel testing. The response can be described by a first order system response with a time constant of 0.1s (Figure 25), formulated as: 𝒅𝜹𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝟏 + 𝜹𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 = 𝜹𝒊𝒏𝒑𝒖𝒕 𝒅𝒕 𝝉
(5)
Figure 25 – Measured CRTEF response to a step in input flap angle. Comparison with a first order linear model (with a time constant τ =0.1s).
3.5.2 Results Polar measurements were performed for two different Reynolds numbers (1.6e6, 2.6e6). The standard procedure for polar measurements was utilized, where time signals of measured postprocessed aerodynamic coefficients are averaged into 1 degree angle of attack bins. Drag measurements were performed, utilizing the available wake rake. Although the airfoil surface was relatively clean, the boundary layer is expected to be turbulent due to the considerable inflow turbulence. The resulting angles of attack are calculated from the geometric ones utilizing the flow corrections for the specific test section setup [19]. Figure 26, shows the measured polars at Re = 1.6e106 for the two different flap deflections. The polars for Re = 2.6e106 are shown in Figure 27. For the higher Re cases, a limited range of angles of attack is available, where data averaging is also less reliable towards the ends of the range. For all cases the typical behaviour for an airfoil with flap is visible. With increasing flap deflection all polars shift to larger absolute values. The Clmax value increases with increasing flap deflection, but the angle at which Clmax appears decreases.
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(a)
(b)
(c)
(b)
(c)
Figure 26: (a) Cl-α; (b) Cd-α; (c) Cm-α polars for Re=1.6e6.
(a)
Figure 27: (a) Cl-α; (b) Cd-α; (c) Cm-α polars for Re=2.6e6.
Measured pressure distributions for an angle of attack around 5° are shown in Figure 28 (a) and (b) for Re=1.6e6 and Re=2.6e6, respectively. The flap influence on the whole pressure distribution is shown, despite the missing pressure points on the flap region. For the dynamic flap cases, the flap angle is following a lagged step signal with a period of 10s as described above. The flap angle and Cl response for Re=1.6e6 and Re=2.6e6 are given in Figure 29 and Figure 30, respectively.
(a)
(b)
Figure 28: Cp distribution for α=5.45° (a) Re=1.6e6 (b) Re=2.6e6.
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(a)
(b)
Figure 29: (a) Flap angle and (b) Cl response with flap step input at α=5.45° and Re=1.6e6.
(a)
(b)
Figure 30: (a) Flap angle and (b) Cl response with flap step input at α=5.33° and Re=2.6e6.
3.6
Unsteady measurements of the DU95W180 airfoil with oscillating flap
This section presents the experimental set up and the collected data for measurements on the DU95W180 airfoil in steady and unsteady flow, for different angle of attack and flap settings, including unsteady oscillatory trailing-edge-flap motion. Different flap oscillation amplitudes and reduced frequencies were employed. The experiments were conducted in the Low Turbulence Wind Tunnel of Delft University of Technology with a model of 0.6m chord at a Reynolds number of Re ≈ 10e6 and a freestream Mach number of Ma ≈ 0.073. Data includes lift, drag and moment coefficient and pressure distribution over the surface of the airfoil, for both steady and unsteady flow. A digital database of the experimental data is available. A full and extended report is uploaded in the share site of the Avatar project. 3.6.1 Wind-Tunnel and experimental set-up The experimental method follows the approach used in previous airfoil measurements at TU Delft and also previously used for this airfoil model for steady flow [1]. For unsteady flow, an actuator was added to the flap and unsteady pressure measurements were conducted.
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Wind tunnel The measurements were performed in the Low-speed, Low-turbulence wind tunnel (LTT) of the Faculty of Aerospace Engineering of Delft University of Technology. The wind tunnel has a closed single-return circuit with a total length of 72.7m. Upwind of the test section, the circuit has a contraction ratio of 17.8 to 1. The octagonal test section is 2.6m long, 1.25m high, and1.80m wide. At a wind speed of 25m/s, the free-stream turbulence level is approximately 0.02%. Figure 31 shows the schematic of the wind tunnel. Table 6 presents the key specifications. A discussion of wind tunnel corrections, pressure data correction and data averaging is presented in the extended report. The DU95W180 airfoil model The DU95W180 airfoil model has a chord of c=0.6m and a span of b=1.25m. The model is produced in fibre-glass composite with a polished polyester gelcoat surface. The surface deviation is expected to be below 0.1mm [1]. The specific DU 95-W-180 airfoil model has been previously measured in steady conditions in TU Delft’s LTT wind tunnel. The airfoil has a maximum thickness t/c = 18%. The geometry of the airfoil for different flap deflections β is shown in Figure 32. One-hundred chordwise pressure taps were installed in staggered formation towards the centre of the wing, with a diameter of 0.4mm. Some of these pressure orifices were obstructed by zigzag (ZZ) tape used for the forced transition cases, the flap motion or simply obstructed by pollution. Tables in the extended report show the location and index of the pressure probes for five configurations of flap deflection, indicating which are active for the cases of free and forced transition and used in the files of the digital database. An electronic pressure transducer interfaces the pressure signals from the wake rake and airfoil model with the data acquisition system. The set of approximately 200 pressure signals were acquired at a frequency of 300Hz or k = 22.6 (226 times larger than the highest flap oscillation frequency).
Figure 31: Schematic of the Low-speed, low-turbulence wind tunnel (LTT) of the Faculty of Aerospace Engineering of Delft University of Technology.
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Figure 32: DU95W180 geometry for flap angles -10°, -5°, 0°, +5° and+10°.
Figure 33: Experimental setup including detail of the model, wake rake and flap actuator.
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ZZ tape was used to fix the transition location for the forced-transition cases. The effectiveness of the trips was verified during the experiment using a stethoscope, ensuring a turbulent boundary layer state along the span of the airfoil just behind the location of the ZZ tape. More model details are listed in Table 7. Figure 33 shows the experimental setup including detail of the model, wake rake and flap actuator. Flap actuation is achieved with a stepper motor, linked to the flap at both ends of the two dimensional model. The transition tape piece at the flap shown in the figure is intended to maintain a smooth and continuous surface. However, for high negative flap angles, one of the pressure taps is covered by the transition strip, rendering its signal unusable. This has been pre-filtered in the data supplied and the pressure at that point is interpolated from the adjacent pressure reading. The stepper motor achieved a reduced frequency up to k = 0.1. The signal form applied is approximately a sinusoidal. Experimental cases The experimental measurements encompass 60 cases: 18 steady and 42 unsteady, varying flap angle, angle of attack, free and forced transition, reduced frequency of the flap oscillation and amplitude of the oscillation. The list of cases can be found in Table 8 and Table 9. 3.6.2 Results At this moment, no in depth analysis and interpretation of the results has been performed. Comments on the quality of the data are, however, relevant. The actuation of the flap implies a hysteresis effect that was observed to lead to maximum uncertainty in Cl of ±0.015 in the steady cases. In the unsteady experiments at α = 18°, the measurements of the flap angle showed a perturbation close to the maximum flap deflection that occurred every fourth cycle, impacting Cl; although this does not impact the median of the phase locked results, it impacts the mean and the standard deviation. The original calibration of the flap actuator proved to have a varying bias at positive flap angles, with a maximum of ≈ 0.95° (corresponding to a displacement of the flap of 0.003c) at β = 5°. The current calibration was corrected (using several static measurements), with current uncertainty of lift coefficient due to flap bias estimated at below 0.015. The measurements of total drag using the wake rake was only possible for the steady cases, at ranges of angle of attack −11° ≤ α ≤ +11°. The pressure drag is integrated from the pressure over the airfoil surface and was used for the remaining range of angles of attack and for the unsteady cases, including for the calculation of wind tunnel correction. The data files in the digital database indicate whether the wake rake drag or the pressure drag was used for each point (see Tables 7, 8 and 9 of the extended report). Figure 34 shows the steady polar results. Figures 7 to 13 of the extended report present the flap motion for the unsteady cases. Figures 14 to 34 of the extended report show the unsteady polars. An initial analysis of some of the pressure distributions shows a significant phase delay in four pressure orifices (see Figure 36). The reason for this additional phase delay in relation to the other probes is yet not determined. In next steps, we will aim to improve these data points or eliminate them from the calculations. 3.6.3 Conclusions Static and dynamic wind tunnel tests were performed on a DU95W180 airfoil with a trailing edge flap with a length of 0.2 chord, in free and forced transition conditions, for varying angles of Page 34 of 106
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attack and flap angles, and three reduced frequencies, in a total sixty experimental cases. The unsteady results clearly show the effect of hysteresis, even at low reduced frequencies. The data might therefore be of value for the validation of 2D unsteady airfoil simulations. The steady and unsteady phase locked average data (median, mean and standard deviation) are made available in a digital database in the Avatar project database. An improvement of the data postprocessing will probably lead to an update of this database. Table 6: LTT wind tunnel specifications.
Feature
Value
Remarks
Circuit length
72.7m
Test Section
2.6m * 1.80m * 1.25m
Contraction Ratio
17.80
Motor
580 kW
Fan
6-bladed fan
Turbulence level
0.02 − 0.07%
At free stream velocities: 25 − 75m/s
Maximum Speed
120m/s
At test section entrance
(length * width * height) DC Electric Motor
Table 7: DU95W180 model specifications.
Feature
Value
Airfoil Chord
0.6m
Model Aspect Ratio
2.1
Airfoil Thickness
0.180c
Pressure taps
100 (56 upper surface; 44 lower surface)
Zigzag tape location
x/c = 0.05c on upper surface; x/c = 0.10 on lower surface
Flap length
0.2c
Flap hinge location
x/c = 0.80 and y /c = −0.01362
Flap deflection range
±10°
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Table 8: Steady test cases.
Case
Transition
α (°)
∆β (°)
k
Re
M
q (Pa)
U∞ (m/s)
Cases with varying angle of attack α and fixed flap angle β; including polar hysteresis. STDY 1 free −20°:30° −10.1 0.0 1003000 0.073 382.79 25.07 STDY 2 free −20°:30° −5.7 0.0 1001000 0.073 386.96 25.21 STDY 3 free −20°:30° −0.8 0.0 1003000 0.073 382.97 25.07 STDY 4 free −20°:30° +4. 0.0 1003000 0.073 386.96 25.22 STDY 5 free −20°:30° +9.2 0.0 1002000 0.073 386.96 25.22 STDY 6 forced −20°:30° −10.1 0.0 981848 0.072 366.36 24.57 STDY 7 forced −20°:30° −5.0 0.0 1000651 0.073 378.55 24.96 STDY 8 forced −20°:30° −0.8 0.0 1001182 0.073 378.09 24.93 STDY 9 forced −20°:30° +4. 0.0 1004000 0.072 375.50 24.87 STDY 10 forced −20°:30° +9.2 0.0 1002000 0.072 371.34 24.73 Cases with fixed angle of attack α and varying flap angle β; including polar hysteresis. STDY 11 free 0° −10.1°:9.2° 0.0 1000000 0.073 381.77 25.16 STDY 12 free 8° −10.1°:9.2° 0.0 998000 0.073 381.95 25.17 STDY 13 free 10° −10.1°:9.2° 0.0 1000000 0.073 380.93 24.14 STDY 14 free 18° −10.1°:9.2° 0.0 1000000 0.072 379.79 25.06 STDY 15 forced 0° −10.1°:9.2° 0.0 1003000 0.073 381.04 25.07 STDY 16 forced 8° −10.1°:9.2° 0.0 100400 0.073 380.00 25.01 STDY 17 forced 10° −10.1°:9.2° 0.0 1002000 0.073 379.02 24.99 STDY 18 forced 18° −10.1°:9.2° 0.0 985800 0.072 367.51 24.63
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Table 9: Unsteady test cases
Case UNST 1 UNST 2 UNST 3 UNST 4 UNST 5 UNST 6 UNST 7 UNST 8 UNST 9 UNST 10 UNST 11 UNST 12 UNST 13 UNST 14 UNST 15 UNST 16 UNST 17 UNST 18 UNST 19 UNST 20 UNST 21 UNST 22 UNST 23 UNST 24 UNST 25 UNST 26 UNST 27 UNST 28 UNST 29 UNST 30 UNST 31 UNST 32 UNST 33 UNST 34 UNST 35 UNST 36 UNST 37 UNST 38 UNST 39 UNST 40 UNST 41 UNST 42 UNST 42
Transition free forced free forced free forced free forced free forced free forced free forced free forced free forced free forced free forced free forced free free free free free free free forced free forced free forced free forced free forced free forced forced
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α (°) 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 18 18 18 18 18 18 18 18 18 18 18 18 18
β (°) −5.0:3.9 −5.0:3.9 −5.0:3.9 −5.0:3.9 −4.9:3.9 −4.9:3.9 −10.1:9.2 −10.1:9.2 −10.1:9.2 −10.1:9.2 −10.0:9.2 −10.0:9.2 −5.0:3.9 −5.0:3.9 −5.0:3.9 −5.0:3.9 −4.9:3.9 −4.9:3.9 −10.1:9.2 −10.1:9.2 −10.0:9.2 −10.1:9.2 −10.0:9.2 −10.0:9.2 −5.0:3.9 −5.0:3.9 −4.9:3.9 −10.1:9.2 −10.1:9.2 −10.0:9.2 −5.0:3.8 −5.0:3.9 −5.0:3.8 −4.9:3.9 −4.9:3.8 −4.9:3.9 −10.1:9.2 −10.1:9.2 −10.1:9.2 −10.1:9.2 −10.0:9.2 −10.0:9.2 −10.0:9.2
k 0.01 0.01 0.05 0.05 0.1 0.1 0.01 0.01 0.05 0.05 0.1 0.1 0.01 0.01 0.05 0.05 0.1 0.1 0.01 0.01 0.05 0.05 0.1 0.1 0.01 0.05 0.1 0.01 0.05 0.1 0.01 0.01 0.05 0.05 0.1 0.1 0.01 0.01 0.05 0.05 0.1 0.1 0.1
Re 1011574.0 1016252.0 1012000.0 1016280.0 1013000.0 1016962.0 1010000.0 1015243.0 1010323.0 1015207.0 1010295.0 1014861.0 1008551.0 1018546.0 1008963.0 1018520.0 1009286.0 1018541.0 1007829.0 1017970.0 1008029.0 1017987.0 1008031.0 1017657.0 1015500.0 1015554.0 1015596.0 1015000.0 1014951.0 1014732.0 1027188.0 1031038.0 1027464.0 1031860.0 1027734.0 1032578.0 1025931.0 1029035.0 1026133.0 1029398.0 1026004.0 1029388.0 1029388.0
M 0.073 0.073 0.073 0.074 0.073 0.074 0.073 0.073 0.073 0.073 0.073 0.073 0.073 0.074 0.073 0.074 0.073 0.074 0.073 0.074 0.073 0.074 0.073 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.074 0.075 0.074 0.075 0.074 0.075 0.074 0.075 0.074 0.075 0.074 0.075 0.075
q (P a) 382.80 386.97 382.98 386.97 383.07 386.97 382.00 386.52 382.15 386.49 382.04 386.24 381.25 389.44 381.44 389.42 381.50 389.38 380.90 389.15 381.02 389.10 380.81 388.84 388.06 388.10 388.03 387.83 387.79 387.66 395.80 399.58 396.03 399.83 396.12 400.07 394.88 398.33 394.99 398.60 394.93 398.46 398.46
U∞ (m/s) 25.07 25.22 25.07 25.22 25.07 25.21 25.05 25.21 25.05 25.21 25.05 25.2 25.03 25.31 25.03 25.31 25.04 25.3 25.02 25.3 25.02 25.3 25.02 25.29 25.3 25.3 25.29 25.29 25.29 25.28 25.52 25.65 25.53 25.66 25.53 25.66 25.49 25.62 25.49 25.62 25.49 25.62 25.62
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Figure 34: Steady experimental polars of the DU95W180 for varying angle of attack and fixed flap angle (Cl − α, Cl − Cd, Cm − α) at Re=1.0e6, with free and forced transition and flap angles β = −10°, −5°, 0°, +5° and +10°.
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Figure 35: Unsteady experimental polars of the DU95W180 for varying flap angle and fixed angle of attack (Cl − β, Cdp − β, Cm − β) at Re=1.0e6, with free and forced transition. α = 8°, −10.0° < β < 9.2°, k = 0.1.
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Figure 36: Cp distribution of the DU95Wl80 for varying reduced frequencies, angle of attack and phase of the flap motion, with free and forced transition.
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4. Description of CFD codes 4.1
CENER
WMB: WMB (Wind Multi Block, [20, 21]) is a CFD code developed and validated by CENER and the University of Liverpool for wind turbine aerodynamics analysis (2D and 3D). It is capable of solving the compressible Unsteady Reynolds Averaged Navier-Stokes (URANS) flow equations on multi-block structured grids using a cell-centred finite-volume method for the spatial discretization. Moving and deforming grids can be calculated using WMB and aeroelastic analysis of structures such as wind turbine blades are analysed based on modal representation. Several turbulence models are implemented in the code. WMB has the capacity to study both fully turbulent and transitional flows around airfoils. In addition, airfoils with distributed roughness on the surface can be calculated using WMB. Simulation details: WMB CFD code was used for the simulation of the static flap cases of part A. The mesh was generated using ICEM CFD with non-dimensional distance of the first node from the wall equal to 4·10-6 corresponding to y+ equal to 1. 400 nodes are used to model the airfoil surface and far field is located at 25 chord distance. Turbulence model and transition models used are k-w baseline and eN. The total number of grid points was 133944. In the stall area the results were averaged to get the mean values AdaptFoil2D: AdaptFoil2D is a code developed in CENER for 2D airfoil aeroelastic modelling based on a potential solution. The aerodynamic part is based on panel methods, numerical approximations employed to represent the aerodynamic behaviour of airfoil geometries. Panel methods comprise the discretization of the geometry into panels and the distribution of singularity elements (sources, vortices or doublets). This set of singularities must fulfil the nonpenetration condition on a discretization of the airfoil surface. Apart of the airfoil geometry, the wake modelling is based on vortex methods to complete the general picture of airfoil and flow. The current version of AdaptFoil2D is developed taking into account a good balance between accuracy and computational effort for aerodynamic modelling, with the following characteristics:
Surface panel code for a thick airfoil section. The wake is a doublet panel attached to the TE, transformed into discrete vortices downstream. A free wake and a direct time-stepping method are used to calculate the wake roll-up. The time marching solution is also used for the aerodynamic and structural coupling with direct application of the dynamic motion equations.
In addition to attached flow, separated flow is considered using a double wake approach. The separation point of the airfoil is prescribed as a function of the angle of attack. The unsteady aerodynamic performance in separated flow conditions and the dynamic stall occurrence are simulated including some engineering concepts based on the Beddoes-Leishman model. Regarding the structural part, the dynamic motion of the airfoil is mainly based on a rigid body motion. The mass and moment of inertia are assumed to be at a single point of the mean line, where a 3-degrees of freedom system of springs and dampers is coupled simulating the Page 41 of 106
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structural properties of the real blade section. Furthermore, the implementation includes an approximation for passive deformations of the LE and TE regions, using a static Euler-Bernoulli beam model with a suitable value of the bending stiffness EI. Simulation details: The AdaptFoil2D potential panel code (vortex method) was used for the dynamic flap simulations of part B. Concretely, the tip and mid sections of the INNWIND.EU rotor blade have been simulated including TE and LE oscillating flaps. Using the original blunt TE geometry of the corresponding airfoils, a sharp profile is created with XFoil divided into 400 panels. The dimensionless time step was approximately 0.0149 for the flap simulations. The attached flow cases need only 2 cycles for convergence while for the cases including conditions of separated flow, the values have been averaged from the 3rd to the 20th cycles. As AdaptFoil2D is a potential code, a viscous correction has been applied based on CFD steady results in order to compare the code with viscous codes. Part C computations were performed using HMB, which is described in section 4.5.
4.2
CRES
CRES developed a phenomenological model for the effect VGs have on the aerodynamic performance of airfoils. The model was implemented in the MaPFlow CFD code (see detailed description in section 4.4). This model was originally developed for incompressible flows [22], but in the present context, the model has been adapted to compressible flow simulations so as to fit in MaPFlow. The turbulence model used is the k-ω Shear Stress Transport (SST) eddy viscosity model [23] and the approach is referenced as VG-Flow in the remaining of the document. According to the model the flow is decomposed to a mean flow field and a vortex flow field. The three-dimensional Navier–Stokes equations, which essentially describe the complex flow around an airfoil-VG configuration, are then spanwise averaged resulting in an equivalent set of two-dimensional equations which include additional source terms. Applying the same decomposition and spanwise averaging to the k-w SST turbulence model an additional part is added to the production term of the turbulence kinetic energy. The new terms are modelled using elementary vortex flow theory.
4.3
DTU
4.3.1 EllipSys The DTU Wind Energy flow solver EllipSys3D is used in all computations presented for the VG problem. The code is developed in co-operation between the former Department of Mechanical Engineering at the Technical University of Denmark and the former Department of Wind Energy at Risø National Laboratory, Risø-DTU, see Michelsen [24, 25] and Sørensen [26]. In the present work the turbulence in the boundary layer is modelled by the k-ω SST turbulence model [23] using fully turbulent conditions. In the present simulations, the EllipSys3D code is used in steady state mode, running local time stepping towards a steady state solution. The diffusive terms are discretized with a second order central differencing scheme. The convective Page 42 of 106
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fluxes are computed using the third order accurate QUICK scheme of Leonard [27], both for the momentum, turbulence equations, and the equations of the transition model. For all simulations, the convergence criterion is a reduction of the residual by a factor of 100.000. VG simulation details: The VG configurations investigated in the present work are in both coand counter-rotating configuration; the co-rotating configuration is seen in Figure 37. In order to limit the computational requirements, only one of the two vanes in a VG unit is simulated, exploiting the geometrical symmetry of a VG unit.
Figure 37: The left side of the figure shows a sketch of a top-down view of an airfoil with the leading edge toward the bottom equipped with VGs. The coloured region indicates the symmetry unit used in the computations. The right side of the figure shows a non-scalable sketch defining the characteristic dimensions of the VG setup.
4.3.2 Q3UIC Q3UIC is a Quasi-three dimensional Unsteady viscous–inviscid Interactive Code designed to predict the aerodynamic behaviour of wind turbine airfoils. The model is based on a viscous– inviscid interaction technique based on a strong coupling between the viscous and inviscid parts via the transpiration velocity concept. The inviscid part is modelled by a two-dimensional panel method, and the viscous part is modelled by solving the integral form of the laminar and turbulent boundary layer equations with extensions for three-dimensional rotational effects. Laminar to turbulent transition is either forced by employing a boundary-layer trip or computed using an en envelope transition method. The Karman-Tsien correction factor is applied to the edge velocity in order to account for compressibility effects in the external flow. In addition, Whitfield definition of the shape factor is used to account for compressibility effects inside the boundary layer. The VG modelling in Q3UIC is carried out through a modification of the integral boundary layer formulation [28]. The turbulence production has been enhanced downstream the location of the vortex generator by modifying the shear-transport rate equation. A step change has been applied to the rate equation at the VG location, which decreases exponentially downstream towards the trailing edge, producing an increase in both the momentum thickness and the skin friction as well as a decrease in the displacement thickness, mimicking in this way the reenergizing effect of the vortex generator inside the boundary layer. In the present approach has been assumed the development of turbulent flow downstream of the VG location, therefore a modification has not been applied to the laminar boundary layer formulation. The present model needs to be further calibrated for a range of VG devices. Page 43 of 106
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4.4
NTUA
4.4.1 MaPFlow MaPFlow [29] is a multi-block MPI enabled compressible solver equipped with preconditioning in regions of low Mach flow. The discretization scheme is cell centred and makes use of the Roe approximate Riemann solver for the convective fluxes. In space the scheme is 2nd order accurate defined for unstructured grids and applies the Venkatakrishnan’s limiter [30]. Also in time the scheme is second order and implicit introducing dual time stepping for facilitating convergence. The solver is equipped with the Spalart-Allmaras (SA) and the k-w SST eddy viscosity turbulence models. The effect of the VGs on the flow is included by means of the BAY model [31], The model assumes that the presence of a zero thickness vane VG can be represented as a source term in the momentum and energy equations. The source term simulates the lift force introduced by the VG in the flowfield. This term aligns the flow with the VG direction. The model was applied in its jBAY variation [32] in which the VG is replaced by a surface with zero thickness. The cells, to which the source term is added, are the cells that intersect this VG surface, see Figure 38 where a schematic representation is given.
Figure 38: Unit vectors for the VG geometry. (Centre) Side and (right) top view of the cells on which the BAY model is applied.
VG simulation details: Unless otherwise stated the simulations without the VGs were 2D and the simulations with the VGs considered a single VG with symmetry conditions at the sides of the computational domain, see Figure 39 (a). When full span simulations are mentioned, the complete wing is considered with symmetry boundary conditions at the centre of the wing and inviscid wall boundary conditions at the side of it, see Figure 39 (b).
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(a)
(b)
Figure 39: (A) Small aspect ratio computational mesh with symmetry conditions at the side wall. Only a single VG is considered and 3D effects cannot be taken into account; (b) Full span computational mesh. Symmetry condition is applied at the centre of the wing and inviscid wall condition at its side.
Flap simulation details: The meshes provided by DTU were used for the simulation of the FFA and the DU-240 airfoils, whereas the TL190-82 mesh was generated using ICEM CFD. The FFA meshes consisted of 131841 nodes, the DU-240 mesh consisted of 98945 nodes and the TL190-82 mesh consisted of 150192 nodes. In all meshes the non-dimensional distance of the first node from the wall was less or equal to 10-5. For both the 1P and 6P cases, 720 time steps per cycle were found to give accurate results combined with a maximum dual step error criterion of 10-4. In most of the cases 5 cycles were enough to reach a periodic solution. Exception is the LE flap cases for the FFA-W3-248 airfoil for which at least 15 cycles were necessary in order to achieve full convergence. 4.4.2 GENUVP GENUVP [33] is a 3D potential free wake aerodynamic model based on: A panel representation of the blade surface over which a piecewise constant distribution of sources is combined with linear dipole distributions. The spanwise distribution of circulation is determined by applying the zero pressure condition along the line of vorticity emission. Vorticity is released in the flow along the trailing edge and the tip. A vortex particle representation of the wake. The evolution of the wake is obtained by solving the vorticity equation in Lagrangian description. Tree algorithms and particle mesh techniques are applied in combination with MPI parallelization. The code runs unsteady and steady state results are obtained upon time convergence. Loads are calculated using the pressure distribution obtained directly from the flow solver. Pressure is determined by integrating the momentum equation. This procedure includes the pressure given by the Bernoulli equation plus the wake contribution obtained through the solution of a Poisson equation for the wake added pressure term.
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An a posteriori viscous correction is applied using the provided 2D tables. The correction is based on the estimation of an effective angle of attack and an effective relative velocity. The effective angle of attack is obtained from the potential load calculation assuming that potential force per strip corresponds to lift. The effective relative velocity is taken as the average per strip relative surface velocity. GENUVP was mainly used for the 3D flapping simulations. Results were provided for the potential and the viscous corrected version of the code. For the InnWind rotor each blade was discretized by a grid with 51 strips and 59 panels per strip, whereas for the AVATAR rotor the selected grid had 39 strips and 51 panels per strip. Both grids were extracted from the provided CFD DTU grids. The reported simulations were made with 72 time steps per rotation. This is a small compromise according to previous experience which indicates 90 steps per rotation. For non-flapping simulations the difference has been checked at 11m/s and was found small (~23%). Simulations lasted 10 full rotations. Practically, for the cases studied time convergence was achieved after 5-6 rotations. 4.4.3 FoiL2W Foil2W [34] is a viscous-inviscid interaction code developed at NTUA. The potential flow part is simulated by singularity distributions along the airfoil geometry and the wake. The wake is represented by vortex particles which are allowed to freely move with the local flow velocity. The viscous flow solution is obtained by solving the unsteady integral boundary layer equations. The coupling of the two sets of equations is achieved through a transpiration velocity distribution along the airfoil surface that represents the mass flow difference over the boundary layer height between the real viscous flow and the equivalent inviscid flow. The boundary layer equations are discretized using finite differences and the final set of the non-linear equations are solved simultaneously using the Newton-Raphson algorithm. The boundary layer solution is supplemented by a transition prediction model based on the eN spatial amplification theory and by a dissipation closure equation for the maximum shear stress coefficient over the turbulent part. Simulation details: Foil2w was used in the 2D static and dynamic flapping simulations. The blunt original airfoil profiles were made sharp using the XFoil tool and discretized with a number of 100 panels. For the dynamic flap simulations 400 time steps per cycle were used and convergence was achieved after 2 cycles.
4.5
ULIV
In this study the flow in the 2D and 3D TE and LE flap simulations is computed using the Helicopter Multi-Block (HMB) flow solver developed at University of Liverpool. The code is a 3D multi-block structured solver and solves the Navier-Stokes equations in the 3D Cartesian frame of reference. HMB solves the Navier-Stokes equations in integral form using the arbitrary Lagrangian-Eulerian formulation for time-dependent domains with moving boundaries. It has so far been validated for wind turbine applications, using the NREL Phase VI experiments [35] as well as the pressure and PIV data of the MEXICO project [36]. The solver uses a cell-centred finite volume approach combined with an implicit dual-time method. Osher's upwind scheme is Page 46 of 106
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used to resolve the convective fluxes. Central differencing (CD) spatial discretisation method is used to solve the viscous terms. The non-linear system of equations that is generated as a result of the linearization is then solved by integration in pseudo-time using a first-order backward difference method. A Generalised Conjugate Gradient (GCG) method is then used in conjunction with a Block Incomplete Lower-Upper (BILU) factorisation as a pre-conditioner. The HMB solver has a library of turbulence closures including several one- and two- equation turbulence models, and turbulence simulation is also possible using either the Large-Eddy or the Detached-Eddy simulation approach. The solver was designed with parallel execution in mind and the MPI library along with a load-balancing algorithm are used to this end. The flow solver can be used in serial or parallel modes. Depending on the purposes of the simulations, steady and unsteady wind turbine CFD simulations can be performed in HMB using single or full rotor meshes generated using the ICEM-Hexa tool. Rigid or elastic blades can be simulated using static or dynamic computations. HMB allows for sliding meshes to simulate rotor-tower interaction cases [37]. Alternatively, overset grids can be used [38]. To account for low-speed flows, the Low-Mach Roe scheme (LM-Roe) developed by Rieper [39, 40] is employed in wind turbine cases. In addition to the flap modelling methods in HMB, new functions were developed for HMB, to implement the deformable, blended flaps required for the AVATAR project. Simulation details: For the 2D flap simulations, a multi-block structural mesh was generated around the DU-240 aerofoil in ICEM CFD. The whole mesh contained 71294 nodes, 71290 quads and 35256 hexas. The numbers of nodes in each block are indicated in Figure 40. The non-dimensional distance of the first node from the wall was 10-5. In the unsteady flap simulations, for 1P cases, 2000 time-steps/cycle were used; for 6P cases, 600 time-steps per cycle were used. Dependant on the flap deflection angle, frequency etc., the unsteady convergence (tolerance set to be 0.005) can be achieved after 70 ~ 200 pseudo-time steps. For the 3D flap simulations a mesh of 9.7 million cells was generated around the blades of the AVATAR rotor. The time step corresponded to 0.5° of rotor revolution. For the turbulence modelling the k-ω SST model was implemented. In the flap simulations, the deformed surface meshes of the flaps at the maximum up/down deflections were provided with the volume meshes of the aerofoil with flaps at the neutral position (no deflections). The flap motion can be represented by the sum of the harmonics. The solver interpolated (sinusoidal) and calculated mesh deformation and mesh velocity according to the time steps. This flap motion algorithm has been developed to implement arbitrary shape of the flap with any shape of maximum positive and negative deflections in HMB
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(a)
(b)
Figure 40: (a) Mesh around the DU-240 aerofoil with the numbers of nodes in each block; (b) trailing edge detail.
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5. Description of the test matrix of control devices In this section the Matrix of Test cases that have been analysed within AVATAR WP3 T3.1 is defined. The test matrix is divided in three parts:
Part A includes 2d cases for which experimental data are available (Table 10) Part B includes 2d cases for which there are no experimental data (Table 11) Part C includes the 3D cases (Table 12)
For each test case the relevant conditions are defined and the provided output is specified in Appendix 1. An overview of the relevant information is provided below in Table 10, Table 11 and Table 12, while in the attached AVATAR WP3 T3.1 Test Matrix.xlsx file (which should be regarded as reference) the same information is given in detail. Table 10: Test matrix for Part B
Part A: 2D cases WITH experimental data to compare Device
Vortex Generators
TE Flap static
Description DU97 W 300, Re=2.0e6 (see section 3.1) NTUA-t18, Re=1.0e6 & 0.87e6, Tripped (see section 3.2) TL 190-82, Re=2.5 6 10 , Clean (see section 3.4) TL 190-82, Re=2.5 6 10 , Tripped at 5% (see section 3.4)
Output (Appendix 1)
Conditions
Specifications
α = -2°:19°, Δα=2°
Triangular, contra, downwash
Polar
α = -5°:16°, Δα=2°
Triangular, contra, upwash
Polar, Field data
α~-5°:15°, Δα=2°
Flap=±10, ±5, 0
Polars
α~-5°:15°, Δα=2°
Flap=±10, ±5, 0
Polars
Table 11: Test matrix for Part B
Part Β: 2D cases WITHOUT experimental data Device
Description
VG
InnWind & AVATAR root [1] section , Tripped
TE Flap dynamic
LE Flap dynamic
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InnWind & AVATAR tip & mid [1] sections , Tripped
InnWind & AVATAR mid[1] section , Tripped
Conditions Operating [2] α range Operating α range α= rated α= rated+4 α= rated α= rated+4
Specifications Triangular, contra, [3] downwash Triangular, contra, [3] upwash Width=10% chord Δα=5,10, freq=nominal [4] and 6p Width=10% chord, Δα=5,10 freq=nominal [4] and 6p Width 20% chord, Δα=5,10 freq=nominal [4] and 6p Width 20% chord, Δα=5,10 freq=nominal [4] and 6p
Output (Appendix 1) Polar Polar Time signals
Time signals
Time signals
Time signals
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[1] The selection of sections for both rotors correspond to r/R=0.35, 0.60, 0.75 respectively for the root, mid and tip locations. The rationale of this choice is the following: the root section is placed well within the aerodynamic part of the blade (for the InnWind rotor it starts at r/R=0.20) so that a substantial spanwise length is allowed for placing a similar VG array in the 3D cases; the tip section is centred at max loading which also allows a substantial spanwise length for placing a 3D flap of ~10% of the blade length; finally the mid-section is just chosen in between. [2] The operating angles of attack for the InnWind rotor have been estimated within the InnWind project by NTUA using GENUVP. By comparing the pressure distributions as obtained by GENUVP and the corresponding CFD simulations using MaPFlow, the angles of attack have been checked. A similar approach has been followed also for the AVATAR rotor within the present project. The final computations extended beyond the operating range in order to examine the post stall behaviour of the models. [3] The VG lay-outs are based on the geometry already considered in Part A. Note that the dimensions are linked to the VG height (h) which in turn is set ~δ (i.e. the boundary layer thickness). Also note that the dimensions of the downwash and upwash concepts are the same for comparison reasons (Figure 41, Figure 42). The estimation of the boundary layer thickness has been based on a 2D simulation at α = 0°. Based on the pressure data the flow velocity at the end of the boundary layer can be estimated from: 𝑼 = √𝟏 − 𝑪𝒑 𝑼∞
(6)
Then δ is obtained as the distance from the blade surface at which the flow velocity is 0.99𝑼. For the DU331 airfoil at Re=15.8e6, δ=0.00457c. The boundary layer height was considered unchanged for the FFAW3-333 airfoil, at Re=14.0e6 [4] The choice of the TE flap width is made under the understanding that flaps will be used for controlling the loads. For the LE flap, it is assumed that its operation is similar to that of the TE flap. The width in this case is increased to 20% so as to allow a smooth transition of surface slope. Then as regards the choice of frequencies, the nominal rotor speed is here selected as a reference and then the 6p is selected in order to also consider a higher frequency.
Table 12: Test matrix for Part C
Part C: 3D cases Device
Description
Conditions
InnWind & AVATAR rotor, Tripped
Rated
TE Flap dynamic
InnWind & [7] AVATAR rotors , Tripped
α= rated
LE Flap dynamic
InnWind & [7] AVATAR rotors , Tripped
α= rated
VG
[5]
Specifications Triangular, contra, downwash, deployed over 10% of the [6] blade length Triangular, contra, upwash deployed over 10% of the [6] blade length Width=10% chord, Length 10% of the blade centred at tip, Δα=10, freq=nominal, less dumped and 6p Width 20% chord, Length 10% of the blade centred at mid span, Δα=10, freq=nominal, less dumped and 6p
Output (Appendix 1) Blade loads Flow data Blade loads Flow data
Time signals
Time signals
[5] The VG cases are considered with flaps at zero position. Two configurations are considered: the upwash and the downwash in accordance to Part B test cases. [6] The spanwise length is set at 10% of the blade length so as the keep the computational effort at this exploratory stage reasonable. The same VG lay-out will be used as in the Part B cases [7] The LE and TE flaps are centred at the positions already considered in Part B. For the TE cases the tip case is considered while for the LE the mid case.
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Definition of the Vortex Generator lay outs A contra rotating set up was selected with triangular VGs. Layout details for the VG configuration are given in Table 13 and Figure 41 (downwash set up) and Figure 42 (upwash set up). Table 13: Downwash vortex generator configuration parameters
Parameter x/c β h l D d
Downwash VG lay out 0.3 20° δ 3h 9.5h 2h
U∞
Upwash VG lay out 0.3 20° δ 3h 9.5h 4h
Definition Chordwise position of the VG array, where c is the wing chord VG angle to the free stream flow VG height VG length Distance between two VG pairs Spanwise distance between the LE of two VGs of the same pair
d β
D
Figure 41: Part B, Downwash Lay out
U
∞
d β
D
Figure 42: Part B, Upwash Lay-out
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Definition of the LE and TE flap deformation The deformation of the flaps is defined with respect to the mean line of the airfoils as indicated ⃗ 𝒎 denote the mean line and 𝒉(𝒙) the thickness distribution. in Figure 43 and Figure 44. Let ⃗𝑿 With respect to a curvilinear (𝝃, 𝜼) system following the mean line the deformation can be defined as 𝜼(𝝃) = 𝜶𝝃𝒎 (𝝃 + 𝜷), 𝝃 ∈ [𝟎, 𝟏]. Then the upper (+) and lower (-) sides of the airfoil will be: ⃗⃗⃗⃗ 𝒎 ⃗⃗ (±) = 𝑿 ⃗⃗ 𝒎 + 𝜼(𝝃)𝑵 ⃗⃗ 𝒎 + 𝒉(𝒙)𝑵′ 𝑿 ⃗ 𝒎 denotes the unit normal to the mean line and ⃗⃗⃗⃗ In the above expression ⃗𝑵 𝑵′𝒎 the unit normal to ⃗⃗ ′𝒎 = 𝑿 ⃗⃗ 𝒎 + 𝜼(𝝃)𝑵 ⃗⃗ 𝒎 the deformed mean line defined by 𝑿 The process is as follows: For 𝒙 > 𝒙𝒐 (the point at which flap starts) ⃗ 𝒎 (𝒙), 𝒉(𝒙), ⃗𝑵 ⃗ 𝒎 (𝒙) 1. Get ⃗𝑿 2. Define 𝝃 = 𝝃(𝒙) based on the length along the mean line ⃗⃗⃗⃗′ 𝒎 (𝝃) ⃗⃗ ′𝒎 (𝝃) = 𝑿 ⃗⃗ 𝒎 (𝒙) + 𝜼(𝝃)𝑵 ⃗⃗ 𝒎 (𝒙) and get 𝑵 3. Define the deformed mean line: 𝑿 ⃗⃗⃗⃗ 𝒎 ⃗ (±) = ⃗𝑿 ⃗ 𝒎 + 𝜼(𝝃)𝑵 ⃗⃗ 𝒎 + 𝒉(𝒙)𝑵′ 4. Get ⃗𝑿 With respect to the definition of 𝜼(𝝃) = 𝜶𝝃𝒎 (𝝃 + 𝜷) a. At 𝝃 = 𝟎 value and first derivative should be zero b. At 𝝃 = 𝟏 the 2nd derivative is set to zero For = 𝟐 ⇒ 𝜼(𝝃) = 𝜶𝝃𝟐 (𝟑 − 𝝃)/𝟐 . Then 𝒂 is providing the deflection. In principle 𝒂 = 𝒂(𝒕) = 𝒂𝒎 𝐬𝐢𝐧(𝝎𝒕) where 𝒂𝒎 denotes the max value which is determined by the max deflection angle 𝜽 (See Appendix 2).
Figure 43: Definition conditions for the TE flap deformation. 𝜽 is the deflection angle.
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Figure 44: Definition conditions for the LE (b) flap deformation. 𝜽 is the deflection angle.
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6. Validation and cross-checking 6.1
Part A – Comparison with experimental data
6.1.1 Vortex Generators Case A – VGs on the DU97w300 airfoil at Re = 2.0e6 In this section a comparison is made between experimental data provided by TU DELFT (see section 3.1) and numerical results provided by CRES using VG-Flow (see section 4.2), DTU using the viscous inviscid interaction code Q3UIC (see section 4.3.2) and NTUA using the CFD code MaPFlow with the BAY model (see section 4.4). A DU97-w-300 is examined with VGs at 20% or 30% chord at Re = 2.0e6. Very good agreement is observed between experimental and CFD results in the linear part of the lift polar (Figure 45 - a), up to Clmax, for all cases. Beyond that point MaPFlow over predicts Lift and under predicts Drag (Figure 45 - b), while VG-Flow simulations tend to under predict Lift. Q3UIC also over predicts Lift beyond Clmax apart from the case with VGs at 20% where the agreement is good at all angles of attack. It is common for 2D CFD simulations to over predict Lift under three-dimensional separated flow conditions [5]. Unfortunately, no information regarding the three-dimensionality of the flow beyond Clmax is available from the experiments. However, a simulation of a DU97w300 wing with aspect ratio (AR) equal to that of the wind tunnel model showed that SCs do form on the suction side of this wing. Two-dimensional and small AR simulations like the ones performed here cannot predict 3D separation due to the limited space in the spanwise direction and conceivably this is the reason for the discrepancy between simulations and experimental results at angles of attack beyond Clmax [41].
(a)
(b)
Figure 45: Comparison between computational and experimental data. (a) Lift and (b) drag variation with angle of attack. DU97w300 airfoil at Re = 2.0e6 without VGs and with VGs at 0.3c
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examined. The drag increase caused by the VGs at the lower part of the polar is underpredicted by both CFD and the viscous inviscid interaction code. This could be partially attributed to the fact that in the experiments VGs where mounted on the wing using a 0.2mm VG strip which causes additional drag of at least a few drag units. This trip was not modelled in the simulations. Case B – VGs on the NTUA-t18 airfoil at Re = 1.0e6 and 0.87e6 Vortex Generators at 30% In this section a comparison is made between experimental data provided by NTUA (see section 3.2) and numerical results provided by CRES using VG-Flow (see section 4.2), DTU using the viscous inviscid interaction code Q3UIC (see section 4.3.2) and NTUA using the CFD code MaPFlow with the BAY model (see section 4.4). The examined airfoil is NTUA-t18 with VGs at 30% chord at Re = 1.0e6. The lift and drag variation with angle of attack is shown in Figure 46. The results lead to conclusions similar to the previous case. BAY model results over predict lift beyond Clmax and under predict the drag penalty at lower angle of attacks. The 2D RANS VG model (VG-Flow) is very close to the experimental values in terms of both lift and drag. Q3UIC gives promising results with regard to lift but under predicts drag.
(a)
(b)
Figure 46: Comparison between computational and experimental data. (a) Lift and (b) drag variation with angle of attack. NTUA-t18 airfoil at Re = 1.0e6 without VGs and with VGs at 0.3c.
Vortex Generators at 40% For the case with VGs at 40% chord full span simulations were performed with MaPFlow, see Figure 47. In the full span simulations VG effectiveness is underpredicted. This could possibly be attributed to the fact that BAY model simulations under predict VG vortex peak vorticity [41, 42] and hence their ability to control separation. Agreement between experiments and full span CFD is better at higher angles of attack, where VGs fail to prevent separation. On the other hand small AR simulations predict an increasing lift polar up to 16°. This is because 3D separation is not taken into account. Q3UIC and VG-Flow simulations again provide results that agree well with the experiments, in the latter case not only for lift but also for drag.
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Pressure coefficient distribution at 11° and 16° (Figure 48) show that as long as the VGs work the low AR simulations provide qualitatively correct results but when the VG effect is cancelled by the appearance of Stall Cells only full span simulations can predict the extent of the separated flow.
(a)
(b)
Figure 47: Comparison between computational and experimental data. (a) Lift and (b) variation with angle of attack. NTUA-t18 airfoil at Re = 1.0e6 without VGs and with VGs at 0.4c.
(a)
(b)
Figure 48: Comparison between computational and experimental data. Pressure distribution along the chord at the centre of the wing. NTUA-t18 airfoil with VGs at x/c=0.4. Comparison between experimental, full span CFD and low aspect ratio CFD. (a) 11° and (b) 16° [41].
Flow field comparisons The flow field data obtained from the MaPFlow-BAY model simulations were compared with the available stereo PIV data. The comparison in terms of streamwise velocity and vorticity is given in Figure 49. The CFD results are qualitatively correct as the vortex appears to be more diffused in the simulations than in the experiments.
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Figure 49: Comparison between Stereo PIV (positive z/h) and numerical data (negative z/h). Left: Normalized streamwise velocity contours. Right: Normalized vorticity contours. Vorticity isolines for ω = ω max/2 for each vortex are also plotted. Top, middle and bottom row correspond to plane A (x/c=0.6, Δx=27.2h), B (x/c=0.7, Δx=37.2h) and C (x/c=0.8, Δx=47.2h), respectively. The wing surface is at y/h=0 and z/h=0 is the centreline between the two VGs of the same upwash VG pair [41].
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6.1.2 Trailing edge flap static cases with experimental data Simulations have been performed to reproduce the articulated static TE flap tests described in section 3.4 for the TL190-82 airfoil (Figure 50)
Figure 50: Articulated TE flap for the TL190-82 airfoil
TL190-82 airfoil, Re=2.5·106, Free transition (Figure 51, Figure 52) Clean conditions are simulated with free transition modelling. Comparison shows that all models predict lift well in the linear region. Differences among predictions appear at higher AOAs and are more pronounced in the post-stall region. The eN transition model seems to better predict the transition point compared to the γ-Reθ model. Measurements exhibit a shift of the stall position at lower AOAs with increasing flap which is not reproduced by predictions. As a result, for positive flaps, stall is predicted at higher AOAs compared to the measurements. Lift and drag coefficient comparisons are given in Figure 51 and Figure 52, respectively. TL190-82 airfoil, Re=2.5·106, Fixed transition (Figure 53, Figure 54) For the fixed transition case, MaPFlow and HMB2 CFD simulations were fully turbulent, whereas the WMB CFD code and the boundary layer Foil2w code applied forced transition at 5% chord. Agreement between predictions and measurements is good in the linear region. Measurements show a strong effect of tripping on both lift and drag resulting in stall appearing at lower AOAs. This effect is less pronounced in model predictions, resulting in larger differences between predictions and measurements compared to clean conditions. All CFD models produce similar results up to almost 12°. As expected they predict drag better than the boundary layer model. Regarding turbulence models, the k-ω SST provides drag values closer to the experimental ones compared to the baseline k-ω model. Lift and drag coefficient comparisons are given in Figure 53 and Figure 54, respectively.
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(a)
(b)
(c)
(d)
(e) 6
Figure 51: CL polars for TE static flap, TL190-82 airfoil, Re=2.5·10 . (a) Flap=-10°, (b) Flap=10°, (c) Flap=-5°, (d) Flap=5°, (e) Flap=0. Free transition case.
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(a)
(b)
(c)
(d)
(e) 6
Figure 52: CD polars for TE static flap, TL190-82 airfoil, Re=2.5·10 . (a) Flap=-10°, (b) Flap=10°, (c) Flap=-5°, (d) Flap=5°, (e) Flap=0. Free transition case.
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(a)
(b)
(c)
(d)
(e) 6
Figure 53: CL polars for TE static flap, TL190-82 airfoil, Re=2.5·10 . (a) Flap=-10°, (b) Flap=10°, (c) Flap=-5°, (d) Flap=5°, (e) Flap=0. Fixed transition case.
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(a)
(b)
(c)
(d)
(e) 6
Figure 54: CD polars for TE static flap, TL190-82 airfoil, Re=2.5·10 . (a) Flap=-10°, (b) Flap=10°, (c) Flap=-5°, (d) Flap=5°, (e) Flap=0. Fixed transition case.
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6.2
Part B
6.2.1 Vortex generators Case A – VGs on the FFA-W3-333 airfoil at Re = 14.0e6 In Figure 55 the lift and drag variation with angle of attack is shown. Results from the viscousinviscid interaction code, Q3UIC, and the CFD code, MaPFlow, are compared. Both approaches predict that the VGs will delay separation and increase Clmax, but significant differences are observed between them. This is possibly due to the fact that the viscous-inviscid code was calibrated for lower Reynold number flows.
(a)
(b)
Figure 55: Comparison between computational results. (a) Lift and (b) drag variation with angle of attack. FFA-W3-333 airfoil at Re = 15.8e6.
Case B – VGs on the DU331 airfoil at Re = 15.8e6 The agreement between lift predictions of the CFD simulations is good at lower angles of attack (Figure 56 - a) and differences at higher angles are attributed to the different approach with regard to turbulence modelling and the unsteady nature of the flow. EllipSys simulations are steady state and use the k-w SST turbulence model, while MaPFlow simulations were unsteady using the S-A turbulence model. It is worth noting that both CFD simulations predict a higher drag penalty for the downflow VG configuration (Figure 56 - b). As in the previous case, Q3UIC results significantly deviate from the CFD ones even for the case without VGs. In Figure 57 the pressure distribution for the cases with upflow VGs and without VGs is given. The agreement between the two CFD approaches is good at 16° (Figure 57 – a) where the flow is mainly attached, but significant differences appear at 20° even without the VGs. The latter is attributed to the different turbulence model used and the different treatment of time in the solution. The Q3UIC predictions differ significantly in the case without VGs, but are relatively close to the RANS results at 16° with VGs.
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Figure 56: Comparison between computational results. (a) Lift and (b) drag variation with angle of attack. DU331 airfoil at Re = 15.8e6.
Figure 57: Comparison between computational results. Pressure coefficient distribution along the wing chord at (a) 16° and (b) 20°. DU331 airfoil at Re = 15.8e6.
Flow field comparisons The evolution of the VG vortices in terms of vorticity magnitude is shown in Figure 58 and Figure 59 for the cases of downflow and upflow VG set up, respectively. Regardless of the VG set up, the fully resolved VG vortices appear much stronger very close to the VG trailing edge. Also, both simulations predict that VG strength very close to the VG TE is not affected by the VG set up and that in the downflow case the vortices from the same VG pair move away from each other approaching the neighbouring pair of counter rotating vortices. Diffusion is significant in both simulations, but lower in the fully resolved VG case as the grid used was 8 times denser than the BAY model grid. Finally, according to both numerical results, in the case of upflow VGs the vortices appear to move away from the wing surface under mutual induction. This could explain the reduced drag penalty of the upflow set up, as vortices further away from the surface would induce lower velocities close to the surface and hence reduce friction drag. Figure 60 shows vorticity magnitude contours for the upflow VG case at 20°. In the fully resolved VG simulation the vortex has been lifted from the wing surface and reversed flow has appeared Page 64 of 106
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beneath it. It is not clear, however, if this difference in behaviour is solely due to the VG numerical treatment or the different turbulence model as mentioned earlier. x=0.315
x = 0.4
BAY
FR
x = 0.5
BAY
FR
BAY
FR
Figure 58: Vorticity magnitude contours at x=0.315 (right after the VG TE), x = 0.4 and x = 0.5. DU331 airfoil, downflow VG set up, α = 16°.
x=0.315
x = 0.4
BAY
FR
x = 0.5
BAY
FR
BAY
FR
Figure 59: Vorticity magnitude contours at x=0.315 (right after the VG TE), x = 0.4 and x = 0.5. DU331 airfoil, upflow VG set up, α = 16°.
x=0.315
BAY
x = 0.5
FR
BAY
x = 0.7
FR
BAY
FR
Figure 60: Vorticity magnitude contours at x=0.315 (right after the VG TE), x = 0.5 and x = 0.7. DU331 airfoil, upflow VG set up, α = 20°.
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6.2.2 Dynamic TE flap cases Simulations reproduced the dynamic TE flap movement defined in section 5 (and detailed in Appendix 2) for the FFA-W3-241, FFA-W3-248 and DU-240 airfoils as shown in Figure 61. CFD predictions were derived using fully turbulent simulations. Predictions of the boundary layer with the Foil2w code were derived using forced transition close to the leading edge of the airfoil. Viscosity corrections were applied on the predictions of the potential AdaptFoil2D code.
Figure 61: Dynamic TE flap cases for the FFA-W3-241, FFA-W3-248 and DU-240 airfoils
DU-240 airfoil, tip section of the AVATAR rotor blade (Figure 62 to Figure 65) and mid-section of the AVATAR rotor blade (Figure 66, Figure 67) Differences in the predicted CL-β loops among the models are caused by the differences in the CL-AOA polars (see section 6.1.2). The small rated AOA (=1.05°) results in small differences in the CL-AOA polars, especially between the two CFD codes (Figure 63). As the AOA increases within the linear region (AOA=5.05°), the differences between the CFD polars remain small, but the CFD polar of the boundary layer code has a different gradient. Therefore, the predicted CL-β loops of the CFD codes present a good agreement with small differences attributed to the use of different meshes. As expected, they deviate significantly from the loops of the boundary layer code in terms of gradient and shape (Figure 63). Similar observations can be made for the CD-β Page 66 of 106
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loops (Figure 64 and Figure 65). The differences between the CFD codes and the boundary layer code results in the CD-β loops are larger than differences in the CL-β, because the drag prediction strongly depends on the turbulence model. Similar observations can be made for the mid-section of the AVATAR rotor blade, where the rated AOA is slightly higher (1.31°). Comparisons for the mid-section are shown in Figure 66 and Figure 67. FFA-W3-241 airfoil, tip section of the InnWind rotor blade (Figure 68 to Figure 71) and FFAW3-248 airfoil, mid-section of the InnWind rotor blade (Figure 72, Figure 73) In the InnWind rotor cases the rated AOAs are higher. As a result the differences in the CL-AOA and CD-AOA polars between the CFD and the boundary layer code become larger. At AOA=8° the boundary layer code shows already deviation from the linear region (Figure 68 and Figure 70), whereas at AOA=12° the maximum lift has been reached (Figure 69). According to the CFD predictions, stall appears at significantly higher AOAs. These large differences in the CL-AOA and CD-AOA polars explain the differences in the CL-β and CD-β loops (Figure 69 and Figure 71). A close agreement in the mean values is observed between the CFD and the potential code. However, the shape of the loops predicted by the potential code presents instabilities probably due the onset of separation which appears to have a strong effect on the loads. Similar observations can be made for the mid-section of the InnWind rotor blade (FFA-W3-248 airfoil), where the rated AOA is slightly lower (=7.5°). Comparisons for the mid-section are shown in Figure 72 and Figure 73.
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(a)
(b)
(c)
(d)
(e) Figure 62: CL-β loops for dynamic TE flap, DU-240 airfoil, AOA=1.06°. Corresponds to the tip section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 63: CL-β loops for dynamic TE flap, DU-240 airfoil, AOA=5.06°. Corresponds to the tip section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 64: CD-β loops for dynamic TE flap, DU-240 airfoil, AOA=1.06°. Corresponds to the tip section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CD-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 65: CD-β loops for dynamic TE flap, DU-240 airfoil, AOA=5.06°. Corresponds to the tip section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CD-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 66: CL-β loops for dynamic TE flap, DU-240 airfoil, AOA=1.31°. Corresponds to the mid-section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 67: CL-β loops for dynamic TE flap, DU-240 airfoil, AOA=5.31°. Corresponds to the mid-section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 68: CL-β loops for dynamic TE flap, FFA-W3-241 airfoil, AOA=8.1°. Corresponds to the tip section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 69: CL-β loops for dynamic TE flap, FFA-W3-241 airfoil, AOA=12.1°. Corresponds to the tip section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 70: CD-β loops for dynamic TE flap, FFA-W3-241 airfoil, AOA=8.1°. Corresponds to the tip section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CD-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 71: CD-β loops for dynamic TE flap, FFA-W3-241 airfoil, AOA=12.1°. Corresponds to the tip section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CD-AOA polars
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(a)
(b)
(c)
(d)
Figure 72: CL-β loops for dynamic TE flap, FFA-W3-248 airfoil, AOA=7.5°. Corresponds to the mid-section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies
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(a)
(b)
(c)
(d)
Figure 73: CL-β loops for dynamic TE flap, FFA-W3-248 airfoil, AOA=11.5°. Corresponds to the mid-section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies
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6.2.3 Dynamic LE flap cases Simulations reproduced the dynamic LE flap movement defined in section 5 (and detailed in Appendix 2) for the DU-240 and the FFA-W3-248 airfoils as shown in Figure 74. CFD predictions were derived using fully turbulent simulations. Predictions of the boundary layer with the Foil2w code were derived using forced transition close to the leading edge of the airfoil
Figure 74: Dynamic flap LE cases for the DU-240 and FFA-248 airfoils
DU-240 airfoil, mid-section of the AVATAR rotor blade (Figure 75, Figure 76) Similar conclusions with the TE flap cases can be drawn from the comparison of the C L-β loops. The gradients and the thicknesses of the loops predicted by the CFD codes seem identical whereas there are some small differences in the mean value. This is justified by the two CFD CL-AOA polars which exhibit the same gradient in the linear region. On the other hand the loops predicted by the boundary layer code differ from the CFD ones in gradient and shape due to the different gradient of the CL-AOA polar. FFA-W3-248 airfoil, mid-section of the InnWind rotor blade (Figure 77, Figure 78) The higher AOAs result in larger differences in the CL-β loops. Although the comparison of the CL-AOA polars is not available, behaviour similar to that of the FFA-W3-241 airfoil is expected. Therefore, significant differences between the CFD and the boundary layer code are expected. The loops predicted by the CFD and the potential code have a similar gradient and thickness, but they differ in the mean value.
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(a)
(b)
(c)
(d)
(e) Figure 75: CL-β loops for dynamic LE flap, DU-240 airfoil, AOA=1.31°. Corresponds to the mid-section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
(e) Figure 76: CL-β loops for dynamic LE flap, DU-240 airfoil, AOA=5.31°. Corresponds to the mid-section of the AVATAR rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies, (e) Comparison of predicted CL-AOA polars
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(a)
(b)
(c)
(d)
Figure 77: CL-β loops for dynamic LE flap, FFA-W3-248 airfoil, AOA=7.5°. Corresponds to the mid-section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies
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(a)
(b)
a
(d)
Figure 78: CL-β loops for dynamic LE flap, FFA-W3-248 airfoil, AOA=11.5°. Corresponds to the mid-section of the InnWind rotor blade. (a), (b) flap amplitude=5° at 1P, 6P frequencies, (c)-(d) flap amplitude 10 ° at 1P, 6P frequencies
6.3
Part C: 3D rotor cases
6.3.1 Dynamic TE flap cases Full 3D rotor simulations of dynamic flaps were performed for the AVATAR and InnWind rotors. The flap was centred at 75% of the blade and its span was 10% of the blade radius. The target was to establish a bridge between the 3D and the equivalent 2D calculations presented in part B. The comparison between the 3D and 2D results is expected to give an estimation of the 3D effects of rotation and wake development on the loading of the blade sections. All three rotor blades are included in the present 3D simulations therefore 3D effects include also interaction among the blades through the wake.
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AVATAR rotor (Figure 79, Figure 80) In Figure 79 (a), (b) the CN-β loops predicted by the 3D potential free wake GENUVP code and the equivalent 2D calculations are compared. The load coefficients predicted by GENUVP were normalized using the induced velocity so that the 3D and 2D predictions are comparable. Good agreement in the gradients of the loops can be observed. The higher CN values produced by the 3D free wake code can be justified by the underlying potential theory. A post-process viscous correction does not change the results significantly. In 3D calculations an effective angle of attack, α, can be defined by the directions of the predicted lift and the chord. The comparisons of the predicted CN-α loops are presented in Figure 79 (c), (d). It is observed that the 3D effects from the blade rotation and the wake development reduce the range of the effective angle of attack compared to a 2D simulation. In Figure 80, the load coefficients CN, CT, CM predicted by the 3D CFD solver HMB2 are compared to GENUVP results. For that comparison, the load coefficients predicted by GENUVP have been normalized using the sum of the rotational and the free stream velocity, the same as those predicted by HMB2. A satisfactory agreement can be observed in terms of the gradient, range and thickness of the loops, indicating that the potential free wake code is capable of reproducing the basic flow features close to the rotor blades. The largest deviations can be seen in the CN predictions of the 1P case, at the large positive flap angles. Such differences can be attributed to the 3D viscous effects. This first comparison is encouraging in the sense that a potential code with substantially lower computational demands can produce acceptable results in 3D. However, more simulations should be performed for further validation InnWind rotor (Figure 81) The rated operation of the InnWind rotor is characterized by higher angles of attack. As a result the differences in lift (and normal force) between the 3D potential and the 2D turbulent calculations are expected larger compared to those of the AVATAR rotor simulation. Therefore, the differences in the gradients of the CN-β loops increase as shown in Figure 81 (a),(b). In addition, the 3D effects due to the blade rotation and the wake development become stronger as the AOA increases resulting in large differences in the CN-α loops. (Figure 81 (c), (d)). In both AVATAR and InnWind rotor simulations, the results show that 3D effects increase with flapping frequency and that the amplitude of the CN variation does not change significantly compared to that of the corresponding 2D simulations.
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(a)
(b)
(c)
(d)
Figure 79: AVATAR rotor, dynamic TE flap centred at 75% of the radius, extent of flap is 10% of the radius. Comparison between 3D and equivalent 2D results (a), (b) CL-β loops for flap amplitude 10° at 1P, 6P frequencies. (c), (d) CL-α loops for flap amplitude 10° at 1P, 6P frequencies
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(a)
(b)
(c)
(d)
(e)
(f)
Figure 80: AVATAR rotor, dynamic TE flap centred at 75% of the radius, extent of flap is 10% of the radius. Comparison between the 3D results for flap amplitude 10° at 1P, 6P frequencies (a), (b) CN-β loops. (c), (d) CTβ loops (e), (f) CM loops. The asterisk in GENUVP predictions denotes that the normalization of load 2 2 2 coefficients done using U =(ωR) +Uinf
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(a)
(b)
(c)
(d)
Figure 81: InnWind rotor, dynamic TE flap centred at 75% of the radius, extent of flap is 10% of the radius. Comparison between 3D and equivalent 2D results (a), (b) CL-β loops for flap amplitude 10° at 1P, 6P frequencies. (c), (d) CL-α loops for flap amplitude 10° at 1P, 6P frequencies.
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7. Discussion 7.1
Vortex generators
In order to quantitatively evaluate numerical predictions against the available experimental results lift, drag and the lift polar gradient (dCl/dα) have been selected as metrics. Lift and drag are examined at two angles of attack, namely at 0° and at 𝛼 = 𝛼|𝐶𝑙max , defined as the angle at which Cl = Clmax for the experimental case. Lift polar gradient is examined well within the linear part of the polar, from 0° to 6°. The difference in the predicted and the measured 𝛼|𝐶𝑙max is also examined. The selection of angles at which the comparison is performed is based on the following rationale. At 0° the ability of a code to predict minimum drag can be estimated while at 𝛼|𝐶𝑙max the prediction of Clmax is examined. The lift polar gradient provides a measure of the overall prediction quality in the linear region, which is of primary interest in wind energy applications. The region post α_Clmax was not included in this comparison because, as discussed in section 6.1.1, flow becomes 3D in that region and the present simulations are not relevant. The comparison results are given in Table 14, Table 15 and Table 16 for the DU97w300, NTUAt18 and DU331 airfoils, respectively. The mentioned quantities are defined in the equations below, where the subscripts num and ref declare numerical and reference results, respectively. In the case where experimental results were available (Part A, section 6.1.1), they were used as reference. In Part B (section 6.2.1), where no experimental results were available, the fully resolved data were used as reference. In this case the comparison is made only for the MaPFlow – BAY model results, as the Q3UIC simulations cannot directly compare to the relevant upflow/downflow fully resolved data. ΔCl = Clnum − Clref
(7)
ΔCd = Cdnum − Cdref
(8)
Cl error = ΔCl⁄Clref
(9)
Cd error = ΔCd⁄Cdref
(10)
dCl dCl dCl dCl error = ( − )⁄ dα dα num dα ref dα ref
(11)
𝛼|𝐶𝑙max error = 𝛼|𝐶𝑙max
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num
− 𝛼|𝐶𝑙max
ref
(12)
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Table 14: Comparison between numerical predictions and experimental results for the DU97w300 airfoil at Re =2.0e6.
0°
12°
α_Clmax Cl ΔCl error 0.077 5%
-13%
16°
-0.047
-0.002
-10%
14°
-18%
0.007
64%
-0.031
-12%
0.002
-0.051
-18%
-0.065
Case
dCl/dα error
α_Clmax error
-0.004
Cd error -21%
4%
0°
-2%
-0.045
-66%
2%
0°
-0.017
-1%
-0.011
-33%
1%
0°
12°
0.001
0%
0.017
87%
6%
2°
12%
16°
0.124
6%
-0.023
-34%
7%
4°
0.004
22%
14°
-0.017
-1%
0.007
21%
7%
6°
-24%
0.004
39%
12°
-0.068
-4%
0.012
66%
3%
2°
-0.043
-16%
-0.002
-10%
16°
-0.167
-8%
-0.024
-35%
4%
0°
-0.060
-22%
0.000
-2%
14°
-0.239
-12%
0.004
12%
1%
0°
0.018
Cl error 7%
α_Clmax
0.002
Cd error 22%
0.009
4%
-0.002
0.004
1%
-0.050
ΔCl
MaPFlow
3
Q UIC
No VGs VGs at 20% VGs at 30% No VGs VGs at 20% VGs at 30%
VG-Flow
No VGs VGs at 20% VGs at 30%
ΔCd
ΔCd
Table 15: Comparison between numerical predictions and experimental results for the NTUA-t18 airfoil at Re =1.0e6.
VG-Flow
MaPFlow Full Span
MaPFlow
3
Q UIC
0°
α_Clmax Cl ΔCl error
ΔCd
Cd error
dCl/dα error
α_Clmax error
-2%
-0.029
-79%
-5%
6°
-0.160
-10%
-0.056
-69%
-3%
-3°
12%
0.041
3%
-0.038
-75%
4%
0°
10%
8°
0.151
13%
-0.016
-41%
11%
4°
0.000
2%
15°
0.228
14%
-0.042
-52%
15%
0°
1%
0.000
3%
12°
0.168
11%
-0.020
-38%
8%
4°
-0.005
-1%
0.002
12%
8°
0.075
7%
-0.017
-43%
1%
2°
VGs at 40%
0.005
1%
0.000
3%
12°
-0.235
-16%
-0.010
-19%
4%
-2°
No VGs
-0.009
-2%
0.000
-1%
8°
0.113
10%
-0.017
-44%
12%
2°
VGs at 30%
0.014
3%
-0.001
-7%
15°
-0.129
-8%
-0.018
-22%
7%
-1°
VGs at 40%
0.011
3%
-0.003
-17%
12°
-0.008
-1%
-0.017
-32%
8%
0°
Case
ΔCl
Cl error
No VGs
-0.023
-5%
-0.004
-39%
8°
-0.026
VGs at 30%
0.021
5%
-0.005
-36%
15°
VGs at 40%
0.042
10%
-0.007
-42%
No VGs
0.023
5%
0.001
VGs at 30%
0.029
7%
VGs at 40%
0.005
No VGs
Page 90 of 106
ΔCd
Cd error
α_Clmax
WP no.: 3.1
Table 16: Comparison between BAY model and fully resolved RANS predictions for the DU331 airfoil at Re =1.0e6.
3
Q UIC
0°
α_Clmax
Case
ΔCl
Cl error
ΔCd
Cd error
α_Clmax
ΔCl
Cl error
ΔCd
Cd error
dCl/dα error
α_Clmax error
No VGs
0.004
2%
0.001
6%
16°
0.136
8%
0.000
1%
3%
0°
VGs at 30%
0.003
1%
0.001
5%
18°
0.090
4%
0.000
1%
0%
2°
VGs at 40%
0.012
5%
0.000
3%
18°
0.148
7%
0.008
24%
-1%
2°
The comparison between the experimental and numerical results for the VG cases leads to the following main conclusions.
As long as the flow remains attached BAY model simulations provide satisfactory results with regard to lift prediction. Overall, BAY model predictions were of satisfactory quality as compared to the more accurate but also more expensive fully resolved simulations. At angles of attack higher than Clmax, 3D separation occurs in the experiments with or without VGs. In that range of angles of attack full span simulations provide better results. Full span simulations with the BAY model under predict VG effectiveness, possibly due to under prediction of the VG vortex strength. Small aspect ratio simulations (both BAY and fully resolved) over predict VG effectiveness because 3D separation is not taken into account Differences between RANS simulations in the case without VGs are attributed to different turbulence modelling and different approach with regard to the unsteady nature of the flow. Averaged steady state simulations provide lower lift values than unsteady simulations. All RANS simulations (BAY, fully resolved and VG-Flow) simulations underpredict the VG drag penalty. This is partially attributed to VG positioning in the experiments and possibly to drag measurement techniques. Simpler and cheaper models, such as Q3UIC and VG-Flow, can provide very good results, as long as they are calibrated correctly. Currently no calibration exists that can provide acceptable results for all the cases examined in this study. Both sets of RANS results suggest that downflow VG pairs have a higher drag penalty BAY model simulations produce vortices that diffuse and decay faster than in the experiments Locating the VGs further upstream along the wing chord provides flow separation control for a larger range of AOAs
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7.2
Trailing Edge flap – Leading Edge Slat
7.2.1 Static TE flap cases - Comparison with experimental data As in the case of VG simulations, in the case of static TE flap simulations the lift and drag coefficients error, as defined in Eqns. (9) and (10), have been selected as metric to quantitatively evaluate numerical predictions against the available experimental results. In Figure 82 and Figure 83 these errors have been plotted for the 0° and 10° flap angles in free and fixed transition respectively. From these figures it is clear that Cl errors increase significantly in the post-stall region, therefore it was decided to distinguish two regions for the mean error comparison, the linear and the post-stall region. Experimental results for the Cd error are available only in the linear region. Another remark concerns the high increase of the Cl error at the negative AOAs over the linear region, between -4° and 0°, which was not observed at positive AOAs (Figure 51 and Figure 53). This is because of the very small measured Cl values that give the wrong impression of excessively high errors. Regarding the Cd errors, their large values in the free transition cases mainly originate from the inefficiency of the models to correctly predict the transition points. Smaller but still significant errors are observed in the fixed transition cases. CFD fully turbulent calculations seem to better predict drag in fixed transition. A synopsis of the mean errors is given in Table 17 and Table 18. In the free transition cases, the mean errors of the CFD codes vary between 3% and 6% in the linear region. The boundary layer code produces larger errors at the large flap angles (-10°, 10°). However, in the post-stall region the Cl errors increase too much reaching almost 30% in some cases. In that region, predictions of WMB CFD code with the eN transition model are closer to the measurements, giving errors between 4% and 11%. Large deviations from the measurements have been recorded for the predicted Cd, ranging from 10% to 40%. Again, the eN transition model in WMB and Foil2w codes performs better than the γ-Reθ model, in MaPFlow and HMB2. Similar observations can be made for the mean Cl error in the fixed transition cases. Here the fully turbulent CFD calculations (MaPFlow, HMB2) seem to perform better than those using fixed transition modelling (WMB, Foil2w). In the linear region the errors of the CFD codes vary between 3% and 8%, with the largest ones appearing again at the higher flap angle of 10°. In the post-stall region Cl errors are lower compared to those of the free transition cases ranging between 10% and 18%. Regarding Cd, fully turbulent calculations predict significantly smaller errors, between 4.5% and 10.5%, compared to the fixed transition models that produce errors higher than 16%. Summarizing, the following main conclusions can be drawn from the comparison between predictions and measurements:
In both free and fixed transition cases, numerical models give acceptable Cl errors in the linear region In free transition cases, the eN transition model behaves better than the γ-Reθ transition model, apparently because it predicts the transition location more accurately
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WP no.: 3.1
In the post-stall region the predicted errors are almost doubled compared to those found in the linear region. The location of the Clmax is not well reproduced by the numerical models. In general, large deviations from the measurements are observed in the predicted Cd values. The differences are smaller when fully turbulent calculations are performed in the fixed transition cases.
(a)
(b)
(c)
(d)
Figure 82: Static TE flap cases, TL190-82 airfoil, free transition - Cl, Cd errors of the numerical methods with respect to the measurements
Page 93 of 106
WP no.: 3.1
(a)
(b)
(c)
(d)
Figure 83: Static TE flap cases, TL190-82 airfoil, fixed transition at 5% - Cl, Cd errors of the numerical methods with respect to the measurements
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WP no.: 3.1
Table 17: Static TE flap cases, TL190-82 airfoil, free transition - Comparison of the mean Cl and Cd errors of the numerical methods with respect to the measurements
Flap angle
Mean Cl error Linear region
Mean Cl error Post-stall region
Mean Cd error Linear region
-10°
-5°
0°
5°
10°
MaPFlow
4.0%
3.8%
4.8%
4.1%
5.9%
WMB
7.3%
4.5%
5.0%
3.9%
3.3%
HMB2
-
5.3%
-
3.9%
Foil2w
14.8%
2.7%
5.0%
6.0%
8.6%
MaPFlow
5.7%
7.4%
12.1%
29.1%
9.2%
WMB
3.9%
7.6%
9.5%
11.3%
10.4%
HMB2
-
16.1%
-
14.3%
Foil2w
7.7%
10.5%
10.7%
26.1%
5.9%
MaPFlow
22.6%
23.9%
22.0%
26.6%
38.9%
WMB
10.1%
12.4%
15.8%
19.8%
30.9%
HMB2
-
24.8%
-
28.0%
Foil2w
19.7%
12.8%
11.9%
15.2%
15.3%
Table 18: Static TE flap cases, TL190-82 airfoil, fixed transition at 5% - Comparison of the mean Cl and Cd errors of the numerical methods with respect to the measurements
Flap angle
Mean Cl error Linear region
Mean Cl error Post-stall region
Mean Cd error Linear region
-10°
-5°
0°
5°
10°
MaPFlow
-
5.6%
4.1%
3.2%
8.4%
WMB
-
5.9%
6.9%
7.0%
7.0%
HMB2
-
-
4.4%
-
5.8%
Foil2w
-
2.5%
8.3%
10.0%
17.1%
MaPFlow
-
10.0%
10.7%
12.4%
14.8%
WMB
-
13.5%
15.0%
18.0%
18.4%
HMB2
-
-
15.0%
-
14.4%
Foil2w
-
12.1%
15.8%
13.6%
12.6%
MaPFlow
-
10.5%
7.9%
6.2%
4.4%
WMB
-
27.8%
27.7%
16.2%
20.2%
HMB2
-
6.4%
-
9.2%
Foil2w
-
23.2%
20.8%
17.6%
43.8%
7.2.2 2D dynamic TE and LE flap cases - Comparison among predictions In order to assess the differences among the predictions of the various models, the relative deviations in lift and drag coefficients during one time period have been estimated and plotted. In the case of the AVATAR tip and mid-section simulations (DU-240 airfoil) predictions were provided by two CFD codes, MaPFlow and HMB, and one boundary layer code, Foil2w. In Figure 84, the relative deviations of the two CFD codes from the Foil2w code are depicted for a TE flap case with 5° flap amplitude and 1P flapping frequency. When AOA is small (rated AOA=1.06°) the maximum deviations in Cl do not exceed 6% (Figure 84 (a),(b)). As the AOA Page 95 of 106
WP no.: 3.1
increases to 5.06° these differences also increase reaching a maximum of 9%, despite the fact that lift is still in the linear region. Significantly larger deviations, reaching 60%, are observed in the Cd predictions (Figure 84 (c),(d)). Again, the differences increase as AOA changes from 1.06° to 5.06°. Similar observations can be made for the LE flap cases. Relative deviations in Cl range between 2% and 4.5% when AOA=1.06° and increase to 3%-5% when AOA=5.06° (Figure 85 (a), (b)). However, the differences in drag are much larger and reach excessively high levels for AOA=5.06° (Figure 85 (c), (d)). A synopsis of the mean deviations is given in Table 19 and Table 20 for the TE and LE flap cases of the AVATAR rotor, respectively. For the TE flap cases, the mean Cl deviation ranges from 2% to 8%, whereas for the LE flap cases, it ranges from 2.7% to 5%. The mean Cd deviations systematically exceed 30% and reach more than 100% in some cases. In the case of the InnWind rotor simulations predictions were provided by one CFD code, MaPFlow, one potential code with viscous correction, AdaptFoil2D, and one boundary layer code, Foil2w. In Table 21, the mean relative deviations of the AdaptFoil2D and Foil2w from the MaPFlow predictions have been estimated for the mid-section (FFA-W3-248 airfoil) with 5° flap amplitude and 1P flapping frequency. Again, the Cl deviations increase (from 4% to 11%) as the AOA increases from 8.1° (rated) to 12.1°. In fact, it is expected that the differences between the CFD and the potential or boundary layer codes increase as the stall region, dominated by the viscous flow phenomena, is approached. In general the following main conclusions can be drawn from the comparison between the various model predictions in the 2D dynamic flap cases:
Deviations in the Cl predictions between CFD and simpler potential or boundary layer codes do not exceed 8% at small AOAs in the linear region. These deviations increase as the stall region is approached Deviations in the Cd predictions between CFD and simpler potential or boundary layer codes are too large even in the linear region. This is a result of the fact that the drag coefficient is highly dependent on the turbulence modelling which is essentially different in the various models.
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WP no.: 3.1
(a)
(b)
(c)
(d)
Figure 84: Dynamic TE flap cases, DU-240 airfoil, tip section of the AVATAR rotor. Cl, Cd relative deviations of the CFD models MaPFlow and HMB from the boundary layer code Foil2w. Flap amplitude is 5°, flapping frequency equals the rotating frequency. Left column: rated AOA, Right column: rated AOA+4°
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WP no.: 3.1
(a)
(b)
(c)
(d)
Figure 85: Dynamic LE flap cases, DU-240 airfoil, mid-section of the AVATAR rotor. Cl, Cd relative deviations of the CFD models MaPFlow and HMB from the boundary layer code Foil2w. Flap amplitude is 5°, flapping frequency equals the rotating frequency. Left column: rated AOA, Right column: rated AOA+4°.
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WP no.: 3.1
Table 19: Mean Cl, Cd deviations of the CFD models MaPFlow and HMB from the boundary layer code Foil2w.
TE flap, DU-240 airfoil, tip section of AVATAR rotor AOA
rated
Flapping frequency
rated+4°
1P
Flap amplitude
6P
1P
6P
5°
10°
5°
10°
5°
10°
5°
10°
Mean Cl deviation from Foil2w
MaPFlow
5.6%
6.9%
5.5%
6.1%
7.23%
8.16%
7.0%
7.4%
HMB
3.1%
2.0%
3.63%
5.0%
4.89%
5.88%
2.8%
5.3%
Mean Cd deviation from Foil2w
MaPFlow
29.9%
39.4%
28.5%
63.2%
57.4%
68.8%
88.7%
51.3%
HMB
33.6%
41.8%
31.9%
50.4%
65.0%
73.5%
43.8%
67.3%
Table 20: Mean Cl, Cd deviations of the CFD models MaPFlow, HMB from the boundary layer code Foil2w
LE flap, DU-240 airfoil, mid-section of AVATAR rotor AOA
rated
Flapping frequency
rated+4°
1P
Flap amplitude
6P
1P
6P
5°
10°
5°
10°
5°
10°
5°
10°
Mean Cl deviation from Foil2w
MaPFlow
3.7%
3.6%
3.6%
3.7%
5.0%
5.0%
4.9%
4.9%
HMB
2.8%
2.7%
2.7%
2.7%
3.4%
3.3%
3.4%
3.2%
Mean Cd deviation from Foil2w
MaPFlow
41.4%
35.2%
41.4%
34.6%
129.4%
116.5%
131.2%
119.1%
HMB
46.6%
41.4%
46.6%
41.1%
167%
154.0%
170.0%
162.0%
Table 21: Mean Cl, Cd deviations of the potential code AdaptFoil2D and the boundary layer code Foil2w from the CFD code MaPFlow
TE flap, FFA-W3-248 airfoil, mid-section of InnWind rotor AOA
rated
Flapping frequency Flap amplitude
rated+4°
1P
6P
1P
6P
5°
10°
5°
10°
5°
10°
5°
10°
Mean Cl deviation from MaPFlow
AdaptFoil2D
2.5%
3.1%
3.1%
0.5%
4.96%
4.5%
5.3%
3.8%
Foil2w
3.5%
5.0%
2.4%
4.1%
9.82%
11.1%
9.0%
9.6%
Mean Cd deviation from MaPFlow
AdaptFoil2D
26.4%
39.9%
64.0%
7.64%
42.9%
49.9%
80.6%
2.2%
Foil2w
80.4%
115.6%
175.9%
45.2%
111.7%
135.4%
174.8%
59.5%
Page 99 of 106
WP no.: 3.1
8. Conclusions The present task was divided in three main parts: a) The creation of an experimental database for airfoils with flow devices such as passive vortex generators and static and dynamic flaps. This has been successfully achieved. Some of the data were provided by partners as in – kind contributions, while new experiments were also performed by TU Delft as provisioned. b) The creation of a computational database to compliment the experimental one. To this end, a test matrix was defined in three parts. Part A included cases for which experimental data were available, Part B contained typical cases from the INNWIND.EU and AVATAR rotors in (non-rotating) sectional context; and finally Part C contained rotating 3D tests again from both rotors. To a large extent this test matrix has been completed. In Part A predictions were compared to tunnel test data while in Part B code-to-code comparisons were carried out. Where it was deemed necessary the original matrix was extended so that a more complete picture would be obtained. Due to the high cost of 3D rotating simulations, Part C has not been fully completed. With respect to blades equipped with VGs preliminary results were obtained and will be presented in subsequent reports. c) The critical discussion on the comparative study that could serve as guideline for the subsequent tasks in WP3, in view of adding missing elements or improving the models. This part has also been completed and is detailed in the previous section.
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WP no.: 3.1
Appendix 1 Output [content] specifications Polar: A step of 2deg is proposed covering the range of data required (-20-20deg or as defined in the experimental data) Columns: alpha (degrees), CL, CD, CM, sdvCL, sdvCD, freqCL, freqCD In case of an unsteady calculation the sdv of CL & CD together with the corresponding frequency: freqCL, freqCD are included Blade loads: Contains the steady radial force distribution . Columns: r/R, Fx, Fy, My Fx = the axial force Fz = the drive force My= pitching moment Flow data: In this case the processing of the data will be carried out with techplot. If applicable different planes could appear as separate ZONES Columns: X,Y,Z,U,V,W [Ox,Oy,Oz,Reuu,Revv,Reww,Reuv,Reuw,Revw] X,Y,Z the point coordinates U,V,W the velocity components Ox,Oy,Oz
the vorticity components (for the VG cases only)
Re*
the Re stresses (for the VG cases only)
Time signals: Time signals are needed in the cases with Flaps and concern the corresponding Polar (TPolar). Time signals are also required in the Rotor cases with Flaps and concern the polars at selected radial stations as well as radial distribution of loads. TPolar (2D): Columns: time, alpha (degrees), beta (degrees),CL, CD, CM, Xsep alpha is the angle of the airfoil beta
is the flap angle defined with respect to the chord of the airfoil
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WP no.: 3.1
TPolar (rotor). Same as previous except that the file will contain the polars on all sections as separate ZONES (ZONE r/R=).3, …) TForce (rotor). Contains the radial force distribution . Columns: time, azimuth, r/R, Fx,Fy, My Fx = the axial force Fz = the drive force My= pitching moment
Name conventions: [ID]_[partner_code]_[content]_[revision] [ID] See xls file, [partner_code] e.g. [NTUA_MaPFlow], [content] e.g. [Polar]
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WP no.: 3.1
Appendix 2 TE & LE Flap deflection (FORTRAN code) ! Let X(i), Y(i) denote the coordinates of the nodes on the airfoil ! Input: Xo (x/c location), amax (max angle), freq (frequency) ! function: f(x,t)=amax*sin(2.*pi*freq*t)*ksi**2*(3.-ksi)/2. ! N number of points on the airfoil !Note: all dimensions are normalized to the chord ! TE Flap motion: do i=1,N Ynew=Y(i); dYnew=0. If(X(i).ge.Xo) then ksi=(X(i)-Xo)/(XTE-Xo) ! XTE=1. dmax=(XTE-Xo)*sin(amax)/cos(amax) Ynew=Y(i)+ dmax*sin(2.*pi*freq*t)*ksi**2*(3.-ksi)/2. dYnew= 2*pi*freq*dmax*cos(2.*pi*freq*t)*ksi**2*(3.-ksi)/2. endif enddo ! LE Flap motion: do i=1,N Ynew=Y(i); dYnew=0. If(X(i).le.Xo) then Ksi=(Xo-X(i))/Xo dmax=Xo*sin(amax)/cos(amax) Ynew=Y(i)+ dmax*sin(2.*pi*freq*t)*ksi**2*(3.-ksi)/2. dYnew= 2*pi*freq*dmax*cos(2.*pi*freq*t)*ksi**2*(3.-ksi)/2. endif enddo
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WP no.: 3.1
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