Simulation of a MW rotor equipped with vortex generators using CFD and an actuator shape model

Transcription

1 Simulation of a MW rotor equipped with vortex generators using CFD and an actuator shape model Niels Troldborg, Frederik Zahle Niels N. Sørensen, Technical University of Denmark, Wind Energy Department, 4 Roskilde, Denmark This article presents a comparison of CFD simulations of the DTU 1 MW reference wind turbine with and without vortex generators installed on the inboard part of the blades. The vortex generators are modelled by introducing body forces determined using a modified version of the so-called BAY model. The vortex generator model is validated by applying it for modelling an array of VGs on an airfoil section compared to both wind tunnel measurements and fully gridded CFD. I. Introduction A vortex generator (VG) is an aerodynamic device originally introduced by Taylor, 26 which is now widely used by the aircraft and wind turbine industry for passive flow control. 9,1,24,25 It is a small winglet attached at an angle to the oncoming flow on the suction side of the wing/blade, which generates longitudinal vortices and thereby causes local mixing of the flow, re-energizing the boundary layer and consequently delays/prevents flow separation. Therefore, VGs can be used to improve the effectiveness of wings/blades at high angles of attack. From an engineering point of view, there is a strong need for knowledge on how to incorporate VGs into the design process at an early stage, in order to choose the size, shape, position and inclination angles of the VGs. In the design codes used by wind industry today, the influence of equipping an airfoil section is incorporated through its modified lift, drag and moment polars. The usual way to obtain the polars are through wind tunnel experiments, which can be costly and also difficult to perform at the high Reynolds numbers needed today and for the relatively thick airfoils sections typically used on modern wind turbine blades. Alternatively, one can use Navier-Stokes based CFD methods to compute the effect of the VGs. 23 However, due to the large range of scales present for a wing equipped, it is computationally very costly to directly simulate a full wind turbine blade equipped with a large number of VGs. To overcome this difficulty Bender et al. 3 developed the so-called BAY model in which the VG is modelled by adding body forces in the momentum equations thereby removing the need of a mesh around the individual VG. The applied forces are determined from the Prandtl lifting theory and are normal to the local flow direction, parallel to the surface and simulates the side force induced by the VG. The model has been validated and calibrated against both measurements and fully gridded CFD for a variety of flow cases. 1,3 5,9 Through these studies the BAY model has proven capable of capturing the effect of the VG with far fewer grid points than fully resolved (FR) CFD. In the present work we use CFD and a modified version of the BAY model to simulate the DTU 1 MW reference wind turbine 2 equipped with a span-wise array of VGs on the inner part of the blades and compare its aerodynamic performance to its baseline design. As part of the work we initially validate the modified BAY model by applying it for modelling an array of VGs attached on a FFA-W3-31 airfoil section and compare it to both wind tunnel measurements and fully gridded CFD. Senior Scientist, DTU Wind Energy, 4 Roskilde, Denmark Professor, DTU Wind Energy, 4 Roskilde, Denmark 1 of 1

2 II. Actuator VG model In the present work the VGs are modelled using an actuator VG model, which is based on the BAY model 3 and the actuator shape model. 18 The basic idea behind the model is to let the VG be represented by a lift force which depends on the local flow conditions and the VG shape and is determined using an analogy to thin aerofoil theory, see Figure 1. In the original formulation of Bender et al., 3 the force applied to a cell, Figure 1. Sketch of VG with definition of terms in the BAY model which is intersected by the VG, depends on the ratio of the volume of the cell to the total volume of all cells that are intersected by the VG. Here we use a formulation of the model, which is similar to that of Jirásek, 5 where the force applied to a given computational cell, i, is proportional to the area of the intersection between the VG and the cell, i.e. L i = C V G ρa i U 2 αe L (1) where e L = U b U α cosαsinα = U t U U n U and A i is the area of the intersection between cell i and the VG and C V G is a calibration coefficient. If C V G is set to a very high value the flow will be aligned with the VG (α ) and consequently L i will be independent of C VG. Initial studies showed that for C V G > 1, the simulation results were rather insensitive to C V G and therefore we use C VG = 4 throughout this article. The forces on the VGs are applied into the computational domain by using the actuator shape model 18 and a modified Rhie-Chow algorithm 17 to avoid odd/even pressure decoupling. III. Flow solver - EllipSys3D TheVGmodelhasbeenimplementedintheNavier-StokesflowsolverEllipSys3DdevelopedbyMichelsen 13,14 and Sørensen. 19 Thiscode solvesthe incompressiblefinite volumereynolds-averagednavier-stokes(rans) equations in general curvilinear coordinates in a collocated grid arrangement to facilitate complex mesh geometries. In all simulations, the EllipSys3D code is used in steady state mode, running local time stepping towards a steady state solution. Furthermore, the coupled momentum and pressure-correction equations are solved using the SIMPLE 16 algorithm while the convective terms are discretized using the QUICK 8 scheme. IV. Validation of the VG model Themodified BAYmodel is validatedbyapplyingit for modellinganarrayofvgs attachedtothe suction side ofaffa-w3-31airfoilsectionand compareit to wind tunnel measurements 27 and fully griddedcfd of 1

3 IV.A. Vortex generator set-up In the considered configuration the VGs are shaped as delta wings with h =.1c, l =.38c and with their leading edge at x =.2c, where c denotes the chord of the airfoil. The VGs are positioned in pairs in a counter rotating configuration with β = ±15.5 o, 1 =.4c and 2 =.5c, see Figure 2. Figure 2. Left: Top-down view of the airfoil equipped with an array of VGs. The coloured region indicates the symmetry unit used in the computations and the incoming flow is from down. Right: A sketch defining the characteristic dimensions of the VG setup IV.B. Simulation set-up The simulation set-up is as in the fully gridded simulations by Sørensen et al.: 23 The Reynolds number based on airfoil chord is Re = 3 1 6, the turbulence in the boundary layer is modelled using the k ω SST 11 model and laminar/turbulent transition is modelled with the γ Re θ correlationbased transition model. 12,22 IV.C. Computational meshes The grids used for the simulations has an O-mesh structure with a radius of approximately 16c. In order to limit the computational requirements of the fully gridded CFD simulations, only one of the two vanes in a VG unit was simulated exploiting the geometrical symmetry of a VG unit (see Figure 2). This grid has N c = 448 grid cells in the chord-wise direction, N n = 128 normal to the airfoil and N s = 64 in the span-wise direction. In order to establish the overall requirements for the grid when using the modified BAY model, a grid sensitivity study was carried out. The study mainly focused on the sensitivity of the model to span-wise resolution. This was achieved by increasing the span, L s, of the simulated aerofoil section and hence also the number of VGs, N VG. The tested grid configurations are listed in Table 1, where G represents the grid used for the fully gridded simulation. Grid N c N n N s L s /c N VG G G G G G Table 1. Grid configurations used for the sensitivity study 3 of 1

4 IV.D. Results Figure 3 compares the lift and drag curves obtained using the BAY model on different grids with the fully resolved results. As seen the BAY model predicts the lift quite accurately on all grids. On grid G4 the drag C L Clean (exp) VG (exp) Clean (G) VG (FR,G) VG (BAY,G1) VG (BAY,G2) VG (BAY,G3) VG (BAY,G4) C D VG (exp) Clean (G) VG (FR,G) VG (BAY,G1) VG (BAY,G2) VG (BAY,G3) VG (BAY,G4) aoa aoa Figure 3. Comparison of lift and drag curves for the FFA-W3-31 aerofoil obtained on different grids. is seen to be slightly over predicted at high angles of attack, when compared to the predictions on the other grids. The simulated drag is seen to be underestimated on all grids in comparison with the measurements, which is most likely a consequence of not simulating the bed that the VGs are installed on in the experiment. V. Simulation of the DTU 1 MW turbine In this section we simulate the DTU 1 MW wind turbine both with and without an array of VGs installed on the inboard part of the blades and compare the aerodynamic performance. V.A. The DTU 1 MW Reference Wind Turbine The DTU 1 MW reference wind turbine is a fully open source research turbine design, which includes fully documented geometry, aeroelastic and structural models as well as 3D CFD rotor meshes. The rotor has a radius of m and uses the publicly available FFA-W3 airfoil series along the entire blade. V.B. Vortex generator set-up The VG configuration is as as shown in Figure 2, where β = ±16 o, h =.1c max, l =.4c max, 1 =.45c max and 2 =.55c max, where c max = 6.2 m is the max chord of the blade. The leading edge of the VGs are positioned along a line starting at a chord-wise position of.5c at a span-wise position of r = 5 m and ends at.21c at r = 3 m, where c denotes the local chord length. This yields a total of 4 VG pairs on each blade. V.C. Simulation set-up The rotor simulations used the steady state moving mesh option in EllipSys3D 21 and assumed a fully developed turbulent boundary layer on the blade surface using the k ω SST 11 turbulence model. V.D. Computational mesh The 3D mesh was made on the rotor configured with no prebend, no coning and no spinner and nacelle. The surface mesh was generated using an automated procedure that uses an in-house set of Python scripts. The rotor surface mesh consisted of 256 cells in the chord-wise direction and 48 cells in the span-wise direction with a cells tip cap on each blade tip. In the region of the blades where VGs are installed the cell 4 of 1

5 length in the span-wise direction is.775 m, corresponding to 8 cells per VG pair in agreement with the requirements found in section IV.D. Figure 4 shows the rotor surface mesh including the VGs. The volume mesh was of the O-O type and was generated using the hyperbolic mesh generator HypGrid. 2 Figure 4. Left) Surface mesh for the DTU 1MW RWT rotor; Right) Close view of surface mesh at the inboard section To obtain a y+ of less than 2 the height of the first cell in the boundary layer was set to m. The volume mesh was grown away from the surface using 128 cells in the normal direction to form a sphere with a radius of approximately 18 m, corresponding to 2 rotor radii. V.E. Flow characteristics In order to illustrate the overall effect of the VGs, Figures 5 and 6 show the surface restricted streamlines on the blade without and at a free-stream velocity of 1 m/s. Also included in the plots are the contours of the tangential component of the vorticity at a cross section through the blade axis. The counter rotating vortices induced by the VGs are clearly seen from the vorticity contours and the streamlines reveal that these vortices effectively prevent flow separation causing the flow to be rather two-dimensional here. The individual vortices generated by the inboard part of the VG row are not visible in the vorticity contours, which is probably because the VGs here are fully submerged in the boundary layer. As a consequence this part of the VGs are unable to prevent separation and therefore there is a strong radial flow here as is also seen on the blade. Figure 5. Surface restricted streamlines and tangential vorticity at the inboard part of the clean blade 5 of 1

6 Figure 6. Surface restricted streamlines and tangential vorticity at the inboard part of the blade V.F. Rotor performance Figure 7 compares the normal and tangential forces along the span of the blade with and at wind speeds of 6 m/s, 1 m/s and 12 m/s. The VGs cause and increase in both tangential and normal forces at the inboard part of the blade. Interestingly, the VGs not only affect the inboard region of the blade loads. For the 6 m/s and 1 m/s cases, the VGs cause a slight reduction in both the tangential and normal forces on the outer part of the blade compared to the corresponding cases. At these wind speeds the rotor is designed to extract maximum energy from the wind and therefore the increased loading near the VGs may increase the axial induction so that the blade operates at lower efficiency. A similar reduction in the outboard part of the blade was found by Johansen et al. 6 when they redesigned a rotor to extract more power from the root region. In the 12 m/s case the blade has higher loads than the clean blade along almost the entire blade span. The reason that the VGs increase the loads at 12 m/s is that the blade is pitched at this wind speed to reduce loads and hence the clean blade operates further away from its optimum. Figure 8 compares the thrust and power curves of the turbine with and. Below F n [N/m] m/s 1 m/s F t [N/m] m/s 1 m/s 6 m/s 1 6 m/s r [m] r [m] Figure 7. Normal and tangential forces along the blade with and at three different wind speeds. 6 of 1

7 the rated wind speed of 12 m/s the VGs only marginally increase power and thrust, which is because the increase in loading near the VGs is accompanied by a decrease in loading on the outboard span of the blades as shown in Figure 7. The power increase due to the VGs is only.25%,.51% and.41% at wind speeds of 6 m/s, 1 m/s and 12 m/s, respectively. From 12 m/s and above the blades are pitched in order to keep the electrical power around 1 MW and here the VGs therefore increase both thrust and power more significantly. Figures 7 and 8 show that even Thrust [kn] V [m/s] Mech. power [kw] V [m/s] Figure 8. Normal and tangential forces along the blade with and at three different wind speeds. though VGs may improve the aerodynamic behaviour locally one the blade one cannot simply attach VGs on an existing blade design and expect correspondingly higher power since the VGs have a global effect on the rotor loads. Thus, ideally the layout (shape, spacing, size and position) of the VGs should be integrated in the design process. V.G. Airfoil data Airfoil data has been derived from the rotor simulations using the azimuthal averaging technique (AAT), 7,15 in which the axial and tangential velocities are extracted in the flow field at a given radius at different axial locations over an annulus, averaged azimuthally and linearly interpolated at the position of the rotor. The local angle of attack is then determined as: α = atan V t V z (φ+θ p ) (2) where θ p and φ are the blade pitch and local blade twist, r is the local radius, Ω is the rotational speed ([rad/s]) while V t and V z are the tangential and axial velocity in the rotor plane. The airfoil data was computed with the rotoroperating at 1 m/s at the design rotationalspeed of8.6rpm by varying the pitch setting across the range [ 16 o,16 o ] with increments of 4 o. Figures 9-11 show the lift and drag curves with and at the radial positions r = 18 m,24 m and 3 m, with corresponding cross section thickness of approximately 57%, 41% and 34%. Note that the presented airfoil data for the blade differ somewhat from those presented by Zahle et al. 28 The reason for the deviations is partly a difference in grid resolution and partly that different methods were used to interpolate the velocities to the rotor plane in the AAT method. Despite, the high thickness of the considered sections the lift coefficient is seen to become rather high at high angles of attack due to the well known 3D effects caused by centrifugal forces in the boundary layer and the span-wise pressure gradients generated by the Coriolis force. At r = 18 m the VGs do not have a clear effect on neither lift nor drag in the entire range of angles of attack. The same trend was observed for the sections further inboard on the rotor and is probably because they are fully submerged in the boundary layer. At r = 24 m and r = 3 m the VGs increase the lift over a wide range of angles of attack but also cause a more abrupt stall, which eventually causes a lower lift and higher drag at r = 24 m. For low angles of attack 7 of 1

8 the drag is increased by the presence of the VGs but is generally reduced at intermediate angles of attack below stall. In future work we will compare the presented airfoil data on the rotor with airfoil data on the same sections in a non-rotating flow and thereby investigate whether 3D effects are less dominant when VGs are present C L C D Figure 9. Lift and drag polars for the section at r = 18 m where the airfoil thickness is 57% C L 1.2 C D Figure 1. Lift and drag polars for the section at r = 24 m where the airfoil thickness is 41%. VI. Conclusions A BAY type vortex generator (VG) model has been presented and applied for simulating both the FFA- W3-31 airfoil with a row of VGs and for representing a row of VGs on the inboard part of the blade of the DTU 1 MW reference wind turbine. The simulations on the airfoil showed good agreement with both wind tunnel measurements and fully gridded CFD and revealed that a span-wise resolution of 8 grid cells per VG pair is sufficient to accurately capture the effect of the VGs. The simulations on the DTU 1 MW turbine showed that VGs may effectively delay flow separation and therefore can improve the aerodynamic characteristics of the inner part of the blade. However, even though the VGs may improve the local aerodynamic behaviour of the blade they do not necessarily improve significantly the power production of the turbine since they have a global effect on the rotor loads. Thus, the 8 of 1

9 C L C D Figure 11. Lift and drag polars for the section at r = 3 m where the airfoil thickness is 34%. positioning and configuration of the VGs should ideally be an integrated part of the design process. Acknowledgments This work has been funded by the Danish Energy Agency under the EUDP programme within the projects Overcoming critical design challenges of wind turbines and by the EUDP-211 II project Demonstration of Partial Pitch 2-Bladed Wind Turbine Performance as well as the EERA AVATAR project. References 1 B.G. Allan, C.S. Yao, and J.C Lin. Numerical Simulation of Vortex Generator Vanes and Jets on a Flat Plate. AIAA, , C. Bak, F. Zahle, R. Bitsche, T. Kim, A. Yde, L.C. Henriksen, P.B. Andersen, A. Natarajan, and M.H. Hansen. Design and performance of a 1 MW wind turbine. To be submitted for Wind Energy, E.E. Bender, B.H. Anderson, and P.J. Yagles. Vortex generator modeling for Navier-Stokes codes. Proceedings of the rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, California, USA, FEDSM , E.E. Bender, P.J. Yagles, D.N. Miller, and P.P Traux. A Study of MEMS Flow Control for the Management of Engine Distortion in Compact Inlet Systems. Proceedings of the rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, California, USA, FEDSM99-692, A.Jirasék. A Vortex Generator Model and its Application to Flow Control. Proceedings of the 22nd Applied Aerodynamics Conference and Exhibit, Providence, Rhode Island, AIAA , J. Johansen, H.Aa. Madsen, N.N. Sørensen, and C. Bak. Numerical investigation of a wind turbine rotor with an aerodynamically redesigned hub-region. EWEA conference, Brussels, Belgium, J. Johansen and N.N. Sørensen. Airfoil characteristics from 3D CFD rotor computations. Wind Energy, 7, B. P. Leonard. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meth. in Appl. Mech. and Engrng., 19:59 98, J.C. Lin. Review of research on low-profile vortex generators to control boundary layer separation. Progress in Aerospace Sciences, 38:389 42, J.C. Lin, S.K. Robinson, R.J. McGhee, and W.O. Valerezo. Separation Control on High-Lift Airfoils via Micro-Vortex Generators. Journal of Aircraft, 31: , F.R. Menter. Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows. AIAA Journal, (93-296), F.R. Menter, R.B. Langtry, S.R. Likki, Y.B. Suzen, P.G. Huang, and S. Völker. A Correlation-Based Transition Model Using Local Variables, Part I - Model Formulation. Proc. of ASME Turbo Expo, Power for Land, Sea and Air. Vienna, Austria, J.A. Michelsen. Basis3D - a platform for development of multiblock PDE solvers. Technical report AFM 92-5, Technical University of Denmark, Lyngby, J.A. Michelsen. Block structured multigrid solution of 2D and 3D elliptic PDEs. Technical Report AFM 94-6, Technical University of Denmark, Hansen M.O.L. and J. Johansen. Tip studies using CFD and computation with tip loss models. Wind Energy, 7, S. V. Patankar and D. B. Spalding. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer, 15: , of 1

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