COMPUTATIONAL MODELING OF WIND ENERGY SYSTEMS

Transcription

1 The Eighth Asia-Pacific Conference on Wind Engineering, December 10 14, 2013, Chennai, India COMPUTATIONAL MODELING OF WIND ENERGY SYSTEMS T. Shah 1, R. Prasad 2 and M. Damodaran 3 1 Project Associate, Mechanical Engineering, IIT Gandhinagar, GJ, India, - tapanshah@iitgn.ac.in 2 Graduate Student, Mechanical Engineering, IIT Gandhinagar, GJ, India, - rachit.prasad@iitgn.ac.in 3 Professor, Mechanical Engineering, IIT Gandhinagar, GJ, India, - murali@iitgn.ac.in ABSTRACT Computational modeling of flow fields in the vicinity of the blades of the low cost horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT) windmills are outlined in this paper. Computed pressure fields, wakes, vorticity structures for an assumed free stream velocity and as well as for a assumed atmospheric boundary layer profile are shown along with estimates of time variation of the torque generated by the windmill as it rotates in a time varying free stream velocity. These models form the basis for the design optimization of the blade profiles which would ensure as close to an uniform output of the torque around the axis of rotation in the presence of the temporal and spatially varying wind speeds that prevail over the area where the windmills are sited in order to improve the performance of the windmill by examining its performance metrics in the next phase of work. Keywords:- HAWT, VAWT, CFD, Atmospheric Boundary Layer. 1. Introduction Harnessing wind energy for domestic needs has been an age old tradition not only in India, but around the world. Modern design techniques using Computational Fluid Dynamics (CFD) are rapidly replacing the traditional approaches of designing multi-purpose wind turbines. The aim of this work is to use CFD to compute the aerodynamics of Horizontal Axis Wind Turbine (HAWT) and a Vertical Axis Wind Turbine (VAWT) designs for low-cost rural applications such as pumping of brine water, irrigation, and electricity generation. The model will also serve as a basis for examining the aerodynamic considerations for the placement of wind turbines in a wind farm and the blade wake interactions from these turbines. The approaches have been used to model wind turbine characteristics using CFD in the past fall into low-order models, or steady, non-rotating two dimensional studies and three-dimensional flows. While low-order and two-dimensional models provide useful insight, important flow physics associated with complex three-dimensional flows are usually lost. There are also efforts to study the time accurate aerodynamic characteristics of wind turbines. Benjanirat and Sankar (2003) have carried out a comparison between different turbulence models and their performance in predicting wind turbine characteristics. Sezer-Uzol and Long (2006) have carried out a time accurate, unsteady, inviscid computation of a two blade wind turbine. Turbine blades under yawed flow have been addressed in Tongchitpakdee et al. (2005). Experimental and computational study of VAWT was carried out by Howell et al. (2005). However there is a paucity of discussions on how the free stream wind conditions affect the rate of rotation of the turbine. HAWT and VAWT are mounted on structural frameworks (henceforth referred as structure) and most studies have only focused on the blades isolated from the framework. The present study aims to compute steady and unsteady viscous threedimensional blade rotation rate and hence the torque which is the output required to drive useful wind powered applications in the presence of the structural mount. The aerodynamic characteristics and flowfield of a HAWT was first studied in isolation without presence of the Proc. of the 8th Asia-Pacific Conference on Wind Engineering Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds) Copyright c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: doi: /

2 structure. Then the impact of including the structure on the HAWT aerodynamics is assessed. A standard practice is to compute the torque acting on the turbine rotating at a fixed rotation rate. In the actual scenario, the rotation of the turbine is a function of the aerodynamic moment acting on it, which depends on the free stream wind speed and direction. In this study the torque generated is estimated from the rotation of the turbine induced by the wind speed which may be steady or unsteady. The standard atmospheric boundary layer (ABL) profile described in Garratt et al. (1982) is used in place of uniform velocity profiles which are used for turbine alone studies in literature since wind turbines are mounted on structural frameworks mounted on the ground. 2. Computational Modeling of HAWT and VAWT Aerodynamics Time accurate unsteady flow past a HAWT and VAWT is computed by solving the unsteady incompressible Reynolds Averaged Navier-Stokes (RANS) equations using a finite volume based method within the framework of Star-CCM+(2012) which is a commercial CFD software package. The incompressible RANS model in finite-volume formulation is given as: ( b U U ) ds = 0 (1(a)) S d ρ UdV + U ( U U b). nds = pnds + (( μ + μt ) τ) nds + ρ f dv dt V S S S V 1(b)) where the vector U defines the velocity field, p is the pressure field and U b is the velocity of the moving mesh boundary. From the CAD drawings of a full scale model of the HAWT, a three-dimensional CAD model is first constructed. Similarly a VAWT model is also developed as a starting design, keeping in mind the small scale and economical application in the rural sector. The computational mesh is then created within the computational domain of interest where the RANS model is solved by appropriate spatial and temporal discretization schemes to compute the unsteady evolution of the flow field which provides insight into the flow patterns and structures in the wake region of the turbine. Composite grids involving arbitrary moving mesh to facilitate free rotation of the mesh around and fixed to the turbines blades which moves relative to the rest of the computational mesh. The exchange of information between the moving and the stationary regions is done using a sliding mesh technique. The convective flux in the momentum equation Eqn. (1(b)) is discretized using the second order upwind scheme. The flow variables are then advanced in time with the help of implicit time stepping scheme. The mesh that had been created has been refined near the turbine blade surfaces and also in the wake region to effectively capture the wakes created by the turbine motion (rotation in case of VAWT, rotation and yaw in case of HAWT). The flow is assumed to be turbulent; the turbulence has been modeled using the Spalart-Allmaras (1992) turbulence model which solves a transport equation to determine the turbulent dynamic viscosity T which is added to the laminar viscosity.in order to resolve the boundary layer at the ground and wing surface, a thin conformal structured prismatic mesh consisting of 15 layers of structured cells have been created over the wall surface in order to obtain a y+ value of 11.4 is created along the ground and blade surfaces. 2.1 Computational Domain and Boundary Conditions Figure 1 shows the computational domains used for this study pertaining to unsteady aerodynamics of HAWT and VAWT. At the inflow boundary, the velocity is set to the free stream velocity. At the outflow, the pressure is interpolated from within the domain by setting 1239

3 the pressure gradient to zero. The no slip boundary condition is specified on the blade surfaces and one the ground plane. At the far field boundary, the pressure is set to the free stream value. The structure is considered as a wall and no slip condition has been set there. In the case of HAWT with the complete structure, portions of the structure have been modeled as porous surfaces to account for airflow through framework strut gaps which will be outlined in the full paper. The initial conditions for the different cases have been discussed in the method of approach section. Figure 1: Computational Domain used for the study of HAWT 2.2 Mesh Generation The computational domain is discretized into a mesh of polygonal elements using the mesh generator in the within the framework of the commercial CFD software Star-CCM+ (2012). The mesh refinement to resolve the flow structures in the vicinity of the HAWT and in the evolving wake region where the mesh has been refined in the region downstream of the turbine in order to capture the wake patterns effectively are shown in Fig. 2. (a) Mesh used for the study of HAWT with structure. (b) Zoomed in view of the mesh created HAWT. (c) Prism layer on the turbine blade surface to capture near wall flows (d) Mesh used for the computational study of VAWT (e) Zoomed in view of the mesh near VAWT. Figure 2: Computational Meshes (f) Perspective view of the mesh for VAWT 1240

4 The total number of mesh elements in the domain varies from case to case; however the order of mesh elements used in these studies runs into approximately a million elements. The rotation of the turbine blades is handled by rotating the cylindrical region encompassing the blade and the mesh generated within it relative to the rest of the stationary mesh outside the cylinder. In the case of the HAWT the yawing motion of the directional vane fixed to the turbine is also accounted for. The computed flow variables are interpolated in a conservative manner across the boundaries of the stationary and rotating regions of the domain using the sliding mesh technique. Details of the interpolation of flow variables to ensure conservation across the sliding mesh interface can be found in the work of Steijl et al. (2008). The mesh in the computational domain has been refined on similar lines as it has been done so in the case shown previously Method of Approach The unsteady computations carried out in this study, for both HAWT and VAWT, have been done in three different phases. Each phase uses the result from the previous phase as its initial condition. In the first phase, a preliminary steady flow field is generated by rotating the turbine at a fixed rotation determined from field data obtained from a rural application for brine water pumping in the coastal areas of Gujarat in the presence of the corresponding free stream wind speed or ABL wind profile. This computed steady flow field is then used as initial conditions in the next phase, where the turbine blade is allowed to rotate freely under the influence of the aerodynamic torque acting on it. The purpose of this phase is to have the turbine blades rotate at a steady rotation rate which depends on its shape and free stream velocity. In this study, the angular velocity has been determined implicitly from a 1 DOF dynamics equation, = I, where is the aerodynamic torque acting on the turbine blades, I is the moment of inertia of the turbine about its axis of rotation and is the angular acceleration of the turbine. The torque is estimated using the computed surface pressure distribution on the turbine blades at each time step Δ t. Using a simple first order Euler integration, the relationship between the angular rotation at two consecutive time levels can be established as τ n ωn+ 1 = ωn + Δt (2) I Equation (2) allows the angular speed of the turbine to change at every time step thereby readjusting the aerodynamic torque at each step as well. The third phase is then initiated by varying the free stream velocity of wind, in order to study the unsteady response of the turbine to rapidly changing wind speeds and direction. 3. Results and Discussions 3.1 HAWT (without structure) As mentioned in the previous section, the approach of the computational study involves carrying out the computation in three phases. The free stream velocity, torque experienced by the blade, and the angular velocity of the blade can be seen in Fig. 3 for all the three phases. It can be seen that rotating the turbine at a fixed rotation rate leads to a steady non- zero torque. However, when the rotation rate of the turbine is coupled to the aerodynamic moment experienced by it using Eqn. (2), as in the second phase, both the value of torque and the rotation rate begin to change with time. The rotation rate reaches a steady value, and the torque also reduces to a steady value of zero. This physically makes sense, as for a steady free stream velocity, the turbine will observe a steady rotation rate. From Eqn. (2), in order 1241

5 for the rotation rate to be steady with time, the rate of change of rotation rate will be zero, and thus will also be the torque experienced by the turbine, which is what has been observed. In the third phase, the response of the turbine has been studied to the varying free stream velocity of the wind. From Fig. 3, it can be observed that the wind velocity has been varied piecewise linearly, according to a random distribution. This change in wind velocity disturbs the flow field, giving rise to changes in pressure distribution across the turbine blade surfaces, and hence leading to a non-zero torque, as shown in Fig. 3. From Eqn. (2) it is known, that a non-zero torque changes the angular rotation rate of the turbine which is shown in Fig. 3 as well. Visualization of the flow field obtained at the end of second phase has been displayed in Fig. 4. The swirl of the wake can be clearly seen from the plots of the velocity and vorticity contours on several Trefftz planes in the wake region of the turbine blades. Figure 3: Variation of torque, angular speed of the turbine and free stream velocity of the wind with time across all three phases. (a) Filled velocity contours on a Trefftz plane. (b) Vorticity contours on various Trefftz planes. (c) Velocity contours on a series of Trefftz plane. (d) Pressure distribution on the upstream side of the turbine blades. Figure 4: Computed flowfield patterns for the case involving HAWT without the structure. 3.2 VAWT (without Structure) A similar computational approach has been used to study VAWT flowfields. Initial condition for the 1st phase for VAWT was set up in exactly the same manner as for the HAWT, for the second phase, the torque and rotation rate have been coupled with help of Eqn. (2). Figure 5 shows the computed variation of RPM with time and varying wind velocities. 1242

6 (a) Variation of aerodynamic moment. (b) Variation of rotation rate and velocity Figure 5: Variation of parameters of VAWT with respect to time. From Fig. 5 we see that airflow at a constant velocity over a VAWT produces a torque which is oscillating about a fixed non-zero value. It is also observed that the torque increases with increase in inflow velocity and decreases with a reduction in inflow air velocity. It was observed that unlike the case of HAWT, the torque in VAWT never tends to zero but oscillates about zero value because the VAWT blades observe different angles of attack as they rotate about the vertical axis, whereas in the case of HAWT the blades always see the same angle of attack and velocity. As seen in Fig. 6, it can be seen that the orientation of the VAWT blades changes at every time step. Because of this, the relative angle of attack the blade sees at every time step also changes, and so will the magnitude of the relative wind. At a certain instance of time t n, the blade is at an angle of n with the free stream velocity. At this instance the blade is experiencing a relative wind which is a vector sum of V and n. In order to compute the relative velocity and the relative angle of attack, assume the airfoil to be at a certain orientation as shown in Fig. 6(b). (a) (b) Figure 6: (a) Relative angle of attack for different blade orientation, (b) Vector diagram for relative angle of attack. 1243

7 The angle between the chord of the blade and the free stream velocity n is given by: θ = ω Δ t + θ. (3) ( ) n n 1 n 1 Now, there are two vectors inclined to each other at an angle n, the resultant of these two vectors is given by: 2 2 Rv = ( V ) + ( ω ) + 2V ω cos θ n n n (4) By resolving basic trigonometric relations an expression for the relative angle of attack can be obtained as 1 ωnsinθn α = θn sin ( ) R v (5) From these relations it can be observed that the variation of relative velocity, relative angle of attach and variation of moment for a single rotation of blade is shown by Fig. 7. Similar results can be found in the work carried out by Castelli et al (2011). (a) Relative angle of attack (b) Magnitude of relative velocity (c) Aerodynamic moment Figure 7: Variation with respect to angular position. Flow field about a VAWT can be visualized with the help of Fig. 8. The blade leading edge experiences high pressure coefficient and it goes to maximum when it the blade leading edge faces the inflow velocity. In Fig. 8, the wake generated by VAWT can be seen to extend till the end of the computational domain, and the strength decreasing gradually in the direction downstream of the VAWT. (a) (b) (c) (d) Figure 8: (a) Pressure coefficient on Cut plane through VAWT, (b) Velocity contours on Cross- planes through VAWT, (c) Pressure coefficient on ground and VAWT with velocity contours in downstream region, (d) Vorticity contours in downstream of the VAWT. 1244

8 3.3 HAWT with Structure In this section the effect of including the structure of the wind turbine and make necessary comparisons with results without the structure. As the structure consists of many struts and links an approximation to represent the base structure to be built of porous plates conforming to the shape of the structural framework has been used from the point of view of computational economy. The porosity was estimated as a fraction of empty space and the total space occupied by the struts on the assumed plate and the estimate of the porosity for the supporting structure of the wind turbine was found to be Non-uniform porosity distributions to better represent the approximation are being explored at the moment. Figure 9 shows various computed contours of flow variables in the wake region of the turbine. In Fig. 9(a), the wake from the turbine can be seen to be interacting with the wake from the structure. It can also be seen that the flow velocities near the blade tips are higher than that near the root regions showing typical expected characteristics of rotating bodies. It can be observed from the computations that the structure facing the inflow experiences a higher surface pressure than that of the structure facing downstream. The computations also reveal that since the structure interacts with the wake emerging from the rotating blades, there is a cyclical intermittent fluid-structure interaction taking place between the rotating turbine blades and the structure, the region of this interaction on the structure experiences a higher pressure than that of the rest of the structure as shown in Fig. 9(d). (a) (b) (c) (d) Figure 9: Computed (a) Velocity Contours on a cut section through the HAWT (b) Pressure coefficient contours on the HAWT and Velocity contours in the downstream wake region (c) vorticity contours in the downstream wake region (d) Pressure coefficient contours on the HAWT structure. The impact of the presence of the structure on the HAWT moment and torque variation is shown in Fig. 10 it can be seen that, in the case of the turbine blades with the structure there is a sinusoidal variation in the aerodynamic moment about a mean value. This is due to the pressure rise on the suction side of the blade (Fig. 9(d)) due to the fluid-structure interaction between the moving turbine blade, the static structure and the fluid contained between these two entities, each time the blade passes the structure, thereby giving rise to changes in the surface pressure on the blade. 1245

9 Figure 10: Variation of torque acting on turbine and free stream velocity with time in the presence of the structure. 3.4 Effect of Atmospheric Boundary Layer(ABL) The results discussed in the previous sections are for a uniform velocity inflow condition. However, in real conditions, a turbine will encounter an atmospheric boundary layer because of its close proximity to the terrain. In order to simulate with parameters closer to the real life atmospheric conditions, the Atmospheric Boundary layer (ABL) outlined in Garratt et al. (1982) has been used as an inflow condition. The ABL used in this study is based on the averaging of wind data provided by various internet sources providing real time and summarized details of wind and temperature conditions in a desired geographical region of α 1 ref India. The ABL flow conditions used as inflow condition is defined as U Z Z, U ref = where α = ln 10 Z o where U is the velocity at the altitude Z, U ref is the reference velocity at reference altitude Z ref, and Zo is the ground roughness length. For this study U ref, Z ref, and Zo are assumed to be 10ms -1, 25 m and 0.02 respectively. Figure 11 shows the variation of the computed velocity profiles in the downstream region of HAWT and VAWT. (a) HAWT (b) VAWT Figure 11: Velocity contours plotted in different Trefftz planes. It can be noted that using the atmospheric boundary layer inflow condition captures the wake patterns in the vicinity of the wind turbine mixing with ABL thereby changing the overall wake patterns as observed in Fig 11, where computed velocity contours are shown on various Trefftz planes in the downstream region of the turbine. Note: Selected animations of selected computed flow field variables past the VAWT and HAWT can be viewed at the YouTube channel by clicking on the following link:

10 4. Conclusion The high fidelity CFD models for assessing the performance of a single HAWT and VAWT in various modes (with and without structural framework) in this study can now be used to assess various performance aspects of wind farms. On the basis of the present work, future effort will be focused on the assessment of fluid- blade surface and structure interaction, studying the interaction of wakes from a wind farm, optimal spacing between the various HAWT/VAWT units and the impact of the wakes on the environment. For this the plan will be to use LES simulations. The models will also serve as the basis for blade design optimization and assessment of power characteristics for various operational applications such as brine water pumping and electricity generation in the rural sector. References Benjanirat, S., Sankar, L. N., & Guanpeng X.. Evaluation of turbulence models for the prediction of wind turbine aerodynamics, AIAA Paper Castelli, R. M., Englaro A., Benini E., The Darrieus wind turbine: Proposal for a new performance prediction model based on CFD, Elseiver, Journal of Energy, 36(8), Howell, R., Qin, N., Edwards, J. and Durrani, N. Wind tunnel and numerical study of a small vertical axis wind turbine. Renewable Energy, 35(2), , Garratt, J. R., Wyngaard, J. C., & Francey, R. J. (1982). Winds in the atmospheric boundary layer-prediction and observation. Journal of Atmospheric Sciences, 39, Sezer-Uzol, N., & Long, L. N. 3-D time-accurate CFD simulations of wind turbine rotor flow fields. AIAA Paper , 44 th Aerospace Sciences Meeting and Exhibit, Reno, NV. Spalart, P.R., and Allmaras S.R., "An one-equation turbulence model for aerodynamic flows." AIAA, Aerospace Sciences Meeting and Exhibit, 30 th, Reno, NV StarCCM+, Computational Fluid Dynamics and Multi-Physics Engineering Software, Version 7.06, (2012) CD-Adapco, Lebanon, NH, USA. Steijl, R., and G. Barakos. "Sliding mesh algorithm for CFD analysis of helicopter rotor fuselage aerodynamics." International journal for numerical methods in fluids 58.5 (2008): Tongchitpakdee, C., Benjanirat, S., & Sankar, L. N. (2005). Numerical simulation of the aerodynamics of horizontal axis wind turbines under yawed flow conditions. Transactions- ASME, Journal of Solar Energy Engineering, 127(4),