Andrew Baker
Wind turbine blade tip analysis using CFD
Abstract
Computational Fluid Dynamics is a highly cost effective method to optimise both turbine blade and ideal site specific credentials. CFD is a highly flexible numerical modelling method, capable of modelling a variety of scenarios, airflows and turbine operational ranges for wind turbines.
The article identifies how simulation software can be used to address some of the challenges that face renewable technologists in site selection such as the prediction of Wind Power Density across a complex terrain and the identification of local wind flow features.
The main body of this article focuses on numerically analysing wind turbine blade geometry using CFD.
Introduction
The scope of this article is to examine the use of Computational Fluid Dynamics (CFD) in the computer modelling of wind farms. Traditionally CFD was used for more high-tech. industries such as automotive or aerospace. CFD began to be used in power generation in the development of efficient gas turbine and stream turbine blade design. This work was based upon CFD research for aeronautics. CFD design was then extended to the design of wind turbine blades and eventually as a computer simulation tool for site assessment. As a detailed CFD analysis of a proposed site increases ROI through the optimisation of blade structural modelling approaches.
Figure 1: Sample CFD Analysis of a Wind Turbine Site, [1].
CFD is a detailed numerical modelling process with a wide variety of applications such as water treatment, process piping design for fluids and aerodynamic design for car, plane and ship hull design. In the evaluation of the CFD process the article is structured as follows:
Introduction of the CFD process at high level.
Why CFD meshing is important.
Cost saving associated with layout design optimisation for turbine sites.
Turbine blade aerodynamics.
How the wake is formed through boundary layer separation.
Typical Analysis set-up.
Paper review.
Discussion of the method.
What is CFD?
CFD stands for finite volume method. The fluid domain is discretized into a finite set of control volumes. The general conservation (transport) equations for mass, momentum, energy, species, etc. are solved on this set of control volumes. Partial differential equations are discretized into a system of algebraic equations. All algebraic equations are then solved numerically for the flow field to render a solution. Solutions are obtained by iterative methods.
Figure 2: CFD Finite Volume, [7].
The generic version of the governing equation, (Reynolds Transport Equation) is given below.
In the following example, the system has 3 unknowns so there will be three equations, one for each unknown parameter based upon the generic version:
Mass conservation:
, [7]
Momentum conservation:
, [7]
Internal energy, (no viscous heating):
, [7]
Each of these equations is solved to determine the unknown parameters above. Boundary layer conditions are applied to the above equations under certain conditions to enable the unknown variable be calculated for the flow field.
Steps in applying the CFD method:
Figure CFD Analysis Process, [3].
CFD Meshing
CFD analysis can be carried out in 2D or 3D. Meshing is one of the critical stages of the CFD analysis process. If the mesh is too course the accuracy of the solution is compromised. If the mesh is too fine, the model will take too long to solve and require vast amounts of computing power. The finer the mesh, the more nodal the point, the smaller the finite volumes are. Too complex a model will inhibit correct computer operation due to the amount of computing power required. If this occurs, then it is possible for the computer to crash, with results lost. The entire process will have to be commenced again. Typical mesh elements are given below:
Figure 4: CFD 2D & 3D Mesh Elements, [3]
Figure 5: Typical 2D mesh for a turbine blade analysis, [7]
For most turbine site analysis, the CFD work is done in 3D like figure 1 above. To simulate an aerofoil section, the analysis can be done in 2D. For the 3D elements, the Hexahedron is considered the most accurate as it has the most nodes per element. The disadvantage of this is that it does not fit very well into complex CAD geometries thus leading on increased skew-ness. The Pyramid is less accurate but more flexible, reliable and used in complex CAD geometries.
Skewness is a measure of the quality of the mesh in the CAD geometry. It identifies how well the regular mesh elements fit into the geometry profile. In some cases near edge of the geometry, the mesh element shape becomes skew to fit into the boundary of the CAD geometry. The average skewness is measured by the CFD software. Three values on skew-ness are detailed, maximum, average and minimum. Skew-ness quality values are detailed in the table below.
Table1. Skewness quality values, [7].
The mesh density is also a relevant parameter of mesh quality. With a low mesh density, the solution to analyse may be of poor quality and can have a major impact on the accuracy of the solution. This is particularly true for regions such as boundary layer of critical importance to global flow. For turbine analysis (especially for the development of wakes, wall shear stress and boundary layer detachment would be vital). To evaluate close wall behaviour, the fluent theory guide advises that a region consisting of a minimum of 5 layers deep of cell should mesh just above a boundary that defines the wall condition.
The distance for the wall boundary to the centroid of the first cell is called the Dy value. A y+-value is used to define the mesh quality for certain modelling applications. For turbulent modelling, the Dy / y+ = 8.6 X Length X (Reynolds Number) -13/14, [8]. For the application of modelling flow over a turbine blade, this is a requirement to monitor flow behaviour from viscous sub layer right through to boundary layer separation. Fluent guide advises that the y +- value will be 5 for this application, [8]. Knowing this value we can calculate the required depth for the first row of cells. This is cross checked against the theoretical calculation for the boundary layer thickness and the minimum number element layers in the boundary layer for that application as detailed by the Fluent Theory Guide. This is called the wall treatment function in the CFD software.
Why Use CFD?
CFD can be used to optimise the layout design of the wind farm by minimising the formation of the wake from the turbines through numerical calculation. This is important in environmental terms to minimise concern of:
Noise generation by reducing vibrations.
Wind-take and optimise performance of turbine at a spacing of 1Km.
The critical parameter associated with the correct match of the turbine (aerofoil) to the site is reducing turbulence and wake. By doing this, more energy is taken from the wind and a higher return on a substantial investment is gained.
Costs Associated With Site Layout
Detailed design of a site involves the use of wind modelling software to optimise the design. Two vital factors impacting on the layout design is the positioning and spacing of the turbines. Schlez and Tindal state “The appropriate spacing for turbines is strongly dependent on the nature terrain and the wind rose at the site. If turbines are spaced closer than 5 rotor diameters in a frequent wind direction it is likely that unacceptably high wake will result”, [2].
Schlez and Tindal also propose that every 1% optimised on a 50MW farm using a software package that there is an increase in annual revenue from €50,000 to €100,000. The software does hundreds of iterations and many permutations of wind farm size, turbine type and hub height to determine the optimum conditions, [2].
Site Selection
Wolfgang Schlez and Andrew Tindal of Garrad Hassan & Partners Ltd proposed that the following should be considered for the potential site under consideration.
Is there a sufficient wind resource available?
Can the grid be connected cost effectively?
Is the grid sufficient for the size of the proposed development?
Is the correct access available?
If not, can access be constructed cost effectively?
What are the issues associated with the rights for use of the land? [2]
Does a wind turbine blade work?
Boyle explained in his book “Renewable Energy”, the angle of attack is defined as the direction at which the movement of air hits the blade measured relative to a line through the object called the chord line. The blade profile can be formed such that higher lifting forces are induced by altering the angle of attack. Most turbine blades have a profile of a wing. The typical profile is with a convex raising profile, rounded leading edge and sharp pointed trailing edge.
Using the Bernoulli’s principle, as air accelerates along the upper convex, the velocities increase with decreasing pressure. The velocity of the air travelling on the underside of the profile is lower and hence there is a greater pressure under the blade. Therefore a pressure differential is caused resulting in lift effect causing the turbine blade to rotate. There are two types of blade, symmetrical and asymmetrical. It is the underside that distinguishes the two.
“The asymmetrical is configured to produce the most lift when the underside is closest to the direction from which the air is flowing. Symmetrical aerofoils are able to induce lift quality equally well when the air flow is coming from either side of the blade. When the air is directed at the underside of the blade, the angle of attack is considered to be positive.” [5], similarly the upper side is considered to be negative. The length of the blade from the tip of the leading edge to trailing edge is called the cord. Types (a), (b) and (c) in the figure below are asymmetrical, type (d) is symmetrical.
Figure 6: Asymmetrical & Symmetrical Blades, [5].
There are a range of lift and drag coefficients for the different profile of blades. Each individual angle of attack will also have different lift and drag coefficients. Lift and drag forces are both proportional to the energy in the wind.
Figure 7: Lift coefficient, CL drag coefficient, Cd and lift to drag ration, (CL/ Cd) versus the angle of attack, a, for a Clark Y aerofoil section, [5].
In the above figure, the region just to the right of the peak in the CL curve corresponds to the angle of attack at which stall occurs.
The drag coefficient is defined as:
Cd = D
0.5 V Ab
Where: D is the drag force in Newton’s.
r Is the air density in kilograms per cubic meter (Kg/m3).
V is the velocity of the air approaching the blade in meters per second (m/s).
Ab is the area of the blade in square meters(m2).
The blade area is given by mean chord X length of the blade.
The lift coefficient is defined as:
CL = L
0.5 V Ab
Where: L is drag force in Newton’s. All other units are similar to above.
Lift and drag characteristics of a blade profile are determined by wind tunnel testing. Each aerofoil section of a blade has an angel of attack that gives maximum CL /Cd ratio generating maximum force (power). It is at this point that the turbine is determined to be most efficient.
Stall is another characteristic of a turbine blade that is important. This is the angle of attack where a drag force is at its maximum. “Flow of air suddenly leaves the suction side of the aerofoil causing loss of lift, (the angle of attack becomes too large”, [5].
Two types of turbine are used to harness the power of the wind based upon an aerodynamic effect. They are the Horizontal Axial Wind Turbine, (HAWT) and the Vertical Axial Wind Turbine; (VAWT).It should be noted that vectors define magnitude in a given direction.
For the operation of the HAWT the angle of attack remains positive throughout. For a given point on the blade, there is a velocity vector equivalent to the undisturbed wind direction and a tangential velocity vector. (The tangential velocity, m/sec, is not the angular velocity, radians per minute). The resultant vector of the undisturbed wind vector and the tangential velocity vector, u, is called the relative wind velocity vector, W. The tangential velocity, u, is a product of the angular velocity of the rotor,W and local radius at that point, r. (i.e. u = WX r).
The relative wind angle F is the vector angle formed between the relative wind vector and the tangential velocity vector, u. Another way of defining the relative wind angle is along a given blade radius r, F is the angle that relative wind velocity vector makes with the blade.
The operation of HAWT depends on many factors such as the number of blades, aerofoil section, blade pitch angle and the angle of attack. The diagram below shows how the various forces and how the resultant forces act. The undisturbed wind velocity vector upstream of the blade is called Vo. Downstream of the blade, the disturbed wind velocity vector is called V1. V1 = VO reduced by a factor called axial interference factor, a. The axial interference factor accounts for the power removed from the air by the turbine.
he Betz limit states that the maximum fraction of the wind power that can be extracted is 59.3%. This occurs when the undisturbed wind velocity is reduced by one third, (i.e. when a = 1/3).
For any point on the blade the angle of attack for the wind can be compared against the relative wind angle to determine the performance of a particular turbine for a given site. The blade pitch angle of the turbine can be calculated as a relative wind angle less the angle of attack. Thus the simulated results can determine a theoretical blade pitch angle for comparison with a turbine blade under consideration for that site.
As can be seen from the diagram below, the driving force of the component of the lift force, L, i.e. the force rotating the blade is L sinF. The drag force, D, acting on the blade is given by the component D cosF.
The torque, T for that point on the blade, (moment of rotation, around the centre), is generated from the net driving force, F, is:
F = L sin F - D cosF.
Torque T = Fr, where r is the radius distance from the blade point where the forces act on the center of the turbine hub.
Figure 8: Vector Diagram showing a section though a HWAT rotor blade.
It should be noted from the above figure that drag force, D, at the point shown is acting in line with the direction of the relative wind, W and the lift force, L is acting at 900 to it. For total torque, Q, Boyle states “the magnitude and direction of the relative wind angle, F varies along the length of the blades according to the local radius, r. This is because the local tangential speed, u, of a given blade element is equal to the rotor’s angular velocity,W times the local radius of the blade element, r. As the tangential speed decreases toward the hub, the relative angle progressively increases. If a blade is designed with a constant angle of attack along its length, it will have a constant built in twist. The amount of twist will vary as the relative wind angle varies progressively from tip to root as shown below in Figure 9.
Most of the turbine manufacturers will build twist into blades where possible to increase efficiency.” Straight blades are considered less efficient.
Figure 9: 3D view of a HAWT rotor blade showing how the relative wind angle changes along the blade span, [5].
Stall control
‘For stall let us consider a turbine with constant rotation speed and fixed blade pitch angle. When wind speed increases, the tip speed ratio decreases and the relative wind angle increases increasing the angle of attack. It is possible to control a turbine with this characteristic. As the wind increases, the turbine becomes less efficient, with the angle of attack approaching an angle called a stall angle. When stall angle is reached it causes a loss of lift and torque. Thus some regions of the blades are in “stall”. This is referred to as the stall control technique and has been applied to HAWT successfully.” [5].
Boundary Layer Separation
When air flows over an aerofoil of a turbine blade, vortices are generated in the wake. The mechanism by which the vortices are generated is called boundary layer separation. The figure below shows two velocity profiles, the upstream velocity V and the free stream velocity, u. (The free stream velocity is defined as the velocity of central air stream upon which friction has no effect). As the air approaches the curved surface, (here being a cylinder), t reaches a point called the forward stagnation point. At this point u reaches a value of zero and the pressure gradient reaches a maximum value, the fluid then accelerations around the surface of the cylinder due to the pressure gradient.
As fluids move around the curved surface, the velocity of the stream increase, (i.e. du/dx > 0) and the pressure gradient and the acceleration decreases, (dP/dx < 0). The deceleration of the fluids causes the fluid layer nearest the surface to stagnate and become unable to overcome the surface friction forces. The velocity of this fluid layer eventually becomes zero due to “insufficient momentum to overcome pressure gradients and continue downstream.
Since on coming flow fluids preclude flow back of the fluid Boundary layer separation/transition must occur,” [6]. The point at which this occurs is called the separation point. As the boundary layer detaches from the surface a wake is formed in the downstream region. The point at which boundary layer transition occurs is dependent on the on a parameter called Reynolds number.
Reynolds number is a parameter used to determine if the flow of the fluid is laminar or turbulent. This factor has a major impact on the CFD modelling. Reynolds number is defined as:
Re = rVD/ µ
Where Re is the Reynolds Number, r is the density, V is the velocity of the fluid; D is the diameter of the blade and r is the dynamic viscosity. The separation point in the turbulent boundary layer occurs later than the separation point in the laminar boundary layer. This is due to the greater level of momentum in the turbulent boundary layer. “If Re < 2 X 105 then boundary layer is considered laminar. If Re > 2 X 105 boundary layer is considered turbulent”, [6].
Figure 10: Turbulent Boundary Layer Development, [7].
Figure 11a: Turbulent Boundary Layer Separation, [7]
Figure 11b: Turbulent Boundary Layer Separation over Turbine Blade Aerofoil Section, [5]
Boundary layer separation has an impact on the drag force, Fd, acing on the cylinder. This force has two components friction drag which is the boundary layer surface shear stress and the other component is the pressure differential drag causing the formation of the wakes. This behaviour of this drag can described as a drag coefficient, Cd, defined above. Therefore it may be concluded that the drag coefficient is dependent on the Reynolds number. For laminar Reynolds number the effects are negligible as the friction drag component dominates. Increasing the Reynolds number to turbulent levels delays the separation due to boundary layer transition. Thus of Re values greater than 2 X 105 on curved surfaces, the Cd magnitude and effect are greatly reduced with less wake formation.
CFD Turbine Models Solver comparison
From the point of discussing turbulent solvers, four models are taken from ANSYS’s Fluent Software version 1.2. In figure 12 below, the plate on the left is modelled to determine the behaviour of the boundary layer using the four solvers. The results are shown on the right. It can be seen that the Standard k-e model gives the least accurate results while the Reynolds Stress gives the most accurate. The Standard k- e model uses the least computing power, while the Reynolds Stress uses the most. Examination of turbulent solvers is conducted below.
Figure 12 Improvement in RNG accuracy over standard k-e models, [7]
Figure 13: Effect of Reynolds on vortex formation, [7].
The effect of the Reynolds model on the boundary layer separation is given in the figure above. Typically for wind turbine analysis, (with winds speeds greater than 5m/s) turbulent flow taken so therefore we would be assuming a Re > 3.5 X 106, high swirl with high pressure gradient. The model solver selected must suit the characteristics of this type of flow field.
The Fluent Theory guide states: “Standard k-e Model: The simplest “complete models” of turbulence are the two-equation models in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined. For the standard k-e model, the transport equation for k is derived from the exact equation, while the model transport equation for e was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart”, [8].
The Standard k-e Model known limitations are:
Performs poorly for flows with larger pressure gradient, strong separation, high swirling component and large streamline curvature.
Inaccurate prediction of the spreading rate of round jets.
Reduction of k is excessive (unphysical) in regions with large strain rate (for example, near a stagnation point), resulting in very inaccurate model predications.
Therefore this type of model would not be suitable for a turbulent boundary layer separation flow field.
The RNG k- e model is considered to be more suitable and accurate due to:
“Enhancing accuracy for swirling flows.
Effective viscosity that accounts for low-Reynolds-number effects. Effective use of this feature does, however, depend on an appropriate treatment of the near-wall region. These features make the RNG k- e model more accurate and reliable for a wider class of flows than the standard k- e model.
The RNG theory provides an analytical formula for turbulent Prandtl numbers, while the standard k-e model uses user-specified constant values.
In the derivation of the k-e model, the assumption is that the flow is fully turbulent and the effects of molecular viscosity are negligible. The RNG k-e model is therefore valid only for fully turbulent flows.” [8].
The assumption that the flow is fully turbulent cannot be fully substantiated especially in the viscous sub-layer. We want to investigate the cause of what limits the boundary separation, so analysis of what happens in the viscous sub-layer is a key behaviour to be observed.
The Shear Stress Transport k–ω (SSTKW) model (Menter) uses a blending function to gradually transition from the standard k–ω model near the wall to a high-Reynolds-number version of the k–ε model in the outer portion of the boundary layer. This model can determine flow pattern behavior in the viscous sub-layer by using a robust low-Reynolds-number (LRN) formulation. It can observe compressibility effects, transitional flows and shear-flow conditions. Compared to the RNG K-e model, it has improved behavior under adverse pressure gradient.
The SSTKW model contains a modified turbulent viscosity formulation to account for the transport effects of the principal turbulent shear stress. This model generally gives accurate prediction of the onset and the size of separation under adverse pressure gradient which are characteristic of turbulent flow boundary separation. The model is most widely adopted in the aerospace and turbo-machinery communities.
Reynolds Stress Models, (RSM), have limitations and weakness of eddy viscosity models:
Linear algebraic stress-strain relationship results in poor performance where stress transport is important, including non-equilibrium flows and separating flows.
Inability to account for extra strain due to streamline curvature, rotation and highly skewed flows.
Poor performance where turbulence is highly anisotropic.
Attempting to avoid these shortcomings, transport equations for the six distinct Reynolds stress components are derived by averaging the products of velocity fluctuations and Navier-Stokes equations. A turbulent dissipation rate equation is also needed. RSM is most suitable for highly anisotropic and three dimensional flows. With addition of the averaging effect for the transport equation, the computational cost is higher compared to the other k-e or k-w solvers. Currently RSM’s still do not always provide indisputable superior performances over the k-e or k-w solvers, for the addition required computation power and costs and for boundary layer separation flow fields. To model a turbine site with this solver would be extremely costly and time consuming. The RSM is target mainly for research work, [7].
Research Paper Review No. 1
David Hartwanger and Dr. Andrej. Horvat of Intelligent Fluids Solutions evaluated the use of Computational Fluid Dynamics to predict the influents effecting turbine performance in specific local environments.
Hartwanger and Horvat examined three models used to assess turbine performance:
The Betz Model.
The Glauert Model.
The GGS Model, (Gorban Gorlov and Silantyev).
The Betz Model
Consider the finite volume detail below in Figure 1. The air stream enters the finite volume with a velocity Vo acting over an area Ao. The rotor represents an “actuator disk” and this creates a pressure discontinuity of area with varying local velocities at points 1 and 2. The air stream passes through the turbine blades causing a turbulent flow, resulting in vortices. The resulting air stream has lower downstream velocity acting over a wide area, (point 3).
Figure 14: Control volume for the idealized actuator-disk analysis, [4].
The following assumptions are made:
“The flow is ideal and rectilinear across the turbine i.e. steady, homogenous, inviscid, irrotational and incompressible.
Both the flow and thrust are uniform across the disk.
The static pressure at the upwind and downwind boundaries is equal to the ambient static pressure”, [4].
The power coefficient, Cp, defines as the ratio between extracted power and the available power is given by:
Cp = 4a (1-a) 2 [4].
Where a = An axial induction factor, (“The fractional decrease in wind velocity between free stream and the rotor plane”, [4]). a has a maximum value of 0.5.
When Axial Induction Factor is plotted against Power Coefficient, it shows Cp reaches a maximum value of 0.593 when a = 0.32. This called the Betz limit for an ideal frictions turbine.
Figure 15: Power Coefficient for an ideal Betz model wind turbine, [4].
Hartwanger and Horvat stated that this model was limited for real turbine applications because:
“The model is independent of turbine rotational speed and requires a uniform pressure distribution over the disk area. In reality turbine would not achieve this efficiency level due to
Rotation in the wake caused by the reaction with the spinning rotor
A non-uniform pressure distribution in the turbine plane
Aerodynamic drag due to viscous effects.
Energy loss due to vortices at the blade tips”, [4].
The Glauert Model
In 1935 Glauert developed an expression:
, [4].
Where p1-p2 is the pressure change across turbine blade.
w is the angular velocity of the turbine.
r is the radius of the annular stream tube at the rotor plane.
For the Glauert model, when Tip Speed Ratio is plotted against Power Coefficient, then it can be seen that a low angular induction factor and high tip speed will deliver better efficiency.
Figure 16: Theoretical maximum power coefficient, [4].
Hartwanger and Horvat investigations concluded the following about the Glauert model:
“Glauert’s wake rotation model is still subject to the assumptions of a uniform pressure distribution and zero radial velocity in the turbine plane (as in the Betz analysis). These assumptions lead to an overestimation of the forces and torque applied to the turbine. Therefore, Glauert’s model asymptotes towards the Betz limit as the tip-speed ratio tends to infinity, i.e. as the rotation in the wake tends to zero.”
The GGS Model.
Gorban et al developed the GGS model in 2001. A pitch angle is introduced in the GGS model and is defined as the same angel at any point on the blade that the flow must cross. The GGS model equation for power extraction is given by:
, [4].
The flow field for the GGS model is shown below. This flow field can be solved using a modified Kirchhoff analysis. The GGS model can optimize the flow passing through the turbine’s swept areas with respect to the pitch angle.
Figure 17: GGS curvilinear flow model in incompressible flow, [4].
When efficiency & flow through were plotted against pitch angle, the GGS model predicts peak efficiency at 30.1% at a flow through of 0.613 and pitch angel, f, of 67.50. This most conservative compared to the previous to models.
Figure 18: Power Coefficient versus Flow through the turbine, [4].
From the graph above it also shows that “the GGS model predicts that peak efficiency is achieved when the flow through the turbine is approximately 61% which is very similar to the Betz result of 2/3rd”, [4].
For the models Hartwanger and Horvat concluded:
“Real wind turbines do not attain the levels predicted by Betz or Glauert. They do achieve and exceed the level predicted by Gorlov et al.
Glauert model is optimistic, while the GGS model is conservative and highly efficient real turbines possibly lie somewhere in between.
For a wind turbine to attain near ideal efficiency it should exhibit the following characteristics:
Relatively low resistance to the flow, allowing approximately 65% of the stream to pass through.
High tip-speed ratios so that the angular momentum in the wake is low.
The performance of real wind turbines is limited by the following factors:
Non-uniform pressure and turbulence distribution over the swept area.
Angular momentum in the wake.
Blade tip losses as a result of tip vortices.
Aerodynamic drag and boundary layer separation due to viscous related effects.”, [4].
CFD Model Results & Validation
All CFD models need to be validated by similar experimental results to verify that the modeling methodology is correct. To verify these results, Hartwanger and Horvat chose the results from a 3-bladed Vestas turbine, 52m in diameter with a rated power output of 850 kW. The blade pitch was variable and controlled by a microprocessor. The UAE turbine is a full-scale experimental turbine designed and built by the US Department of Energy’s National Renewable Energy Laboratory (NREL) to specifically advance the current understanding and prediction of wind turbine performance, [4], for full 3D analysis.
A 2D analysis was conducted first on the aero-foil blade. Hartwanger and Horvat stated the purpose of this analysis as
“To assess the general predictive accuracy of the numerical tools in terms of the 2D lift and drag polar.
Assess the relative difference between a high fidelity CFD model and a lower fidelity more practical model, to serve as a guide for the 3D analyses. ”, [4].
High computational power and time resources are required to conduct the advanced turbulence and transition modeling as required for 3D wind turbines. A lower fidelity CFD model would demand fewer resources, so the lower fidelity CFD model was investigated in order to assess the potential loss in predictive accuracy.
The results were compared to data collected from test program known as the Unsteady Aerodynamics Experiment (UAE). The unit is a 2-bladed, 10m diameter, 20 kW wind turbine and was tested at the NASA-Ames Research Centre Wind Tunnel.
For the 2D analysis Hartwanger and Horvat concluded that” that the high- fidelity CFD model would be most suitable for high tip-speed ratios (>3), while tending to over-predict performance at low tip-speed ratios (<2).The normal fidelity model is likely to under-predict performance at high tip-speed ratios”, [4]. The high fidelity was used in the 3D Model.
UAE Turbine 3D Model Set-up
Hartwanger and Horvat constructed a 3D CFD model of the Unsteady Aerodynamics Experiment (UAE) 2-bladed, 10m diameter turbine. The purpose of this model was to estimate approximate axial and angular factors to complete population of the momentum equations, (Thrust and torque).
They used a steady state k-epsilon turbulence model with inflate layers. Convergence was achieved on the solution after approximately 1,000 iterations. The modelling code was “ANSYS CFX”. Hartwanger and Horvat stated that the results of their 3D model compared well with experimental data from the NREL At the lower winds speeds, (TSR<3), the CFD model under-predicted the turbine performance. They stated that for operation within the majority of flow regime, the CFD model under-predicted lift and over predicted drag. Also the flow separation flow from the CFD model over-predicted performance because of over-predicting aerodynamics lift.
Full Turbine 3D Model Set-up
In their full model set-up, Hartwanger and Horvat again used a steady state CFD model similar to the UAE Turbine 3D Model set-up. Upon completion of their analysis, they found that integrated torque correlation used to determine torque output from the turbine compared favorably with experimental data from the 52m diameter turbine except for one condition wind speed of 15m/s. No explanation was given to account for this. Comparisons of experimental and numerical results are shown below:
Figure 19: Torque Distribution calculated from the measured angular induction factor, [4].
Hartwanger and Horvat concluded that this provided a good benchmark test for the application of CFD to optimise turbine selection and placement to suit particular local environments over a wind speed range. The application of this type of numerical modelling allows numerous scenarios to be examined without the expense of experimental modelling. They did however recognise that this was the initial stage of their work and that further research work on this topic will be conducted. One of the specific issues they high-lighted, was that there was little difference in the end results obtained from the full turbine 3D model when using the normal fidelity model or the high fidelity model from the UAE CFD model. Using the normal fidelity model would save significant computing resources. They also noted that the use of the low fidelity model would yield inaccurate results in the full 3D CFD for turbine performance, [4].
Analysis of the Paper
This paper was written in 2008. There has been limited published work on the use of CFD in the design of turbines since then and appears to be quite an unexplored area. This highlights that there has been no critical experimental work conducted to validate CFD numerical models for designers of wind farms. Hartwanger and Horvat is one of the few published papers on this topic and there are only in the initial stages of their research. The author’s view is that CFD is a powerful tool, but it needs to be proven more before being applied to commercial use in wind farm design.
Hartwanger and Horvat offered no explanation why they chose the k-epsilon turbulence model. It is known as a good standard model but it is more suitable for applications like tank mixing. The k-epsilon model is limited in conditions of high velocity and pressure gradients i.e. high swirl applications, with conditions similar to what occurs downstream of a turbine at wind speed of 15m/s, circa 35 MPH. The k-epsilon model will over estimate point of boundary layer separation and hence over estimate turbine performance. The k-omega model is better for flows with a high swirl and hence better at the estimation of boundary layer separation. The problem with the k-omega model is that it requires more computation power resulting in higher costs.
There are many other factors influencing the outcome of the model, which would require an in-depth analysis and discussion. Such a discussion is outside the scope of this article. The analysis of the paper by Hartwanger and Horvat was to show by example the CFD technology, it’s usefulness and some of the issues utilising it when designing a wind farm.
CFD Analysis Set-up
For this article it was decided to look at the wake behaviour of airflow over a turbine blade under steady state conditions to evaluate the CFD method in this application. The parameters of interest from this model were:
Velocity behaviour.
Pressure behaviour (to see effect that generates the lift).
Wake behaviour.
Steady State modelling would not be recommended for the modelling of turbine sites. An accelerometer survey of the site will reveal varying wind conditions. Steady state conditions assume one constant air flow. So for each wind speed a simulation will have to be done for each one to establish a trend if using a steady state. The rotation of the blade with reference to the relative wind velocity vector cannot be assessed under steady state conditions. It is therefore recommended for using CFD, for site evaluation, transient time dependent modelling is used. This type of modelling is common for turbulent applications.
For assessing the performance of a blade aerofoil design, steady state modelling can be used for this application. A simulation is done for each wind speed and a trend of performance under varying conditions is established to determine if the blade aerofoil design is of good or poor design.
A turbulent model is advised by the Fluent Theory Guide for this application, [8]. The k-w model is recommended based on its efficiency for computing the flow fields with high gradient and high swirl. This type of solver is required for this application because at the separation point, the flow on the surface of the blade being stagnant and adverse pressure gradients cause the boundary layer to separate in a fully turbulent flow. The airflow velocity is modelled at 0.7 mach. It is predicted that the Reynolds number will be greater than 2 X 105 and thus the boundary layer can be considered turbulent. The surface behaviour of the boundary layer transforming from laminar to turbulent will be of interest to evaluate trailing wake behaviour.
For modelling operation of turbine blades in CFD software, the wake generated after the blade is of keen interest to the wind farm design team. For this the behaviour of the fluid in the near wall treatment is observed in the near wall region. The turbulent boundary layer is very thin and the gradients are very high, accurate calculations in the near wall region are paramount to the success of the operation. The wall function recommended is the Enhanced Wall Treatment. In the analysis this is the viscous sub- layer with low Reynolds Number developing to a turbulent boundary layer prior to boundary layer separation. Wanting to minimise wake is the objective of the analysis so remaining with the viscous sub-layer for as long as possible is the objective of the design be evaluated. The Enhanced Wall Treatment method is recommended. It combines a two-layer model with enhanced wall functions. The mesh must be constructed so that the near wall mesh is capable of resolving the viscous, (y+ < 5), with a minimum of 10-15 cells across the inner layer comprising of the viscous, buffer and log law layers. (The y+ for our model = 3.6789) If the near-wall mesh is fine enough to be able to resolve the viscous sub layer, then the enhanced wall treatment will be identical to the traditional two-layer zonal model. It should be noted that there is a restriction, that the near-wall mesh may be too fine everywhere to impose too large a computational requirement. Excessive error can be incurred for the intermediate meshes where the first near-wall node is placed in the fully turbulent region. The Fluent Theory Guide advises typically for the Enhanced Wall Treatment that the first near-wall node be placed at y+
1 where the Reynolds numbers are sufficiently low, [8].
The discretisations schemes are recommended by a 2nd order upwind Pressure Momentum and are used when accuracy is desired. The 2nd order solves quantities at the cell face. In this approach, higher-orderaccuracy is achieved at cell faces through a Taylor series expansion of the cell-cantered solution about the cell centroid.
Fluent Theory guide advises that “Because the mean quantities have larger gradients in turbulent flows than in laminar flows, it is recommended that you use high-order schemes for the convection terms. This is especially true if you employ a triangular or tetrahedral mesh. Note that excessive numerical diffusion adversely affects the solution accuracy.” During the analysis it is expected that the boundary layer will transverse from laminar to turbulent flow prior to boundary layer separation.
Results:
Figure 20: 2D Turbine Blade-CFD Dynamic Pressure Results, (Taken from Assignment Model).
Figure 21: 2D Turbine Blade-CFD Static Pressure Results, (Taken from Assignment Model).
Figure 22: 2D Turbine Blade-Velocity – Mach number Results, (Taken from Assignment Model)
The CFD model was set-up as described in the CFD analysis set-up section above. Figures 20 through 22 follow the predicted path for both velocity and pressure for boundary separation as detailed above. With reference to Figure 13 above, we may conclude that this is a 3X107 < RE < 3.5X 106. This confirms that the boundary layer transitioned from viscous to turbulent.
These figures also clearly indicate the stagnation point and the point of separation for the boundary layer that are at the approximate estimated locations. What is unexpected? Is that the partial re-attachment of the boundary layer as the velocity decreases and the pressure increases over the profile of the blade? It can also be observed that the wake after the trailing point of the blade is quite narrow in width. This is confirmed by Figure 23 below.
Figure 23: 2D Turbine Blade Turbulent Viscosity Results, (Taken from Assignment Model).
From Figure 23, it may be concluded that the wake profile is narrow and hence both turbulence and noise generation are not significant issues with this profile design.
Discussion
CFD is widely used numerical modelling software for dynamic fluid problems and is ideally suited for use in wind farm design to optimise turbine layout designs. It can also be used for optimising the design of the wind turbine blades. The use of this technology is applied both in Europe and the US in the wind energy sector
Hartwanger and Horvat of Intelligent Fluids Solutions stated that CFD is a powerful tool. They determined that the results of their work to date showed that there was little difference in the end results obtained from the full turbine 3D model and the results from a 3-bladed 52m diameter Vestas turbine built by the US Department of Energy’s National Renewable Energy Laboratory (NREL). They believed that CFD can make a positive contribution to the design and optimization of wind turbines and farms.
It was the intension of this article to demonstrate what Hartwanger and Horvat about CFD. From the model results, it can be concluded that they concur with Hartwanger and Horvat statement and support their conclusions about the use of CFD in wind energy design.
The advantage of numerical modelling like CFD is that a variety of turbine blades can be designed in CAD packages and evaluated using CDF to estimate their behaviour. This has a sufficient saving in Turbine R&D costs in not having to make and physically test every blade profile.
Schlez and Tindal stated that every 1% optimised on a 50MW farm using a software package that there is an increase in annual revenue from €50,000 to €100,000. If the software package increases efficiency by just 2% (which is not beyond the capacity of the software), a potential saving of €200,000 could be made on 50MW farm. Therefore it is well worth considering CFD analysis for this application.
As can be seen from results above, CFD can be used to reduce the wake profile and hence reduce the adverse effects that cause noise generation. It will also make the wind take more efficient. The most positive potential outcome of this would be a higher population density of turbines on sites.
The use of CFD in wind turbine design is not totally a new application from start. A lot of CFD modelling work has been complete on aircraft wing design. This knowledge can be transferred to the wind turbine applications and built upon.
Some of the major research work is currently on-going in CFD analysis in the comparison of CFD to real full size operation turbines to refine the modelling techniques used in CFD for the improvement of wind energy applications.
Conclusions
CFD can be used to optimise turbine blade design.
CFD can be used to optimise turbine layout design for sites.
CFD can be used to reduce wake profile, increasing turbine efficiency and reducing the generation of noise.
CFD analysis can be used to reduce wind take per turbine and increase the number of turbines on a given site.
CFD can reduce R&D costs associated with the improvement of turbine designs.
References
[2] Schlez , W., and Tindal, A., Garrad Hassan and Partners Ltd,, “Wind Farm Siting and Layout Design” www.garradhassan.com/products/ghwindfarmer/index.php, Accessed 25.11.2011.
[3] Crane Co., (1988), “Flow Of Fluids”, Technical Paper No. 410M, Crane Co, Ipswitch.
[4] Hartwanger, D. and Horvat, A., (2008), “3D Modelling Of A Wind Turbine Using CFD”,
NAFEMS Conference, UK.
[5] Boyle, G., (2004), Renewable Energy, 2nd Edition, Oxford, Newyork.
[6] Incropera, F.P. et al., (2007), Fundamentals of Heat & Mass Transfer, 6th Edition, Wiley,
Hoboken.
[7] ANSYS UK Ltd., (2009), “Introduction to FLUNET Release 12 Training Manual”, 2nd Edition,
ANSYS INC, Sheffield.
[8] ANSYS UK Ltd., (2009), “Fluent Theory Guide”, ANSYS INC, Sheffield.