Research Article Investigation of the Unsteady Flow Behaviour...

Research ArticleInvestigation of the Unsteady Flow Behaviour ona Wind Turbine Using a BEM and a RANSE Method

Israa Alesbe,1,2 Moustafa Abdel-Maksoud,1 and Sattar Aljabair1,2

1 Institute for Fluid Dynamics and Ship Theory (M8), Hamburg University of Technology (TUHH), Hamburg, Germany2Mechanical Engineering Department, University of Technology, Baghdad, Iraq

Correspondence should be addressed to Israa Alesbe; [email protected]

Received 12 April 2016; Revised 2 August 2016; Accepted 6 September 2016

Academic Editor: Adrian Ilinca

Copyright © 2016 Israa Alesbe et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Analyses of the unsteady flow behaviour of a 5MW horizontal-axis wind turbine (HAWT) rotor (Case I) and a rotor with tower(Case II) are carried out using a panel method and a RANSE method. The panel method calculations are obtained by applyingthe in-house boundary element method (BEM) panMARE code, which is based on the potential flow theory. The BEM is a three-dimensional first-order panel method which can be used for investigating various steady and unsteady flow problems. Viscous flowsimulations are carried out by using the RANSE solver ANSYS CFX 14.5.The results of Case I allow for the calculation of the globalintegral values of the torque and the thrust and include detailed information on the local flow field, such as the pressure distributionon the blade sections and the streamlines. The calculated pressure distribution by the BEM is compared with the correspondingvalues obtained by the RANSE solver. The tower geometry is considered in the simulation in Case II, so the unsteady forces due tothe interaction between the tower and the rotor blades can be calculated. The application of viscous and inviscid flow methods topredict the forces on the HAWT allows for the evaluation of the viscous effects on the calculated HAWT flows.

1. Introduction

One of the best alternative renewable energy resources todayis wind energy: it is free and clean, meaning that designingand constructing wind turbines (WT) is a rapidly growingfield of technology. However, maximising power output andminimising operation costs require a continuous improve-ment of their aerodynamic performance. An accurate pre-diction of the aerodynamic properties is still a challenge,especially since the dimensions of system have becomelarger. In particular, wind turbine blades can experience largechanges in angles of attack associated with sudden largegusts, changes inwind direction, atmospheric boundary layerinfluence, and strong interaction with tower.

There are several methods of varying levels of complexitythat can be used to predict the aerodynamic loads on thewind turbine (WT) aerodynamic parts. The blade elementmomentum method has been very popular for WT designand analysis as shown in Ingram [1]. This method is highlyefficient and inexpensive, but it is incapable of modellingthree-dimensional flow effects, the interaction between rotor

and tower, and tip relief effects. Empirical corrections areused to consider tip vortex losses. Many researchers, such asShen et al. [2] and Ceyhan [3], have attempted to increasethe accuracy of the blade element momentum method byimproving the model for considering the tip vortex effects onthe flow in the outer radii region.

Potential flow based methods have been introduced tosimulate theWT aerodynamics with high computational effi-ciency. Different formulations of the potential flow methodcan be applied, such as lifting line, vortex lattice, and panelmethod. Generally, in these methods, the blade can bemodelled as a lifting line, lifting surface, or panels andthe wake can be modelled by either trailing vortices orvortex ring elements. Compared with the blade elementmomentum method, potential flow methods can be appliedto study more complex flow phenomenon such as theconsideration of the nonaxial inflow velocity distributiondue to the tower influence on the inflow as well as theinteraction between the rotor and the tower flows. But suchmethods suffer from the limitation of the potential flowtheory regarding the consideration of the viscous effects.

Hindawi Publishing CorporationJournal of Renewable EnergyVolume 2016, Article ID 6059741, 12 pageshttp://dx.doi.org/10.1155/2016/6059741

2 Journal of Renewable Energy

Potential flow methods are not able to predict importantviscous phenomena such as stall. Abedi et al. [4] used threedifferent approaches which are lifting line, lifting surface,and panel method to calculate the aerodynamic loads onrotor blades. The results show the ability of the applied panelmethod to provide detailed information on the pressure andvelocity distributions over the blade surface as comparedwith other applied approaches. A three-dimensional panelmethod was also used by Bermudez et al. [5] for simulatingthe aerodynamic behaviour of horizontal-axis wind turbines,and the comparison between experimental data and thecomputed results with the panel method shows a goodagreement. Gebhardt et al. [6] utilized the vortex-latticemethod to simulate the unsteady aerodynamic behaviour oflarge horizontal-axis wind turbines. The aerodynamic of theblade-tower interaction has been satisfactorily captured aswell as the effects of land surface and the boundary layerof the inflow. Kim et al. [7] have used the same method tosimulate the blade-tower interaction over the NREL PhaseVI and additionally used the nonlinear vortex correctionmethod to investigate the rotor turbine while consideringwind shear, yaw influence, distance from blade to tower, anddifferent tower dimensions. The lifting lines model was usedby Dumitrescu and Cardos [8] to simulate HAWTs, and theresults obtained by using a nonlinear iterative prescribedwake analysis were more accurate than the results calculatedby the free wake model.

More accurate simulations can be achieved by employingflow simulation methods such as Reynolds Averaged Navier-Stokes Equation (RANSE) solvers with an accompanyingturbulence model. RANSE methods are commonly usedfor this purpose and are more accurate than potential flowmethods but also more expensive in terms of computationaltime. Lee et al. [9] used RANS Equations solver in combina-tion with the Spalart-Allmaras turbulence model to evaluatethe performance of a blade with blunt aerofoil which isadapted at the blade’s root by increasing the blunt trailing-edge thickness to 1%, 5%, and 10% of the chord. The blunttrailing-edge blade helps to improve both the structure andthe aerodynamic performance of the blades. Further, the SSTturbulence model, see Menter [10], is widely used for windturbine simulations due to its ability to simulate attached andlightly separated airfoil flows. This turbulence model is alsoused in Keerthana et al. [11] to calculate the aerodynamiccharacteristics of a 3 kW HAWT. Derakhshan et al. [12]compared the results obtained by Spalart-Allmaras, 𝑘-𝜀,and SST turbulence models for estimating the aerodynamicperformance of wind turbine blades. The results show thatthe three turbulence models predict nearly the same powerat low wind speeds, but the results obtained by the 𝑘-𝜀 aremore accurate at higher wind speeds.

The aim of the present work is to analyse the unsteadyflow behaviour of a 5MW HAWT utilizing two differentnumerical methods: a three-dimensional first-order panelmethod, which is the in-house panMARE code, and a RANSEmethod, which is the commercial ANSYS CFX solver. Ageneral comparison between the results of both methods willhighlight the viscous effects on HAWT flow that are notconsidered in panel code. Based on the computed results,

the capabilities and limitations of the applied inviscid flowmethod to predict the complex WT flow will be illustrated.The panMARE code is successfully applied for simulatingthe flow of ship propellers and return reliable results forcomplicated flow conditions, such as in Bauer and Abdel-Maksoud [13] and Greve [14].

2. Wind Turbine Geometry

Due to the availability of its geometry and reference data[15], the NREL 5MW offshore wind turbine is consideredin the numerical study. It is a modern wind turbine with acomplex geometry shape.While only the rotor is investigatedin the first simulation Case I, the full geometry is consideredin Case II, including the rotor, tower, and nacelle. The windturbine rotor has three blades with a blade span of 61m andattached to a hub with a radius of 2m, which gives a totalrotor radius (𝑅) of 63m. The blade is composed of severalaerofoil shapes which are described at different radial bladesections in Table 1 in [16]. The NREL 5MW offshore windturbine tower is typically circular with a height of 90m andhas a diameter of 6m at the tower base and 3.87m at the towertop.

3. Numerical Model for Panel Method

The in-house boundary element solver panMARE (panelcode for MAritime Applications and REsearch) is appliedin the simulations. The method is able to simulate poten-tial flows for arbitrary steady and unsteady applications.The code is based on a three-dimensional first-order panelmethod, where the body’s surfaces are discretized by meansof quadrilateral panels, where each panel has a constant-strength singularity distribution of sources and dipole. Foreach 𝑁 body’s surface panel, the solver’s governing equationand the boundary conditions are satisfied at a control point(in the centre of the panel). Potential theory drives thegoverning equation, where the flow is considered to beirrotational, incompressible, and inviscid. The equations forthe conservation of mass and momentum are then simplifiedto Laplace’s equation for the total potential:

∇2Φ∗ = 0. (1)

The solution of the Laplace equation is a linear combinationof several sources and dipoles superimposed with the inflowvelocity potential (Φ∞). The general solution of (1) on thebody’s surface (SB) and the wake (𝑊) is defined in Katz andPloklin [17] as

Φ∗ (𝑥, 𝑦, 𝑧) = Φ (𝑥, 𝑦, 𝑧) + Φ∞ (𝑥, 𝑦, 𝑧)= 14𝜋 ∫

SB+𝑊𝜇 𝜕𝜕𝑛 (

1𝑟) 𝑑𝑆

− 14𝜋 ∫

SB𝜎(1𝑟) 𝑑𝑆 + Φ∞ (𝑥, 𝑦, 𝑧) ,

(2)

where the vector (𝑛) is the local normal to the surface (SB)and (𝑟) is the distance between the panel control point and

Journal of Renewable Energy 3

any other control point; (𝜇) denotes the dipole strength and(𝜎) source strength, which are defined as

𝜇 = − (Φ − Φinner) ,𝜎 = −(𝜕Φ𝜕𝑛 − 𝜕Φinner

𝜕𝑛 ) . (3)

Since at an inner point of the boundary the inner potentialcan be chosen arbitrary, it will be an advantage to considerΦinner = Φ∞; in this case the dipole strength and sourcestrength can be defined as follows: −𝜇 = Φ, −𝜎 = 𝜕Φ/𝜕𝑛.

The velocity potential can be calculated by applying thefollowing boundary conditions:

(i) Direct boundary condition (Dirichlet): when (2) isconsidered in an inner point of the body, the overallpotential will be defined as

Φ∗ = Φinner − Φ∞. (4)

Because the inner potential is arbitrary at an innerpoint of the boundary, Φ∗ = Φ∞ is chosen andthe following equation for the velocity potential isobtained:

14𝜋 ∫

SB+𝑊𝜇 𝜕𝜕𝑛 (

1𝑟) 𝑑𝑆 −

14𝜋 ∫

SB𝜎(1𝑟) 𝑑𝑆 = 0. (5)

(ii) Neumann boundary condition: the total velocity nor-mal to the surface is required to be zero:

∇Φ∗ ⋅ �� = 0; (6)

and by applying the Neumann boundary conditionon the lifting panel, the value of the source can bedetermined by

−𝜎 = −�� ⋅ ��∞, (7)

where ��∞ is the inflow velocity vector; so in thelifting body case, only the strength of the dipolesis unknown, and in the non-lifting body case, thereare no dipoles and the strength of the source can bedetermined by (2).

The boundary conditions can be transformed into a set oflinear equations, the solutions of which provide the requiredstrength of each dipole (𝜇) or source (𝜎). Moreover, thecalculated 𝜇 and 𝜎 values are used to compute the inducedvelocities on each body surface panel. The pressure distribu-tion (𝑝) on each panel of the body is calculated by applyingthe Bernoulli equation:

𝑝 + 𝜌𝑔𝑧 + 0.5𝜌V2 + 𝜌𝜕Φ∗𝜕𝑡 = const, (8)

where V is the induced velocity, 𝑡 is the time, and 𝜌 and 𝑔 arethe water density and the gravity constant, respectively.

Thewake surface is a sheet or thin layer of dipoles. On thewake surface, it is necessary that the oscillation of the normal

velocity component aswell as the force difference between thelower and upper sides vanish.

The Kutta boundary condition is applied at the bladetrailing edge in order to obtain the dipole strength (𝜇𝑡⋅𝑒) ofeach first wake panel connected to the trailing edgewhich canbe calculated by using

𝜇𝑡⋅𝑒 = 𝜇upper − 𝜇lower, (9)

where 𝜇upper and 𝜇lower are the dipole strengths on the upperand lower sides of the aerofoil’s trailing edge. The geometryof the wake surfaces is iteratively adapted to be parallel to thelocal velocity vector, so that the normal velocity componentto the wake surface becomes zero. In the steady case, thestrength of the dipoles varies in the radial direction in order tomeet the Kutta boundary condition, which remains constantin the axial direction. In contrast, the strength of the wakesurface dipoles changes in radial and in axial direction inthe unsteady case. In each time step, the Kutta boundarycondition is applied and the dipole strength of the panelconnected to the trailing edge is calculated. In the next timestep, a new panel is generated behind the trailing edge, whilethe old panel, which was connected to the trailing edge, willkeep its strength but will be transported further downstreamaccording to the local flow velocity.

The BEM uses an iterative procedure to solve the rotor-tower interaction as shown in Figure 1(b). First, it solvesthe rotor and tower problems separately, after which thetime-dependent influence of each component on the othercomponents is considered by including the induced velocitiesof the adjacent structure, respectively.

The unsteady solution is initialized based on a steadycalculation. The steady calculation is very important inpredicting the initial wake panel’s primary location.This priorcalculation is followed by unsteady calculation, in whichat each time step the free wake moves with the inducedvelocity that is calculated at each panel. Each unsteady timestep, or “explicit step,” involves few implicit steps (i.e., inneriterations).

In order to avoid unstable fluctuations on the towerpanel’s properties that intersect with the rotor wake panels, allthe wake panels inside the blade-tower interaction region areexcluded from the calculations by using the split techniquepresented in Figure 1(a). Accordingly, all recognized wakepanels’ dipole strengths will have a value of zero, so it will nothave any effect on the tower panels. It should be mentionedthat these dipoles which have already been saved before thecollisionwill return to set again after passing the tower region.

The in-house CAD-code is used to build all geometrydetails and to generate the surface grid of the panels. Thenumerical grid on the blade is refined in the leading edgeand trailing edge areas in order to capture the high pressuregradients. A smooth change of the panel size on the blade intothe wake and on the blade tip is achieved to avoid panels withhigh aspect ratios. The blade grid in the radial direction islimited to 𝑟/𝑅 = 0.99 to avoid high distorted panel shapes.

Two numerical studies have been conducted to investi-gate the dependency of the result on the blade grid and thesimulated wake length. The results of the sensitivity studies


Split

fact

or

1

0.75

0.5

0.25

0

XY

Z

(a)

Start

Solve tower part

Add induced velocity of thetower on the rotor

Solve rotor part

Add induced velocity of therotor on the tower

Convergedsolution

Time = Timemax

Print results

No

NoYes

Yes

Time = time + dt

(b)

Figure 1: Blade-tower interaction treatments: (a) split technique and (b) flowchart solution.

CQ

‡

‡

‡‡ ‡ ‡

0.05

0.06

0.07

0.08

1000 1500 2000 2500 3000500 NOP

CQ

‡

‡

‡

‡‡ ‡ ‡ ‡ ‡

0.05

0.06

0.07

0.08

1 2 3 4 50Wake length (rev)

Figure 2: Variation of the torque coefficient as a function of the number of grid points and wake length.

are shown in Figure 2. The torque coefficient value (𝐶𝑄) isused to show the monotonic convergence toward a constantvalue, which is obtained by the finest mesh and longest wakelength, where the numbers of panels (NOPs) in the blade’sradial and in circumferential directions are verified with aconstant ratio between them. According to the results of thesensitivity study, the lowest panel number that can be appliedis 1113 per blade (43 × 26 panels in circumferential and radialdirections, resp.), while a wake length of 1.5 revolutions issufficient.

The total number of used panels in Case I for the rotor is4000. In Case II 4050 panels are applied for the rotor and 450for the tower, as shown in Figure 3.The investigated operationcondition is a uniform wind speed of 11.4m/sec with zero

yaw angles and a rotor rotational speed of 1.267 rad/sec,which gives a tip speed ratio of 7. Therefore, one revolution iscompleted in 5 seconds. The Reynolds number at the radius𝑟/𝑅 = 0.7 is 1×107.The 𝑥-axis is the rotation axis and the 𝑧-𝑦plane is the rotation plane. The time step in the simulation ischosen such that the rotor blades advance 6.118 deg. within asingle time step.

4. Numerical Model for RANSE Simulation

The RANSE solver ANSYS CFX 14.5 is employed for calcu-lating the viscous flow on the wind turbine. The governingequations are discretized using the Finite Volume Method,while the Shear Stress Transport (SST) turbulence model


Figure 3: 5MW full wind turbine and blade geometry.

Figure 4: Surface mesh and boundary layer on the blade.

is applied. The SST model is a combination of 𝑘-𝜀 for theouter region and 𝑘-𝜔 for the near-wall region, which makesthe best use of a good performance of 𝑘-𝜔 near the wallwhile avoiding the sensitivity of this model to the freestream omega value; see Menter [10]. An improved near-wall formulation used in this model leads to a reduction ofthe near-wall grid resolution requirements, meaning that thesolution is insensitive to the 𝑦+ value.Thus, employing SST incomplicated cases like wind turbines is convenient because ofthe difficulties in achieving a low 𝑦+ value.

A tetrahedral mesh is generated using the ANSYS ICEMCFD. The applied hybrid tetrahedral mesh includes layers ofprism elements near the wall boundary surfaces and tetra-hedral elements in the interior region. The prism-meshinglayer has elements perpendicular to the surface and makesit possible to keep the 𝑦+ value nearly constant over thewall regions. The surface mesh type is a triangle with amaximum size element of 0.5m2 and a maximum deviationof 0.01, where the use of such low deviation values allowsfor the subdivision of the element surface on the centroidof a triangle element in order to enhance mesh deformationaround the surfaces. Figure 4 shows the surface mesh aroundthe bladewith a 2D section of the blade boundary-layermesh.The resulting boundary-layer mesh for each blade consists of15 layers with a first-layer thickness of about 2.85 × 10−3mand a growth ratio of 1.2. Tetrahedral elements are chosen

for the flow volume domain so that the mesh refined inthe inner region allows for a better flow resolution near therotor.

Due to the different boundary conditions it is appro-priate to divide the computation domain into two domains,which are stationary and rotating domains. The simulationsdomains considered in this study are shown in Figure 5; inCase I the rotor is housed in a cylindrical rotating domain thatis enclosed by another cylindrical stationary flow domain.Interfaces have been defined between the stationary domainand the rotating domain to weakly impose the continuityof the kinematics and traction. Case II has a similar setupas Case I, but the stationary domain contains the nacelleand tower. Due to the near-wall refinement, the maximumcalculated 𝑦+ value is 200. Finally, the total numbers ofelements in Case I and Case II are about 10.218 and 11.326million cells, respectively.

The next step is to define the boundary conditions for theentire domain. First, a uniform wind speed and an air tem-perature of 25∘C are set at the inlet boundary. At the outlet,an opening boundary condition is applied, which means theflow can exit or enter through this boundary surface. A staticpressure value is specified at zero so that the pressure at theoutlet is equal to the atmospheric pressure (standard pressureat sea level is 101,325 Pa). The opening boundary condition isalso applied on the side boundaries as well as on the top andbottom boundaries of the computational domain. A no-slipboundary condition is applied on thewall of the blades, tower,and ground.

In order to solve the transient problem, the initialconditions must be specified in the stationary and rotatingsubdomains. For the stationary subdomain, a parallel inflowvelocity is applied. For the rotating subdomain, the rotor'sangular velocity is considered. The selected size of the timestep is 1 × 10−4 sec. The time step allows for an appropriatetime resolution of the flow problem and for maintaining thecourant number below 1.

The computation using the RANSE solver is carried outby employing 32 processors in an in-house cluster, with2.2GHz for each processor and 121.7 GB of memory. The


Case I setup

Case II setup

Stationary domain Rotating domain

Stationary domain

Rotating domain

Inlet

Inlet

Outlet

Outlet

Drotor

Ground

X

Y

Z

3Drotor

3Drotor

2Drotor

4Drotor

2Drotor

Length = 6Drotor, height = 2Drotor and width = 3.2Drotor

Figure 5: Domain dimensions.

CPU time is thus 96 and 104 hours for Case I and Case II,respectively.TheBEMuses 4 processorswith 3.3 GHz for eachprocessor and 7GBofmemory.TheCPU time is thus 12 hoursfor Case I and 24 hours for Case II.

5. Results

As mentioned above the flow on a 5MW HAWT hasbeen analysed using two different methods, a BEM anda RANSE method. The aerodynamics loads are calculatedin the RANSE simulation by considering both pressureand viscous forces, where in the BEM simulation only thepressure force is considered. The comparison between theresults of both applied numerical methods is given for thepressure distribution on the rotor blade, the thrust, andtorque coefficients.

Figure 6 gives an overview on the calculated pressure onthe blade surface. In general, a good agreement between theresults of both methods can be noted, with the exception ofresults obtained for the region close to the blade root.

The first portion of the blade has a cylindrical similarshape which follows by a series of DU (Delft University)airfoils which twists with high angle of attack. The BEMunderpredicts the drag in this region, whereas the results of

the RANSE solver show a thick boundary layer and a severeflow separation due to the strong adverse pressure gradient,which leads to a high drag force. This region starts at theblade root and continues until 𝑟/𝑅 = 0.40. Compared withBEM, the applied RANSE solver is able to capture the mostimportant viscous effects in this region of the rotor blade suchas the high thickness of the boundary layer displacement andits influence on the pressure distribution.

In order to carry out a more detailed comparison,different results will be presented for four blade sections(𝑟/𝑅 = 0.31, 0.63, 0.80, and 0.95). The blade radius 𝑟/𝑅 =0.63 is considered to be representative to aerodynamic rotorat the middle of the blade, while at 𝑟/𝑅 = 0.95 sectionstrong influence of the tip vortex must be expected; andthe radius of 𝑟/𝑅 = 0.80 is considered to be representativeto the flow between the middle and the tip. The bladesection at 𝑟/𝑅 = 0.31 is close to blade root and has apronounced separation region as mentioned before. Figure 7shows pressure coefficient distributions for the four 2D bladesections against the normalized chord. The nondimensionalpressure coefficient is calculated using the following formula:

𝐶𝑝 = (𝑝 − 𝑝∞)(0.5𝜌∞ [V2∞ + (Ω𝑟)2]) , (10)


Face blade (pressure) side

1200

−12

00

−80

0

400

1600

2000800

−400

−16

00 0−20

00

Pressure (Pa)

(a)

Face blade (pressure) side

1200

−12

00

−80

0

400

1600

2000800

−400

−16

00 0

−20

00

Pressure (Pa)

(b)

Back blade (suction) sideLimited region

1200

−12

00

−80

0

400

1600

2000800

−400

−16

00 0

−20

00

Pressure (Pa)

(c)

Back blade (suction) side

1200

−12

00

−80

0

400

1600

2000800

−400

−16

00 0

−20

00

Pressure (Pa)

(d)

Figure 6: Pressure distribution on the blade surfaces: CFX (a and c) and panMARE (b and d).

panMARECFX

Cp

r/R = 0.31

−4

−3

−2

−1

0

1

2

0.2 0.4 0.6 0.8 10x/c

(a)

panMARECFX

Cp

r/R = 0.6

−3

−2

−1

0

1

2

0.2 0.4 0.6 0.8 10x/c

(b)

panMARECFX

Cp

r/R = 0.8

0.2 0.4 0.6 0.8 10x/c

−3

−2

−1

0

1

2

(c)

Cp

panMARECFX

r/R = 0.95

0.2 0.4 0.6 0.8 10x/c

−3

−2

−1

0

1

2

(d)

Figure 7: Pressure coefficient distributions at different blade sections.


where (V∞) is the inflow velocity, (Ω) is the rotor angularvelocity, and (𝑟) is the radius. The BEM results include thepressure distribution on the blade, which can be integratedto calculate the force vector acting on the blade surface. Asis well known, the component of this force vector normal tothe inflow velocity is the lift force, and in the direction ofthe inflow, it is the pressure-induced drag force. The BEMis able to calculate the pressure-induced drag force; however,the viscous component of the drag force cannot be estimatedbecause important viscous effects such as boundary layer andflow separated flows are neglected. It should be mentionedthat the viscous drag force can be added as an external forcewhich can be calculated using an empirical formula for thefriction coefficient. The friction coefficient can be calculatedbased on the Reynolds number built by the local velocity onthe body surface panel. In the presented results of the study,no external drag force is taken into account.

As shown in Figure 7, the stagnation pressure value atthe aerofoil tip 𝑥/𝑐 = 0 is higher than the middle and rootsections on both the suction side (bottom curve) and pressureside (upper curve), and its value equals 1. An acceptableagreement can be seen on the pressure side (upper curve)where the pressure is almost positive, while there are alsodifferences on the suction side (bottomcurve) and the trailingedge regions. At the suction side, the pressure until 𝑥/𝑐 = 0.3has the lowest value with the highest Reynolds number; afterthis region, the pressure increases from its minimum value tothe value at the trailing edge. The value of 𝐶𝑝 at 𝑥/𝑐 = 1 isalmost zero at the trailing edge. The pressure at the trailingedge is influenced by the aerofoil thickness and shape nearthe trailing edge; if the aerofoil is thick, the pressure is slightlypositive (the velocity is a bit less than the free streamvelocity).But with sharp trailing-edge aerofoils, the 𝐶𝑝 value is closeto zero, as in the presented aerofoils. Large positive values of𝐶𝑝 at the trailing edge imply more severe adverse pressuregradients. Determining the pressure coefficient is a hardertest for the simulation since it is a local quantity.

Figure 8 shows the streamlines over the same four bladesections. Only the flow at the blade section 𝑟/𝑅 = 0.31 showsseparation region near the leading edge, whichmay be a resultof the high angle of attack (about 10∘) at this blade section.Theeffect of boundary layer separation increases with an increasein the angle of attack. The results of the other blade sectionsshow tiny separation areas near at the trailing edge.

It is evident that the presence of the tower has a strongeffect on the inflow velocity and on the wake behaviourdownstream, with a considerable reduction in wind speed infront of the tower. The axial distance between the rotor planeand the tower is generally kept as small as possible to limitthe length of the nacelle. On one hand, a high nacelle lengthwill increase the moments induced by the rotor blades on thetower. On the other hand, a small distance between the rotorand the tower increases the aerodynamic interaction betweenflow around the tower and the rotor blades.The reduced flowvelocity to the rotor blades as they pass through the towerregion has a significant impact on the performance of thewhole unit. The reduced velocity in front of the tower canlead to a strong change in the effective aerodynamic angle ofattack of the rotor blade. Both effects lead to a sudden change

of the lift force on the rotor blade, which strongly affects theaerodynamic loading of the wind turbine. The actual 5MWwind turbine uses blades with increasing tower clearancewithout a large rotor overhang. Therefore, precone and tiltangle are considered relative to the baseline wind turbine toreduce these negative effects [15].

Figures 9(a) and 9(b) show pressure coefficient distribu-tion against a normalized chord predicted by both the BEMandCFX at spanwise cross section 80% from the blade lengthon two rotor blades, which have an instantaneous angularposition of 0∘ and 120∘ degrees relative to the tower. Themaximum value of the pressure coefficient at 0∘ underlies apressure drop of 10–15%.

The influence of the rotor on the pressure distribution ofthe tower is illustrated in Figures 10 and 11. Figures 10(a)–10(c)include the results for 0∘ relative angle between the towerand the blade. The corresponding results for 60∘ degreesare presented in Figures 11(a)–11(c). The calculated pressuredistribution obtained by the CFX method can be seen inFigures 10(a) and 11(a) and the corresponding values by theBEM are presented in Figures 10(b) and 11(b). Moreover,Figures 10(c) and 11(c) contain a comparison of the stagnationpressure values on the tower leading edge. The results showthat the pressure decreases on the tower leading edge whenthe blade passes the tower, where this sudden drop createsa definite impact on the tower and the blade loading duringevery blade passage, and has a great effect on the fatigue lifeof the blade and the tower. The differences between the BEMand RANSE method results in the region close to the towertop may be because the nacelle geometry is neglected and thewake treatment in the BEM is simplified.

The unsteady nature of the flow, due to unsteady interac-tion between the rotor and tower, is introduced for a periodof 35 sec (7 revolutions) in order to ensure that the convergedperiodical behaviour of the results has been achieved.

Figure 12 shows the time history of the torque andthrust for Case I and Case II (with and without presenceof the tower). The results of both solvers show that therotor develops an aerodynamic torque, which corresponds to5MW, similar to the results presented in Bazilevs and Hsu[18]. As the calculated values of both methods give similarresults for the torque, it can be assumed that the appliednumerical grid and the employed boundary conditions aswell as the used setup of the computations are accurateenough to characterise the temporal and spatial natures ofthe flow of the HAWT.The results presented for Case II showthat the calculated thrust and torque values have a periodicalbehaviour due to the blade-tower interaction where everypeak refers to one blade passage in front of tower. Themean thrust value and the amplitude of the thrust oscillationobtained by panMARE are slightly higher than the resultscalculated by CFX; however, the amplitude of the torqueoscillation obtained by panMARE is lower. It is clear from thisresult that RANSE solver needsmore than two revolutions foran accurate results predication.

Figure 13 shows the force time history on the tower in theflow direction (𝑥-direction). Both computational methodspredict nearly the same amplitude and force fluctuation.It is also observed that the time history curve shows


r/R = 0.31

panMARECFX 120

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)

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panMARECFX

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Figure 8: Velocity contour over blade in different sections.

multipeaks for the force in both results. The wake effectson the tower force predicted by the BEM are stronger andthe peak takes place directly after the blade passing. Themagnitude of the force is reduced after passing the tower.The calculated tower force characteristics in the BEM maybe strongly influenced by the applied method to treat thewake singularity. The tower force obtained by the RANSEsolver shows different behaviour but the calculated amplitudeof the force fluctuation by both methods is nearly thesame.

Furthermore, the cylindrical shape of the tower meansa large separated flow region takes place; the separatedflow region and its influence on the tower forces cannotbe predicted by the panel method so the devolution of

the tower forces cannot be expected to show a similartendency.

6. Conclusions

The flow on a 5MWHAWT is simulated by using two differ-ent methods: BEM and a RANSE solver.The BEM is based onthe potential theory, where the flow is assumed to be incom-pressible, irrotational, and inviscid. The RANSE method isthe ANSYS CFX, which solves the RANS equations. In thepresented study, the SST turbulence model is used. The BEMand RANSE methods have shown a strong potential forsimulating the aerodynamics of wind turbines. The RANSEmethod is able to capture complex flow phenomenon such as


Blade in front of towerBlade has 120 deg. from tower

0.2 0.4 0.6 0.8 10x/c

−3

−2

−1

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1

2C

p

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Cp

Blade in front of towerBlade has 120 deg. from tower

−3

−2

−1

0

1

2

0.2 0.4 0.6 0.8 10x/c

(b)

Figure 9: Pressure coefficient distribution for 𝑟/𝑅 = 0.80 at different blades position from the tower predicted by (a) CFX and (b) panMARE.

−100

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−40 0 40 80 120−80

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Figure 10: Pressure distribution on the tower when the blade has 0 deg. from tower: (a) CFX; (b) panMARE; (c) on the tower leading edgefor both codes.

separation and tip vortex flows as compared with the BEM;however, the application of theRANSEmethod ismore costly.TheBEMpredicts the attached flow around the blade surfaceswithout the consideration of the boundary layer region,separation, and stall flow effects, which can be calculatedby a RANSE solver. The comparison of the calculated localpressure distribution and the velocity streamlines aroundfour blade sections by the two solvers shows an acceptableagreement on blade pressure side but small deviations on theblade suction side, especially near the leading edge area inthe root region. The flow over the leading edge of the bladedoes not show any noticeable separation with an exceptionin the root region until 𝑟/𝑅 = 0.40, due to the cylindrical

shape of the blade sections in the root region and the highangle of attack of its aerofoils. The results show a smallseparation region near the trailing edge of the sections nearthe blade tip. The calculated torque and thrust values by theBEM method are nearly similar to the results obtained bythe RANSE solver. The calculated time histories of torqueand thrust due to the blade-tower interaction by the twosolvers are compared. The time histories obtained by the twosolvers show different characteristics but the amplitude of thefluctuation is nearly the same. The computation using theRANSE solver is carried out in an in-house cluster and theCPU time is thus 96 and 104 hours for Case I and Case II,respectively. The BEM uses the personal computer and the


−100

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400403

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sure

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−100

−80

−60

−40

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Figure 11: Pressure distribution on the tower when the blade has 60 deg. from tower: (a) CFX; (b) panMARE; (c) on tower leading edge forboth codes.

CFX

Case ICase II

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Figure 12: Time history of aerodynamic torque and thrust for Case I and Case II.


panMARECFX

Fx(T

ower

)(k

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4 8 120Time (sec)

−40

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Figure 13: Time history of force on the tower at inflow direction.

CPU time is thus 12 hours for Case I and 24 hours for CaseII.

The simulation results confirm that a BEM such aspanMARE is able to capture the main flow properties aroundwind turbine blades, including the blade-tower interaction,with less cost and time than RANSE methods and that theBEM can be a powerful tool to support the design process ofHAWTs.

Competing Interests

The authors declare that they have no competing interests.

References

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[6] C. G. Gebhardt, S. Preidikman, and J. C. Massa, “Numericalsimulations of the aerodynamic behavior of large horizontal-axis wind turbines,” International Journal of Hydrogen Energy,vol. 35, no. 11, pp. 6005–6011, 2010.

[7] H. Kim, S. Lee, and S. Lee, “Influence of blade-tower interactionin upwind-type horizontal axis wind turbines on aerodynam-ics,” Journal of Mechanical Science and Technology, vol. 25, no. 5,pp. 1351–1360, 2011.

[8] H. Dumitrescu and V. Cardos, “Wind turbine aerodynamicperformance by lifting line method,” International Journal ofRotating Machinery, vol. 4, no. 3, pp. 141–149, 1998.

[9] S. G. Lee, S. J. Park, K. S. Lee, and C. Chung, “Performanceprediction of NREL (National Renewable Energy Laboratory)Phase VI blade adopting blunt trailing edge airfoil,” Energy, vol.47, no. 1, pp. 47–61, 2012.

[10] F. R. Menter, “Two-equation eddy-viscosity turbulence modelsfor engineering applications,” AIAA Journal, vol. 32, no. 8, pp.1598–1605, 1994.

[11] M. Keerthana,M. Sriramkrishnan, T. Velayutham, A. Abraham,S. Selvi Rajan, and K. M. Parammasivam, “Aerodynamic analy-sis of a small horizontal axis wind turbine using CFD,” Journalof Wind and Engineering, vol. 9, no. 2, pp. 14–28, 2012.

[12] S. Derakhshan, A. Tavaziani, and N. Kasaeian, “Numericalshape optimization of a wind turbine blades using artificial beecolony algorithm,” Journal of Energy Resources Technology, vol.137, no. 5, Article ID 051210, 2015.

[13] M. Bauer and M. Abdel-Maksoud, “Propeller induced loadson quay walls,” in Proceedings of the 2nd Workshop on Portsfor Container Ships of Future Generations, vol. 22, Instituteof Geotechnics and Construction Management of HamburgUniversity of Technology, Hamburg, Germany, February 2011.

[14] M. Greve, Non-viscous calculation of propeller forces underconsideration of free surface effects [Ph.D. thesis], Fluid Dynamicand Ship Theory Institute, Hamburg University of Technology,2015.

[15] J. Jonkman, S. Butterfield, W. Musial, and G. Scott, “Definitionof a 5-MW reference wind turbine for offshore system devel-opment,” Tech. Rep. NREL/TP-500-38060, National RenewableEnergy Laboratory, Golden, Colo, USA, 2009.

[16] Y. Bazilevs, M.-C. Hsu, I. Akkerman et al., “3D simulation ofwind turbine rotors at full scale. Part I: geometry modeling andaerodynamics,” International Journal for Numerical Methods inFluids, vol. 65, no. 1–3, pp. 207–235, 2011.

[17] J. Katz and A. Ploklin, Low-Speed Aerodynamics, CambridgeUniversity Press, Cambridge, UK, 2001.

[18] Y. Bazilevs and M.-C. Hsu, “Fluid-structure interaction mod-eling of wind turbines: simulating the full machine,” Computa-tional Mechanics, vol. 50, no. 6, pp. 821–833, 2012.

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Research Article Investigation of the Unsteady Flow Behaviour...

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