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EPTT-2022-0008

Assessment of Turbulence Models for the Simulation of the Flow Through a

Megawatt Scale Wind Turbine Rotor

Marielle de Oliveira

marielledeoliveira@usp.br

Rodolfo C. Puraca

rodolfo.puraca@usp.br

Bruno S. Carmo

bruno.carmo@usp.br

Department of Mechanical Engineering, Escola Politécnica - University of São Paulo - Brazil

Abstract. The increase of the size of wind turbines to deliver power at megawatt scale, particularly for offshore applica-

tion, brings a number of engineering challenges. The numerical modeling of these systems, considering the wind turbine

geometry in full scale, is a valuable tool for design and performance analysis. To properly model the interaction between

the turbine and the wind we need a proper turbulence model. This paper presents a comparison of two of the most used

turbulence models, the Unsteady Reynolds Averaged Navier-Stokes (URANS) k-ωSST and the two-equation Detached

Eddy Simulation (DES) applied in blade-resolved simulations of the NREL 5 MW reference wind turbine, in order to

predict the rotor performance when it operates in optimal wind-power conversion efﬁciency, for a wind speed of 10 m/s

at hub height. The power production, generated thrust, and forces distribution along the blade span were estimated.

The computational analyses were carried out using a Computational Fluid Dynamics (CFD) methodology employing the

Finite Volume Method (FVM) implemented in the OpenFOAM software. A numerical veriﬁcation was conducted by com-

paring the CFD results against values obtained using the blade element momentum theory, implemented in OpenFAST.

The performance of each turbulence model was assessed considering the computational cost and accuracy of the results.

Both turbulence models presented satisfactory results when comparing with the results from OpenFAST, for the same

environmental condition investigated. However the wake internal gradient present different patterns. For the DES model

it was possible to observe with higher resolution the effects of the blade in the near wake region. In addition, a different

behavior of the ﬂow that detaches along the blade span and transitions to the wake external pattern was also observed

when comparing the turbulence models.

Keywords: NREL 5 MW Wind Turbine Rotor, Blade-resolved Simulations, Iterative PISO Solver, Turbulence Models,

Computational Cost Analysis

1. INTRODUCTION

With the continued expansion of the wind energy industry over the past decade, which aims to contribute signiﬁ-

cantly to the global energy transition, besides the increase of wind power in emerging markets such as China, India, and

Brazil, the growth of wind turbines operating in offshore installations was also noticed (Council, 2022; El Bassam, 2021).

Consequently, due to the development of wind energy in offshore areas, which can present outstanding wind resources

(Ostachowicz et al., 2016; Karimirad, 2014), the changes in the size of wind turbines to higher scales present intrinsic

challenges.

The offshore sites present environmental conditions such as atmospheric boundary layer and turbulence varying spa-

tially, which directly affects the prediction of the aerodynamic loads and wake behaviour of the wind turbines. Therefore,

along with the arising of the new generation of wind turbines which include higher costs associated in both fabrication

and installation process, the need of better tools to accurately predict the loads acting in the offshore wind turbines (OWT)

become an important task.

Up to date, the experimental campaigns which were conducted to obtain information about the unsteady three-

dimensional aerodynamic behaviour of horizontal-axis wind turbine (HAWT), such as presented by Hand et al. (2001a,b),

have shown that the aerodynamic loads and that 3D effects are prevalent, resulting in a complex system to be accurately

represented experimentally. Even though the data have been used to validate and enhance engineering models, due to

the ever increasing power capacity of OWTs to scales of 3 MW, 6 MW (Hayes et al., 2021), and more recently DTU

10 MW, GE’s Haliade-X 14 MW, and IEA 15 MW (Bak et al., 2013; Jiang, 2021; Gaertner et al., 2020), the development

of high ﬁdelity numerical models capable of capturing the inﬂuence of these three-dimensional effects to better predict

the OWT performance is necessary as a reliable tool in the OWT design (Hand et al., 2001b; Zhang et al., 2019). Among

the numerical options to deal with these effects, computational ﬂuid dynamics (CFD) has been applied through different

methods, and has shown to be a mature approach to investigate the unsteady aerodynamic behaviour of the ﬂow around

wind turbine blades and generated wakes (Sanderse et al., 2011; Thé and Yu, 2017).

The numerical investigations available in the literature which considered a CFD approach to investigate the ﬂow around

M. Oliveira, R. C. Puraca and B. S. Carmo

Assessment of Turbulence Models for the Simulation of the Flow Through a Megawatt Scale Wind Turbine Rotor

a wind turbine rotor blade with a blade-resolved modeling (Sorensen and Hansen, 1998; Duque et al., 1999, 2003; Zhang

et al., 2019) showed that the numerical solution of the Navier-Stokes (N-S) equations, which needs special treatment to

proper represent the turbulence effects, still requires efforts since the solution through the direct numerical simulations

(DNS) to analyse the wind turbine performance is yet not feasible.

A different approach is given by the large-eddy simulation (LES) method, in which the equations are solved taking into

account a ﬁltered velocity ﬁeld, so the larger scales of the turbulent motion are represented, whereas the smaller scales of

the turbulent motions, also called as subgrid-scales (SGS), are modeled (Pope, 2001; Wilcox et al., 1998). As part of the

turbulence modeling technique considered in the numerical investigations of engineering problems, the Reynolds-Average

Navier-Stokes (RANS) procedure is vastly applied, due to the solution of the Reynolds equations which determines the

mean velocity ﬁeld (Pope, 2001). In sequence, the Unsteady Reynolds-Averaged Navier-Stokes (URANS) nomenclature

started to be used, since the RANS models are unsteady even when considering steady boundary conditions (Spalart,

2000). In addition, as a result of this mathematical procedure, the Reynolds stress tensor requires the use of turbulence

models to be evaluated (Wilcox et al., 1998; Pope, 2001).

Among the ample variety of turbulence models, to represent the aerodynamic loads under the inﬂuence of considerably

adverse pressure gradient, the URANS approach is commonly linked to the two-equation k-ωSST turbulence model

(Menter, 1992, 1993, 1994). To date, the URANS k-ωSST turbulence model has been used in the modeling of wind

turbines conducted in the OpenFOAM software for a small-scale HAWT and presented good agreement in terms of the

wind turbine performance coefﬁcient between the CFD results and the calibrated experimental tests (Rocha et al., 2014).

More qualitative and quantitative agreement between the results from the CFD modeling of a similar problem, consid-

ering the same turbulence modeling and experimental tests, were found also in the prediction of the velocity proﬁles in the

wake region in the MEXICO project (Sørensen et al., 2014). More recently, the URANS k-ωSST turbulence model was

successfully applied to represent the turbulence effects in the numerical modeling of the NREL 5 MW wind turbine in full

scale, including the tower inﬂuence, to represent the ﬂow around the blades and in the wake region. Since there was no ex-

perimental data available, the authors conducted a veriﬁcation procedure benchmarking the blade-resolved results against

the results obtained with the OpenFAST software for the same environmental conditions, and presented good agreement

in terms of the power production, generated thrust and distributed forces along the blade span (de Oliveira et al., 2022).

Usually, the preference for URANS-based models instead of LES or DNS approaches is related to the computational

costs which is largely determined by the resolution requirements (Pope, 2001). Even though LES is advantageous when

comparing to URANS in the modeling of anisotropic turbulent ﬂow, in which large-scale structures are dominant, in the

numerical analysis of the ﬂow around wind turbines, the model is recommended to be applied only in the wake region

(Sanderse et al., 2011), due to the fact that the LES approach present difﬁculties to determine the ﬂow properties in the

wall region of the boundary layer (Wilcox et al., 1998; Spalart, 2000).

In this regard, since LES even when implemented with a proper wall-region modeling is not viable to predict unsteady

aerodynamic loads (Spalart, 1997), the hybridization of LES into a improved approach such as the Detached-Eddy Simu-

lation (DES) model allow the numerical modeling of the turbulence effects to a manageable computational demand even

for ﬂows at high Reynolds numbers (Shur et al., 1999; Nikitin et al., 2000; Spalart, 1997).

Whereas the application of DES in aerodynamics is promising due to the possibility of applying the URANS-based

models in the large areas of the boundary layer while in the regions in which the momentum transfer is dominated by

large structures LES is efﬁciently applied (Spalart, 2000), few investigations have implemented the DES approach in the

blade-resolved CFD simulations of a megawatt scale wind turbine, due the difﬁculties of proper connecting the numerical

model setup with the more suitable spatial and temporal discretization. For example, in the investigations performed by

Lawson et al. (2019), the authors used DES to represent the ﬂow around the NREL 5 MW wind turbine blades and wake

region. However, the quasi-steady regime for the power and thrust, which typically requires around 5-6 rotor revolutions

to be established, was not achieved even for the coarsest mesh tested, due to the mesh strategy employed, which presented

a high computational demand, indicating that more efforts were still required to better comprehend the efﬁciency of the

method when comparing the results accuracy and computational costs.

With the increase in the wind turbines scale such as 15 MW, the numerical modeling in full scale becomes even more

challenging, and the need of a optimized turbulent model to represent the unsteady aerodynamics load more evident.

Therefore, in order to cover these needs, the target of this paper is to present a comparison between the URANS k-ω

SST and DES-two equations turbulence models applied in the blade-resolved CFD simulations to adequately predict the

aerodynamic loads of the baseline NREL 5 MW wind turbine rotor in full scale (Jonkman et al., 2009), under the operating

condition of optimal wind-power conversion efﬁciency.

Since these simulations are computationally expensive and challenging to set up the turbulence model properly, in the

present investigation we are not taking into account the tower inﬂuence, nevertheless we hope the discussion and results

presented in the next sections regarding the rotor-only investigation, considering different turbulence models, can be used

to help in the modeling and simulation of other large wind turbines.

13th Spring School on Transition and Turbulence

September 19th-23rd, 2022, Blumenau, SC, Brazil

2. METHODOLOGY

To conduct the numerical investigations and capture the effects of the different turbulence models tested, we considered

the same numerical discretization schemes and also the same spatial and temporal discretization strategies for each case.

The investigations were carried out considering the open source OpenFOAM software and the performance of the wind

turbine rotor-only simulations was evaluated in terms of power production, generated thrust, distributed forces along

the blade span and wind proﬁle in different positions in the wake region. As a veriﬁcation procedure, the CFD results

were benchmarked against the results obtained with OpenFAST (National Renewable Energy Laboratory, 2021), which

implements the blade element momentum method, considering the same NREL 5 MW wind turbine rotor-only, at the

same environmental conditions. Finally a computational cost analysis was conducted between the two different turbulence

models to allow us to understand the performance of each one considering the numerical arrangement chosen.

In this section we describe the governing equations considered to model the problem and also some details about the

solver parameters and discretizations schemes employed in the CFD investigation.

2.1 Governing Equations

As the problem being investigated is represented by a transient three-dimensional incompressible ﬂow, the governing

set of equations is given respectively by the conservation of mass and conservation of momentum equations, as:

∇ · U= 0,(1)

∂U

∂t +∇ · (UU) = −∇p+∇ · (ν∇U) + f,(2)

where tis time, νis the kinematic viscosity, Uis the velocity vector, pis the kinematic pressure and frepresents the body

forces.

In this work we discretize the governing equation given by Eqs. 1 and 2 considering the ﬁnite volume method (FVM)

in which detailed information can be found in Versteeg and Malalasekera (2007); Patankar (2018). In this regard, the

discretization of the non-linear term given by the convective term in Eq. (2) leads to

∇ · (UU) = X

f

S(Uf)(Uf) = X

f

F(Uf),(3)

∇ · (UU) = aPUP+X

N

aNUN,(4)

where the coefﬁcients aPand aNare related to the values interpolated at the faces of the control volume P and its

neighbors indicated by N, and are functions of the velocity U.Ufis the control volume velocity at the face cell, and

Sis the area vector pointing out of the volume cell with magnitude equal to the face area, while Frepresents the term

S·(ρU)f, which is the mass ﬂux through a general face.

Due to the complexity of the non-linear solvers and consequent computation effort required, a linearisation of the

convective term is recommended. Considering the type of ﬂow being investigated, the calculation of the Fterm is

performed using a numerical upwind-based method, to guarantee the boundedness of the solution by preserving positive

coefﬁcients in the linear algebraic equation matrices (Jasak, 1996; Versteeg and Malalasekera, 2007).

The discretized form of the continuity equation, Eq. (1), is given by

∇ · U=X

f

SUf= 0.(5)

More details about the step-by-step in the discretization process by the FVM can be found in de Oliveira et al. (2022);

Versteeg and Malalasekera (2007). Therefore, the discretized form of the incompressible Navier-Stokes equations are

given by

aPUP=H(U)−X

f

S(p)f,(6)

X

f

Sh 1

aPf(∇p)fi=X

f

SH(U)

aPf,(7)

with the calculation of the face ﬂuxes Fgiven by

F=SUf=ShH(U)

aPf

−1

aPf(∇p)fi.(8)

M. Oliveira, R. C. Puraca and B. S. Carmo

Assessment of Turbulence Models for the Simulation of the Flow Through a Megawatt Scale Wind Turbine Rotor

2.2 Turbulence Modeling

To complete the numerical arrangement to conduct the blade-resolved CFD simulations, an additional set of transport

equations to represent the turbulence are required in order to obtain an approximate solution for the Navier-Stokes set of

equations. According to Wilcox et al. (1998), an ideal turbulence model should minimize the complexity of the ﬂow ﬁeld

in order to capture the features of the most signiﬁcant part of the physical system. As aforementioned mentioned in the

section 1., the main objective of our work is to compare different turbulence modeling approaches in the blade-resolved

simulation of a megawatt scale wind turbine rotor, focusing on the estimate of the rotor performance through the prediction

of the power production, generated thrust, distributed forces along the blades, wind proﬁle at different positions of the

wake region and the comparison of the ﬂow structures obtained by each approach.

Even though the URANS method along with the two-equations k-ωSST turbulence model is the most common

and vastly used method to represent the physics of similar investigation (Rocha et al., 2014; Sorensen and Hansen, 1998;

Robertson et al., 2015; de Oliveira et al., 2022), with the increase in the wind turbine scale to cover the offshore application

needs, the DES model has been put forward as a promising solution since it improves the accuracy of the results prediction,

with less computational cost than LES (Zhang et al., 2015).

2.2.1 URANS k-ωSST Approach

The URANS approach comes from a statistical averaging procedure applied to the Navier-Stokes equations, from

which the nonlinear Reynolds stresses tensor term and consequent closure problem arise requiring the turbulence models

to establish a sufﬁcient number of equations to solve all the ﬂow properties (Wilcox et al., 1998; Pope, 2001).

One way to obtain a solution for the Reynolds stresses tensor in means of known quantities is using the mean velocity

gradient. In this regard, the most popular approach is to use the turbulent-viscosity hypothesis, introduced by Boussinesq

(Pope, 1975) which, according to the hypothesis, the deviatoric part of the Reynolds stress tensor is proportional to the

mean rate of strain (Pope, 2001).

Therefore, the relation between the turbulent tensor and the turbulent viscosity, also called as eddy viscosity, imposes

the idea that the transfer of momentum by diffusion in molecular level is similar to the transfer of momentum in a turbulent

ﬂow due to the turbulent ﬂuctuations. The evaluation of the kinematic eddy viscosity, νt, can be made by solving the

transport equations with the use of auxiliary relations. However, the most common method to obtain the kinematic eddy

viscosity is considering a function which correlates it with the speciﬁc turbulent kinetic energy and its speciﬁc dissipation

rate, such approach stands out for the so called two-equations turbulent model (Wilcox et al., 1998; Pope, 2001).

In this work for the URANS turbulence modeling approach we employed the two-equations k-ωSST model from

Menter (1994), due its ability of predict ﬂows with strong adverse pressure gradient with higher performance when

compared to the variation of the k-ωmodels from Wilcox et al. (1998), and the baseline from Menter (1993). Thus, by

considering the k-ωSST model, a new set of governing equations is obtained. In the ﬂow region close to the rotor walls,

low-Reynolds corrections are applied due to the near-wall region treatment.

2.2.2 DES k-ωSST Approach

According to Spalart (2000), the limitations of the RANS approach to represent the physics in the boundary layer

region relies in the outer region, where LES captures well the straining, cross-ﬂow and curvature effects, although with

a considerable computational demand over RANS. Therefore, by thanking into account the idea of entrust the RANS

approach in the attached eddies region of the boundary layer, which refers to the region close to the walls, while LES

is applied in the separated region, also called as the detached eddies region, the hybridization of the LES and RANS

models brings out the DES hybrid approach (Spalart, 1997). In addition, DES is an attractive solution for external ﬂows,

since the model is simple to be implemented, and preset stability for both URANS turbulence models, such as, one and

two-equations (Robertson et al., 2015). However, the main challenge in the use of DES model is regarding the user skills

in the determination of a suitable mesh resolution (Spalart, 1997).

Therefore, based on the results obtained by the authors in previous investigations about the blade-resolved simulations

of the NREL 5 MW wind turbine, including the tower interference (de Oliveira et al., 2022), we designed a strategical

spatial discretization, in order to capture the inﬂuence of the hybrid model over the RANS model in terms of the results

accuracy and less computational demand, to be able to perform blade-resolved simulations of a megawatt scale wind

turbine rotor with a more robust turbulence model. Thus, we employed for DES the same turbulence model used for

the URANS approach model, the k-ωSST turbulence model, which is also the reason the approach is called as DES

2-Equations.

13th Spring School on Transition and Turbulence

September 19th-23rd, 2022, Blumenau, SC, Brazil

Figure 1: Visualization of the case being investigated, which includes a 5 MW wind turbine rotor in full scale, (without

the tower an nacelle parts,) operating under a uniform non-turbulent wind proﬁle.

2.3 Near-wall region treatment

As well mentioned in the previous section, the features of the turbulent ﬂow changes considerably by getting closer to

the wall region, in which an appropriated model is required for the estimation of the kinematic eddy viscosity νt. Thus,

a strategical mesh reﬁnement must be considered to estimate the turbulent ﬂow close to the wall, which must satisfy the

requirement of the turbulence model based on the y+variable. In the current investigations, for both turbulence models

being investigated, kand ωwere modeled by the low Reynolds wall functions, which represents a model which can switch

between the viscous and logarithmic regions of the boundary layer according to the position of y+, and also avoid the

buffer layer region at the same time.

Following the same methodology, the kinematic eddy viscosity νtwas calculated using the Spalding wall function

model (Spalding, 1961), which can also switch between viscous and logarithmic regions based on the value of y+.

3. NUMERICAL SIMULATIONS

In this section the setup and parameters considered in each numerical investigations are presented. The main objective

of the CFD simulations were to predict the performance of the NREL baseline 5 MW offshore wind turbine rotor in full

scale, in terms of power production, generated thrust, blade loading and wake aerodynamics pattern analysis considering

two different turbulence models. The rotor geometry in full scale is composed by three blades and the hub, more detailed

information regarding the rotor design are available in Jonkman et al. (2009).

Fig. 1 illustrates the case being investigated, which consists of a 5 MW wind turbine rotor for offshore application

(without the tower interference), placed on an site of operation, under the inﬂuence of a uniform non-turbulent wind

proﬁle.

The simpliﬁcations which were made in the case being modeled, such as, the consideration of a uniform wind proﬁle

and the absence of the tower and nacelle parts in the wind turbine geometry, are typical of rotor-only CFD investigations

(Duque et al., 1999, 2003; Zhang et al., 2019).

3.1 Computational Domain and Boundary Conditions

The rotor and hub geometries were built using the software Solid Edge and imported into OpenFOAM, whereas all

other parts of the computational domain were built around the rotor geometry using the snappyHexMesh utility. Fig. 2

illustrates the computational domain dimensions in meters and the boundary conditions, which were deﬁned based in Hsu

and Bazilevs (2012); de Oliveira et al. (2022).

For both turbulence model investigation, the dimensions of the computational domain were the same, 480 m wide,

640 m long, 480 m high, and the rotor region of 160 m to settle the rotor diameter which is considered as 124 m to take

into account the hub distance between the blades. The same boundary conditions were also considered in the turbulence

models investigation for both cases, in which for the inﬂow the boundary condition for the velocity was of Dirichlet type,

given by a prescribed uniform wind proﬁle of 10 m/s, which was chosen based on Jonkman et al. (2009). According to the

authors, at this wind speed the rotor operates in optimal wind-power conversion efﬁciency. Still at the inﬂow, the boundary

condition for the pressure was a null gradient (Neumann condition). For the turbulent quantities, Dirichlet conditions were

employed, with prescribed values estimated based on the most critical Reynolds number (at the blade tip), through the

turbulence Reynolds number parameter (ReL)as suggested by Pope (2001). Based on that, the turbulence length scale

for this region was 0.175 m, the turbulence kinetic energy k= 3.2651 m2s−2, and the dissipation rate, ω= 20.5649 s−1,

while the kinematic eddy viscosity was calculated based on the internal ﬁeld everywhere. As the wind proﬁle is uniform

for all the side walls, the boundary conditions for the velocity were symmetric plane condition, which corresponds to null

normal velocity and zero normal gradient for the tangential velocity, pressure and turbulent quantities. For the rotor walls,

M. Oliveira, R. C. Puraca and B. S. Carmo

Assessment of Turbulence Models for the Simulation of the Flow Through a Megawatt Scale Wind Turbine Rotor

Inflow

Outflow

Side walls

Rotor zone

Rotor walls

Figure 2: NREL baseline 5 MW offshore wind turbine rotor, computational domain dimensions (in meters) and boundary

conditions.

Far-field

Wake refinement

Rotor refinement

Figure 3: Strategic partition of the computational domain to apply different mesh reﬁnements.

no slip condition was imposed. Since the mesh around this region is dynamic, a uniform rotor velocity of 1.1649 rad/s

was prescribed, which is the rotor speed for a wind speed of 10 m/s, and Neumann boundary condition is applied for the

pressure as a null gradient, while the turbulence properties receive the proper wall function treatment according with the

y+value in the near wall region. At the outﬂow, Dirichlet condition was applied for the pressure as a ﬁxed value equal to

zero, and for the velocity and turbulence quantities had Neumann condition as null gradient.

3.2 Spatial discretization

To perform the turbulence model investigation, for both blade-resolved simulations the same spatial discretization

were considered. The mesh was built considering a strategy similar to the one which was employed by de Oliveira et al.

(2022) in Mesh-2, since it was adequate to present both accuracy in the predicted results at a accessible computational

cost. One of the most important steps during the mesh design is related with the division of the the computational domain

in which the different stages of reﬁnement are applied.

In this regard, for the mesh being used in the present investigations, the computational domain was decomposed in

three main regions as presented in Fig. 3, where in the far-ﬁeld region the ﬁnite volume cells are of the size of 25 m

which decreases into 1.6 m in the wake region and to 0.5 m in the rotor region. In the rotor region the cells size are

reﬁned from 0.5 m to 0.0625 m close to the blades and into 0.001 m at the ﬁrst cell attached to the blades wall in order

to respect the y+parameter within the adequate range for the application of the turbulence model at the near-wall region.

13th Spring School on Transition and Turbulence

September 19th-23rd, 2022, Blumenau, SC, Brazil

Regarding the mesh communication between the static and dynamic parts of the mesh, an arbitrary mesh interface (AMI)

methodology was considered based in (Farrell and Maddison, 2011). Therefore, the spatial discretization strategy applied

resulted in a mesh composed by 25,314,125 ﬁnite volume cells, with a maximum aspect ratio of 75, skewness of 3.9 and

non-orthogonality of 64.4.

3.3 Numerical schemes

The same numerical arrangement regarding the discretization schemes were employed for both turbulence models. The

divergence terms were discretized using a second-order upwind scheme, chosen based on the modeling of similar problems

to compute the convective ﬂuxes. Central differences were employed for the Laplacian terms, and the second order Gauss

scheme was adopted with linear Gaussian integration for the gradient terms. The set of linear equations was solved

based on Muratova et al. (2020); Moukalled et al. (2016), using the geometric-algebraic multi-grid (GAMG) algorithm

for the symmetric matrices, and the preconditioned bi-conjugate gradient (PBiCG) with the DILU preconditioner for the

non-symmetric matrices.

Regarding the temporal discretization, the second order implicit backward scheme was employed, along with the

limited CFL number equal to 1, which was controlled by an adaptive time step to guarantee stability during the iterative

process.

3.4 Solver information

The iterative PISO with face ﬂux correction, as presented in (de Oliveira et al., 2022), was chosen as solver, in which 5

sub-iterations and 2corrections for pressure was performed in each time step for both turbulence models being considered.

For both DES and URANS turbulence models, the solution was considered converged when the residuals of the set of

estimated variables was equal or less than 10−6based in the convergence parameters for transient problems suggest by

Versteeg and Malalasekera (2007). For each case, the initial conditions for the transient problem for all properties were

obtained considering the steady state solution for the problem after 500 iterations, calculated with the steady form of

the SIMPLE algorithm solver. The computations were carried out in the Brazilian supercomputer SDumont. To run the

simulations, in each case the mesh was partitioned into 240 sub-domains using scotch decomposition, using 10 nodes,

where each node had two 12 core Intel Xeon Cascade Lake Gold 6252 processors, 3.7 GHz, and 256 Gb of RAM.

4. RESULTS AND DISCUSSION

First, the results obtained by the two different turbulence models are presented in terms of power production and gen-

erated thrust. Next, a comparison between the computations of the distributed normal and tangential forces are presented.

In sequence, the ﬂow pattern and the vortical structures captured by the URANS and DES are illustrated along with the

analysis of the wind velocity proﬁle at different positions of the wake region. Finally, a comparison in terms of compu-

tational cost is shown in order to understand the performance of each turbulence model considered in the blade-resolved

simulations to predict the unsteady aerodynamic loads of a megawatt scale wind turbine rotor.

4.1 Veriﬁcation with OpenFAST

In order to understand the accuracy in the obtained results by the CFD simulations, the veriﬁcation and validation are

the main recommended methods to quantify the errors and uncertainties (Versteeg and Malalasekera, 2007). However,

in our case there is no experimental data available, so we performed a veriﬁcation procedure by making a comparison

between the results obtained with each turbulence model against the results obtained with a different numerical method

for the same environmental conditions, which was the OpenFAST v2.5.0 code by NREL (National Renewable Energy

Laboratory, 2021). OpenFAST is a code certiﬁed by Germanischer Lloyd (GL) National Renewable Energy Laboratory

(2005), and calibrated by Coulling et al. (2013), which uses the blade element momentum theory and tip corrections to

calculate the aerodynamic loads of three-bladed HAWT, including different environmental conditions in the time domain.

Figure 4 illustrates a comparison of the wind turbine power production and the generated thrust for both turbulence

models tested, the DES 2-Equations, and the URANS k−ωSST. Both turbulence models presented similar results in terms

of integral power and thrust. The mean value for the power was of 3.75 MW by DES and 3.53 MW by the URANS model,

while for the thrust the mean value was of 635 kN, 624.6 kN for both DES and URANS respectively. This similarity

between in results by boh turbulence models were also obtained by (Mittal et al., 2016) for a comparable CFD simulation,

where the author investigated the same turbulence models for a reduced scale wind turbine. Probably the similarity in the

performance results is due to the modeling of the region close to the blades wall, since both turbulence models solve the

same equations.

In addition, the distribution of the mean forces along the blades were also investigated and compared. As presented

in Fig. 5, both methodologies presented similar behaviour in the normal and tangential forces prediction along the blade

span, for the positions of the blade being analyzed. The 0◦azimuth angle represents the blade aligned in the z-direction

M. Oliveira, R. C. Puraca and B. S. Carmo

0 5 10 15 20 25 30 35 40

Time [s]

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

Power [MW]

DES 2-Equations CFL=1

Mean power = 3.75 MW

URANS k- SST CFL=1

Mean power = 3.53 MW

OpenFAST - AeroDyn v15

Mean power = 3.58 MW

(a) Power.

0 5 10 15 20 25 30 35 40

Time [s]

400

450

500

550

600

650

700

750

800

Thrust [kN]

DES 2-Equations CFL=1

Mean thrust = 635.0 kN

URANS k- SST CFL=1

Mean thrust = 624.6 kN

OpenFAST - AeroDyn v15

Mean thrust = 663.1 kN

(b) Thrust.

Figure 4: Generated power and thrust comparison between the DES 2-Equations and URANS k−ωSST turbulence

models, benchmarked against OpenFAST results.

5 10 15 20 25 30 35 40 45 50 55 60 65

Radius [m]

0

1

2

3

4

5

6

7

Normal Force [kN]

DES 2-Equations CFL=1

URANS k- SST CFL=1

OpenFAST - AeroDyn v15

Azimuth angle = 0°

(a) Normal Force.

5 10 15 20 25 30 35 40 45 50 55 60 65

Radius [m]

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Tangential Force [kN]

DES 2-Equations CFL=1

URANS k- SST CFL=1

OpenFAST - AeroDyn v15

Azimuth angle = 0°

(b) Tangential Force.

Figure 5: Distributed forces along the blade span comparison between the DES 2-Equations and URANS k−ωSST

turbulence models, benchmarked against OpenFAST results.

orthogonal with the ﬂow in the x-direction. The agreement between the results is remarkable.

Besides the quantitative analyses of the normal and tangential forces acting on the blades, we performed a comparison

about the instantaneous wind velocity proﬁles after 7 complete revolution at 5 different positions downstream in the wake

region. These results are presented in Fig. 6 along with the instantaneous iso-contours of the mean velocity ﬁeld for

both turbulence models being investigated considering approximately the last 20 seconds of the simulation. It is possible

to observe that both turbulence approach led to similar results in terms of the mean velocity ﬁeld properties. However,

differences in the ﬂow pattern ca also be observed in all positions of the wake region.

A computational cost analysis considering the performance of each of the tested turbulence models showed that both

approaches took approximated 24 hours to complete the simulation of one time unit. However, the execution time to

calculate one time step was on average 18.38 s for the DES 2-Equations, against 18.83 s for the URANS k−ωSST.

Therefore, considering the computational cost comparison, the performance of DES k−ωSST model was slightly better

over the URANS k−ωSST.

5. CONCLUSIONS

A numerical investigation about the performance of a 5 MW wind turbine rotor was conducted considering for the same

numerical arrangement two difference turbulence models, one vastly applied in the investigation of similar blade-resolved

simulations, and another yet being implemented in the simulations of the new generation of wind turbines modeled in its

full scale. In this paper, the rotor-only blade-resolved simulations were performed considering the NREL 5 MW reference

wind turbine for offshore applications. The CFD simulations provided signiﬁcant data from which the performance of

the NREL 5 MW offshore wind turbine rotor in full scale was evaluated, in terms of, power production, generated thrust,

blade loading and wake aerodynamics pattern analysis considering the two different turbulence models tested.

In terms of the computations of the power production, generated thrust and distributed mean tangential and normal

forces along the blade span, both turbulence models presented similar and satisfactory results. However signiﬁcant amount

13th Spring School on Transition and Turbulence

September 19th-23rd, 2022, Blumenau, SC, Brazil

0.125 0.25 0.5 1.0 1.5 0.125 0.25 0.5 1.0 1.5

0.125 0.25 0.5

1.0 1.5

0

2

4

6

8

10

12

Velocity Magnitude

DES URANS

0.4 0.8 1.2

-1.5

-1

-0.5

0

0.5

1

1.5

y/R

x/D = 0.125

0.4 0.8 1.2

Ux/Uh

x/D = 0.25

0.4 0.8 1.2

x/D = 0.5

0.4 0.8 1.2

x/D = 1

0.4 0.8 1.2

x/D = 1.5

DES 2-Equations CFL=1 URANS k- SST CFL=1 Velocity boundary condition at inflow

0.125 0.25 0.5

1.0 1.5

Figure 6: Comparison of the instantaneous wind velocity proﬁles after 7 complete rotor revolutions at 5 x/D different

positions downstream in the wake region along with the iso-contours of the mean velocity ﬁeld at the same positions for

both turbulence models being investigated.

0 500 1000 1500 2000 2500

Time steps amount

15

16

17

18

19

20

Execution time per time step [s]

DES 2-Equations CFL=1

Mean execution time=18.38 s

URANS k- SST CFL=1

Mean execution time=18.83 s

(a) Execution time per time step.

0 5 10 15 20 25

Execution time to complete one time unit [h]

0

0.2

0.4

0.6

0.8

1

Time unit [s]

DES 2-Equations CFL=1

URANS k- SST CFL=1

(b) Execution time to complete one time unit of simulation.

Figure 7: Computational demand comparison between the DES 2-Equations and URANS k−ωSST turbulence models.

M. Oliveira, R. C. Puraca and B. S. Carmo

of ﬂow structures with indicated with higher deﬁnition the ﬂow behaviour were captured considering the DES k−ωSST

over RANS k−ωSST with less computational demand, becoming an attractive solution to be implemented in the modeling

of the new generation of larger wind turbines.

6. ACKNOWLEDGEMENTS

M. de Oliveira acknowledges FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), the São Paulo

Research Foundation, for the PhD grant - Process number 2018/26207-4. R. C. Puraca acknowledges FUSP/Petrobras for

the PhD grant Project number 2019/00171-6. B. S. Carmo acknowledges the support from FAPESP, Proc. 2019/01507-8,

for this research, and thanks the Brazilian National Council for Scientiﬁc and Technological Development (CNPq) for

ﬁnancial support in the form of a productivity grant, number 312951/2018-3. The authors also acknowledge the grant

from the National Laboratory of Scientiﬁc Computing (LNCC), CADASE project, which allowed the use of the Santos

Dumont supercomputer to run the simulations that generated the results reported in this paper. This work is part of the

European Commission Project “High Performance Computing for Wind Energy (HPCWE)” with agreement no. 828799.

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8. RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.