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Assessment of turbulence models for the simulation of the flow through a megawatt scale wind turbine rotor

Authors:
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+ · (νU) + 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=ShH(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 m2s2, and the dissipation rate, ω= 20.5649 s1,
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 106based 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 kωSST. 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 0azimuth angle represents the blade aligned in the z-direction
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
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 kωSST 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 kωSST
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 kωSST.
Therefore, considering the computational cost comparison, the performance of DES kωSST model was slightly better
over the URANS kωSST.
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 kωSST turbulence models.
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
of flow structures with indicated with higher definition the flow behaviour were captured considering the DES kωSST
over RANS kωSST 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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