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137

Advances in Renewable Energies Offshore – Guedes Soares (Ed.)

© 2019 Taylor & Francis Group, London, ISBN 978-1-138-58535-5

Blade-resolved CFD analysis and validation of blockage correction

methods for tidal turbines

G. Tampier Brockhaus

Faculty of Engineering Sciences, Universidad Austral de Chile, Valdivia, Chile

F. Zilic de Arcos

Department of Engineering Science, University of Oxford, Oxford, UK

ABSTRACT: Blockage, the ratio between a turbine’s swept area and the channel cross-sectional area,

affects the torque and thrust characteristics of the rotor. These effects are relevant for many reasons,

including the calculation of mechanical, structural and mooring systems, energy production assessment,

etc. The present work describes the analysis and validation of six different blockage correction methods

for tidal turbines, described in literature, with blade-resolved RANS-CFD simulations. The simulations

were performed to seven different blockage rations and 5 tip speed ratios for each blockage case. The

blocked results were corrected with the different methods and compared to the quasi open-flow results

as a measure of the effectiveness of each one of them, showing a relatively good agreement for 4 out of 6

methods. Finally, this paper provides practical recommendations regarding the application of the different

correction methods, including an assessment of the required variables and their scope of application.

β is the blockage expressed as the ratio between tur-

bine area and channel cross-section.

A more complex approach to the problem of

modelling a turbine has been done by the appli-

cation of the Blade Element Momentum method

(BEM), widely employed for turbine and propeller

design (Hansen et al., 2006). The method has been

expanded by several authors to consider effects

such as tip-losses (Wimshurst & Willden, 2017),

turbulent wake effects (Buhl, 2005) and transient

phenomena (Hansen et al., 2004).

Turbine modelling can also be carried on by

means of viscous Computational Fluid Dynam-

ics solvers (RANS-CFD). Different approaches to

model the actual turbines have been implemented

within CFD codes such as actuator disks, actuator

lines or CFD-BEM models.

These provide different levels of detail depend-

ing on the implementation and requirements, rang-

ing from simple wake simulations to actual turbine

design for particular cases. The most complex

approach, however, consists in fully blade-resolved

simulations, where the blade geometry is modelled

as a solid, rotating boundary. This approach gives

insights about the flow in the domain, accounting

inherently for effects such as spanwise flow, flow

separation, etc. (Tampier et al., 2017).

From an engineering perspective, blockage is rel-

evant as it changes significantly the way a turbine

1 INTRODUCTION

Blockage is defined as the interaction effect

between a body under a constrained-flow con-

dition, and the boundaries surrounding it. Its

effects have long been discussed since the early

experimentation in circulation tanks for aero- or

hydrodynamics (Glauert, 1933a). The interaction

effects are typically seen, for the particular case of

turbines, as an increase in both power and thrust

forces when compared to the open-flow condi-

tion. This is caused by different effects such as an

increased flow speed around the body, a change of

pressure in the wake, differences in flow-develop-

ment for lifting surfaces such as foil sections and

longitudinal pressure gradients associated to the

tank boundary layer and fluid losses (Glauert,

1933a; Pope & Harper, 1966).

The earliest attempts to explain the behavior

of a turbine were made by the means of the one-

dimensional actuator-disc theory. This concept was

employed to derive the energy extraction limit for an

open-flow condition, set by a maximum power coef-

ficient

CP max =16 27/

known as the Lanchester-Betz

limit (Betz, 1920; Lanchester, 1915). These formu-

lation was complemented by Garret and Cummins

(Garrett & Cummins, 2007) showing that the maxi-

mum power coefficient for an actuator disk in a

constrained flow is

CP max = −

( )

−

16 27 1 2

/ ,

β

where

138

will behave, and corrections are required. It could

be to take the results of laboratory experiments

to a real-life scenario, to calculate the expected

power and loads on a tidal turbine that is already

designed, or to economically assess the deployment

of a farm in a particular spot.

For these reasons, the availability of quick block-

age correction methods that can be employed over

existing results obtained from different sources

(Experiments, CFD or BEM) is highly valuable

from a scientific, engineering and commercial per-

spective when assessing performance and behavior

under different operational and deployment condi-

tions is necessary.

The present work exposes a series of transient,

blade-resolved, RANS CFD simulations of a

horizontal axis hydrokinetic turbine under differ-

ent blockage and tip speed ratio conditions with

the purpose of providing information regarding

the scope and validity of different blockage cor-

rection methods. RANS CFD results are used to

compare six different blockage correction methods

(Bahaj et al., 2007; Glauert, 1933b; Maskell, 1965;

Mikkelsen & Sørensen, 2002; Pope & Harper,

1966; Werle, 2010).

2 VALIDATION CASE

To analyze the different blockage methods, the

SANDIA MHKF1 hydrokinetic turbine was

selected as a benchmark case. This is a three-bladed

horizontal axis turbine designed by the SANDIA

National Laboratories and UC Davis, and for

which experimental data is published including

turbine flow field quantification, performance

characterization and cavitation, among other

results (Fontaine et al., 2013a).

For the SANDIA MHKF1 hydrokinetic tur-

bine, shown in Fig. 1, simulations for 7 different

blockage ratios were made (see Table1). For each

of these conditions, the turbine was simulated

rotating at 5 different tip speed ratios λ, from 3.5

to 5.0 in 0.5 increments, leading to a total of 35

simulations.

The simulations were validated against experi-

mental results for a blockage ratio β=0.210.

Thrust and torque are obtained by integrating

the pressures over the turbine surfaces, and results

are converted to non-dimensional power and thrust

coefficients CP and CT.

In addition to these results, the axial induction

factors a are also obtained from the simulations,

with a defined as:

a U UT

= −10/

where UT is the average flow velocity at the turbine

plane and U0 the undisturbed flow velocity.

3 BLOCKAGE CORRECTION METHODS

Most of the blockage correction methods are based

on the traditional actuator disc theory, adapted for

the special case of a blocked flow. As usual, the

turbine is considered as an actuator disc where a

pressure discontinuity occurs.

From the diagram shown in Fig.2, several vari-

ables are identified. At the inlet, the undisturbed

flow velocity UT is considered as constant through-

out the entire cross-sectional area of the tunnel C.

At the turbine plane, the velocity is defined as U1

and outside as U3. Downstream, the velocity in

the wake region is defined as U2 and, outside this

region, as U4. At this point, the cross-sectional area

of the wake is AW. From momentum theory AW can

be defined as:

Figure1. Sandia MHKF1 hydrokinetic turbine and foil

sections.

Table1. Blockage cases.

Blockage

β

Domain

diameter

[-] [m]

0.001 63.2456

0.020 14.1421

0.050 8.9443

0.100 6.3246

0.150 5.1640

0.210 4.3636

0.400 3.1623

139

A A a

a

W=−

−

1

1 2

Most blockage correction methods attempt

to obtain an equivalent free-flow velocity UF as

function of different variables such as blockage β,

thrust coefficient CT, wake expansion or induction

factors.

For each blockage correction method, a relation

between the tank velocity UT and a corresponding

free-stream velocity UF is given, leading to follow-

ing corrections for λ, CT and CP:

λ λ

c

T

F

U

U

=

C C U

U

Tc T

T

F

=

2

C C U

U

Pc P

T

F

=

3

where the subscript c is meant for corrected or

equivalent free-flow values. In Table2, each of the

blockage correction is presented. Full details are

given in each of the cited articles.

4 NUMERICAL METHODS

The data-set of this study was obtained by numeri-

cally solving the Reynolds-Averaged Navier-Stokes

equations (RANS) under constant-density and

constant temperature assumptions (details e.g. in

(Ferziger & Peric, 2002)).

The simulations used a modified version of the

k-ω SST turbulence model with the correlation-

based

γ

θ

Re

transition model. This allows for the

prediction of the onset of transition in a turbulent

boundary layer (Malan et al., 2009; Menter et al.,

2005; Nichols, 2014).

The employed setup is the same used for the

bare turbine case described in (Tampier et al.,

2017). CD-Adapco’s STAR-CCM+ software was

employed to solve the models previously described.

All cases were configured as implicit unsteady sim-

ulations. Boundary conditions were defined within

the software as velocity inlet, pressure outlet, and

free slip wall for the domain limits. The turbine

itself was defined as a non-slip wall inside a rota-

tory subdomain.

The stationary and rotatory domains are sepa-

rated by an interface which is automatically defined

by the software.

The mesh was generated using the STAR-

CCM+ unstructured polyhedral mesher. The tur-

bine was configured to have a prism layer with 20

elements normal to the surface, being fine enough

to maintain a Y+<1 for the blade surfaces.

A mesh independence assessment was made

to the validation case and the results are shown

in Table 3. The intermediate mesh configura-

tion was considered sufficiently accurate for this

analysis.

For the remaining cases, the same turbine sur-

face configuration remained constant, as well as

the inflation layers and the element sizes inside

the rotatory domain and in the surrounding area.

A transverse cut of the mesh and a detailed view

of the blade mesh can be seen in Figs. 3 and 4

respectively.

Table2. Correction methods.

Method UT/UFObs.

Glauert

14 1

1

+−

−

β

C

C

T

T

only if CT<1

Maskell

1−ε

β

CT

ε empirical factor

Pope

11

+

( )

−

ε

t

εt empirical factor

Mikkelsen

uC

u

T

+

−

4

1

u=1 - a

Bahaj

U U

U

U

C

T

T

T

1

1

2

4

/

+

U1 as in orig. art.

Werle 1-βpreliminary

method

Table3. Mesh independence study.

Case No. of cells CPCT

Coarse 1.9 M 0.53433 0.94560

Medium 4.5 M 0.54027 0.91590

Fine 5.7 M 0.54171 0.90557

Figure2. Momentum diagram.

140

5 RESULTS AND DISCUSSION

The validation case was defined for a blockage ratio

of β=0.210, which is the same condition of the

experimental results obtained by Fontaine (Fon-

taine etal., 2013). In Figure5, CFD results for the

validation case are shown for thrust and power

coefficients CT and CP, along with experimental and

CFD results from ARL (Fontaine etal., 2013b).

Good agreement can be observed, especially for

the power coefficient curve.

Although acceptable for this study, larger differ-

ences are observed between numerical and experi-

mental results for thrust that were also reported by

Fontaine on their CFD simulations (Fontaine etal.,

2013b). This is likely to be caused by the differ-

ences between the simulations and the experiments

regarding the presence of structures associated to

the measuring equipment in the laboratory setup

Figure4. Detailed view of the blade mesh.

Figure 5. CFD results for validation case (β= 0.210)

compared to experimental and CFD results from

Fontaine et al. (2013b).

Figure6. Normalized axial velocities of the validation

case (β= 0.210) in longitudinal plane. From top to

bottom: λ=3, 4 and 5.

that are neglected in the computational models.

Normalized axial velocities (UX=UT) in the lon-

gitudinal plane are shown in Fig.6. As mentioned

Figure3. Mesh cut at turbine plane of the bare turbine

domain.

141

in section 2 and detailed in Table1, CFD simula-

tions were carried out for a blockage range from

β=0.001 to 0.400.

In Figure 7, the obtained thrust and power

coefficient results are shown for each blockage

condition.

From these results, the lowest blockage ratio

(β=0.001) is considered as a quasi-free flow condi-

tion, and will be used as a reference for the applied

corrections. The results for β=0.210 represent the

validation case, as described previously.

The presented results for β=0.020 to 0.400 were

corrected by each of the presented methods, as

shown in Figure8.

As expected, most of the correction methods

provide results which are very close to the quasi

free-flow case (β=0.001), giving a first overview

of the effectiveness of each one of them. Due to

the superposition of results, not each CTc or CPc

curve is visible for a specific blockage ratio. Forthe

Glauert correction, results are shown only for

results with CT < 1.

From the obtained results, an error analysis was

made, considering the relative error as:

E

C C

C

C

X X

X

X

C

=−0

0

where the subscript X corresponds to thrust or

power (T or P), subscript c corresponds to cor-

rected results, and subscript 0 to unblocked results

(β=0.001). The relative error is obtained for each

method along the corrected range of λc for each

blockage ratio. In order to obtain a global over-

view of error for each method, mean absolute error

values were obtained for

ECT

and

ECP:

MAE E

X CX

=

The results are shown in Table4 for each correc-

tion method.

From this table, it can be observed that the mini-

mum error is obtained by the Mikkelsen & Sørensen

method, followed by the Bahaj method. For the

Glauert method, even if only results from data with

CT<1 were considered, a higher total error can be

observed. The Werle method has an unexpectedly

high error, and is therefore not recommendable for

its application as a correction method for a large

blockage and tip speed ratio range.

Figure 7. Uncorrected thrust (in blue) and power

coefficients (in green) CT and CP, for blockage range

(β=0.001 to 0.400). Free-flow reference values (β=0.001)

are given in red for CT and magenta for CP.

Figure 8. Blockage corrected thrust (blue) and power

(green) coefficients CTc and CPc. Free-flow reference values

(β=0.001) are given in red for CT and magenta for CP

.

Table 4. Mean absolute error of thrust and power

corrections.

Method MAET (%) MAEP (%)

Glauert 5.69 9.69

Maskell 2.60 4.68

Pope & Harper 2.00 3.18

Mikkelsen & Sørensen 0.76 0.69

Bahaj 1.54 2.78

Werle 28.05 29.49

142

6 CONCLUSIONS

The use of a RANS-CFD tool to model the per-

formance of a hydrokinetic turbine over a wide

range of blockage conditions can provide useful

data to analyze existing blockage correction meth-

ods, propose improvements to these or to propose

new methods for specific applications.

The used CFD method shows good agreement

with results from literature (both numerical

and experimental for the bare turbine), giving a

validation of the presented results. Additionally, it

would be advisable to carry out experimental tests

under different blockage conditions, to have a full

validation of these cases as well.

From the presented results, the authors

recommend the use of the Mikkelsen and Sørensen

method for the correction of the blockage for hori-

zontal axis turbines subject to experimental test

or numerical simulations under conditions similar

to the presented here, especially in case of avail-

able induction factor data. In case that induction

factors are not available, the Bahaj correction is

recommended.

It is also recommended, considering the pre-

sented results, to avoid using the Werle and Glau-

ert methods, considering that other simple and

more reliable methods, such as those by Maskell or

Pope & Harper, are available.

The study of a series of different blockage ratios

for other turbines, tank sections (such as square or

rectangular sections) or other arrangements could

allow the development of new blockage correction

methods.

Further investigation could consider free surface

effects and the interaction with other devices (as in

tidal farms), to consider these effects in blockage

corrections as well.

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