Repository - Scientific Journals of the Maritime University of Szczecin - Hydrodynamic performance of the horizontal...

of the Maritime University of Szczecin

Akademii Morskiej w Szczecinie

2018, 55 (127), 23–33

ISSN 1733-8670 (Printed) Received: 16.08.2018

ISSN 2392-0378 (Online) Accepted: 16.09.2018

DOI: 10.17402/298 Published: 17.09.2018

Hydrodynamic performance of the horizontal axis

tidal stream turbine using RANS solver

Hassan Ghassemi

1

, Hamidreza Ghafari

2

, Esmaeil Homayoun

3

Amirkabir University of Technology Hafez Ave., Tehran, Iran

e-mail: 1_{gasemi@aut.ac.ir,} 2 _{hamidghafari230@yahoo.com,} 3 _{homayoun73223@gmail.com}  _{corresponding author}

Key words: tidal turbine, duct, number of blades, pressure, hydrodynamic performance, HATST Abstract

This current work investigates the effect of duct and number of blades on the hydrodynamic performance of the horizontal axis tidal stream turbine (HATST). The numerical method based on Reynolds averaged Navi-er-Stokes (RANS) equations is employed to compare the hydrodynamic performance for various cases of this device. For validation of the numerical results, a 3-blade HATST without-duct has been compared against experimental data. The analysis and comparison of the simulation results show that using duct for HATST has increased the power coefficient, the torque coefficient, the trust coefficient, and the force on the blade. In addi-tion, the simulation results of the cases with a greater number of blades shows that the trust coefficient increased and the force on the blade decreased. Therefore, it is recommended to use ducted HATST with a great number of blades to extract more energy from the tidal stream.

Nomenclature CT – thrust coefficient, CP – power coefficient, CQ – torque coefficient, C – a log-layer constant, D – diameter of turbine, F2, F1 – blending function, L – blade chord,

n – number of revolutions per second, P – power of turbine,

P – local pressure,

Pref – reference hydrostatic pressures,

Q – rotor torque (Nm), R – radius of turbine,

ReL – Reynolds number based on the chord length,

Rex – Reynolds number based on the distance along the chord,

T – rotor thrust (N),

TSR – tip-speed-ratio,

Uin – stream velocity,

Ut – velocity tangent to the wall,

u+ _{– the near wall velocity,} uτ – friction velocity,

y+ _{– dimensionless wall distance,}

Ω – turbine’s angular velocity (rad/s),

κ – von Karman, ρ – water density, τij – shear stress,

∆y – the distance of the first node from the wall. Introduction

Increased global warming due to fossil fuel con-sumption has led to increased research into renew-able energy in recent years. Marine energy has a great potential for providing renewable energy, in the form wave, wind and tidal stream energy. When compared to different types of renewable energy resources, tidal stream is regular, predictable and an eco-friendly marine energy source (Rourke, Boyle & Reynolds, 2010).

Amongst the many types of tidal stream ener-gy extraction devices, horizontal axis tidal stream turbine (HATST) has been most utilized (Goundar & Ahmed, 2013). HATST is a device which works using a similar concept as the wind turbine. It con-verts kinetic energy from tidal stream into electri-cal energy when the fluid flow causes rotation of the propellers and generator.

Numerical simulations and experimental tests are useful methods to predict and investigate the behav-ior of wind and tidal turbines. Therefore, in recent years, many studies have been employed these meth-ods (Wang & Chen, 2008; Song et al., 2012; Jung, Kanemoto & Liu, 2017; Ren et al., 2017). Mason-Jones et al. (Mason-Mason-Jones et al., 2012) showed that the power, torque and thrust coefficients of HATST are not dependent on its scale. With consideration for the depth of the turbine installation, Noruzi et al. (Noruzi, Vahidzadeh & Riasi, 2015) used numerical simulations to investigate the hydrokinetic perfor-mance of HATST, both with and without a gravity wave condition.

Hee Jo et al. (Hee Jo et al., 2012) designed a tidal turbine blade from a reliable numerical model.

The turbine configurations have a great influence on the hydrodynamic performance of HATSTs. The effect of the winglet on the hydrodynamic perfor-mance of HATST was carried out by Ren et al. (Ren et al., 2017). Shi et al. (Shi et al., 2016) investigated the effect of leading-edge tubercles on a underwater HATST with radiated noise and cavitation.

Many studies have been carried out with ducted turbine. Shives and Crawford (Shives & Crawford, 2012) used a CFD simulation to gain base pressure, flow separation, and viscous loss effects on the ducted turbine performance. A tidal turbine with an extend-ed blade gains the same power as a shroudextend-ed tidal turbine with smaller blades (Shahsavarifard, Bibeau & Chatoorgoon, 2015). Transient RANS CFD meth-ods have been used for diffuser augmented, diffuser, and bare hydrokinetic turbine simulations (Tampier, Troncoso & Zilic, 2017). The analyses of marine current turbine with added postpositional bulb, both with and without a diffuser, using RANS-CFD meth-od has been investigated by Chen and Zhou (Chen & Zhou, 2014). The experimental work was com-pleted in order to study the effect of a brimmed dif-fuser on power generation efficiency for tidal current turbine system (Sun & Kyozuka, 2012).

So far, many pieces of research have been com-pleted on HATST, and there are still ways to improve energy efficiency. Hence, it is valuable to investigate methods for gaining an improvement in performance.

The present paper focus on the hydrodynamic performance of HATST in different cases, includ-ing turbines with 3, 4 and 5-blades and both with a duct and without a duct. Firstly, numerical simu-lations based on RANS CFD are carried out for the 3-blades HATST and compared with experimental data. Next, numerical simulations are carried out for the other cases of HATST. Then, numerical results of the hydrodynamic performance are presented and compared for various cases of HATST.

Governing equations

By introducing the Reynolds decomposition, the variables of the Navier-Stokes equations in the Reynolds averaging can be divided into mean and fluctuating components (Pope, 2001). From the Reynolds-averaged Navier-Stokes (RANS) meth-od, the incompressible Navier-Stocks equations can be solved by modeling the hydrodynamics of the tidal wind turbine. The equation of continuity and momentum conservation, which are written in the finite volume format are defined as follows:

0 d d d d _{ }





S i i V n u V t   (1)





_









         V M S ij i j j S i S i j j V i V S n u u n p n u u V u t d d d d d d d     (2) where u and p are the velocity vector and pressure, respectively, and the direction is defined by indices

i or j = 1,2,3. dn is the outward normal surface

vec-tor, S indicates the integration regions of the surface,

V indicates the integration regions of the volume, SM

is a source term, and τij is the shear stress, which can

be written as:               i j j i ij  _xu u_x  (3)

where μ is dynamic viscosity. By using the turbu-lence models, the Reynolds stress term ρu'iu'j can be determined.

In commercial CFD codes, the k – ε turbulence model that was developed by Jones and Launder (Jones & Launder, 1972), is the most widely used turbulence closure models (Pope, 2001). In particu-lar, the k – ε model can predict free shear flows ade-quately, but it has been shown that, the k – ε model was not able to resolve adverse pressure gradients and wall bounded flows. When integrated through

the viscous sub layer, an associated numerical stiff-ness of the equations is present.

The k – ω turbulence closure model developed for boundary layer flows, by Wilcox (Wilcox, 1998), to solve this problem, allows this model to modify and fix the problem of stream wise pressure gradi-ents as well as the viscosity near wall regions. Using the k – ω model, a more robust and accurate model is presented for the flows measured under wall effects. On the outside of the shear layer, the free-stream vorticity values strongly affect the results, which are a known shortcoming of this turbulence model.

In this study, k – ω SST (shear stress transport) turbulence model used was developed by Menter (Menter, 1994). The k – ω SST model combines the suitability of k – ε properties in the far field region and of the Wilcox’s k – ω model properties in the near wall region.

Equations of the Shear-Stress Transport (SST) model are given by:

  







                    i t k i k i i x k x k P x k U t k         * ~ ₍₄₎

  











i i i t i i i x x k F x x S x U t                                           1 1 2 1 2 2 2 (5) The blending function F1 in above Eqn. (5) is defined as:                                4 2 2 2 *

1 tanh min max k_y,500_y v ,4_{CD y}k

F k      (6) where:            10 2 1 ,10 2 max i i k _xk _x CD_ _{ }  (7)

where y and v are the distance to the nearest wall and the kinematic viscosity, respectively. Inside the boundary layer, F1 = 1 (k – ω model) and away from the surface (k – ε model) F1 = 0.

When limited to the formulation of the eddy-vis-cosity, the proper transport behavior vt can be derived

as:



₁1 , ₂



max a SF k a vt  _ (8)

where F2 and S are a second blending function and the invariant measure of the strain rate, respectively.

F2 is de defined as:                        2 2 * 2 tanh max _2 _k_y,500_{y }v F (9)

In stagnation regions of the SST model, a pro-duction limiter is used to prevent the build-up of turbulence.



  



 k P P x U x U x U P k k i j j i j i t k * 10 , min ~ _                   (10) All constant coefficients in the k – ω turbulence model and the k – ε turbulence model are solved by

α = α1F + α2 (1 – F), where α1 and α2 are constant coefficients in the k – ε and the k – ω model equation. The constants for this model are shown in Table 1. Table 1. Constants coefficients

α1 5/9 β1 3/40

α2 0.44 β2 0.0828

σk1 0.85 σk2 1

σω1 0.5 σω2 1/.0856

β* _0.09

The hydrodynamic performance of a HATST is defined by a dimensionless torque coefficient (CQ),

dimensionless thrust coefficient (CT), and

dimen-sionless power coefficient (CP), as follow:

3 2 current extracted 2 2 2 3 π 5 . 0 π 5 . 0 π 5 . 0 in P in T in Q U R Q P P C U R T C U R Q C         (11)

where, Q and T are the measured torque and thrust produced by the HATST, P is the rotor power, and Ω is the turbine’s angular velocity (rad/s), Uin is the

stream velocity and ρ = 1024 (kg/m3_{) is the water} density. The hydrodynamic performance, CQ, CT and CP can be represented as a function of the tip-speed-ratio (TSR), as given in the following:

in in U nR U R 2π TSR   (12)

where, n is the number of revolutions per second and

Numerical setup

By developing computer software and using the CFD, the numerical responses of the HATST simu-lation in current flows can be obtained. In this article the tidal turbine is modeled using the Ansys-CFX R16.2 and the ANSYS TurboGrid programs. Tidal turbine and duct section characteristics are shown in Table 2.

Table 2. Characteristics of the turbine and duct

Turbine type Horizontal axis tidal stream turbine

Turbine diameter 0.7 m

Hub diameter 0.105 m

Foil section NACA 63-418

Turbine’s angular velocity 270 rpm Duct

Foil section S1223

Chord length 0.2295 m

Gap 0.0257 D

Airfoil chord angle 26 degree Duct exit diameter 0.947 m Duct throat diameter 0.718 m Geometry

The turbine has 3 blades with a diameter of 0.7 m and a hub with a diameter of 0.105 m. Figure 1 shows a photo image of the HATST model test and Figure 2 shows a cross-sectional profile of the blade.

The NACA63-418 foil section along the tip side of the blade (0.3~1.0)R is chosen for the blade rotor

and an ellipse shape profile is used near the root. By twisting any foil section (0.3~1.0)R along the blade, about the point located at 0.25% of chord length from the leading edge for any foil section, the pitch angle of blade obtained. The twist angle and the applied chord length according to radial length of the HATST model is shown in Figure 3.

0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 0 0.2 0.4 0.6 0.8 1 Ch ord (m m ) Tw ist A ng le (d eg ) r/R

Twist Angle Chord Length

Figure 3. Twist angle, radius length and chord length of the HATST model

The duct section characteristics of the turbine blades are shown in Figure 4.

Figure 4. The HATST with duct Computational Domain

For this analyze the whole computational domain consists of two main parts. The first domain is an outer zone and stationary domain (Figure 5) and the second domain is an inner zone considered the rotating domain (Figure 6). The outer zone was modelled using ANSYS geometry, and also the TurboGrid software is used for modeling the inner zone, which includes the turbine blade. The size of the domain is 3R to the radial direction, and 3R upstream and 6R downstream in the longitudinal axis, where R is the turbine radius. To reduce the number of elements and analysis time, one-third of the domain using the periodic boundary condition for tidal turbine with 3 number of blades, has been applied.

Figure 1. A scale model of the HATST (Song et al., 2012)

Figure 2. Cross-sectional profile of the blade

Chord length = 0.2295 m

Gap=0.0257D

Boundary condition

As shown in Figure 5 for the inlet, outlet and top location, the opening boundary conditions are con-sidered, so that the inlet boundary condition is set as a uniform incoming velocity and the relative pres-sure is zero at the tap and at the outlet boundary in the stationary domain. A no-slip condition has been used for the hub and turbine blade surfaces. The interface condition is the common location between the stationary and rotating domains. It should be not-ed that the size of the elements in the inner and outer zone interface are not equal. Hence, for non-match-ing interfaces between the stationary and rotatnon-match-ing domains, the general grid-interface (GGI) interpola-tion method has been utilized.

To simulate the rotation of the inner zone in a steady state solution, in the CFX, a moving refer-ence frame (MRF) method is employed. It is import-ant to note that in MRF method for the tidal turbine simulation causes the frozen rotor option to be used for the interface model between the rotating and sta-tionary zones.

Using the MRF method, the numerical solution without moving the rotating zone elements, a solu-tion can be achieved so that the water around the turbine blade in the rotating zone is set as the MRF, while the hub and turbine blade to the rotating zone are relatively stationary. The rotational periodicity

condition is given on the slice side boundary for both the stationary and rotating domains. The fluid is considered to be incompressible water, at 25°C, and its reference pressure is set to 1 atm. The advection term is discretized using the high-resolution upwind method and the residual convergence criterion is set to 10–5_{. The numerical settings are summarized in} Table 3.

Table 3. Numerical setting

Parameter Setting Analysis type Steady state Material Water at 25°C Turbulence model k – ω SST

Wall No slip, smooth wall

Inlet Normal speed, turbulent intensity 5%

Outlet Opening

Top Opening

Interface Frozen rotor

Outer zone mesh

In order to create structured meshing in the outer zone, this domain is divided into several parts and then controlled by edge sizing mesh in the Ansys meshing.

As shown in Figure 7, the element size near the turbine’s location is finer.

Inner zone mesh

ANSYS TurboGrid, can generate structured cells with excellent quality for turbo machine systems by using the Automatic Topology and Meshing (ATM) method. Figure 8 shows the ATM topology for the HATST blade.

The meshes of the inner zone are shown in Figure 9.

The near wall velocity, u+_{, can be obtained by the}

following logarithmic equation:

 

y C u U u _ t _ 1_ln  _   (13) where uτ and Ut are the friction velocity and the known

velocity tangent to the wall, respectively. Ut is

mea-sured at a distance of Δy from the wall. C and κ are a log-layer constant depending on the wall rough-ness and the von Karman constant, respectively. The near-wall node spacing is the distance between the first layer of nodes from the wall and a hub or blade wall. The y+ _{method in ANSYS TurboGrid allows}

the user to set the near wall spacing, Δy, based on the specified size of y+_{. The following equation}

Figure 5. The outer zone (stationary domain)

Outlet

Inlet

Rotational Periodicity

Rotational Periodicity

Rotational Periodicity Interface (frozen rotor) 6R

3R

3R

Interface (frozen rotor)

represents the relationship between y+ _{and the near}

wall spacing (Δy) (TurboGrid, 2016):

L x _Re Re y L y_{ }  80 1/14 1  (14)

where, Δy+ _{in the above equation is the specified}

tar-get y+ _{value, L is the current turbine blade chord, Re} L

and Rex are the Reynolds number based on the chord

length and the distance along the chord, respective-ly. For modeling turbulent flow fields in CFD, the Reynolds Averaging method is a very popular alter-native. The Reynolds number of this full-scale flow is 2.86×106_{, which is defined as} v U c R R R n  0.7 , where





2 2 0 0.7πnD U UR   .

Here, c0.7R and D are the chord length at 0.7R and the diameter of the turbine, respectively.

To obtain the appropriate number of elements for the domains, the size of the required mesh has been changed several times for both stationary and rotat-ing domains. The number of totals meshes examined are presented in Figure 10.

In order to improve computational accuracy and reduce the number of elements and at the same time accelerate the solution convergence for the HATST simulation, approximately 3.6 million structured elements for the rotating zone in TurboGrid soft-ware and 1.4 elements million structured elements for the stationary zone in ANSYS Meshing are used. It should be noted that with an increasing the Figure 9. The inner zone mesh

Decreasing

mesh size locationTurbine Decreasing mesh size

Top view

Front view

Figure 7. Structural meshing for outer domain

number of elements above these numbers, a signifi-cant change in the power coefficient is not observed and this increase can only lead to an increased solu-tion convergence time. The y+ _{of the turbine and}

duct surface for the present computational proce-dure was in the range of 30–300 for all six simula-tion, which is acceptable for the k – ω SST turbu-lence model.

Numerical results and discussion

Validation

To verify the present CFD results, a comparison is made with the experimental data (case 2) for a 3 blades turbine reported by Song et al. (Song et al., 2012), where HATST was experimentally tested in a tow basin, at the Busan National University, Korea, over a range of TSRs (from 4 to 10). The wave tank has 100 m length, 8 m wide, and is 3.5 m deep with a maximum towing speed of 7 m/s.

Figure 11 shows that the numerical results obtained from the present computational procedure for power and torque coefficients for a 3-blade tur-bine and these results agree well with the experimen-tal data reported by Song et al. (Song et al., 2012).

In this study, the RANS and an MRF in the steady state analysis is employed to simulate the HATST for both the states with and without duct turbine, and for a 3, 4 and 5-blade system via ANSYS CFX. The turbine’s angular velocity and inlet velocity was kept at 1.98 m/s and 270 rpm to acquire the TSR = 5, for each case in the study.

Pressure coefficient distribution

In order to investigate the effect of the number of blades and duct on the HATST, the comparisons of pressure coefficient distribution (CPress) between the

various blade numbers, both with and without-duct HATSTs, on a span section at r/R = 0.5 were con-ducted (Figure 10).

The pressure coefficient distribution is defined as 2 5 . 0 u P P C ref Press _   , where _{u u}2



_{2 nrπ}



2 in 

is the free stream velocity, Pref is the reference

hydro-static pressures, P is the local pressure, and ρ is fluid density. The horizontal axis (x/c) is the cross-section of the span normalized.

As shown in Figure 12, the CPress of all the

three-turbine configured with a duct is greater than that of those without a duct turbine. Also, it was found that by increasing the number of blades, the CPress is decreased in the cases with and

with-out ducts. With an increasing number of blades, the decrease rate in CPress of the HATSTs with a duct was

greater than that of the turbine without a duct. When using a duct, with the same number of blades, the differences among maximum of CPress using 3-blades

case is 46%, but the values of 4-blades and 5-blades are 28% and 9%, respectively. From a comparison between the with-duct and without-duct cases, it is evident that for a greater number of blades, the effect of adding duct on the CPress when compared to using

the same number of blades is less.

0.35 0.45 0.55 0.65 0.75 1.5 3.0 4.5 6.0 CP Number of elements (106₎ Mesh dependence Lack of increased accuracy

Figure 10. Power coefficient of the tidal turbine relative to the number of elements

0.0 0.1 0.2 0.3 0.4 0.5 4 5 6 7 8 9 10 11 CP TSR Exp Num 0.00 0.01 0.02 0.03 4 5 6 7 8 9 10 11 CQ TSR Exp Num

Figure 11. Comparison of the power and torque coefficients between numerical results and experimental data for 3-blades turbine (Song et al., 2012)

The pressure coefficient distributions for with and without-duct turbine with 3-blades on three span sections in the direction of the current turbine blade, are shown in Figure 13.

Comparisons of CPress on the three span sections

show that by increasing the distance from the hub along the blade, CPress for both the with and

with-out-duct cases decreases. But these changes are more pronounced in the duct than in the with-out-duct case.

Force contour on the blade

Figures 14 and 15 show the force couture on the blade turbine for both the with- and without-duct cases and for 3, 4 and 5-blades.

The distribution of the resultant force acted on the radial direction of the blade is shown in Figure 16, for different blade numbers both with and with-out duct. The horizontal axis of the graph shows the dimensionless distance from root to tip of the blade.

When the number of blades is increased, the variation in the force along the radial direction for both the with and without-duct turbine all showed the similar trends. The value of F applied to the blade of the turbine from the root to 0.8R has an upward trend, and it then decreased. The maximum

F applied to the blade decreased as the number of

blades increased. The results are shown that when using the duct in HATST the increase of the maxi-mum F of the 3-blades turbine is 28% while for the 4-blades and 5-blades turbine are 17% and 10%, -4 -3 -2 -1 0 1 2 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 CPress x/c 3 blades w duct 3 blades w/o duct

-4 -3 -2 -1 0 1 2 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 CPr ess x/c 4 blades w duct 4 blades w/o duct

-4 -3 -2 -1 0 1 2 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 CPr ess x/c 5 blades w duct 5 blades w/o duct

Figure 12. Comparisons of CPress in various blade numbers, both with and without duct turbine

-5 -4 -3 -2 -1 0 1 2 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 CPress x/c w duct at r = 0.4R w duct at r = 0.6R -5 -4 -3 -2 -1 0 1 2 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 CPr ess x/c w/o duct at r = 0.4R w/o duct at r = 0.6R

Figure 14. Force contour on the blade face

Figure 15. Force contour on the blade back

Figure 16. Force acted along the radial direction of the blade

3 blades 4 blades 5 blades With-duct Without-duct Force [N] Force [N] 3 blades 4 blades 5 blades With-duct Without-duct

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.0 0.2 0.4 0.6 0.8 1.0 Fo rce [N ] r/R 3 blades w duct 3 blades w/o duct

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.0 0.2 0.4 0.6 0.8 1.0 Fo rce [N ] r/R 4 blades w duct 4 blades w/o duct

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.0 0.2 0.4 0.6 0.8 1.0 Fo rc e [ N ] r/R 5 blades w duct 5 blades w/o duct

respectively. Hence, when the number of blades is increased the effect of the duct may be ineffective on the force acted on the blades.

The hydrodynamic performance

An investigation into the effect of the number of blades and utilizing a duct on the hydrodynamic per-formance, such as the dimensionless torque coeffi-cient (CQ), dimensionless power coefficient (CP), and

dimensionless thrust coefficient (CT) of the HATSTs,

the numerical results obtained from ANSYS-CFX are presented in Figure 17.

By comparing the two with and without ducted cases (Figure 17), it is clear that increasing the num-ber of blades increases the torque and power coeffi-cient. As demonstrated in these figures, adding ducts in the HATSTs by using the same number of blades causes increases of the CQ and CP parameters in

the 3-blade turbine by 39% and for the 4-blade and 5-blade turbines increase by 45% and 55%, respec-tively, while the increase of the CT for the 3-blade

turbine is 20% and for the 4-blade and 5-blade tur-bines are 23% and 27%, respectively.

The differences between the CP with and

with-out-duct using 4-blades are 6.6% and is 2.3% when using 3-blades, but the value of the CP for using

5-blades is almost 16.6% (with-duct) and 4.6% (without-duct) against using 3-blades. It was found

that, when using a duct, the value of CP significantly

increased with the number of blades, whilst for the without-duct case the changes are almost negligible.

Conclusions

This paper has investigated the effect of the num-ber of blades on the HATST, both with and with-out-ducts. For the six considered HATSTs, numerical simulations were employed by using a commercial CFD code, CFX based on the RANS solver. Based on the numerical results, the following conclusions can be drawn:

By adding a duct to the tidal stream turbine: • Increases in the pressure coefficient (CPress)

distri-bution on the tidal turbine blades is observed. • Increases in the changing of pressure coefficient

(CPress) distribution in the distance hub to tip (r/R)

of the tidal turbine blades is predicted.

• Increases in the amount of force (F) applied to the tidal turbine blades is seen.

• Increases in the torque coefficient (CQ) and the

power coefficient (CP).

By increasing the number of blades for tidal stream turbine:

• Decreases in the pressure coefficient (CQress)

dis-tribution on the tidal turbine blades.

• Decreases in the amount of force (F) applied to the tidal turbine blades.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

3 blades 4 blades 5 blades

CP

w/o duct w duct

0 0.01 0.02 0.03 0.04 0.05 0.06

3 blades 4 blades 5 blades

CQ

w/o duct w duct

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

3 blades 4 blades 5 blades

CT

w/o duct w duct

• Increases in the torque coefficient (CQ) and the

power coefficient (CP) for tidal turbine with

a duct, and the insignificance of this increase for a tidal turbine without a duct.

And also:

• By increasing the number of blades, changing the value of CPress for with-duct case is greater than

the without-duct case.

• For a greater number of blades (e.g. 5-blades), the difference CPress between with and without-duct

will be less.

The results show that adding a duct to tidal tur-bines would increase the CQ, CP and F. On the

oth-er hand, the addition of blades increased CQ and CP

and reduced F. Therefore, increasing the number of blades is recommended to reduce the effect of F in tidal turbines with a duct.

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