DOE Analysis and Improvement of a Rotor Design for OWC Radial

Impulse Turbines

Khalid Elatife

and Abdelatif El Marjani

**1

Labo. de Turbomachines, Ecole Mohammadia d’Ingénieurs, Université Mohammed V

B.P. 765 Agdal, Rabat, Maroc

Corresponding author: Fax: +212 5 37 77 88 53 Email: elmarjani@emi.ac.ma

Keywords: Wave energy, OWC devices, impulse radial turbine, rotor blade optimization, design of experiment, turbine

efficiency.

Abstract: Wave energy exploitation is of great interests nowadays due to its sustainability, reliability and large potential.

A brief analyze of wave energy potential in the Moroccan coastline with an idea on the importance of

implementing WEC, and presents secondly an implementation of the experimental design method to optimize

the self-rectifying impulse radial turbine in the OWC devices, which is the most exploited system, for wave

energy extraction are presented in this paper. A novel design with circular arcs and straight lines for the rotor

blade will be presented. A first work of optimizing the rotor blade design in terms of the turbine efficiency by

the design of experiment method has been done. The work has done as outputs two optimal rotor blade

profiles, one for the exhalation and the other for the inhalation modes. As a second part of the work, optimizing

the solidities of the guide vanes and of the rotor by implementing a second design of experiment will be

established.

NOMENCLATURE

)(









: Input coefficient

RRRR

rAu

)(









: Torque coefficient



: Total pressure drop

: Mean radius

: Characteristic area



: Air density

wru 

: Circumferential velocity at







: Mean radial velocity

: Flow rate

: Rotor blade height



: Turbine efficiency

: Radius of the suction side of the blade rotor

: Radius of the pressure side of the blade rotor

: Blade chord*

t: Inter-distance between centre of the two circular

arcs of the blade rotor

β*: Geometrical angle in the leading and trailing

edges of the blade rotor

α: Guide vane incidence angle



: Flow coefficient

1 INTRODUCTION

One of the most abundant resources of renewable

energy in the world is the ocean energy. In the world,

its potential is estimated of about 8 000-80 000

TWh/year (AEA Energy & Environment on the

behalf of Sustainable Energy Ireland for the IEA’s

Implementing Agreement on Ocean Energy Systems,

2006), and on the Moroccan coasts to 25-30 kW/m,

which is for about 700 to 900 TWh/year (ELATIFE

& EL MARJANI, 2014). It encloses energy resources

such as: wave energy, tidal energy, thermal energy

and marine currents energy. In the R&D field, great

efforts were made during the last decades, in order to

harvesting this huge energy for covering the

continuous growing of the human energy needs. For

the wave energy extraction field for instance, several

energy system converters were introduced, especially

the oscillating Water Column (OWC) which is the

most used design for its low cost of installation and

the simplicity of its maintenance.

The OWC devices are composed of three parts: air

chamber, air turbine and electrical generator. The first

component is used to convert wave energy to

pneumatic one; the second one is used to convert this

pneumatic energy to mechanical energy which is

finally converted to electrical energy in the generator.

Several OWC devices are built in 1990s and are still

working, such as the Picot plant in Azores, Portugal

(FALCAO, 2000) and the LIMPET plant in Islay,

Scotland (Heath &Whitakker & Boake, 2000).

The air turbine equipping the OWC device should

rotate in one direction despite of the bidirectional air

flow over it due to the water oscillating inside the air

chamber. The first turbines used in the OWC

prototypes are the Wells type turbines. However,

through exploitation of this turbine, some

disadvantages have been encountered (Falcao, 2003),

such as: high efficiency in a narrow range of flow

rates, poor starting characteristics, high speed

operation, high noise level, high periodical axial

thrust and finally the crucial problem of stall. An

alternative type turbine was proposed by I.A.

Babinstev in order to overcome these drawbacks

(Babinstev, 1975), which is impulse type turbine.

The axial and the radial are the two configuration

types of impulse turbine that have been introduced.

According to research investigations, it has been

found that the radial impulse turbine has some

advantages compared to the axial one in terms of low

manufacturing cost, high torque due to the radial

configuration and the absence of the oscillating axial

thrust. However, a main problem of the large

aerodynamic losses due to the important incidence air

flow angle in the inner and outer guide vanes can be

presented for the impulse turbine. It is due to the

required symmetry of the two rows of guide vanes

because of the bidirectional movement of the air flow.

In order to optimise the impulse turbine

performances, several investigation researches were

elaborated since the early 1990s. In the last decade,

many improvements in turbine geometries were

proposed. According to investigation results of

reference (Pereiras & Castro & El marjani &

Rodriguez, 2011), improved performances can be

obtained in both operating modes (inhalation and

exhalation) by modifying the aerodynamic design of

the inner guide vanes in the radial impulse turbine. A

model of his improved turbine has been manufactured

and installed in the EMI’ Turbomachinery Laboratory

for experimental tests. An alternative design of the

axial impulse turbine has been introduced (Takao &

Setogushi, 2012) in which the solution consists of

coupling two turbines installed in a twin

configuration for optimizing the efficiency in

inhalation and in exhalation operating modes. Tests

have revealed significant improvement in the

efficiency. a varying radius model of the axial

impulse turbine is another design that has been also

considered in order to reduce the aerodynamic losses

and consequently increase the efficiency (Natanzi &

Teixeira & Laird, 2011). Recently, a novel bi-radial

turbine has been proposed for which a notable

increasing efficiency (close to 80 %) has been reached

(Falcao & Gato & Nunes, 2013a; Falcao & Gato &

Nunes, 2013b).

In this paper, we will analyse the wave energy

potential in the Moroccan coastline that can gives an

idea on the importance of implementing WEC, and

presenting a numerical experimental design method

with ANSYS FLUENT for optimizing the impulse

radial turbine in terms of some design parameters. A

new rotor blade design has been proposed with two

circular arcs that have dependent radii and two

straight lines in the leading and trailing edges. This

work has consisted on optimizing the blade rotor

design by drawing up a numerical experimental

design of four factors; the radius of the suction side,

the chord, the inter-distance between centre of the two

circular arcs and the geometrical angle in the leading

and trailing edges of the blade rotor. Two optimal

rotor blade profiles have been found, one for the

exhalation and the other for the inhalation modes. The

future research work will consist on optimizing the

solidities of the inner and outer guide vanes and of the

rotor by implementing a second design of experiment.

2 WAVE ENERGY IN THE

MOROCCAN COASTLINE

Over the last years, a set of fixed, floating and

submerged wave energy converters has been installed

in order to estimate the wave energy potential. Each

device is regarded to extract wave energy over a range

of operating conditions in terms of wave period and

height.

To justify the interest of implementing wave

energy converters in the coastlines of any country, it

is required to analyse its wave power.

Figure 1: Worldwide average wave power potential (kW/m)

(Lagune & Benalia & Benbouzid, 2010)

Figure 1 shows the distribution of the wave energy

potential in the world. It can be noticed from this

figure that the average annual wave power in the

Moroccan coasts is estimated to be between 25 and 30

kW/m.

According to the previous graphs, it can be

noticed that the implementation of the wave energy

converters in the Moroccan coastlines will be highly

profitable in terms of the amount of energy that can

be extracted from wave. The Moroccan coastline

energy potential is estimated for the length of 3400

km to 900 TWh/year.

One of the most studied wave energy converters

is the OWC device, which is due to its simplicity. The

OWC devices are composed of three parts: air

chamber, air turbine and electrical generator. The first

component is used to convert wave energy to

pneumatic one, and the second from the pneumatic to

mechanical one, and finally from mechanical to

electrical energy in an electrical generator. As a result,

the global efficiency will depend on the efficiency at

each phase of this energy conversion chain. For high

OWC performances, great attention should be paid in

the design of the turbine (El marjani & Castro &

Rodriguez & Parra Santos, 2008).

For this reason, our present work consists on

optimizing the impulse radial turbine efficiency,

especially the rotor blade design, for a better

harvesting of the huge wave energy in the Moroccan

coastlines.

3 A NEW ROTOR BLADE

DESIGN OF IMPULSE

TURBINE

From the literature, several aerodynamic problems

have been investigated for the self-rectifying impulse

turbine, like the flow separation at the outlet guide

vanes (Setoguchi & Takao & Kinoue & Kaneko &

Santhakumar & Inoue, 1999). Another problem that

leads to energy losses is the separation of the

boundary layer in the suction side of the rotor blade.

In order to minimize theses energy losses, a new rotor

blade design with circular arcs in the pressure and

suction sides has been elaborated. The Figure 2 shows

the new blade geometry.

Figure 2: New blade rotor geometry

4 EXPERIMENTAL DESIGN FOR

OPTIMIZING THE ROTOR

BLADE

Method Approach. Experimental design is an

optimization method that uses experimental testing

by ordered sequence called experimental design of an

experiment, each to acquire new knowledge by

controlling one or more input parameters to obtain

results validating a model with a good economy

(number of trials as low as possible, for example).

For our case, a 2D numerical experimental design

has been used for the radial impulse turbine and

considering as the input parameters the geometrical

characteristics of the blade rotor. The other

parameters have been fixed and based on the values

of the reference (Setoguchi & Santhakumar & Takao

& Kanako, 2002). Four variables parameters have

been considered; the radius of the suction side rs, the

blade chord lr, the inter-distance between centre of

the two circular arcs t, and the geometrical angle in

the leading and trailing edges of the blade rotor β*.

The guide vane incidence angle α has been chosen

with respect of the triangle velocity of the air flow.

The output result considered is the turbine efficiency.

The radius of the pressure side rp and of the suction

side rs are joined by a Brilling rule that found in the

literature:

rr .



(1)

The mathematical model for this case of study is

as follows:



= a

+ a

.rs + a

.lr + a

. β* + a

.t (2)

Each input parameter has two levels of variation,

as presented in the Table 4:

Table 1: Dimensionless values of the four input parameters

for the two levels (with respect to the value: 55 mm)

Level r

(mm)

β* t (mm)

-1 0.436 0.818 25° 0.545

1 0.545 1 35° 0.6

Instead of using an exhaustive experimental

design which needs 24 tests, it is interesting to

use an optimized experimental design (Lundstedt,

1998) that needs lesser tests, for example the matrix

of Hadamard that needs just 8 tests for this case. This

matrix is presented in the Table 2.

Table 2: Hadamard matrix for four parameters and two

levels

N°

β* t

1 1 1 1 -1

2 -1 1 1 1

3 -1 -1 1 1

4 1 -1 -1 1

5 -1 1 -1 -1

6 1 -1 1 -1

7 1 1 -1 1

8 -1 -1 -1 -1

The values of ai, i=1,…,5 , for the two phases;

inhalation and exhalation, have been obtained in

matrix form as follows:

[



] = [H] . [a] (3)

With: [



]t=[



1,…,



8] ; [a]t= [a1,…, a5] ; [H] is

the Hadamard matrix for a dimension of 8 × 5 with

the first column is a unitary column.

The numerical tests have been performed with

ANSYS FLUENT for the rotor torque extraction for

different flow coefficient



. The standard k-ε model

has been used to model the flow turbulence. A

segregated solver has been used to solve the coupled

conservation equations of mass, momentum and

energy. The algorithm of SIMPLEC is adopted to

perform the pressure-velocity coupling

The turbine is composed of a rotating part, the

rotor, and a fixed part, the stator, Figure 3. In order to

manage the relative movement between the fixing and

the moving part of the turbine, the sliding mesh

technique is used. The boundary conditions adopted

is a uniform total pressure at the inlet and a uniform

static pressure at the flow outlet. The condition of

non-slip is adopted for all the walls.

Figure 3: Rotor and stator of radial impulse turbine

(Pereiras & Castro & El marjani & Rodriguez, 2011)

Results and Discussion. The turbine efficiency η is

expressed in terms of the torque coefficient CT, input

coefficient CA and the flow coefficient



mentioned above:











(4)

With the rotational speed of the rotor

chosen

is 234 rpm.

The results of the eight tests by numerical

simulation in both two phases; exhalation and

inhalation are plotted in Figures 4 and 5,



=f (



Figure 4-a) and 4-b): Turbine efficiency for exhalation

mode for the eight tests

Figure 5-a) and 5-b): Turbine efficiency for inhalation mode

for the eight tests

For the rest of the work, three flow coefficients

have been chosen to optimize the turbine efficiency

for both phases; exhalation and inhalation, which are:

0.5, 1.5 and 2.5.

The values of the coefficients ai, i=1,…,5 are

presented in the two Tables 3 for exhalation and

inhalation modes.

Table 3: The coefficients a

, i=1,..,5 for exhalation and

inhalation

Inhalation Exhalation



-0.5 -1.5 -2.5 0.5 1.5 2.5

a1 58.35 54.87 50.25 59.54 59.74 54.6

a2 24 24 24 24 24 24

a3 55 55 55 55 45 45

a4 25 25 25 35 35 35

a5 33 33 30 33 30 30

5 OPTIMIZATION OF BLADE

ROTOR GEOMETRY

In order to determine the combination (s) of the four

input parameters that maximize the turbine efficiency

for the two phases of functioning, an optimizing

program has been elaborated with MATLAB.

The objective function is the equation (2) and the

variable inputs are the input parameters of the design

of experiment. Their variation is inside their two

levels with a step of 1 mm for rs, lr and t, and 2° for

β*.

The optimal combination for the three flow

coefficient values in both phases is presented in the

Table 4 below:

Table 4: Dimensionless values of optimal combinations for

the three flow coefficient values for exhalation and

inhalation modes

Exhalation

;β*; t)

Inhalation

;β*; t)



=0.5

(0.436;1;35°;0.6) (0.436

; 1 ;

25° ; 0.6)



=1.5

(0.436

; 0.818 ; 35°

; 0.545)

(0.436

; 1 ;

25° ; 0.6)



=2.5

(0.436

; 0.818 ; 35°

; 0.545)

(0.436

; 1 ;

25° ; 0.6)

It can be noticed that there are two optimal

combinations for exhalation; C1(0.436;1;35°;0.6) and

0123

Efficiency(%)

Flowcoefficient

Test1

Test2

Test3

Test4

0123

Efficiency(%)

Flowcoefficient

Test5

Test6

Test7

Test8

0123

Efficiency(%)

Flowcoefficient

Test

0123

Efficiency(%)

Flowcoefficient

Test5

Test6

Test7

Test8

C2(0.436 ; 0.818 ; 35° ; 0.545), and one for

inhalation; C3= (0.436 ; 1 ; 25° ; 0.6). The

combination C3 is chosen for optimizing the turbine

efficiency in inhalation mode, and for choosing one

of the two combinations C1 and C2 that optimizes the

efficiency for the exhalation mode, new simulation

tests has been done for the two combinations in

exhalation mode in order to choose the one which

maximise the some of the three efficiencies for

different flow coefficients. The Table 5 represent the

values of efficiencies for the combinations C1 and

C2.

Table 5: Turbine efficiency for the combinations C1 and C2

in exhalation mode



C1 C2

0.5 58% 62%

1.5 54% 58.5%

2.5 51.2% 52.7%

From the numerical tests results, the combination

C2 for the exhalation mode has the maximum

efficiency in all the three flow coefficients. So C2 is

the optimal combination for the exhalation mode.

The Table 6 represent a recapitulation of the

optimal combinations for exhalation and inhalation

modes.

Table 6: Dimensionless values of optimal combinations for

exhalation and inhalation modes

Mode (r

;β*; t)

Exhalation (0.436 ; 0.818 ; 35° ; 0.545)

Inhalation (0.436 ; 1 ; 25° ; 0.6)

The optimized rotor profiles for the two phases;

exhalation and inhalation are presented in Figures 6

and 7.



Figure 6: Optimized rotor

blade profile for

exhalation

Figure 7: Optimized rotor

blade profile for inhalation

6 CONCLUSION

In this paper, we have applied the design of

experiemnt method to optimize the rotor blade

geometry in order to maximise the turbine efficiency.

The tests have been done by 2D numerical simulation

with ANSYS FLUENT for time exigencies. Four

variables parameters has been chosen as inputs; the

radius of the suction side, the blade chord, the inter-

distance between centre of the two circular arcs, and

the geometrical angle in the leading and trailing edges

of the blade rotor, and one as output; the turbine

efficiency. The other parameters have been fixed.

An optimizing program has been elaborated with

MATLAB and two combinations of the inputs

parameters that maximize the output parameter; the

turbine efficiency, in exhalation and inhalation modes

have been found; (rs ;lr ;β*; t) = (0.436 ; 0.818 ; 35° ;

0.545) for exhalation and (rs ;lr ;β*; t) = (0.436 ; 1 ;

25° ; 0.6) for inhalation.

For the future work, a second design of

experiment will be elaborated for optimizing the

guide vanes and the rotor solidities, in order to find

an optimal design of the turbine in exhalation and

inhalation modes.

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