Natural energy such as wind, wave and other natural vibrations is one of the high potential renewable energy sources. The Wells turbine is based on the use of bidirectional turbines, which act as axial-flow self-rectifying turbines that employs a symmetrical blade profile and rotating unidirectionally in reciprocating airflows generated by the air chamber to extract energy from vibrations. These topics have been extensively studied both numerically and experimentally such as research on the parameters of the effects of structure, angle of attack, blade shape, etc. In this paper, numerical simulation is carried out using commercially available tool Fluent for fluid dynamics analysis and focus on oscillating predictions, with particular attention to the behavior of the flow. Based on the Numerical Wave Tank (NWT) model is simulated in a two dimensional used in this model, which is constructed mainly based on the spatially averaged Navier Stokes equation with the k-ε model for simulating the turbulence and modeled with Volume of Fluid (VOF). Axial-flow turbines system and future development as well as the proposed limitations will be discussed in detail

Nguyen, Sang Quang

Thien, Truong Tich

Tran, Bang Kim

English

Vietnam Academy of Science and Technology: Journals Online

  
Vietnam Journal of Science and Technology 57 (6A) (2019) 1-9  
doi:10.15625/2525-2518/57/6A/14002 
THE ANALYSIS OF FLUID DYNAMICS OF WAVE POWER 
STATION WITH WELLS TURBIN BY CFD  
Kim-Bang Tran, Quang-Sang Nguyen, Tich-Thien Truong
*
 
Department of Engineering Mechanics, Faculty of Applied Science, Ho Chi Minh city University 
of Technology, VNU-HCMC, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City 
*
Email: tttruong@hcmut.edu.vn 
Received: 22 July 2019; Accepted for publication: 13 January 2020 
Abstract. Natural energy such as wind, wave and other natural vibrations is one of the high 
potential renewable energy sources. The Wells turbine is based on the use of bidirectional 
turbines, which act as axial-flow self-rectifying turbines that employs a symmetrical blade 
profile and rotating undirectionally in reciprocating airflows generated by the air chamber to 
extract energy from vibrations. These topics have been extensively studied both numerically and 
experimentally such as research on the parameters of the effects of structure, angle of attack, 
blade shape, etc. In this paper, numerical simulation is carried out using commercially available 
tool Fluent for fluid dynamics analysis and focus on oscillating predictions, with particular 
attention to the behavior of the flow. Based on the Numerical Wave Tank (NWT) model is 
simulated in a two dimensional used in this model, which is constructed mainly based on the 
spatially averaged Navier Stokes equation with the k-ε model for simulating the turbulence and 
modelled with Volume of Fluid (VOF). Axial-flow turbines system and future development as 
well as the proposed limitations will be discussed in detail. 
Keywords: Oscillating Water Column (OWC), Volume of Fluid (VOF), dynamic flow, wave 
energy, Computational fluid dynamics (CFD). 
Classification numbers: 3.4.1, 5.4.4. 
1. INTRODUCTION 
Wave energy converter (WEC) is considered a promising renewable energy source. They 
have the ability to harness the periodic rise and fall of the wave. Oscillating Water column 
(OWC) is one of the most important wave energy conversion device of the most developed 
WEC types. The OWC uses the air flow produced by the pressure change inside the oscillating 
water column, which is open below the water surface, allowing water to flow in and out an 
internal chamber and generating electricity. Multiple authors have conducted to better 
understand the performance of different OWC devices, the fundamentals to perform 
mathematical modeling of OWC devices [1]. Studies on OWC's properties and performance 
based on linear wave theory and nonlinear small amplitude waves theory are conducted [2, 3]. 
The instantaneous water surface elevation inside the OWC chamber is spatially variant and can 
only be regarded as uniform when the chamber size meets the design requirements that the 
 
 
Kim Bang Tran, Quang Sang Nguyen, Truong Tich Thien 
 
 
2 
studies have given [4, 5]. the product of air pressure in the chamber and the air flow rate of an 
OWC using a two phase VOF model in FLUENT, and found that the amplitudes of the wave 
elevation within the chamber obtained from the 2D Numerical Wave Tank (NWT) compared 
well with experimental data [6]. Because of this bidirectional air flow, axial-flow Wells turbines 
are used in most prototypes. It was introduced in 1976 at Queen’s University in Belfast some 
research into different aerodynamic blade profiles of the Wells turbine and modifications related 
to the airflow velocities [7-9]. A series of useful studies on OWC have been carried out by some 
authors from the application of the theory and boundary conditions to improve the properties and 
performance of OWC, the numerical model the flow was assumed to be inviscid, unsteady and 
incompressible were modeled in a NWT two-dimensional and k-ε turbulent model, where the 
Volume of Fluid (VOF) model were used [10-17]. ANSYS Fluent is a commercial software 
which solves the continuity and momentum Navier-Stokes equations based on the finite volume 
method. The aim of the present study is to carry out a numerical study to calculate the effect of 
the model on the wave amplitude relative to the direction of the flow of the chamber front wall. 
2. NUMERICAL SETUP 
2.1. Geometric model 
The Oscillating Water Column devices are, basically, steel or concrete hollow structures 
partially submerged in a rectangle with a rectangular vent above. 
 
Figure 1. Schematic diagram of oscillating water column. 
The NWT dimension has been introduced in Figure 2 shows a schematic and the boundary 
condition of NWT which were implemented. Reflection appearance is an important issue that 
Wells turbine 
Incident wave 
 
 
The analysis of fluid dynamics of wave power station with wells turbin by CFD 
 
3 
should be considered through wave simulation. In fact, the reflection occurs when the ocean 
waves strike a solid object and is negatively affected such as the impact on the cliffs or in the 
NWT experiments or in digital wave tank experiments, the waves will be bounced off when 
exposed to the wall. In physical modeling, wave energy will be dissipated using porous material 
in the end of the wave flume. In numerical approach there is also several methods for example 
using coarser mesh or using a longer flume. Another way is to use a porous zone. In this paper, a 
longer flume is considered to investigate the wave amplitude for a period of time how long 
OWC's performance will change.  
 
Figure 2. Schematic representation of the computational domain . 
The regular and in real scale wave in the present work has the following characteristics, 
where water depth is h = 10.0 m, wave height is H = 1.0 m, the period T is set to 5s, LT = 188 m 
and HT = 13 m. Besides, as already mentioned, the hydropneumatic chamber length L = 16.7097 
m and height H1 = 2.2501 m, chimney outlet length l = 2.3176  m and its height H2 = 6.9529 
m, and the submergence depth H3 = 9.5 m of the device were defined in agreement with the best 
OWC shape proposed by [12], being these values given by: L = 16.7097 m, H1 = 2.2501 m, l = 
2.3176 m, H2 = 6.9529 m and H3=9.5 m. 
2.2. Mathematical model 
The continuity and momentum (Navier-Stokes) equations based on the finite volume 
method. This is the dominant equation that the fluid problem is based on and it is integrated into 
Fluent tools in ANSYS: 
 
 0 1,2i
i
u
i
t x
 
  
 
 (1) 
 
  1,2i j ji i i i
i i j j i
u u uu u
f F i
t x x x x x
 
 
     
         
         
 (2) 
where: ρ is the specific mass of the fluid density (kg/m3), t is the time (s), p is the static pressure 
(N/m
2
), μ is the molecular viscosity (kg/m.s),  is the stress tensor (N/m2) and g is the 
gravitational acceleration (m/s
2
); xi, xj are longitudinal coordinate and vertical coordinate 
 
 
Kim Bang Tran, Quang Sang Nguyen, Truong Tich Thien 
 
 
4 
respectively, ui (m/s) represent horizontal and vertical velocity components respectively and f1 = 
0 , f2 = -g, Fi are the source terms. 
In this study, the VOF method is applied for consequently free surface capture is an in 
dispensable part of this study. Hence, other governing equations are introduced. The VOF 
formulation is based on the fact that two or more phases are immiscible. This condition is used 
to delineate the limits of two phases without penetrating each other. In each control volume, the 
sum of the volume fraction of all phases: 
 
1
1
n
q
q
f

  (3) 
In each volume, if fq = 1 shows that the volume is full of water, when fq = 0 the volume 
contain only air and if 0 < fq < 1 the volume shows the interface. 
The geometrical characteristics of the device are shown in Figure 2. the wave maker is 
placed in the left side of the wave tank. The wave characteristics are chosen so that it is well 
represented by Stokes second order solution. This methodology consists of applying the 
horizontal ) and vertical v components of wave velocity as boundary conditions(velocity inlet) of 
the computational model, by means a User Defined Function (UDF) by Fluent tools in the 
ANSYS software [18]. The wave considered in this study has a constant period T, wavelength λ 
and incoming wave height H. According to the second order theory, the equation of the free 
surface elevation is [19]: 
 
 
 
 
   
2
4
k cosh
cos 2 cosh 2 cos2
2 16 sinh
khH H
kx t kh kx t
kh
        (4) 
 
 
 
 
 
 
 
2
4
cosh cosh 23
cos cos2
2 cosh 16 sinh
k y h k h yHgk H k
u kx t kx t
x kh kh
 
 

 
    

 (5) 
 
 
 
 
 
 
 
2
4
cosh cosh 23
sin sin 2
2 cosh 16 sinh
k y h k h yHgk H k
v kx t kx t
y kh kh
 
 

 
    

 (6) 
In Equations (5, 6) the first function is linear, the second function is Stoke 2
nd
. 
No slip wall boundary conditions were set at the bottom wall, back wall and chamber wall. 
The top outlet and of the numerical tank were set as constant pressure boundaries. The velocity 
and free surface elevation of the water for the inlet at the left hand end of the domain were 
defined so as to represent an incident wave according equations (4-6). Vertical elements were 
variable also, so that finer mesh was applied near still water level where the variation of water 
level and capturing free surface level was important.  
The standard k-ε turbulence model has been used to simulate mean flow characteristics for 
turbulant flow conditions 
 
t
k
j k j
Dk k
P
dt x x

  

   
     
    
 (7) 
 
 1 2
t
k
j e j
D
C P C
dt x x k
 
  
  

   
     
    
 (8) 
where, the characteristic parameters σk = 1, σe = 1.3, Cε1 = 1.44, Cε2 = 1.92, Cμ = 0.09. It is often 
used for the problem with relatively small pressure gradients that fit the model in this paper. 
 
 
The analysis of fluid dynamics of wave power station with wells turbin by CFD 
 
5 
In this article, geo-reconstruct scheme in Figure 3 is enabled to capture the free surface. 
This scheme is the most accurate and is applicable for general unstructured meshes. The first 
step in this reconstruction scheme is to calculate the position of the linear interface relative to the 
center of each partially-filled cell, based on information about the volume fraction and its 
derivatives in the cell. The second step is to calculate the advection amount of fluid through each 
face using the computed linear interface representation and information about the normal and 
tangential velocity distributions on the face. The third step is to calculate the volume fraction in 
each cell using the balance of fluxes calculated during the previous step. 
 
 a b 
Figure 3. (a) The curve boundary of a phase and (b) using geo-constructed scheme. 
3. SIMULATION RESULTS 
The differences between the analytical and numerical results arise from the assumptions 
for the mathematical modelling in both approaches. To summarize, in the analytical 
approach, it’s assumed that the air flow is compressible, the air chamber remains 
stationary and Bernoulli’s theorem is used for the air flow through the nozzle. Thus, the 
problem is considered one dimensional and the wave profile outside the OWC is 
assumed to be sinusoidal. In the numerical approach, VOF Model feature of the Fluent software 
is used, so that the flow is governed by incompressible Navier Stokes equations where the flow 
is viscous, and the wave profile is generated by the wall motion of the numerical wave tank. As 
a result, two dimensional velocity and pressure fields are obtained for both water and air phases. 
Calculations in this study are performed by considering an incident wave that physical 
parameters satisfy the Stokes second-order theory. In all transient analysis performed in the 
present study the time step is set to 0.01 s. The movement of the free surface is obtained by 
converting the hydrostatic pressure to a height of fluid column. The numerical solution and 
analytical solution for wave amplitude are listed in Figures 4-6 and simulation field in ANSYS 
software in Figure 7 and Figure 8 as follows: 
 
 
Kim Bang Tran, Quang Sang Nguyen, Truong Tich Thien 
 
 
6 
 
Figure 4. Wave amplitude at x = 50 m. 
 
Figure 5. Wave amplitude at x = 83.56 m. 
 
Figure 6. Wave amplitude at x = 150 m. 
9.4
9.6
9.8
10
10.2
10.4
10.6
0 10 20 30
A
m
p
li
tu
d
e 
[m
] 
Time [s] 
Numerical
Analytical
9.4
9.6
9.8
10
10.2
10.4
10.6
0 10 20 30
A
m
p
li
tu
d
e 
[m
] 
Time [s] 
Numerical
Analytical
9.4
9.6
9.8
10
10.2
10.4
10.6
0 10 20 30
A
m
p
li
tu
d
e 
[m
] 
Time [s] 
Numerical
Analystical
 
 
The analysis of fluid dynamics of wave power station with wells turbin by CFD 
 
7 
 
Figure 7. Wave propagation.  
 
Figure 8. Velocity field. 
4. CONCLUSION 
The simulation results show that the wave velocity and amplitude are suitable for 
oscillating water column device in this paper, which uses the air flow produced by the pressure 
change inside the column. The numerical results of wave amplitude show that at the maximum 
and minimum position of the wave or wave crest position, the shape tend to maintain state which 
 
 
Kim Bang Tran, Quang Sang Nguyen, Truong Tich Thien 
 
 
8 
is difference with the shape of the wave crest of the analytical results due to the solution based 
on steady solution while the transient solution will show the true shape of the wave crest but 
usually consuming computer cost. 
The analytical results are based on the theory of a compressible air flow neglecting the 
losses in the fluid-fluid and the fluid-structure interactions while flow was assumed to be viscous 
and incompressible for the numerical model. Possibility of financial support to obtain the 
equipment for the wave tank experiments reveals the third approach, the experimental method, 
which will be the next subject of research of this study. 
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THE ANALYSIS OF FLUID DYNAMICS OF WAVE POWER STATION WITH WELLS TURBIN BY CFD

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