Hydrodynamic Analysis of Oscillating Water Column Using CFD Code

Introduction

Energy has been the bedrock for techno-industrial development globally. Hence, researching into its sources will never cease. This has been the reason for the scouting of environmentally friendly energy source devoid of any kind of health and environment challenging issues. So the introduction of OWC wet energy source is significantly imperative at this time. The OWC energy source is a sea or ocean based energy source capable for the generation of electric power. Its effectiveness and workability is immeasurable as the sector is set to compete with its rivals and the conventional source of energy. This affirms an established European Union (EU) report which attests that the global energy demand could be fulfilled with just 0.1% availability of ocean energy if fully harnessed [1, 2]. Thus, a scholarly research unveils that this energy source may contribute significantly to the electrical energy supply of countries with coasts facing the ocean [3, 4]. Conversely, a similar investigative research upholds that 100% total energy consumption will be achieved if renewable energy sources like the solar, wind and wave respectively is exploit extensively [5, 6, 7].

In this respect a wide variety of technologies has been proposed, studied, and tested in some cases at full size in real ocean conditions. Therefore, it has become necessary to overview analytically the hydrodynamics of OWC in this paper presentation. However, the evaluation of related studies shows that the hydrodynamic performance of OWC depends on the interactions with ocean waves [8]. Thus, different scholarly research performs a hydrodynamic model test and numerical analyses on an inclined OWC wave energy converter. According to their separate findings, results from their practical evaluation affirms an improved economic viability of the OWC wave energy converter. This has enhanced an improvement in the applicability of the sloppy breakwater section thus reducing cost in construction of chamber structure [9, 10, 11, 12].

Consequently, reviewed literature reveals the application and incorporation of complex physical effects such as non-linearity and Power Take-Off (PTO) damping in the analysis of OWC hydrodynamics for more reliable performance of the device. It has been systematically proven the effect of the OWC efficiency by magnitude and amplitude as non-linearity is introduced to the device. This tends to decrease with increase in wave height; reversely it increases with decrease in wave height [13, 14, 15, 16]. This is a clear attestation for this application that even smaller wave height is capable of reliable performance from the device. However, a comparative analytical study to determine a 2D OWC efficiency between a linear and nonlinear PTO confirms maximum efficiency of the device with strongly nonlinearity PTO which is slightly inferior to linear PTO [17].

In bid of analyzing the performance of OWC device different methods has been carried out by different researchers. The adoption of a finite element model to study scattered waves around single and multiple OWC wave energy conversion devices based on linear wave theory has been carried out in a research study. It was found that the presence of neighboring OWCs has a significant influence on the power captured and the efficiency of the individual devices [17]. Another is a numerical study of the hydrodynamic performance of a shoreline-mounted OWC device using boundary element method. This assures the topographical effects of the bottom slope and water depth on the OWC device [18]. The application of a commercial 3D linear boundary element method was carried out on a model in a study to fix the dynamic chamber pressure of OWC [19].

Meanwhile, in this paper presentation of hydrodynamic analysis of OWC using CFD code is aimed to improve on the performance of the OWC device as recently studied by different scholars. All these are targets to ensure effective performance of the device for better productivity, reliability and sustainability for better electric power supply.

OWC Modelling and Simulation

The modelling process of the OWC was carried out in solidworks modelling software which has friendly interface as shown in Figure 1 and it is imported to the CFD simulation code. This code enables the numerical analysis of the device and is initiated by the geometry creation, meshing, simulation setup. The process is followed up with physics constraint initiation parameters, materials selection, model theory specification, boundary loading conditions, solution initialization and calculation.

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The meshing process was carried out where components were divided into smaller elements for the application of uniformly distributed loads. It produces the most appropriate mesh for accurate, efficient and multiphysics solutions. Hence, the model of the OWC chamber yields the following discretization meshing output of 302603 tetrahedral cells. This is with zones 1 – 3 having 595589 triangular interior faces, 672 triangular velocity-inlet faces and 18202 triangular wall faces respectively. Others are zones 6 – 8 with 42 triangular pressure-outlet faces, 318 triangular pressure- outlet faces, and 55440 nodes flags respectively.

Conversely, with the completion of the meshing process a simulation setup was conducted where all the mathematical models for computational analysis are assigned to a domain in the CFD fluent solver. Meanwhile, this simulation physics is governed by fluid flow equations which analyze the hydrodynamics of the working fluid within the OWC device. Equations 1 – 6 are capable of estimating the turbulent-flow behaviour, the turbulent dissipation rate, momentum, energy and partial mass balance, as well as Shear Stress Transport (SST) [19].

Turbulent Kinetic Energy (k) Equation:

( ) i t k b M k i j k j $$ + \frac {\delta \rho k u _ {i}}{\delta x _ {i}} + \frac {\delta}{\delta x _ {j}} \left[ \left(\mu + \frac {\mu_ {t}}{\sigma_ {k}}\right) \frac {\delta k}{\delta x _ {j}} \right] + P _ {k} + P _ {b} + P \in - Y _ {M} + S $$ k ku k P P P Y S t x x x δ ρ δρ µ δ δ µ δ δ δ σ δ (1) Turbulent Dissipation rate (∈) equation:

( ) ( ) $$ \frac {\left(\rho \in\right)}{\partial t} + \frac {\delta \rho \in u _ {i}}{\delta x _ {i}} + \frac {\delta}{\delta x _ {j}} \left[ \left(\mu + \frac {\mu_ {t}}{\sigma_ {\epsilon}}\right) \frac {\delta \in}{\delta x _ {j}} \right] + C _ {1 \in} \frac {\in}{k} \left(P _ {k} + C _ {3 \in} P _ {b}\right) - \rho C _ {2 \in} \frac {\in^ {2}}{k} + S $$ δ ρ δρ µ δ δ µ ρ δ δ δ σ δ ∈ ∈ ∈ ∈ ∈

2 u C P C P C S t x x x k k

1 3 2 i t k b i j j (2)

Momentum Equation:

$$ \frac {\delta \rho U}{\delta t} + \nabla \bullet \rho U U = - \nabla \rho + \nabla \tau + \rho g \tag {3} $$ Species Mass Fraction Equation:

$$ \frac {\delta \rho m _ {i}}{\delta t} + \nabla \bullet \rho U m _ {i} = \nabla \bullet D _ {e} \rho \nabla m _ {i} - R _ {i} \tag {4} $$ SST Model Equations:

( ) ( ) * j k t j j j $$ + \frac {\delta \rho u _ {j} k}{\delta x _ {j}} = \frac {\delta}{\delta x _ {j}} \left[ \left(\mu + \sigma_ {k} \mu_ {t}\right) \frac {\delta k}{\delta x _ {j}} \right] + \rho - \rho $$ u k k k k t x x x δρ δ ρ δ δ µ σ µ ρ β ρω δ δ δ δ (5) ( ) ( ) 2 j d u k k P t x k x x x x ω δ ρ ω δ ρω ρσ γω δ ρ δω δ δω βρω µ σ δ δ δ ω δ ω δ δ $$ \frac {1}{\lambda} + \frac {\delta \left(\rho u _ {j} \omega\right)}{\delta x _ {j}} = \frac {\gamma \omega}{k} P - \beta \rho \omega^ {2} + \frac {\delta}{\delta x _ {j}} \left[ \left(\mu + \sigma_ {\omega} \frac {\rho k}{\omega}\right) \frac {\delta \omega}{\delta x _ {j}} \right] + \frac {\rho \sigma_ {d}}{\omega} \cdot \frac {\delta k}{\delta x _ {j}} \cdot \frac {\delta}{\delta x _ {j}} $$ j j j j j (6)

Presentation of Results

The following are presentation of pneumatic pressure results according to variation of vent opening. It shows the pressure distribution across the interior of the OWC chamber with varying open chamber vent diameter (OCVD) undergoing 2 – phase (water-liquid and air) volume of fluid (VOF) flow process simulation. They are shown in Figures 2-5.

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Other results are contour plots of air flow velocity across the OWC chamber with variation in the vent opening. They are presented in Figures 6-9.

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Similarly, the results for volume fraction for both water- liquid and air phases are equally presented for discussion. The solver is made to simulate and computes the ratio of the equation of continuity for the phases and the density of the material operating on it. Figures 10-13 are the contour plots for the volume fraction.

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Other simulation results automatically generated are presented in the graphical plots to analyze the performance variations as some desirable parameters of the wave are considered. These illustrations are shown in Figures 14 & 15.

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Discussion of Results

The contour plots of the pneumatic pressure is an ideal illustration of the hydrodynamics and the physics behind the fluid motion in the OWC device. The pressure distribution across the interior section of the device varies with respect to the variation of the vent diameter of the chamber. In the simulation results, the highest and lowest pneumatic pressure of 8.447E+4Pa and −1.083E+3Pa is observed at the bottom (red spots) and top (blue spots) respectively of the chamber in figure 2 with a vent diameter of 1m. Apparently, in the simulation results of figures 3 – 5 a similar scenario is observed with the highest values of pneumatic pressure of 3.646E+5Pa, 6.546E+5Pa and 1.077E+5Pa respectively. Conversely, the simulation of the estimated air velocity at the inlet of the turbine is observed to be 23.98, , 22.92 and 1.615 respectively at the vent opening is programmed to decrease from 1m to 0.2m. However, the investigation of the volume fraction at the different vent diameters from the simulation results are also observed as 0.1224, 0.3030, 0.1212, and 0.06061 for 1.0m, 0.8m, 0.6m and 0.2m respectively.

The effect of wave height variation on the OWC efficiency is shown in figure 14. It indicates that the hydrodynamic efficiency of the OWC is in relationship with the wave height. Records attests that the highest and lowest hydrodynamic efficiencies of 45.57% and 43.85% are observed at wave height ratios of 0.238 and 0.051 respectively. This affirms that the hydrodynamic efficiency increases with corresponding rise in wave height. Similarly, figure 15 is a demonstration of the ratio of wave amplitude against efficiency of the OWC. It shows that there is progressive increase in wave amplification with the increase of relative wave height which is an influencing factor to the component efficiency. Also, to achieve the maximum height of a wave is depending upon the depth of water bodies. Consequently, in the graphical plot a maximum wave amplitude of 0.119 gives the highest OWC efficiency of 45.57% at water depth of 1.7m. Meanwhile, an amplitude of 0.026 gives 43.85% at a water depth of 0.4m. It therefore attests that OWC efficiency increases with increase in amplitude. This is a clear indication that the wave amplification is an important criterion in deciding the OWC geometry.

Conclusion

In the above discussion a common sequence of results is identified. At the pneumatic pressure, result of vent diameter 0.6m is confirmed as the highest, whereas result for vent diameter 0.8m for air velocity and volume fraction are observed as the highest likewise. Therefore, the summary of the contour plots of results attests that 0.8m vent diameter opening for the construction of OWC device will produce efficient output. In another test of result indicate wave height as a controlling factor to the hydrodynamic efficiency of OWC. Thus, the turbine efficiency is a direct dependent to the hydrodynamic efficiency. Hence, it could be concluded that the wave height is directly proportional to the turbine efficiency in an OWC device. Analyzed results attest that the effect of the wave period in the determination of its amplitude can vary the OWC efficiency. However, the depth of water where an OWC device is constructed is a serious consideration mostly for site selection analysis.