REVIEW OF FLUID-STRUCTURE INTERACTION MODEL IN A NUMERICAL WAVE TANK WITH OFFSHORE STRUCTURES NEAR THE FREE SURFACE

The effects of the surface waves generated by the wind have a significant effect on the currents. A wave current coupled model plays an important role in the design of offshore structures. The interaction between fluids such as incompressible ocean waves and current and offshore structures is significant with many real-time applications in offshore engineering. These coupled models can be applied to Offshore Floating Production Operating and offloading (FPSO), Wind or current turbines and offshore pipelines. The complex issues related to the design are analyzed by using Computational Fluid Dynamics, which requires an investigation of the multiphase flow between wave and current and the structure which is considered restrictive due to the computational cost. If viscous effects are neglected then the single-phase flow models have been recommended, where wave-current interaction have been modelled successfully. Models have been developed where velocities and pressure are computed and the results can be verified with the experimental results available in the literature. In this study the existing numerical methods, mesh types are discussed along with their coupling methods. Here single-phase and multiphase models with small and medium movement are reviewed and their applications are highlighted.


Introduction
The offshore structures serve not only for Oil and gas exploration but they are also used for the degeneration of energy from non-renewable energy sources like ocean winds, waves and currents such as windmills, current energy generator. The deepwater offshore structures are more vulnerable to environmental loadings such as wind-induced water waves and currents than shallow water. To make them operational throughout their design life; it is utmost necessary to ensure the safety of such structures. In past; due to their location and dealing with sensitive material, and environmental hazards associated with the fossil fuels these structures had been designed with conservative loadings. Recently, due to advance in shell technologies the hydrocarbon fuel prices have decreased. It is time to design offshore structures efficiently to reduce the extra costs associated with them. For proper structural design, it is necessary to consider the real environmental loads on the structure. The coupled and non-coupled wave-current interaction has been observed in many cases on the structure [1]. The analysis of such interactions needs different mathematical approaches, observations and experiments. This interaction has been considered as the most complex phenomenon, where current is superimposed with waves.
Initially, studies were performed in laboratory-based wave tanks but after the computational evolution, the experimental tanks have been replaced by Computational Fluid Dynamics (CFD) numerical wave tanks involving computational costs only. The combined wave-current interaction based on Navier-Stokes equations has been studied by various researchers [2, 3, 4, 5, 6, 7, and 8]. Most of these studies are done under Numerical wave tank simulations with different CFD solver techniques. Various open-source and commercial codes are available for the simulation of flow dynamics. The accuracy of such simulation depends upon the comparison of model validation results with available experimental works. The experimental works regarding wave and current interaction have not been much studied due to limitations of cost, space and measurements. Under such circumstances, the studies of one CFD techniques could be compared with the results of other CFD technique as done in the study of [7 & 9].
The involvement of current with waves make flow characteristics complex. The superimposition of current onto the wave in a numerical wave tank can be achieved either by introducing pressure inlet boundary condition [4 & 6] or by velocity inlet boundary condition [3 & 11]. The velocity of waves remains the same throughout the depth with velocity wavemaker while waves generated with pressure wavemaker have varying current velocities with the depth. The FLUENT is a CFD commercial software of ANSYS incorporation based on Finite volume method. The software is very effective in modelling the physical phenomenon of flow and turbulence. The world supercomputing record has been set by this software with scaling to 172,000 cores. It is very effective for RANS simulations. It has been successfully used in the studies of [3, 4, 7, 8, 11, and 12].

Previous Studies
The simultaneous occurrence of wave and current in ocean environments make their interaction as the most prominent factor for the analysis of hydrodynamics of oceans [5]. The major environmental forces for this region are considered to be waves and currents [6]. Every offshore structure before its design requires the analysis of such hydrodynamic forces. Offshore structures have been studied by many authors using frequency domain analysis [13,14,15] and Time domain analysis [13,15,16,17]. The forces have been determined by using the Morison equation and linear diffraction wave theory. The main determination of the study involved capturing random wave responses in a surge, heave and pitch [18]. Such a response is called Response Amplitude Operator (RAO).
The wave-current interaction with structures involved the numerical approaches in these studies. This numerical approach is based on the potential flow theory, linear waves and small current velocity approximation. The coexisting field of the wave with current involves the separation of the velocity potential. This separation is done into the unsteady potential of wave and current. It becomes easier to determine the elevation of water surface around an offshore structure under the coexisting field of wave and current. The unsteady wave potential and current velocity are substituted in first-order dynamic surface boundary condition to obtain the water surface elevation [19]. One of the studies involved the time-domain method [13]. The regular waves diffraction and radiation effects were determined due to current with a 2-D body. The observation proved the current effects on offshore structures and a non-linear relation with currents was shown with first and second-order results.
Surface wind stress, bottom friction, wave climate, wave field, depth and current refraction and modulation of the absolute and relative wave period are the most common wave-current interaction mechanisms reviewed [16,17,18]. The change is slow drift motions, wave run-up and wave forces have been observed due to the combination of waves and currents [19]. It has been observed that wave and current occur at the same time in the oceans. A resonance is normally created when wave and current interact with the structure. This resonance causes slow drift motions. The prediction of such motions is also very important from the engineering perspective. The pure wave interaction with the offshore structures has been observed differently as compared to wave current coupled interaction. When time-domain results were compared with the frequency domain, no difference was found in these studies.
The long-crested wave along with current produce more forces as compared to short crested wave involving current. The experimental study of [20] made comparisons between short crested wave with current and long-crested wave with currents. It was found in the study that long-crested wave with the current was able to produce 45% more forces as compared to short crested wave with the current. The author of the study suggested that further study was required to be conducted regarding short crested waves involving six-degree-of-freedom. It has been observed that in intermediate and shallow waters, the short crested wave remains dominant while for the deep waters long-crested waves are dominant. Due to lack of proper data, the offshore structures are designed for the long-crested waves.
The short crested waves along with current produce different results than the long-crested waves with the current. In the analytical study of [2], the effects of the current having uniform velocity were studied on the short crested wave. The wave parameters on which the effect was studied were wave frequency, wave run-up, wave force and inertia. The water depth was found to be in inverse relation with the short crested wave having uniform current and total wave number was having a direct relation. The wave frequency was influenced by the current velocity and current incident angle. Details of various numerous studies involving wave, current and structure have been briefly described with the purpose, observations and suggestions of the study in Table 1.

Wave and Current Fields in offshore environments
The dimensionless quantities are the key to the numerical analysis of flow so non-dimensional parameters are preferred. The most used non-dimensionless parameters are, wave height (H/ 2 ), wave steepness (H/L) and water depth (d/ 2 ). In a numerical wave tank, the waves are generated at the inlet to simulate the wave parameters as shown in Figure 1. Without the presence of current, the free surface displacement Eq. 1 and velocity potential Eq. 2 can be written as; Where, is free surface displacement, H is wave height, ( − ) is wave phase angle, ∅ is velocity potential, g is the acceleration due to gravity, h is water depth, k is wave number, and t is time. The long-crested waves with current were found to produce (45%) more responses than short crested waves with the current. Suggestion 1: Further study needs to be conducted by considering wind loads also. Suggestion 2: The study should include surge, sway, heave, roll, pitch and yaw (Six degree-of-freedom). Exp.
--Wave-current interaction with truss spar Dynamic responses of the truss spar model due to wave with current are greater as compared to wave without current. Maybe because current velocity provides additional lateral force in the water body which increased the structure resonance. Dynamic responses were found to be greater under wave with the current. One-unit increase in the current velocity was found to increase surge by 24 The free surface displacement has two parameters associated with it i.e. Kinematic and dynamic both of which need to be satisfied with velocity potential. If pressure is assumed to be consistent at free surface = ( , ) than dynamic boundary condition for the free surface can be represented with the Bernoulli equation as eq. (3): The description of water particle in the horizontal direction can be made as: Where Ak is the velocity component for the horizontal direction and it is small in magnitude so ( ) 2 is just negligible. So now the Eq. (3) for z=0 can be written as Eq. (6) or eq. (7): − cos ℎ ℎ ( − ) + The water particle velocity should be within specified physical conditions to satisfy the boundary condition so if satisfied, water particle motion will be considered as the kinematic boundary condition. So under this situation, − ( , ) = 0 at any arbitrary moment in the boundary. Now kinematic boundary condition at the free surface will be as shown in Eq. (8); When we arrange Eq. (8) by linear terms, it can be rewritten as Eq. (9): The currents are directed motions of seawater generated by the action of earth rotation, wind, temperature, water salinity and gravity of sun and moon. They are not like waves and flows at greater distances in the oceans and play a vital role in the earth's climate. They can be divided into deep water currents and surface water currents. The deepwater currents move under the influence of temperature and density of water while the surface currents move under the influence of wind.
By assuming a uniform current for the whole depth of the tank, the velocity potential of Eq. (2) can be rewritten as Eq. (10): = cos ℎ ( ℎ + ) cos( − ) − Where U is current velocity, H is wave height, k is wave number, h is water depth, is frequency, and The amplitude of wave with the consideration of current can be written as Eq. (11): By putting, and in equation (6), we can obtain the equation for the dispersion relation with current velocity (U) as shown in Eq. (12); Where is the absolute frequency and is encounter frequency.

Numerical Wave Tank Approach
The wave, current and their interaction can be measured by different technologies currently available. Previously, the ocean environments have been studied on the laboratory basis only. But due to limitations involved with the experimental works, the wave-current interaction has not extensively been studied under field conditions. The advancement in the computational field has created new opportunities for fluid dynamics. The most cost-effective way to study such an environment is by the  Table 2 shows some of the recent studies of numerical wave tank simulation with RANS equations. Most of the Numerical tanks mentioned in Table 2 have applied the turbulent model. All the numerical wave tank use the artificial damping zone to reduce the reflection effects of the waves generated in the tank. Every model involves initial and boundary conditions. The waves and currents are generated at the inlet of the tank while the reflected waves are absorbed at the outlet of the tank. The numerical wave-current flume shown in Figure 2 gives the full details of initials and boundaries.

Figure 2.
A numerical wave tank defined with each of its boundary [30] Providing the most favourable initial and boundary conditions is the key to towards the successful simulations. Some of the studies under review involved the pressure based waver maker at the inlet boundary of the wave tank [4,6]. While on the contrary, the studies of [3,11] involved velocity based wavemaker. When the authors compared their obtained results with the results of experimental works, the studies involving velocity wavemaker gave the best comparisons. The pressure-based studies provided the best results for the wave condition only. While for current and wave-current interaction, their simulation was not promising enough. The wave tank based on the pressure as a current producing source provided fluctuating current values concerning the depth of the water while in case of velocity, the value of current remained the same throughout the depth. The author of study [6] concluded that the location of the current source in the model should be further studied to get the best results for the current and wave-current interaction cases too.
The RANS equations are most common among the researchers involving less computational costs. The simulations based on RANS equations provide the best simulation results. The accuracy of simulations mainly depends upon the boundary conditions chosen. Most of the studies mentioned in this paper involve the same source region for waves and current except the study of [6] where two separate sources were chosen. This study also involved two separate beaches too, to avoid the reflection effect of these sources. Most of these studies were performed in the two-dimensional domain. Involvement of the Threedimensional domain consumes an extra computer memory and requires some special computers. The accuracy of such simulation depends upon the comparison of model validation results with available experimental works. The experimental works regarding wave and current interaction have not been much studied due to limitations of cost, space and measurements. Under such circumstances, the studies of one CFD techniques could be compared with the results of other CFD technique as done in the study of [7,9].
Most of the studies mentioned in Table 2 were carried out with commercial CFD solver "FLUENT" which is the most popular tool for the simulations of turbulence. Some studies have involved the use of open source tools too. The most popular CFD opensource software is OpenFOAM. The commercial software is intended to provide ease to the user while open source software involves not many favourable user-friendly interfaces.
Kim et al [3], studied wave-current interaction and load analysis using finite volume method (FVM) based numerical wave tank. CFD studies were done in FLUENT software, where governing equations were discretized by the finite volume method. He used 3 rd order Monotone upstream centred scheme (MUSCL) for convection term. The velocity and pressure coupled with Pressure implicit with the splitting of operator (PISO) method. The k-ε model was used for the turbulent stress term in the governing equation. He used Volume of the fluid method with implicit High-resolution interface capturing (HRIC) for the air-water interface.
Zhang et al. [4], developed a numerical wave tank in FLUENT software by using Navier Stokes equations to study the wave and current interaction in the bottom boundary layer. The flow was modelled by RANS equations and the Volume of the fluid method was used to track the free surface. K-ε model was used and at the bottom boundary layer, a low Reynolds number scheme was used instead of high Reynolds's Number scheme. The waves generated were second-order Stokes waves by using velocity inlet boundary. The validation of the wave tank was made by using the experimental data of Kemp, [23]. The implicit highresolution interface capturing method was used.
Markus et al. [24 & 25], also used the same approach as [3] but he used Fenton model [26] to create the depth varying currents The results were found to be more successful but he used nonlinear waves with unsteady flow conditions using Unsteady Reynold's Averaged Navier-Stokes (URANS) equations. He used stream function wave theory to validate his waves generated in the wave tank and compared the results of non-uniform current with uniform currents. His studies mostly involved wave kinematics and no offshore structure was used in the model.

Summary and Conclusion:
For the safety of offshore structures, it is important to account all the environmental loads acting on the structure. Previously, these forces were assessed and analysed using experimental and analytical approaches. The advancement in computational power has replaced the method of analysis from the traditional one to computational fluid dynamics (CFD). Various CFD Tools including open source and commercial software are available now a day. Open-foam and ANSYS FLUENT software has most widely been used for the application of CFD in offshore engineering. Due to the user-friendly interface, the fluent software has been the choice of researchers for the applications of CFD in offshore engineering. These studies have taken the simplest form of offshore structure but due to the complex interaction of wavecurrent with offshore structures, it is necessary to use the geometry of offshore structure close to the actual one.