A new CFD-based framework for modelling the interaction of open ocean aquaculture structures and complex free surface hydrodynamics
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The work presented in this PhD thesis provides the first numerical framework for the detailed simulation of open ocean aquaculture structures in the sea environment. It enables the simulation of the fluid-structure interaction of rigid floating structures and nets with a viscous fluid including a free surface. As part of the thesis, new approaches for modelling mooring dynamics, dynamics of nets and the rigid body dynamics of floating structures as well as their interaction with the fluid are developed by the author. All models are integrated into the viscous two-phase Computational fluid dynamics (CFD) solver REEF3D. This is in contrast to existing numerical approaches which either neglect important non-linearities or the interaction between the structures and the fluid. The Reynolds-averaged Navier-Stokes equations including a free surface are solved as the basis of the two-phase numerical wave tank REEF3D. Here, a k-w turbulence model including an additional source term for the free surface treatment is applied. The equations are solved on a staggered rectilinear grid using finite differences. The convection terms are discretised using fifth-order accurate weighted essentially non-oscillatory (WENO) schemes. An incremental pressure-correction algorithm is added by the author for handling the pressure-velocity coupling. The free surface is represented implicitly by the zero level set of a smooth signed distance function. This function is propagated in time and space by solving the linear advection equation. Waves are generated at the inlet using the relaxation method, and a numerical beach prevents excessive reflections at the end of the tank. Full parallelisation is enabled using a ghost-point approach and the message passing interface (MPI) protocol. An improved version of a continuous direct forcing immersed boundary method is derived in this thesis for modelling rigid floating objects in the three-dimensional numerical wave tank. It is based on a new implicit representation of the body on a stationary grid using a level set function. The motion of the rigid body is described using Euler parameters and Hamiltonian mechanics. The dynamic boundary conditions are enforced by coupling the conservation laws of fluid and rigid body dynamics at the interface between fluid and structure. This effectively avoids computationally expensive reconstruction processes as used in existing approaches and enables the application to large three-dimensional structures. In addition, a new quasi-static mooring model is presented. Here, each mooring cable is divided into finite truss elements, and the static force equilibria are solved at each knot in each time step. Thus, the steady-state solution for the shape of an elastic cable and the tension force distribution under consideration of hydrodynamic loads is found. A successive approximation is applied to the resulting system of equations which leads to a significant reduction of the matrix size in comparison to the usage of Newton-Raphson methods. Here, the unknown internal and external forces are separated, and the system is corrected iteratively using the intermediate results for the unit vectors until convergence is reached. The resulting model presents a novel compromise between dynamic and analytical solutions for mooring lines because it combines the flexibility of a generically formulated numerical approach with similar efficiency and simplicity as an analytical solution. The structural dynamics of large tensile and flexible structures undergoing large motions and deformations, such as nets, are solved with a novel approach based on the lumped mass method. The discrete structure is represented by several elastic bars and knots connecting up to four bars. Non-linear material laws are incorporated which is in contrast to previous models for this type of structures. An implicit system of equations is derived from the fundamental relations of dynamics, kinematics and material laws. It is solved using an improved Newton’s method. Hence, a robust model is derived which can be easily coupled to any fluid dynamics solver without restricting the general time step criterion. In contrast to common tensile structures such as membranes, the considered nets are characterised by high porosities and consist of a large number of individual twines. The length scale of the flow around each twine is significantly smaller than the length scale of the flow around the whole floating structure. This prevents the resolution of the net on the same numerical grid as the fluid domain, and an alternative representation of the fluid-structure interaction between net and fluid has to be introduced. Within this thesis, the author presents a new Lagrangian approach to account for this coupling. The model is based on solving the momentum equations for the fluid on the Eulerian grid and including a source term to account for the disturbances due to the presence of the net. These disturbances represent the momentum transfer between fluid and net and are calculated from the acting forces on the structure. The forces are approximated using a screen force model on Lagrangian points discretising the surface of the net. A suitable interpolation kernel is applied to distribute the forcing term on the fluid domain. In comparison to approaches based on porous media representations, the new model is based on a physical derivation and is suitable for arbitrary geometries and large motions. Multiple validation cases are presented for the different modules in the course of establishing the framework. It includes the simulation of current flows and wave propagation through fixed and flexible nets as well as the analysis of moored-floating objects in waves with and without nets attached. Finally, a semi-submersible and a mobilefloating open ocean aquaculture structure are investigated to highlight the possibilities of the numerical approach for future applications in this field.
Består avPaper 1: Martin, Tobias; Kamath, Arun; Bihs, Hans. Accurate modelling of the interaction of constrained floating structures and complex free surfaces using a new quasi-static mooring model. International Journal for Numerical Methods in Fluids 2021 ;Volum 93.(2) s. 504-526 https://doi.org/10.1002/fld.4894 This is an open access article under the terms of the Creative Commons Attribution License (CC BY 4.0)
Paper 2: Martin, Tobias; Kamath, Arun; Bihs, Hans. A Lagrangian approach for the coupled simulation of fixed net structures in a Eulerian fluid model. Journal of Fluids and Structures 2020 ;Volum 94. s. 1-26 https://doi.org/10.1016/j.jfluidstructs.2020.102962
Paper 3: Martin, Tobias; Bihs, Hans. A non-linear implicit approach for modelling the dynamics of porous tensile structures interacting with fluids. Journal of Fluids and Structures 2021 ;Volum 100. https://doi.org/10.1016/j.jfluidstructs.2020.103168 This is an open access article distributed under the Creative Commons Attribution License (CC BY 4.0)
Paper 4: Martin, Tobias; Bihs, Hans. A Numerical Solution for Modelling Mooring Dynamics, Including Bending and Shearing Effects, Using a Geometrically Exact Beam Model. Journal of Marine Science and Engineering 2021 ;Volum 9.(5) https://doi.org/10.3390/jmse9050486 This is an open access article distributed under the Creative Commons Attribution License (CC BY 4.0)
Paper 5: Martin, Tobias; Bihs, Hans. A CFD approach for modelling the fluid-structure interaction of offshore aquaculture cages and waves. ASME 40th International Conference on Ocean, Offshore and Artic Engineering, OMAE2021,