CFD SIMULATION OF MOTION RESPONSES OF A TRIMARAN IN REGULAR HEAD WAVES

CFD has proved to be an effective method in solving unsteady Reynolds–Averaged Navier-Stokes (RANS) equations for analysing ships in free surface viscous flow. The research reported in this paper is intended to develop a better understanding of the parameters influencing high-speed trimaran motions responses. Variations of gridding system and time step have been investigated and reliability analysis was performed in solving the RANS equations. Different turbulence models were investigated, and the SST Menter K Omega turbulence model proved a more accurate model than Realizable K-epsilon model. In order to validate the CFD method, the results of the motions response of a high- speed trimaran are compared against a set of experimental and numerical results from a 1.6 m trimaran model tested in various head seas conditions. The results suggest that CFD offers a reliable method for predicting pitch and heave motions of trimarans in regular head waves when compared to traditional low speed strip theory methods. Unlike strip theory, the effect of breaking waves, hull shape above waterline and green seas are considered in CFD application. A wave resonance phenomenon was observed and wave deformation as a result of wave-current-wind interaction in CFD was identified as the main source of discrepancy. The results from this work form the basis for future analysis of trimaran motions in oblique seas for developing a better understanding of the parameters influencing the seakeeping response, as well as passenger comfort.

Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.

Direct CFD Simulation and Experimental Study on Coupled Motion Characteristics of Ship and Tank Sloshing in Waves

It is of great significance to study the tank sloshing, especially the coupling motion between tank sloshing and ship in waves with strong non-linearity and randomness. In this study, the response of the ship with/without tank in regular wave is studied by EFD method and CFD method. All the simulations are carried out by in-house CFD code HUST-Ship (hydrodynamic unsteady simulation technology of ship) to solve RANS equations coupled with six degrees of freedom solid body motion equations. RANS equations are solved by finite difference method and PISO algorithm. A two-equation Shear Stress Transport (SST) k-w turbulence model is used. The simulation results are in good agreement with the experimental results, which also indicates that the result of the tank sloshing simulated by in-house CFD code is reliable. The influence of sloshing on ship motions is estimated by comparing the experimental results between the ship with/without tank in different wave conditions. The coupling motion characteristics between the liquid in the tank and the ship is further studied by the CFD method. The study shows that the influence of tank sloshing on ship motion is different under the action of different regular waves.

An artificial compressibility method for axisymmetric swirling flows

Purpose This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows. Design/methodology/approach The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure. Findings A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy. Originality/value This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

Advances in Numerical Reynolds-Averaged Navier–Stokes Modelling of Wave-Structure-Seabed Interactions and Scour

This review paper presents the recent advances in the numerical modelling of wave–structure–seabed interactions. The processes that are involved in wave–structure interactions, which leads to sediment transport and scour effects, are summarized. Subsequently, the three most common approaches for modelling sediment transport that is induced by wave–structure interactions are described. The applicability of each numerical approach is also included with a summary of the most recent studies. These approaches are based on the Reynolds-Averaged Navier–Stokes (RANS) equations for the fluid phase, and mostly differ in how they tackle the seabed response. Finally, future prospects of research are discussed.