L. Qian

A free-surface capturing method for two fluid flows with moving bodies

A two-fluid solver has been developed for flow problems with both moving solid bodies and free surfaces. The underlying scheme is based on the solution of the incompressible Navier–Stokes equations for a variable density fluid system with a free surface. The cut cell method is used for tracking moving solid boundaries across a stationary background Cartesian grid. The computational domain encompasses fully both fluid regions and the fluid interface is treated as a contact discontinuity in the density field, which is captured automatically without special provision as part of the numerical solution using a time-accurate artificial compressibility method and high resolution Godunov-type scheme. A pressure-splitting algorithm is proposed for the accurate treatment of the normal pressure gradient at the interface in the presence of a gravity term. The Cartesian cut cell technique provides a highly efficient and fully automated process for generating body fitted meshes, which is particularly useful for moving boundary problems. Several test cases have been calculated using the present approach including a moving paddle as a wave generator and the initial stages of entry into still water of rigid wedges. The results compare well with other theoretical results and experimental data. Finally, test cases involving the entry into water and subsequent total immersion of a two-dimensional rigid wedge-shaped body as well as the inverse problem of wedge egress have been calculated to demonstrate the ability of the current method to tackle more general two fluid flows with interface break-up, reconnection, entrapment of one fluid into the other, as well as handling moving bodies of complex geometry.

A compressible multiphase flow model for violent aerated wave impact problems

This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.

Pure and aerated water entry of a flat plate

This paper presents an experimental and numerical investigation of the entry of a rigid square flat plate into pure and aerated water. Attention is focused on the measurement and calculation of the slamming loads on the plate. The experimental study was carried out in the ocean basin at Plymouth University’s COAST laboratory. The present numerical approach extends a two-dimensional hydro-code to compute three-dimensional hydrodynamic impact problems. The impact loads on the structure computed by the numerical model compare well with laboratory measurements. It is revealed that the impact loading consists of distinctive features including (1) shock loading with a high pressure peak, (2) fluid expansion loading associated with very low sub-atmospheric pressure close to the saturated vapour pressure, and (3) less severe secondary reloading with super-atmospheric pressure. It is also disclosed that aeration introduced into water can effectively reduce local pressures and total forces on the flat plate. The peak impact loading on the plate can be reduced by half or even more with 1.6% aeration in water. At the same time, the lifespan of shock loading is prolonged by aeration, and the variation of impulse is less sensitive to the change of aeration than the peak loading.

Numerical Simulation of Wave Power Devices Using a Two Fluid Free Surface Solver

A generic two-fluid (water/air) numerical model has been developed and applied for the simulation of the complex fluid flow around a wave driven rotating vane near a shoreline in the context of a novel wave energy device OWSC (Oscillating wave surge converter). The underlying scheme is based on the solution of the incompressible Euler equations for a variable density fluid system for automatically capturing the interface between water and air and the Cartesian cut cell method for tracking moving solid boundaries on a background stationary Cartesian grid. The results from the present study indicate that the method is an effective tool for modeling a wide range of free surface flow problems.

Cartesian Cut Cell Free Surface Capturing Solver for Wave Floating Body Interactions

A newly developed free surface capturing code based on a two fluid formulation of Navier-Stokes equations and Cartesian cut cell grid system has been applied to study wave/floating body interaction problems. The basic flow solver uses an efficient dual time-stepping artificial compressibility algorithm and modern Riemann solver based upwind schemes of the Godunov-type which capture the moving free surface accurately as part of the numerical solution. Mesh generation in the conventional sense is eliminated in favour of defining local cut cell data on a stationary background Cartesian grid. For wave/floating body interaction problems where bodies can undergo arbitrary movement in response to the incoming waves, the only required changes to the meshing procedures consist of local updates to the cut cell data at the boundaries that are in motion. A test case has been simulated and the results are in a good agreement with available experimental data. The numerical model is generic and can be applied to a number of engineering flow problems such as green water overtopping of vessels and offshore floating structures.

Simulation of parallel blade–vortex interaction using a discrete vortex method

Numerical results are presented for two-dimensional vortex-aerofoil interaction using a grid-free discrete vortex method. The effects of the passing vortex on the surface pressure distribution and hence the aerodynamic force and moment of the aerofoil are examined in detail for a variety of interaction geometries. For some head-on interaction cases, vortex-induced local flow separation is also predicted on the aft part of the aerofoil surfaces

Computational Fluid Dynamics (CFD) Models

Fundamental principles of computational fluid dynamic (CFD) modelling are presented together with a brief review of CFD applied to wave energy converters. Results are presented for a range of models including incompressible and compressible two-phase flows. Limitations of CFD modelling are discussed together with future developments in CFD.

Simulation of Focused Waves Using a Free‐Surface Capturing Code

In this paper, the focused wave groups, which have been used in physical flumes for testing the survivability of offshore installations under extreme wave conditions, are generated numerically by using a recently developed two‐fluid free‐surface capturing code (AMAZON‐SC). The finite volume based method solves Navier‐Stokes equations for a variable density fluid on a Cartesian grid and the movement of the wave maker (a piston‐type paddle) is simulated efficiently and accurately by adopting a generic cut cell mesh approach for moving boundaries. Two test cases of the focused wave group with different frequency bandwidths have been calculated and results are in generally good agreements with the relevant experimental data.

Development of a 3D Free Surface Capturing Code for Coastal Engineering Flow Problems

A free surface capturing code has been developed for 3D hydraulic and coastal engineering flow problems. The underlying scheme is based on the solution of the incompressible Navier-Stokes equations for a variable density fluid system. The free surface is captured automatically during the calculation using a time-accurate artificial compressibility method and high resolution Godunov-type Riemann solver based algorithm. The accuracy of the code is being validated against some experimental results.

A Two-fluid Solver For Hydraulic Applications

A two-fluid solver for hydraulic applications including the prediction of vi- olent overtopping of waves at seawalls has been developed. The scheme is based on the solution of the incompressible Navier-Stokes equations for a variable density fluid system using the artificial compressibility method. The computational domain encompasses both water and air regions and the interface between the two fluids is treated as a contact discontinuity in the density field which is captured automatically as part of the solution. A time+accurate solution has been achieved by using an implicit dual-time iteration technique. Several classical test cases includhg the low amplitude sloshing tank and the broken dam problems, as well as a collapsing wa- ter column hitting a downstream obstacle have been calculated using the present approach and the results compare very well with other theoretical and experimental results.