Deborah Greaves

Quadtree grid generation: Information handling, boundary fitting and CFD applications

When solving partial differential equations by numerical methods, an automatic mesh generation technique which can accommodate local mesh refinement adaptively is desirable. One efficient technique for producing such meshes in two-dimensional space is to subdivide recursively the domain into quadrants using a quadtree to store and manipulate the mesh information. Here, the quadtree grid generation technique is reviewed and its programming discussed. Three data storage methods are examined. The conversion of the quadtree grid to a triangular finite element mesh is also described, along with methods for fitting the mesh to smooth boundary contours. Results from viscous flow and standing wave simulations are used to illustrate mesh adaptivity about internal and boundary features.

The effect of viscosity on the transient free-surface waves in a two-dimensional tank

The paper attempts to develop some understanding of the interaction between viscous flow and a free surface by analysing the unsteady flow in an idealised two-dimensional rectangular tank. The mathematical model used is based on the linearized Navier-Stokes equations which are solved by use of the Laplace transform. Various results are provided to show the effect of viscosity on the free surface waves.

On the use of adaptive hierarchical meshes for numerical simulation of separated flows

This paper describes the use of adaptive hierarchical grids to predict incompressible separated flow at low Reynolds number. The grids consist of a quadtree system of hierarchical Cartesian meshes which are generated by recursive subdivision about seeding points. The governing equations are discretized in collocated primitive variable form using finite volumes and solved using a pressure correction scheme. The mesh is locally adapted at each time step, with panel division or removal dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in array size. Results are presented for unidirectional, impulsively started flow past a circular and a square cylinder at various Reynolds numbers up to 5000 and 250 respectively. It is clear that hierarchical meshes may offer gains in efficiency when applied to complex flow domains or strongly sheared flows. However, as expected, the stepped approximation to curved boundaries resulting from the Cartesian quadtree representation adversely affects the accuracy of the results for flow past a circular cylinder.

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 and physical modeling of extreme waves at Wave Hub

ABSTRACT Ransley, E., Hann, M., Greaves, D., Raby, A. and Simmonds, D., 2013. Numerical and physical modelling of extreme waves at Wave Hub With a history of international failures, the survivability of coupled systems of wave energy devices and their moorings, particularly those to be installed at development sites like Wave Hub, is surrounded by uncertainty. Potential design solutions require a better understanding of the hydrodynamics and structural loading experienced during extreme events, like rogue wave impact, in order to mitigate the risk of device and mooring failure. Rogue waves are waves with amplitudes far greater than those expected, given the surrounding sea conditions. Intense study into these events stems from their potential for catastrophic impact on ocean engineering structures. However, little is known about their physical origins and, currently, there is no consensus on their definition or explanation of the mechanism which drives them. This paper concerns the numerical modeling and experimental validation of extreme rogue wave examples at the Wave Hub site. Using hindcast data, the 100 year extreme wave at the Wave Hub site is determined. This extreme wave is replicated in Plymouth Universitys new COAST Lab using a NewWave, dispersive focusing input. To simulate and analyse these events, we duplicate these conditions in a numerical wave tank (NWT), solving the fully nonlinear Navier-Stokes equations, with a free surface, using the Volume of Fluid (VoF) method and open source CFD library OpenFOAM®. The comparison shows that the CFD software is capable of simulating focused waves similar to those produced in the physical tank but tends to overestimate the crest heights. It is also noted that nonlinear effects are important when considering the shape and location of focused wave events.

Wave energy devices with compressible volumes

We present an analysis of wave energy devices with air-filled compressible submerged volumes, where variability of volume is achieved by means of a horizontal surface free to move up and down relative to the body. An analysis of bodies without power take-off (PTO) systems is first presented to demonstrate the positive effects a compressible volume could have on the body response. Subsequently, two compressible device variations are analysed. In the first variation, the compressible volume is connected to a fixed volume via an air turbine for PTO. In the second variation, a water column separates the compressible volume from another volume, which is fitted with an air turbine open to the atmosphere. Both floating and bottom-fixed, axisymmetric, configurations are considered, and linear analysis is employed throughout. Advantages and disadvantages of each device are examined in detail. Some configurations with displaced volumes less than 2000 m3 and with constant turbine coefficients are shown to be capable of achieving 80% of the theoretical maximum absorbed power over a wave period range of about 4 s.

Wave energy absorption by a floating air bag

A floating air bag, ballasted in water, expands and contracts as it heaves under wave action. Connecting the bag to a secondary volume via a turbine transforms the bag into a device capable of generating useful energy from the waves. Small-scale measurements of the device reveal some interesting properties, which are successfully predicted numerically. Owing to its compressibility, the device can have a heave resonance period longer than that of a rigid device of the same shape and size, without any phase control. Furthermore, varying the amount of air in the bag is found to change its shape and hence its dynamic response, while varying the turbine damping or the air volume ratio changes the dynamic response without changing the shape.

Coastal impacts of marine renewables: perception of breaker characteristics by beach water users

ABSTRACT Stokes, C., Beaumont, E., Russell, P., Greaves, D., 2014. Coastal Impacts of Marine Renewables: Perception of Breaker Characteristics by Beach Water Users. In: Green, A.N. and Cooper, J.A.G. (eds.), Proceedings 13th International Coastal Symposium (Durban, South Africa), Journal of Coastal Research, Special Issue No. 70, pp. 389–394, ISSN 0749-0208. Beach water users such as bathers and surfers are of economic importance to tourism in Cornwall, UK. Wave energy converters soon to be trialed at the ‘Wave Hub’ marine renewables test site in Cornwall, may reduce inshore wave heights and have an unknown effect on wave period, therefore potentially affecting water recreation and tourism on the beaches in its lee. There is little existing research to indicate what surf conditions are ‘preferred’ by various beach water user groups, and how they perceive different wave conditions has never been investigated. Without an understanding of how waves are observed and described by water users, little can be said about how likely they are to be affected by, or if they will correctly perceive, any changes to inshore waves caused by Wave Hub or future renewables projects. To investigate how waves are perceived, nearshore wave buoy measurements collected in 10 m water depth and transformed to breaking height, were compared to concurrent visual observations of mean breaker height and period made by 354 participants. Ratios of observed over measured height and period were used to quantify the perceptions. The vast majority of water users underestimated significant wave height and period at breaking, and their average perceptions can be approximated by Hvis ≈ 0.70Hb and Tvis ≈ 0.83T1/3 (for waves 0.5≤Hb≤ 3.5 m and 3 ≤T1/3 ≤ 15 s). Although perceptions were highly varied, average perceptions did not change significantly under different wave conditions. Perception of wave period did not change significantly between the different water user groups considered. Expert water users and surfers generally under predicted wave height the most, especially for small and/or short period waves, while novices and non-surfing water users made height observations closer to measurements.

Calibration, Validation, and Analysis of an Empirical Algorithm for the Retrieval of Wave Spectra from HF Radar Sea Echo

AbstractThe accuracy of the wave products retrieved by a 12-MHz high-frequency (HF) phased-array radar is evaluated for a 5-month period. The two stations composing the system were deployed in 2011 to overlook the Wave Hub, a test site for marine renewable energy devices located on the southwestern coast of the United Kingdom. The system was conceived and configured to reduce the inaccuracies introduced by short time averaging and minimal overlap between stations, both associated with the most traditional HF radar deployments, whose primary activity is current measurement. Wave spectra were retrieved by an empirical algorithm distributed with Wellen Radars (WERA), which were calibrated using in situ measurements collected within the radar footprint. Evaluated through comparison against measurements acquired by three in situ devices, the results revealed estimates of significant wave height with nearly zero bias, linear correlations higher than 90%, and RMS errors that range from 29 to 44 cm. The relative ...

Wave energy absorption by a submerged air bag connected to a rigid float

A new wave energy device features a submerged ballasted air bag connected at the top to a rigid float. Under wave action, the bag expands and contracts, creating a reciprocating air flow through a turbine between the bag and another volume housed within the float. Laboratory measurements are generally in good agreement with numerical predictions. Both show that the trajectory of possible combinations of pressure and elevation at which the device is in static equilibrium takes the shape of an S. This means that statically the device can have three different draughts, and correspondingly three different bag shapes, for the same pressure. The behaviour in waves depends on where the mean pressure-elevation condition is on the static trajectory. The captured power is highest for a mean condition on the middle section.