Richard Willden

Richard Willden
University of Oxford | OX · Department of Engineering Science

About

58
Publications
11,127
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2,053
Citations
Citations since 2017
16 Research Items
1424 Citations
2017201820192020202120222023050100150200250
2017201820192020202120222023050100150200250
2017201820192020202120222023050100150200250
2017201820192020202120222023050100150200250

Publications

Publications (58)
Article
Full-text available
This paper presents an analytic model for the analysis of co-planar turbine fences that partially span the width of a channel in which the flow is driven by a sinusoidally oscillating driving head. The thrust presented by the turbines reduces the flow rate through the channel leading to a solution for overall power that is dependent upon turbine re...
Article
The limit of power extraction by a device which makes use of constructive interference, i.e. local blockage, is investigated theoretically. The device is modelled using actuator disc theory in which we allow the device to be split into arrays and these then into sub-arrays an arbitrary number of times so as to construct an $n$ -level multi-scale de...
Conference Paper
Full-text available
Uncertainty in tidal turbine loading contributes significantly to conservatism in turbine design. This uncertainty originates not only from a lack of knowledge of the flow field at a particular site, but also from lack of understanding of the fundamental physics which govern the loading and performance of tidal turbines in unsteady and turbulent fl...
Article
Concerns about energy production and climate change are driving transitions towards renewable electricity sources around the world. Tidal stream energy has been identified as an energy source with potential as both a renewable and predictable resource, particularly in regions with established offshore industries. Tidal stream technology is at a rel...
Article
An array of ten 1 MW turbines, with a one diameter inter-turbine spacing, is simulated in a hypothetical tidal channel using the depth-averaged flow solver TELEMAC-2D. It has been shown for idealised turbines that mean power extraction from tidal channels can be enhanced by tuning turbine resistance for a given channel. Blade element momentum theor...
Article
A key hydrodynamic difference between tidal current and wind turbines is the volume-flux constrained flow field in which tidal turbines operate and the resulting streamwise static pressure difference that develops in the flow passage. Blade Element Momentum (BEM) theory is extended to account analytically for the effects of blockage and the develop...
Article
Full-text available
An embedded Reynolds-Averaged Navier-Stokes blade element actuator disk model is used to investigate the hydrodynamic design of tidal turbines and their performance in a closely spaced cross-stream fence. Turbines designed for confined flows are found to require a larger blade solidity ratio than current turbine design practices imply in order to m...
Article
Blade resolved computations of two different horizontal axis rotors are conducted to investigate the tip loss mechanism experienced by horizontal axis rotors. The tip loss mechanism specifically refers to the effect of the vorticity that is shed from the outboard blade sections, which results in the blade loading dropping off as the tip is approach...
Conference Paper
An embedded Reynolds-Averaged Navier-Stokes blade element actuator disk model is used to investigate the hydrodynamic design of tidal turbines and their performance in a closely spaced cross-stream fence. Turbines designed for confined flows are found to require a larger blade solidity ratio than current turbine design practices imply in order to m...
Conference Paper
Full-text available
Actuator line computations of two different tidal turbine rotor designs are presented over a range of tip speed ratios. To account for the reduction in blade loading on the outboard sections of these rotor designs, a spanwise flow correction is applied. This spanwise flow correction is a modified version of the correction factor of Shen et al. (Win...
Article
An embedded Reynolds-Averaged Navier-Stokes blade element actuator disk model is used to investigate the performance of a closely spaced cross-stream fence of four turbines. The flow characteristics of such fences are found to be dependent on both the local turbine scale flow problem and the array in channel flow scale problem. The mean fence power...
Article
A one-dimensional head driven channel flow model is used to investigate the characteristics of tidal stream energy extraction for large tidal farms deployed in tidal channels with specific focus on the limitations to realizable farm power due to turbine support structure drag and constraints on volume flow rate reduction. Support structures are see...
Article
The power available to a tidal stream turbine fence depends on the turbine resistance, the mass flux through the array, as well as the flow speed variation within the array. Depth-averaged simulations are often used to analyse the power available at a site, where the array is modelled as a region of enhanced flow resistance. Without special treatme...
Article
It is imperative to include three-dimensional tip flow corrections when using low-order rotor models that rely on the flow independence principle to compute the blade forces. These corrections aim to account for the effect of pressure equalization at the tips and the accompanying spanwise pressure gradients on the outboard sections, by reducing the...
Article
A theoretical model is proposed for a row of sub-arrays of tidal turbines aligned in a cross-stream fashion across part of a wide channel. This model builds on previous work investigating the behaviour of a single partial row array that split the problem into two flow scales; device and channel. In the present work, three flow scales are proposed:...
Conference Paper
Blade boundary layer resolved simulations of two different tidal turbine rotor designs are presented. The first rotor was designed to achieve its maximum power coefficient at tip speed ratio of 5 in unblocked conditions and the other was designed to achieve its maximum power coefficient at a tip speed ratio of 5 but at a higher local blockage ratio...
Article
This paper presents a numerical investigation of ducted tidal turbines, employing three-dimensional Reynolds-averaged Navier-Stokes simulations. Bidirectional ducted turbines are modelled with and without apertures, referred to as ducted and open-centre turbines respectively. The turbine rotors are represented through a CFD-integrated blade element...
Article
Low order rotor models such as the actuator line method are desirable as an efficient method of computing the large range of operating and environmental conditions, required to design wind and tidal rotors and arrays. However, the integrated thrust and torque predictions for each rotor are dominated by the blade loading on the outboard sections, wh...
Conference Paper
An embedded RANS-Blade Element actuator disk model is used to design a three bladed, 8.1m diameter, d, rotor in a closely spaced configuration. The width is kept low to enable turbines to be later arrayed in closely spaced cross-stream fences with a tip-to-tip spacing of 0.2d. Specifying the locally normalised loading distribution to be constant al...
Article
Full-text available
Commercially available wind yield assessment models rely on superposition of wakes calculated for isolated single turbines. These methods of wake simulation fail to account for emergent flow physics that may affect the behaviour of multiple turbines and their wakes and therefore wind farm yield predictions. In this paper wake-wake interaction is mo...
Article
Three-dimensional Reynolds-averaged Navier–Stokes computations are presented for an actuator disc representation of an ideal tidal stream energy extracting device, operating within a channel that slopes in the streamwise direction. Downwards facing, horizontal and upwards facing slopes are considered at the same mass flow rate and depth at the devi...
Article
Several commercial tidal turbine designs feature axial flow rotors within bi-directional ducts. Such devices are typically intended to increase power extraction through a flow-concentrating effect, operating on flood and ebb tides without a yawing mechanism. Research focused on such devices has been limited so far, with available results indicating...
Conference Paper
Full-text available
Computations of the blade loading and the local flow field around the Model Rotor Experiments In Controlled Conditions (MEXICO) rotor are presented using an actuator line method, implemented within the open source code OpenFOAM. The nacelle and near wake mesh refinement are shown to have little influence on the computed blade loads but a significan...
Article
The effect of free surface deformation on the power extracted by a tidal turbine array partially spanning a wide channel is investigated using a theoretical model. Two predominant flow scales are assumed; turbine-scale flow, and array-scale flow, which are analysed as quasi-inviscid open channel flow problems in which conservation of mass, momentum...
Article
The performance-enhancing effects of closely packing tidal turbines in single row arrays (tidal fences) are evaluated in this computational study. Infinitely long tidal fences are simulated with a range of lateral rotor spacings using a blade element momentum method embedded in a Reynolds averaged Navier–Stokes solver (RANS-BEM). First, a rotor des...
Conference Paper
Blockage-corrected blade element momentum theory is employed to investigate the performance of tidal turbine arrays in a head-driven oscillating tidal channel. Two arrays are compared, one with power capping, and one without. Power capping is widely used in the wind turbine industry as a means of finding an economic balance between the power (and h...
Conference Paper
The renewable tidal current resource has attracted significant global interest as a predictable energy resource. Although the understanding of the tidal current resource has advanced considerably by transferring knowledge from the wind energy industry, a number of important differences exist between wind and tidal current turbines. Chief among thes...
Article
Three-dimensional incompressible Reynolds-Averaged Navier-Stokes (RANS) computations are performed of water flow past an array of tidal turbines, modelled as actuator disks. While recent analytical models provide useful insight into the limit of power extraction and efficiency of tidal turbine arrays, they assume that the turbines are operated unif...
Article
Full-text available
This paper presents limits for stability of projection type schemes when using high order pressure-velocity pairs of same degree. Two high order h/p variational methods encompassing continuous and discontinuous Galerkin formulations are used to explain previously observed lower limits on the time step for projection type schemes to be stable [18],...
Article
A Reynolds-averaged Navier–Stokes-embedded actuator line model for wind and tidal turbine simulation has been implemented and validated using the National Renewable Energy Laboratory Phase VI wind tunnel experimental results. Actuator line models, first introduced by Sørensen and Shen, represent the blades virtually, enabling time-resolved rotor si...
Chapter
Full-text available
Modelling of turbine blade-induced turbulence (BIT) is discussed within the framework of three-dimensional Reynolds-averaged Navier-Stokes (RANS) actuator disk computations. We first propose a generic (baseline) BIT model, which is applied only to the actuator disk surface, does not include any model coefficients (other than those used in the origi...
Article
Full-text available
The characteristics of flow past a partial cross-stream array of (idealized) tidal turbines are investigated both analytically and computationally to understand the mechanisms that determine the limiting performance of partial tidal fences. A two-scale analytical partial tidal fence model reported earlier is further extended by better accounting fo...
Conference Paper
The power potential of a fence of tidal turbines depends on the mass flux through the array and the variation of the flow velocity within the array. The shallow water equations (SWE) are often used to analyse the power potential of a site, where the turbine array is modelled as a region of enhanced flow resistance. This method leads to errors in th...
Article
A two-scale modelling approach is discussed to predict the performance and energetics of a large number (more than a few hundred) of marine turbines installed as a power farm in a general coastal environment. The kernel of this approach is that the outer (coastal-scale) model/simulation is to assess the reduction of flow passing through a given far...
Article
The paper presents a computational study of ducted bidirectional tidal turbines using three-dimensional Reynolds-averaged Navier-Stokes simulations. We model the outer duct as a solid body and use a porous disc to represent the turbine rotor, a simplification that captures changes in linear momentum and thus the primary interaction of the turbine w...
Conference Paper
Recent discoveries on the limiting efficiency of tidal fences are reviewed, followed by a new theoretical investigation into the effect of wake mixing on the efficiency of ‘full’ tidal fences (i.e. turbines arrayed regularly across an entire channel span). The new model is based on the momentum and energy balance equations but includes several uncl...
Article
This paper explores the influence of blockage and free-surface deformation on the hydrodynamic performance of a generic marine cross-flow turbine. Flows through a three-bladed turbine with solidity 0.125 are simulated at field-test blade Reynolds numbers, O(10(5)-10(6)), for three different cross-stream blockages: 12.5, 25 and 50 per cent. Two repr...
Article
Full-text available
When a pair of tandem cylinders is immersed in a flow the downstream cylinder can be excited into wake-induced vibrations (WIV) due to the interaction with vortices coming from the upstream cylinder. G. R. S. Assi, P. W. Bearman and J. R. Meneghini [J. Fluid Mech. 661, 365–401 (2010; Zbl 1205.76004)] concluded that the WIV excitation mechanism has...
Article
Full-text available
A new theoretical model is proposed to explore the efficiency of a long array of tidal turbines partially blocking a wide channel cross-section. An idea of scale separation is introduced between the flow around each device (or turbine) and that around the entire array to assume that all device-scale flow events, including ‘far-wake’ mixing behind e...
Article
Full-text available
We present the development of a sliding mesh capability for an unsteady high order (order ⩾ 3) h/p Discontinuous Galerkin solver for the three-dimensional incompressible Navier–Stokes equations. A high order sliding mesh method is developed and implemented for flow simulation with relative rotational motion of an inner mesh with respect to an outer...
Article
Three-dimensional incompressible Reynolds-averaged Navier–Stokes (RANS) computations are performed for water flow past an actuator disk model (representing a tidal turbine) placed in a rectangular channel of various blockages and aspect ratios. The study focuses on the effects of turbulent mixing behind the disk, as well as on the effects of channe...
Article
Full-text available
The paper presents an unsteady high order Discontinuous Galerkin (DG) solver that has been developed, verified and validated for the solution of the two-dimensional incompressible Navier–Stokes equations. A second order stiffly stable method is used to discretise the equations in time. Spatial discretisation is accomplished using a modal DG approac...
Article
Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations...
Article
Full-text available
The wake transition of the flow around two circular cylinders placed in staggered arrangements with fixed streamwise separation of 5D and cross-stream separation varying from 0 to 3D has been studied. The wake transition is compared to that of a single isolated cylinder. Linear stability analysis utilizing Floquet theory and direct numerical simula...
Conference Paper
Presented in this paper is a comparison between numerical and experimental investigations of the Vortex-Induced Vibrations of a model scale marine riser pipe, length-to-diameter ratio of approximately 1400, that was subjected to sub-critical Reynolds number flows. The experiments, which were commissioned by the Norweigan Deepwater Programme, were c...
Article
The paper reports and discusses the results of a numerical investigation of the low-Reynolds-number transverse Vortex-Induced Vibrations (VIV) of low-mass-ratio elastically supported circular cylinders. Simulations were conducted over a large range of reduced velocities, from 2.5 to 20.0, at Reynolds numbers from 50 to 400. The objective of the stu...
Conference Paper
The paper presents the results of a numerical investigation of the transverse Vortex-Induced Vibrations of an undamped, low mass ratio elastically supported circular cylinder that was subjected to a uniform flow that resulted in a Reynolds number of 104 . The numerical simulations were performed using a two-dimensional Large Eddy Simulation model....
Article
This paper compares laboratory measurements of the vortex-induced vibrations of a riser in a stepped current with blind predictions obtained with 11 different numerical models. Results are included on in-line and transverse displacements and curvatures, and dominant frequencies. In general, empirical models were more successful at predicting cross-...
Conference Paper
The paper reports results from two strip theory CFD investigations of the Vortex-Induced Vibrations of model riser pipes. The first investigation is concerned with the vibrations of a vertical riser pipe that was subjected to a stepped current profile. An axial spatial resolution study was conducted to determine the number of simulation planes requ...
Article
Full-text available
This paper compares laboratory measurements of the vortex-induced vibrations of a riser in a stepped current with blind predictions obtained with 11 different numerical models.. Results are included on in-line and transverse displacements and curvatures, and dominant frequencies. In general, empirical models were more successful at predicting cross...
Article
The transverse Vortex-Induced Vibrations of a long (length to diameter ratio, L/D=1544), flexible pipe, that was subjected to a uniform current profile (Reynolds number, Re=2.84×105) have been simulated using a strip theory Computational Fluid Dynamics model. The pipe's mass ratio (the ratio of the pipe's mass to the mass of fluid displaced by it)...
Article
Two-dimensional and quasi-three-dimensional numerical methods have been employed to simulate the vortex-induced vibrations of a circular cylinder. A low Reynolds number two-dimensional study at low mass ratio and zero damping revealed lock-in across a large range of reduced velocities. For the low mass ratio cylinder simulated, the oscillatory freq...
Article
Full-text available
This paper presents a numerical investigation of the influence of solidity on the hydrodynamics of a generic tidal cross-flow turbine. Flows through two-and four-bladed turbines were simulated at a high laboratory Reynolds number, O(10 5). The corresponding turbine solidities were 0.019 and 0.038. It was found that increasing the number of blades l...
Article
Full-text available
An unsteady high order Discontinuous Galerkin (DG) code has been devel-oped, verified and validated for the solution of the two-dimensional incompressible Navier-Stokes equations. A second order stiffly stable method has been used to discretise the equations in time. Spatial discretisation is accomplished using a modal DG approach, in which the int...

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Projects (3)
Archived project
The need for an alternative to the use of non-renewable energies is increasing over the last few years. The intense use of fossil fuel burning, such as mineral coal and oil, brings with it health problems with the increasing of air pollution and environmental degradation related to climate change. In this context, the search for renewable energy sources has been intensifying, with consequent rise of the participation from these sources in the energy matrix. Solar and wind energy are the most known in these panel, however, the study about ocean energy has also been increasing. In this branch, energy can be generated by waves, tides, thermal gradients and ocean currents. The present project aim to study tidal energy, having as specific objective the optimization of a tidal turbine located in a canal, where there are blockage effects. For the realization of this study, it will be developed a numerical method based on CFD (Computational Fluid Dynamics). In a first moment, computational simulation will be realized reproducing the flow around the turbine with forced rotation. With the data collected, a comparative analysis and validation with the literature will be performed in order to implement the model with free rotation. Subsequently, a comparison will be done between the turbine performance in situation with blockage and without, and in the end, develop turbine geometries for these two conditions in order to optimize your efficiency
Project
The study of the conversion of kinetic energy from wind to electrical energy in wind farms should not be done from a individual turbine perpective. Flow through the turbine generates a complex phenomenon known as wake, characterized by speed drop and increased turbulence . Turbines immersed in the wake of others undergo loss of efficiency and additional stress on their structure. From these factors comes the importance of in-depth study of the flow in wind farms. There are no generic solutions for the development and characterization of wakes in a set of turbines on an offshore platform, because the problem is a function of a large number of non-generalizable parameters. Eventhough considerable amount of wind tunnel tests were already conducted, the existing results less than desired. The project aims to contribute to filling this experimental gap. The result is a wind turbine prototype, that can be used for further studies of the effect in the wake of the variation of distances and angles between three turbines.