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Papers by Richard Willden

Research paper thumbnail of Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

Three-dimensional incompressible Reynolds-averaged Navier-Stokes (RANS) computations are performe... more 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 channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.

Research paper thumbnail of Three distinct response regimes for the transverse Vortex-Induced Vibrations of circular cylinders at low Reynolds numbers

Research paper thumbnail of Multi-modal Vortex-Induced Vibrations of a vertical riser pipe subject to a uniform current profile

The transverse Vortex-Induced Vibrations of a long (length to diameter ratio, L/D = 1544), flexib... more 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 × 10 5 ) 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) was varied between 1.0 and 3.0 in order to study its effect upon the vibrational behaviour of the pipe. Despite the inflow current being uniform the pipe was observed to vibrate multi-modally. Furthermore, all of the excited modes vibrated at the excitation (Strouhal) frequency. The fluid, via its added mass, was found to be able to excite modes whose natural frequencies differed from the excitation frequency. This ability was observed to decrease with increasing mass ratio.

Research paper thumbnail of Investigation of tidal turbine array tuning using 3D Reynolds-Averaged Navier–Stokes Simulations

International Journal of Marine Energy, 2015

ABSTRACT

Research paper thumbnail of An actuator line method with novel blade flow field coupling based on potential flow equivalence

Research paper thumbnail of Low-Order Modelling of Blade-Induced Turbulence for RANS Actuator Disk Computations of Wind and Tidal Turbines

Research Topics in Wind Energy, 2014

ABSTRACT

Research paper thumbnail of Numerical Simulations of the Flow Past Cross-Flow Oscillating Circular Cylinders and Marine Riser Pipes

Volume 3: Pipeline and Riser Technology; CFD and VIV, 2007

Research paper thumbnail of Wake transition in the flow around two circular cylinders in staggered arrangements

Journal of Fluid Mechanics, 2008

Research paper thumbnail of A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes

"We present the development of a sliding mesh capability for an unsteady high order (order>3) h/p... more "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 static mesh, through the use of curved boundary elements and mixed triangular-quadrilateral meshes.

A second order stiffly stable method is used to discretise in time the Arbitrary Lagrangian-Eulerian form of the incompressible Navier-Stokes equations. Spatial discretisation is provided by the Symmetric Interior Penalty Galerkin formulation with modal basis functions in the x-y plane, allowing hanging nodes and sliding meshes without the requirement to use mortar type techniques. Spatial discretisation in the z-direction is provided by a purely spectral method that uses Fourier series and allows computation of spanwise periodic three-dimensional flows. The developed solver is shown to provide high order solutions, second order in time convergence rates and spectral convergence when solving the incompressible Navier-Stokes equations on meshes where fixed and rotating elements coexist.

In addition, an exact implementation of the no-slip boundary condition is included for curved edges; circular arcs and NACA 4-digit airfoils, where analytic expressions for the geometry are used to compute the required metrics.

The solver capabilities are tested for a number of two dimensional problems governed by the incompressible Navier-Stokes equations on static and rotating meshes: the Taylor vortex problem, a static and rotating symmetric NACA0015 airfoil and flows through three bladed cross-flow turbines. In addition, three dimensional flow solutions are demonstrated for a three bladed cross-flow turbine and a circular cylinder shadowed by a pitching NACA0012 airfoil."

Research paper thumbnail of Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

International Journal of Heat and Fluid Flow, 2012

Three-dimensional incompressible Reynolds-averaged Navier-Stokes (RANS) computations are performe... more 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 channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.

Research paper thumbnail of A high order Discontinuous Galerkin Finite Element solver for the incompressible Navier–Stokes equations

The paper presents an unsteady high order Discontinuous Galerkin (DG) solver that has been develo... more 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 approach, in which the inter-element fluxes are approximated using the Symmetric Interior PenaltyGalerkin formulation. The non-linear terms in the Navier-Stokes equations are expressed in the convective form and approximated through the Lesaint-Raviart fluxes modified for DG methods.

Verification of the solver is performed for a series of test problems; purely elliptic, unsteady Stokes and full Navier-Stokes. The resulting method leads to a stable scheme for the unsteady Stokes and Navier-Stokes equations when equal order approximation is used for velocity and pressure. For the validation of the full Navier-Stokes solver, we consider unsteady laminar flow pasta square cylinder at a Reynolds number of 100 (unsteady wake). The DG solver shows favourably comparisons to experimental data and a continuous Spectral code.

Research paper thumbnail of Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

Three-dimensional incompressible Reynolds-averaged Navier-Stokes (RANS) computations are performe... more 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 channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.

Research paper thumbnail of Three distinct response regimes for the transverse Vortex-Induced Vibrations of circular cylinders at low Reynolds numbers

Research paper thumbnail of Multi-modal Vortex-Induced Vibrations of a vertical riser pipe subject to a uniform current profile

The transverse Vortex-Induced Vibrations of a long (length to diameter ratio, L/D = 1544), flexib... more 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 × 10 5 ) 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) was varied between 1.0 and 3.0 in order to study its effect upon the vibrational behaviour of the pipe. Despite the inflow current being uniform the pipe was observed to vibrate multi-modally. Furthermore, all of the excited modes vibrated at the excitation (Strouhal) frequency. The fluid, via its added mass, was found to be able to excite modes whose natural frequencies differed from the excitation frequency. This ability was observed to decrease with increasing mass ratio.

Research paper thumbnail of Investigation of tidal turbine array tuning using 3D Reynolds-Averaged Navier–Stokes Simulations

International Journal of Marine Energy, 2015

ABSTRACT

Research paper thumbnail of An actuator line method with novel blade flow field coupling based on potential flow equivalence

Research paper thumbnail of Low-Order Modelling of Blade-Induced Turbulence for RANS Actuator Disk Computations of Wind and Tidal Turbines

Research Topics in Wind Energy, 2014

ABSTRACT

Research paper thumbnail of Numerical Simulations of the Flow Past Cross-Flow Oscillating Circular Cylinders and Marine Riser Pipes

Volume 3: Pipeline and Riser Technology; CFD and VIV, 2007

Research paper thumbnail of Wake transition in the flow around two circular cylinders in staggered arrangements

Journal of Fluid Mechanics, 2008

Research paper thumbnail of A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes

"We present the development of a sliding mesh capability for an unsteady high order (order>3) h/p... more "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 static mesh, through the use of curved boundary elements and mixed triangular-quadrilateral meshes.

A second order stiffly stable method is used to discretise in time the Arbitrary Lagrangian-Eulerian form of the incompressible Navier-Stokes equations. Spatial discretisation is provided by the Symmetric Interior Penalty Galerkin formulation with modal basis functions in the x-y plane, allowing hanging nodes and sliding meshes without the requirement to use mortar type techniques. Spatial discretisation in the z-direction is provided by a purely spectral method that uses Fourier series and allows computation of spanwise periodic three-dimensional flows. The developed solver is shown to provide high order solutions, second order in time convergence rates and spectral convergence when solving the incompressible Navier-Stokes equations on meshes where fixed and rotating elements coexist.

In addition, an exact implementation of the no-slip boundary condition is included for curved edges; circular arcs and NACA 4-digit airfoils, where analytic expressions for the geometry are used to compute the required metrics.

The solver capabilities are tested for a number of two dimensional problems governed by the incompressible Navier-Stokes equations on static and rotating meshes: the Taylor vortex problem, a static and rotating symmetric NACA0015 airfoil and flows through three bladed cross-flow turbines. In addition, three dimensional flow solutions are demonstrated for a three bladed cross-flow turbine and a circular cylinder shadowed by a pitching NACA0012 airfoil."

Research paper thumbnail of Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

International Journal of Heat and Fluid Flow, 2012

Three-dimensional incompressible Reynolds-averaged Navier-Stokes (RANS) computations are performe... more 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 channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.

Research paper thumbnail of A high order Discontinuous Galerkin Finite Element solver for the incompressible Navier–Stokes equations

The paper presents an unsteady high order Discontinuous Galerkin (DG) solver that has been develo... more 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 approach, in which the inter-element fluxes are approximated using the Symmetric Interior PenaltyGalerkin formulation. The non-linear terms in the Navier-Stokes equations are expressed in the convective form and approximated through the Lesaint-Raviart fluxes modified for DG methods.

Verification of the solver is performed for a series of test problems; purely elliptic, unsteady Stokes and full Navier-Stokes. The resulting method leads to a stable scheme for the unsteady Stokes and Navier-Stokes equations when equal order approximation is used for velocity and pressure. For the validation of the full Navier-Stokes solver, we consider unsteady laminar flow pasta square cylinder at a Reynolds number of 100 (unsteady wake). The DG solver shows favourably comparisons to experimental data and a continuous Spectral code.