Richard H.J. Willden

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 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.

Blockage effects on the hydrodynamic performance of a marine cross-flow turbine

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(105–106), for three different cross-stream blockages: 12.5, 25 and 50 per cent. Two representations of the free-surface boundary are considered: rigid lid and deformable free surface. Increasing the blockage is observed to lead to substantial increases in the power coefficient; the highest power coefficient computed is 1.23. Only small differences are observed between the two free-surface representations, with the deforming free-surface turbine out-performing the rigid lid turbine by 6.7 per cent in power at the highest blockage considered. This difference is attributed to the increase in effective blockage owing to the deformation of the free surface. Hydrodynamic efficiency, the ratio of useful power generated to overall power removed from the flow, is found to increase with blockage, which is consistent with the presence of a higher flow velocity through the core of the turbine at higher blockage ratios. Froude number is found to have little effect on thrust and power coefficients, but significant influence on surface elevation drop across the turbine.

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

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 original RANS turbulence model) and is expected to be valid in the limiting case where BIT is fully isotropic and in energy equilibrium. The baseline model is then combined with correction functions applied to the region behind the disk to account for the effect of rotor tip vortices causing a mismatch of Reynolds shear stress between short- and long-time averaged flow fields. Results are compared with wake measurements of a two-bladed wind turbine model of Medici and Alfredsson [Wind Energy, Vol. 9, 2006, pp. 219-236] to demonstrate the capability of the new model.

The Efficiency of Tidal Fences: A Brief Review and Further Discussion on the Effect of Wake Mixing

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 unclosed terms, which depend on the actual (three-dimensional) characteristics of turbine near-wake mixing and therefore need to be modelled empirically. The new model agrees well with three-dimensional actuator disk simulations when those unclosed terms are assessed based on the simulations themselves, suggesting that this low-order model could serve as a basis to analyse how various physical factors (such as the design of turbines) affect the limiting efficiency of tidal fences via changes in those terms describing the characteristics of turbine near-wake mixing. Also discussed is the effect of wake mixing on the efficiency of ‘partial’ tidal fences.Copyright