SUMMARYThis paper presents the implementation of all‐Mach Roe‐type schemes in a fully implicit CFD solver. Simple 2D cases, such as the flow around inviscid and viscous aerofoils, were used for an initial validation of these methods, along with more challenging computations consisting of the 3D flow around the Model Experiments in Controlled Conditions wind turbine, in parked and rotating conditions. This work is motivated by the increased interest of the wind turbine industry in larger diameter wind turbines where compressibility effects near the blade tips may be important. Instead of using an incompressible flow solver, this paper explores the option of modifying an existing, efficient, compressible flow solver for use at lower Mach numbers. The good performance of the Roe solver and its popularity influenced the selection of schemes for this work. The results suggest that effective all‐Mach solutions are possible with implicit solvers, and the paper defines the implementation of the new fluxes and Jacobian, including an investigation of some numerical parameters, using as platform the Helicopter Multi‐Block solver of Liverpool University. Copyright © 2013 John Wiley & Sons, Ltd.

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This paper presents a computational investigation of the wake of the MEXICO rotor. The compressible multi-block solver of Liverpool University was employed, using a low-Mach scheme to account for the low-speed flow near the blade and in the wake. In this study, computations at wind speeds of 10, 15 and 24 m s 1 were performed, and the three components of the velocity were compared against experimental data around the rotor blade up to one and a half rotor diameters downstream. Overall, fair agreement was obtained with the computational fluid dynamics showing good vortex conservation near the blade. Vorticity values revealed discontinuities in the wake at approximately 70%R, where two different aerofoils with different zero-lift angles are blended. The results suggest that all-Mach schemes for compressible computational fluid dynamics methods can deliver good performance and accuracy over all wind speeds for flows around wind turbines, without the need to switch between incompressible and compressible flow methods.

This work explores the breakdown of the wake downstream of the Model Experiments in Controlled Conditions Project (known as the MEXICO project) wind-turbine rotor and assesses the capability of computational fluid dynamics in predicting its correct physical mechanism. The wake is resolved on a fine mesh able to capture the vortices up to eight rotor radii downstream of the blades. At a wind speed of 15 m∕s, the main frequency present in the computational fluid dynamics signals for up to four radii was the blade-passing frequency (21.4 Hz), where the vortex cores fall on a perfect spiral. Between four and five radii downstream, higher-frequency content was present, which indicated the onset of instabilities and results in vortex pairing. The effect of modeling a 120 deg azimuthally periodic domain and a 360 deg three-bladed rotor domain was studied, showing similar predictions for the location of the onset of instabilities. An increased frequency content was captured in the latter case. Empirical and wake models were also explored, they were compared with computational fluid dynamics, and a combination of kinematic and field models was proposed. The obtained results are encouraging and suggest that the wake instability of wind turbines can be predicted with computational fluid dynamics methods, provided adequate mesh resolution is used. Nomenclature= rotor radius, m R = residual Re = Reynolds number r = radial position. m S = source vector in Navier-Stokes equations T = thrust, N Tu = turbulence intensity, % u = axial velocity, m∕s u ∞ = freestream velocity, m∕s V = cell volume v = radial velocity, m∕s x = axial position, m x, y, z = Cartesian coordinates λ = tip speed ratio ϕ = pitch angle, deg ω = vorticity, 1∕s