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 Analysis of the 3D unsteady aerodynamics of a Darrieus wind turbine blade in motion  Highly spatially and temporally refined time-dependent simulations carried out with the COSA code  One month calculation time on more than 16.000 processors on a IBM BG/Q cluster  Detailed description of: tip losses, dynamic stall, vortex propagation and blade/wake interaction ACCEPTED MANUSCRIPT Energized by the recent rapid progress in high-performance computing and the growing The reported CFD results provide a valuable and reliable benchmark for the calibration 36 of lower-fidelity models, which are still key to industrial design due to their very high execution 37 speed.

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SUMMARYIn recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint ow analysis to e ciently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic ow unsteadiness.The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes.

Multimegawatt horizontal axis wind turbines often operate in yawed wind transients, in which the resulting periodic loads acting on blades, drive-train, tower, and foundation adversely impact on fatigue life. Accurately predicting yawed wind turbine aerodynamics and resulting structural loads can be challenging and would require the use of computationally expensive high-fidelity unsteady Navier-Stokes computational fluid dynamics. The high computational cost of this approach can be significantly reduced by using a frequency-domain framework. The paper summarizes the main features of the COSA harmonic balance Navier-Stokes solver for the analysis of open rotor periodic flows, presents initial validation results on the basis of the analysis of the NREL Phase VI experiment, and it also provides a sample application to the analysis of a multimegawatt turbine in yawed wind. The reported analyses indicate that the harmonic balance solver determines the considered periodic flows from 30 to 50 times faster than the conventional time-domain approach with negligible accuracy penalty to the latter. KEYWORDS harmonic balance Navier-Stokes equations, horizontal axis wind turbine aerodynamics, NREL Phase VI wind turbine, NREL 5 MW wind turbine, yawed wind aerodynamics 1 INTRODUCTION Wind energy is a key low-carbon energy source, playing a crucial role in lowering global greenhouse gas emissions, and it is now viewed as one of the most cost-effective climate change mitigation technologies. Current utility-scale horizontal axis wind turbines (HAWTs) already feature fairly high aerodynamic efficiencies; however, because of the spatial and temporal variability of the environmental conditions, HAWTs often experience unsteady flow conditions, which induce fatigue and lower the energy harvest. Several of such regimes can be viewed as periodic, and typical examples include the blades rotating (a) through stratifications of the atmosphere associated with the atmospheric boundary layer, with the wind velocity varying by as much as 6 m/s over a 100-m rotor diameter, 1 (b) through the variable pressure field due to the downwind tower, and (c) in yawed wind, occurring when the freestream wind velocity is no longer orthogonal to the turbine rotor. 2 In all these cases, the fundamental frequency of the periodic excitation is a multiple of the rotor speed.Regarding yawed wind, utility-scale HAWTs typically feature yaw control systems that monitor the wind direction and turn the entire nacelle to realign wind and rotor normal. 2 Yaw actuators, however, adjust the nacelle position after a relatively long time interval from the yaw misalignment detection, and thus, fatigue due to yaw misalignment can be significant. The yawed wind condition also reduces the power produced by the turbine, and the reduction increases nonlinearly with the cosine of the yaw misalignment. Above certain wind speed-and turbine-dependent yaw misalignment thresholds, dynamic stall also occurs, and this aggravates further unsteady loads because of hysteretic force and mom...

The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest. The solution procedure of the linear harmonic Euler/Navier-Stokes solver of the HYDRA suite of codes consists of a preconditioned fixed-point iteration, which in some circumstances becomes numerically unstable. Previous work had already highlighted the physical origin of these numerical instabilities and demonstrated the code stabilization achieved by wrapping the core part of the linear code with a Generalized Minimal Residual (GMRES) solver. The implementation and the use of an alternative algorithm, namely, the Recursive Projection Method, is summarized. This solver is shown to be well suited for both stabilizing the fixed-point iteration and improving its convergence rate in the absence of numerical instabilities. In the framework of the linear analysis of turbomachinery aeroelasticity, this method can be computationally competitive with the GMRES approach.

This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time- and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.