Comparative assessment of the harmonic balance Navier–Stokes technology for horizontal and vertical axis wind turbine aerodynamics

Campobasso, M. Sergio; Drofelnik, Jernej; Gigante, Fabio

doi:10.1016/j.compfluid.2016.06.023

Cited by 24 publications

(17 citation statements)

References 41 publications

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“…The definition of generalized diffusive flux vector

{\underline{Φ}}_{d}

is reported in Campobasso et al, and the source term S is given by

boldS = {([], 0 - ρ normalΩ v ρ normalΩ u 0 0 S_{k} S_{ω})}^{T},

where Ω denotes the modulus of

\underline{Ω}

and S k and S ω denote, respectively, the source terms of the k and ω equations of the SST turbulence model. The definitions of S k and S ω are provided in Campobasso et al…”

Section: Governing Equationsmentioning

confidence: 98%

“…Thus, turbulent compressible flows are determined by solving a system of N p d e =7 partial differential equations (PDEs) and an equation of state linking fluid density, pressure, and internal energy. Although compressibility effects in HAWT flows may presently be relatively small, because of the blade tip speed of modern HAWTs not exceeding the Mach 0.3 threshold, the compressible flow formulation was adopted in COSA to develop and maintain a single code for both low‐speed and high‐speed problems.…”

Section: Governing Equationsmentioning

confidence: 99%

“…The finite volume cell‐centered parallel NS CFD COSA code solves both the T D RANS and SST equations and their H B counterparts using structured multiblock grids. The discretization of the convective fluxes of both RANS and SST PDEs uses Van Leer's MUSCL extrapolations and Roe's flux‐difference splitting with Van Albada's flux limiter.…”

Section: Numerical Solutionmentioning

confidence: 99%

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Harmonic balance Navier‐Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

2018

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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...

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“…The definition of generalized diffusive flux vector

{\underline{Φ}}_{d}

is reported in Campobasso et al, and the source term S is given by

boldS = {([], 0 - ρ normalΩ v ρ normalΩ u 0 0 S_{k} S_{ω})}^{T},

where Ω denotes the modulus of

\underline{Ω}

and S k and S ω denote, respectively, the source terms of the k and ω equations of the SST turbulence model. The definitions of S k and S ω are provided in Campobasso et al…”

Section: Governing Equationsmentioning

confidence: 98%

Section: Governing Equationsmentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

See 1 more Smart Citation

Harmonic balance Navier‐Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

2018

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“…The discussion below on the construction of the numerical dissipation for strongly coupled solvers of the RANS and two-equation turbulence model equations is relevant to both explicit and implicit codes. The considered fully coupled integration approach is the explicit multigrid integration of the finite volume 80 structured multi-block COSA code [27,28,29], which uses the k − ω SST model for the turbulence closure. The paper provides all the information required to implement this approach in other CFD codes.…”

Section: Introductionmentioning

confidence: 99%

Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier–Stokes equations and two-equation turbulence models

Campobasso

Yan

Bonfiglioli

et al. 2018

Aerospace Science and Technology

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Please cite this article in press as: M.S. Campobasso et al., Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier-Stokes equations and two-equation turbulence models, Aerosp. Sci. Technol. (2018), https://doi. AbstractComputational fluid dynamics codes using the density-based compressible flow formulation of the Navier-Stokes equations have proven to be very successful for the analysis of high-speed flows. However, solution accuracy degradation and, for explicit solvers, reduction of the residual convergence rates occur as the local Mach number decreases below the threshold of 0.1. This performance impairment worsens remarkably in the presence of flow reversals at wall boundaries and unbounded high-vorticity flow regions. These issues can be resolved using low-speed preconditioning, but there exists an outstanding problem regarding the use of this technology in the strongly coupled integration of the Reynoldsaveraged Navier-Stokes equations and two-equation turbulence models, such as the k − ω shear stress transport model. It is not possible to precondition only the RANS equations without altering parts of the governing equations, and * Corresponding author Email addresses: m.s.campobasso@lancaster.ac.uk (M.S. Campobasso), m.yan@lancaster.ac.uk (M. Yan), aldo.bonfiglioli@unibas.it (A. Bonfiglioli), there did not exist an approach for preconditioning both the RANS and the SST equations. This study solves this problem by introducing a turbulent lowspeed preconditioner of the RANS and SST equations that does not require any alteration of the governing equations. The approach has recently been shown to significantly improve convergence rates in the case of a one-equation turbulence model. The study focuses on the explicit multigrid integration of the governing equations, but most algorithms are applicable also to implicit integration methods. The paper provides all algorithms required for implementing the presented turbulent preconditioner in other computational fluid dynamics codes. The new method is applicable to all low-and mixed-speed aeronautical and propulsion flow problems, and is demonstrated by analyzing the flow field of a Darrieus wind turbine rotor section at two operating conditions, one of which is characterized by significant blade/vortex interaction. Verification and further validation of the new method is also based on the comparison of the results obtained with the developed density-based code and those obtained with a commercial pressure-based code.

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“…Campobasso et al presented a comparative study of the performance and accuracy of the harmonic balance method for aerodynamic analysis and design applications of horizontal and vertical axis wind turbines. 18 A nonlinear unsteady flows of self-excited-vibration blade were investigated using a mixed time/frequency domain harmonic balance technique by Huang and Ekici. 19 Dai et al presented a harmonic balance method with a dealiazing scheme to obtain the aeroelastic solutions of a subsonic airfoil.…”

Section: Introductionmentioning

confidence: 99%

An aerodynamic ROM of the blade subjected to wake based on Fourier method for flow

Zhang²,

Xiao

et al. 2018

Numerical Methods in Fluids

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Summary A reduced‐order model (ROM) is presented based on Fourier method for flow to predict aerodynamic forces of blades subjected to periodic time‐varying upstream wakes. In the method, a time‐varying wake is decomposed into harmonic waves by fast Fourier transformation. Using the Fourier method for flow and neglecting the cross‐coupling between harmonics, the aerodynamic forces caused by the wake are represented by a linear combination of harmonics with the same frequencies as the wake. The coefficients of the aerodynamic force harmonics are interpolated at the per‐fitted curves of the normalized Fourier coefficients (coefficients of aerodynamic forces harmonics corresponding to a unit simple harmonic excitation)–frequency relationship. A blade example is used to show the ability of the proposed method. The results indicate that the ROM method can predict the aerodynamic forces of blades caused by wakes efficiently and accurately. The amplitude levels of wakes have a linear impact on the accuracy of the ROM. Neglecting the higher‐order cross‐coupling between the harmonics in the ROM method is acceptable.

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Comparative assessment of the harmonic balance Navier–Stokes technology for horizontal and vertical axis wind turbine aerodynamics

Cited by 24 publications

References 41 publications

Harmonic balance Navier‐Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

Harmonic balance Navier‐Stokes aerodynamic analysis of horizontal axis wind turbines in yawed wind

Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier–Stokes equations and two-equation turbulence models

An aerodynamic ROM of the blade subjected to wake based on Fourier method for flow

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