Unsteady Analysis of Wind Turbine Flows Using the Harmonic Balance Method

Howison, Jason; Ekici, Kivanc

doi:10.2514/6.2013-1107

Cited by 7 publications

(13 citation statements)

References 24 publications

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“…This runtime can be significantly reduced by solving the governing equations in the frequency domain. A widespread method of this type is the harmonic balance ( H B ) NS technology, initially introduced for turbomachinery blade aeroelasticity and successively also used for multistage turbomachinery aerodynamics, several vibratory motion modes of aircraft configurations, and recently also for wind turbine aerodynamics and aeroelasticity . The use of the H B NS method for the simulation of this type of periodic flows has been shown to reduce by 1 to 2 orders of magnitude CFD runtimes with respect to conventional T D NS analyses.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

2018

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“…Also, poor quality of the elements close to the leading and trailing edges of the flat plate with vanishing thickness can be another cause for this difference. 3 The ratio of the eddy to the free-stream viscosity and the non-dimensional velocity profile at x = 0.97 using WSCM and present preconditioners are compared with the results of the CFL3D solver and are shown in Figure 4. A close agreement is obtained with other solvers for the viscosity ratio.…”

Section: B Turbulent Flow Over a Flat Plate With Zero Pressure Gradientmentioning

confidence: 99%

“…The application of a harmonic balance (HB) method 1 to Navier-Stokes (NS) solvers has proven to be a promising tool for turbomachinery and wind turbine flow problems. [1][2][3][4] The aforementioned HB-NS solver can be enhanced with a one-equation Spalart-Allmaras 5 turbulence model that incorporates a rotation correction that reduces the eddy viscosity in the vicinity of regions where the vorticity surpasses the strain rate. 6,7 The spatial discretization of the convective and diffusive terms includes the central difference formula that can be stabilized and further enhanced with an artificial or numerical dissipation that uses a blend of second and fourth differences.…”

Section: Introductionmentioning

confidence: 99%

A Turbulent Low-Speed Preconditioner for Unsteady Flows About Wind Turbine Airfoils

Djeddi

Ekici

2015

22nd AIAA Computational Fluid Dynamics Conference

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A harmonic balance method is used to study the unsteady flows at low-speed regimes typically seen for wind turbines. The frequency-domain technique is applied to the Reynoldsaveraged Navier-Stokes governing system of equations with the Spalart-Allmaras turbulence model. The convergence, stability and accuracy of the compressible solver is improved via a fully coupled viscous preconditioning designed for low speed flows that fall in the essentially incompressible flow regime. The viscous preconditioner couples the NavierStokes equations to the turbulence model through the correct implementation of the preconditioning matrix and the subsequently matrix-valued artificial dissipation term. Finally, the viscous low-speed preconditioning is enhanced with a mixed-mechanism that would increase the stability and improve the convergence of the harmonic balance solver used for the simulation of unsteady periodic flows.

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“…Thus, existing well‐developed steady computational fluid dynamics techniques may be used to efficiently solve the nonlinear harmonic balance equations, with a comparable number of iterations required. Validation of the solver used for the results in this paper may be found in previous work .…”

Section: Harmonic Balance Approachmentioning

confidence: 99%

Dynamic stall analysis using harmonic balance and correlation-basedγ- Reθt¯ transition models for wind turbine applications

Howison

Ekici

2014

Wind Energ.

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In this paper, we use the harmonic balance method to study an oscillating S809 airfoil in dynamic stall. The periodic behavior of this problem makes it well suited for the harmonic balance method, which is able to model unsteady aerodynamics at greatly reduced computational costs when compared with time‐accurate unsteady‐flow solvers. A finite‐volume technique based on the lower–upper symmetric Gauss–Seidel scheme with Roe fluxes is used to solve the Reynolds‐averaged Navier–Stokes equations. The turbulent viscosity is computed with the one‐equation Spalart–Allmaras turbulence model. In addition, the laminar–turbulent transition is modeled using a correlation‐based approach originally developed by Langtry and Menter. Comparisons with experimental data for steady flows with the S809 airfoil highlight the necessity of the transition model to accurately predict the onset of static stall. For unsteady cases, the transition model provides improved agreement with experimental data, predicting dynamic stall when the fully turbulent model cannot. Copyright © 2014 John Wiley & Sons, Ltd.

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Unsteady Analysis of Wind Turbine Flows Using the Harmonic Balance Method

Cited by 7 publications

References 24 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

A Turbulent Low-Speed Preconditioner for Unsteady Flows About Wind Turbine Airfoils

Dynamic stall analysis using harmonic balance and correlation-basedγ- Reθt¯ transition models for wind turbine applications

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