An aeroelastic model for wind turbine blades derived from the unsteady Navier‐Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart‐Allmaras turbulence model. The computation times for the aerodynamic solution are significantly reduced using the harmonic balance method compared to a time‐accurate solution. This model is significantly more robust than standard aeroelastic codes that rely on blade element momentum theory to determine the aerodynamic forces. Comparisons with published results for the Caradonna‐Tung rotor in hover and the classical AGARD 445.6 flutter case are provided to validate the aerodynamic model and aeroelastic model, respectively. For wind turbines, flutter of the 1.5 MW WindPACT blade is considered. The results predict that the first flapwise and edgewise modes dominate flutter at the rotor speeds considered.
In this paper, we use the harmonic balance method to study the unsteady aerodynamics of a pitching S809 wind turbine airfoil. The periodic behavior associated with some wind turbine problems are particularly well-suited for the harmonic balance method, which is designed to model unsteady aerodynamics at greatly reduced computational costs when compared to time accurate unsteady flow solvers. A finite volume technique based on the Jameson scheme is used to solve the Reynolds-averaged Navier-Stokes (RANS) equations. Convergence acceleration techniques such as local time stepping, residual smoothing, and multigrid are employed. Low speed preconditioning is also utilized to accelerate convergence and improve accuracy at low Mach numbers. The turbulent viscosity is computed with the one equation Spalart-Allmaras turbulence model. Comparisons with other flow solvers and experimental data are included here to validate the flow solver. Results indicate that the solver performs well overall but has difficulty modeling cases with massively separated flows.
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.
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