Blade-resolved numerical simulations of wind energy applications using full blade and tower models are presented. The computational methodology combines solution technologies in a multi-mesh, multi-solver paradigm through a dynamic overset framework. The coupling of a finite volume solver and a high-order, hp-adaptive finite element solver is utilized. Additional technologies including in-situ visualization and atmospheric microscale modeling are incorporated into the analysis environment. Validation of the computational framework is performed on the National Renewable Energy Laboratory (NREL) 5MW baseline wind turbine, the unsteady aerodynamics experimental NREL Phase VI turbine, and the Siemens SWT-2.3-93 wind turbine. The power and thrust results of all single turbine simulations agree well with low-fidelity model simulation results and field experiments when available. Scalability of the computational framework is demonstrated using 6, 12, 24, 48, and 96 wind turbine setups including the 48 turbine wind plant known as Lillgrund. The largest case consisting of 96 wind turbines and a total of 385 overset grids are run on 44,928 cores at a weak scaling efficiency of 86%. Demonstration of the coupling of atmospheric microscale and Computational Fluid Dynamics (CFD) solvers is presented using the National Center for Atmospheric Research (NCAR) Weather Research and Forecasting Model (WRF) solver and the NREL Simulator fOr Wind Farm Applications (SOWFA) solver.
A high-order Petrov-Galerkin finite element scheme is used to compute turbulent flow over a NACA 0012 airfoil at a freestream Mach number of 0.15, an angle of attack of 10 deg, and a Reynolds number based on the airfoil chord of 6 million. Results are obtained on a series of grids available on the NASA Turbulence Modeling Resource Web site and are compared with reference solutions that have been obtained using the FUN3D and CFL3D finite volume solvers on meshes with as many as 14.6 million degrees of freedom. Forces, moments, pressure distributions, skin friction, and profiles of velocity and turbulence working variable for the Spalart-Allmaras turbulence model are compared between the finite element and the finite volume solutions. It is demonstrated that the finite element scheme shows similar results as the finite volume schemes for most of the comparisons, but demonstrates significantly less dissipation of the wake profiles downstream of the airfoil. It is shown that, when the same number of degrees of freedom is used in the simulations, solutions obtained with quadratic elements are more accurate than those obtained using linear elements with only minor increases in computational cost. Finally, initial results with an adjoint-based hpadaptive methodology are obtained that further demonstrate that the high-order finite element framework can efficiently yield accurate results.
NomenclatureA, B, k = flux Jacobian matrices C D = total drag coefficientviscous flux vector N = Lagrangian or hierarchical basis function p = polynomial order Q = solution variables (ρ, u, v, T) S = source term t = time x, y = Cartesian coordinates Γ = surface of control volume τ = stabilization matrix ϕ = weighting function Ω = control volume
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