High-performance computing of wind turbine aerodynamics using isogeometric analysis☆
Introduction
The present costs for wind energy are dominated by the operations and maintenance of the wind turbine system. It is shown in [1] that a typical wind turbine has averaged of 2.6 component failures per year during the first 10 years of operation. However, the industry is currently unable to predict these failure mechanisms and the component failure leads to the unscheduled downtime and reduced capacity. At the same time, offshore wind turbines are receiving increased attention. Winds in the offshore environment are usually stronger and more sustained, providing a more reliable source of energy. However, offshore wind turbines are exposed to harsh environments and must be designed to withstand more severe loads than the inland wind turbines. Rotor blades of much larger diameter (>120 m) are being designed and built for better performance. These are significant engineering challenges that must be addressed through advanced research and development, which also involves advanced and large-scale simulations.
Due to the computational modeling challenges involved (and only recently developed interest in the application), state-of-the-art in wind turbine simulation is not as advanced as in other fields of engineering. In recent years, standalone fluid mechanics simulations of wind turbine configurations were reported in [2], [3], [4], [5], while standalone structural analyses of rotor blades under assumed load conditions were reported in [6], [7]. Our recent work [8] has shown that coupled fluid–structure interaction (FSI) modeling of wind turbines is important in order to accurately predict their mechanical behavior. However, in order to perform fully-coupled FSI simulation of wind turbines at full spatial scale, advanced high-performance computing (HPC) resources, robust and accurate numerical methodology, and software with good parallel scalability are required. In this paper, we describe our computational procedures that enable efficient simulation of wind turbine rotors at full scale.
This paper is outlined as follows. In Section 2, we introduce the arbitrary Lagrangian–Eulerian (ALE) form of the Navier–Stokes equations of incompressible flow suitable for moving domain problems. We also present the residual-based variational multiscale (RBVMS) formulation of the Navier–Stokes equations and turbulence modeling [9]. We review the basics and state-of-the-art of isogeometric analysis [10]. In Section 3, we describe our parallel implementation strategy in detail. In Section 4, we present our simulation and parallel scalability results for the turbulent Taylor–Couette flow and the NREL 5 MW offshore baseline wind turbine rotor. In Section 5, we draw conclusions.
Section snippets
Navier–Stokes equations of incompressible flow in a moving domain
We begin by considering a weak formulation of the Navier–Stokes equations of incompressible flow in a moving domain. Let denote the fluid domain at the current time and Γ = ∂Ω is its boundary. Let and be the infinite-dimensional trial solution and weighting function spaces, respectively, and (·, ·)Ω denote the L2-inner product over Ω. The variational formulation corresponding to the arbitrary Lagrangian–Eulerian (ALE) form is stated as follows: find the velocity–pressure pair such
Parallel implementation
Turbulent flows, especially in the regime of large eddy simulation (LES), require substantial grid resolution for accuracy. Parallel computing is thus essential to efficiently compute turbulence. Although several references present applications of isogeometric analysis to turbulent flow, no discussion is given with regard to parallel implementation employed and parallel performance achieved by NURBS discretizations. For this reason, here, for the first time, we describe our parallel
Turbulent Taylor–Couette flow at Re = 8000
A turbulent Taylor–Couette flow at Re = 8000 is simulated on a mesh consisting of 256 × 64 × 128 quadratic NURBS elements in the azimuthal, radial and axial directions, respectively. The problem setup is same as the one reported in [27]. A uniform mesh is used in the azimuthal and axial directions. In the radial direction, a hyperbolic tangent mesh stretching is used to better capture the boundary-layer turbulence. No-slip boundary conditions are imposed weakly using the methodology presented in [36]
Conclusions
This paper presents a computational framework for advanced flow simulation that is based on the RBVMS turbulence modeling and isogeometric analysis. Particular emphasis is placed on the parallel implementation of the methodology and scalability results. Near-perfect linear parallel scaling is shown on two challenging flow cases: the turbulent Taylor–Couette flow and the NREL 5 MW offshore baseline wind turbine rotor at full scale. For wind turbine simulation the results of aerodynamic torque, a
Acknowledgements
We thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. M.-C. Hsu was partially supported by the Los Alamos–UC San Diego Educational Collaboration Fellowship. This support is gratefully acknowledged. I. Akkerman is supported in part by an appointment to the Postgraduate Research Participation Program at the US Army Engineering Research and Development Center,
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This paper was originally submitted to the ParCFD 2010 special issue which was published in Volume 45, Issue 1 of Computers and Fluids.