Analysis of Unsteady Flows Past Horizontal Axis Wind Turbine Airfoils Based on Harmonic Balance Compressible Navier-Stokes Equations With Low-Speed Preconditioning

Abstract

This paper presents the numerical models underlying the implementation of a novel harmonic balance compressible Navier-Stokes solver with low-speed preconditioning for wind turbine unsteady aerodynamics. The numerical integration of the harmonic balance equations is based on a multigrid iteration, and, for the first time, a numerical instability associated with the use of such an explicit approach in this context is discussed and resolved. The harmonic balance solver with low-speed preconditioning is well suited for the analyses of several unsteady periodic low-speed flows, such as those encountered in horizontal axis wind turbines. The computational performance and the accuracy of the technology being developed are assessed by computing the flow field past two sections of a wind turbine blade in yawed wind with both the time- and frequency-domain solvers. Results highlight that the harmonic balance solver can compute these periodic flows more than 10 times faster than its time-domain counterpart, and with an accuracy comparable to that of the time-domain solver.

Shared-memory, distributed-memory, and mixed-mode parallelisation of a CFD simulation code

“…It can be seen from the results that a significant reduction in the overall runtime has been achieved on both machines, approximately 4 times quicker than the pure MPI code, albeit using somewhere between 6 and 8 times the number of cores. Whilst this approach would be more costly in terms of the overall amount of computational time used it does significantly reduce the time to solution (so from 38 hours for our example simulation using MPI down to 9 1 2 hours for the hybrid code). Given that most large HPC systems have limits to the maximum time an applications can be run for (12 or 24 hours is common) this is a significant improvement in the usability of the application.…”

“…the best speedup is seen with the Block code but even it is only at most half the ideal speedup). The parallel speedups are not brilliant but if you look at the time required for the program to complete it is somewhere in the region of 1 3 to 1 4 the time used when only a single core is used which is a significant improvement over the serial code.…”

“…This paper presents some different approaches to the parallelisation of a harmonic balance Navier-Stokes solver for unsteady aerodynamics [1]. Computational fluid dynamics (CFD) simulations such as the Navier-Stokes solver being parallelised for this paper can be extremely computationally intensive, hence the requirement to implement a parallel version of the application.…”

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

“…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.…”

Unsteady Analysis of Wind Turbine Flows Using the Harmonic Balance Method

“…Use of the harmonic balance method to analyze wind turbines has already begun appearing in the literature. 10 In this paper, a two-dimensional flow solver based on the finite volume Jameson scheme used to solve the Reynolds averaged Navier-Stokes (RANS) equations is presented. This solver, called UT WIND herein, is validated through comparison with other reputable solvers and published experimental data for steady flow over a flat plate and steady low speed flow over a NACA 0012 airfoil.…”