Time-domain and harmonic balance turbulent Navier-Stokes analysis of wind turbine aerodynamics using a fully coupled low-speed preconditioned multigrid solver

摘要

The research work reported in this thesis stems from the development of an accurate and computationally efficient Reynolds-Averaged Navier-Stokes (RANS) research code, with a particular emphasis on the steady and unsteady aerodynamics analysis of complex low speed turbulent flows. Such turbulent flow problems include horizontal axis wind turbine (HAWT) and vertical axis wind turbine (VAWT) operating at design and off-design conditions. On the algorithmic side, the main contribution of this research is the successful development of a rigorous novel approach to low-speed preconditioning (LSP) for the multigrid fully coupled integration of the steady, time-domain and harmonic balance RANS equations coupled to the two-equation shear stress transport (SST) turbulence model. The design of the LSP implementation is such that each part of the code affected by LSP can be validated individually against the baseline solver by suitably specifying one numerical input parameter of the LSP-enhanced code. The thesis has investigated several important issues on modelling and numerical aspects which are seldom thoroughly analysed in the computational fluid dynamics problems of the type presented herein. The first and most important modelling issue is the necessity of applying the low speed preconditioning to both RANS and SST equations and maintaining the turbulent kinetic energy in the definition of the total energy, which, to the best knowledge of author, has never been seen in any published literature so far. Based on the results obtained in the analysis of the vertical axis wind turbine application, we have demonstrated that by preconditioning the SST turbulence equations, one can significantly improve the convergence rate; and keeping the turbulence kinetic energy in the total energy has a great positive effect on the solution accuracy. The other modelling issue to be analysed is the sensitivity of the flow solution to the farfield boundary conditions, particularly for low speed problems. The analyses reported in the thesis highlight that with a small size of the computational domain, the preconditioned farfield boundary conditions are crucial to improve the solution accuracy. As for the numerical aspects, we analyse the impact of using the relative velocity to build the preconditioning parameter on the flow solutions of an unsteady moving-grid problem. The presented results demonstrate that taking into account the grid motion in building the preconditioning parameter can achieve a noticeable enhancement of the solution accuracy. On the other hand, the nonlinear frequency-domain harmonic balance approach is a fairly new technology to solve the unsteady RANS equations, which yields significant reduction of the run-time required to achieve periodic flows with respect to the conventional time-domain approach. And the implementation of the LSP approach into the turbulent harmonic balance RANS and SST formulations is another main novelty presented herein, which is also the first published research work on this aspect. The newly developed low speed turbulent flow predictive capabilities are comprehensively validated in a wide range of tests varying from subsonic flow with slight compressibility to user-defined extremely low speed incompressible flows. The solutions of our research code with LSP technology are compared with experiment data, theoretical solutions and numerical solutions of the state-of-the-art CFD research code and commercial package. The main computational results of this research consist of the analyses of HAWT and VAWT applications. The first one is a comparative analysis of 30% and 93.5% blade sections of a VESTAS multi-megawatt HAWT working in various regimes. The steady, time-domain and frequency-domain results obtained with the LSP solver are used to analyse in great detail the steady and unsteady aerodynamic characteristics in those regimes. The main motivation is to highlight the predictive capabilities and the numerical robustness of the LSP-enhanced turbulent steady, time-domain and frequency domain flow solvers for realistic complex and even more challenging problems, to quantify the effects of flow compressibility on the steady and yawed wind-induced unsteady aerodynamics in the tip region of a 82-m HAWT blade in rated operating condition, and to assess the computational benefits achieved by using the harmonic balance method rather than the conventional time-domain method. The second application is the comparative aerodynamic analyses of the NREL 5MW HAWT working in the inviscid steady flow condition. The main motivation of this analysis is to further demonstrate the predictive capabilities of the LSP solver to simulate the threedimensional wind turbine flows. The last application is the time-domain turbulent flow analysis of the VAWT to the aim of demonstrating the accuracy enhancement of the LSP solver for this particular problem, the necessity of applying the full preconditioning strategy, the important effect of the turbulent kinetic energy on the solution accuracy and the proper implementation of the preconditioning parameter required for an accurate numerical solution to an unsteady moving grid low-speed problem.