CFD modelling of wind turbine airfoil aerodynamics

This paper reports the first findings of an ongoing research programme on wind turbine computational aerodynamics at the University of Glasgow. Several modeling aspects of wind turbine airfoil aerodynamics based on the solution of the Reynoldsaveraged Navier-Stokes (RANS) equations are addressed. One of these is the effect of an a priori method for structured grid adaptation aimed at improving the wake resolution. Presented results emphasize that the proposed adaptation strategy greatly improves the wake resolution in the far-field, whereas the wake is completely diffused by the non-adapted grid with the same number and distribution of grid nodes. A grid refinement analysis carried out with the adapted grid shows that the improvements of flow resolution thus achieved are of a smaller magnitude with respect to those accomplished by adapting the grid keeping constant the number of nodes. The proposed adaptation approach can be easily included in the structured generation process of both commercial and in-house structured mesh generators systems. The study also aims at quantifying the solution inaccuracy arising from not modeling the laminar-to-turbulent transition. It is found that the drag forces obtained by considering the flow as transitional or fully turbulent may differ by 50 %. The impact of various turbulence models on the predicted aerodynamic forces is also analyzed. All these issues are investigated using a special-purpose hyperbolic grid generator and a multi-block structured finitevolume RANS code. The numerical experiments consider the flow field past a wind turbine airfoil for which an exhaustive campaign of steady and unsteady experimental measurements was conducted. The predictive capabilities of the CFD solver are validated by comparing experimental data and numerical predictions for selected flow regimes. The incompressible analysis and design code XFOIL is also used to support the findings of the comparative analysis of numerical RANS-based results and experimental data

Low-speed preconditioning for strongly coupled integration of Reynolds-averaged Navier–Stokes equations and two-equation turbulence models

Computational fluid dynamics codes using the density-based compressible flow formulation of the Navier–Stokes equations have proven to be very successful for the analysis of high-speed flows. However, solution accuracy degradation and, for explicit solvers, reduction of the residual convergence rates occur as the local Mach number decreases below the threshold of 0.1. This performance impairment worsens remarkably in the presence of flow reversals at wall boundaries and unbounded high-vorticity flow regions. These issues can be resolved using low-speed preconditioning, but there exists an outstanding problem regarding the use of this technology in the strongly coupled integration of the Reynolds-averaged Navier–Stokes equations and two-equation turbulence models, such as the k − ω shear stress transport model. It is not possible to precondition only the RANS equations without altering parts of the governing equations, and there did not exist an approach for preconditioning both the RANS and the SST equations. This study solves this problem by introducing a turbulent low-speed preconditioner of the RANS and SST equations that does not require any alteration of the governing equations. The approach has recently been shown to significantly improve convergence rates in the case of a one-equation turbulence model. The study focuses on the explicit multigrid integration of the governing equations, but most algorithms are applicable also to implicit integration methods. The paper provides all algorithms required for implementing the presented turbulent preconditioner in other computational fluid dynamics codes. The new method is applicable to all low- and mixed-speed aeronautical and propulsion flow problems, and is demonstrated by analyzing the flow field of a Darrieus wind turbine rotor section at two operating conditions, one of which is characterized by significant blade/vortex interaction. Verification and further validation of the new method is also based on the comparison of the results obtained with the developed density-based code and those obtained with a commercial pressure-based code

Stabilization of linear flow solver for turbomachinery aeroelasticity using recursive projection method

The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest. The solution procedure of the linear harmonic Euler/Navier–Stokes solver of the HYDRA suite of codes consists of a preconditioned fixed-point iteration, which in some circumstances becomes numerically unstable. Previous work had already highlighted the physical origin of these numerical instabilities and demonstrated the code stabilization achieved by wrapping the core part of the linear code with a Generalized Minimal Residual(GMRES)solver. The implementation and the use of an alternative algorithm, namely, the Recursive Projection Method, is summarized. This solver is shown to be well suited for both stabilizing the fixed-point iteration and improving its convergence rate in the absence of numerical instabilities. In the framework of the linear analysis of turbomachinery aeroelasticity, this method can be computationally competitive with the GMRES approach

Effects of flow instabilities on the linear analysis of turbomachinery aeroelasticity

The linear analysis of turbomachinery aeroelasticity is based on the linearization of the unsteady How equations around the mean flow field, which can be determined by a nonlinear steady solver. The unsteady periodic flow can be decomposed into a sum of harmonies, each of which can be computed independently by solving a set of linearized equations. The analysis considers just one particular frequency of unsteadiness at a time, and the objective is to compute a complex How solution that represents the amplitude and phase of the unsteady How. The solution procedure of both the nonlinear steady and the linear harmonic Euler/Navier-Stokes solvers of the HYDRA suite of codes consists of a preconditioned fixed-point iteration. The numerical instabilities encountered while solving the linear harmonic equations for some turbomachinery test cases are documented, their physical origin highlighted, and the implementation of a GMRES algorithm aiming at the stabilization of the linear code summarized. Presented results include the flutter analysis of a two-dimensional turbine section and a civil engine fan

Analysis of the effect of mistuning on turbomachinery aeroelasticity

Abstract. This paper looks at the eect of alternate and random mis-tuning on utter and forced response in turbomachinery. Two levels of asymptotic analysis are used, and their accuracy is assessed by comparison with the exact solution obtained by direct numerical computation. Monte Carlo simulations are used to assess the eects of random mistuning. The results demonstrate the eectiveness of mistuning in improving utter sta-bility, and the dependence of the maximum amplitude of forced response on the mistuning pattern, the ratio of mistuning to coupling, and the mode number of the excitation. 1

Computing three-dimensional turbomachinery flows with an implicit fluctuation splitting scheme

Progress on the development and the application of an accurate and efficient flow solver for steady turbomachinery flows is reported. The code uses unstructured tetrahedral grids, its space-discretization is based on a fluctuation splitting scheme and an implicit strategy is used for the time integration. Results include the three-dimensional analysis of the flow field of a compressor stator and thorough comparisons with experimental data and numerical results obtained with other codes

Adjoint calculation of sensitivities of turbomachinery objective functions

An overview is presented of the steady and harmonic adjoint methods for turbomachinery design using the discrete approachin which the discretized nonlinearEuler/Navier–Stokes equationsare linearized and the resulting matrix is then transposed. Steady adjoint solvers give the linear sensitivity of steady-state functionals such asmass � ow and average exit � ow angle to arbitrary changes in the geometry of the blades, and this linear sensitivity information can then be used as part of a nonlinear optimization procedure. The harmonic adjoint method is based on a single frequency of unsteadiness and allows one to determine the generalized force acting on the blades due to arbitrary incoming time-periodic gusts. When the forcing is due to the wakes of the upstream blades, the adjointapproach can be used to tailor the shape of the incomingwakes to reduce greatly the level of forced vibration they induce. The presented suite of test cases includes the inlet guide vane and the rotor of a high-pressure turbine

Parallel unstructured three-dimensional turbulent flow analyses using efficiently preconditioned newton-krylov solver

No abstract available