Non-Linear Time and Frequency Domain Methods for Multi-Row Aeromechanical Analysis

Abstract

An unsteady Navier-Stokes solution system for aeromechanical analysis of multiple blade row configurations is presented. A distinctive feature of the solver is that unified numerical methods and boundary condition treatments are consistently used for both a nonlinear time-domain solution mode and a frequency-domain one. This not only enables a wider range of physical aeromechanical problems to be tackled, but also provides a consistent basis for validating different computational models, identifying and understanding their relative merits and adequate working ranges. An emphasis of the present work is on a highly efficient frequency-domain method for multi-row aeromechanic analysis. With a new interface treatment, propagations and reflections of pressure waves between adjacent blade rows are modeled within a domain consisting of only a single passage in each blade row. The computational model and methods are firstly described. Then, extensive validations of the frequency-domain method against both experimental data and the nonlinear time-domain solutions are described. Finally the computational analysis and demonstration of the intra-row reflection effects on the rotor aerodynamic damping are presented.

Aeromechanical Analysis of a Complete Wind Turbine Using Nonlinear Frequency Domain Solution Method

“…These three sets of equations are simultaneously solved in a similar way to that of the steady RANS equations with the extra term being treated as a source term. A pseudo time derivative term is added to the three sets of equations so that the Runge-Kutta method can be used to time-march their solutions to a steady-state [19][20][21][22].…”

“…where Ω is the volume, S is the surface, U is the vector of the conservative variables, ST is the source term, and ⃗ and ⃗ are the inviscid and viscous flux vectors, respectively. Spalart-Allmaras turbulence model is employed in this work and the above equation can be simply written in a semi-discrete form as [19][20][21][22]: GTP-20-1672…”

“…These methods have been widely used in turbomachinery. Rahmati et al [21][22] also developed a nonlinear frequency domain method for the multi-row aeromechanical analysis of turbomachines and showed that a fully coupled multi-row configuration should be considered rather than a simplified isolated one to produce better accuracy in predicting flutter behaviour of the blades. Despite the fact that the Experiments In Controlled Conditions) Experiment wind turbine, is selected for this study.…”

“…For the periodic boundaries of the rotor, the direct periodic (repeating) condition is applied for the time domain method whereas only a single passage domain is required for the frequency domain solution method. With the frequency domain method, the harmonic components are phase-shifted between the periodic boundaries by a given Inter Blade Phase Angle (IBPA), σ, as expressed in the following equations[19][20][21][22] where the subscript 1 and 2 are corresponding to the referenced passage and its neighbouring one, respectively.…”

Comparison of Frequency Domain and Time-Domain Methods for Aeromechanical Analysis

“…In fact, the current aerodynamic blade and airfoil designs have achieved high aerodynamic performance by using the steady flow model. The solution of unsteady flow equations is much more costly, requiring substantial computer resources [6][7][8].…”