Flutter and forced response, as two main branches of aeroelasticity, can lead to high-cycle fatigue failure of turbomachinery blades. Efficiently and accurately assessing aeroelastic performance of turbomachinery blad...Flutter and forced response, as two main branches of aeroelasticity, can lead to high-cycle fatigue failure of turbomachinery blades. Efficiently and accurately assessing aeroelastic performance of turbomachinery blades is essential in the routine design. In this work, the Time Collocation Method (TCM) which uses the cubic B-spline to approximate flow variables is first thoroughly studied and then combined with the moving grid technique to analyze aeroelastic flow fields. To showcase its advantage over the Harmonic Balance (HB) method which uses a truncated Fourier series to approximately represent flow variables, a matrix analysis of the one-dimensional advection equation is first performed. The results of stability analysis are verified by two test cases: the Durham linear oscillating turbine cascade and a two-blade-row transonic compressor. The vibration of the blade of the first case is driven by a motor while the excitation force of the second case comes from blade row interaction. The results show that the time collocation method has a faster convergence rate and is more stable than the harmonic balance method, especially for cases with a large maximum grid reduced frequency. More importantly, the time collocation method is capable of accurately predicting aeroelastic performance of turbomachinery blades.展开更多
This paper presents a thorough study of the effect of the Constant Eddy Viscosity(CEV)assumption on the optimization of a discrete adjoint-based design optimization system.First,the algorithms of the adjoint methods w...This paper presents a thorough study of the effect of the Constant Eddy Viscosity(CEV)assumption on the optimization of a discrete adjoint-based design optimization system.First,the algorithms of the adjoint methods with and without the CEV assumption are presented,followed by a discussion of the two methods’solution stability.Second,the sensitivity accuracy,adjoint solution stability,and Root Mean Square(RMS)residual convergence rates at both design and offdesign operating points are compared between the CEV and full viscosity adjoint methods in detail.Finally,a multi-point steady aerodynamic and a multi-objective unsteady aerodynamic and aeroelastic coupled design optimizations are performed to study the impact of the CEV assumption on optimization.Two gradient-based optimizers,the Sequential Least-Square Quadratic Programming(SLSQP)method and Steepest Descent Method(SDM)are respectively used to draw a firm conclusion.The results from the transonic NASA Rotor 67 show that the CEV assumption can deteriorate RMS residual convergence rates and even lead to solution instability,especially at a near stall point.Compared with the steady cases,the effect of the CEV assumption on unsteady sensitivity accuracy is much stronger.Nevertheless,the CEV adjoint solver is still capable of achieving optimization goals to some extent,particularly if the flow under consideration is benign.展开更多
基金supported by the Science Center for Gas Turbine Project,China(No.P2022-C-II-001-001)the National Science and Technology Major Project,China and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX2022045).
文摘Flutter and forced response, as two main branches of aeroelasticity, can lead to high-cycle fatigue failure of turbomachinery blades. Efficiently and accurately assessing aeroelastic performance of turbomachinery blades is essential in the routine design. In this work, the Time Collocation Method (TCM) which uses the cubic B-spline to approximate flow variables is first thoroughly studied and then combined with the moving grid technique to analyze aeroelastic flow fields. To showcase its advantage over the Harmonic Balance (HB) method which uses a truncated Fourier series to approximately represent flow variables, a matrix analysis of the one-dimensional advection equation is first performed. The results of stability analysis are verified by two test cases: the Durham linear oscillating turbine cascade and a two-blade-row transonic compressor. The vibration of the blade of the first case is driven by a motor while the excitation force of the second case comes from blade row interaction. The results show that the time collocation method has a faster convergence rate and is more stable than the harmonic balance method, especially for cases with a large maximum grid reduced frequency. More importantly, the time collocation method is capable of accurately predicting aeroelastic performance of turbomachinery blades.
基金supported by the National Science and Technology Major Project,China(No.2017-II-0009-0023)China’s 111 project(No.B17037)sponsored by Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China.
文摘This paper presents a thorough study of the effect of the Constant Eddy Viscosity(CEV)assumption on the optimization of a discrete adjoint-based design optimization system.First,the algorithms of the adjoint methods with and without the CEV assumption are presented,followed by a discussion of the two methods’solution stability.Second,the sensitivity accuracy,adjoint solution stability,and Root Mean Square(RMS)residual convergence rates at both design and offdesign operating points are compared between the CEV and full viscosity adjoint methods in detail.Finally,a multi-point steady aerodynamic and a multi-objective unsteady aerodynamic and aeroelastic coupled design optimizations are performed to study the impact of the CEV assumption on optimization.Two gradient-based optimizers,the Sequential Least-Square Quadratic Programming(SLSQP)method and Steepest Descent Method(SDM)are respectively used to draw a firm conclusion.The results from the transonic NASA Rotor 67 show that the CEV assumption can deteriorate RMS residual convergence rates and even lead to solution instability,especially at a near stall point.Compared with the steady cases,the effect of the CEV assumption on unsteady sensitivity accuracy is much stronger.Nevertheless,the CEV adjoint solver is still capable of achieving optimization goals to some extent,particularly if the flow under consideration is benign.
