Unsteady Adjoint Optimization Of Turbomachinery

Due to the relative motion of neighbouring blade rows,turbomachinery flows are essentially unsteady.Although the unsteady simulation has been widely used in the flow analysis of turbomachinery,few researches adopt the unsteady simulation in the numerical optimization of turbomachinery.To further improve the reliability of the turbomachinery optimization system,it is necessary to adopt the more accurate unsteady simulation for performance evaluations.As the unsteady flow simulation is far more expensive than the steady flow simulation for turbomachinery flow,the key in developing a practical unsteady optimization system for turbomachinery is to reduce the cost of the unsteady simulation.This work reduces the computational cost in two ways: one is to adopt the harmonic balance method for the unsteady flow simulation,which reduces the cost of each unsteady flow simulation;the other is to adopt the gradient-based optimization algorithm with the adjoint method for gradient calculation,which reduces the number of unsteady flow simulations needed in the optimization.An unsteady flow solver of turbomachinery is developed based on the harmonic balance method,with an efficient implicit solution scheme for improved convergence when the frequency of the unsteady flow is high and the number of harmonics is large.With the application to the unsteady flow simulation of a transonic compressor stage and a 1.5-stage turbine,the accuracy and efficiency of the harmonic balance method is validated against the traditional time marching method.After that,the harmonic balance method is applied to the unsteady flow simulation of a two-stage shrouded high-pressure turbine,with comparisons to experimental data,to investigate its accuracy and efficiency in multistage turbomachinery.Based on the unsteady flow solution method,the harmonic-balance adjoint method for turbomachinery is extended to the unsteady flow in multiple blade rows.A harmonicbalance adjoint solver is developed for sensitivity analysis of unsteady turbomachinery flow.The accuracy of the sensitivity information obtained by the adjoint method is verified with a series of test cases.After that,the harmonic-balance adjoint solver is applied to the unsteady adjoint solution of a single stage transonic turbine and a 1.5-stage high load turbine.Based on the harmonic-balance flow solver and adjoint solver,an unsteady adjoint optimization system for turbomachinery is developed in this work.A mathematically simple method,the free-form deformation method is adopted for geometric modelling.Constraints on key geometric parameters of turbomachinery such as the blade thickness are implemented to ensure the optimal geometric shapes are practically usable.For the grid modification after geometric modification,two methods are implemented: one is based on the radial basis function which is very popular and the other is a cheap algebraic interpolation method.The unsteady adjoint optimization system is applied to the aerodynamic optimization of a single stage transonic turbine and a 1.5-stage transonic compressor to demonstrate the reliability of the optimization system.In summary,an unsteady adjoint optimization system for turbomachinery is developed based on the harmonic-balance method,which provides a tool for high-fidelity turbomachinery optimization.