Nonlinear uncertainty quantification of the impact of geometric variability on compressor performance using an adjoint method

Flow uncertainty is commonly encountered in turbomachinery. To mitigate the negative effects caused by the flow uncertainty, a framework coupled with adaptive polynomial chaos expansion (PCE) and discrete adjoint method for robust aerodynamic design optimization (RADO) of turbomachinery blades is developed. The optimization framework relies on gradient algorithms, which effectively avoids “dimensional curse” problem. Adaptive PCE method improves the efficiency of uncertainty quantification and only once PCE model need to be constructed in per optimization step, making the framework highly efficient. The PCE matrix and chain rule are employed to determine the gradient of the RADO objective function. This framework is employed for optimizing turbine blade, considering both inviscid and viscous flow. Monte Carlo simulation and finite difference PCE are used to validate the reliability of uncertainty quantification and gradient propagation methods. A comparative analysis of the optimization results obtained by both RADO and deterministic aerodynamic design optimization (DADO) is demonstrated. The higher robustness brought by RADO indicates the practicality of this framework in robust optimization of turbomachinery blades. 

A discrete adjoint framework coupled with adaptive PCE for robust aerodynamic optimization of turbomachinery under flow uncertainty

Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solutions for unstable problems caused by physical instability and numerical instability. Optimization is a better choice for solving unstable problems because the steady-state solution is always the extreme point of optimization regardless of whether the problem is unstable or ill-conditioned, but it is difficult to solve partial differential equations (PDEs) due to too many optimization variables. In this study, we propose an Online Dimension Reduction Optimization (ODRO) method to enhance the convergence of the traditional iterative method to obtain the steady-state solutions of unstable problems. This method performs proper orthogonal decomposition (POD) on the snapshots collected from a few iteration steps of CFD simulation, optimizes the POD mode coefficients to minimize the PDE residual to obtain a solution with a lower residual in the POD subspace, and then continues to iterate with the optimized solution as the initial value, repeating the above three steps until the residual converges. Several typical cases show that the proposed method can efficiently calculate the steady-state solution of unstable problems with both the high efficiency and robustness of the iterative method and the good convergence of the optimization method. In addition, this method avoids specific knowledge about the underlying numerical scheme of the CFD code and is easy to implement in almost any iterative solver with minimal code modification.

A novel convergence enhancement method based on Online Dimension Reduction Optimization

The MDAO framework has become an essential part of almost all fields, apart from mechanical, transportation, and aerospace industries, for efficient energy conversion or otherwise. It enables rapid iterative interaction among several engineering disciplines at various fidelities using automation tools for design improvement. An advanced framework from low to high fidelity is developed for ducted and unducted turbomachinery blade designs. The parametric blade geometry tool is a key feature which converts low-fidelity results into 3D blade shapes and can readily be used in high-fidelity multidisciplinary simulations as part of an optimization cycle. The geometry generator and physics solvers are connected to DAKOTA, an open-source optimizer with parallel computation capability. The entire cycle is automated and new design iterations are generated with input parameter variations controlled by DAKOTA. Single- and multi-objective genetic algorithm and gradient method-based optimization cases are demonstrated for various applications. B-splines are used to define smooth perturbation of parametric variables chordwise and spanwise of the blade. The ability to create parametric 3D blade shapes quickly from low-fidelity analyses with advanced control is demonstrated to be unique and enables a rapid 3D design cycle. Non-intuitive designs are feasible in this framework and designers can really benefit from parametric geometry manipulation. Optimization at each fidelity is realized through automation. As part of the multidisciplinary analysis, 3D structural analysis is also performed using the unidirectional fluid–structure interaction for a few cases with imported pressure loads from the 3D RANS solution. Examples of axial turbofans, compressor rotors, turbines, radial compressors, propellers, wind and hydrokinetic turbines are demonstrated to prove generality.

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An Advanced Multifidelity Multidisciplinary Design Analysis Optimization Toolkit for General Turbomachinery

Adjoint methods are widely used for turbomachinery aerodynamic shape optimization. However, for industrial applications, the degradation of robustness and efficiency of adjoint solvers for edge-of-...

Robust Newton–Krylov Adjoint Solver for the Sensitivity Analysis of Turbomachinery Aerodynamics

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Robust Newton–Krylov Adjoint Solver for the Sensitivity Analysis of Turbomachinery Aerodynamics