High-performance compressor design is best achieved with a good trade-off between aerodynamic and structural considerations, which requires efficient and accurate multidisciplinary design and optimization tools. As advanced compressors are defined with a large design space, their optimization is most efficiently achieved using a gradient-based approach, where the gradient can be computed using an adjoint method, at a cost nearly independent of the dimension of the design space. While the adjoint method has been widely used for aerodynamic shape optimization, its use for structural shape optimizations of compressor blades has not been as well studied. This paper discussed a discrete adjoint solver for structural sensitivity analysis developed within the open-source Computational Structural Mechanics (CSM) software CalculiX, and proposed an efficient stress sensitivity analysis method based on the Finite Element Method (FEM) using adjoint. The proposed method is applied to compute the stress sensitivity of a wide-chord fan blade in a high-bypass-ratio engine. The accuracy of the adjoint-based stress sensitivity is verified against central finite differences. In terms of computational efficiency, the adjoint approach is about 4.5 times more efficient than the conventional approach using finite differences. This works marks an important step towards fluid-structural coupled adjoint optimization of wide-chord fan blades.

Manufactured blades are inevitably different from their design intent, which leads to a deviation of the performance from the intended value. To quantify the associated performance uncertainty, many approaches have been developed. The traditional Monte Carlo method based on a Computational Fluid Dynamics solver (MC-CFD) for a three-dimensional compressor is prohibitively expensive. Existing alternatives to the MC-CFD, such as surrogate models and second-order derivatives based on the adjoint method, can greatly reduce the computational cost. Nevertheless, they will encounter ‘the curse of dimensionality’ except for the linear model based on the adjoint gradient (called MC-adj-linear). However, the MC-adj-linear model neglects the nonlinearity of the performance function. In this work, an improved method is proposed to circumvent the low-accuracy problem of the MC-adj-linear without incurring the high cost of other alternative models. The method is applied to the study of the aerodynamic performance of an annular transonic compressor cascade, subject to prescribed geometric variability with industrial relevance. It is found that the proposed method achieves a significant accuracy improvement over the MC-adj-linear with low computational cost, showing the great potential for fast uncertainty quantification.