Adjoint-Based Boundary Condition Sensitivity Analysis

Turbine performance in modern aeroengines is heavily affected by the nonuniform temperature distribution generated in the combustor. The conventional method to study the effect of nonuniform boundary conditions (BCs) is to compare flowfields and performance metrics with the nonuniformity at several typical positions. A much more efficient and intuitive method to analyze the BC sensitivity is proposed in this paper. An inlet guide vane is analyzed as a demonstration. The sensitivity analysis is achieved by pointwise derivatives of objectives with respect to inlet BCs, which are obtained by discrete adjoint method. Furthermore, to study the variation of gradients, a random sampling method that is based on the Gaussian process is proposed to explore the high-dimensional parameter space. When the gradient is invariant within the parameter space, the relationship between objectives and BCs is linear, and the effect of any perturbation of BCs can be directly predicted. In this case, the computational cost of the sensitivity analysis is drastically reduced to one computational fluid dynamics and one adjoint simulation. Interestingly, some gradients are nearly invariant across the parameter space. When the gradient varies, the active subspace method is introduced to reduce the number of dimensions. Then, several models, including the kriging, gradient-enhanced kriging (GEK), and Taylor expansions, are compared to predict objectives. The ordinary kriging model is recommended for its accuracy and stability. The GEK model can also predict the gradient and is a good choice for small BC variations. The method presented here offers a paradigm that extends the gradient-based sensitivity analysis to the global sense, which is suitable for high-dimensional problems such as BCs and spatially varying model parameters.