Supporting Multi-point Fan Design with Dimension Reduction

TL;DR

This paper investigates dimension reduction techniques for turbomachinery CFD simulations, demonstrating that subspaces are consistent across blades and proposing a polynomial variable projection method for efficient identification of these subspaces, aiding design comparison.

Contribution

It introduces a novel polynomial variable projection approach for dimension reduction in turbomachinery simulations, improving efficiency over existing statistical methods.

Findings

Subspaces are largely independent of Mach and Reynolds numbers across blades.

Polynomial variable projection accurately identifies dimension reducing subspaces.

Designs with balanced performance can be visually selected using these subspaces.

Abstract

Motivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades---under the same parametrization---largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, sliced average variance estimation, principal Hessian directions and contour regression. Unsatisfied by these results, we evaluate a new idea based on polynomial variable projection---a non-linear least squares problem. Our results using polynomial variable projection clearly demonstrate that one can accurately identify dimension reducing subspaces for turbomachinery functionals at a fraction of the cost associated with prior methods. We apply these subspaces to the problem of comparing design configurations across different flight points on a working line of a fan blade. We demonstrate how designs that offer a healthy compromise between performance at cruise and sea-level conditions can be easily found by visually inspecting their subspaces.