  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.
