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The measurement of stagnation temperature is important for turbomachinery applications as it is used in the calculation of component efficiency and engine specific fuel consumption. This paper examines the use of polynomial variable projection to identify dimension reducing subspaces for stagnation temperature probes. As an example application we focus on a simplified Kiel probe geometry, but the proposed data-centric approach could be readily applied to new datasets with different geometries, boundary conditions and design objectives. The design of Kiel probes is non-trivial, with a large design space, complex flow physics, and competing design objectives. Two design objectives are considered: (1) the stagnation pressure loss, to reduce instrumentation losses; (2) the change in recovery ratio with respect to Mach number, to reduce temperature measurement uncertainty. Subspaces are obtained for the two design objectives, allowing the influence of seven design parameters to be understood. The entropy generation rate is used to provide physical insights into loss mechanisms. The recovery ratio subspace indicates that for the present probe there is an optimum vent-to-inlet area which minimises the change in recovery ratio with respect to Mach number, and design modifications that yield further small improvements are explored. Finally, the uncertainty in recovery ratio due to manufacturing variability is shown to be important. In comparison to global sensitivity measures, the use of an active subspace is shown to provide important information on what manufacturing tolerances are important for specific designs. New designs can also be selected that are insensitive to given manufacturing tolerances. |
