Assessment of Methods to Compute Distortion in Non-Circular Ducts

This paper assesses several conformal mapping techniques for computing distortion metrics in non-circular ducts. In order to preserve the industry standard of using a 40-probe rake to measure distortion, data taken at a non-circular aerodynamic interface plane (AIP) is mathematically mapped to a circle. Various proportional stretching transformations are used as mapping functions. The techniques are applied to computational fluid dynamics (CFD) solutions at the non-circular exit of serpentine exhaust nozzles to assess the impact of using the mapping techniques to compute thermal distortion. The results indicate that mapping calculations can be more efficient than using bespoke probe positions for each different exit shape, while providing a common point of comparison between designs. Additionally, increasing the total number of probes beyond the traditional 40 significantly altered distortion metrics, which required orders of magnitude more probes to reach a constant value. It is also shown that the same mapping technique used to map the field data onto a circle should be used to distribute the probes on the unmapped field data when computing distortion in order to preserve trends and magnitudes. Additionally, mapping based on equal area distributions produces higher, and thus more conservative, levels of distortion than techniques based on equal circumferential distributions. Because the proposed techniques are mathematically general, they could have applications beyond the example test cases discussed in this paper.