Shape optimization of annular S-ducts by CFD and high-order polynomial response surfaces

Eero Immonen (Faculty of Engineering and Business, Turku University of Applied Sciences, Turku, Finland)

Engineering Computations

ISSN: 0264-4401

Publication date: 16 April 2018



This paper aims to design an optimal shape for an annular S-duct, considering both energy losses and exit flow uniformity, starting from a given baseline design. Moreover, this paper seeks to identify the design factors that affect the optimal annular S-duct designs.


The author has carried out computational fluid dynamic (CFD)-based shape optimization relative to five distinct numerical objectives, to understand their interrelations in optimal designs. Starting from a given baseline S-duct design, they have applied control node-induced shape deformations and high-order polynomial response surfaces for modeling the functional relationships between the shape variables and the numerical objectives. A statistical correlation analysis is carried out across the optimal designs.


The author has shown by single-objective optimization that the two typical goals in S-duct design, energy loss minimization and exit flow uniformity, are mutually contradictory. He has presented a multi-objective solution for an optimal shape, reducing the total pressure loss by 15.6 per cent and the normalized absolute radial exit velocity by 34.2 per cent relative to a baseline design. For each of the five numerical objectives, the best optimization results are obtained by using high-order polynomial models.

Research limitations/implications

The methodology is applicable to axisymmetric two-dimensional geometry models.


This paper applies a recently introduced shape optimization methodology to annular S-ducts, and, it is, to the author’s knowledge, the first paper to point out that the two widely studied design objectives for annular S-ducts are contradictory. This paper also addresses the value of using high-order polynomial response surface models in CFD-based shape optimization.



Immonen, E. (2018), "Shape optimization of annular S-ducts by CFD and high-order polynomial response surfaces", Engineering Computations, Vol. 35 No. 2, pp. 932-954.

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