Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm

Mohammad Hossein Noorsalehi,Kyung Chun Kim,Seyed Hossein Nasrazadani,Mahdi Nili-Ahmadabadi

doi:10.3390/app11114845

Mohammad Hossein Noorsalehi, Kyung Chun Kim + Show 2 more

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https://doi.org/10.3390/app11114845

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Abstract

The upgraded elastic surface algorithm (UESA) is a physical inverse design method that was recently developed for a compressor cascade with double-circular-arc blades. In this method, the blade walls are modeled as elastic Timoshenko beams that smoothly deform because of the difference between the target and current pressure distributions. Nevertheless, the UESA is completely unstable for a compressor cascade with an intense normal shock, which causes a divergence due to the high pressure difference near the shock and the displacement of shock during the geometry corrections. In this study, the UESA was stabilized for the inverse design of a compressor cascade with normal shock, with no geometrical filtration. In the new version of this method, a distribution for the elastic modulus along the Timoshenko beam was chosen to increase its stiffness near the normal shock and to control the high deformations and oscillations in this region. Furthermore, to prevent surface oscillations, nodes need to be constrained to move perpendicularly to the chord line. With these modifications, the instability and oscillation were removed through the shape modification process. Two design cases were examined to evaluate the method for a transonic cascade with normal shock. The method was also capable of finding a physical pressure distribution that was nearest to the target one.

Highlights

Considerable efforts have been made to optimize the systems that include heat transfer or fluid flow in external and internal flows
In the upgraded elastic surface algorithm (UESA), a cascade of sharp-edged blades is assumed as the primary geometry, and its walls are modeled as elastic curved Timoshenko beams
In the validation of an inverse design method such as UESA (Sections 2.4 and 2.5), a known geometry is assumed as the target geometry, and the corresponding pressure distribution is considered as the target pressure distribution

Summary

Introduction

Considerable efforts have been made to optimize the systems that include heat transfer or fluid flow in external and internal flows. The modeling limitations and computational costs are the major challenges when using design methods. Direct methods are based on geometry corrections using feedback from a flow analysis code, and rely heavily on the previous designer’s experience, which makes them time-consuming and inefficient because of the trial-and-error process [1]. Many studies have recently used direct numerical optimization for the aerodynamic shape design. Various optimization algorithms such as adjoint method, neural networks, evolutional algorithm or machine learning are coupled with a flow solver to reach the best cost function [2]. The optimization methods are often time-consuming or mathematically complicated with a high computational cost [3]. The freedom in selecting the multi-objective cost functions and applying the constraints are the benefits of the optimization methods [4,5]

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