Session: 36-01 Adjoint-based approaches - Part 1

Submission Number: 177541

Efficient Gradient Based Parametric Optimization of a Compressor Rotor Using Flow Adjoint and a Novel Geometric Sensitivity Algorithm 

Optimization of rotating machinery such as compressors, turbines, fans, and pumps is an important part of turbomachinery design. One powerful technique relies on automatic differentiation to compute objective and constraint sensitivities which can then be used with a gradient-based optimization algorithm. In the so-called adjoint or reverse mode, automatic differentiation has the desirable characteristic of computing the sensitivity of one response with respect to any number of parameters; making it ideal for exploring large design spaces. These adjoint sensitivities have been used to optimize a variety of rotating machinery by controlling the mesh vertex location during a gradient based optimization. This results in a final design that is defined by the CFD computational mesh from which a CAD model must then be reverse engineered. A more robust workflow involves propagating the mesh surface sensitivities computed by the CFD solver up to the parameters of an underlying CAD model. This would normally require a CAD or blade design tool for which the adjoint of the geometry kernel can be computed. Some draw backs of this approach are the limited availability of such design tools and the inherent difficulty of producing an adjoint for a fully featured CAD kernel. In the current work we undertake to demonstrate a technique for coupling the flow adjoint from a CFD code with any design software without the requirement that it also have an adjoint capability. This is accomplished by means of an intermediate calculation called the geometric sensitivity which can be computed by finite differences and then combined with the flow adjoint. The geometric sensitivity calculation used in this work introduces a novel feature matching algorithm which can be used when the perturbed CAD surfaces have a different number of faces. It has also been shown to give more accurate results particularly around sharp edges which can present a challenge to geometric sensitivity calculations described in literature. The calculation can directly use the CAD geometry but is also compatible with a workflow including intermediate discrete operations (e.g. surface morphing) between the initial CAD model creation and the final CAE model used for simulation. To demonstrate the usefulness of this technique the first stage of the high-pressure compressor from the NASA E3 turbo fan engine was optimized. The technique is then extended to the first two stages of the compressor to evaluate its performance on a multi-stage design problem. A parametric version of the model is developed based on the blade profiles that define the first and second stage rotors. The class function shape function transformation (CST) approach was used to create parametric curves and a least-squares fit was performed to give a close approximation to the non-parametric geometry. The result is a CAD model with 342 parameters. A Latin hypercube DoE is used to demonstrate that the CAD model was very robust to a random sampling of all 342 variables and produced a very flexible design space. A sequential quadratic programming (SQP) algorithm is used to optimize the geometry for efficiency subject to constraints on the mass flow and blade bending moment. In total 11 design evaluations are required to improve the compressor efficiency by nearly 2% for the single stage and 1.5% for the two-stage model. 

Presenting Author: Qingyuan Zhuang Siemens Digital Industries Software

Presenting Author Biography: Qingyuan Zhuang is a Technical Application Specialist at Siemens Industry Software Netherlands. He studied Mechanical Engineering at KTH Royal Institute of Technology in Stockholm, after which he joined ABB and Siemens Energy core engine R&D as staff engineer and aeromechanics specialist.

Authors:

Aaron Godfrey Siemens Digital Industries Software
Qingyuan Zhuang Siemens Digital Industries Software
Remi Feuillet Siemens Digital Industries Software