Topology Optimization of a Turbomachinery Casing Structure Using the Level Set Method

This work presents the development and application of a novel topology optimization method to turbomachinery design problems. Traditional topology optimization methods are density-based, which could lead to physically uninterpretable gray elements at the geometry edges. Many software vendors use this approach as the algorithms are very robust and easy to implement in their software packages. This approach, however, doesn’t deliver clear geometry boundaries as required for many multi-physical problems and hence leads to significant re-work when transferring the results of the back to the CAD system.

In order to overcome this major issue, a novel topology optimization algorithm has been developed based on the level set method. The paper will describe the basic concept of the novel method and will demonstrate the benefits in terms of boundary definition, speed, and applicability to engineering problems on a selected multi-physics turbomachinery design problem.  

As a challenging design problem, a turbomachinery casing structure in the highly loaded high-pressure systems that are under thermal-mechanical loading conditions has been chosen. The topology optimization approach is conducted with a thermo-elastic analysis based on an axisymmetric finite element solver to reduce the computational cost. The pressure loads from the main gas path are transformed into equivalent nodal loads to apply to the structural boundary loads, and the hoop stress on the flange ring at the end of gas path lining is treated as concentrated loads. Both minimum compliance and minimum stress problem formulations are considered in this work to design the stiffest structures with a given amount of material. The corresponding shape sensitivities of the structural compliance and aggregated stress are derived in the context of the axisymmetric finite element analysis, which are then used to obtain the optimal update velocity for updating the level set function. This is the first time that the stress-based level set topology optimization is applied to the axisymmetric thermo-mechanical coupled problem. A series of numerical examples will be presented and discussed to demonstrate the effectiveness of the proposed method.