Numerical Investigation of the Effect of Flutter Instability of the Blade on the Unsteady Flow in a Modern Low-Pressure Turbine

To reduce the carbon footprint of turbo-generators to global warming, a step-change in the design process is needed. Currently, extensive CFD simulations are required to analyse the complex flow phenomena occurring in the blade passage. Hence, to achieve a step-change in the design process these CFD simulations are required to be coupled with a gradient-based optimization algorithm. However, the extraction of gradient information is not trivial due to the high computational cost associated with it and the inherently large number of design variables required to represent the complex blade geometry.

In the 1980s, the adjoint method arose as an efficient technique to compute the gradients. One of the most attractive features of this method being, its ability to compute gradients independent of the number of design variables. This enables one to extract sensitivity of multiple design variable at the cost of one CFD run. This technique is popular for external aerodynamic applications; however, its full potential is yet to be exploited for internal flows. This adjoint solver when integrated with a CAD-Based surface parametrization tool, presents a unique opportunity towards a fully automated design methodology for turbomachinery applications. 

Stemming from the above considerations, a numerical framework for the adjoint-based optimization for 3D turbomachinery geometries is developed. To achieve this, the open-source CFD suite SU2, which incorporates discrete-adjoint solver, is coupled with ParaBlade, an open-source CAD-based blade parametrizer. A spring-analogy-based mesh deformation algorithm is used to update the computational grid in each optimization step. The proposed methodology is applied to a transonic turbine stator test case, also known as the Aachen turbine stator. 

Constrained optimization with the entropy generation as the objective function across the blade passage shows a reduction of 7.6% in the figure of merit. The geometrical constraints were effectively imposed throughout the optimization, thanks to the intuitive CAD-based parametrization.