Abstract
Gradient-based algorithms are one of the pillars of automatic aerodynamic design in the turbomachinery field. Their use is largely extended due to their low computational demand when dealing with hundreds of design variables, especially if gradient computation is performed by means of an adjoint code. Difficulties arise when facing 3D aerodynamic inverse design, trying to obtain automatically a 3D blade geometry that produces a prescribed pressure distribution while fulfilling certain other aerodynamic constraints. Fine-tuning this target pressure distribution along the blade span — with varying fluid conditions along it — generally involves a high number of iterations, making overall automatic design process expensive from a computational point of view.
Many numerical methods have been employed in order to cope with the bad convergence exhibited by basic gradient descent method for ill-conditioned problems: quasi-Newton methods, conjugate gradients, sequential quadratic programming algorithms, among others. However, bad convergence of basic gradient descent method on ill-conditioned problems is not exclusive to 3D aerodynamic inverse design. In the field of artificial intelligence and machine learning, this problem is common when training neural networks.
In order to accelerate the convergence exhibited by gradient descent method on the aforementioned case, this paper makes use of one of the most common adaptive gradient-based methods in the field of neural networks training: Nadam optimizer. Firstly, the principles that allow this method to overcome ill conditioning are explained through Brachistochrone problem example. Secondly, the architecture of this aerodynamic automatic design module is detailed, paying special attention to gradient computation, mesh generation and objective function construction.
Finally, an automatic 3D inverse design of a low-pressure turbine blade, driven by this adaptive step-size algorithm, is performed. The automatic design optimization presented here is carried out in a realistic industrial manner, taking into account different operation conditions in order to mimic human performed design.
