Blade Shape Optimization

An Example of Design of Experiment Study Methods in AxSTREAM

One of the most challenging tasks during turbomachinery design is the definition of aerodynamic shape of the blades, taking into account the complicated flow phenomena and the effect that the shape will have to other disciplines of the design. The rapid increase of computational resources along with the development of CFD has led to a big interference of optimization methods and numerical simulations as part of the design process. There are two main categories in which optimization methods fall: the stochastic models and the gradient-based models. The first family of models focuses on finding the optimum design, while the second uses the gradient information to lead the optimization. Apart from the optimization algorithms, there are several techniques that help designers understand the dependence of design parameters towards others and extract meaningful information for the design. First, the design of experiment approach (DoE) consists of the design of any task that aims to describe or explain the variation of information for conditions that are hypothesized to reflect the variation. Next, we have the surrogate models that are used instead of the optimization algorithms to generate a model that is as accurate as possible while using as few simulation evaluations as possible with low computational cost. The most common surrogate models used for turbomachinery design are the Response Surface Method, the Kriging Model and the Artificial Neural Networks. Last, data mining approaches have recently become very popular as they allow engineers to look for patterns in large data sets to extract information and transform it into an understandable structure for further use.

As far as the aerodynamic design optimization methods is concerned, they can be grouped into inverse and direct designs. Inverse methods rely on definition of pressure distribution and they iterate along blade shape, changing to develop a final profile shape. The computational cost is low and such methods can be combined with an optimization method in an efficient design process. However, the biggest disadvantages lies on the fact that this approach is strongly dependent on the experience of the designer. Young engineers may fail to define a pressure distribution that performs well in design and off-design conditions. In addition, with the inverse method approach the user cannot account for geometric and mechanical constraints.

On the other hand, direct design methods rely on many single flow calculations. The optimization algorithms used with the direct design method are mainly the gradient based methods and the stochastic algorithms. Once more, gradient-based methods use the derivative information for all the objectives and all the constraints to determine the optimization search direction. A single design point is used to start the optimization, and the local gradient of the objective function with respect to changes in the design variables is then used to determine a search direction. The disadvantage of such methods is the finding of a local optimum instead of the global one, while once the number of constraints is increased it may lead to divergence or false results. The most robust optimization algorithms are the stochastic ones which can cope with noisy, multimodal functions, but are also computationally expensive in terms of the necessary number of flow analyses required for convergence since they require multiple points over the entire design space and search for true optimums based on the objective function instead of the local gradient information.

The AxSTREAM platform employs a DOE approach since it allows significant reduction of computation time, while 20 different parameters can be chosen for their optimization based on any combination of criteria using individual, customized weights to define specific optimization tasks. This can all be done while using the meanline and streamline solvers for direct task calculations. At the end of the task, a response surface is created based on a mathematical model that defines the characteristics of the given machine for the provided range of values and parameters. These allow performing very fast optimization tasks and provide the best 5 combinations of values for the selected components. Get in touch with our engineers today to find out more and learn how you can achieve optimized shapes within the blink of an eye.


[1] Li, Z. & Zheng, X. 2017, “Review of design optimization methods for turbomachinery aerodynamics”, Progress in Aerospace Sciences, vol. 93, pp. 1-23.

[2] He, L. & Shan, P. 2011, “Three-dimensional aerodynamic optimization for axial-flow compressors based on the inverse design and the aerodynamic parameters”, Journal of Turbomachinery, vol. 134, no. 3.

[3] Bonaiuti, D. & Zangeneh, M. 2009, “On the coupling of inverse design and optimization techniques for the multiobjective, multipoint design of turbomachinery blades”, Journal of Turbomachinery, vol. 131, no. 2.

[4] Zangeneh, M. 1991, “A compressible three‐dimensional design method for radial and mixed flow turbomachinery blades”, International Journal for Numerical Methods in Fluids, vol. 13, no. 5, pp. 599-624.

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