Aerodynamic Design Methodology
The foundation of modern turbo-machinery is a compromise between fluid-thermo dynamics, structural mechanics and manufacturerability. Making the correct compromises requires appropriate experimental data and design experience. This combination of theory and practice is what defines the design method. As precise as the fundamental equations above are, resultant design methods are many and varied. Addressing this topic, a well known scientist suggests that there are as many design methods around the world as there are designers. Thus, there are many
Focusing on the fluid-thermo element, two logically opposing approaches are used to solve the fundamental aero-thermodynamic equations. The first is to analyze the existing performance of existing hardware. This analysis is a post experiment (aka post-dictive) activity used to explain what has happened. Conversely, the second is to design new hardware. Where design is a predictive activity similar to forecasting the weather.
Currently, popular turbo-machinery design methodologies alternately solve the design then the analysis algorithms. First as a design problem, shaping the air foil, then as an analysis problem, to detail the aerodynamic performance of the design. For "end users/customers" requiring the highest performance, designers incorporate numerical optimization to direct these iterations while in parallel pursuing a parallel experimental program.
In practice, design and analysis uses simplified 1D, 2D equation sets before performing the final 3D solutions. While this expansive aerodynamic problem can and is solved, an equally expansive set of design problems remain involving the structural and manufacture of the centrifugal compressor.
Read more about this topic: Centrifugal Compressor
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—Paul Feyerabend (1924–1994)