3-D inverse design provides efficiency benefits.

### How is the blade geometry parameterized via 3-D inverse design?

Different approaches are used for parameterization of blade geometry. In axial machines, the use of some form of surface definition is customary, while in many radial and mixed flow applications, the blade angle is generally used to control the camber distribution. Several control points are used between the leading edge and the trailing edge on 2-D sections that are then stacked together to form a 3-D geometry.

In 3-D inverse design, the blade loading or pressure jump across the blade is parameterized. The implementation is such that, with four to eight parameters of blade loading, designers can cover as much design space as is covered with more than 30 parameters when using blade angles. This reduction in design parameters makes the application of a surrogate model a practical reality for 3-D design.

### Are there additional benefits to using 3-D inverse design?

Yes, the first instance is in blade loading. It is common to all turbomachinery applications, and this allows for easy parameterizing of any type blade for all turbomachinery applications and all components—such as axial, mixed-flow or pumps and centrifugal fans, compressors, turbines and torque converters. This eliminates the need for different geometry parameterization systems.

Another difficulty in optimization is choosing the correct range of variation of design parameters. Ideally, the parameters should be varied as widely as possible to cover a large part of the design space but at the same time avoid unrealistic designs. By looking at blade loading, it is easy to see the correct range because unrealistic cases—such as negative loading in compressors—can be seen, and the appropriate level can be chosen accordingly.

Another major benefit is that the optimum blade loading for a given flow phenomena seems to have generality and is independent of flow rate or the diameter of the machine.

### What are some applications of 3-D inverse design and automatic optimization?

Many publications and customer testimonials highlight the benefits of 3-D inverse design for turbomachinery design optimization. In the pump industry, both Carver Pumps in the U.S. and Ebara Corporation in Japan have successfully applied this method to the development of new pump series. Also, McQuay in the U.S. recently presented application of coupled 3-D inverse design with DoE for the optimization of a centrifugal compressor stage for the refrigeration industry. P&S