Efficiency Approximation of Centrifugal Compressors in the Cordier Diagram

Authors

Yannick Lattner  - Fachhochschule Dortmund, Germany
Marius Geller - Fachhochschule Dortmund, Germany
Norbert Kluck - Fachhochschule Dortmund, Germany

Abstract

The design process of centrifugal compressors has become increasingly complex. Both the compressor and its development must be efficient. Therefore, a streamlined process, using as few as possible design iterations, simulations and prototypes, is necessary. Additional challenges are the demand for specific operational range rather than a single operational point and a more complex structural mechanic design due to highly loaded and downsized machines. At the start of the design process, the engineer needs as much reliable data as possible to avoid costly iteration loops. When calculating the compressor’s principal dimensions, the overall efficiency must be approximated while other parameters are chosen. This is mostly using the engineer’s experience or multiple empirical models, as no integrated model is available. The development of such a model is the subject of this work. This would provide data about the efficiency as well as characteristics of the operational range linked to parameters known or chosen at the start of the compressor design process. To obtain a reliable database, the design space is divided into two levels: The machine design and the geometric design. The machine design features parameters such as the location within the Cordier diagram and energetic and geometric properties. The geometric parameters define the impeller’s detailed design, like meridional contour and blade geometry. Those do not change the overall machine design but are typically iterated to optimize efficiency, operational characteristics, or structural load. A two-level design of experiments (DOE) is conducted to generate 50 machine designs, distributed over a huge design space and - for each of these machine designs - 50 geometric designs. A sophisticated CFD speed line calculation tool is used to generate a speed line for each design. This ensures that a design with good efficiency can be found for each machine design, as different geometric designs are favorable for different machine designs. The best geometry designs are then analyzed. While a weak correlation between the maximum efficiency value and the location within in the Cordier diagram can be seen, other parameters are necessary to completely describe the maximum efficiency value. Sophisticated software is used to analyze correlations and build metamodels. Various combinations of parameters can be used to precisely predict the maximum efficiency as a function of machine design parameters. The results obtained are compared with known efficiency correlations. The overall distribution is similar, but the author’s data seems to be more complex and is sensitive to more parameters. Additionally, choke and surge as well as the operational point can be approximated using the same technique. These points can be used to provide the mass flow vs. efficiency and mass flow vs. pressure ratio speed lines using parameter driven Bézier splines, which parameters are also predicted by the metamodel. The model is therefore able to provide maximum efficiency values and corresponding speed lines throughout a huge design space for centrifugal compressors. This provides detailed information at the beginning of each compressor’s calculation, which enables a fast and resource efficient design process.