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Abstract

The efficiency definition allows the comparison of two machines with each other. In general, the efficiency is defined as the ratio of usable power to the required power. This raises the question: what is the usable power? Most engineers discuss efficiency on grounds of the energy balance, i.e. the first law of thermodynamics. In this paper, we discuss the benefit of the machine and the effort to reach this benefit. We derive the exegetic efficiency taking the second law of thermodynamics into account, too. For this most general definition of the efficiency, we will see, that both axioms are indeed needed. As a result, its biggest benefit is thus its universal applicability. The exergetic efficiency does not only consider the fluid power from pressure build-up and delivery of a volume flow, but also the contained usable thermal energy to environment. The function of a fan or compressor is to increase the exergy of the delivered gas. The exergy measures the working capacity of the gas relative to its environment. The derivation shows two ways to calculate the exergetic efficiency, but only one is suitable for the application. For a caloric and thermal ideal gas the exergetic efficiency can be calculated without further effort in comparison to standardized performance testing.
On this basis, a comparison between isentropic and exergetic efficiency is given. A high-pressure radial fan is used as an example and the differences between both efficiencies are discussed. Therefore, measurements at a non-adiabatic fan is evaluated and the role of the heat flux to the environment is discussed. For a standard such as ISO 5801 "Fans - Performance testing using standardized airways", efficiency must not only be physically correct. It must also be simple and practical. Against this background, the outlook of this paper discusses when and which efficiency definition is appropriate and best suited for a standard.