Project SECRET - Application of Path Homotopy

Application of Path Homotopy in Twin Screw Compressor Rotor Profile Design


This work explores application of an idea called ‘Path Homotopy’ from Topology in twin screw compressor rotor profile design. It is well known that twin screw rotor profiles impact the overall performance of screw compressors to a great extent. Almost all the well known profiles that are commercially used in twin screw compressors are generated out of analytical curves such as circles, lines and conic sections. Analytical representation has its own advantages in profile design but it limits the search space of all possible shapes that can be incorporated in profiles. This work aims at proposing an approach for rotor profiling that sticks to the analytical nature of curve representation in profiles while simultaneously extending the search space of curves that can be deployed in the design. Path homotopy has been identified as one of such approaches. Profile elements can be defined as homotopies between well known analytical curves (circles, lines and conic sections) and the homotopy parameter can directly influence these curves morphologically in their analytical form itself. In this way, shapes other than those used traditionally in profiling can be explored in search of the better rotor profiles.



Screw rotor is a heart of screw compressor. Any improvement in it directly impacts the screw compressor efficiency and reduces the power consumption for an unit flow of compressed gas under given conditions. Their shapes conventionally defined as rotor profiles on cross section perpendicular to their length, have largest and direct impact on thermodynamic efficiency of compression, leakage areas and hence volumetric efficiency of the compressor. The art of choosing the right curves for a rotor profile in order to achieve the maximum possible performance is termed as rotor profiling. It has a history of close to 90 years since the invention of first screw compressor by Lysholm and William (1938).

The earliest rotor profiles were symmetric wherein main and gate rotor lobes had a single circular arc featured on them (Figure1). Symmetric profiles had large blow hole areas (leakage area at the cusp formed between rotor tips and casing). Rotor profiling was revolutionized by the invention of SRM-A profile by Schibbye (1970) which was asymmetric in nature and reduced the blow hole area by 90%. It was a very practical profile with a good manufacturability. Stosic et al. (2011) lauds SRM-A for making screw compressors commercially viable for the first time.

Figure 1

These profiles were designed and generated by precise mathematical rules and procedures but no literature on theory of profile generation was published until Sakun (1960) who introduced the envelope method from differential geometry to screw rotor profile generation. Following this, Andreev (1961) published his work that elaborated on tooling and manufacturing aspects of screw rotor profiles. Post this period, multiple successful rotor profiles were invented, such as SIGMA profile (Bammert, 1982), SRM-D (Astberg, 1984), CYCLONE profile (Hough et al., 1987) and HYPER profile (Chen, 1995). A particular development in the method of generation of rotor profiles- rack generation- first proposed by Menssen (1977) led to many successful rotor profiles. These include Rinder (1987) profile, N-Profile by Stosic (1997), Cavatorta and Tomei (2014) profile and N-Silent profile by Stosic (2017). This family of profiles is rack generated while those mentioned before them are rotor generated. Rack generation has definitive advantage over rotor generation in terms of ease and error-less generation of profiles. Most of the modern successful rotor profiles are based on rack generation and calculation procedures developed in Stosic and Hanjalic (1997).

This work particularly aims is aimed at identifying the prime challenge in rotor profiling and proposing a promising method priori unused in profiling. The immediate next section lays out the details of this prime challenge in profiling as well as evaluates different attempts in the literature to tackle it. Based on the evaluation of the problem, in the following section, ‘path homotopy’ (Armstrong, 2013) is proposed as an approach to design better rotor profiles. Conclusions following this section are based on the literature review and the proposal to use this novel method in profiling.


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