Positive displacement compressors are essential in many engineering systems, from domestic to industrial applications. Many studies have been devoted to providing more insights into the workings and proposing solutions for performance improvements of these machines. This study aims to present a systematic review of published research on positive displacement compressors of various geometrical structures. This paper discusses the literature on compressor topics, including leakage, heat transfer, friction and lubrication, valve dynamics, port characteristics, and capacity control strategies. Moreover, the current status of the application of machine learning methods in positive displacement compressors is also discussed. The challenges and opportunities for future work are presented at the end of the paper.

The optimization process of compressors is usually regarded as a ‘black-box’ problem, in which the mathematical form underlying the relationship between design parameters and the design objective is impractical and costly to be obtained. To solve the ‘black-box’ problem, Bayesian optimization has been proven as an accurate and efficient method. However, the application of such a method in the design of compressors is rarely discussed, particularly no work has been reported in terms of the positive displacement type compressor. Therefore, this paper aims to introduce the Bayesian optimization to the design of positive displacement compressors through the optimization process of the novel limaçon compressor. In this paper, a two-stage optimization process is presented, in which the first stage optimizes the geometric parameters as per design requirements and the second stage focuses on revealing an optimum setting of port geometries that improves machine performance. A numerical illustration is offered to prove the validity of the presented approach.

Limaçon machine, of which the relative motion between the rotor and housing follows the limaçon curve, belongs to a class of rotary positive displacement machines. The profiles of rotors and housings of those machines can be constructed of either limaçon or circular curves, hence the names: limaçon-to-limaçon, circolimaçon, and limaçon-to-circular machines. This paper presents the investigation into the thermodynamic performance of the limaçon-to-circular machines with the presence of apex seals and inlet valve. This paper sets out by briefly introducing the limaçon technology and the construction of the limaçon-to-circular machine working volume. The mathematical descriptions of ports' positions and areas have also been introduced. The paper then discusses the flow and phase composition of working fluid through the working chambers as well as how the fluid velocity is modeled and calculated. Then the seal dynamic model and response of inlet valve are presented followed by the machine thermodynamic model. A case study has also been presented to show the responses of seals and inlet valve during the machine operation.

A limaçon machine is a rotary positive displacement device, in which the housing and rotor are constructed of limaçon of Pascal curves. Previous works have been published to investigate the working of these machines in two applications: gas expanders and compressors. This article presents a theoretical investigation into the potential of modifying the rotor profile of the limaçon machines to simplify the machine’s manufacturing process and to reduce production cost. The proposed modification will produce new characteristics for the housing–rotor interaction. An outcome that motivates the need to obtain new mathematical models to investigate the housing–rotor interference and describe the volumetric relationship of the new machine. This article also employs an optimization approach to design the best machine for a given set of operating conditions, i.e., expander, compressor, and pump. The outcome of this study confirms the validity of the proposed modification and its potential to produce a limaçon machine with favorable characteristics.