Geometric Design of the Limaçon-to-Circular Fluid Processing Machine

Abstract

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 paper presents a theoretical investigation into the potential of modifying the rotor prole of the limaçon machines in order 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 relationships of the new machine. This paper sets out by introducing a background on the limaçon technology in a simple yet adequate fashion. The housing-rotor inference has been discussed from two different mathematical standpoints, i.e. the tangent method and the radial clearance method. The paper then introduces the volumetric relationship for the proposed modified machine and combines all the models produced in an optimisation endeavour to design the best machine for a given set of operating condition. Case studies of different fluid processing applications are considered to demonstrate the soundness of the proposed modifications and models. The outcome of this study confirms the validity of the proposed modification and its potential to produce a limaçon machine with favourable characteristics.

A Literature Review of the Positive Displacement Compressor: Current Challenges and Future Opportunities

“…The authors reported that the Sultan and Kalim [116] presented a two-level hybrid optimisation, which incorporates the simultaneous perturbation stochastic approximation (SPSA), to find the best piston trajectory of the reciprocating compressor driven by the geared five-bar mechanism. Later, Phung and Sultan [117] also employed the SPSA method to optimise the dimensions of the limaçon positive displacement machine for given operating conditions. Qi et al [118] employed principal component analysis (PCA) to denoise the large-scale data, and the denoised data were then used by the support vector machine (SVM) classifier to obtain the sparse coefficient for the fault-diagnosis model.…”

An Optimized Artificial Neural Network Model of a Limaçon-to-Circular Gas Expander with an Inlet Valve

“…Phung et al investigated the possibility of realizing gas-expander operation using L2C configuration and provided sophisticated mathematical models of expander rotor profile and apex seal [33,34]. Recently, Phung and Sultan have furthered this work by investigating the possibility of rotor profile modifications to simplify the manufacturing process and reduce cost [35].…”

On the Design of a Class of Rotary Compressors Using Bayesian Optimization

“…Sultan and Kalim [3] adopted the simultaneous perturbation stochastic approximation (SPSA) method to find the best piston trajectory of the reciprocating compressor, and the authors also employed the gradient-based optimization to determine the machine dimensions which can realize such a trajectory. Recently, the SPSA approach has also been utilized in the work of Phung and Sultan [4] to design a new embodiment of the limaçon machine referred to as the limaçon-to-circular machine. Like other limaçon machine embodiments, this new design can be used as expanders, compressors, and potentially pumps.…”