Design and optimisation of the limaçon rotary compressor

The limaçon positive displacement machine is characterised by its internal geometry and unique mechanical motion; both based on a mathematical curve known as the limaçon of Pascal. The limaçon technology offers many advantages, such as compact size and double‐acting functionality, and its great potential for fluid processing applications has been proven by a number of patents and innovative designs in engines, expanders, and pumps. However, no commercial application of the limaçon technology in the field of positive displacement compressors has been reported in the literature. This could be attributed to the fact that the potential of the limaçon technology for gas compression has not been established as yet. The process of establishing potential is necessary before funds and resources are dedicated to investing in prototyping and testing. This process entails a considerable amount of modelling, coding and analysis as one must ensure the embodiment is geometrically capable of delivering suction and compression strokes, ports can be arranged to support the workings of these strokes, a number of measurable parameters can be identified as impacting compressor performance and it is possible to calculate a set of parameters which optimise this performance. To achieve this objective, a comprehensive mathematical model of a limaçon machine, implemented as a compressor,was first developed. The model, which is multi‐physical in nature, spans such domains as kinematics, fluid dynamics, characteristics of the port flow, internal leakage due to seal vibration, dynamics of the discharge valve, and thermodynamics. Subsequently, the simulation of the model has been performed to numerically study the operational characteristics of the limaçon compressor and to investigate the effect of various parameters on the compressor performance. It was found that the increase in the operating speed and pressure ratio would lead to negative effects on machine performance, especially on volumetric efficiency. Additionally, the results of simulations indicated that the level of fluid over‐compression is influenced by the characteristics of the discharge valve. To ensure the suitability of limaçon technology for use in positive displacement compressors, a study was undertaken to determine whether such an embodiment lent itself to optimisation efforts. For this purpose, the thorough mathematical model which has been developed to simulate compressor workings was then used for optimisation purposes whereby a Bayesian optimisation procedure was applied. The optimisation procedure was conducted in a two‐stage fashion where the first stage optimises the machine dimensions to meet volumetric requirements specified by the designer; and the second stage focuses on revealing the optimum combination of port geometries that improves machine performance. A numerical illustration was presented to prove the validity of the presented approach, and the results show that considerable improvements in the isentropic and volumetric efficiencies can be attained. Moreover, the optimised design was tested under different operating speeds and pressure ratios to investigate its robustness. It was found that the optimised design can exhibit relatively stable performance when the working conditions vary within a small bandwidth around that used in the optimisation procedure. The limaçon technology has three embodiments, namely the limaçon‐to‐limaçon (L2L), the limaçon‐to‐circular, and the circolimaçon. The circolimaçon embodiment features using circular arcs, rather than limaçon curves, to develop profiles for the rotor and housing. This embodiment simplifies the manufacturing process and reduces the production cost associated with producing a limaçon technology. A feasibility study of the circolimaçon embodiment was conducted by comparing its performance with that of the L2L type device. The machine dimensions and port geometries obtained from the optimisation procedure were used in the comparative study. A nonlinear three‐degree of freedom model was presented to describe the dynamic behaviour of the apex seal during the machine operation. Additionally, the leakage through the seal‐housing gap was formulated by considering the inertia and viscous effects of the flow. The results from the case study suggest that the circolimaçon embodiment exhibits comparable performance to the L2L‐type machine, despite having more significant seal vibrations. Moreover, it was also discovered that the circolimaçon compressor with a small capacity undergoes a lower level of seal dynamics, indicating better machine reliability.Doctor of Philosoph

Multi-task CNN Model for Attribute Prediction

This paper proposes a joint multi-task learning algorithm to better predict attributes in images using deep convolutional neural networks (CNN). We consider learning binary semantic attributes through a multi-task CNN model, where each CNN will predict one binary attribute. The multi-task learning allows CNN models to simultaneously share visual knowledge among different attribute categories. Each CNN will generate attribute-specific feature representations, and then we apply multi-task learning on the features to predict their attributes. In our multi-task framework, we propose a method to decompose the overall model's parameters into a latent task matrix and combination matrix. Furthermore, under-sampled classifiers can leverage shared statistics from other classifiers to improve their performance. Natural grouping of attributes is applied such that attributes in the same group are encouraged to share more knowledge. Meanwhile, attributes in different groups will generally compete with each other, and consequently share less knowledge. We show the effectiveness of our method on two popular attribute datasets.Comment: 11 pages, 3 figures, ieee transaction pape

On the design of a class of rotary compressors using bayesian optimization

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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

An energy-based discontinuous Galerkin method for the nonlinear Schr\"odinger equation with wave operator

This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schr\"odinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with some simple mesh-independent numerical fluxes we designed. We establish error estimates in the energy norm that require careful selection of a test function for the auxiliary equation involving the time derivative of the displacement variable. A critical part of the convergence analysis is to establish the L2 error bounds for the time derivative of the approximation error in the displacement variable by using the equation that determines its mean value. Using a specially chosen test function, we show that one can create a linear system for the time evolution of the unknowns even when dealing with nonlinear properties in the original problem. Extensive numerical experiments are provided to demonstrate the optimal convergence of the scheme in the L2 norm with our choices of the numerical flux