A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations

In this paper, a compact third-order gas-kinetic scheme is proposed for the compressible Euler and Navier-Stokes equations. The main reason for the feasibility to develop such a high-order scheme with compact stencil, which involves only neighboring cells, is due to the use of a high-order gas evolution model. Besides the evaluation of the time-dependent flux function across a cell interface, the high-order gas evolution model also provides an accurate time-dependent solution of the flow variables at a cell interface. Therefore, the current scheme not only updates the cell averaged conservative flow variables inside each control volume, but also tracks the flow variables at the cell interface at the next time level. As a result, with both cell averaged and cell interface values the high-order reconstruction in the current scheme can be done compactly. Different from using a weak formulation for high-order accuracy in the Discontinuous Galerkin (DG) method, the current scheme is based on the strong solution, where the flow evolution starting from a piecewise discontinuous high-order initial data is precisely followed. The cell interface time-dependent flow variables can be used for the initial data reconstruction at the beginning of next time step. Even with compact stencil, the current scheme has third-order accuracy in the smooth flow regions, and has favorable shock capturing property in the discontinuous regions. Many test cases are used to validate the current scheme. In comparison with many other high-order schemes, the current method avoids the use of Gaussian points for the flux evaluation along the cell interface and the multi-stage Runge-Kutta time stepping technique.Comment: 27 pages, 38 figure

A review of linear compressors for refrigeration

Linear compressor has no crank mechanism compared with conventional reciprocating compressor. This allows higher efficiency, oil-free operation, lower cost and smaller size when linear compressors are used for vapour compression refrigeration (VCR) system. Typically, a linear compressor consists of a linear motor (connected to a piston) and suspension springs, operated at resonant frequency. This paper presents a review of linear compressors for refrigeration system. Different designs and modelling of linear compressors for both domestic refrigeration and electronics cooling (miniature VCR system) are discussed. Key characteristics of linear compressor are also described, including motor type, compressor loss, piston sensing and control, piston drift and resonance. The challenges associated with the linear compressors are also discussed to provide a comprehensive review of the technology for research and development in future

Numerical study of water effects on the laminar burning velocity of methanol

Using light alcohols in spark-ignition engines can improve energy security, engine performance and pollutant emissions. Methanol has gained popularity due to its ease in production compared to ethanol. Methanol could absorb water easily. In the present work, the adiabatic laminar burning velocity of methanol containing water is investigated both experimentally and numerically. Numerical simulations using CHEMKIN-PRO were undertaken to predict the burning velocities of six mixtures with different water volume fractions (up to 0.6) from the latest San Diego chemical-kinetic mechanism. The burning velocities of three mixtures with different water volume fractions (up to 0.4) were measured using a constant volume vessel and a Schlieren imaging system for a wide range of temperature (380-450 K), pressure (100-400 kPa) and equivalence ratio (0.7-1.4). Results showed a decrease in burning velocity with pressure and an increase with temperature. Water as a diluent led to reduction of the burning velocity. The chemical-kinetic mechanism over predicts the burning velocity

Analysis of oil-free linear compressor operated at high pressure ratios for household refrigeration

Compared with conventional reciprocating compressor for vapour compression refrigeration (VCR) system, linear compressor offers higher energy efficiency and oil-free operation, which allows the use of mini/micro-channel heat exchangers. However, there are key challenges when oil-free linear compressors are used for household refrigeration with typical high pressure ratios (above 10), such as high clearance loss, high piston offset, and very nonlinear gas spring. Previous papers by the author have demonstrated the feasibility of oil-free linear compressor for electronics cooling at lower pressure ratios (below 3.5). This paper presented comprehensive analysis of these issues as a key step towards developing oil-free linear compressor for household refrigeration. The model of non-linear gas spring at high pressure ratios is validated by measurements of a previous prototype linear compressor with minimum flow. Piston offset can be effectively controlled by solenoid valve at 1 Hz. Gas leakage increases by a factor of 2.5 if the piston is fully eccentric in the cylinder. The gas leakage loss can be 27% of power input for pressure ratio of 13.6 using R600a

Hidden Markov models for simultaneous testing of multiple gene sets and adaptive and dynamic adaptive procedures for false discovery rate control and estimation

This dissertation explored important issues of adaptive multiple testing problems. In Chapter 2, we showed that a class of dynamic adaptive procedures provides conservative point estimations for the proportion of true null hypotheses and FDR. These procedures are truly adaptive procedures because of their ability to adapt to the data when estimating null proportion. Thus, the dynamic adaptive procedures offer a solution to the problem of choosing the tuning parameters for adaptive procedures. In Chapter 3, we discussed important issues of gene set testing, which are commonly used in biological research, and the related multiple testing problems. We developed new methodology based on a hidden Markov model to test multiple gene sets of the Gene Ontology. Our method not only honors the logical relationships among the null hypotheses but also uses them to achieve more powerful results than other existing methods. In a sense, our method is able to adapt to dependences among null hypotheses to make better inference. In Chapter 4, we developed a more computationally efficient method to implement our hidden Markov methodology