Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7

Publications

7 A Study of Numerical Reaction-Diffusion Systems on Closed Surfaces

Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Numerical Solutions, reaction-diffusion systems, Close surfaces, high-order approach

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 879
6 A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces

Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation Laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1059
5 Mixing Behaviors of Shear-Thinning Fluids in Serpentine-Channel Micromixers

Authors: Rei-Tang Tsai, Chih-Yang Wu, Chia-Yuan Chang, Ming-Ying Kuo

Abstract:

This study aims to investigate the mixing behaviors of deionized (DI) water and carboxymethyl cellulose (CMC) solutions in C-shaped serpentine micromixers over a wide range of flow conditions. The flow of CMC solutions exhibits shear-thinning behaviors. Numerical simulations are performed to investigate the effects of the mean flow speed, fluid properties and geometry parameters on flow and mixing in the micromixers with the serpentine channel of the same overall channel length. From the results, we can find the following trends. When convection dominates fluid mixing, the curvature-induced vortices enhance fluid mixing effectively. The mixing efficiency of a micromixer consisting of semicircular C-shaped repeating units with a smaller centerline radius is better than that of a micromixer consisting of major segment repeating units with a larger centerline radius. The viscosity of DI water is less than the overall average apparent viscosity of CMC solutions, and so the effect of curvature-induced vortices on fluid mixing in DI water is larger than that in CMC solutions for the cases with the same mean flow speed.

Keywords: Microfluidics, Mixing, vortex, non-Newtonian fluids, curved channel

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1494
4 Longitudinal Vortices Mixing in Three-Stream Micromixers with Two Inlets

Authors: Yi-Tun Huang, Chih-Yang Wu, Shu-Wei Huang

Abstract:

In this work, we examine fluid mixing in a full three-stream mixing channel with longitudinal vortex generators (LVGs) built on the channel bottom by numerical simulation and experiment. The effects of the asymmetrical arrangement and the attack angle of the LVGs on fluid mixing are investigated. The results show that the micromixer with LVGs at a small asymmetry index (defined by the ratio of the distance from the center plane of the gap between the winglets to the center plane of the main channel to the width of the main channel) is superior to the micromixer with symmetric LVGs and that with LVGs at a large asymmetry index. The micromixer using five mixing modules of the LVGs with an attack angle between 16.5 degrees and 22.5 degrees can achieve excellent mixing over a wide range of Reynolds numbers. Here, we call a section of channel with two pairs of staggered asymmetrical LVGs a mixing module. Besides, the micromixer with LVGs at a small attack angle is more efficient than that with a larger attack angle when pressure losses are taken into account.

Keywords: Microfluidics, Mixing, longitudinal vortex generators, two stream interfaces

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1665
3 Numerical Study of Fluid Mixing in a Grooved Micro-Channel with Wavy Sidewalls

Authors: Yu-Sin Lin, Chih-Yang Wu, Yung-Ching Chu

Abstract:

In this work, we perform numerical simulation of fluid mixing in a floor-grooved micro-channel with wavy sidewalls which may impose perturbation on the helical flow induced by the slanted grooves on the channel floor. The perturbation is caused by separation vortices in the recesses of the wavy-walled channel as the Reynolds number is large enough. The results show that the effects of the wavy sidewalls of the present micromixer on the enhancement of fluid mixing increase with the increase of Reynolds number. The degree of mixing increases with the increase of the corrugation angle, until the angle is greater than 45 degrees. Besides, the pumping pressure of the micromixer increases with the increase of the corrugation angle monotonically. Therefore, we would suggest setting the corrugation angle of the wavy sidewalls to be 45 degrees.

Keywords: Microfluidics, Fluid Mixing, grooved channel, separation vortex

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1891
2 Heat Transfer in a Parallel-Plate Enclosure with Graded-Index Coatings on its Walls

Authors: Jiun-Wei Chen, Chih-Yang Wu, Ming-Feng Hou

Abstract:

A numerical study on the heat transfer in the thermal barrier coatings and the substrates of a parallel-plate enclosure is carried out. Some of the thermal barrier coatings, such as ceramics, are semitransparent and are of interest for high-temperature applications where radiation effects are significant. The radiative transfer equations and the energy equations are solved by using the discrete ordinates method and the finite difference method. Illustrative results are presented for temperature distributions in the coatings and the opaque walls under various heating conditions. The results show that the temperature distribution is more uniform in the interior portion of each coating away from its boundary for the case with a larger average of varying refractive index and a positive gradient of refractive index enhances radiative transfer to the substrates.

Keywords: Coatings, Radiative Transfer, parallel-plate enclosure, varying refractive index

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1092
1 Family-size Biogas Plant Using Manure and Urine Mixture at Ambient Temperature in Semi-arid Regions of Northwestern China

Authors: Wenguang Ding, Yang Wu, Xia Wang, Yayu Gao

Abstract:

Biogas, a clean renewable energy, is attracting a growing concern of researchers and professionals in many fields. Based on the natural and climatic conditions in semi-arid regions of northwestern China, the present study introduces a specifically-designed family-size biogas plant (with a digester of 10m3) with manure and urine of animals and humanity as raw materials. The biogas plant is applicable to areas with altitudes of more than 2000 meters in northwestern China. In addition to the installation cost, a little operational expenditure, structure, characteristics, benefits of this small-scale biogas plant, this article introduces a wide range of specific popularization methods such as training, financial support, guided tour to the biogas plant, community-based group study and delivery of operational manuals. The feasibility of the biogas plant is explored on the basis of the availability of the raw materials. Simple operations contained in the current work increase the possibility of the wide use of this small-scale biogas plant in similar regions of the world.

Keywords: Biogas, Popularization, Northwestern China, family-size biogas plant

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2432