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.
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.
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.
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.
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.
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.
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.