Simplified three-dimensional computer simulation formulae for film thickness distribution in the LPCVD process

1987 ◽  
Vol 27 (4) ◽  
pp. 792
Keyword(s):  
Computer Simulation ◽  
Film Thickness ◽  
Thickness Distribution ◽  
Three Dimensional

scholarly journals Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell

2019 ◽  
Vol 874 ◽  
pp. 1021-1040 ◽  
Author(s):  
Isha Shukla ◽  
Nicolas Kofman ◽  
Gioele Balestra ◽  
Lailai Zhu ◽  
François Gallaire
Keyword(s):  
Film Thickness ◽  
Thickness Distribution ◽  
Three Dimensional ◽  
Droplet Velocity ◽  
Immiscible Fluid ◽  
Oil Viscosity ◽  
Lubrication Film ◽  
Lubrication Equation ◽  
Lubricating Film ◽  
Hele Shaw Cell

We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number $Ca$ lying between $0.03$ and $0.35$, where $Ca=\unicode[STIX]{x1D707}_{o}U_{d}/\unicode[STIX]{x1D6FE}$ is built with the surrounding oil viscosity $\unicode[STIX]{x1D707}_{o}$, the droplet velocity $U_{d}$ and surface tension $\unicode[STIX]{x1D6FE}$. The experimental data show that in this regime the droplet velocity is not influenced by the thickness of the thin lubricating film and the dynamic meniscus. For iso-viscous cases, experimental and three-dimensional numerical results of the film thickness distribution agree well with each other. The mean film thickness is well captured by the Aussillous & Quéré (Phys. Fluids, vol. 12 (10), 2000, pp. 2367–2371) model with fitting parameters. The droplet also exhibits the ‘catamaran’ shape that has been identified experimentally for a pressure-driven counterpart (Huerre et al., Phys. Rev. Lett., vol. 115 (6), 2015, 064501). This pattern has been rationalized using a two-dimensional lubrication equation. In particular, we show that this peculiar film thickness distribution is intrinsically related to the anisotropy of the fluxes induced by the droplet’s motion.

Three-dimensional film thickness distribution of horizontal tube falling film with column flow

2019 ◽  
Vol 154 ◽  
pp. 140-149 ◽  
Author(s):  
Jie Wang ◽  
Xue Chen ◽  
Tao Lu ◽  
Xueshuo Chen ◽  
Shengqiang Shen ◽  
...  
Keyword(s):  
Film Thickness ◽  
Thickness Distribution ◽  
Three Dimensional ◽  
Horizontal Tube ◽  
Falling Film

scholarly journals Coupled Fluid–Solid Numerical Simulation for Flow Field Characteristics and Supporting Performance of Flexible Support Cylindrical Gas Film Seal

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 97
Author(s):  
Junfeng Sun ◽  
Meihong Liu ◽  
Zhen Xu ◽  
Taohong Liao ◽  
Xiangping Hu ◽  
...  
Keyword(s):  
Flow Field ◽  
Film Thickness ◽  
Fluid Dynamic ◽  
Structural Characteristics ◽  
Structural Parameters ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
High Rotational Speed ◽  
Flexible Support ◽  
Flow Field Characteristics

A new type of cylindrical gas film seal (CGFS) with a flexible support is proposed according to the working characteristics of the fluid dynamic seal in high-rotational-speed fluid machinery, such as aero-engines and centrifuges. Compared with the CGFS without a flexible support, the CGFS with flexible support presents stronger radial floating characteristics since it absorbs vibration and reduces thermal deformation of the rotor system. Combined with the structural characteristics of a film seal, an analytical model of CGFS with a flexible wave foil is established. Based on the fluid-structure coupling analysis method, the three-dimensional flow field of a straight-groove CGFS model is simulated to study the effects of operating and structural parameters on the steady-state characteristics and the effects of gas film thickness, eccentricity, and the number of wave foils on the equivalent stress of the flexible support. Simulation results show that the film stiffness increases significantly when the depth of groove increases. When the gas film thickness increases, the average equivalent stress of the flexible support first decreases and then stabilizes. Furthermore, the number of wave foils affects the average foils thickness. Therefore, when selecting the number of wave foils, the support stiffness and buffer capacity should be considered simultaneously.

scholarly journals Controlling Film Thickness Distribution by Magnetron Sputtering with Rotation and Revolution

Coatings ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 599
Author(s):  
Handan Huang ◽  
Li Jiang ◽  
Yiyun Yao ◽  
Zhong Zhang ◽  
Zhanshan Wang ◽  
...  
Keyword(s):  
Magnetron Sputtering ◽  
Film Thickness ◽  
Multilayer Film ◽  
Thickness Distribution ◽  
Parabolic Cylinder ◽  
Particle Model ◽  
Planetary Motion ◽  
X Rays ◽  
X Ray ◽  
Sputtering System

The laterally graded multilayer collimator is a vital part of a high-precision diffractometer. It is applied as condensing reflectors to convert divergent X-rays from laboratory X-ray sources into a parallel beam. The thickness of the multilayer film varies with the angle of incidence to guarantee every position on the mirror satisfies the Bragg reflection. In principle, the accuracy of the parameters of the sputtering conditions is essential for achieving a reliable result. In this paper, we proposed a precise method for the fabrication of the laterally graded multilayer based on a planetary motion magnetron sputtering system for film thickness control. This method uses the fast and slow particle model to obtain the particle transport process, and then combines it with the planetary motion magnetron sputtering system to establish the film thickness distribution model. Moreover, the parameters of the sputtering conditions in the model are derived from experimental inversion to improve accuracy. The revolution and rotation of the substrate holder during the final deposition process are achieved by the speed curve calculated according to the model. Measurement results from the X-ray reflection test (XRR) show that the thickness error of the laterally graded multilayer film, coated on a parabolic cylinder Si substrate, is less than 1%, demonstrating the effectiveness of the optimized method for obtaining accurate film thickness distribution.

Three-dimensional predator–prey interactions: a computer simulation of bird flocks and aircraft

1986 ◽  
Vol 64 (11) ◽  
pp. 2624-2633 ◽  
Author(s):  
Peter F. Major ◽  
Lawrence M. Dill ◽  
David M. Eaves
Keyword(s):  
Computer Simulation ◽  
Prey Species ◽  
Three Dimensional ◽  
Aircraft Engine ◽  
Aquatic Environments ◽  
Aircraft Engines ◽  
Predator Prey ◽  
Simulation Techniques ◽  
Computer Simulation Techniques ◽  
Individual Prey

Three-dimensional interactions between grouped aerial predators (frontal discs of aircraft engines), either linearly arrayed or clustered, and flocks of small birds were studied using interactive computer simulation techniques. Each predator modelled was orders of magnitude larger than an individual prey, but the prey flock was larger than each predator. Expected numbers of individual prey captured from flocks were determined for various predator speeds and trajectories, flock–predator initial distances and angles, and flock sizes, shapes, densities, trajectories, and speeds. Generally, larger predators and clustered predators caught more prey. The simulation techniques employed in this study may also prove useful in studies of predator–prey interactions between schools or swarms of small aquatic prey species and their much larger vertebrate predators, such as mysticete cetaceans.The study also provides a method to study problems associated with turbine aircraft engine damage caused by the ingestion of small flocking birds, as well as net sampling of organisms in open aquatic environments.

Sign in / Sign up

Export Citation Format

Share Document