Design of Turbomachinery Blading in Transonic Flows by the Circulation Method

1992 ◽  
Vol 114 (1) ◽  
pp. 141-146
Author(s):  
T. Q. Dang
Keyword(s):  
Fourier Series ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Fourier Series Expansion ◽  
Main Task ◽  
Design Technique ◽  
Transonic Flows ◽  
Circulation Method ◽  
Expansion Technique ◽  
Volume Method

The newly developed three-dimensional design technique for turbomachinery blading based on the circulation method has been successfully extended into the transonic flow regime. The main task involves replacing the classical Fourier series expansion technique by a finite-volume method. Calculations were carried out for the design of infinitely thin cascaded blades in transonic flows, including shocked and shock-free cascaded blades.

scholarly journals Automatic Page-Turning Mechanism with Near-Field Electroadhesive Force for Linearly Correctable Imaging

2016 ◽  
Author(s):  
Junseok Lee
Keyword(s):  
Fourier Series ◽  
Success Rate ◽  
Near Field ◽  
Three Dimensional ◽  
Fourier Series Expansion ◽  
Portable Devices ◽  
Geometrical Configuration ◽  
Image Correction ◽  
Force Ratio ◽  
Turning Mechanism

Recently, demand for digitization of books has increased in tandem with thespread of portable devices for electronic books. However, in a number ofinvented book-scanning devices, pages are turned manually by users, orpricey three-dimensional cameras are needed for image correction. Ourautomatic page-turning mechanism employs near-field electroadhesive forceto turn a single page. As the near-field electroadhesive force on theclosest sheet of paper is far stronger than that on the second, only asingle sheet of paper can be lifted. Using Fourier series expansion, weprove that regardless of the geometrical configuration of electrodes, theforce ratio on the closest to the second is dominantly controlled by theperiod of the configuration. Based on this, a novel electrode configurationis designed aiming to give higher force ratio than the conventionalinterdigital patterns. The advantage of our mechanism in image processingis that perspective correction is compatible with our mechanism, hence notrequiring devices for acquiring 3-D information to reconstruct images. Ourautomatic page-turning mechanism with a fair success rate and the reducednumber of components shows that it is a promising method for automaticlow-cost book-scanning devices.

scholarly journals Diffusion in Semiconductors by Using Fourier Series Expansion Technique

2014 ◽  
Vol 11 (2) ◽  
pp. 90-97
Author(s):  
M El-Adawi ◽  
S Abdel-Ghany ◽  
S Shalaby
Keyword(s):  
Fourier Series ◽  
Diffusion Equation ◽  
Mass Balance ◽  
Series Expansion ◽  
Theoretical Approach ◽  
Balance Equation ◽  
Concentration Function ◽  
Fourier Series Expansion ◽  
Mass Balance Equation ◽  
Expansion Technique

Doping by diffusion is still one of acceptable and important methods that have essential technological applications. A theoretical approach to study diffusion in semi-conductors is introduced. The diffusion equation together with Fick's law and mass balance equation are solved to obtain the concentration function and the mass penetration depth using Fourier Series expansion technique. Doping of indium, phosphorus, gallium and Arsenic in Silicon as illustrative examples are given.

A Fully Three-Dimensional Inverse Method for Turbomachinery Blading in Transonic Flows

1993 ◽  
Vol 115 (2) ◽  
pp. 354-361 ◽  
Author(s):  
T. Q. Dang
Keyword(s):  
High Pressure ◽  
Boundary Conditions ◽  
Centrifugal Compressor ◽  
Transonic Flow ◽  
Inverse Method ◽  
Three Dimensional ◽  
Blade Profile ◽  
Transonic Flows ◽  
Blade Passage ◽  
Highly Loaded

This paper presents a procedure to extend a recently developed fully three-dimensional inverse method for highly loaded turbomachine blades into the transonic-flow regime. In this inverse method, the required three-dimensional blade profile to produce a prescribed swirl schedule is determined iteratively using the blade boundary conditions. In the present implementation, the flow is assumed to be inviscid and the blades are assumed to be infinitely thin. The relevant equations are solved in the conservative forms and are discretized in all three directions using a finite-volume technique. Calculations are carried out for the design of high-pressure axial- and centrifugal-compressor rotors. These examples include prescribed swirl schedules corresponding to blade designs that are shock-free and blade designs that have rapid compression regions in the blade passage.

scholarly journals Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yuzhen Mi
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fourier Series ◽  
Small Perturbation ◽  
Homoclinic Solution ◽  
Fourier Series Expansion ◽  
Volterra System ◽  
Perturbation Theorem ◽  
Expansion Technique ◽  
The Fixed Point Theorem

This paper investigates Lotka-Volterra system under a small perturbationvxx=-μ(1-a2u-v)v+ϵf(ϵ,v,vx,u,ux),uxx=-(1-u-a1v)u+ϵg(ϵ,v,vx,u,ux). By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that nearμ=0the system has a generalized homoclinic solution exponentially approaching a periodic solution.

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