Forced and Free Flow in a Vertical Annular Duct Under Nonaxisymmetric Conditions

2005 ◽  
Vol 127 (6) ◽  
pp. 606-613 ◽  
Author(s):  
A. Barletta ◽  
S. Lazzari
Keyword(s):  
Expansion Method ◽  
Axial Direction ◽  
Boussinesq Approximation ◽  
Free Flow ◽  
Fourier Series Expansion ◽  
Dimensionless Temperature ◽  
Thermal Boundary Conditions ◽  
Annular Duct ◽  
Fanning Friction Factor ◽  
Analytical Expressions

The combined forced and free flow in a vertical annular duct is studied under the hypothesis of steady-state parallel laminar flow. The Boussinesq approximation is invoked and the viscous dissipation is considered as negligible. The thermal boundary conditions are such that axial symmetry does not occur and temperature does not change in the axial direction. The dimensionless local balance equations are solved analytically by means of the Fourier series expansion method. The analytical expressions of the dimensionless temperature field, of the dimensionless velocity field, and of the Fanning friction factor are obtained.

scholarly journals Second Law Analysis of Laminar Flow in a Circular Pipe Immersed in an Isothermal Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Vishal Anand ◽  
Krishna Nelanti
Keyword(s):  
Laminar Flow ◽  
Entropy Generation ◽  
Circular Tube ◽  
Dimensionless Temperature ◽  
Bejan Number ◽  
Uniform Wall Temperature ◽  
Thermal Boundary Conditions ◽  
Fluid Properties ◽  
Isothermal Fluid ◽  
Uniform Wall

Entropy generation and pumping power to heat transfer ratio (PPR) of a laminar flow, for a circular tube immersed in an isothermal fluid, are studied analytically in this paper. Two different fluids, namely, water and ethylene glycol, are chosen to study the influence of fluid properties on entropy generation and PPR. The expressions for dimensionless entropy generation, Bejan number and PPR are derived in a detailed way and their variations with Reynolds number, external Biot number, and the dimensionless temperature difference are illustrated. The results of the analysis are compared with those for a laminar flow in a circular tube with uniform wall temperature boundary condition. Finally, a criterion is established to determine which type of thermal boundary conditions is more suitable for a particular fluid, with respect to its influence on entropy generation.

Effect of unbalanced magnetic pull on the thermal characteristics of traction motor bearing

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Tingting Wang ◽  
Dongli Song ◽  
Weihua Zhang ◽  
Shiqi Jiang ◽  
Zhiwei Wang
Keyword(s):  
Thermal Analysis ◽  
High Speed ◽  
Thermal Characteristics ◽  
Expansion Method ◽  
Fourier Series Expansion ◽  
High Speed Train ◽  
Traction Motor ◽  
Content Type ◽  
Unbalanced Magnetic Pull ◽  
Motor Bearing

Purpose The purpose of this paper is to analyze the unbalanced magnetic pull (UMP) of the rotor of traction motor and the influence of the UMP on thermal characteristics of traction motor bearing. Design/methodology/approach The unbalanced magnetic pull on the rotor with different eccentricity was calculated by Fourier series expansion method. A bearing thermal analysis finite element model considering both the vibration of high-speed train caused by track irregularity and the UMP of traction motor rotor was established. The validity of the model is verified by experimental data obtained from a service high-speed train. Findings The results show that thermal failure of bearing subassemblies most likely occurs at contact area between the inner ring and rollers. The UMP of rotor of traction motor has a significant effect on the temperature of the inner ring and roller of the bearing. When the eccentricity is 10%, the temperature can even be increased by about 12°C. Therefore, the UMP of rotor of traction motor must be considered in thermal analysis of traction motor bearing. Originality/value In the thermal analysis of the bearing of the traction motor of high-speed train, the UMP of the rotor of the traction motor is considered for the first time

A dynamic shell model for diagnostics of rotating machinery under periodic excitation

2021 ◽  
Vol 263 (2) ◽  
pp. 4120-4131
Author(s):  
Murat Inalpolat ◽  
Enes Timur Ozdemir
Keyword(s):  
Boundary Conditions ◽  
Shell Model ◽  
Dynamic Model ◽  
Shell Structure ◽  
Acoustic Radiation ◽  
Circular Cylindrical Shell ◽  
Expansion Method ◽  
Rotating Machinery ◽  
Forced Response ◽  
Fourier Series Expansion

In this paper, a generalized dynamic model of a shell structure has been developed and utilized for diagnostics purposes. The dynamic model is three-dimensional, includes the effects of rotary inertia and shear deformation, and can handle moving loads in radial, tangential and axial directions. The model is utilized to determine in-plane radial displacements of the shell structure under concentrated radial loads for different boundary conditions. The periodic loads are constructed using harmonics obtained through the Fourier series expansion method. The modal expansion technique is implemented for calculation of the steady state forced response of the shell structure. A simplified acoustic radiation model is also implemented in conjunction with the dynamic shell model to predict the noise radiated from a rotating circular cylindrical shell structure under different kinematic, loading and boundary conditions. Moreover, forced vibration response and acoustic radiation predicted will be employed to reveal patterns in the signals that can potentially be used for diagnostics of rotating machinery applications. The shell model is derived using a comprehensive approach and thus can be used to model prevalent engineering applications ranging from electric motors to gears and bearings.

Predicting Apple Firmness and Soluble Solids Content Based on Hyperspectral Scattering Imaging Using Fourier Series Expansion

2017 ◽  
Vol 60 (4) ◽  
pp. 1053-1062
Author(s):  
Wei Wang ◽  
Min Huang ◽  
Qibing Zhu
Keyword(s):  
Fourier Series ◽  
Least Squares ◽  
Series Expansion ◽  
Fourier Coefficients ◽  
Expansion Method ◽  
Soluble Solids ◽  
Fourier Series Expansion ◽  
Support Vector ◽  
Soluble Solids Content ◽  
Solids Content

Abstract. This article reports on using a Fourier series expansion method to extract features from hyperspectral scattering profiles for apple fruit firmness and soluble solids content (SSC) prediction. Hyperspectral scattering images of ‘Golden Delicious’ (GD), ‘Jonagold’ (JG), and ‘Delicious’ (RD) apples, harvested in 2009 and 2010, were acquired using an online hyperspectral imaging system over the wavelength region of 500 to 1000 nm. The moment method and Fourier series expansion method were used to analyze the scattering profiles of apples. The zeroth-first order moment (Z-FOM) spectra and Fourier coefficients were extracted from each apple, which were then used for developing fruit firmness and SSC prediction models using partial least squares (PLS) and least squares support vector machine (LSSVM). The PLS models based on the Fourier coefficients improved the standard errors of prediction (SEP) by 4.8% to 19.9% for firmness and by 2.4% to 13.5% for SSC, compared with the PLS models using the Z-FOM spectra. The LSSVM models for the prediction set of Fourier coefficients achieved better SEP results, with improvements of 4.4% to 11.3% for firmness and 2.8% to 16.5% for SSC over the LSSVM models for the Z-FOM spectra data and 3.7% to 12.6% for firmness and 5.4% to 8.6% for SSC over the PLS models for the Fourier coefficients. Experiments showed that Fourier series expansion provides a simple, fast, and effective means for improving Keywords: Apples, Firmness, Fourier series expansion, Hyperspectral scattering imaging, Least squares support vector machine, Partial least squares, Soluble solids content.

Analytical solutions for turbulent Boussinesq fountains in a linearly stratified environment

2011 ◽  
Vol 691 ◽  
pp. 487-497 ◽  
Author(s):  
Rabah Mehaddi ◽  
Olivier Vauquelin ◽  
Fabien Candelier
Keyword(s):  
Theoretical Model ◽  
Asymptotic Analysis ◽  
Flow Rate ◽  
Vertical Velocity ◽  
Analytical Solutions ◽  
Boussinesq Approximation ◽  
Singular Case ◽  
Maximal Height ◽  
Analytical Integration ◽  
Analytical Expressions

AbstractThis paper theoretically investigates the initial up-flow of a vertical turbulent fountain (round or plane) in a linearly stratified environment. Conservation equations (volume, momentum and buoyancy) are written under the Boussinesq approximation assuming an entrainment proportional to the vertical velocity of the fountain. Analytical integration leads to exact values of both density and flow rate at the maximal height reached by the fountain. This maximal height is expressed as a function of the release conditions and the stratification strength and plotted from a numerical integration in order to exhibit overall behaviour. Then, analytical expressions for the maximal height are derived from asymptotic analysis and compared to experimental correlations available for forced fountains. For weak fountains, these analytical expressions constitute a new theoretical model. Finally, modified expressions are also proposed in the singular case of an initially non-buoyant vertical release.

scholarly journals Analysis of Propagation Characteristics along an Array of Silver Nanorods Using Dielectric Constants from Experimental Data and the Drude-Lorentz Model

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1280 ◽  
Author(s):  
Zong ◽  
Zhang
Keyword(s):  
Experimental Data ◽  
Propagation Constant ◽  
Single Mode ◽  
Expansion Method ◽  
Dielectric Constants ◽  
Fourier Series Expansion ◽  
Lorentz Model ◽  
Silver Nanorods ◽  
Complex Propagation ◽  
Multi Mode

In this study, the Fourier series expansion method (FSEM) was employed to calculate the complex propagation constants of plasma structures consisting of infinitely long, silver nanorod arrays in the range of 180–1900 nm, and the characteristics of the complex propagation constant were analyzed in depth. According to the results of FSEM using dielectric constants from Johnson experimental data, a multi-mode frequency band appears in the propagation stage, which can be adopted to achieve a multi-mode communication, multi-mode transceiver, integrated filter with single multi-mode combination. In the meantime, the comparison between the three sets of results with only single mode transmission of the generalized multipole technique (GMT) using dielectric constants from Johnson experimental data, FSEM using dielectric constants from Palik experimental data, and FSEM using dielectric function from Drude–Lorentz model suggested that the results of the four sets of complex propagation constants were well consistent with each other. Furthermore, a finite array of only 40 silver nanorods was studied, and the ability of guided waves when a finite array is excited by a plane wave at a specific wavelength was explored. According to different guiding abilities—propagation, attenuation, and cut off, it can be applied to waveguides, sensor, filters, etc.

A Variational Method for Fully Developed Laminar Heat Transfer in Ducts

1959 ◽  
Vol 81 (2) ◽  
pp. 157-164 ◽  
Author(s):  
E. M. Sparrow ◽  
R. Siegel
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Variational Method ◽  
Cross Section ◽  
Cross Sections ◽  
Axial Direction ◽  
Circular Sector ◽  
Thermal Boundary Conditions ◽  
Temperature Distributions ◽  
Good Agreement

A variational method is presented for determining fully developed velocity and temperature distributions for laminar flow in noncircular ducts. The heat addition to the fluid is taken to be uniform in the axial direction, but a variety of thermal boundary conditions are considered around the periphery of the duct cross section. Several illustrative examples are given, and comparisons are made which show good agreement with available exact solutions. These examples include ducts of rectangular and circular-sector cross sections.

A Transverse Dynamic Deflection Model for Thin Plate Made of Saturated Porous Materials

2016 ◽  
Vol 71 (10) ◽  
pp. 943-948
Author(s):  
Zhou Feng-xi ◽  
Cao Xiao-lin
Keyword(s):  
Porous Materials ◽  
Thin Plate ◽  
Expansion Method ◽  
Fourier Series Expansion ◽  
Saturated Porous Media ◽  
Governing Equations ◽  
Transverse Dynamic ◽  
Transverse Vibrations ◽  
Porosity And Permeability ◽  
Series Expansion Method

AbstractIn this article, a transverse dynamic deflection model is established for thin plate made of saturated porous materials. Based on the Biot’s model for fluid-saturated porous media, using the Love–Kirchhoff hypothesis, the governing equations of transverse vibrations of fluid-saturated poroelastic plates are derived in detail, which take the inertial, fluid viscous, mechanical couplings, compressibility of solid, and fluid into account. The free vibration and forced vibration response of a simply supported poroelastic rectangular plate is obtained by Fourier series expansion method. Through numerical examples, the effect of porosity and permeability on the dynamic response, including the natural frequency, amplitude response, and the resonance areas is assessed.

Sign in / Sign up

Export Citation Format

Share Document