Analysis of Eccentric Annular Incompressible Seals: Part 1—A New Solution Using Fast Fourier Transforms for Determining Hydrodynamic Force

1988 ◽  
Vol 110 (2) ◽  
pp. 354-359 ◽  
Author(s):  
C. C. Nelson ◽  
D. T. Nguyen
Keyword(s):  
Fourier Transforms ◽  
Solution Procedure ◽  
Fast Fourier Transforms ◽  
Analysis Procedure ◽  
Bulk Flow ◽  
Governing Equations ◽  
Zeroth Order ◽  
Static Displacement ◽  
Flow Equations ◽  
Flow Variables

A new analysis procedure is presented which solves for the flow variables of an incompressible-flow annular pressure seal in which the rotor has a large static displacement from the centered position. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction equation. No simplification of these bulk-flow equations are required for the solution procedure. Perturbation of the flow variables yields a set of zeroth and first-order equations. The zeroth-order equations (which model the large static displacement) are integrated by means of an efficient new method which employs Fast Fourier Transforms. Further integration of the zeroth-order pressures yields the hydrodynamic reactive force. Predictions for the hydrodynamic forces from this analysis procedure are in excellent agreement with available experimental results.

Analysis of Eccentric Annular Incompressible Seals: Part 2—Effects of Eccentricity on Rotordynamic Coefficients

1988 ◽  
Vol 110 (2) ◽  
pp. 361-366 ◽  
Author(s):  
C. C. Nelson ◽  
D. T. Nguyen
Keyword(s):  
Flow Model ◽  
Element Model ◽  
Analysis Procedure ◽  
Governing Equations ◽  
Zeroth Order ◽  
Static Displacement ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
Flow Variables ◽  
Factor Equation

In Part 1 of this paper, a new analysis procedure is presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. This part of the paper (Part 2) incorporates the solutions from Part 1 to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations by means of the method described in Part 1, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare very well with available experimental data, and are clearly more accurate than the predictions based on a Finite Element model.

Theoretical and Experimental Characterization of Emulsion Flow in a Cavity Transfer Mixer

2003 ◽  
Author(s):  
A. H. Raza ◽  
R. A. Lai-Fook ◽  
C. J. Lawrence
Keyword(s):  
Flow Characteristics ◽  
Axial Direction ◽  
Solution Procedure ◽  
Modes Of Operation ◽  
Flow Equations ◽  
Recirculating Flow ◽  
Rectangular Pattern ◽  
Mean Pressure ◽  
Emulsion Processing ◽  
Dependent Flow

A theoretical model of time-dependent flow based on Reynolds equation using emulsion processing in a Cavity Transfer Mixer (CTM) has been developed in Mathematica and is presented in this work. It is a continuum model, which allows the study of materials undergoing rapid deformation. The flow of a fluid in a CTM is examined using a finite difference analysis (FDA) to solve the flow equations for an unwound section with cavities arranged in a rectangular pattern. Periodic boundary conditions are included in the model to predict the pressure distribution, which allows subsequent determination of the flow field. The solution procedure gives a smooth function for the pressure field, with equal pressures at the boundaries in the y-direction and an overall mean pressure gradient in the x-direction. Once the pressure has been found, several flow properties follow directly. The flow in the downstream axial direction is seen to consist of purely pressure-driven flow. In contrast, the flow in the cross-cavity direction is a recirculating flow driven by the drag velocity of the moving rotor surface. These two flows taken together combine into a helical flow travelling through the cavity. Because of this, there is likely to bre a high degree of laminar and distributive flow in this type of machine. The experimental part of this work addresses the processing of an emulsion in the CTM when it is run under batch and continuous modes of operation. The flow characteristics have been studied for varying rotor speeds of 0 rpm, 16 rpm, 32 rpm, 48 rpm and 64 rpm. Also studied were the changes that the emulsion exhibits along the mixer length and with time in the mixer. The experiments indicate that increase in the rotational speed causes the viscosity to reduce systematically in both batch and continuous modes of operation.

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

2021 ◽  
pp. 2150145
Author(s):  
Shuang-Shuang Zhou ◽  
M. Ijaz Khan ◽  
Sumaira Qayyum ◽  
B. C. Prasannakumara ◽  
R. Naveen Kumar ◽  
...  
Keyword(s):  
Heat Source ◽  
Lewis Number ◽  
Solution Procedure ◽  
Energy Concentration ◽  
Gyrotactic Microorganisms ◽  
Dimensionless Parameters ◽  
Flow Equations ◽  
Fluid Parameter ◽  
Source Sink ◽  
The Impact

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

Data Acquisition and Processing of Weak Low-Frequency Magnetic Signals

2011 ◽  
Vol 65 ◽  
pp. 299-302 ◽  
Author(s):  
Shou Qiang Men ◽  
Christian Resagk
Keyword(s):  
Magnetic Field ◽  
Data Acquisition ◽  
Fourier Transforms ◽  
Low Frequency ◽  
Fast Fourier Transforms ◽  
Two Dimensional ◽  
Calibration System ◽  
Magnetic Field Sensors ◽  
Data Acquisition And Processing

A simple calibration system for magnetic field sensors was designed, and experiments were carried out to calibrate two-dimensional fluxgate sensors and a sensor ring composed of eight fluxgate sensors. Fast Fourier Transforms and trapezoidal numerical integrals were applied to deal with the raw signals. It is found that it is not suitable to apply fast Fourier Transforms only to deal with signals with several peaks close to each other, but trapezoidal numerical integrals should also be used in combination with the FFT method.

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