scholarly journals Spectra of operators associated with flow around an infinite cylinder

2019 ◽  
Keyword(s):  
Infinite Cylinder

The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow

1960 ◽  
Vol 7 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Alar Toomre
Keyword(s):  
Shear Flow ◽  
Lateral Displacement ◽  
Reynolds Numbers ◽  
Infinite Cylinder ◽  
List Type ◽  
Displacement Effect ◽  
Simple Method ◽  
Viscous Shear ◽  
Parallel Shear Flow ◽  
Viscous Shear Flow

A simple method is presented in this paper for calculating the secondary velocities, andthe lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’) in the plane of symmetry ahead of an infinitely long cylinder situated normal to a steady, incompressible, slightly viscous shear flow; the cylinder is also perpendicular to the vorticity, which is assumed uniform but small. The method is based on lateral gradients of pressure, these being calculated from the primary flow alone. Profiles of the secondary velocities are obtained at several Reynolds numbers ahead of two specific cylindrical shapes: a circular cylinder, and a flat plate normal to the flow. The displacement effect is derived and, rathe surprisingly, is found to be virtually independent of the Reynolds number.

Spin-up from rest of a compressible fluid in a rapidly rotating cylinder

1992 ◽  
Vol 237 ◽  
pp. 413-434 ◽  
Author(s):  
Jae Min Hyun ◽  
Jun Sang Park
Keyword(s):  
Mach Number ◽  
Compressible Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Axial Direction ◽  
Ekman Layer ◽  
Infinite Cylinder ◽  
Full Time ◽  
Viscous Effects ◽  
Initial State

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.

scholarly journals Use of the Distance Transform for Integration of Local Measurements: Principle and Application in Chemical Engineering

2016 ◽  
Vol 22 (2) ◽  
pp. 422-431 ◽  
Author(s):  
Loïc Sorbier ◽  
Frédéric Bazer-Bachi ◽  
Yannick Blouët ◽  
Maxime Moreaud ◽  
Virginie Moizan-Basle
Keyword(s):  
Chemical Engineering ◽  
Least Square ◽  
Infinite Cylinder ◽  
Distance Transform ◽  
High Symmetry ◽  
Object A ◽  
Local Measurements ◽  
Symmetrical Object ◽  
Relative Errors ◽  
The Cost

AbstractWe propose an original methodology to integrate local measurement for nontrivial object shape. The method employs the distance transform of the object and least-square fitting of numerically computed weighting functions extracted from it. The method is exemplified in the field of chemical engineering by calculating the global metal concentration in catalyst grains from uneven metal distribution profiles. Applying the methodology on synthetic profiles with the help of a very simple deposition model allows us to evaluate the accuracy of the method. For high symmetry objects such as an infinite cylinder, relative errors on global concentration are lower than 1% for well-resolved profiles. For a less symmetrical object, a tetralobe, the best estimator gives a relative error below 5% at the cost of increased measurement time. Applicability on a real case is demonstrated on an aged hydrodemetallation catalyst. Sampling of catalyst grains at the inlet and outlet of the reactor allowed conclusions concerning different reactivity for the trapped metals.

scholarly journals Stable Numerical Evaluation of Finite Hankel Transforms and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Manoj P. Tripathi ◽  
B. P. Singh ◽  
Om P. Singh
Keyword(s):  
Stability Analysis ◽  
Heat Equation ◽  
Numerical Experiments ◽  
Numerical Evaluation ◽  
Radiation Condition ◽  
Hankel Transform ◽  
Basis Functions ◽  
Infinite Cylinder ◽  
Stable Algorithm ◽  
Hankel Transforms

A new stable algorithm, based on hat functions for numerical evaluation of Hankel transform of order ν>-1, is proposed in this paper. The hat basis functions are used as a basis to expand a part of the integrand, rf(r), appearing in the Hankel transform integral. This leads to a very simple, efficient, and stable algorithm for the numerical evaluation of Hankel transform. The novelty of our paper is that we give error and stability analysis of the algorithm and corroborate our theoretical findings by various numerical experiments. Finally, an application of the proposed algorithm is given for solving the heat equation in an infinite cylinder with a radiation condition.

scholarly journals Effect of Deformation on Semi–infinite Viscothermoelastic Cylinder Based on Five Theories of Generalized Thermoelasticity

2017 ◽  
Vol 6 (1) ◽  
pp. 17-35 ◽  
Author(s):  
D. K. Sharma ◽  
Himani Mittal ◽  
Sita Ram Sharma ◽  
Inder Parkash
Keyword(s):  
Heat Conduction ◽  
Laplace Transformation ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Generalized Thermoelasticity ◽  
Dynamical Problem ◽  
Infinite Cylinder ◽  
Matlab Software ◽  
Voigt Model ◽  
Laplace Transformations

We considera dynamical problem for semi-infinite viscothermoelastic semi infinite cylinder loaded mechanically and thermally and investigated the behaviour of variations of displacements, temperatures and stresses. The problem has been investigated with the help of five theories of the generalized viscothermoelasticity by using the Kelvin – Voigt model. Laplace transformations and Hankel transformations are applied to equations of constituent relations, equations of motion and heat conduction to obtain exact equations in transformed domain. Hankel transformed equations are inverted analytically and for the inversion of Laplace transformation we apply numerical technique to obtain field functions. In order to obtain field functions i.e. displacements, temperature and stresses numerically we apply MATLAB software tools. Numerically analyzed results for the temperature, displacements and stresses are shown graphically.

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