Numerical Study of Some Three-Dimensional Laminar Free Convective Flows

1976 ◽  
Vol 98 (4) ◽  
pp. 570-575 ◽  
Author(s):  
P. H. Oosthuizen
Keyword(s):  
Numerical Study ◽  
Finite Difference Methods ◽  
Three Dimensional ◽  
The Body ◽  
Three Dimensional Flow ◽  
Constant Property ◽  
Convective Flows ◽  
Boundary Layer Equations ◽  
Dimensional Flow ◽  
Acceleration Component

Three-dimensional buoyancy-induced flows over plates and cylinders have been considered. The three-dimensional flow results either from the fact that the body is inclined to the horizontal or from the fact that there is a longitudinal acceleration component. Both the cases where this acceleration component is constant and the case where it varies linearly with the distance along the body have been considered. The study is based on the use of the constant-property boundary-layer equations. These equations have been rewritten in terms of dimensionless variables, and thus the resulting equations do not explicitly depend on the nature of mechanism causing the three-dimensional flow. These equations have been solved numerically using finite-difference methods, with heat-transfer distributions for various representative situations being deduced.

Transient Growth of Three-Dimensional Vortex Perturbations During Near-Parallel Collision With a Circular Cylinder

2006 ◽  
Author(s):  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Circular Cylinder ◽  
Vortex Core ◽  
Computational Study ◽  
Three Dimensional ◽  
The Body ◽  
Transient Growth ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Features

A computational study is reported that examines the transient growth of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. The degree of perturbation amplification as the vortex approaches the cylinder is quantified and shown to be mostly dependent on the dominant axial wavenumber of the perturbation. The perturbation amplification is observed to be greatest for perturbations with axial wavelength of about 1.5 times the cylinder diameter.

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