Shear-Driven Flow in a Toroid of Square Cross Section

2003 ◽  
Vol 125 (1) ◽  
pp. 130-137 ◽  
Author(s):  
J. A. C. Humphrey ◽  
J. Cushner ◽  
M. Al-Shannag ◽  
J. Herrero ◽  
F. Giralt
Keyword(s):  
Cross Section ◽  
Finite Length ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Radius Of Curvature ◽  
Infinite Length ◽  
Core Flow ◽  
Reynolds Number Flow ◽  
End Wall

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature Rc reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, δ=D/Rc, this flow configuration represents a more general paradigm for fluid mechanics research.

Heat Transfer for Laminar Flow in Spiral Ducts of Rectangular Cross Section

2005 ◽  
Vol 127 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

Laminar Flow and Heat Transfer in Spiral Ducts of Rectangular Cross Section

2004 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Flow And Heat Transfer ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined with the aide of the FLUENT computational fluid dynamics program. Peripherally-averaged coefficients of friction and Nusselt numbers are presented as a function of distance from the inlet and of the Dean number. Fully-developed values of friction coefficient and Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in post-entry regions. These results are applicable to spiral-plate heat exchangers.

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

Geometry Effects in Eulerian/Granular Simulation of a Turbulent FCC Riser with a (kg-?g)-KTGF Model

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Hamid Reza Nazif ◽  
Hassan Basirat Tabrizi ◽  
Farhad A Farhadpour
Keyword(s):  
Cross Section ◽  
Large Scale ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Good Prediction ◽  
Model Predictions ◽  
Secondary Circulations ◽  
Sharp Corners ◽  
Granular Simulation

Three-dimensional, transient turbulent particulate flow in an FCC riser is modeled using an Eulerian/Granular approach. The turbulence in the gas phase is described by a modified realizable (kg-?g) closure model and the kinetic theory of granular flow (KTGF) is employed for the particulate phase. Separate simulations are conducted for a rectangular and a cylindrical riser with similar dimensions. The model predictions are validated against experimental data of Sommerfeld et al (2002) and also compared with the previously reported LES-KTGF simulations of Hansen et al (2003) for the rectangular riser. The (kg-?g)-KTGF model does not perform as well as the LES-KTGF model for the riser with a rectangular cross section. This is because, unlike the more elaborate LES-KTGF model, the simpler (kg-?g)-KTGF model cannot capture the large scale secondary circulations induced by anisotropic turbulence at the corners of the rectangular riser. In the cylindrical geometry, however, the (kg-?g)-KTGF model gives good prediction of the data and is a viable alternative to the more complex LES-KTGF model. This is not surprising as the circulations in the riser with a circular cross section are due to the curvature of the walls and not due to the presence of sharp corners.

Curvature-induced deformations of the vortex rings generated at the exit of a rectangular duct

2019 ◽  
Vol 864 ◽  
pp. 141-180 ◽  
Author(s):  
Abbas Ghasemi ◽  
Burak Ahmet Tuna ◽  
Xianguo Li
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Single Mode ◽  
The Self ◽  
Vortex Rings ◽  
Potential Core ◽  
Vortex Pairing ◽  
Time Space ◽  
Axis Switching

Rectangular air jets of aspect ratio $2$ are studied at $Re=UD_{h}/\unicode[STIX]{x1D708}=17\,750$ using particle image velocimetry and hot-wire anemometry as they develop naturally or under acoustic forcing. The velocity spectra and the spatial theory of linear stability characterize the fundamental ($f_{n}$) and subharmonic ($f_{n}/2$) modes corresponding to the Kelvin–Helmholtz roll-up and vortex pairing, respectively. The rectangular cross-section of the jet deforms into elliptic/circular shapes downstream due to axis switching. Despite the apparent rotation of the vortex rings or the jet cross-section, the axis-switching phenomenon occurs due to reshaping into rounder geometries. By enhancing the vortex pairing, excitation at $f_{n}/2$ shortens the potential core, increases the jet spread rate and eliminates the overshoot typically observed in the centreline velocity fluctuations. Unlike circular jets, the skewness and kurtosis of the rectangular jets demonstrate elevated anisotropy/intermittency levels before the end of the potential core. The axis-switching location is found to be variable by the acoustic control of the relative expansion/contraction rates of the shear layers in the top (longer edge), side (shorter edge) and diagonal views. The self-induced vortex deformations are demonstrated by the spatio-temporal evolution of the phase-locked three-dimensional ring structures. The curvature-induced velocities are found to reshape the vortex ring by imposing nonlinear azimuthal perturbations occurring at shorter wavelengths with time/space evolution. Eventually, the multiple high-curvature/high-velocity regions merge into a single mode distribution. In the plane of the top view, the self-induced velocity distribution evolves symmetrically while the tilted ring results in the asymmetry of the azimuthal perturbations in the side view as the side closer to the acoustic source rolls up in more upstream locations.

Optimal Extrusion Die Design for Production of Polymer Tensile Test Specimen

2020 ◽  
Author(s):  
Sebastián Acosta Andrade ◽  
Andrés Rigail-Cedeño ◽  
Clotario V. Tapia-Bastidas ◽  
Eduardo Castillo-Orozco
Keyword(s):  
Tensile Test ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Die Design ◽  
Optimum Shape ◽  
Flow Profile ◽  
Cross Model ◽  
Tensile Test Specimen ◽  
Extrusion Die

Abstract This work aims to present the design of an extrusion die for the production of polymeric tensile test specimens. Computational Fluid Dynamics is used during the optimization process to minimize the overall pressure drop across the die, achieve uniform exit velocity, low energy consumption, high throughput, and excellent properties of the extruded specimens. A three-dimensional incompressible viscous flow is considered and the Cross model is employed for taking into account the non-Newtonian behavior of the flow. Several geometries are analyzed before devising an optimum shape. The final design includes, in the beginning, a conical flow profile and then it gradually transitions into the rectangular cross-section of the slab. The die land is an elongated flow restriction channel of smaller cross-section, where the material experiences gradually-decreasing pressures along the length of the land and finally converging the molten polymer into a melt laminate at the exit.

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