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TECHNICAL PAPERS

Numerical Procedure for the Laminar Developed Flow in a Helical Square Duct

[+] Author and Article Information
V. D. Sakalis, P. M. Hatzikonstantinou, P. K. Papadopoulos

Department of Engineering Science, University of Patras, GR 26500 Patras, Greece

J. Fluids Eng 127(1), 136-148 (Mar 22, 2005) (13 pages) doi:10.1115/1.1852483 History: Received August 08, 2003; Revised October 14, 2004; Online March 22, 2005
Copyright © 2005 by ASME
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References

Cheng,  K. C., Lin,  R., and Ou,  J. W., 1976, “Fully Developed Laminar Flow in Curved Rectangular Channels,” ASME J. Fluids Eng., 98, pp. 41–48.
Ghia,  K. N., Ghia,  U., and Shih,  C. T., 1987, “Study of Fully Developed Incompressible Flow in Curved Ducts Using a Multigrid Technique,” ASME J. Fluids Eng., 109, pp. 226–235.
Hwang,  G. J., and Chao,  C. H., 1991, “Forced Laminal Convection in a Curved Isothermal Duct,” ASME J. Heat Transfer, 113, pp. 48–56.
Hatzikonstantinou,  P. M., and Sakalis,  V. D., 2004, “A Numerical-Variational Procedure for a Laminar Flow in Curved Square Ducts,” Int. J. Numer. Methods Fluids, 45, pp. 1269–1289.
Sakalis, V. D., and Hatzikonstantinou, P. M., 2002, “Predictions and Accuracy of the CVP Numerical Method for the Developed Laminar Flow in Curved Ducts,” Proceedings of the 4th GRACM Congress on Computational Mechanics, University of Patras, Patras, Greece, Tsahalis, D., ed., IV , pp. 1400–1410.
Wang,  C. I., 1981, “On the Low Reynolds Number Flow in a Helical Pipe,” J. Fluid Mech., 108, pp. 185–194.
Germano,  M., 1982, “On the Effect of Torsion in a Helical Pipe Flow,” J. Fluid Mech., 125, pp. 1–8.
Kao,  H. C., 1987, “Torsion Effect on Fully Developed Flow in a Helical Pipe,” J. Fluid Mech., 184, pp. 335–356.
Tuttle,  E. R., 1990, “Laminar Flow in Twisted Pipes,” J. Fluid Mech., 219, pp. 545–570.
Xie,  D. E., 1990, “Torsion Effect on Secondary Flow in a Helical Pipe,” Int. J. Heat Mass Transfer, 11, pp. 114–119.
Chen,  W. H., and Fan,  C. N., 1986, “Finite Element Analysis of Incompressible Viscous Flow in a Helical Pipe,” J. Computational Mech.,1, pp. 281–292.
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Germano,  M., 1989, “The Dean Equations Extended to a Helical Pipe Flow,” J. Fluid Mech., 203, pp. 289–305.
Bolinder, C. J., 1995, “Numerical Visualization of the Flow in a Helical Duct of Rectangular Cross Section,” ASME FED, presented at the Third Symposium on Experimental and Numerical Flow Visualization, New Orleans, USA, 172 , pp. 329–338.
Bolinder,  C. J., 1995, “The Effect of Torsion on the Bifurcation Structure of Laminar Flow in a Helical Square Duct,” ASME J. Fluids Eng., 117, pp. 242–248.
Bolinder,  C. J., and Sunden,  B., 1996, “Numerical Prediction of Laminar Flow and Forced Convective Heat Transfer in a Helical Square Duct With a Finite Pitch,” Int. J. Heat Mass Transfer, 139(15), pp. 3101–3115.
Chen,  W. H., and Jan,  R., 1993, “The Torsion Effect on Fully Developed Flow in Helical Square Ducts,” J. Fluid Mech., 115, pp. 292–301.
Chen,  W. H., 1993, “The Torsion Effect on Fully Developed Laminar Flow in Helical Square Ducts,” ASME J. Fluids Eng., 115, pp. 292–301.
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Figures

Grahic Jump Location
(a) Helical duct. (b) Coordinate system.
Grahic Jump Location
Effect of the grid on the axial velocity u1/Uav along the x (y=0) axes, when κ=0.25, τ=0.1, and De=214
Grahic Jump Location
Profiles of u1/Uav along the x (y=0) axes when κ=0.01, τ=0.01, and De=59, 142, 243
Grahic Jump Location
Profiles of u1/Uav along the x (y=0) axes when κ=0.01, τ=0.1, and De=79, 158
Grahic Jump Location
Profiles of u1/Uav along the y (x=0) axes when κ=0.01, τ=0.01, and De=59, 142, 243
Grahic Jump Location
Profiles of u1/Uav along the y (x=0) axes when κ=0.01, τ=0.1, and De=79, 158
Grahic Jump Location
Contours of u1/Uav when κ=0.1, τ=0.05, and De=84, 300
Grahic Jump Location
Contours of the transverse velocity, shown the effect of torsion on the secondary flow when κ=0.1, τ=0.15, and 0.2 for ps=−10,000
Grahic Jump Location
Contours of the transverse velocity, shown the effect of torsion on the secondary flow when κ=0.1, τ=0.01, 0.15, 0.2, 0.25 for ps=−300,000
Grahic Jump Location
Contours of the transverse velocity shown the effect of Dean number on the secondary flow when κ=0.1 and τ=0.05
Grahic Jump Location
Contours of the transverse velocity shown the effect of torsion on the secondary flow when (a) ε=1 with κ=0.01, τ=0.01, and De=183 and (b) ε=10 with κ=0.01, τ=0.1, and De=158

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