# zbMATH — the first resource for mathematics

Investigation of laminar flow in a helical pipe filled with a fluid-saturated porous medium. (English) Zbl 1060.76114
Summary: Laminar flow in a helical pipe filled with a fluid saturated porous medium is investigated numerically. The analysis is based on a full momentum equation for the flow in porous media that accounts for Brinkman and Forchheimer extensions of Darcy law as well as for the flow inertia. Accounting for the flow inertia is shown to be important for predicting secondary flow in a helical pipe. The effects of Darcy number, of Forchheimer coefficient as well as of the curvature and torsion of the helical pipe on axial flow velocity and secondary flow are investigated numerically.

##### MSC:
 76S05 Flows in porous media; filtration; seepage 76M12 Finite volume methods applied to problems in fluid mechanics
##### Keywords:
orthogonal helical coordinates; secondary flow
Full Text:
##### References:
 [1] Dean, W.R., Note on the motion of fluid in a curved pipe, Philos. magazine, 4, 208-223, (1927) · JFM 54.0909.05 [2] Germano, M., On the effect of torsion on a helical pipe flow, J. fluid mech., 125, 1-8, (1982) · Zbl 0533.76029 [3] Germano, M., The Dean equations extended to a helical pipe flow, J. fluid mech., 203, 289-305, (1989) · Zbl 0675.76040 [4] Liu, S.; Masliyah, J.H., Axially invariant laminar flow in helical pipes with a finite pitch, J. fluid mech., 251, 315-353, (1993) · Zbl 0775.76036 [5] Liu, S.; Masliyah, J.H., Developing convective heat transfer in helical pipes with finite pitch, Int. J. heat fluid flow, 15, 66-74, (1994) [6] Yang, G.; Dong, Z.F.; Ebadian, M.A., Laminar forced convection in a helicoidal pipe with finite pitch, Int. J. heat mass transfer, 38, 853-862, (1995) · Zbl 0925.76614 [7] Hüttl, T.J., Navier Stokes solutions of laminar flows based on orthogonal helical coordinates, Numer. methods in laminar and turbulent flow, 10, 191-202, (1997) [8] Hüttl, T.J., Influence of curvature and torsion on turbulent flow in curved and helically coiled pipes, Int. J. heat fluid flow, 21, 345-353, (2000) [9] Pharoah, J.G.; Litster, S.; Djilali, N., Mass transfer enhancement in membrane separation – rotating vs. helical modules, (), 28-30 [10] Zheng, B.; Lin, C.X.; Ebadian, M.A., Combined laminar forced convection and thermal radiation in a helical pipe, Int. J. heat mass transfer, 43, 1067-1078, (2000) · Zbl 0971.76082 [11] Lin, C.X.; Zhang, P.; Ebadian, M.A., Laminar forced convection in the entrance region of helical pipes, Int. J. heat mass transfer, 40, 3293-3304, (1997) · Zbl 0936.76533 [12] Sandeep, K.P.; Zuritz, C.A.; Puri, V.M., Modeling non-Newtonian two-phase flow in conventional and helical-holding tubes, Int. J. food sci. technol., 35, 511-522, (2000) [13] L. Cheng, A.V. Kuznetsov, Investigation of a laminar flow of a non-Newtonian fluid in a helical pipe. Int. J. Appl. Mech. Engrg., in press · Zbl 1195.76013 [14] Nield, D.A.; Kuznetsov, A.V., Forced convection in a helical pipe filled with a saturated medium, Int. J. heat mass transfer, 47, 5175-5180, (2004) · Zbl 1098.76612 [15] Nield, D.A.; Bejan, A., Convection in porous media, (1999), Springer New York · Zbl 0924.76001 [16] Patankar, S.V., Numerical heat transfer and fluid flow, (1980), Hemisphere New York · Zbl 0521.76003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.