Accurate Evaluation of the Loss Coefficient and the Entrance Length of the Inlet Region of a Channel

[+] Author and Article Information
R. M. Sadri, J. M. Floryan

The University of Western Ontario, Department of Mechanical and Materials Engineering, London, Ontario N6A 5B9, Canada

J. Fluids Eng 124(3), 685-693 (Aug 19, 2002) (9 pages) doi:10.1115/1.1493813 History: Received March 31, 2000; Revised January 14, 2002; Online August 19, 2002
Copyright © 2002 by ASME
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Shah, R. K., and London, A. L., 1978, Advances in Heat Transfer, Laminar Flow Forced Convection in Ducts, Academic Press, New York.
Sparrow,  E. M., and Anderson,  C. E., 1977, “Effect Of Upstream Flow Processes On Hydrodynamic Development In A Duct,” ASME J. Fluids Eng., 99, pp. 556–560.
Sadri, R. M., 1997, “Channel Entrance Flow,” Ph.D. thesis, The University of Western Ontario, London, Ontario, Canada.
Kays, W. M., and London, A. L., 1984, Compact Heat Exchangers, McGraw-Hill, New York.
Gravesen,  P., Branebjerg,  J., and Jensen,  O. S., 1993, “Microfluidic-a Review,” J. Micromech. Microeng., 3, pp. 168–182.
Zou,  Q., Liu,  Z., and Goldberg,  I. S., 1993, “On Non-Axisymmetric Entry Flow At Very Low Reynolds Numbers,” Math. Biosci., 113, pp. 245–260.
Bodoia,  J. R., and Osterle,  J. F., 1961, “Finite Difference Analysis Of Plane Poiseuille And Couette Flow Developments,” Appl. Sci. Res., 10, pp. 265–276.
Schmidt,  F. W., and Zeldin,  B., 1969, “Laminar Flows In Inlet Sections Of Tubes And Ducts,” American Institute of Chemical Engineers Journal, 15, pp. 612–614.
Han,  L. S., 1960, “Hydrodynamic Entrance Lengths For Incompressible Laminar Flow In Rectangular Ducts,” ASME J. Appl. Mech., 27, pp. 403–409.
Sparrow,  E. M., Liu,  S. H., and Lundgren,  T. S., 1964, “Flow Development In The Hydrodynamic Entrance Region Of Tubes And Ducts,” Phys. Fluids, 7, pp. 338–347.
Schlichting,  H., 1934, “Laminare Kanaleinlaufstömung,” Zeitschrift für angewandte Mathematik und Mechanik, 14, pp. 368–373.
Schlichting, H., 1973, Boundary Layer Theory, McGraw-Hill, New York.
Collins,  M., and Schowalter,  W. R., 1962, “Laminar Flow In The Inlet Region Of A Straight Channel,” Phys. Fluids, 5, pp. 222–228.
Chen,  R. Y., 1973, “Flow In The Entrance Region At Low Reynolds Numbers,” ASME J. Fluids Eng., 95, pp. 153–158.
Nguyen,  T. V., and Maclaine-Cross,  I. L., 1988, “Incremental Pressure Drop Number In Parallel-Plate Heat Exchangers,” ASME J. Fluids Eng., 110, pp. 93–96.
Lundgren,  T. S., Sparrow,  E. M., and Starr,  J. B., 1964, “Pressure Drop Due To The Entrance Region In Ducts Of Arbitrary Cross Section,” ASME J. Basic Eng., 88, pp. 620–626.
Beavers,  G. S., Sparrow,  E. M., and Magnusun,  R. A., 1970, “Experiments On Hydrodynamically Developing Flow In Rectangular Ducts Of Arbitrary Aspect Ratio,” Int. J. Heat Mass Transf., 13, pp. 689–702.
Morihara,  H. K., and Cheng,  R. T., 1973, “Numerical Solution Of The Viscous Flow In The Entrance Region Of Parallel Plates,” J. Comput. Phys., 11, pp. 550–572.
Narang,  B. S., and Krishnamoorthy,  G., 1976, “Laminar Flow In The Entrance Region Of Parallel Plates,” ASME J. Appl. Mech., 43, pp. 186–188.
Jeffery,  G., 1915, “The Two-Dimensional Steady Motion Of A Viscous Fluid,” Philos. Mag., 6, pp. 455–465.
Hamel,  G., 1916, “Spiralfömrige Bewegungen zäher Flüssigheiten,” Jahresbericht der Deutschen Math. Vereinigung,, 3, pp. 34–60.
Atkinson,  B., Brocklebank,  M. P., Card,  C. C. H., and Smith,  J. M., 1969, “Low Reynolds Number Developing Flows,” American Institute of Chemical Engineers Journal,, 15, pp. 548–553.
Williamson,  J. W., 1969, “Decay Of Symmetrical Laminar Distorted Profiles Between Flat Parallel Plates,” ASME J. Basic Eng., 91, pp. 558–560.
Rokicki,  J., and Floryan,  J. M., 1999, “Higher-Order Unstructured Domain Decomposition Method For The Navier-Stokes Equations,” Comput. Fluids, 28, pp. 87–120.
Floryan,  J. M., and Czechowski,  L., 1995, “On The Numerical Treatment Of Corner Singularity In The Vorticity Field,” J. Comput. Phys., 118, pp. 168–182.
Moffat,  H. K., 1964, “Viscous And Resistive Eddies Near A Sharp Corner,” J. Fluid Mech., 18, pp. 1–18.
Fox, R. W., McDonald, A. T., 1989, Introduction to Fluid Mechanics, Wiley, New York.
McComas,  S. T., 1967, “Hydrodynamic Entrance Length For Ducts Of Arbitrary Cross Section,” ASME J. Basic Eng., 89, pp. 847–850.
Emery,  A. F., and Chen,  C. S., 1968, “An Experimental Investigation Of Possible Methods To Reduce Laminar Entry Length,” ASME J. Basic Eng., 90, pp. 134–137.
Brandt,  A., and Gillis,  J., 1966, “Magnetohydrodynamic Flow In The Inlet Region Of A Straight Channel,” Phys. Fluids, 9, pp. 690–699.
Hwang,  C. L., and Fan,  L. T., 1978, “A Finite Difference Analysis Of Laminar Magneto-Hydrodynamic Flow In The Entrance Region Of A Flat Rectangular Duct,” Appl. Sci. Res., Sect., 13, pp. 329–343.


Grahic Jump Location
Flow pattern in a sharp-edged entrance
Grahic Jump Location
Distribution of vorticity ζ along the line y=−1 for Re=1000 obtained with different grid sizes h
Grahic Jump Location
Pressure distribution along the channel centerline, 0.01≤Re≤2000
Grahic Jump Location
Pressure drop along the centerline of the channel for Re=2200. S denotes the pressure drop due to the change of the kinetic energy, M stands for the pressure drop associated with the Poiseuille flow, and N denotes the additional pressure drop occurring due to the entrance effects.
Grahic Jump Location
Distribution of the loss coefficient along the channel
Grahic Jump Location
Variations of the loss coefficient k(∞), the incremental pressure drop K(∞) and the additional pressure loss coefficient Ki as a function of Re. Dashed lines denote correlations given in Section 4.2.1.
Grahic Jump Location
Variations of the eigenvalues describing decay of the perturbations of Jeffery-Hamel flow. Figure 6(a)-0≤Re≤10, Fig. 6(b)-0≤Re≤∞.
Grahic Jump Location
Variations of the eigenvalues describing decay of the perturbations in the Poiseuille flow as a function of Re. Figure 7(a)-imaginary part βi; Fig. 7(b)-real part βr.
Grahic Jump Location
Variations of the length of the channel entrance zone as a function of Re. Letters A,[[ellipsis]], G correspond to the different criteria used to determine the length of the entrance zone, discussed in Section 4.3.2. Dashed lines correspond to the correlations developed in the present study. The numerical method used does not provide sufficient accuracy for application of the criteria F and G when Re<80 and thus the corresponding curves are omitted from the insert plot.



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