Advertisement

An Experimental Investigation of Pulsatile Laminar Flow Separation in Exponentially Diverging Tubes

  • Frederick J. Walburn
  • Daniel J. Schneck

Abstract

Since the turn of the century, when Ludwig Prandtl formulated the theoretical concept of the boundary layer, the phenomenon of boundary layer or flow separation has been associated mostly with trouble, i.e., energy losses, reverse flow, vortex formation, wakes, stalling, increased drag, decreased lift, wall scouring effects, etc. One of the more serious problems with which flow separation has been associated in recent years is cardiovascular disease. There is an ever increasing abundance of evidence which suggests indirectly that the pathogenesis, localization and/or aggravation of certain forms of cardiovascular disease may be related to the incidence, persistence and consequences of internal, unsteady, laminar-flow separation. This very same evidence, because of its indirect speculative nature, has also brought to light an area of fluid mechanics that has hitherto been conspicuously neglected.

Keywords

Reynolds Number Test Section Flow Separation Separation Point Flow Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Prandtl, L., “Uber Flussigkeitsbewegung bei sehr kleiner Reibung,” Verhandlung des III Intern. Math. — Kongresses, Heidelberg, zur Hydrodynamik u. Aerodynamik, Gottingen, 1927, pp. 1–8, and Edwards Bros., Ann Arbor, Mich., 1943.Google Scholar
  2. 2.
    Blasius, H. Von., “Laminare Stromung in Kanalen Wechselnder Breite,” Zeitschr. F. Math. u. Phys., 58: 225–233, 1910.MATHGoogle Scholar
  3. 3.
    Patterson, G.N., “Flow Forms in a Channel of Small Exponential Divergence,” Canad. J. Res., 11: 770–779, 1934.Google Scholar
  4. 4.
    Patterson, G.N., “Viscosity Effects in a Channel of Small Exponential Divergence,” Canad. J. Res., 12: 676–685, 1935.Google Scholar
  5. 5.
    Gutstein, W.H., and Schneck, D.J., “In Vitro Boundary Layer Studies of Blood Flow in Branched Tubes,” J. Atheroscler. Res., 7 (No. 3): 295–299, June, 1967.CrossRefGoogle Scholar
  6. 6.
    Forrester, J.H., and Young, D.F., “Flow Through a Converging-Diverging Tube and its Implications in Occlusive Vascular Disease — I. Theoretical Development,” J. Biomechanics, 3: 297–305, 1970.CrossRefGoogle Scholar
  7. 7.
    Bentz, J.C., and Evans, N.A., “Hemodynamic Flow in the Region of a Simulated Stenosis,” ASME Paper Number 75-WA/Bio-10, December, 1975.Google Scholar
  8. 8.
    Manton, M.J., “Low Reynolds Number Flow in Slowly Varying Axisymmetric Tubes,” J. Fluid Mech., 49: 451–459, 1971.MATHCrossRefGoogle Scholar
  9. 9.
    Kandarpa, K., and Davids, N., “Analysis of the Fluid Dynamic Effects on Atherogenesis at Branching Sites,” J. Biomechanics, 9: 735–741, 1976.CrossRefGoogle Scholar
  10. 10.
    Lee, J.S., and Fung, Y.C., “Flow in Locally Constricted Tubes at Low Reynolds Numbers,” J. App. Mech., 37: 9–16, 1970.MATHCrossRefGoogle Scholar
  11. 11.
    Young, D.F., and Tsai, F.Y., “Flow Characteristics in Models of Arterial Stenoses — I. Steady Flow,” J. Biomech., 6: 395–410, 1973.CrossRefGoogle Scholar
  12. 12.
    Young, D.F., “Effect of a Time-Dependent Stenosis on Flow Through a Tube,” J. Engng. Ind. Trans. ASME, 90: 248–254, 1968.CrossRefGoogle Scholar
  13. 13.
    Rott, N., “Unsteady Viscous Flow in the Vicinity of Stagnation Point,” Quart. Appl. Math., 13: 444–451, 1956.MathSciNetMATHGoogle Scholar
  14. 14.
    Sears, W.R., “Some Recent Developments in Airfoil Theory,” J. Aero. Sci., 23: 490–499, 1956.MathSciNetMATHGoogle Scholar
  15. 15.
    Moore, F.K., “On the Separation of the Unsteady Laminar Boundary Layer,” in: Gortler, J., (ed.), Boundary Layer Research, Proc. Symp. of Int. Union of Theoret. and Appl. Mech., Berlin, Springer, 1958, pp. 296–311.Google Scholar
  16. 16.
    Sears, W.R., and Telionis, D.P., “Boundary-Layer Separation in Unsteady Flow,” SIAM J. Appl. Math., 28 (no. 1): 215–235, January, 1975.MATHCrossRefGoogle Scholar
  17. 17.
    Telionis, D.P., “Calculations of Time-Dependent Boundary Layers,” in: Kinney, R.B., (ed.), Unsteady Aerodynamics, Proc. Symp. Univ. Ariz., The Arizona Board of Regents, 1975, pp. 155–190.Google Scholar
  18. 18.
    Despard, R.A. and Miller, J.A., “Separation in Oscillating Laminar Boundary-Layer Flows,” J. Fluid Mech., 47 (Part 1): 21–31, 1971.CrossRefGoogle Scholar
  19. 19.
    Schneck, D.J., and Ostrach, S., “Pulsatile Blood Flow in a Channel of Small Exponential Divergence -- I. The Linear Approximation for Low Mean Reynolds Number,” ASME Paper Number 74-WA/Bio-14, Trans. ASME, J. Fluids Eng., 97 (Ser. 1, No. 3): 353–360, Sept., 1975.CrossRefGoogle Scholar
  20. 20.
    Schneck, D.J., and Walburn, F.J., “Pulsatile Blood Flow in a Channel of Small Exponential Divergence -II. Steady Streaming Due to the Interaction of Viscous Effects With Convected Inertia,” Trans. ASME, J. Fluids Eng., 98: 707–714, December, 1976.CrossRefGoogle Scholar
  21. 21.
    Schneck, D.J., “Pulsatile Blood Flow in a Channel of Small Exponential Divergence -- III. Unsteady Flow Separation,” Trans. ASME, J. Fluids Eng., 99: 333–338, June, 1977.CrossRefGoogle Scholar
  22. 22.
    Schneck, D.J., and Ostrach, S., “Pulsatile Blood Flow in a Diverging Circular Channel,” Case Western Reserve University, Division of Fluid, Thermal and Aerospace Sciences, Technical Report Number FTAS/TR73–86, Cleveland, Ohio, January, 1973.Google Scholar
  23. 23.
    Schneck, D.J., and Ostrach, S., “Oscillating Blood Flow in a Cylindrical Channel of Small Exponential Divergence,” Proc. 3rd Ann. Meeting Biomed. Eng. Soc., p. 40, April, 1972.Google Scholar
  24. 24.
    Schneck, D.J., and Ostrach, S., “Dependence of Unsteady Flow Separation on Frequency of Oscillation,” Proc. 26th Ann. Conf. Eng. Med. Biol., 15: 309, October, 1973.Google Scholar
  25. 25.
    Tsahalis, D.T., “Unsteady Boundary Layers and Separation,” Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, August, 1974.Google Scholar
  26. 26.
    Tsahalis, D.T., and Telionis, D.P.,“ Oscillating Laminar Boundary Layers and Unsteady Separation,” AIAA Journal, 12 (#11): 1469–1476, November, 1974.MATHCrossRefGoogle Scholar
  27. 27.
    Walburn, F.J., and Schneck, D.J., “An Experimental Technique for Quantifying Unsteady Flow Separation in Diverging Circular Channels. Schneck, D.J. (ed.), Proc. First Mid-Atlantic Conf. on Bio-Fluid Mech., Blacksburg, Virginia, Virginia Polytechnic Institute and State University, 1978, pp. 161–170.Google Scholar
  28. 28.
    Schneck, D.J., and Walburn, F.J., “Unsteady Laminar-Flow Separation in Tubes -- II. The Effect of Variatiions in the Frequency and Amplitude of Flow Oscillations”, Virginia Polytechnic Institute and State University Technical Report #VPI-E-79–21, June, 1979.Google Scholar
  29. 29.
    Koromilas, C., “Experimental Investigation of Unsteady Separation,” Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, August, 1978.Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Frederick J. Walburn
    • 1
  • Daniel J. Schneck
    • 2
  1. 1.Departments of Medicine and SurgeryHenry Ford HospitalDetroitUSA
  2. 2.Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations