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The Dynamics of Unsteady Bifurcation Flows

  • R. J. Liou
  • M. E. Clark
  • J. M. Robertson
  • L. C. Cheng

Abstract

Since arterial bifurcations are susceptible to disease, it is important to understand the hemodynamics associated with this common cardiovascular non-uniformity. This paper seeks to extend our understanding of bifurcation flows by using a symmetrical geometry and comparing balanced and unbalanced flows in the branches. Finite difference methods are employed in the vorticity transport-stream function formulation and are aided by a coordinate transform. The basic characteristics of unsteady flow are amply portrayed using the simple oscillatory forcing function. The particular flow division ratios used in this study were QR = 1/2 and 2/3; these values were held constant throughout the period of oscillation. The Karman number and Stokes number of the trunk flow, the basic flow similarity parameters, were taken as 1000 and 10π, respectively. Kinematic results are presented and compared in terms of stream function and vorticity contour plots. Kinetic results are summarized in the form of shear distributions over the regions of interest both in time and space.

Keywords

Unsteady Flow Pulsatile Flow Stokes Number Balance Flow Flow Division 
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.

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References

  1. 1.
    M.E. Clark, J.M. Robertson, L.C. Cheng and S.P. Girrens, “Unsteady Flow in a Stenosed Bifurcation,” Digest XII Int. Conf. Med. and Bio. Eng., Israe1,1979,Part IV, 88. 8.Google Scholar
  2. 2.
    W.E. Stebbins, “Turbulence of Blood Flow”, Quart J. Experimental Physiology, 44, 1959, 110–117.Google Scholar
  3. 3.
    A. Wesolowski, C.C. Fries and P.N. Sawyer, “Development of Turbulence in Hemic Systems”, Trans. Am. Soc. Artif. Organs, 8, 1967, 18.Google Scholar
  4. 4.
    E.D. Attinger, “Flow Patterns and Vascular Geometry”, in Pulsatile Blood Flow, E. Attinger, Ed., McGraw-Hill, 1966, 179.Google Scholar
  5. 5.
    L.J. Krovitz, “The Effect of Vessel Branching of Hemodynamic Stability”, Phys.Med.Biol., 10, 1965, 417–427.CrossRefGoogle Scholar
  6. 6.
    R. Brech and B.J. Bellhouse, “Flow in Branching Vessels”, Cardiovascular Res., 1, 1973, 593–600.CrossRefGoogle Scholar
  7. 7.
    F.F. Mark, C.B. Bargeron, O.J. Deters andM.H. Friedman, “Experimental Investigation of Steady and Pulsatile Laminar Flow in a 90° Branch”,ASME J.Appl.Mech.,44,1977,372–377.Google Scholar
  8. 8.
    O.A. El Masry, I.A. Feurstein and G.F. Round, “Experimental Evaluation of Streamline Patterns and Separated Flows in a Series of Branching Vessels with Implications for Atherosclerosis and Thrombosis”, Circulation Res. 43, 197, 608–618.Google Scholar
  9. 9.
    N. Talukder, “An Investigation on the Flow Characteristics in Arterial Branchings”, ASME paper 75-APMB-4, April 1975.Google Scholar
  10. 10.
    G.M. Rodkicwicz and C.L. Roussel, “Fluid Mechanics in a Large Arterial Bifurcation”, ASME J. Fluids Eng. 95, 1973, 108–112.CrossRefGoogle Scholar
  11. 11.
    N.S. Lynn, V.E. Fox and L.W. Ross, “Computation of Fluid Dynamical Contributions to Atherosclerosis at Arterial Bifurcations”, Biorheol. 9, 1972, 61–66.Google Scholar
  12. 12.
    H. Greenfield and W. Kolff, “The Prosthetic Heart Valve and Computer Graphics”, J. Amer. Med. Assn., 219, 1972, 69–74.CrossRefGoogle Scholar
  13. 13.
    M.H. Friedman, V. O’Brien and L.W. Ehrlich, “Wall Shear and Separation in Pulsatile Flow Through a Branch”, Proc. 26th ACEMB, 1972, 305.Google Scholar
  14. 14.
    R.T. Cheng, “On the Study of Convective Dispersion Equation”, in Finite Elements in Flow Problems, T.J. Oden et al., Ed., UAH Press 1974, 29–47.Google Scholar
  15. 15.
    R.C. Fernandez, K.J. DeWitt and M.R. Botwin, “Pulsatile Flow Through a Bifurcation with Applications to Arterial Disease”, J. Biomech. 9, 1976, 575–580.CrossRefGoogle Scholar
  16. 16.
    L.C. Cheng, M.E. Clark, J.M. Robertson and N.A. Chao, “Effects of Flow Division on Bifurcation Flow Characteristics, Proc. 1st Mid-Atlantic Conf. on Bio-Fluid Mech., VPI, Blacksburg, 1978, 151–160.Google Scholar
  17. 17.
    V.V. Gokhale, R.I. Tanner and K.B. Bischoff, “Finite Element Solution of the Navier-Stokes Equations for Two-Dimensional Steady Flow Through a Section of a Canine Aorta Model”, J. Biomech., 11, 1978, 241–249.CrossRefGoogle Scholar
  18. 18.
    T.C. Kung and S.A. Naff, “A Mathematical Model of Systolic Blood Flow Through a Bifurcation”, Proc. 8th Int. Conf. Med. and Bio. Eng., 1969, 20–11.Google Scholar
  19. 19.
    L.W. Ehrlich, M. Friedman and V. O’Brien, “Digital Simulation of Periodic Flow in a Bifurcation”, Proc. 25th ACEMB, 1972, 215.Google Scholar
  20. 20.
    M.H. Friedman, V. O’Brien and L.W. Ehrlich, “Wall Shear and Separation in Pulsatile Flow Through a Branch”, Proc. 20th ACEMB, 1973, 305.Google Scholar
  21. 21.
    V. O’Brien, L.W. Ehrlich and M.H. Friedman, “Unsteady Flow in a Branch”, J. Fluid Mech., 75, 1976, 315–336.MATHCrossRefGoogle Scholar
  22. 22.
    M.E. Clark and J.M. Robertson and L.C. Cheng. Cheng, “Interactive and Non-Uniform Unsteady Physiological Flows by Finite Difference Transforms”, Proc. Symp. Computer Methods in Eng., USC, Aug. 1977, 1, 497–506.Google Scholar
  23. 23.
    L.C. Cheng, M.E. Clark and J.M. Robertson, “Numerical Calculations of Oscillating Flow in the Vicinity of Square Wall Obstacles in Plane Conduits”, J. Biomech., 5, 1972, 467–484.CrossRefGoogle Scholar
  24. 24.
    P.J. Roache, Computational Fluid Mechanics, Hermosa Publ., 1972, Albuquerque, 143.Google Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • R. J. Liou
    • 1
  • M. E. Clark
    • 1
  • J. M. Robertson
    • 1
  • L. C. Cheng
    • 2
  1. 1.Dept.T.A.M.Univ. of IllinoisUrbanaUSA
  2. 2.Dept.M.E.Wichita State Univ.WichitaUSA

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