Computation of physiological bifurcation flows using a patched grid

Abstract A finite volume method in a boundary-fitted coordinate system together with a zonal grid method is employed to compute the flow field of a real-shape two-dimensional aortic bifurcation. The steady terms in the governing equations are treated by a fully explicit scheme. The zonal gridding procedure is discussed in detail. The numerical method is first tested in a laminar backward facing step flow to demonstrate the features of the method. The effect of the interface treatment on the flow fields can be significant. A 90° T-junction is then computed. The results are in good agreement with the available experimental data. The method is then applied to simulate the flows of an atherosclerotic human aorta. Both the steady and pulsatile flows are considered. It is shown that the mean shear stresses in recirculation regions of a pulsatile flow cannot be adequately described by a corresponding steady flow with a mean Reynolds number. In pulsatile flows, a sinusoidal input pulse and a realistic input pulse are both used in the computations. It is found that the “averaged” flow behavior is similar in both cases. However, the details of the flow field are significantly different. During pulsatile flow, permanent eddies are not present. That is, for a certain period in a cycle, the entire wall is free from eddies. On the other hand, in another period, the overall wall is almost completely in the reversing flow near the walls. These phenomena have been observed by other authors experimentally. Distributions of wall shear stresses and locations of recirculation zones in a realistic flow are shown and discussed briefly.

[1]  V. Turitto,et al.  Platelet interaction with subendothelium in flowing rabbit blood: effect of blood shear rate. , 1979, Microvascular research.

[2]  D. L. Fry Acute Vascular Endothelial Changes Associated with Increased Blood Velocity Gradients , 1968, Circulation research.

[3]  Michael A. Leschziner,et al.  Computation of three-dimensional turbulent flow in non-orthogonal junctions by abranch-coupling method , 1989 .

[4]  J. Chiu,et al.  Covariant velocity-based calculation procedure with nonstaggered grids for computation of pulsatile flows , 1992 .

[5]  R. Lutz,et al.  Comparison of steady and pulsatile flow in a double branching arterial model. , 1983, Journal of biomechanics.

[6]  R M Nerem,et al.  Vascular endothelial morphology as an indicator of the pattern of blood flow. , 1981, Journal of biomechanical engineering.

[7]  L. Fuchs Calculation of flows in complex geometries using overlapping grids , 1990 .

[8]  H. Nasr-El-Din,et al.  Steady laminar flow in a 90 degree planar branch , 1989 .

[9]  Theo G. Keith,et al.  Numerical simulation of axisymmetric turbulent flow in combustors and diffusers , 1989 .

[10]  Michael M. Resch,et al.  Numerical flow studies in human carotid artery bifurcations: basic discussion of the geometric factor in atherogenesis. , 1990, Journal of biomedical engineering.

[11]  P. Stein,et al.  Velocity profiles in symmetrically branched tubes simulating the aortic bifurcation. , 1981, Journal of biomechanics.

[12]  D. L. Fry Certain Histological and Chemical Responses of the Vascular Interface to Acutely Induced Mechanical Stress in the Aorta of the Dog , 1969, Circulation research.

[13]  C. Caro Transport of 14C-4-cholesterol between perfusing serum and dog common carotid artery: a shear dependent process. , 1974, Cardiovascular research.

[14]  Computational aspects of aortic bifurcation flows , 1985 .

[15]  Robert W. Walters,et al.  A Patched-Grid Algorithm for Complex Configurations Directed Towards the F/A-18 Aircraft , 1989 .

[16]  H. Goldsmith,et al.  Flow Patterns in Vessels of Simple and Complex Geometries a , 1987, Annals of the New York Academy of Sciences.

[17]  M. Rai A conservative treatment of zonal boundaries for Euler equation calculations , 1986 .

[18]  D. M. Sloan,et al.  Numerical solution for two-dimensional flow in a branching channel using boundary-fitted coordinates , 1987 .

[19]  S. Patankar Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[20]  Edward F. Leonard,et al.  Effects of Shear Rate on the Diffusion and Adhesion of Blood Platelets to a Foreign Surface , 1972 .

[21]  M. Perić,et al.  FINITE VOLUME METHOD FOR PREDICTION OF FLUID FLOW IN ARBITRARILY SHAPED DOMAINS WITH MOVING BOUNDARIES , 1990 .

[22]  J. Frangos,et al.  The Effect of Fluid Mechanical Stress on Cellular Arachidonic Acid Metabolism a , 1987, Annals of the New York Academy of Sciences.

[23]  B. Armaly,et al.  Experimental and theoretical investigation of backward-facing step flow , 1983, Journal of Fluid Mechanics.

[24]  L. Fuchs Numerical computation of viscous incompressible flows in systems of channels , 1987 .

[25]  J. Khodadadi,et al.  LAMINAR FORCED CONVECTIVE HEAT TRANSFER IN A TWO-DIMENSIONAL 90° BIFURCATION , 1986 .

[26]  M. Rai,et al.  Three-dimensional, conservative, Euler computations using patched grid systems and explicit methods , 1986 .

[27]  Hemodynamics and the Arterial Wall: An Introduction , 1981 .

[28]  S. Majumdar Role of underrelaxation in momentum interpolation for calculation of flow with nonstaggered grids , 1988 .

[29]  M. M. Rai,et al.  Applications of a conservative zonal scheme to transient and geometrically complex problems , 1986 .

[30]  H. Goldsmith,et al.  Particle flow behavior in models of branching vessels. II. Effects of branching angle and diameter ratio on flow patterns. , 1985, Biorheology.

[31]  H. Goldsmith,et al.  Particle flow behaviour in models of branching vessels: I. Vortices in 90 degrees T-junctions. , 1979, Biorheology.

[32]  P. Stein,et al.  Flow visualization in a mold of an atherosclerotic human abdominal aorta. , 1981, Journal of biomechanical engineering.

[33]  M. H. Friedman A biologically plausible model of thickening of arterial intima under shear. , 1989, Arteriosclerosis.

[34]  COMPUTATION OF NONREACTING FLOWS OF A TWO-RING FLAME STABILIZER USING A ZONAL GRID METHOD , 1991 .

[35]  G. Hutchins,et al.  Shear-dependent thickening of the human arterial intima. , 1986, Atherosclerosis.

[36]  R. Schroter,et al.  Atheroma and arterial wall shear - Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis , 1971, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[37]  C. Rhie,et al.  Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , 1983 .

[38]  D. Liepsch,et al.  Measurement and calculations of laminar flow in a ninety degree bifurcation. , 1982, Journal of biomechanics.