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Article

Simulating Pulsatile Flows Through a Pipe Orifice by an Immersed-Boundary Method

[+] Author and Article Information
Alexander Yakhot

The Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel

Leopold Grinberg

Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beersheva 84105, Israel

Nikolay Nikitin

Institute of Mechanics, Moscow State University, 1 Michurinski prospekt, 119899 Moscow, Russia

J. Fluids Eng 126(6), 911-918 (Mar 11, 2005) (8 pages) doi:10.1115/1.1845554 History: Received July 24, 2003; Revised March 26, 2004; Online March 11, 2005
Copyright © 2004 by ASME
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References

Swarztrauber,  P. N., 1974, “A Direct Method for the Discrete Solutions of Separable Elliptic Equations,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal., 11, 1136–1150.
Peskin,  C. S., 1972, “Flow Patterns Around Heart Valves: A Numerical Method,” J. Comput. Phys., 10, 252–271.
Balaras,  E., 2004, “Modeling Complex Boundaries Using an External Force Field on Fixed Cartesian Grids in Large-Eddy Simulations,” Comput. Fluids, 33, 375–404.
Mohd-Yusof, J., “Combined Immersed Boundaries/B-Splines Method for Simulations of Flows in Complex Geometries,” CTR Ann. Res. Briefs, NASA Ames/Stanford University, 1997.
Fadlun,  E. A., Verzicco,  R., Orlandi,  P., and Mohd-Yusof,  J., 2000, “Combined Immersed-Boundary Finite-Difference Methods for Three-Dimensional Complex Flow Simulations,” J. Comput. Phys., 161, 35–66.
Kim,  J., Kim,  D., and Choi,  H., 2001, “An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries,” J. Comput. Phys., 171, 132–150.
Mills,  R. D., 1968, “Numerical Solutions of Viscous Flow Through a Pipe Orifice at Low Reynolds Numbers,” J. Mech. Eng. Sci., 10, 133–140.
White, F. M., Viscous Fluid Flow, McGraw-Hill, New York, 1991.
Sexl,  T., 1930, “Über den von E. G. Richardson entdeckten annulareffekt,” Z. Phys., 61, 349.
Yakhot,  A., and Grinberg,  L., 2003, “Phase Shift Ellipses for Pulsating Flows,” Phys. Fluids, 15, 2081–2083.
Sisavath,  S., Jing,  X., Pain,  C. C., and Zimmerman,  R. W., 2002, “Creeping Flow Through an Axisymmetric Sudden Contraction or Expansion,” J. Fluids Eng., 124, 273–278.
Davis,  A. M. J., 1991, “Creeping Flow Through an Annular Stenosis in a Pipe,” Q. Appl. Math., 49, 507–520.
Wang,  C. Y., 1996, “Stokes Flow Through a Tube With Annular Fins,” Eur. J. Mech. B/Fluids, 15, 781–789.

Figures

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Schematic design of a pipe with an orifice
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L2-norm error in the no-slip boundary condition; steady flow
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Time history of the L2-norm error in the no-slip boundary condition; pulsatile flow
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L2-norm error in the no-slip boundary condition vs Δt2; pulsatile flow
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Discharge coefficient, Cd. 1—experiment, 2—present, 3— Ref. 7.
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Creeping flow. Streamlines and vorticity contours, Rem=0.01.
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Creeping flow. Dimensionless (a) pressure drop Δpc and (b) maximum velocity excess ΔUc vs d/D.
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ϕQ vs Ws,d/D=0.75, solid line—Sexl 9
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ϕQ vs Ws,d/D=0.5, solid line—Sexl 9
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Lb(t) vs Δp(t),Rem=14,d/D=0.5
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Lb(t) vs Q(t),Rem=14,d/D=0.5

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