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Direct numerical simulation of stenotic flows. Part 2. Pulsatile flow


Direct numerical simulations (DNS) of stenotic flows under conditions of steady inlet flow were discussed in Part 1 of this study. DNS of pulsatile flow through the 75% stenosed tube (by area) employed for the computations in Part 1 is examined here. Analogous to the steady flow results, DNS predicts a laminar post-stenotic flow field in the case of pulsatile flow through the axisymmetric stenosis model, in contrast to previous experiments, in which intermittent disturbed flow regions and turbulent breakdown were observed in the downstream region. The introduction of a stenosis eccentricity, that was 5% of the main vessel diameter at the throat, resulted in periodic, localized transition to turbulence. Analysis in this study indicates that the early and mid-acceleration phases of the time period cycle were relatively stable, with no turbulent activity in the post-stenotic region. However, towards the end of acceleration, the starting vortex, formed earlier as the fluid accelerated through the stenosis at the beginning of acceleration, started to break up into elongated streamwise structures. These streamwise vortices broke down at peak flow, forming a turbulent spot in the post-stenotic region. In the early part of deceleration there was intense turbulent activity within this spot. Past the mid-deceleration phase, through to minimum flow, the inlet flow lost its momentum and the flow field began to relaminarize. The start of acceleration in the following cycle saw a recurrence of the entire process of a starting structure undergoing turbulent breakdown and subsequent relaminarization of the post-stenotic flow field. Peak wall shear stress (WSS) levels occurred at the stenosis throat, with the rest of the vessel experiencing much lower levels. Turbulent breakdown at peak flow resulted in a sharp amplification of instantaneous WSS magnitudes across the region corresponding to the turbulent spot, accompanied by large axial and circumferential fluctuations, even while ensemble-averaged axial shear stresses remained mostly low and negative. WSS levels dropped rapidly after the mid-deceleration phase, when the relaminarization process took over, and were almost identical to laminar, axisymmetric shear levels through most of the acceleration phase.

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Ahmed, S. A. & Giddens, D. P. 1983 Velocity measurements in steady flow through axisymmetric stenoses at moderate Reynolds number. J. Biomech. 16, 505516.
Ahmed, S. A. & Giddens, D. P. 1984 Pulsatile poststenotic flow studies with laser Doppler anemometry. J. Biomech. 17, 695705.
Cassanova, R. A. & Giddens, D. P. 1978 Disorder distal to modeled stenoses in steady and pulsatile flow. J. Biomech. 11, 441453.
Eliahou, S., Tumin, A. & Wygnanski, I. 1998 Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. J. Fluid Mech. 361, 333349.
Fischer, P. F., Kruse, G. & Loth, F. 2002 Spectral element methods for transitional flows in complex geometries. J. Sci. Comput. 17, 8198.
Han, G., Tumin, A. & Wygnanski, I. 2000 Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. Part 2. Late stage of transition. J. Fluid Mech. 419, 127.
Hinze, J. O. 1975 Turbulence. Mcgraw-Hill.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Khalifa, A. M. A. & Giddens, D. P. 1981 Characterization and evolution of post-stenotic flow disturbances. J. Biomech. 14, 279296.
Kim, B. M. & Corcoran, W. H. 1974 Experimental measurements of turbulence spectra distal to stenoses. J. Biomech. 7, 335342.
Ku, D. N. 1997 Blood flow in arteries. Annu. Rev. Fluid Mech. 29, 399434.
Lieber, B. B. & Giddens, D. P. 1988 Apparent stresses in disturbed pulsatile flows. J. Biomech. 21, 287298.
Lieber, B. B. & Giddens, D. P. 1990 Post-stenotic core flow behavior in pulsatile flow and its effects on wall shear stress. J. Biomech. 23, 597605.
Lu, P. C., Gross, D. R. & Hwang, N. H. C. 1980 Intravascular pressure and velocity fluctuations in pulmonic arterial stenosis. J. Biomech. 13, 291300.
Mittal, R., Simmons, S. P. & Najjar, F. 2003 Numerical study of pulsatile flow in a constricted channel. J. Fluid Mech. 485, 337378.
Ojha, M., Cobbold, C., Johnston, K. & Hummel, R. 1989 Pulsatile flow through constricted tubes: An experimental investigation using photochromic tracer methods. J. Fluid Mech. 13, 173197.
Scotti, A. & Piomelli, U. 2001 Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13, 13671384.
Shan, H., Ma, B., Zhang, Z. & Nieuwstadt, F. T. M. 1999 Direct numerical simulation of a puff and a slug in transitional cylindrical pipe flow. J. Fluid Mech. 387, 3960.
Sherwin, S. J. & Blackburn, H. M. 2005 Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows. J. Fluid Mech. 533, 297327.
Stettler, J. C. & Hussain, A. K. M. F. 1986 On transition of the pulsatile pipe flow. J. Fluid Mech. 170, 169197.
Stroud, J., Berger, S. & Saloner, D. 2000 Influence of stenosis morphology on flow through severely stenotic vessels: Implications for plaque rupture. J. Biomech. 33, 443455.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Varghese, S. S., Frankel, S. H. & Fischer, P. F. 2007 Direct numerical simulation of stenotic flows. Part 1. Steady flow. J. Fluid Mech. 582, 253280.
Waleffe, F. 1997 On self-sustaining process in shear flows. Phys. Fluids 9, 883900.
Welch, P. D. 1967 The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short modified periodograms. IEEE Trans. Audio Electroacoust. AU 15, 7073.
Wilcox, D. 1993 Turbulence Modeling for CFD. La Cañada, California, CA: DCW Industries.
Womersley, J. R. 1955 Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553563.
Wootton, D. M. & Ku, D. N. 1999 Fluid mechanics of vascular systems, diseases, and thrombosis. Annu. Rev. Biomed. Engng 1, 299329.
Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59, 281335.
Wygnanski, I. J., Sokolov, M. & Friedman, D. 1975 On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283304.
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Journal of Fluid Mechanics
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