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Research Papers

Large Eddy Simulation of Transitional Flow in an Idealized Stenotic Blood Vessel: Evaluation of Subgrid Scale Models

[+] Author and Article Information
Abhro Pal, Yann Delorme, Niranjan Ghaisas, Dinesh A. Shetty, Steven H. Frankel

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907

Kameswararao Anupindi

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: kamesh.a@gmail.com

1Corresponding author.

Manuscript received January 28, 2013; final manuscript received April 4, 2014; accepted manuscript posted May 7, 2014; published online May 22, 2014. Editor: Victor H. Barocas.

J Biomech Eng 136(7), 071009 (May 22, 2014) (8 pages) Paper No: BIO-13-1048; doi: 10.1115/1.4027610 History: Received January 28, 2013; Revised April 04, 2014; Accepted May 07, 2014

In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, “Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow,” J. Fluid Mech., 582, pp. 253–280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, “Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method,” J. Comput. Phys., 227(13), pp. 6660–6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, “General Circulation Experiments With the Primitive Equations,” Mon. Weather Rev., 91(10), pp. 99–164), recently developed Vreman model (Vreman, 2004, “An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications,” Phys. Fluids, 16(10), pp. 3670–3681), and the Sigma model (Nicoud et al., 2011, “Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations,” Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) (“OpenFOAM,” http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo.

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References

Ku, D. N., 1997, “Blood Flow in Arteries,” Annu. Rev. Fluid Mech., 101(1), pp. 157–434.
Giddens, D. P., Zarins, C. K., and Glagov, S., 1993, “The Role of Fluid Mechanics in the Localization and Detection of Atherosclerosis,” ASME J. Biomech. Eng., 115(4B), pp. 588–594. [CrossRef]
Ahmed, S., and Giddens, D., 1983, “Velocity Measurements in Steady Flow Through Axisymmetric Stenoses at Moderate Reynolds Number,” J. Biomech., 16, pp. 505–516. [CrossRef]
Ahmed, S., and Giddens, D., 1983, “Flow Disturbance Measurements Through a Constricted Tube at Moderate Reynolds Numbers,” J. Biomech., 16, pp. 955–963. [CrossRef]
Ahmed, S., and Giddens, D., 1984, “Pulsatile Poststenotic Studies With Laser Doppler Anemometry,” J. Biomech., 17, pp. 695–705. [CrossRef]
Ojha, M., Cobbold, C., Johnston, K. H., and Hummel, R. L., 1989, “Pulsatile Flow Through Constricted Tubes: An Experimental Investigation Using Photochromic Tracer Methods,” J. Fluid Mech., 203, pp. 173–197. [CrossRef]
Peterson, S. D., and Plesniak, M. W., 2008, “The Influence of Inlet Velocity Profile and Secondary Flow on Pulsatile Flow in a Model Artery With Stenosis,” J. Fluid Mech., 616, pp. 263–301. [CrossRef]
Sherwin, S. J., and Blackburn, H. M., 2005, “Three-Dimensional Instabilities and Transition of Steady and Pulsatile Axisymmetric Stenotic Flows,” J. Fluid Mech., 533, pp. 297–327. [CrossRef]
Varghese, S. S., Frankel, S. H., and Fischer, P. F., 2007, “Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow,” J. Fluid Mech., 582, pp. 253–280. [CrossRef]
Varghese, S. S., Frankel, S. H., and Fischer, P. F., 2007, “Direct Numerical Simulation of Stenotic Flows. Part 2. Pulsatile Flow,” J. Fluid Mech., 582, pp. 281–318. [CrossRef]
Stroud, J. S., Berger, S. A., and Saloner, D., 2000, “Influence of Stenosis Morphology on Flow Through Severely Stenotic Vessels: Implications for Plaque Rupture,” J. Biomech., 33(4), pp. 443–455. [CrossRef]
Varghese, S. S., Frankel, S. H., and Fischer, P. F., 2008, “Modeling Transition to Turbulence in Eccentric Stenotic Flows,” ASME J. Biomech. Eng., 130(1), p. 014503. [CrossRef]
Tan, F. P. P., Wood, N. B., Tabor, G., and Xu, X. Y., 2011, “Comparison of LES of Steady Transitional Flow in an Idealized Stenosed Axisymmetric Artery Model With a RANS Transitional Model,” ASME J. Biomech. Eng., 133(5), p. 051001. [CrossRef]
Mittal, R., Simmons, S. P., and Udaykumar, H. S., 2001, “Application of Large-Eddy Simulation to the Study of Pulsatile Flow in a Modeled Arterial Stenosis,” ASME J. Biomech. Eng., 123(4), pp. 325–332. [CrossRef]
Mittal, R., Simmons, S. P., and Najjar, F., 2003, “Numerical Study of Pulsatile Flow in a Constricted Channel,” J. Fluid Mech., 485, pp. 337–378. [CrossRef]
Paul, M. C., Mamun Molla, M., and Roditi, G., 2009, “Large-Eddy Simulation of Pulsatile Blood Flow,” Med. Eng. Phys., 31(1), pp. 153–159. [CrossRef]
Smagorinsky, J., 1963, “General Circulation Experiments With the Primitive Equations,” Mon. Weather Rev., 91(10), pp. 99–164. [CrossRef]
Vreman, A. W., 2004, “An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications,” Phys. Fluids, 16(10), pp. 3670–3681. [CrossRef]
Nicoud, F., Toda, H. B., Cabrit, O., Bose, S., and Lee, J., 2011, “Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations,” Phys. Fluids, 23(8), p. 085106. [CrossRef]
Shetty, D. A., Fisher, T. C., Chunekar, A. R., and Frankel, S. H., 2010, “High-Order Incompressible Large-Eddy Simulation of Fully Inhomogeneous Turbulent Flows,” J. Comput. Phys., 229(23), pp. 8802–8822. [CrossRef]
Mark, A., and Vanwachem, B., 2008, “Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method,” J. Comput. Phys., 227(13), pp. 6660–6680. [CrossRef]
Ghaisas, N., Shetty, D., and Frankel, S., 2013, “Large Eddy Simulation of Thermal Driven Cavity: Evaluation of Sub-Grid Scale Models and Flow Physics,” Int. J. Heat Mass Transfer, 56(1), pp. 606–624. [CrossRef]
Jiang, G.-S., and Shu, C.-W., 1996, “Efficient Implementation of Weighted ENO Schemes,” J. Comput. Phys., 228(126), pp. 202–228. [CrossRef]
Gustafsson, B., 2008, High Order Difference Methods for Time Dependent PDE ( Springer Series in Computational Mathematics), Springer, Berlin.
Shetty, D. A., Shen, J., Chandy, A. J., and Frankel, S. H., 2011, “A Pressure-Correction Scheme for Rotational Navier–Stokes Equations and Its Application to Rotating Turbulent Flows 1 Introduction 2 Mathematical formulation,” J. Comput. Phys., 9(3), pp. 740–755.
Delorme, Y., Anupindi, K., Kerlo, A., Shetty, D., Rodefeld, M., Chen, J., and Frankel, S., 2013, “Large Eddy Simulation of Powered Fontan Hemodynamics,” J. Biomech., 46(2), pp. 408–422. [CrossRef]
Delorme, Y., Anupindi, K., and Frankel, S. H., 2013, “Large Eddy Simulation of FDA's Idealized Medical Device,” Cardiovasc. Eng. Tech., 4(4), pp. 392–407. [CrossRef]
Jeong, J., and Hussain, F., 1995, “On the Identification of a Vortex,” J. Fluid Mech., 285, pp. 69–94. [CrossRef]
Leriche, E., and Gavrilakis, S., 2000, “Direct Numerical Simulation of the Flow in a Lid-Driven Cubical Cavity,” Phys. Fluids, 12(6), pp.1363–1376. [CrossRef]
Meyers, J., Geurts, B. J., and Baelmans, M., 2005, “Optimality of the Dynamic Procedure for Large-Eddy Simulations,” Phys. Fluids, 17(4), p. 045108. [CrossRef]

Figures

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Fig. 1

Grid 3 used for WenoHemo simulations

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Fig. 2

Comparison of mean axial velocity profiles for various grid sizes considered. Dotted line represents grid 1, Solid line represents grid 2, dashed-dotted line represents grid 3. DNS data is represented by solid dots. The scale represents 5 velocity units (u/Um) for each axial unit (x/D).

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Fig. 3

(a) Normalized mean axial velocity profiles (u¯/Um) at indicated locations along the axial direction. Solid lines correspond to WenoHemo simulation, solid dots indicate DNS [9]. Scale represents 1 axial unit (x/D) equals 5 velocity units (u¯/Um). (b) Contours of normalized vorticity magnitude (|ω→|D/Um) on XY-plane at Z = 0.

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Fig. 4

Contours of normalized vorticity magnitude (|ω→|D/Um) on the XZ-plane, at Y = 0 for DNS and LES simulations as indicated

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Fig. 5

Normalized mean axial velocity (u¯/Um) profiles at indicated locations. Lines show present simulations using WenoHemo and dots indicate the DNS result.

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Fig. 13

TKE profiles at the indicated locations for the SGS models considered. Lines indicate the present simulation result obtained using OpenFOAM and dots indicate the DNS result.

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Fig. 12

Normalized mean axial velocity (u¯/Um) profiles at the indicated locations for the SGS models considered. Lines denote result from present simulation using OpenFOAM and dots indicate the DNS result.

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Fig. 11

Mesh of approximately 1.0 × 106 cells used in OpenFOAM simulations

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Fig. 10

Turbulent energy spectra E11 for the indicated SGS models and S represents nondimensional frequency

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Fig. 9

Instantaneous coherent structures, identified by the λ2 criterion defined by Ref. [30], colored by instantaneous normalized vorticity magnitude |ω→|D/Um. The inset shows a close-up view of the structures.

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Fig. 8

Contour plots of time averaged SGS activity 〈Asgs〉 (top), and vorticity magnitude |ω→|D/Um (bottom) predicted by WenoHemo for eccentric model

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Fig. 7

Turbulent kinetic energy profiles at indicated axial locations. Solid line indicates LES using WenoHemo, solid dots indicate DNS [9].

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Fig. 6

RMS of velocity fluctuations at indicated axial locations. Solid lines indicate LES with Smagorinsky Model using WenoHemo, solid dots indicate DNS [9].

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