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Research Papers

Quantifying Turbulent Wall Shear Stress in a Stenosed Pipe Using Large Eddy Simulation

[+] Author and Article Information
Roland Gårdhagen1

Department of Management and Engineering and Center for Medical Image Science and Visualization (CMIV), Linköping University, SE-581 83 Linköping, Swedenroland.gardhagen@liu.se

Jonas Lantz

Department of Management and Engineering, Linköping University, SE-581 83 Linköping, Swedenjonas.lantz@liu.se

Fredrik Carlsson

 ANSYS Sweden, SE-416 64 Gothenburg, Swedenfredrik.carlsson@ansys.com

Matts Karlsson

Department of Management and Engineering and Center for Medical Image Science and Visualization (CMIV), Linköping University, SE-581 83 Linköping, Swedenmatts.karlsson@liu.se

1

Corresponding author.

J Biomech Eng 132(6), 061002 (Apr 16, 2010) (7 pages) doi:10.1115/1.4001075 History: Received November 30, 2009; Revised January 13, 2010; Posted January 21, 2010; Published April 16, 2010; Online April 16, 2010

Large eddy simulation was applied for flow of Re=2000 in a stenosed pipe in order to undertake a thorough investigation of the wall shear stress (WSS) in turbulent flow. A decomposition of the WSS into time averaged and fluctuating components is proposed. It was concluded that a scale resolving technique is required to completely describe the WSS pattern in a subject specific vessel model, since the poststenotic region was dominated by large axial and circumferential fluctuations. Three poststenotic regions of different WSS characteristics were identified. The recirculation zone was subject to a time averaged WSS in the retrograde direction and large fluctuations. After reattachment there was an antegrade shear and smaller fluctuations than in the recirculation zone. At the reattachment the fluctuations were the largest, but no direction dominated over time. Due to symmetry the circumferential time average was always zero. Thus, in a blood vessel, the axial fluctuations would affect endothelial cells in a stretched state, whereas the circumferential fluctuations would act in a relaxed direction.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The circular pipe used for the computations

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Figure 2

Turbulent WSS represented by the axial and circumferential components. Each spatial component is decomposed into time averages WSS¯ax and WSS¯circ for the axial and circumferential components, respectively, fluctuating components wssax′ and wsscirc′ for (a) Iin=0% and (b) Iin=10%.

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Figure 3

Turbulent WSS represented by the magnitude of the WSS vector. The magnitude is decomposed into a time average |WSS¯| and fluctuating component |wss|′, together with the corresponding WSS magnitude of a SST k−ω RANS model for (a) Iin=0% and (b) Iin=10%.

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Figure 4

The angle WSSΦ over time along a line on the poststenotic surface

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Figure 5

Instantaneous velocity vectors close to the wall in the recirculation zone for Iin=0%. The region is indicated by the rectangle on the pipe. The main flow direction is from left to right. Small vortices inside the recirculation zone are seen between Z=3 and Z=3.1, and between Z=3.18 and Z=3.28.

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Figure 6

The distribution of the angle WSSΦ over the pipe length for (a) Iin=0% and (b) Iin=10%. The thick black line represents the average value, the gray area represents the standard deviation, the dark gray area represents the minimum values, and the light gray represents the maximum values.

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Figure 7

Instantaneous WSS magnitude for the entire poststenotic surface

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