Breaking axi-symmetry in stenotic flow lowers the critical transition Reynolds number

Abstract

Flow through a sinuous stenosis with varying degrees of non-axisymmetric shape variations and at Reynolds number ranging from 250 to 750 is investigated using direct numerical simulation (DNS) and global linear stability analysis. At low Reynolds numbers (Re < 390), the flow is always steady and symmetric for an axisymmetric geometry. Two steady state solutions are obtained when the Reynolds number is increased: a symmetric steady state and an eccentric, non-axisymmetric steady state. Either one can be obtained in the DNS depending on the initial condition. A linear global stability analysis around the symmetric and non-axisymmetric steady state reveals that both flows are linearly stable for the same Reynolds number, showing that the first bifurcation from symmetry to antisymmetry is subcritical. When the Reynolds number is increased further, the symmetric state becomes linearly unstable to an eigenmode, which drives the flow towards the non-axisymmetric state. The symmetric state remains steady up to Re = 713, while the non-axisymmetric state displays regimes of periodic oscillations for Re ≥ 417 and intermittency for Re 525. Further, an offset of the stenosis throat is introduced through the eccentricity parameter E. When eccentricity is increased from zero to only 0.3% of the pipe diameter, the bifurcation Reynolds number decreases by more than 50%, showing that it is highly sensitive to non-axisymmetric shape variations. Based on the resulting bifurcation map and its dependency on E, we resolve the discrepancies between previous experimental and computational studies. We also present excellent agreement between our numerical results and previous experimental results. C 2015 AIP Publishing LLC.

Direct numerical simulation of transitional hydrodynamics of the cerebrospinal fluid in Chiari I malformation: The role of cranio‐vertebral junction

“…The fluctuations were markedly less in Patient1 because of less severe obstruction. These observations are similar to those of studies of transition to turbulence in stenotic flows, where the degree of stenosis has been shown to govern the onset and sustainment of transitional flow …”

“…These observations are similar to those of studies of transition to turbulence in stenotic flows, where the degree of stenosis has been shown to govern the onset and sustainment of transitional flow. 50 Studies of transition in pipe flows have suggested that the mechanisms responsible for the generation of turbulence in oscillatory pipe flows are similar to those for steady flows. 49 Moreover, it has been shown that the acceleration of flow has a stabilizing effect on the flow field while the deceleration phase of the flow intensifies turbulence.…”

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“…Several attempts have been made to investigate flow in diverging-converging channels at the conventional and microscales, for which flow physics and different flow scenarios have been studied [18][19][20][21][22][23][24][25][26][27]. It is observed that the flow through mild converging-diverging tube is laminar for Reynolds number, Re < 900 [18], while flow through converging-diverging tube with relatively large convergence/divergence angle shows flow instability and turbulence when Re > 400 [28].…”

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“…From the symmetric difference to the binarized image d S (x, y), a more accurate outline of the basketball action can be detected, but only some information is included. Since the gray level of the basketball action target is similar to the background gray level [16][17][18], the foreground image d b (x, y) will result in a complete foreground image F k (x, y) at each pixel location:…”