# Transition to turbulence in an oscillatory flow through stenosis

## Abstract

Onset of flow transition in a sinusoidally oscillating flow through a rigid, constant area circular pipe with a smooth sinusoidal obstruction in the center of the pipe is studied by performing direct numerical simulations, with resolutions close to the Kolmogorov microscales. The studied pipe is stenosed in the center with a 75% reduction in area in two distinct configurations—one that is symmetric to the axis of the parent pipe and the other that is offset by 0.05 diameters to introduce an eccentricity, which disturbs the flow thereby triggering the onset of flow transition. The critical Reynolds number at which the flow transitions to turbulence for a zero-mean oscillatory flow through a stenosis is shown to be nearly tripled in comparison with studies of pulsating unidirectional flow through the same stenosis. The onset of transition is further explored with three different flow pulsation frequencies resulting in a total of 90 simulations conducted on a supercomputer. It is found that the critical Reynolds number at which the oscillatory flow transitions is not affected by the pulsation frequencies. The locations of flow breakdown and re-stabilization post-stenosis are, however, respectively shifted closer to the stenosis throat with increasing pulsation frequencies. The results show that oscillatory physiological flows, while more stable, exhibit fluctuations due to geometric complexity and have implications in studies of dispersion and solute transport in the cerebrospinal fluid flow and understanding of pathological conditions.

## Keywords

Lattice Boltzmann method Transitional flow Stenosis Kolmogorov scale## Notes

### Acknowledgements

Compute resources on *SuperMUC* and *SuperMUC-NG* were provided by the Leibniz Supercomputing Center (LRZ), Munich, Germany, and on *Hazel Hen* by the High-Performance Computing Center (HLRS), Stuttgart, Germany. The author is grateful to colleagues at LRZ and HLRS, and in particular to the considerate support from Dr. Martin Ohlerich from LRZ.

### Compliance with ethical standards

### Funding

No funding was received for this specific work.

### Conflict of interest

The authors declare that they have no conflict of interest.

## Supplementary material

## References

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