Direct numerical simulation of transitional flow in a finite length curved pipe

ABSTRACT

Transition to turbulent flow in a curved pipe has been well studied through experiments and numerical simulations. Numerical simulations often use a helical pipe with an infinite length such that the inlet and outlet boundary conditions can be modelled as periodic which greatly reduces computational time. In this study, we examined a finite length curved pipe with Poiseuille flow imposed at the inlet and a stress-free boundary condition at the outlet. Direct numerical simulation of the Navier-Stokes equations for rigid walls and a Newtonian fluid was performed using nek5000. Straight extensions were added to the inlet and outlet such to diminish the impact of boundary conditions on the flow field in the region with curvature. The examined model has a pipe radius of curvature that is three times the pipe radius. The model has ∼355 million nodes and required an order of magnitude greater computational time when compared with an infinite length curved pipe. Results show that the critical Reynolds number, the lowest value with instabilities present in the flow, is much greater than that of a straight pipe and occurs near Re=5000–5200. This is larger than the critical Reynolds number typically reported for an infinite length curved pipe (Re=4200–4300).

KEYWORDS:

• Transitional flow
• secondary flow
• curved pipe
• direct numerical simulation
• critical Reynolds number

Acknowledgements

The authors thank Ohio Supercomputer Center and XSEDE program for providing computational hours. The authors also want to thank Dr. Aleks Obabko for his helps and support.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Francis Loth http://orcid.org/0000-0001-7651-521X

Additional information

Funding

This work was supported by C&S Patient Education Foundation.