What is it about?

We present a computational analysis of the fluid dynamics of laminar, rheological flow in regular polygonal ducts, which is important for its fundamental value and application potential in various industries. The power of theoretical understanding is combined here with the power of computational fluid dynamics to achieve a generalized physical understanding from a large set of accurate numerical simulations. We propose simple correlations to predict entry length, the shape of the fully developed axial velocity profile and friction factor based on two newly introduced geometric parameters, viz., the factor of approach and integrity index. While it was well-known that turbulent flow through non-circular ducts typically induces Prandtl's secondary flow of the second kind, the present study reveals the occurrence of such secondary flow associated with the corner convexities of the primary velocity profile, even within the laminar regime. We demonstrate three distinct fluid dynamic regimes using the vortex line representation. The methodology developed here may be extended to related flow configurations.

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Why is it important?

We numerically study the fluid dynamics of laminar, rheological flow in regular polygonal ducts. The present study reveals the occurrence of Prandtl's secondary flow of the second kind associated with the corner convexities of the primary velocity profile, even within the laminar regime. We capture a counter-rotating vortex pair at each corner of the polygonal duct as evidence of the secondary flow. Further, we propose simple correlations to predict entry length, the shape of the fully developed axial velocity profile and friction factor based on two newly introduced geometric parameters, viz., the factor of approach and integrity index. We demonstrate three distinct fluid dynamic regimes using the vortex line representation: the near-wall region, the inner core, and an intermediate region.

Perspectives

While it was well-known that turbulent flow through non-circular ducts typically induces Prandtl's secondary flow of the second kind, the present study reveals the occurrence of such secondary flow associated with the corner convexities of the primary velocity profile, even within the laminar regime.

Sayantan Sengupta
NATIONAL INSTITUTE OF TECHNOLOGY DURGAPUR

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This page is a summary of: Morphology of laminar rheological flow in polygonal ducts, Physics of Fluids, August 2024, American Institute of Physics,
DOI: 10.1063/5.0217982.
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