Effect of aspect ratio on the similarity between developing laminar flows in orthogonally rotating ducts and stationary curved ducts

Abstract

Purpose

To investigate the effect of aspect ratio on the quantitative analogy between developing laminar flows in orthogonally rotating straight ducts and stationary curved ducts

Design/methodology/approach

A fractional step method is used to obtain the numerical solution of the governing equations by decoupling the solution of the momentum equations from the solution of the continuity equation. In order to clarify the similarity of the two flows, dimensionless parameters K_LR and Rossby number, Ro, in a rotating straight duct were used as a set corresponding to Dean number, K_LC, and curvature ratio, λ, in a stationary curved duct.

Findings

Under the condition that the aspect ratio was larger than one and that the magnitude of Ro or λ was large enough to satisfy the “asymptotic invariance property” the quantitative analogy between the two flows was established clearly.

Research limitations/implications

As the aspect ratio decreased below one, the difference between the secondary flow intensities of these two flows increased, and therefore, the analogy between the two flows was not as evident as that for the larger aspect ratios.

Practical implications

Based on this methodology, the characteristics of the developing flow in orthogonally rotating ducts of higher aspect ratio can be predicted by considering the flow in stationary curved ducts, and vice versa.

Originality/value

The results obtained in this study will suggest an optimal criterion for the application of this approach to the flow similarity analysis in rectangular ducts with arbitrary aspect ratios.

Citation

Hee Lee, G. and Hyun Baek, J. (2006), "Effect of aspect ratio on the similarity between developing laminar flows in orthogonally rotating ducts and stationary curved ducts", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 4, pp. 494-508. https://doi.org/10.1108/09615530610653109