Stability of the flow in a helical tube

Abstract

The flow in a helical tube of small curvature and its linear stability are theoretically investigated for a wide range of the torsion parameter β0, which is defined as β = λ/√2δ with the dimensionless torsion λ and curvature δ. It is shown that the torsion has a destabilizing effect on the flow. The critical Dean number at the onset of unstable flow first decreases as β0 increases, reaches a minimum at β0 ≈ 1.4, and then increases again. The minimum Dean number is about 600. The stability characteristics obtained are favorably compared with those in the previous experiment by Yamamoto et al., Fluid Dyn. Res. 16, 1995.