Instability of steady flows in helical pipes

A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent experimental and numerical results in a previous study. A possible power dependence of the friction factor on the Reynolds and Dean numbers is examined. The stability results are reported as dependences of the critical Reynolds number, critical wave number and the critical frequency on the dimensionless pipe curvature and torsion. A multiplicity of different disturbance modes becoming most unstable at different values of the governing parameters, is observed. Patterns of the most unstable modes are reported and classified. Different routes to instability including viscous and inviscid mechanisms, locally developing boundary and mixing layers, interaction between the Dean vortices, and the through flow are described.