Laminar flow and linear stability in helical pipes

A linear global stability analysis of flows in helical pipes has been performed. The numerical setup exploits helical coordinates in an orthogonal reference frame where the base flow is two-dimensional (2D), thus allowing an extensive range of curvature and torsion to be considered. A spatial spectral Fourier-Chebyshev discretisation is employed. Particular attention is given to the accuracy of the base flow solution and the discretisation of the eigenmodes, by checking the decay of the spectral coefficients. This allowed to identify and analyse the phenomena of spurious modes, commonly affecting the solution of incompressible Navier-Stokes equations in primitive variables on non-staggered grids. In addition, a robust confirmation of the correctness of the volume force, called forcing, used in the literature to drive the flow has been carried out, by comparing with experimental data and a steady Direct Numerical Simulation (DNS) making use of inflow-outflow boundary conditions. The dependence of the laminar base flow on the pipe geometry (curvature, torsion) is analysed in detail, by mapping some relevant quantities, among which the friction factor. Combining the base flow and stability analysis, the critical Reynolds number could be computed with a high accuracy, by means of a continuation method allowing to follow the neutral curve for each pipe geometry. The stability results show generally a good agreement with the unique work present in the literature, but some remarkable differences are also identified. Finally, a qualitative analysis of the marginally stable modes is presented.