  A computational study of three-dimensional instability of steady flows in a
helical pipe of arbitrary curvature and torsion is carried out for the first
time. The problem is formulated in Germano coordinates in two equivalent but
different forms of the momentum equation, so that results obtained using both
formulations cross verify each other. An additional formulation in the
cylindrical coordinates is applied for a limiting case of the toroidal pipe.
The calculations are performed by the finite volume and finite difference
methods. Grid independence of the results is established for both steady flows,
the eigenvalues associated with the linear stability problem, and the critical
parameters. The calculated steady flows agree well with experimental
measurements and previous numerical results. The computed critical Reynolds
numbers corresponding to the onset of oscillatory instability agree well with
the most recent experimental results, but disagree with the earlier ones. Novel
results related to the parametric stability study are reported.
