Flow in Helical Annular Pipe

In this paper, the axial and the secondary flow in a helical annular pipe are examined by a perturbation method in a curvilinear coordinate system, and the second-order perturbation solution is obtained completely. The secondary flow, the axial velocity, and the flux ratio are studied in detail. When the torsion is zero, the secondary flow behaves as four vortexes, and they are symmetrical up and down. When it is not zero, the symmetry is destroyed, and the intensity and number of the secondary flow vortexes are affected by the Dean number and the radius ratio of the inner/outer circle wall of the annular cross section. The maximum of the axial velocity appears near the inner bend when the Dean number is small, and it is moved toward the outer bend as the Dean number increases.