MULTIPLE, 2-DIMENSIONAL SOLUTIONS IN A ROTATING STRAIGHT PIPE

The multiplicity features and the secondary flow structure of the full y developed, laminar flow of a Newtonian fluid in a straight pipe that is rotating about an axis perpendicular to the pipe axis are examined . The governing equations of motion are solved numerically using the c ontrol volume method and the SIMPLE algorithm. The solution structure is governed by two dynamical parameters, Ekman number, Ek = v/D-2 Omeg a and Rossby number, Ro = U/D Omega, where D is the pipe diameter, v i s kinematic viscosity, Omega is rotational speed, and U is velocity sc ale. Results are presented for a fixed Ekman number of Ek = 0.01 and a range bf Rossby numbers between 0 to 20. The primary solution branch begins as a unique solution at low Rossby numbers. Its secondary flow structure consists of two-cells. At higher values of Ro a hitherto unk nown solution with a four-cell flow structure appears, which coexists with the two-cell how structure over a range of Ro up to 20. Transient , two-dimensional simulations were carried out to determine the stabil ity of the solutions to two-dimensional perturbations. The two-cell ho w structure is stable to both symmetric and asymmetric perturbations. Pour-cell how structure is stable to symmetric perturbations and unsta ble to asymmetric perturbations, where it breaks down to a two-cell. f low structure. (C) 1995 American Institute of Physics.