THE CHARACTERISTICS OF LAMINAR-FLOW IN A HELICAL CIRCULAR PIPE

The fully developed laminar flow in a helical circular pipe under the influence of both curvature and torsion is studied analytically. The solutions are obtained by the double series expansion method which perturbs the exact solution derived in this work for a twisted circular pipe. The perturbed parameters selected are dimensionless curvature kappa and dimensionless torsion tau. Since the expanded governing equations and series solutions have been arranged in a compact form, the complete solutions can be computed by a systematic procedure on computer. In addition, the accuracy of the solutions is only confined by the natural limitation of the series expansion method because no approximation was made in the governing equations. The 'torsion number' Tn which can be considered as the measure of the torsion effect that swirls the flow is defined Tn = 2tauR, where R is the Reynolds number. The characteristics of the flow in the helical circular pipe are thus controlled by three parameters: R, Dean number K and Tn. The flow rate solution of the extended Dean equations of Germano (1989) is then found. The effects of finite curvature and torsion on the flow rate, axial velocity and secondary flow are also found. The inconsistency of torsion effect on the secondary flow between Wang (1981) and Germano (1982, 1989) is also quantitatively explained by the different coordinate systems used.