On some asymptotics of laminar flow in a coiled pipe
Abstract
Several limits of helically coiled pipe flow are examined, using an orthogonal helical coordinate system first introduced by in 1982 for this problem. The fully developed laminar flow in the pipe with a circular crosssection is solved by perturbing the Poiseuille flow. The first limit is the loosely coiled pipe, of which the centerline has a curvature small compared with the radius of the pipe cross section. In the second and third limits, the pitch angle tends to 90 degrees. However, the ratio of the radii is kept constant in the second limit whereas it tends to infinity in the third limit. The relation between the first two asymptotic expansions can be found by relating the small parameters used for the two expansions. The solution for the second limit can be compared to the solution of the flow in a twisted pipe with an elliptic cross section. The solution for the last limit cannot be derived from those for the first two limits and it is much more difficult to find analytically.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........53C
 Keywords:

 Asymptotic Methods;
 Helical Windings;
 Laminar Flow;
 Pipe Flow;
 Cross Sections;
 Curvature;
 Expansion;
 Fluid Dynamics;
 Orthogonality;
 Fluid Mechanics and Heat Transfer