Analysis and numerical solution of viscous flow in curved ducts of regular crosssections
Abstract
The laminar threedimensional flow in curved ducts has been analyzed for an incompressible viscous fluid. The mathematical model is formulated using threedimensional parabolized NavierStokes equations. The equations are generalized using two indices which permit the choice of Cartesian or cylindrical coordinate systems and straight or curved ducts. The solutions are obtained numerically using an ADI method for a number of duct geometries and flow parameters. The study presents detailed results for developing laminar flow in rectangular curved ducts; also, the effect of longitudinal curvature on secondary flow is fully analyzed. An investigation is made of the occurrence of Dean's instability and, for curved square ducts, it is found to first appear at a Dean number of 143.
 Publication:

ASME Numerical/Laboratory Computer Methods in Fluid Mechanics
 Pub Date:
 December 1976
 Bibcode:
 1976asme.meet...53G
 Keywords:

 Ducted Flow;
 Laminar Flow;
 NavierStokes Equation;
 Numerical Analysis;
 Three Dimensional Flow;
 Viscous Flow;
 Alternating Direction Implicit Methods;
 Aspect Ratio;
 Computer Programs;
 Curvature;
 Flow Geometry;
 Incompressible Flow;
 Rectangles;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer