Analysis and numerical solution of viscous flow in curved ducts of regular cross-sections
Abstract
The laminar three-dimensional flow in curved ducts has been analyzed for an incompressible viscous fluid. The mathematical model is formulated using three-dimensional parabolized Navier-Stokes 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:
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- Ducted Flow;
- Laminar Flow;
- Navier-Stokes 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