Steady laminar flows in coiled annular ducts are investigated numerically. Numerical solutions are obtained by solving the incompressible Navier-Stokes equation with finite volume method.
For developing flow computations, a SIMPLE type procedure is adopted. Effect of radius ratio on the flow development is given particular attention. Computational results indicate that the secondary flow in a half cross-section (above or below the line of symmetry) for the case of moderate radius ratio is characterized by a pair of counter-rotating vortices; the flow in the core region is toward the outside bend and the flow near the inner and outer walls is toward the inside bend. However, when the radius ratio is very large, say greater than 0.8, the secondary flow is unidirectional and is toward the inside bend owing to the strong viscous effect. It is also found that the downstream flow development is greatly affected by the radius ratio. When the radius ratio is moderate, the centroid of the first moment of streamwise velocity lies on the outside half plane; when the radius ratio is very large, the centroid lies on the inside half plane. In contrast to the case of straight annular duct, the flow in a curved annular duct is not necessarily fully developed earlier when the radius ratio is larger owing the complicated interaction between the viscous and the centrifugal forces.
For fully developed flow computations, an artificial compressibility technique is employed. The computations are carried out for the forced and mixed convection flows with the Dean number lying in the range $10 < \kappa < 1000$, and the radius ratio in the range from 0.1 to 1.0. When the Dean number is small, the centroid of the first moment of streamwise velocity is found to lie near the inside bend. As the Dean number increases, the centroid gradually travels toward the outside bend.
The friction ratio and the overall average Nusselt number become larger as the radius ratio increases for a give Dean number. It is observed that the friction ratio and the overall average Nusselt number are proportional to $\kappa^{1/2}$ for the wide range of the Dean number used here.
Fully developed mixed convection flow in a loosely curved annulus is also examined. Analytic solutions in power series form are derived. In deriving the solution, the radius ratio, which is a fundamental parameter since the flow passage is annular, is properly taken into account. To investigate the validity of the analytic solution, numerical calculations are carried out to yield a reference data. It is found that the analytic solution compares favorably with the numerical solution only when the radius ratio is small.
Numerical solutions for fully developed mixed convection flows with constant wall temperature boundary conditions are obtained to examined the effect of buoyancy on the flow and heat transfer. Secondary flows and heat transfer characteristics are investigated for the cases of buoyancy dominated flows, centrifugal force dominated flows and the intermediate flows.