Steady Flow in a Curved Pipe with Circular Cross-Section. Comparison of Numerical and Experimental Results

Numerical solution has been obtained of the equations of motion of a viscous incompressible fluid in a curved annular conduit with circular cross-section. These equations are approximated by finite-difference equations which are of the second-order accuracy with respect to the grid sizes. The computed results are presented for the range 96 D 8000 , where D is the Dean number of the flow and for various sizes of core radii, the limiting cases of a very large and a very small core being also studied. It is shown that in the case of a small core radius, the variation of the Dean number affects significantly the flow properties, situation which is not observed when the core radius is large. INTRODUCTION Steady flow into curved pipes has been studied extensively due to the applications in engineering. Annular flow is an important feature in double-pipe heat exchangers, in chemical mixing and drying machinery. The theoretical exploration of the steady flow in a pipe of slight curvature was first considered by Dean [1, 2]. It was shown that the effect of curvature is to reduce the flux, and that the non-dimensional volume flux depends only on the so-called Dean number K = 2 R W max / ( ) 2 where and R are, respectively, the radius and the radius of curvature of the pipe, Wmax is the maximum axial velocity in a straight pipe of the same radius and pressure gradient and is the kinematic viscosity of the fluid. Dean’s solution is valid for K 576. Dean’s work was extended by McConalogue and Srivastava [3] who adopted the parameter