Developing fluid flow in a curved duct of square cross-section and its fully developed dual solutions

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Abstract
Developing fluid flow in a curved duct of square cross-section is studied numerically by a factored ADI finite-difference method on a staggered grid. A central-difference scheme with primitive variables is used inside the computational domain to reduce numerical diffusion. Two Reynolds numbers, 574 and 790, based upon a bulk velocity and hydraulic diameter are chosen for curvature ratios of 1/6.45 and 1/2.3, respectively. It is found that the secondary flow is far more complicated than expected, with the appearance of at least two pairs of vortices. Main-flow separation is also observed for the higher curvature ratio. Furthermore, it is observed that the flow develops into two quite different states downstream, depending upon the inlet conditions.Solution of the fully developed Navier-Stokes equations is shown to be not unique beyond a certain critical Reynolds number. Developing flow seems to evolve into the fully developed state along a particular branch, into which the fully developed solution bifurcates.

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