A Numerical Study of the Impact of Wavy Walls on Steady Fluid Flow Through a Curved Tube

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Abstract
In this paper, we discuss the impact of a wavy-walled pipe cross-section on steady flow in a curved tube at moderate Dean numbers and small tube radius-to-radius-of-curvature ratios. Parameters investigated include the protrusion height, the number of protrusions around the tube circumference, and the pipe curvature. This work extends a previous analytical investigation that employed a double perturbation expansion to elucidate the flow field as a function of these parameters. Due to the rapid growth in the solution complexity as the number of terms in each expansion increases, the analytical work is relegated to small wall perturbations and low Dean numbers. These barriers are removed in the present study by numerically solving the Navier–Stokes equations at Dean numbers up to 2500. The impact on the axial and secondary flow structures are emphasized, along with the resulting wall shear stress distributions.

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