Calculation of Unsteady Flows in Curved Pipes

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Abstract
Highly unsteady three-dimensional flows in curved pipes with significant variation of flow geometry and flow parameters are studied. Using improvements in computational efficiency, detailed knowledge concerning flow structures is obtained. The numerical solutions of the Navier-Stokes equations have been obtained with a variation of the projection method, and the numerical method was enhanced by new algorithms derived from the physics of the flow. These enhancements include a prediction of the flow unsteady pressure gradient based on fluid acceleration and global pressure field corrections based on mass flow. This new method yields an order of magnitude improvement in the calculation’s efficiency, allowing the study of complex flow problems. Numerical flow simulations for oscillating flow cycles show that the curved pipe flows have a significant inviscid-like nature at high values of the frequency parameter. The shape of the velocity profiles is strongly influenced by the frequency parameter, whereas the influence of variations on the pipe cross-sectional area is shown to be rather weak. For large values of the frequency parameter the flow history strongly influences the low mass flow part of the cycle leading to highly unusual velocity profiles. The wall shear stress is studied for all the flows calculated. Our results show that wall shear stress is sensitive to area constrictions, the frequency parameter, as well as the shape of the entrance profile.

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