Fully developed viscoelastic flows in rotating curved pipes with circular cross section are investigated theoretically and numerically employing the Oldroyd-B fluid model. Based on Dean’s approximation, a perturbation solution up to the secondary order is obtained. The governing equations are also solved numerically by the finite volume method. The theoretical and numerical solutions agree with each other very well. The results indicate that the rotation, as well as the curvature and elasticity, plays an important role in affecting the friction factor, the secondary flow pattern and intensity. The co-rotation enhances effects of curvature and elasticity on the secondary flow. For the counter-rotation, there is a critical rotational number RΩ′, which can make the effect of rotation counteract the effect of curvature and elasticity. Complicated flow behaviors are found at this value. For the relative creeping flow, RΩ′ can be estimated according to the expression RΩ′=−4We. Effects of curvature and elasticity at different rotational numbers on both relative creeping flow and inertial flow are also analyzed and discussed.
Curvature; Elasticity; Fluid dynamics; Rotational motion; Viscoelastic materials
Fluid Dynamics | Mechanical Engineering
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Viscoelastic Flow in Rotating Curved Pipes.
Physics of Fluids, 18(8),