Abstract
This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.
Highlights
Many fluids of practical interest exhibit a complex behavior that cannot be predicted using mathematical models employing the classical Newtonian rheological laws
The original Newtonian constant viscosity can be replaced by other, even simpler generalized Newtonian models to capture the shear-thinning behavior of blood. Such variable viscosity generalization has been adopted by several authors, including our studies (e.g., [16,17,18]) leading to the generalized Oldroyd-B model with shear-thinning viscosity given by the Cross model with appropriate physiological parameters, as specified below in this paper (Section 3)
In the figures presented below we always group the results from the generalized Oldroyd-B model (GOB) model with the corresponding predictions of the Johnson–Segalman model obtained by setting the parameter a to a = −0.9, −0.8, −0.7
Summary
Many fluids of practical interest exhibit a complex behavior that cannot be predicted using mathematical models employing the classical Newtonian rheological laws. Newtonian models follow this concept, but allow the proportionality coefficient (viscosity) to be variable, typically depending on some relevant physical quantities, most importantly the invariants of the rate of strain tensor Classical representative of this class of generalized. The original Newtonian constant viscosity can be replaced by other, even simpler generalized Newtonian models to capture the shear-thinning behavior of blood Such variable viscosity generalization has been adopted by several authors, including our studies (e.g., [16,17,18]) leading to the generalized Oldroyd-B model with shear-thinning viscosity given by the Cross model with appropriate physiological parameters, as specified below in this paper (Section 3). Our aim in this paper is to present a preliminary numerical study of the rate type shear-thinning viscoelastic Johnson–Segalman model in order to better understand its behavior in some practically relevant situation—the blood flow in stenosed vessel. Numerical results have been obtained to illustrate and provide comparative analysis of the flow dynamics on the generated flow patterns of the pressure, axial velocity and radial velocity for both models in different flow regimes
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