Unsteady simple shear flow in a viscoplastic fluid: comparison between analytical and numerical solutions |
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Authors: | Irene Daprà Giambattista Scarpi |
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Institution: | (1) DISTART—University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy |
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Abstract: | In this paper, an unsteady flow of a viscoplastic fluid for simple shear flow geometry is solved numerically using two regularizing
functions to overcome the discontinuity for zero shear rate of the Bingham constitutive law. The adopted models are the well-known
Papanastasiou relation and one based on the error function. The numerical results are compared with the analytical solution
of the same problem obtained by Sekimoto (J Non-Newton Fluid Mech 39:107–113, 1991). The analysis of the results emphasizes that the errors are much smaller in the yielded than in the unyielded region. The
models approximate closer the ideal Bingham model as the regularization parameters increase. The differences between the models
tend to vanish as the regularization parameters are at least greater than 105. |
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