Numerical simulation of flow-induced fiber orientation using normalization of second moment |
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| Authors: | Amin Moosaie Anne Le Duc Michael Manhart |
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| Institution: | 1. IRMAR, ENS Cachan Bretagne, Univ. Rennes 1, CNRS, UEB, av. Robert Schuman, 35170 Bruz, France;2. Université Pierre et Marie Curie (Univ. Paris 6) and Institut Universitaire de France, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France;3. BCAM – Basque Center for Applied Mathematics, Mazarredo, 14 E-48009 Bilbao, Basque Country, Spain;4. Ikerbasque, Basque Foundation for Science, Alameda Urquijo 36-5, Plaza Bizkaia, E-48011 Bilbao, Basque Country, Spain;1. Department of Chemical Engineering, Virginia Tech, Blacksburg, VA 24061, USA;2. Macromolecules and Interfaces Institute, Virginia Tech, Blacksburg, VA 24061, USA;3. Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA |
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| Abstract: | A normalization scheme for the numerical solution of the moment approximation equation in fiber suspension flows is presented. Here, normalization refers to rescaling the trace of the second moment tensor to unity at each time step. The equivalence between the normalization scheme and the quadratic closure model is analytically proved. The performance of the scheme is investigated in simple shear flow with respect to the quadratic and hybrid closures, and a stochastic Monte-Carlo simulator that provides exact solution. The proposed scheme is a computationally efficient alternative to the quadratic closure: it performs equally well and is more efficient regarding computational time. |
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