Fully-developed pipe and planar flows of multimode viscoelastic fluids |
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| Affiliation: | 1. School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA;2. Manufacturing and Mechanical Engineering Technology, Rochester Institute of Technology, Rochester, NY 14623, USA;1. Shenzhen Key Laboratory of Complex Aerospace Flows, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China;2. Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen 518055, China;3. Department of Mechanics, Huazhong University of Science and Technology (HUST), Wuhan 430074, China;4. School of Computer Science and Technology, Xi''an University of Science and Technology, Xi''an 710054, China;5. Center for Complex Flows and Soft Matter Research, Southern University of Science and Technology, Shenzhen 518055, China;1. College of Marine Engineering, Dalian Maritime University, Dalian 116026, PR China;2. Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921 USA;3. School of Instrument Science and Opto-electronic Engineering, Hefei University of Technology, Hefei 230009, PR China;4. Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA;5. College of Controlling Science and Engineering, China University of Petroleum, Qingdao 257061, PR China;6. Maritime College, Guangdong Ocean University, Zhanjiang 524088, PR China |
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| Abstract: | Two solutions are presented for fully-developed pipe and planar flows of multimode viscoelastic models. The fluids have a Newtonian solvent contribution and the polymer modes are described by the Phan-Thien—Tanner (PTT), the FENE-P or the Giesekus equation. The first solution is exact and can handle any number of modes, but is only semi-analytical. The second solution, which is presented only for the PTT model with a linear stress coefficient and the FENE-P model, can also handle any number of modes. It is based on a truncated series expansion and is completely analytical, but provides only an approximated solution. The complexity of the multimode solutions is investigated first with the exact semi-analytical method and it is shown that at high Deborah number flows the high-order stresses can become as important as the stress of the first mode. It is also under these conditions that the approximated analytical solution deviates from the exact semi-analytical solution. A criterion for the accurate use of the approximated solution is presented. Fortran codes are provided to obtain these solutions at the internet address at the end. |
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