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Article Dans Une Revue Journal of Non-Newtonian Fluid Mechanics Année : 2018

Development of a thermal Reduced Order Model with explicit dependence on viscosity for a generalized Newtonian fluid

Résumé

This work falls within the general framework of melted polymers flows characterization. It deals with the development of a thermo-rheological Reduced Order Model (ROM) which could be used in future works for on-line estimation of viscosity from temperature measurements in the flow, especially in high shear zones. A steady incompressible flow of a pseudo-plastic fluid in a circular runner is considered. The dynamic viscosity is thus described by a shear rate power law defined by consistency index K and flow behavior index n. An approach is developed for building a ROM able to compute a radial temperature profile at the channel outlet for any (K, n) couple in a predefined range. Assuming the temperature field approximation on a reduced set of m space functions, the general form of the ROM is obtained through a Galerkin projection of the energy equation. The ROM constitutive parameters are then identified through an optimization procedure using temperature data for a set of (K, n) couples in the construction ranges K ϵ [5000; 20, 000] and n ϵ [0.3; 0.6]. These data are computed by a Finite Elements reference model experimentally validated on an instrumented apparatus. A series of ROMs of order m = 1 to 5 is identified and then tested for a second set of (K, n) couples. The order 5 ROM is able to reproduce the temperature profile computed by the reference model with a r.m.s. error of about 10^−2 °C. The temperature profile computed with ROMs is also compared to the profile measured for a real flow.
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Dates et versions

hal-01835901 , version 1 (22-02-2021)

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Manuel Girault, Julien Launay, Nadine Allanic, Pierre Mousseau, Rémi Deterre. Development of a thermal Reduced Order Model with explicit dependence on viscosity for a generalized Newtonian fluid. Journal of Non-Newtonian Fluid Mechanics, 2018, 260, pp.26 - 39. ⟨10.1016/j.jnnfm.2018.04.002⟩. ⟨hal-01835901⟩
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