TY - GEN

T1 - Numerical modeling of non-affine viscoelastic fluid flow including viscous dissipation through a square cross section duct

T2 - ASME 2020 International Mechanical Engineering Congress and Exposition, IMECE 2020

AU - Hagani, Fouad

AU - Boutaous, M'Hamed

AU - Knikker, Ronnie

AU - Xin, Shihe

AU - Siginer, Dennis

N1 - Publisher Copyright:
© 2020 ASME.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - Non-isothermal laminar flow of a viscoelastic fluid including viscous dissipation through a square cross section duct is analyzed. Viscoelastic stresses are described by Giesekus modele orthe Phan-Thien Tanner model and the solvent shear stress is given by the linear Newtonian constitutive relationship. The flow through the tube is governed by the conservation equations of energy, mass, momentum associated with to one non affine rheological model mentioned above. The mixed type of the governing system of equations (elliptic parabolic hyperbolic) requires coupling between discretisation methods designed for elliptic type equations and techniques adapted to transport equations. To allow appropriate spatial discretisation of the convection terms, the system is rewritten in a quasi-linear first-order and homogeneous form without the continuity and energy equations. With the rheological models of the Giesekus type, the conformation tensor is by definition symmetrical and positivedefinite, with the PTT model the hyperbolicity condition is subject to restrictions related to the rheological parameters. Based on this hyperbolicity condition, the contribution of the hyperbolic part is approximated by applying the characteristic method to extract pure advection terms which are then discretized by high ordre schemes WENO and HOUC. The algorithm thus developed makes it possible, to avoid the problems of instabilities related to the high Weissenberg number without the use of any stabilization method. Finally, a Nusselt number analysis is given as a function of inertia, elasticity, viscous dissipation, for constant solvent viscosity ratio and constant material and rheological parameters.

AB - Non-isothermal laminar flow of a viscoelastic fluid including viscous dissipation through a square cross section duct is analyzed. Viscoelastic stresses are described by Giesekus modele orthe Phan-Thien Tanner model and the solvent shear stress is given by the linear Newtonian constitutive relationship. The flow through the tube is governed by the conservation equations of energy, mass, momentum associated with to one non affine rheological model mentioned above. The mixed type of the governing system of equations (elliptic parabolic hyperbolic) requires coupling between discretisation methods designed for elliptic type equations and techniques adapted to transport equations. To allow appropriate spatial discretisation of the convection terms, the system is rewritten in a quasi-linear first-order and homogeneous form without the continuity and energy equations. With the rheological models of the Giesekus type, the conformation tensor is by definition symmetrical and positivedefinite, with the PTT model the hyperbolicity condition is subject to restrictions related to the rheological parameters. Based on this hyperbolicity condition, the contribution of the hyperbolic part is approximated by applying the characteristic method to extract pure advection terms which are then discretized by high ordre schemes WENO and HOUC. The algorithm thus developed makes it possible, to avoid the problems of instabilities related to the high Weissenberg number without the use of any stabilization method. Finally, a Nusselt number analysis is given as a function of inertia, elasticity, viscous dissipation, for constant solvent viscosity ratio and constant material and rheological parameters.

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U2 - 10.1115/IMECE2020-23558

DO - 10.1115/IMECE2020-23558

M3 - Conference contribution

AN - SCOPUS:85101277350

T3 - ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

BT - Fluids Engineering

PB - American Society of Mechanical Engineers(ASME)

Y2 - 16 November 2020 through 19 November 2020

ER -