A convective weakly viscoelastic rotating flow with pressure Neumann condition
The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with...
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| Published in | International journal for numerical methods in fluids Vol. 60; no. 3; pp. 295 - 322 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
30.05.2009
Wiley |
| Subjects | |
| Online Access | Get full text |
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| Abstract | The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr) . The numerical results show that for high Weissemberg numbers (We>7.4 × 10−5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr>17 × 10−4) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd. |
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| AbstractList | The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (
We
) and Grashof numbers (
Gr
) . The numerical results show that for high Weissemberg numbers (
We
>7.4 × 10
−5
) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (
Gr
>17 × 10
−4
) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd. The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity-pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr). The numerical results show that for high Weissemberg numbers (We > 7.4 X 10-5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr > 17 X 10-4), the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr) . The numerical results show that for high Weissemberg numbers (We>7.4 × 10−5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr>17 × 10−4) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd. |
| Author | Asenjo, Elba Bravo Rubio, Obidio Claeyssen, Julio R. |
| Author_xml | – sequence: 1 givenname: Julio R. surname: Claeyssen fullname: Claeyssen, Julio R. email: julio@mat.ufrgs.br organization: IM-Promec, Universidade Federal do Rio Grande do Sul, P.O. Box 10673, 90001-970 Porto Alegre, RS, Brazil – sequence: 2 givenname: Elba Bravo surname: Asenjo fullname: Asenjo, Elba Bravo organization: UNASP-Adventist University Center of São Paulo, SP, Brazil – sequence: 3 givenname: Obidio surname: Rubio fullname: Rubio, Obidio organization: Facultad de Ciencias, Universidad Nacional de Trujillo, La Libertad, Peru |
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| Keywords | Rectangular pipe Viscoelastic fluid Rotating flow Computational fluid dynamics incompressible flow Digital simulation Boundary conditions pressure Neumann condition Rotating pipe Combined convection Algorithms finite differences methods mixed convection Modelling non-Newtonian Incompressible fluid Secondary flow Mesh generation Heat transfer Finite difference method |
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| References | Chen HB, Nandakumar K, Finlay WH, Ku HC. Three-dimensional viscous flow through rotating channel: a pseudospectral matrix method approach. International Journal for Numerical Methods in Fluids 1996; 23:379-396. Lee KT, Yan WM. Mixed convection heat and mass transfer in radially rotating rectangular ducts. Numerical Heat Transfer, Part A 1998; 34:747-767. Jin YY, Chen CF. Instability of convection and heat transfer of high Prandtl number fluids in a vertical slot. Journal of Heat Transfer 1996; 118:359-365. Roache PJ. Computational Fluid Dynamics. Hermosa Publications: Albuquerque, NM, 1982. Nonino C, Comini G. An equal-order velocity-pressure algorithm for incompressible thermal flows, part 1: formulation. Numerical Heat Transfer, Part B 1997; 32:1-15. Sheu TWH, Wang MMT, Tsai SF. Pressure boundary condition for a segregated approach to solving incompressible Navier-Stokes equations. Numerical Heat Transfer, Part B 1998; 34:457-467. Yamaguchi H, Fujiyoshi J, Matsui H. Spherical Couette flow of a viscoelastic fluid. Part I: experimental study of the inner sphere rotation. Journal of Non-Newtonian Fluid Mechanics 1997; 69:29-46. Claeyssen JR, Bravo E, Rubio O. Rotating incompressible flow with a pressure Neumann condition. International Journal for Numerical Methods in Fluids 2006; 50:1-26. Nonino C, Croce G. An equal-order velocity-pressure algorithm for incompressible thermal flows, part 2: validation. Numerical Heat Transfer, Part B 1997; 32:17-35. Speziale CG. Numerical solution of rotating internal flows. Lecture Notes in Applied Mathematics 1985; 22:261-288. Claeyssen JR, Bravo E, Platte R. Simulation in primitive variables of incompressible flow with pressure Neumann condition. International Journal for Numerical Methods in Fluids 1999; 30:1009-1026. Govatsos PA, Papantonis DE. A characteristic based method for the calculation of three-dimensional incompressible, turbulent and steady flows in hydraulic turbomachines and installations. International Journal for Numerical Methods in Fluids 2000; 34:1-30. Yang Z. Large eddy simulation of fully developed turbulent flow in a rotating pipe. International Journal for Numerical Methods in Fluids 2000; 33:681-694. Vanyo PJ. Rotating Fluids in Engineering and Science. Dover Publications, Inc.: Mineola, New York, 1993. Lee E, Lee YH, Pai YT, Hsu JP. Flow of a viscoelastic shear-thinning fluid between two concentric rotating spheres. Chemical Engineering Science 2002; 57:507-514. Speziale CG. Numerical study of viscous flow in rotating rectangular ducts. Journal of Fluid Mechanics 1982; 122:251-271. Ladyzhenskaya O. The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach: New York, 1969. Abdallah S. Numerical solutions for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid. Journal of Computational Physics 1987; 70:182-192. Harlow FH, Welch JE. Numerical calculation of time dependent viscous incompressible flow of fluid with free surface. Physics of Fluids 1965; 8:2182-2189. Liqiu W. Buoyancy-force-driven transitions in flow structures and their effects on heat transfer in rotating curved channel. International Journal of Heat and Mass Transfer 1997; 40(2):223-235. Ferguson J, Kemblowski Z. Applied Fluid Rheology. Elsevier Applied Science: London, 1991. Morse PM, Feschbach H. Methods of Theoretical Physics, Part I. McGraw-Hill: New York, 1953. Gresho PM, Sani RL. On pressure boundary conditions for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1987; 7:1111-1145. Joseph DD. Fluid Dynamics of Viscoelastic Liquids. Springer: New York, 1990. Ames WF. Numerical Methods for Partial Differential Equations (3rd edn). Academic Press: New York, 1992. Temam R. Navier-Stokes Equations, Theory and Numerical Analysis (3rd edn). North-Holland: Amsterdam, 1984 (reprint AMS Chelsea Publishing, Providence, RI, 2004). Park HM, Hong SM, Lim JY. Estimation of rheological parameters using velocity measurements. Chemical Engineering Science 2007; 62:6806-6815. Khayat RE. On overstability in thermal convection of viscoelastic fluids. Developments in Non-Newtonian Flows AMD 1993; 175:71-83. Hart JE. Instability and secondary motion in a rotating channel flow. Journal of Fluid Mechanics 1971; 45:341-351. Robertson AM. On viscous flow in curved pipes of non-uniform cross-section. International Journal for Numerical Methods in Fluids 1996; 22:771-798. Ferziger JH, Perić M. Computational Methods for Fluid Dynamics (2nd edn). 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| References_xml | – reference: Morse PM, Feschbach H. Methods of Theoretical Physics, Part I. McGraw-Hill: New York, 1953. – reference: Nonino C, Croce G. An equal-order velocity-pressure algorithm for incompressible thermal flows, part 2: validation. Numerical Heat Transfer, Part B 1997; 32:17-35. – reference: Liqiu W. Buoyancy-force-driven transitions in flow structures and their effects on heat transfer in rotating curved channel. International Journal of Heat and Mass Transfer 1997; 40(2):223-235. – reference: Claeyssen JR, Bravo E, Platte R. Simulation in primitive variables of incompressible flow with pressure Neumann condition. International Journal for Numerical Methods in Fluids 1999; 30:1009-1026. – reference: Chen HB, Nandakumar K, Finlay WH, Ku HC. Three-dimensional viscous flow through rotating channel: a pseudospectral matrix method approach. International Journal for Numerical Methods in Fluids 1996; 23:379-396. – reference: Hart JE. Instability and secondary motion in a rotating channel flow. Journal of Fluid Mechanics 1971; 45:341-351. – reference: Speziale CG. Numerical study of viscous flow in rotating rectangular ducts. Journal of Fluid Mechanics 1982; 122:251-271. – reference: Govatsos PA, Papantonis DE. A characteristic based method for the calculation of three-dimensional incompressible, turbulent and steady flows in hydraulic turbomachines and installations. International Journal for Numerical Methods in Fluids 2000; 34:1-30. – reference: Claeyssen JR, Bravo E, Rubio O. Rotating incompressible flow with a pressure Neumann condition. International Journal for Numerical Methods in Fluids 2006; 50:1-26. – reference: Speziale CG. Numerical solution of rotating internal flows. Lecture Notes in Applied Mathematics 1985; 22:261-288. – reference: Vanyo PJ. Rotating Fluids in Engineering and Science. Dover Publications, Inc.: Mineola, New York, 1993. – reference: Temam R. Navier-Stokes Equations, Theory and Numerical Analysis (3rd edn). North-Holland: Amsterdam, 1984 (reprint AMS Chelsea Publishing, Providence, RI, 2004). – reference: Park HM, Hong SM, Lim JY. Estimation of rheological parameters using velocity measurements. Chemical Engineering Science 2007; 62:6806-6815. – reference: Ferziger JH, Perić M. Computational Methods for Fluid Dynamics (2nd edn). Springer: Berlin, 1999. – reference: Yamaguchi H, Fujiyoshi J, Matsui H. Spherical Couette flow of a viscoelastic fluid. Part I: experimental study of the inner sphere rotation. Journal of Non-Newtonian Fluid Mechanics 1997; 69:29-46. – reference: Lee KT, Yan WM. Mixed convection heat and mass transfer in radially rotating rectangular ducts. Numerical Heat Transfer, Part A 1998; 34:747-767. – reference: Abdallah S. Numerical solutions for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid. Journal of Computational Physics 1987; 70:182-192. – reference: Harlow FH, Welch JE. Numerical calculation of time dependent viscous incompressible flow of fluid with free surface. Physics of Fluids 1965; 8:2182-2189. – reference: Yang Z. Large eddy simulation of fully developed turbulent flow in a rotating pipe. International Journal for Numerical Methods in Fluids 2000; 33:681-694. – reference: Robertson AM. On viscous flow in curved pipes of non-uniform cross-section. International Journal for Numerical Methods in Fluids 1996; 22:771-798. – reference: Joseph DD. Fluid Dynamics of Viscoelastic Liquids. Springer: New York, 1990. – reference: Roache PJ. Computational Fluid Dynamics. Hermosa Publications: Albuquerque, NM, 1982. – reference: Jin YY, Chen CF. Instability of convection and heat transfer of high Prandtl number fluids in a vertical slot. Journal of Heat Transfer 1996; 118:359-365. – reference: Gresho PM, Sani RL. On pressure boundary conditions for the incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1987; 7:1111-1145. – reference: Ferguson J, Kemblowski Z. Applied Fluid Rheology. Elsevier Applied Science: London, 1991. – reference: Ladyzhenskaya O. The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach: New York, 1969. – reference: Lee E, Lee YH, Pai YT, Hsu JP. Flow of a viscoelastic shear-thinning fluid between two concentric rotating spheres. Chemical Engineering Science 2002; 57:507-514. – reference: Nonino C, Comini G. An equal-order velocity-pressure algorithm for incompressible thermal flows, part 1: formulation. Numerical Heat Transfer, Part B 1997; 32:1-15. – reference: Sheu TWH, Wang MMT, Tsai SF. Pressure boundary condition for a segregated approach to solving incompressible Navier-Stokes equations. Numerical Heat Transfer, Part B 1998; 34:457-467. – reference: Khayat RE. 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| Snippet | The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct... |
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| SubjectTerms | Computational methods in fluid dynamics Convection and heat transfer Exact sciences and technology finite differences methods Fluid dynamics Fundamental areas of phenomenology (including applications) Hydrodynamic stability incompressible flow mixed convection non-Newtonian Non-newtonian fluid flows Physics pressure Neumann condition rotating flow Secondary instability Turbulent flows, convection, and heat transfer |
| Title | A convective weakly viscoelastic rotating flow with pressure Neumann condition |
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