Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the N... more Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the Newtonian flow in a curved channel exhibits transverse recirculations at ``Dean'' numbers beyond the critical value of 36. More recently, Joo and Shaqfeh (Phys. Fluids A, 1991, 1992) extended Dean's original work for viscoelastic fluids through a linear stability analysis. This work
Journal of Non-newtonian Fluid Mechanics, Dec 1, 2006
The purpose of the present study is to compare numerical simulations of viscoelastic flows using ... more The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in
Emerging Technology in Fluids, Structures, and Fluid Structure Interactions: Volume 1, Fluid Dynamics and Fluid Structure Interactions, 2004
The principle of material frame indifference (MFI) is a fundamental and controversial principle o... more The principle of material frame indifference (MFI) is a fundamental and controversial principle of continuum mechanics which has been invoked to derive recent nonlinear algebraic models for stresses of viscoelastic liquids (Mompean, Thompson, and Souza Mendes [2003]) and for Newtonian turbulent fluids (Rumsey, Gatski, and Morrison [2000]). The purpose of the present study is to identify regions of a flow field where MFI should be considered. Such regions are identified by computing the angular velocity of the principal directions of the rate-of-deformation tensor in order to obtain a Euclidean objective vorticity tensor. The method is applied to the planar flow through an abrupt 4:1 contraction. The main results are: (i) MFI should be taken into account in regions characterized by the transition between two different viscometric kinematics and significant velocities (ii) MFI can be safely ignored in regions of pure viscometric behavior as well as in recirculation regions.
Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the N... more Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the Newtonian flow in a curved channel exhibits transverse recirculations at ``Dean'' numbers beyond the critical value of 36. More recently, Joo and Shaqfeh (Phys. Fluids A, 1991, 1992) extended Dean's original work for viscoelastic fluids through a linear stability analysis. This work
The purpose of the present study is to compare numerical simulations of viscoelastic flows using ... more The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in
Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the N... more Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the Newtonian flow in a curved channel exhibits transverse recirculations at ``Dean'' numbers beyond the critical value of 36. More recently, Joo and Shaqfeh (Phys. Fluids A, 1991, 1992) extended Dean's original work for viscoelastic fluids through a linear stability analysis. This work
Journal of Non-newtonian Fluid Mechanics, Dec 1, 2006
The purpose of the present study is to compare numerical simulations of viscoelastic flows using ... more The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in
Emerging Technology in Fluids, Structures, and Fluid Structure Interactions: Volume 1, Fluid Dynamics and Fluid Structure Interactions, 2004
The principle of material frame indifference (MFI) is a fundamental and controversial principle o... more The principle of material frame indifference (MFI) is a fundamental and controversial principle of continuum mechanics which has been invoked to derive recent nonlinear algebraic models for stresses of viscoelastic liquids (Mompean, Thompson, and Souza Mendes [2003]) and for Newtonian turbulent fluids (Rumsey, Gatski, and Morrison [2000]). The purpose of the present study is to identify regions of a flow field where MFI should be considered. Such regions are identified by computing the angular velocity of the principal directions of the rate-of-deformation tensor in order to obtain a Euclidean objective vorticity tensor. The method is applied to the planar flow through an abrupt 4:1 contraction. The main results are: (i) MFI should be taken into account in regions characterized by the transition between two different viscometric kinematics and significant velocities (ii) MFI can be safely ignored in regions of pure viscometric behavior as well as in recirculation regions.
Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the N... more Since the pioneering study by Dean (Proc. Roy. Soc. London, Ser. A, 1928), it is known that the Newtonian flow in a curved channel exhibits transverse recirculations at ``Dean'' numbers beyond the critical value of 36. More recently, Joo and Shaqfeh (Phys. Fluids A, 1991, 1992) extended Dean's original work for viscoelastic fluids through a linear stability analysis. This work
The purpose of the present study is to compare numerical simulations of viscoelastic flows using ... more The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in
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