Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-10T15:27:37.287Z Has data issue: false hasContentIssue false

Non-Newtonian flow characteristics in a steady two-dimensional flow

Published online by Cambridge University Press:  12 April 2006

Thomas B. Gatski
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802 Permanent address: NASA Research Center, Hampton, Virginia 23665.
John L. Lumley
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853

Abstract

The two-dimensional steady flow of a non-Newtonian fluid (a dilute polymer solution) is examined. The flow domain is composed of a parallel-walled inflow region, a contraction region in which the walls are rectangular hyperbolae, and a parallel-walled outflow region. The problem is formulated in terms of the vorticity, stream function and appropriate rheological equation of state, i.e. an Oldroyd-type constitutive equation (with no shear-thinning) for the total shear and normal-stress components. Computational results from the numerical solution of the equations are presented. In particular, the molecular extension and pressure distribution along the centre-line are presented as well as contour plots of the different flow variables. The alignment of the molecules with the principal axes of strain rate is shown by a qualitative comparison of the streamwise normal-stress contours with contours of the eigenvalues of the strain-rate matrix.

Type
Research Article
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Black, J. R. & Denn, M. M. 1975 J. Non-Newtonian Fluid Mech. 1, 83.
Black, J. R., Denn, M. M. & Hsiao, G. C. 1975 In Theoretical Rheology (ed. J. F. Hutton, J. R. A. Pearson and K. Walters), p. 3. Barking, England: Applied Science Publ.
Duda, J. L. & Vrentas, J. S. 1973 Trans. Soc. Rheol. 17, 89.
Gatski, T. B. 1976 The numerical solution of the steady flow of Newtonian and non-Newtonian fluids through a contraction. Ph.D. thesis, Pennsylvania State University, University Park.
Gatski, T. B. 1978 Steady flow of a non-Newtonian fluid through a contraction. J. Comp. Phys. (to appear).Google Scholar
Giesekus, H. 1962 Rheol. Acta 2, 50.
Giesekus, H. 1966 Rheol. Acta 5, 29.
Huilgol, R. R. 1975 Rheol. Acta 14, 48.
Lodge, A. S. 1964 Elastic Liquids. Academic Press.
Luxmley, J. L. 1969 Ann. Rev. Fluid Mech. 1, 367.
Lumley, J. L. 1971 Phys. Fluids 14, 2282.
Lumley, J. L. 1972a Symposia Mathematica vol. 9, p. 315. Academic Press.
Lumley, J. L. 1972b Phys. Fluids 15, 217.
Metzner, A. B., Uebler, E. A. & Chun man fong, C. F. 1969 A.I.Ch.E. J. 15, 750.
Oldroyd, J. G. 1950 Proc. Roy. Soc. A 200, 523.
Peterlin, A. 1966 J. Pure Appl. Chem. 12, 563.
Peterlin, A. 1970 Nature 227, 598.
Roache, P. J. 1972 Computational Fluid Dynamics. Albuquerque: Hermosa.
Tanner, R. I. 1975a Trans. Soc. Rheol. 19, 557.
Tanner, R. I. 1975b Trans. Soc. Rheol. 19, 37.
Tanner, R. I. 1976 A.I.Ch.E. J. 22, 910.
Tanner, R. I. & Stehrenberger, W. 1971 J. Chem. Phys. 55, 1958.
Toms, B. A. 1948 Proc. 1st Int. Cong. Rheol. vol. 2, p. 135. North Holland.
Townsend, P. 1973 Rheol. Acta 12, 13.
Waters, N. D. & King, M. J. 1971 J. Phys. D, J. Appl. Phys. 4, 204.