Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Snigerev B. A., Tazyukov F. K. The Feature of Non-Isothermal Viscoelastic Flows Around Sphere at Obstruction Condition. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, vol. 11, iss. 1, pp. 99-104. DOI: 10.18500/1816-9791-2011-11-1-99-104

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.01.2011
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(downloads: 164)
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Russian
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UDC: 
532.517.2:534.2

The Feature of Non-Isothermal Viscoelastic Flows Around Sphere at Obstruction Condition

Autors: 
Snigerev Boris Aleksandrovich, Research Institute of Mechanics and Machinery of Kazan Scientific Center of the Russian Academy of Sciences
Tazyukov Faruk Khosnutdinovich, Kazan National Research Technological University
Abstract: 

The numerical study is performed for study of the viscoelastic flow characteristics and heat transfer around sphere. The flow of liquid is described by equations of conservation of mass, momentum and thermal energy with rheological constitutive equation of Phan-Thien Tanner(PTT). Thismodelrepresents generalizedMaxwell typemodel with two additional parameters developed from kinetic theory of polymers. The nonlinear behaviour of fluid velocity behind body (<>) is observed. The paper numerically shows the essential influence of relaxation time and heating of sphere for viscoelastic structure of the flow in wake. The heat transfer exchange in non-isothermal flow around sphere with slip and noslip condition on walls has been investigated.

References: 
  1. Hassager, O. Negative wake behind bubles in non - Newtonian liquids / O. Hassager // Nature. 1979. Vol. 279. P. 402–403.
  2. Arigo, M.T. An experimental investigation of negative wakes behind spheres settling in shear-thinning visoellastic fluids / M.T. Arigo, G.H. McKinley // Rheol.Acta. 1998. Vol. 37. P. 307–327.
  3. Phan-Thien, N. A new constitutive equation derived from network theory / N. Phan-Thien // J. Non- Newtonian Fluid. Mech. 1979. Vol. 2. P. 353–365.Bird, R.B. Dynamics of Polymeric Liquids. V. 1. Fluid Mechanics. 2nd ed. / R.B. Bird, R.C. Armstrong, O. Hassager. N.Y.: John Wiley and Sons, 1987. 565 p.
  4. Назмеев, Ю.Г. Гидродинамика и теплообмен закрученных потоков реологически сложных жидкостей / Ю.Г. Назмеев. М.: Энергоатомиздат, 1996. 304 с.Коннор, Дж. Метод конечных элементов в механике жидкости / Дж. Коннор, К. Бреббиа. Л.: Судостроение, 1979. 264 с.
  5. Aboubacar, M. High-order finite volume schemes for viscoelastic flows / M. Aboubacar [et al.] // J. Comput. Phys. 2004. Vol. 199. P. 16–40.
  6. Писанецки, О. Технология разреженных матриц / О. Писанецки. Л.: Мир, 1984. 344 с.
  7. Захаренков, С.М. Реализация граничных условий частичного или полного проскальзывания при решении уравнений Навье-Стокса / С.М. Захаренков // Журн. вычисл. мат. и мат. физ. 2001. Т. 41, No 5. С. 796–806.
  8. Luo, X.L. Operator splitting algorithm for viscoelastic flow and numerical analysis for the flow around sphere in tube / X.L. Luo // J. Non-Newtonian Fluid. Mech. 1996. Vol. 48. P. 57–75.