Calculation of the local resistance coefficient of viscous incombressible fluid flow in a pipe with sudden contraction
Most technical applications for fluid transportation include such a structural particularity as sudden contraction. This geometrical feature has an effect on the flow characteristics that should be taken into account in order to provide the appropriate mode and conditions of the flow. This work was intended to investigate the kinematic characteristics and pressure losses of Newtonian fluid flow through an axisymmetric sudden contraction. The mathematical statement of the problem of laminar flow was formulated using stream function and vorticity variables. The stationary solution was obtained using the relaxation method with the following realization of numerical algorithm based on the finite difference alternative directions scheme. The obtained flow pattern showed that the flow structure apart from the one-dimensional zones included two-dimensional regions in the vicinity of contracted part (l1 and l2 are the lengths of two-dimensional regions upstream and downstream of the sudden contraction, respectively; L is the length of recirculation zone in the inner corner). The effect of the main parameters on these characteristics was studied and represented as dependency diagrams. For the calculations of local resistance coefficient (CM), two different formulas were used. Implemented parametrical investigations allowed plotting the local resistance coefficient as a function of the Reynolds number and pipe contraction ratio: CM decreased with an increase in the Reynolds number; an increase in contraction ratio caused an increase in CM. The obtained results were verified and compared with available data.
Keywords
вязкая несжимаемая жидкость,
внезапное сужение,
стационарное течение,
метод установления,
коэффициент местного сопротивления,
число Рейнольдса,
метод прогонки,
viscous incompressible fluid,
sudden contraction,
stationary flow,
relaxation method,
local resistance coefficient,
Reynolds number,
sweep methodAuthors
| Borzenko Evgeniy I. | Tomsk State University | borzenko@ftf.tsu.ru |
| Ryltseva Kira E. | Tomsk State University | kiraworkst@gmail.com |
| Frolov Oleg Yu. | Tomsk State University | frolov@ftf.tsu.ru |
| Shrager Gennady R. | Tomsk State University | shg@ftf.tsu.ru |
Всего: 4
References
Fan C.T., Hwang C.L. Bibliography of hydrodynamic entrance region flow // Kansas State University Bulletin. 1966. V. 50(3).
Boger D.V. Circular entry flows of inelastic and viscoelastic fluids // Advances in Transport Processes. 1982. V. 2. P. 43-104.
Durst F., Loy T. Investigations of laminar flow in a pipe with sudden contraction of cross sectional area // Computers & Fluids. 1985. V. 13(1). P. 15-36.
White S.A., Baird D.G. The importance of extensional flow properties on planar entry flow patterns of polymer melts // J. Non-Newtonian Fluid Mechanics. 1986. V. 20. P. 93-101.
Evans R.E., Walters K. Further remarks on the lip-vortex mechanism of vortex enhancement in planar-contraction flows // J. Non-Newtonian Fluid Mechanics. 1989. V. 32. P. 95-105.
Rothstein J.P., McKinley G.H. The axisymmetric contraction-expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop // J. Non-Newtonian Fluid Mechanics. 2001. V. 98. P. 33-63.
White S.A., Baird D.G. Numerical simulation studies of the planar entry flow of polymer melts // Journal of Non-Newtonian Fluid Mechanics. 1988. V. 30. P. 47-71.
Mompean G., Deville M. Unsteady finite volume simulation of Oldroyd-B fluid through a three-dimensional planar contraction // J. Non-Newtonian Fluid Mechanics. 1997. V. 72. P. 253-279.
Walters K., Webster M.F. The distinctive CDF challenges of computational rheology // Int. J. Numerical Methods in Fluids. 2003. V. 43. P. 577-596.
Astarita G., Greco G. Excess pressure drop in laminar flow through sudden contraction // Ind. Eng. Chem. Fundamentals. 1968. V. 7(1). P. 27-31.
Sylvester N.D., Rosen S.L. Laminar flow in the entrance region of a cylindrical tube // AICHE Journal. 1970. V. 16(6). P. 964-966.
Boger D.V. Viscoelastic flows through contractions // Annual Reviews. Fluid Mechanics. 1987. V. 19. P. 157-182.
Sisavath S., Jing X., Pain C.C., Zimmerman R.W. Creeping flow through axisymmetric sudden contraction or expansion // J. Fluids Eng. (Trans. ASME). 2002. V. 124(1). P. 273278.
Pienaar V.G. Viscous flow through sudden contractions / Dis. Cape Peninsula University of Technology, 2004. 198 p.
Роуч П. Вычислительная гидродинамика / пер. с англ.: В.А. Гущина, В.Я. Митницкого; под ред. П.И. Чушкина. М.: Мир, 1980. 616 с.
Годунов С.К., Рябенький В.С. Введение в теорию разностных схем. М.: Физматгиз, 1962. 340 c.
Яненко Н.Н. Метод дробных шагов решения многомерных задач математической физики. Новосибирск: Наука, 1967. 197 с.
Идельчик И.Е. Справочник по гидравлическим сопротивлениям / под ред. М.О. Штейн-берга. 3-е. изд. М.: Машиностроение, 1992. 672 с.
Кочин Н.Е., Кибель И.А., Розе Н.В. Теоретическая гидромеханика, ч. 2, изд. 4-е. М.: Физматлит, 1963. 728 с.
Monnet P., Menard C., Sigli D. Some new aspects of the slow flow of a viscous fluid through an axisymmetric duct expansion or contraction. II - Experimental part // Appl. Sci. Res. 1982. V. 39. P. 233-248.
Boger D., Hur D., Binnington R. Further observations of elastic effects in tubular entry flows // Journal of Non-Newtonian Fluid Mechanics. 1986. V. 20. P. 31-49.
Kim-E M.E., Brown R.A., Armstrong R.C. The roles of inertia and shear-thinning in flow of an inelastic liquid through an axisymmetric sudden contraction // J. Non-Newtonian Fluid Mech. 1983. V. 13. P. 341-363.
Ajayi K.T., Papadopoulos G., Durst F. Influence of upstream development on the losses incurred by flow past an axisymmetric sudden contraction // American Institute of Aeronautics and Astronautics AIAA-98-0794. 1998.
Christiansen E.B., Kelsey S.J., Carter T.R. Laminar tube flow through an abrupt contraction // AlChE Journal. 1972. V. 18(2). P. 372-380.
Perry R.H., Green D.W., Maloney J.O. Perry's chemical engineers' handbook. 7th ed.: McGraw-Hill, 1997.
Vrentas, J.S., Duda, J.L. Flow of a Newtonian fluid through a sudden contraction // Appl. Sci. Res. 1973. V. 28. P. 241-260.
Binding D.M. An approximate analysis for contraction and converging flows // Journal of Non-Newtonian Fluid Mechanics. 1988. V. 27(2). P. 173-189.
