Моделирование процесса отрыва течения за обратным уступом в канале. Modeling separated ow structure over a backward-facing step
Keywords:
обратный уступ, k-e модель турбулентности, RANS, канал, метод "маркеров и ячеек разделение и воссоединение потоков, отрывное течение, backward-facing step, channel, k-e turbulence model, MAC method, flow separation and reattachment, separated flowAbstract
В работе приводятся численные решения двумерного ламинарного течения за обратным уступом в канале для чисел Рейнольдса не превышающих 400. Для решения двумерных несжимаемых уравнений Навье-Стокса, описывающие течение за обратным уступом, применяется k-e модель турбулентности на основе RANS и решается данная модель численным методом "маркеров и ячеек который использует разнесенную сетку. Полученное уравнение Пуассона, удовлетворяющее дискретному уравнению неразрывности, решается на каждом шаге по времени итерационным методом Гаусс-Зейделя. Разностные уравнения для движения, кинетической энергии турбулентности и ее диссипации решаются простым явным методом. Это предполагает, что давление, кинетическая энергия турбулентности и скорость ее диссипации определяется на пересечении сетки, а компоненты скорости на границах. Для адекватного моделирования течения за обратным уступом с помощью k-e модель турбулентности применятся пристеночные функции. Полученные численные решения ламинарного течения за обратным уступом сравниваются с экспериментальными и численными результатами, приведенные в списке литературы. Целью численного исследования является расширить знания о течении за обратным уступом для углубления знания о внутреннем течении. Numerical solutions of 2-D laminar channel ow over a backward-facing step at Reynolds number up to 400 are presented in this work. The governing 2-D incompressible Navier-Stokes equations that describe flow over a backward-facing step are solved with the k-e turbulence model and numerical method MAC, which uses staggered grids. Poisson equation that satises the discrete continuity equation is solved at each time step by iterative Gauss-Seidel method. Dierence equations for the motion, turbulent kinetic energy and its dissipation solved by a simple explicit method. This implies that the pressure, turbulent kinetic energy and dissipation rate is determined at the intersection of the grid, and the velocity components at the boundaries. For an adequate simulation flow over backward-facing step by k-e turbulence model applied wall functions. Present numerical solutions of the laminar flow over a backward-facing step are compared with experimental and numerical results found in literature. The objective of the numerical investigation is to add to the existing knowledge of the backward-facing step flow to deepen our understanding of the internal flow.References
[1] Abbott D.E., Kline S.J. Experimental investigations of subsonic turbulent fow over single and double backward-facing steps // J. Basic Engng. 1962. - V.84. P. 317.
[2] Sebanr A. Heat transfer to the turbulent separated flows of air downstream of a step in the surface of a plate // J. Heat Transfer. 1964. V.86. P. 259.
[3] Goldsteinr J., Eriksenv L., Olsonr M., Eckerte R.G. Laminar separation, reattachment and transition of flow over a downstream-facing step // J. Basic Engng. 1970. V.92. P. 732.
[4] Durst F., Whitelawj H. Aerodynamic properties of separated gas ows: existing measurements techniques and new optical geometry for the laser-Doppler anemometer // Prog. Heat Mass Transfer. 1971. V.4. P. 311.
[5] Gosmana D., Punw M. Lecture notes for course entitled: `Calculation of recirculating ow' // Heat Transfer Rep. 1974. V.74. P. 2.
[6] Kumara, Yajnikk S. Internal separated flows at large Reynolds number
// J. Fluid Mech. 1980. V.97. P. 27.
[7] Denhama K., Patrick A. Laminar flow over a downstream-facing step in a two-dimensional flow channel // Trans. Inst. Chem. Engrs. 1974. V.52. P. 361.
[8] Etheridqed W., Kemp P.H. Measurements of turbulent flow downstream of a backward-facing step // J. Fluid Mech. 1978. V.86. P. 545.
[9] Armaly B.F., Durst F., Pereira J.C.F., Schoenung B. Experimental and theoretical investigation of backward-facing step flow // J. Fluid Mech. 1983. V.127. - P. 47396.
[10] Guj G., Stella F. Numerical solutions of high Reynolds number recirculating ows in vorticityvelocity form // Int J Numer Methods Fluids. 1988. V.8. P. 40516.
[11] Keskar J., Lyn D.A. Computations of a laminar backward-facing step flow at Re = 800 with a spectral domain decomposition method // Int J Numer Methods Fluids. 1999. V.29. P. 41127.
[12] Gartling D.K. A test problem for outow boundary conditions flow over a backward-facing step // Int J Numer Methods Fluids. 1990. V.11. P. 95367.
[13] Papanastasiou T.C., Malamataris N., Ellwood K. A new outflow boundary condition // Int J Numer Methods Fluids. 1992. V.14. P. 587608.
[14] Erturk E. Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions // J. Comp. &Fluids. 2008. V.37. P. 633-655.
[15] Gresho P.M., Gartling D.K., Torczynski J.R., Clie K.A., Winters K.H., Garratt T.J., et al. Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable? // Int J Numer Methods Fluids. 1993. V.17. P. 50141.
[16] Lee T., Mateescu D. Experimental and numerical investigation of 2-D backward-facing step flow // J. Fluids Struct. 1998. V.12. P. 70316.
[17] Ramsak M., Skerget L.A. Subdomain boundary element method for high-Reynolds laminar flow using stream function vorticity formulation // Int J Numer Methods Fluids. 2004. V.46. P. 81547.
[18] Cruchaga M.A. A study of the backward-facing step problem using a generalized streamline formulation // Commun Numer Methods Eng. 1998. V.14. P. 697708.
[19] Fortin A., Jardak M., Gervais J.J., Pierre R. Localization of Hopf bifurcations in uid flow problems // Int J Numer Methods Fluids. 1997. V.24. P. 1185210.
[20] Barkley D., Gomes M.G.M., Henderson R.D. Three-dimensional instability in flow over a backward-facing step // J. Fluid Mech. 2002. V.473. P. 16790.
[21] Erturk E., Corke T.C., Gokcol C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers // Int J Numer Methods Fluids. 2005. V.48. P. 74774.
[22] Chiang T.P., Tony W.H., Sheu, Fang C.C. Numerical investigation of vortical evolution in backward-facing step expansion flow // Appl. Math. 1999. V.23. P. 915-932.
[23] Fletcher C.A.J. Computational techniques for uid dynamics 2 // Springer-Verlag New York. 1988. V.1. P. 387.
[2] Sebanr A. Heat transfer to the turbulent separated flows of air downstream of a step in the surface of a plate // J. Heat Transfer. 1964. V.86. P. 259.
[3] Goldsteinr J., Eriksenv L., Olsonr M., Eckerte R.G. Laminar separation, reattachment and transition of flow over a downstream-facing step // J. Basic Engng. 1970. V.92. P. 732.
[4] Durst F., Whitelawj H. Aerodynamic properties of separated gas ows: existing measurements techniques and new optical geometry for the laser-Doppler anemometer // Prog. Heat Mass Transfer. 1971. V.4. P. 311.
[5] Gosmana D., Punw M. Lecture notes for course entitled: `Calculation of recirculating ow' // Heat Transfer Rep. 1974. V.74. P. 2.
[6] Kumara, Yajnikk S. Internal separated flows at large Reynolds number
// J. Fluid Mech. 1980. V.97. P. 27.
[7] Denhama K., Patrick A. Laminar flow over a downstream-facing step in a two-dimensional flow channel // Trans. Inst. Chem. Engrs. 1974. V.52. P. 361.
[8] Etheridqed W., Kemp P.H. Measurements of turbulent flow downstream of a backward-facing step // J. Fluid Mech. 1978. V.86. P. 545.
[9] Armaly B.F., Durst F., Pereira J.C.F., Schoenung B. Experimental and theoretical investigation of backward-facing step flow // J. Fluid Mech. 1983. V.127. - P. 47396.
[10] Guj G., Stella F. Numerical solutions of high Reynolds number recirculating ows in vorticityvelocity form // Int J Numer Methods Fluids. 1988. V.8. P. 40516.
[11] Keskar J., Lyn D.A. Computations of a laminar backward-facing step flow at Re = 800 with a spectral domain decomposition method // Int J Numer Methods Fluids. 1999. V.29. P. 41127.
[12] Gartling D.K. A test problem for outow boundary conditions flow over a backward-facing step // Int J Numer Methods Fluids. 1990. V.11. P. 95367.
[13] Papanastasiou T.C., Malamataris N., Ellwood K. A new outflow boundary condition // Int J Numer Methods Fluids. 1992. V.14. P. 587608.
[14] Erturk E. Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions // J. Comp. &Fluids. 2008. V.37. P. 633-655.
[15] Gresho P.M., Gartling D.K., Torczynski J.R., Clie K.A., Winters K.H., Garratt T.J., et al. Is the steady viscous incompressible two-dimensional flow over a backward-facing step at Re = 800 stable? // Int J Numer Methods Fluids. 1993. V.17. P. 50141.
[16] Lee T., Mateescu D. Experimental and numerical investigation of 2-D backward-facing step flow // J. Fluids Struct. 1998. V.12. P. 70316.
[17] Ramsak M., Skerget L.A. Subdomain boundary element method for high-Reynolds laminar flow using stream function vorticity formulation // Int J Numer Methods Fluids. 2004. V.46. P. 81547.
[18] Cruchaga M.A. A study of the backward-facing step problem using a generalized streamline formulation // Commun Numer Methods Eng. 1998. V.14. P. 697708.
[19] Fortin A., Jardak M., Gervais J.J., Pierre R. Localization of Hopf bifurcations in uid flow problems // Int J Numer Methods Fluids. 1997. V.24. P. 1185210.
[20] Barkley D., Gomes M.G.M., Henderson R.D. Three-dimensional instability in flow over a backward-facing step // J. Fluid Mech. 2002. V.473. P. 16790.
[21] Erturk E., Corke T.C., Gokcol C. Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers // Int J Numer Methods Fluids. 2005. V.48. P. 74774.
[22] Chiang T.P., Tony W.H., Sheu, Fang C.C. Numerical investigation of vortical evolution in backward-facing step expansion flow // Appl. Math. 1999. V.23. P. 915-932.
[23] Fletcher C.A.J. Computational techniques for uid dynamics 2 // Springer-Verlag New York. 1988. V.1. P. 387.
Downloads
Issue
Section
Mechanics, Mathematics, Computer Science
