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Comparison of Numerical Schemes for the Problem of Laminar Flow in a Suddenly Expanding Channel

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Abstract

The work presents the numerical study of fluid flow in a two-dimensional channel with a sudden expansion (H/h = 2). In order to study the flow, a number of flow characteristics are calculated at Reynolds numbers ranging from 100 to 800. The calculations are performed for the laminar flow regime based on the numerical integration of the unsteady Navier–Stokes equations. Results are obtained for longitudinal velocity profiles in different channel cross sections behind the ledge, as well as lengths of primary and secondary vortices at different Reynolds numbers. The distribution of the bottom-wall friction coefficient along the channel length at varying Reynolds numbers is presented. The control volume method is employed for the approximation of the initial equations, while the relationship between velocities and pressures is determined through the application of the SIMPLE procedure. The QUICK (Quadratic Upstream Interpolation for Convective Kinematics) scheme of Brian P. Leonard, the second-order accuracy scheme of McCormack, the third-order accuracy scheme of Warming–Kutler–Lomax, and the fourth-order accuracy scheme of Abarbanel–Gottlieb–Turkel are employed to numerically solve the problem. To validate the numerical results, a comparison with the experimental data, sourced from the literature, is conducted.

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REFERENCES

  1. Blasius, H., Laminare Stromung in Kanalen Wechselnder Breite, Zeitschrift fur Math. und Phys., 1910, vol. 58 (10), p. 225.

    Google Scholar 

  2. Honji, H., The starting flow down a step, J. Fluid Mech., 1975, vol. 69 (2), p. 229. https://doi.org/10.1017/S0022112075001413

    Article  Google Scholar 

  3. Sinkha, S.P., Gupta, A.K., and Oberai, M.M., Laminar separated flow around steps and cavities. Part 1. Flow behind a step, Raket. Tekhn. Mekhan., 1981, vol. 19 (12), p. 33.

    Google Scholar 

  4. Armaly, B.F., Durst, F., Pereira, J.C.F., and Schönung, B., Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 1983, vol. 127, p. 473. https://doi.org/10.1017/S0022112083002839

    Article  Google Scholar 

  5. Chang, P.K., Separation of Flow, Oxford: Pergamon Press, 1970.

    Google Scholar 

  6. Gogish, L.V. and Stepanov, G.Yu., Turbulentnye otryvnye techeniya (Turbulent Separated Flows), Moscow: Nauka, 1979.

  7. Le, H., Moin, P., and Kim, J., Direct numerical simulation of turbulent flow over a backward-facing step, J. Fluid Mech., 1997, vol. 330, p. 349. https://doi.org/10.1017/S0022112096003941

    Article  CAS  Google Scholar 

  8. Durst, F., Melling, A., and Whitelow, J.H., Low Reynolds number flow over a plane symmetric sudden expansion, J. Fluid Mech., 1974, vol. 64 (1), p. 111. https://doi.org/10.1017/S0022112074002035

    Article  Google Scholar 

  9. Cherdron, W., Durst, F., and Whitelow, J.H., Asymmetric flows and instabilities in symmetric ducts with sudden expansions, J. Fluid Mech., 1978, vol. 84 (1), p. 13. https://doi.org/10.1017/S0022112078000026

    Article  CAS  Google Scholar 

  10. Macadno, E.O. and Hung, T.-K., Computational and experimental study of a captive annular eddy, J. Fluid Mech., 1967, vol. 28 (1), p. 43. https://doi.org/10.1017/S0022112067001892

    Article  Google Scholar 

  11. Kumar, A. and Yajnik, K.S., Internal separated flows at large Reynolds number, J. Fluid Mech., 1980, vol. 97 (1), p. 27. https://doi.org/10.1017/S0022112080002418

    Article  Google Scholar 

  12. Plotkin A. Calculations by the spectral method of some separated laminar flows in channels, Aerokosmich. Tekh., 1983, vol. 7, p. 75.

    Google Scholar 

  13. Acrivos, A. and Schrader, M.L., Steady flow in a sudden expansion at high Reynolds numbers, Phys. Fluids, 1982, vol. 25 (6), p. 923. https://doi.org/10.1063/1.863844

    Article  CAS  Google Scholar 

  14. Kuon, O., Pletcher, R., and Lewis, J., Calculation of flows with sudden expansion using boundary layer equations, Teor. Osn. Inzh. Rasch., 1984, vol. 106 (3), p. 116.

    Google Scholar 

  15. Lewis, J. and Pletcher, R., Limits of applicability of boundary layer equations for calculating laminar flows with symmetric sudden expansion, Teor. Osn. Inzh. Rasch., 1986, vol. 2, p. 284.

    Google Scholar 

  16. Malikov, Z.M. and Madaliev, M.E., Numerical modeling of flow in a flat suddenly expanding channel based on a new two-fluid turbulence model, Vest. MGTU im. Baumana. Ser. Est. Nauki, 2021, vol. 4 (97), p. 24. https://doi.org/10.18698/1812-3368-2021-4-24-39

    Article  CAS  Google Scholar 

  17. Lee, Y.S. and Smith, L.C., Analysis of power-law viscous materials using complex stream, potential and stress functions, Flow Phenomena and Measurement, Cheremisinoff, N.P., Ed., 1986, vol. 1, p. 1105.

    Google Scholar 

  18. Roache, P.J., Computational Fluid Dynamics, New Mexico: Hermosa, 1972, p. 139.

    Google Scholar 

  19. Taylor, T.D., and Ndefo, E., Computation of viscous flow in a channel by the method of splitting, Lecture Notes in Physics, 1971, vol. 8, p. 356.

    Book  Google Scholar 

  20. Durst, F., and Peireira, J.C.F., Time-dependent laminar backwardfacing step flow in a two-dimensional duct, ASME J. Fluids Eng., 1988, vol. 110, p. 289.

    Article  Google Scholar 

  21. Alleborn, N., Nandakumar, K., Raszillier, H., and Durst, F., Further contributions on the two-dimensional flow in a sudden expansion, J. Fluid Mech., 1997, vol. 330, p. 169.

    Article  CAS  Google Scholar 

  22. Brandt, A., Dendy, J. E., and Ruppel, H., The multigrid method for semi-implicit hydrodynamic codes, J. Comput. Phys., 1980, vol. 34, p. 348.

    Article  CAS  Google Scholar 

  23. Hackbusch, W., Multigrid Methods for Applications, Berlin: Springer, 1985.

    Book  Google Scholar 

  24. Lange, C.F., SchaËfer, M., and Durst, F., Local block refinement with a multigrid flow solver, Int. J. Numer. Methods Fluids, 2002, vol. 38, p. 21.

    Article  Google Scholar 

  25. Kim, J., and Moin, P., Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 1985, vol. 59, p. 308.

    Article  Google Scholar 

  26. Durst, F., Peireira, J.C.F., and Tropea, C., The plane symmetric sudden-expansion flow at low Reynolds numbers, J. Fluid Mech., 1993, vol. 248, p. 567.

    Article  CAS  Google Scholar 

  27. Kaiktsis, L., Karniadakis, G.E., and Orszag, S.A., Unsteadiness and convective instabilities in a two-dimensional flow over a backward-facing step, J. Fluid Mech., 1996, vol. 321, p. 157.

    Article  Google Scholar 

  28. Leonard, B.P., A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Comp. Meth. Appl. Mech. Eng., 1979, vol. 19, p. 59.

    Article  Google Scholar 

  29. MacCormack, R.W., The Effect of Viscosity in Hypervelocity Impact Cratering, AIAA Paper, 1969, vol. 69, p. 354.

    Google Scholar 

  30. Warming, R.F., Kutler, P., and Lomax, H., Second- and third-order noncen tered difference schemes for nonlinear hyperbolic equations, AIAA Jour-J., 1973, vol. 11, p. 189.

    Article  Google Scholar 

  31. Abarbanel, S., Gottlieb, D., and Turkel, E., Difference schemes with fourth order accuracy for hyperbolic equations, SIAM J. Appl. Math., vol. 29, p. 329.

  32. Loitsyansky, L.G., Mekhanika zhidkosti i gaza (Mechanics of Liquids and Gases), Moscow: Nauka, 1987.

  33. Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Abingdon: Taylor&Francis, 1980.

    Google Scholar 

  34. Malikov, Z.M. and Madaliev, M.E., Numerical simulation of two-phase flow in a centrifugal separator, Fluid Dynamics, 2020, vol. 55 (8), p. 1012. https://doi.org/10.1134/S0015462820080066

    Article  CAS  Google Scholar 

  35. Erkinson, M.M., Numerical calculation of an air centrifugal separator based on the sarc turbulence model, J. Appl. Comput. Mech., 2021, vol. 7 (2). https://doi.org/10.22055/JACM.2020.31423.1871

  36. Malikov, Z.M. and Nazarov, F.Kh., Study of a submerged axisymmetric turbulent jet in a comparative analysis of turbulence models, Vest. MGTU im. Baumana, Ser. Estestvozn., 2022, vol. 1, p. 22. https://doi.org/10.18698/1812-3368-2022-2-22-35

    Article  CAS  Google Scholar 

  37. Nazarov, F.Kh., Comparison of turbulence models for swirling flows, Vest. MGTU im. Baumana, Ser. Est. Nauki, 2021, vol. 2 (95), p. 25. https://doi.org/10.18698/1812-3368-2021-2-25-36

    Article  CAS  Google Scholar 

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Funding

The work was supported by ongoing institutional funding. No additional grant to carry out or direct this particular research was obtained.

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Authors and Affiliations

  1. M.T. Urazbaev Institute of Mechanics and Seismic Stability of Structures, Academy of Sciences of the Republic of Uzbekistan, 100007, Tashkent, Uzbekistan

    M. E. Madaliev

  2. Fergana Polytechnic Institute, 100007, Fergana, Uzbekistan

    M. E. Madaliev

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  1. M. E. Madaliev
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Correspondence to M. E. Madaliev.

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Madaliev, M.E. Comparison of Numerical Schemes for the Problem of Laminar Flow in a Suddenly Expanding Channel. Theor Found Chem Eng (2024). https://doi.org/10.1134/S0040579524601055

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