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## Archive of Issues

Russia Kemerovo
Year
2015
Volume
25
Issue
2
Pages
280-294
 Section Mechanics Title Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step Author(-s) Fomin A.A.a, Fomina L.N.b Affiliations Kuzbass State Technical Universitya, Kemerovo State Universityb Abstract The paper deals with the results of solving the problem of steady-state flow of a viscous incompressible fluid in a plane channel with a backward-facing step and a heated bottom wall for the Reynolds number in the range $100\leqslant \text{Re}\leqslant1000$ and the expansion ratio of a plane channel in the range $1.11 \leqslant ER \leqslant 10$. The study was carried out by numerical integration of the 2-D Navier-Stokes equations in velocity-pressure formulation on uniform grids with a step which equals to 1/300. Correction of the results is confirmed by comparing them with the literature data. Detailed flow patterns and fields of stream overheating depending on two basic parameters of the problem $\text{Re}$ and $ER$ are demonstrated. It is shown that with the increase of parameters $\text{Re}$ and $ER$ the structure of flow becomes much more complicated, that is, there is an increase of the number of vortices and their sizes up to the formation of a vortex behind the backward-facing step with two centers of rotation. It is also stated that the typical height of the heating zone of the flow depends weakly on $\text{Re}$ and $ER$ and eventually, near the exit of the channel, equals approximately half of the channel height. For all centers of vortices their main characteristics are defined: location, extremums of stream function, vorticity. Complex nonmonotonic behaviors of the coefficients of friction, hydrodynamic resistance and heat transfer (Nusselt number) along the channel are analyzed. It is shown that these coefficients strongly depend both on Reynolds number and on expansion ratio, reaching the maximum values at the maximum values of $\text{Re}$ and $ER$. Keywords Navier-Stokes equations, a plane channel with backward-facing step, separating flow UDC 519.632.4, 532.516.5 MSC 65N06, 76D05, 80A20 DOI 10.20537/vm150212 Received 12 May 2015 Language Russian Citation Fomin A.A., Fomina L.N. Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 2, pp. 280-294. References Roache P.J. Computational fluid dynamics, Albuquerque: Hermosa Publs., 1976, 446 p. Translated under the title Vychislitel'naya gidrodinamika, Moscow: Mir, 1980, 616 p. Bruyatski E.V., Kostin A.G. Direct numerical simulation of flow in plane suddenly expending channel on the basis of Navier-Stokes equations, Priklad. Gidromekhanika, 2010, vol, 12, no. 1, pp. 11-27 (in Russian). Armaly B.F., Durst F., Pereira J.C.F., Schonung B. Experimental and theoretical investigation of backward-facing step flow, J. Fluid Mech., 1983, vol. 127, pp. 473-496. DOI: 10.1017/S0022112083002839 Sinha S.N., Gupta A.K., Oberai M.M. Laminar separating flow over backsteps and cavities. Part I: Backsteps, AIAA J., 1981, vol. 19, no. 12, pp. 1527-1530. DOI: 10.2514/3.7885 Tihon J., Pěnkavová V., Havlica J., Šimčík M. The transitional backward-facing step flow in a water channel with variable expansion geometry, Exp. Therm. Fluid Sci., 2012, vol. 40, pp. 112-125. DOI: 10.1016/j.expthermflusci.2012.02.006 Rogers S.E., Kwak D. An upwind differencing scheme for the incompressible Navier-Stokes equations, Appl. Numer. Math., 1991, vol. 8, no. 1, pp. 43-64. DOI: 10.1016/0168-9274(91)90097-J Chiang T.P., Sheu Tony W.H., Fang C.C. Numerical investigation of vortical evolution in a backward-facing step expansion flow, Appl. Math. Model., 1999, vol. 23, no. 12, pp. 915-932. DOI: 10.1016/S0307-904X(99)00019-0 Batenko S.R., Terekhov V.I. Friction and heat transfer in a laminar separated flow behind a rectangular step with porous injection or suction, Journal of Applied Mechanics and Technical Physics, 2006, vol. 47, no. 1, pp. 12-21. Bubenchikov A.M., Firsov D.K., Kotovshchikova M.A. Numerical solution of 2D viscous fluid dynamics problems using finite volume method (FVM) on triangular grid, Mat. Model., 2007, vol. 19, no. 6, pp. 71-85 (in Russian). Erturk E. Numerical solutions of 2-D steady incompressible flow over a backward-facing step, Part I: High Reynolds number solutions, Computers & Fluids, 2008, vol. 37, no. 6, pp. 633-655. DOI: 10.1016/j.compfluid.2007.09.003 Poponin V.S., Kosheutov A.V., Grigor'ev V.P., Mel'nikova V.N. Method of spectral elements for resolving of plane viscous fluid dynamics problems on unstructured and nonshifted meshes, Izvestiya Tomskogo Politekhnicheskogo Universiteta, 2010, vol. 317, no. 2, pp. 31-36 (in Russian). Valencia A., Hinojosa L. Numerical solutions of pulsating flow and heat transfer characteristics in a channel with a backward-facing step, Heat Mass Transfer, 1997, vol. 32, no. 3, pp. 143-148. DOI: 10.1007/s002310050104 Batenko S.R., Terekhov V.I. Effect of dynamic prehistory on aerodynamics of a laminar separated flow in a channel behind a rectangular backward-facing step, Journal of Applied Mechanics and Technical Physics, 2002, vol. 43, no. 6, pp. 854-860. Abu-Nada E., Al-Sarkhi A., Akash B., Al-Hinti I. Heat transfer and fluid flow characteristics of separated flows encountered in a backward-facing step under the effect of suction and blowing, J. Heat Transfer, 2007, vol. 129, no. 11, pp. 1517-1528. DOI: 10.1115/1.2759973 Lewis R.W., Nithiarasu P., Seetharamu K.N. Fundamentals of the finite element method for heat and fluid flow, John Wiley & Sons, Ltd., 2004, 341 p. Teruel F.E., Fogliatto E. Numerical simulations of flow, heat transfer and conjugate heat transfer in the backward-facing step geometry, Mecanica Computacional, 2013, vol. 32, no. 39, pp. 3265-3278. Loitsyanskii L.G. Mekhanika zhidkosti i gaza (Fluid mechanics), Мoscow: Nauka, 1978, 736 p. Belotserkovskii O.M., Gushchin V.A., Shchennikov V.V. Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid, USSR Comp. Math. Math. Phys., 1975, vol. 15, no. 1, pp. 190-200. DOI: 10.1016/0041-5553(75)90146-9 Fomin A.A., Fomina L.N. The implicit line-by-line recurrence method in application to the solution of problems of incompressible viscous fluid dynamics, Komp'yuternye Issledovaniya i Modelirovanie, 2015, vol. 7, no. 1, pp. 35-50 (in Russian). Patankar S.V. Numerical heat transfer and fluid flow, Washington-New York-London: Hemisphere Publishing Corporation, 1980, 197 p. Translated under the title Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Мoscow: Energoatomizdat, 1984, 152 p. Fomin A.A., Fomina L.N. Acceleration of the line-by-line recurrent method in Krylov subspaces, Vestnik Tomskogo Gosudarstvennogo Universiteta. Matematika i Mekhanika, 2011, no. 2, pp. 45-54 (in Russian). Full text