Numerical Solution of the Problem of Incompressible Fluid Flow in a Plane Channel with a Backward-Facing Step at High Reynolds Numbers
- 8 Downloads
Numerical solutions of the problem of steady incompressible viscous fluid flow in a plane channel with a backward-facing step have been obtained by the grid method. The fluid motion is described by the Navier–Stokes equations in velocity-pressure variables. The main computations were performed on a uniform 6001 × 301 grid. The control-volume method of the second order in space was used for the difference approximation of the original equations. The results were validated for the range of Reynolds numbers (100 ≤ Re ≤ 3000) by comparing them with the experimental and theoretical data found in the literature. The stability of the computational algorithm at high Reynolds numbers was achieved by using a fine difference grid (a small grid step). The study has been carried out for a short channel at Reynolds numbers from 1000 to 10 000 with a step of 1000. A nonstandard structure of the primary vortex behind the step—the presence of numerous centers of rotation both inside the vortex and in the near-wall region under it—has been revealed. The number of centers of rotation in the primary recirculation zone is shown to grow with increasing Reynolds number. The profiles of the coefficients of friction and hydrodynamic resistance to the flow as a function of Reynolds number have also been analyzed. The results obtained can be useful for comparison and validation of the solutions of problems of such a type.
Key wordsNavier–Stokes equations plane channel with backward-facing step separated flow high Reynolds numbers
Unable to display preview. Download preview PDF.
- 8.Abu-Nada, E., Al-Sarkhi, A., Akash, B., and 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. https://doi.org/10.1115/1.2759973 CrossRefGoogle Scholar
- 10.Bruyatskii, E.V. and Kostin, A.G., Direct numerical simulation of flow in a plane channel with sudden expansion based on the Navier–Stokes equations, Prikl. Gidromekh., 2010, vol. 12, no. 1, pp. 11–27.Google Scholar
- 11.Poponin, V.S., Kosheutov, A.V., Grigor’ev, V.P., and Mel’nikova, V.N., A method of spectral elements for solving plane problems of viscous fluid dynamics on unshifted unstructured grids, Izv. Tomsk. Politekh. Univ., 2010, vol. 317, no. 2, pp. 31–36.Google Scholar
- 12.Fomin, A.A. and Fomina, L.N., Numerical simulation of the viscous incompressible fluid flow and heat transfer in a plane channel with backward-facing step, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, vol. 25, no. 2, pp. 280–294. https://doi.org/10.20537/vm150212 CrossRefzbMATHGoogle Scholar
- 13.Aleksin, V.A. and Manaenkova, T.A., Calculation of incompressible separated fluid flows, taking into account heat transfer, Izv. Mosk. Industr. Univ., 2011, no. 4 (24), pp. 28–38.Google Scholar
- 16.Cruchaga, M.A., A study of the backward-facing step problem using a generalized streamline formulation, Commun. Numer. Meth. Eng., 1998, vol. 14, no. 8, pp. 697–708. https://doi.org/10.1002/(SICI)1099-0887(199808)14:8%3c697::AID-CNM155%3e3.0.CO;2-0 CrossRefzbMATHGoogle Scholar
- 19.Mouza, A.A., Pantzali, M.N., Paras, S.V., and Tihon, J., Experimental and numerical study of backward-facing step flow, in Proceedings of the 5th National Chemical Engineering Conference, Thessaloniki, Greece, 2005. https://doi.org/philon.cheng.auth.gr/philon/site/sdocs/paper%205PESXM_Tihon.pdf.Google Scholar
- 21.Tihon, J., Pénkavová, V., Havlica, J., and 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. https://doi.org/10.1016/j.expthermflusci.2012.02.006 CrossRefGoogle Scholar
- 23.Teruel, F.E. and Fogliatto, E., Numerical simulations of flow, heat transfer and conjugate heat transfer in the backward-facing step geometry, Mec. Comput., 2013, vol. 32, no. 39, pp. 3265–3278. https://doi.org/www.cimec.org.ar/ojs/index.php/mc/article/viewFile/4551/4480.Google Scholar
- 34.Fomin, A.A. and Fomina, L.N., Acceleration of the line-by-line recurrent method in Krylov subspaces, Vestn. Tomsk Univ., Math. Mekh., 2011, no. 2, pp. 45–54.Google Scholar
- 35.Lashkin, S.V., Kozelkov, A.S., Yalozo, A.V., Gerasimov, V.Yu., and Zelensky, D.K., Efficiency analysis of parallel implementation of simple algorithm on multi-processor computers, Vychisl. Mekh. Splosh. Sred, 2016, vol. 9, no. 3, pp. 298–315. https://doi.org/10.7242/1999-6691/2016.9.3.25 Google Scholar