Numerical simulation of channel flow over a skewed equilateral cavity

• Autorzy: Kamel Abanoub G. , Haraz Eman H. , Hanna Sarwat N.

Identyfikatory

DOI

10.17512/jamcm.2020.3.03

• Języki publikacji: EN

Abstrakty

EN

In this paper, an incompressible, two-dimensional (2D), time-dependent, Newtonian, laminar, and internal channel fluid flow over a skewed equilateral cavity is simulated using the finite difference method (FDM) and alternating direction implicit (ADI) technique. Navier-Stokes equations are solved numerically in stream function-vorticity formulation. The goal of tackling this problem depends on its academic significance by studying the difference between lid-driven and shear-driven cavity flows in terms of the formation of Moffatt eddies at the sharp corner, also to obtain the length and intensity ratios of these counter-rotating vortices. The value of velocity components along the centerlines of the skewed cavity was revealed at low and intermediate Reynolds numbers (Re), typically (Re = 200 and 2000) at two different skew angles of mainly 30° and 45°. Likewise, the blocked-off regions’ method is used to deal with the geometry of the skewed cavity especially the sharp corners. Furthermore, as Re increases, the main vortex approaches the skewed cavity center and the counter-rotating vortices get bigger in size and intensity, and their number increases.

Słowa kluczowe

EN

finite difference method; incompressible flow; channel flow; lid-driven; shear-driven; skewed cavity; Navier-Stokes equations

PL

równanie Naviera-Stokesa; przepływ nieściśliwy; metoda różnic skończonych; przepływ kanałowy

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 3
• Strony: 29--43
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Kamel Abanoub G.

• Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University Alexandria 21544, Egypt

autor

Haraz Eman H.

• Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University Alexandria 21544, Egypt

autor

Hanna Sarwat N.

• Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University Alexandria 21544, Egypt

Bibliografia

• [1] Ghia, U., Ghia, K.N., & Shin, C. (1982). High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48(3), 387-411.
• [2] Gupta, M.M., & Kalita, J.C. (2005). A new paradigm for solving Navier-Stokes equations: streamfunction – velocity formulation. Journal of Computational Physics, 207(1), 52-68.
• [3] Ghadimi, P., Fard, M.Y., & Dashtimanesh, A. (2013). Application of an Iterative high order difference scheme along with an explicit system solver for solution of stream function-vorticity form of Navier-Stokes equations. Journal of Fluids Engineering, 135(4), 1401.
• [4] Zhang, T., Shi, B., & Chai, Z. (2010). Lattice Boltzmann simulation of lid-driven flow in trapezoidal cavities. Computers & Fluids, 39(10), 1977-1989.
• [5] Ahmed, M., & Kuhlmann, H.C. (2012). Flow instability in triangular lid-driven cavities with wall motion away from a rectangular corner. Fluid Dynamics Research, 44(2), 5501.
• [6] Abu-Nada, E., & Chamkha, A.J. (2010). Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid. European Journal of Mechanics-B/Fluids, 29(6), 472-482.
• [7] Botella, O., & Peyret, R. (1998). Benchmark spectral results on the lid-driven cavity flow. Computers & Fluids, 27(4), 421-433.
• [8] Ozalp, C., Pinarbasi, A., & Sahin, B. (2010). Experimental measurement of flow past cavities of different shapes. Experimental Thermal and Fluid Science, 34(5), 505-515.
• [9] Wahba, E. (2012). Steady flow simulations inside a driven cavity up to Reynolds number 35,000. Computers & Fluids, 66, 85-97.
• [10] Kuhlmann, H.C., & Romano, F. (2019). The lid-driven cavity. Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics. Springer, 233-309.
• [11] Romano, F., & Kuhlmann, H.C. (2017). Smoothed‐profile method for momentum and heat transfer in particulate flows. International Journal for Numerical Methods in Fluids, 83(6), 485-512.
• [12] Peaceman, D.W., Rachford, J., & Henry H. (1955). The numerical solution of parabolic and elliptic differential equations. Journal of the Society for Industrial and Applied Mathematics, 3(1), 28-41.
• [13] Demirdžić, I., Lilek, Ž., & Perić, M. (1992). Fluid flow and heat transfer test problems for non‐orthogonal grids: bench‐mark solutions. International Journal for Numerical Methods in Fluids, 15(3), 329-354.
• [14] Jaya Krishna, D., Basak, T., & Das, S.K. (2008). Numerical study of lid‐driven flow in orthogonal and skewed porous cavity. Communications in Numerical Methods in Engineering, 24(10), 815-831.
• [15] Mohapatra, R.C. (2016). Study on laminar two-dimensional lid-driven cavity flow with inclined side wall. Open Access Library Journal, 3(03), 1.
• [16] Thohura, S., Molla, M.M., & Sarker, M.M.A. (2019). Numerical simulation of non-Newtonian power-law fluid flow in a lid-driven skewed cavity. International Journal of Applied and Computational Mathematics, 5(1), 14.
• [17] Erturk, E., & Dursun, B. (2007). Numerical solutions of 2‐D steady incompressible flow in a driven skewed cavity. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift fur Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, 87(5), 377-392.
• [18] Romano, F., & Kuhlmann, H.C. (2017). Particle-boundary interaction in a shear-driven cavity flow. Theoretical and Computational Fluid Dynamics, 31(4), 427-445.
• [19] de Vicente, J., Basley, J., Meseguer-Garrido, F., Soria, J., & Theofilis, V. (2014). Three-dimensional instabilities over a rectangular open cavity: from linear stability analysis to experimentation. Journal of Fluid Mechanics, 748, 189-220.
• [20] Jenson, V. (1959). Viscous flow round a sphere at low Reynolds numbers (< 40). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 249(1258), 346-366.
• [21] Haese, P., & Teubner, M. (2002). Heat exchange in an attic space. International Journal of Heat and Mass Transfer, 45(25), 4925-4936.
• [22] Hoffmann, K.A., & Chiang, S.T. (2000). Computational Fluid Dynamics. Vol. I. Engineering Education System.
• [23] Tu, J., Yeoh, G.H., & Liu, C. (2018). Computational Fluid Dynamics: A Practical Approach. Butterworth-Heinemann.
• [24] Kamel, A.G., Haraz, E.H., & Hanna, S.N. (2020). Numerical simulation of three‐sided lid‐driven square cavity. Engineering Reports, 2(4), e12151.
• [25] Moffatt, H.K. (1964). Viscous and resistive eddies near a sharp corner. Journal of Fluid Mechanics, 18(1), 1-18.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).