{"title":"Transient Solution of an Incompressible Viscous Flow in a Channel with Sudden Expansion\/Contraction","authors":"Durga C. Dalal, Swapan K. Pandit","volume":67,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":1158,"pagesEnd":1170,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6810","abstract":"In this paper, a numerical study has been made to\nanalyze the transient 2-D flows of a viscous incompressible fluid\nthrough channels with forward or backward constriction. Problems\naddressed include flow through sudden contraction and sudden\nexpansion channel geometries with rounded and increasingly sharp\nreentrant corner. In both the cases, numerical results are presented for\nthe separation and reattachment points, streamlines, vorticity and\nflow patterns. A fourth order accurate compact scheme has been\nemployed to efficiently capture steady state solutions of the\ngoverning equations. It appears from our study that sharpness of the\nthroat in the channel is one of the important parameters to control the\nstrength and size of the separation zone without modifying the\ngeneral flow patterns. The comparison between the two cases shows\nthat the upstream geometry plays a significant role on vortex growth\ndynamics.","references":"[1] B. F. Armaly, F. Durst, J. C. F. Pereira and B. Schonung, \"Experimental\nand theoretical investigation of backward-facing step flow,\" Journal of\nFluid Mechanics, vol. 127, pp. 473-496, Feb. 1983.\n[2] F. Durst, A. Melling and J. H. Whitelaw, \"Low Reynolds number flow\nover a plane symmetrical sudden expansion,\" Journal of Fluid\nMechanics, vol. 64, no. 1, pp. 111-128, June 1974.\n[3] O. R. Tutty and T. J. Pedley, \"Oscillatory flow in a stepped channel,\nJournal of Fluid Mechanics,\" vol. 247, pp. 179-204, Feb. 1993.\n[4] I. J. Sobey, \"Observation of waves during oscillatory channel flow,\"\nJournal of Fluid Mechanics, vol. 151, pp. 395-426, Feb. 1985.\n[5] W. Cherdron, F. Durst and J. H. Whitelaw, \"Asymmetric flows and\ninstabilities in symmetric ducts with sudden expansions,\" Journal of\nFluid Mechanics, vol. 84, no. 1, pp. 13-31, Jan. 1978.\n[6] F. Durst and J. C. F. Pereira, \"Time dependent laminar backward-facing\nstep flow in a two dimensional duct,\" Trans. ASME: Journal of Fluids\nEngineering, vol. 110, no. 3, pp. 289-296, Sept. 1988.\n[7] F. Durst, J. C. F. Pereira and C. Tropea, \"The plane symmetric sudden\nexpansion flow at low Reynolds numbers,\" Journal of Fluid Mechanics,\nvol. 248, pp. 567-581, March 1993.\n[8] I. J. Sobey and P. G. Drazin, \"Bifurcations of two dimensional channel\nflows,\" Journal of Fluid Mechanics, vol. 171, pp. 263-287, Oct. 1986.\n[9] R. Wille, and H. Fernholz, \"Report on the first European Mechanics\nColloquium on the Coanda effect,\" Journal of Fluid Mechanics, vol. 23,\nno. 4, pp. 801-819, Dec. 1965.\n[10] M. S. Borgas and T. J. Pedley, \"Non-uniqueness and bifurcation in\nannular and planar channel flows,\" Journal of Fluid Mechanics, vol.\n214, pp. 229-250, May 1990.\n[11] M. Shapira, D. Degani and D. Weihs, \"Stability and existence of\nmultiple solutions for viscous flow in suddenly enlarged channels,\"\nComputers and Fluids, vol. 18, no. 3, pp. 239-258, 1990.\n[12] G. Pedrizetti, \"Unsteady tube flow over an expansion,\" Journal of Fluid\nMechanics, vol. 310, no. 5, pp. 89-111, March 1996.\n[13] P. F. A. Mancera and R. Hunt, \"Fourth order method for solving the\nnavier-stokes equations in a constricted channel,\" International Journal\nof Numerical Methods in Fluids, vol 25, no. 11, pp. 1119-1135, June\n1997.\n[14] P. F. A. Mancera, \"A study of numerical solution of the steady two\ndimensional navier-stokes equations in a constricted channel problem by\na compact fourth order method,\" Applied Mathematics and\nComputation, vol. 146, no. 2-3, pp. 771-790, Dec. 2003.\n[15] S. K. Pandit, J. C. Kalita and D. C. Dalal, \"A transient higher order\ncompact scheme for incompressible viscous flows on geometries beyond\nrectangular,\" Journal of Computational Physics, vol. 225, no. 1 pp.\n1100-1124, July 2007.\n[16] J. C. Tannehill, D. A. Anderson and R. H. Pletcher, Computational Fluid\nMechanics and Heat Transfer, Hemisphere Publishing Corporation,\nNew York, 1984.\n[17] C. T. Kelley, Iterative methods for Linear and Nonlinear Equations,\nSIAM Publications, Philadelphia, 1995.\n[18] Y. Saad, Iterative Methods for Sparse Linear Systems, PWS Publishing\nCompany, 1996.\n[19] H. V. D. Vorst, \"BiCGSTAB: A fast and smoothly converging variant of\nBiCG for the solution of nonsymmetric linear systems,\" SIAM J. Sci.\nComput., vol. 13, no. 2, pp. 631-644, 1992.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 67, 2012"}