Studi Pengembangan Model Turbulen κ-ε untuk Sirkulasi Arus II: Aliran Turbulen Dua Dimensi pada Saluran Ekspansi
Abstract
Makalah ini menyajikan hasil studi pemodelan mengenai pola aliran turbulen 2 dimensi pada sebuah saluran yang mengalami ekspansi dengan memanfaatkan model depth averaged κ-ε. Model numerik dikembangkan berdasarkan metoda beda hingga, dimana untuk pemecahan persamaan hidrodinamik digunakan kombinasi metoda ekplisit Mac Cormack dan metoda pemisahan operator splitting. Sebagai tracer untuk melakukan visualisasi struktur aliran digunakan model transport kualitas air. Suku konveksi, difusi, dan reaksi diselesaikan dengan skema QUICKEST, Central Scheme, dan Euler Scheme. Hasil yang dicapai model dalam mensimulasikan pola arus untuk kasus saluran lurus dan ekspansi menunjukan tingkat kesesuaian yang cukup baik dengan hasil pengukuran di Laboratorium. Dibandingkan dengan model non turbulen, hasil model menunjukkan peningkatan akurasi yang signifikan dalam hal besar kecepatan arus, pola arus dan sebaran konstituent kualitas air, terutama pada zona resirkulasi. Model dapat mensimulasikan pola sirkulasi arus dan terbentuknya vorteks pada zona sirkulasi. Namun demikian, untuk aliran dengan bilangan Reynold cukup rendah, osilasi dan ketidakstabilan numerik masih menjadi kendala.References
Adam, E. W., J.P. Johnston and J.K. Eaton, Experiments on the structure of Turbulent Reattaching Flow, ReportbMD-43, Thermosciences division-Dept of Mech Eng.-Stanford Univ., California, 1984.
M. Syahril B. K. And Claud Rey, Visualization of Backward Facing Step Flows, Proc. of Euromech 276, Dynamics of The Urban Atmosphere, Nantes, Perancis, 1992.
Bradshaw, P. and F.Y. Wong, The Reattachment and Ralaxation of Turbulent Shear Layer, JFM, 52, pp113-135, 1972.
Chandrasuda C. and Bradshaw, Turbulent Structure of Reattaching Mixing Layer, JFM, 110, pp171-194, 1981.
Hunt, J.C.R., Coherent Structures-Comments on Mechanism, Seminar Proceeding of Von Karman Institute for Fluid Dynamics, Lecture Series
-03, 1989.
Hussain, A.K.M.F and W.C. Reynolds, The Mechanism of Organized Wave in Turbulent Shear Flow, JFM, 41, part2, 241-258, 1973.
M. Syahril B.K, R.A. Rahayu, H. Kardana and M. Cahyono, Numerical Simulation of Two Dimensional Turbulent Flow in Division Box of an Irrigation Channel Based on .Model, Proceeding of International conference on Fluid and Thermal Energy Conversion, Jakarta, December 10th-14th, 2006.
M. Syahril B.K, R.A. Rahayu, H. Kardana and M. Cahyono, Development Of Turbulent .Model for Assesing Water Quality Distribution in Reservoir, Research Report, Asahi ResearchGrant, 2006.
M. Syahril B. K., M Cahyono & Eka O. N., Development Study of Turbulent K-E Model for Recirculation flow I: Two Dimension Flow in Reservoir, Proceeding ITB, 2004.
M. Syahril B. K., M. Cahyono, Hasan B & Noorsalam, Optimalization on Water Distibution for Fishery Ponds in Indramayu, research report, Dinas Perikanan TK II Indramayu-LP ITB, 1999.
Launder, B.E., and Spalding, D. B., Lectures in Mathematical Models and Turbulence, Academic Press Inc, New York, 1972.
Chapman, R.S, and Kuo, C.Y., Application of the two equation - Turbulence Model to a Two Dimentional, Steady, Free Surface Flow Problem with Separation, International Journal for Numerical Methods in Fluids, Vol.5, 257-268, 1985.
Rastogi, A.K., and Rodi, W., Prediction of Heat and Mass Transfer in Open Channels, J. Hydraulics Div., ASCE, 104 (HY3), 397-420, 1978.
Rastogi, A.K., Private communication with W. Rodi (1980). Turbulence Models and Their Application in Hydraulics: a State of The art review, Presented by IAHR-Section on Fundamentals of Divison II: Experimental and Mathematical Fluid Dynamics, Delft, Netherland, P.50, 1978.
Abbott, M.B., Basco, D.R., Computational Fluid Dynamics an Introduction for Engineers, Longman Scientific & Technical, England, 1989.
Anderson JR, J.D., Computational Fluid Dynamics, McGraw-Hill International Editions, New York, 1995.
Blackwelder, R.F. and Haritonidis, Scaling of Bursting Frequency in Turbulent boundary Layer, JFM, 132, 87-103, 1983
B. Mohammadi & O. Pironneau, Analysis of The K-Epsilon Turbulencve Model, John Wiley & Sons, 1994.
Chapra, Steven C., Surface Water Quality Modelling, The McGraw-Hill Companies Inc., Si
Driver, D.M and H. Lee Seegmiller, Features of Reattacing Turbulent Shear Layer in Divergent Channel, AIAA Journal, 23(21), 1985.
Falconer, R.A., Guiyi, Li, Modelling Tidal Flows in an Island's Wake Using a Two Equation Turbulence Model, Journal of Fluid Mechanics, 1992, 43-53.
Fletcher, C.A.J., Computational Techniques for Fluid Dynamics Volume I-II, Second Edition, Springer-Verlag, London, 1990.
Hirt, C.W., Turbulence Modelling, Flow Science, Inc.
Hoffman, J.D., Numerical Methods for Engineers and Scientists, McGraw-Hill, Singapore, 1993.
Hussain, A.K.M.F and A.R. Clark, On the Coherent Structure of the Axisymmetric Mixing Layer: a Flow Visualization Study, JFM, 104, 263-294, 1981.
Kim, J.J, On the Structure of Wall Bounded Turbulent Flows, Physic of Fluids, 26(8), 2088-2092, 1983.
Launder, B.E., and Spalding, D. B., Thenumerical Computation of Turbulent Flows, Computer Method in applied Mechanics and engineering, 3, 269-289, 1974.
M. Syahril Badri K., M Martono, Hang Tuah & S Legowo, Experimental Study on Spectral Behaviour on Backward Facing Step Flows: Rough
Wall Boundary Layer Cases, The Sixth Asian Congress of Fluid Mechanics,Singapore, pp. 1376-1379, 1995.
M. Syahril B. K. And Hang Tuah, Backward Facing Step Flow: The Effect of Initial Condition on The reattachment of Turbulent Shear Layer, Proc. of 1st International Symposium on Fluid Dynamic & Energy, Bali Indonesia, 1994.
Ni, H.Q., Shen, Y.M., Zhou, L.X., Duan, J.H., Numerical Simulatoin of Multiple Circulating Flows Using A Depth-Averaged - Turbulence Model For The Entire Field, The Sixth Asian Congress of Fluid Mechanics,Singapore, pp. 801-803, 1995.
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., Numerical Recipes The Art of Scientific Computing, Cambridge University Press, New York, 1986.
Rijn, Leo C. van, Principles of Fluid Flow and Surface Waves in River, Estuaries, Seas, and Oceans, Aqua Publications, The Netherlands, 1990.
Strickland, J.H and Simpson, R.L, Bursting Frequencies Obtained From Wall Shear Stress Fluctuations in a Turbulent Boundary Layer, Physics Fluids, 18(2), pp 306-308.
Westphal, R.V, J.P. Johnston and J.K. Eaton, Experimental Study of Flow Reattachment in a Single Sided Sudden Expansion, NASA Contractor Report 3765, 1984.
Wilcox, C. David, Turbulence Modeling For CFD, DCW Industries, Inc, California, 1994.
Younus, Muhammad, Computation of Free-Surface Flow By Using Depth-Averaged - Turbulence Model, Disertasi, Department of Civil
and Environmental Engineering, Washington State University, 1993.
