Numerical Investigation of Internal Flow Transition Using Modified γ-Reθ Model

Document Type : Research Article

Authors

1 Tarbiat Modares University, Tehran, Iran

2 Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

3 Sharif University of Technology

Abstract

The numerical investigation of Transition is one of the challenging issues in turbulence modeling. In the present study, the coefficients of the γ-Reθ model are modified based on the physics of internal flow transition to capture the entrance length properly. To validate the model, the internal flow is simulated using six test cases. A 3D duct, two smooth axisymmetric pipes, a 3D stenosis pipe, two parallel plates, and the backward-facing step configurations are considered at different Reynolds numbers from 2´103 to 3´105. The flow variables, including the average velocity field, friction factor, fully developed friction factor, and the reattachment length are compared against the experimental, theoretical and large eddy simulation results. By comparing the results of average velocity against the semi-empirical relations and experimental data using new coefficients, it is observed the model can estimate the entrance length in accordance with experiments. The earlier coefficients lead to a reduction of entrance length by increasing the Reynolds number. Furthermore, the error percentages reduce by more than 7.6 and 26.7 percent using new coefficients rather than earlier models for fully developed friction factor and reattachment length, respectively.

Keywords

Main Subjects

References

[1] R. Langtry, F. Menter, Transition modeling for general CFD applications in aeronautics, in:  43rd AIAA aerospace sciences meeting and exhibit, 2005, pp. 522.
[2] R.B. Langtry, F. Menter, S. Likki, Y. Suzen, P. Huang, S. Völker, A correlation-based transition model using local variables—part II: test cases and industrial applications, Journal of Turbomachinery, 128(3) (2006) 423-434.
[3] C. Farell, S. Youssef, Experiments on turbulence management using screens and honeycombs, Journal of fluids engineering, 118(1) (1996) 26-32.
[4] R. Thompson, I. Hamilton, Harris, S. Berry, T. Horvath, R. Nowak, Hypersonic boundary layer transition for X-33 phase II vehicle, in:  36th AIAA Aerospace Sciences Meeting and Exhibit, 1997, pp. 867.
[5] H. Schlichting, K. Gersten, Boundary-layer theory, Springer, 2016.
[6] M.V. Morkovin, On the many faces of transition, in:  Viscous drag reduction, Springer, 1969, pp. 1-31.
[7] E. Malkiel, R. Mayle, Transition in a separation bubble, in:  ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition, American Society of Mechanical Engineers, 1995, pp. V001T001A003-V001T001A003.
[8] F. Menter, R. Langtry, S. Volker, Transition modelling for general purpose CFD codes, Flow, turbulence and combustion, 77(1-4) (2006) 303-277.
[9] D.K. Walters, D. Cokljat, A three-equation eddy-viscosity model for Reynolds-averaged Navier─Stokes simulations of transitional flow, Journal of fluids engineering, 130(12) (2008) 121401.
[10] S. Aftab, A.M. Rafie, N. Razak, K. Ahmad, Turbulence model selection for low reynolds number flows, PloS one, 11(4) (2016) e0153755.
[11] A. Hellsten, Some improvements in Menter's k-omega SST turbulence model, in:  29th AIAA, Fluid Dynamics Conference, 1998, pp. 2554.
[12] R.B. Langtry, F.R. Menter, Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes, AIAA journal, 47(12) (2009) 2894-2906.
[13] F. Menter, T. Esch, Elements of industrial heat transfer predictions, in:  16th Brazilian Congress of Mechanical Engineering (COBEM), sn, 2001.
[14] F.R. Menter, M. Kuntz, R. Langtry, Ten years of industrial experience with the SST turbulence model, Turbulence, heat and mass transfer, 4(1) (2003) 625-632.
[15] F.R. Menter, R.B. Langtry, S. Likki, Y. Suzen, P. Huang, S. Volker, A correlation-based transition model using local variables─part I: model formulation, Journal of turbomachinery, 128(3) (2006) 413-422.
[16] A. Draad, F. Nieuwstadt, The Earth's rotation and laminar pipe flow, Journal of Fluid Mechanics, 361 (1998) 297-308.
[17] A.A. Draad, G. Kuiken, F. Nieuwstadt, Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids, Journal of Fluid Mechanics, 377 (1998) 267-312.
[18] J. Abraham, E. Sparrow, J. Tong, Breakdown of laminar pipe flow into transitional intermittency and subsequent attainment of fully developed intermittent or turbulent flow, Numerical Heat Transfer, Part B: Fundamentals, 54(2) (2008) 103-115.
[19] J. Abraham, E. Sparrow, J. Tong, W. Minkowycz, Intermittent Flow Modeling: Part I─Hydrodynamic and Thermal Modeling of Steady, Intermittent Flows in Constant Area Ducts, in:  2010 14th International Heat Transfer Conference, American Society of Mechanical Engineers, 2010, pp. 659-667.
[20] J. Abraham, E. Sparrow, J. Tong, W. Minkowycz, Intermittent Flow Modeling: Part 2─Time-Varying Flows and Flows in Variable Area Ducts, in:  2010 14th International Heat Transfer Conference, American Society of Mechanical Engineers, 2010, pp. 625-633.
[21] R. Lovik, J. Abraham, W. Minkowycz, E. Sparrow, Laminarization and turbulentization in a pulsatile pipe flow, Numerical Heat Transfer, Part A: Applications, 56(11) (2009) 861-879.
[22] J. Abraham, E. Sparrow, W. Minkowycz, R. Ramazani-Rend, J. Tong, Modeling internal flows by an extended menter transition model, Turbulence: Theory, Types, and Simulation (Nova, New York, 2011),  (2011).
[23] E. Kahramanoglu.lu, S. Sezen, S. Bayraktar, Computational fluid dynamics analyses on the hydrodynamic entry length in internal flows, Pamukkale University Journal of Engineering Sciences, 23(4) (2017).
[24] S.S. Varghese, S.H. Frankel, P.F. Fischer, Modeling transition to turbulence in eccentric stenotic flows, Journal of biomechanical engineering, 130(1) (2008) 014503.
[25] S.S. Varghese, S.H. Frankel, Numerical modeling of pulsatile turbulent flow in stenotic vessels, Journal of biomechanical engineering, 125(4) (2003) 445-460.
[26] F. Tan, G. Soloperto, S. Bashford, N. Wood, S. Thom, A. Hughes, X. Xu, Analysis of flow disturbance in a stenosed carotid artery bifurcation using two-equation transitional and turbulence models, Journal of biomechanical engineering, 130(6) (2008).
[27] A. Melling, J. Whitelaw, Turbulent flow in a rectangular duct, Journal of Fluid Mechanics, 78(2) (1976) 289-315.
[28] F. Anselmet, F. Ternat, M. Amielh, O. Boiron, P. Boyer, L. Pietri, Axial development of the mean flow in the entrance region of turbulent pipe and duct flows, Comptes Rendus Mecanique, 337(8) (2009) 573.
[29] S.A. Ahmed, D.P. Giddens, Velocity measurements in steady flow through axisymmetric stenoses at moderate Reynolds numbers, Journal of biomechanics, 16(7) (1983) 505-516.
[30] J. Elcner, F. Lizal, J. Jedelsky, J. Tuhovcak, M. Jicha, Laminar-turbulent transition in a constricted tube: Comparison of Reynolds-averaged Navier–Stokes turbulence models and large eddy simulation with experiments, Advances in Mechanical Engineering, 11(5) (2019) 1687814019852261.
[31] B. Ruck, B. Makiola, Flow separation over the inclined step, in:  Physics of Separated Flows—Numerical, Experimental, and Theoretical Aspects, Springer, 1993, pp. 47-55.
[32] G. Round, An explicit approximation for the friction factor‐Reynolds number relation for rough and smooth pipes, The Canadian Journal of Chemical Engineering, 58(1) (1980) 122-123.
[33] D. Flórez-Orrego, W. Arias, D. López, H. Velásquez, Experimental and CFD study of a single phase cone-shaped helical coiled heat exchanger: an empirical correlation, in:  Proceedings of the 25th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems, 2012, pp. 375-394.
[34] C. Habchi, S. Russeil, D. Bougeard, J.-L. Harion, T. Lemenand, A. Ghanem, D. Della Valle, H. Peerhossaini, Partitioned solver for strongly coupled fluid–structure interaction, Computers & Fluids, 71 (2013) 306-319.
[35] I.B. Celik, U. Ghia, P.J. Roache, Procedure for estimation and reporting of uncertainty due to discretization in {CFD} applications, Journal of fluids engineering, 130(7) (2008).
[36] F. Gessner, J. Po, A. Emery, Measurements of developing turbulent flow in a square duct, in:  Turbulent Shear Flows I, Springer, 1979, pp. 119-136.
[37] F. Durst, B. Ünsal, Forced laminar-to-turbulent transition of pipe flows, Journal of Fluid Mechanics, 560 (2006) 449-464.
[38] D. Drikakis, G. Papadopoulos, Experimental and numerical investigation of laminar-to-transitional pipe flow past a sudden expansion, in:  American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED, 1996, pp. 679-684.
[39] M. Wimmer, J. Zierep, Transition from Taylor vortices to cross-flow instabilities, Acta mechanica, 140(1-2) (2000) 17-30.
[40] H.H. Choi, V.T. Nguyen, J. Nguyen, Numerical investigation of backward facing step flow over various step angles, Procedia Engineering, 154 (2016) 420-425.
Amirkabir Journal of Mechanical Engineering
Volume 54, Issue 7
October 2022
Pages 1533-1552

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