Abstract
One of the newest viscoelastic RANS turbulence models for drag reducing flows with polymer additives is studied considering different rheological properties. A finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model is used to describe the viscoelastic effect of the polymer solutions and the \(k - \varepsilon - \overline {{v^2}} - f\) turbulence framework is applied for turbulence modelling. The geometry in this study is a twodimensional diffuser. The finite volume method (FVM) with a non-uniform collocated mesh is used to solve the momentum and constitutive equations. In order to evaluate the turbulence model, the flow is simulated with different parameters such as the Weissenberg number and the maximum polymer extensibility and compared with the experimental results qualitatively. The velocity profiles, pressure distribution, reattachment length, and the amount of the drag reduction predicted by the turbulence model are in line with the experimental results.
Similar content being viewed by others
References
Azad R.S. and S.Z. Kassab, 1989, Turbulent flow in a conical diffuser: Overview and implications, Phys. Fluids 1, 564–573.
Bird R.B., P.J. Dotson, and N.L. Johnson, 1980, Polymer solution rheology based on a finitely extensible bead–spring chain model, J. Non–Newton. Fluid Mech. 7, 213–235.
Burger E.D., W.R. Munk, and H.A. Wahl, 1982, Flow increase in the Trans Alaska Pipeline through use of a polymeric dragreducing additive, J. Pet. Technol. 34, 377–386.
Coelho P.M. and F.T Pinho, 2003, Vortex shedding in cylinder flow of shear–thinning fluids: I. Identification and demarcation of flow regimes, J. Non–Newton. Fluid Mech. 110, 143–176.
Coelho P.M. and F.T. Pinho, 2004, Vortex shedding in cylinder flow of shear–thinning fluids. III: Pressure measurements, J. Non–Newton. Fluid Mech. 121, 55–68.
Cruz D.O.A., F.T. Pinho, and P.J. Oliveira, 2005, Analytical solutions for fully developed laminar flow of some viscoelastic liquids with a Newtonian solvent contribution, J. Non–Newton. Fluid Mech. 132, 28–35.
Dales C., M.P. Escudier, and R.J. Poole, 2005, Asymmetry in the turbulent flow of a viscoelastic liquid through an axisymmetric sudden expansion, J. Non–Newton. Fluid Mech. 125, 61–70.
Dimitropoulos C.D., R. Sureshkumar, and A.N. Beris, 1998, Direct numerical simulation of viscoelastic turbulent channel flow exhibiting drag reduction: Effect of the variation of rheological parameters, J. Non–Newton. Fluid Mech. 79, 433–468.
Durbin P.A., 1995, Separated flow computations with the k–epsilon–v–squared model, AIAA J. 33, 659–664.
El–behery S.M. and M.H. Hamed, 2011, A comparative study of turbulence models performance for separating flow in a planar asymmetric diffuser, Comput. Fluids 44, 248–257.
Feng J. and L.G. Leal, 1997, Numerical simulations of the flow of dilute polymer solutions in a four–roll mill, J. Non–Newton. Fluid Mech. 72, 187–218.
Gyr A. and H.W. Bewersdorff, 1995, Drag Reduction of Turbulent Flows by Additives, Springer Science & Business Media, Dordrecht.
Iaccarino, G., 2001, Predictions of a turbulent separated flow using commercial CFD codes, J. Fluids Eng.–Trans. ASME 123, 819–828.
Iaccarino G., E.S.G. Shaqfeh, and Y. Dubief, 2010, Reynoldsaveraged modeling of polymer drag reduction in turbulent flows, J. Non–Newton. Fluid Mech. 165, 376–384.
Kalitzin G., G. Medic, G. Iaccarino, and P. Durbin, 2005, Nearwall behavior of RANS turbulence models and implications for wall functions, J. Comput. Phys. 204, 265–291.
Li C.F., R. Sureshkumar, and B. Khomami, 2006a, Influence of rheological parameters on polymer induced turbulent drag reduction, J. Non–Newton. Fluid Mech. 140, 23–40.
Li C.F., V.K. Gupta, R. Sureshkumar, and B. Khomami, 2006b, Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model, J. Non–Newton. Fluid Mech. 139, 177–189.
Lien F.S. and G. Kalitzin, 2001, Computations of transonic flow with the v2–f turbulence model, Int. J. Heat Fluid Flow 22, 53–61.
Lien F.S. and P.A. Durbin, 1996, Non–linear k–ε–v2 modeling with application to high–lift, Proceedings of the Summer Program 1996, Stanford, California, USA, 5–26.
Lu L., L. Zhong, and Y. Liu, 2016, Turbulence models assessment for separated flows in a rectangular asymmetric threedimensional diffuser, Eng. Comput. 33, 978–994.
Masoudian M., F.T. Pinho, K. Kim, and R. Sureshkumar, 2016, A RANS model for heat transfer reduction in viscoelastic turbulent flow, Int. J. Heat Mass Transf. 100, 332–346.
Masoudian M., K. Kim, F.T. Pinho, and R. Sureshkumar, 2013, A viscoelastic k–ε–v2–f turbulent flow model valid up to the maximum drag reduction limit, J. Non–Newton. Fluid Mech. 202, 99–111.
Min T., J.Y. Yoo, H. Choi, and D.D. Joseph, 2003, Drag reduction by polymer additives in a turbulent channel flow, J. Fluid Mech. 486, 213–238.
Norouzi M., M.M. Shahmardan, A. Shahbani Zahiri, 2015, Bifurcation phenomenon of inertial viscoelastic flow through gradual expansions, Rheol. Acta 54, 423–435.
Oliveira P.J., 2003, Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries, J. Non–Newton. Fluid Mech. 114, 33–63.
Park S.I., S.J. Lee, G.S. You, and J.C. Suh, 2014, An experimental study on tip vortex cavitation suppression in a marine propeller, J. Ship Res. 58, 157–167.
Paulo G.S., C.M. Oishi, M.F. Tom, M.A. Alves, and F.T. Pinho, 2014, Numerical solution of the FENE–CR model in complex flows, J. Non–Newton. Fluid Mech. 204, 50–61.
Pinho F.T., 2003, A GNF framework for turbulent flow models of drag reducing fluids and proposal for a k–ε type closure, J. Non–Newton. Fluid Mech. 114, 149–184.
Pinho F.T., B. Sadanandan, and R. Sureshkumar, 2008a, One equation model for turbulent channel flow with second order viscoelastic corrections, Flow Turbul. Combust. 81, 337–367.
Pinho F.T., C.F. Li, B.A. Younis, and R. Sureshkumar, 2008b, A low Reynolds number turbulence closure for viscoelastic fluids, J. Non–Newton. Fluid Mech. 154, 89–108.
Poole R.J. and M.P. Escudier, 2003, Turbulent flow of non–Newtonian liquids over a backward–facing step: Part II. Viscoelastic and shear–thinning liquids, J. Non–Newton. Fluid Mech. 109, 193–230.
Ptasinski P.K., B.J. Boersma, F.T.M. Nieuwstadt, M.A. Hulsen, B.H.A.A. Van Den Brule, and J.C.R. Hunt, 2003, Turbulent channel flow near maximum drag reduction: Simulations, experiments and mechanisms, J. Fluid Mech. 490, 251–291.
Resende P.R., F.T. Pinho, B.A. Younis, K. Kim, and R. Sureshkumar, 2013, Development of a low–Reynolds–number k–ω model for FENE–P fluids, Flow Turbul. Combust. 90, 69–94.
Resende P.R., K. Kim, B.A. Younis, R. Sureshkumar, and F.T. Pinho, 2011, A FENE–P k–ε turbulence model for low and intermediate regimes of polymer–induced drag reduction, J. Non–Newton. Fluid Mech. 166, 639–660.
Richter D., E.S.G. Shaqfeh, and G. Iaccarino, 2011, Numerical simulation of polymer injection in turbulent flow past a circular cylinder, J. Fluids Eng.–Trans. ASME 133, 104501.
Richter D., G. Iaccarino, and E.S.G. Shaqfeh, 2010, Simulations of three–dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers, J. Fluid Mech. 651, 415–442.
Thais L., A.E. Tejada–Martínez, T.B. Gatski, and G. Mompean, 2010, Temporal large eddy simulations of turbulent viscoelastic drag reduction flows, Phys. Fluids 22, 013103.
Tsukahara T., M. Motozawa, D. Tsurumi, and Y. Kawaguchi, 2013, PIV and DNS analyses of viscoelastic turbulent flows behind a rectangular orifice, Int. J. Heat Fluid Flow 41, 66–79.
Tsukahara T., T. Kawase, and Y. Kawaguchi, 2011, DNS of viscoelastic turbulent channel flow with rectangular orifice at low Reynolds number, Int. J. Heat Fluid Flow 32, 529–538.
Virk P.S., H.S. Mickley, and K.A. Smith, 1970, The ultimate asymptote and mean flow structure in Toms’ phenomenon, J. Appl. Mech.–Trans. ASME 37, 488–493.
White C.M. and M.G. Mungal, 2008, Mechanics and prediction of turbulent drag reduction with polymer additives, Annu. Rev. Fluid Mech. 40, 235–256.
Zhang Q., C.T. Hsiao, and G. Chahine, 2009, Numerical study of vortex cavitation supression with polymer injection, CAV2009–Proceedings of the 7th International Symposium on Cavitation, Ann Arbor, Michigan, USA, CAV2009–153.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Azad, S., Moghadam, H.A., Riasi, A. et al. Numerical simulation of a viscoelastic RANS turbulence model in a diffuser. Korea-Aust. Rheol. J. 30, 249–260 (2018). https://doi.org/10.1007/s13367-018-0024-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13367-018-0024-8