Skip to main content
Log in

Numerical simulation of a viscoelastic RANS turbulence model in a diffuser

  • Published:
Korea-Australia Rheology Journal Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Durbin P.A., 1995, Separated flow computations with the k–epsilon–v–squared model, AIAA J. 33, 659–664.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gyr A. and H.W. Bewersdorff, 1995, Drag Reduction of Turbulent Flows by Additives, Springer Science & Business Media, Dordrecht.

    Google Scholar 

  • Iaccarino, G., 2001, Predictions of a turbulent separated flow using commercial CFD codes, J. Fluids Eng.–Trans. ASME 123, 819–828.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Norouzi M., M.M. Shahmardan, A. Shahbani Zahiri, 2015, Bifurcation phenomenon of inertial viscoelastic flow through gradual expansions, Rheol. Acta 54, 423–435.

    Article  Google Scholar 

  • Oliveira P.J., 2003, Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries, J. Non–Newton. Fluid Mech. 114, 33–63.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alireza Riasi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13367-018-0024-8

Keywords

Navigation