Abstract
The paper examines the impact of different modelling choices in second-moment closures by assessing model performance in predicting 3-D duct flows. The test-cases (developing flow in a square duct (Gessner and Emery, ASME J. Fluids Eng. 103, 445–455, 1981), circular-to-rectangular transition-duct (Davis and Gessner, AIAA J. 30, 367–375, 1992), and s-duct with large separation (Wellborn et al., J. Prop. Power 10, 668–675 1994) include progressively more complex strains. Comparison of experimental data with selected 7-equation models (6 Reynolds-stress-transport and 1 scale-determining equations), which differ in the closure of the velocity/pressure-gradient tensor π i j , suggests that rapid redistribution controls separation and secondary-flow prediction, whereas, inclusion of pressure-diffusion modelling improves reattachment and relaxation behaviour.
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References
Adams, J.C., Brainerd, W.S., Hendrickson, R.A., Maine, R.E., Martin, J.T., Smith, B.T.: The Fortran 2003 Handbook. Springer, New York (2009). doi:10.1007/978-1-84628-746-6
AERODYNAMICS: aerodynamics (a library and software package for computational aerodynamics). http://sourceforge.net/projects/aerodynamics (2015). (version 1.0.3)
Aloui, F., Berrich, E., Pierrat, D.: Experimental and numerical investigations of a turbulent flow behavior in isolated and nonisolated conical diffusers. ASME J. Fluids Eng. 133, 011201 (2011). doi:10.1115/1.4003236
Anxionnaz-Minvielle, Z., Cabassud, M., Gourdon, C., Tochon, P.: Influence of the meandering channel geometry on the thermo-hydraulic performances of an intensified heat exchanger/reactor. Chem. Eng. Processing 73, 67–80 (2013)
Atkins, H., Casper, J.: Nonreflective boundary conditions for high-order methods. AIAA J. 32, 512–518 (1994)
Ben Nasr, N., Gerolymos, G.A., Vallet, I.: Low-diffusion approximate Riemann solvers for Reynolds-stress transport. J. Comp. Phys. 268, 186–235 (2014). doi:10.1016/j.jcp.2014.02.010
Bradshaw, P.: Compressible turbulent shear layers. Ann. Rev. Fluid Mech. 9, 33–54 (1977)
Bradshaw, P.: Turbulent secondary flows. Ann. Rev. Fluid Mech. 19, 53–74 (1987)
Brundrett, E., Baines, W.D.: The production and diffusion of vorticity in duct flow. J. Fluid Mech. 19, 375–394 (1964)
Chakravarthy, S.R.: Relaxation methods for unfactored implicit upwind schemes. In: AIAA Paper 1984–0165 (1984)
Chang, D., Tavoularis, S.: Numerical simulation of turbulent flow in a 37-rod bundle. Nucl. Eng. Des. 237, 575–590 (2007)
Chaouat, B., Schiestel, R.: A new partially integrated transport model for subgrid-scale stresses and dissipation rates for turbulent developing flows. Phys. Fluids 17(6), 065106 (2005)
Chaouat, B., Schiestel, R.: From single-scale turbulence models to multiple-scale and subgrid-scale models by fourier transform. Theor. Comp. Fluid Dyn. 21, 201–229 (2007)
Chassaing, J.C., Gerolymos, G.A., Vallet, I.: Reynolds-stress model dual-time-stepping computation of unsteady 3-D flows. AIAA J. 41(10), 1882–1894 (2003)
Craft, T.J., Launder, B.: Principles and performance of TCL-based second-moment closures. Flow Turb. Comb. 66, 355–372 (2001)
Cumpsty, N.A.: Compressor Aerodynamics. Addison Wesley Longman, Essex[GBR] (1989)
Daly, B.J., Harlow, F.H.: Transport equations in turbulence. Phys. Fluids 13, 2634–2649 (1970)
Davis, D.O.: Experimental investigation of turbulent flow through a circular-to-rectangular transition duct. PhD, University of Washington, Seattle [ WA, USA].(also NASA–TM–105210) (1991)
Davis, D.O., Gessner, F.B.: Experimental investigation of turbulent flow through a circular to rectangular duct. AIAA J. 30(2), 367–375 (1992)
Délery, J.M.: Experimental investigation of turbulence properties in transonic shock/boundary-layer interactions. AIAA J. 21, 180–185 (1983). (also AIAA Paper 1981–1245, 1981)
Délery, J.M.: Robert Legendre and Henri Werlé: Toward the elucidation of 3-D separation. Ann. Rev. Fluid Mech. 33, 129–154 (2001)
Demuren, A.O.: Calculation of turbulence-driven secondary motion in ducts with arbitrary cross section. AIAA J. 29(4), 531–537 (1991)
Egorov, Y., Menter, F.R., Lechner, R., Cokljat, D.: The scale-adaptive simulation method for unsteady turbulent flow predictions — ii — application to complex flows. Flow Turb. Comb. 85, 139–165 (2010)
ERCOFTAC: European Research Community on Flow, Turbulence and Combustion Database: Classic Collection. http://cfd.mace.manchester.ac.uk/ercoftac/ (1999). Accessed 5 Nov 2014
Fujii, S., Okiishi, T.H: Curved diffusing annulus turbulent boundary-layer development. J. Aircraft 9(2), 97–98 (1972)
Gerolymos, G.A., Joly, S., Mallet, M., Vallet, I.: Reynolds-stress model flow prediction in aircraft-engine intake double-S-shaped duct. J. Aircraft 47(4), 1368–1381 (2010). doi:10.2514/1.47538
Gerolymos, G.A., Lo, C., Vallet, I.: Tensorial representations of reynolds-stress pressure-strain redistribution. ASME J. Appl. Mech 79(4), 044506 (2012). doi: 10.1115/1.4005558
Gerolymos, G.A., Lo, C., Vallet, I., Younis, B.A.: Term-by-term analysis of near-wall second moment closures. AIAA J. 50(12), 2848–2864 (2012). doi: 10.2514/1.J051654
Gerolymos, G.A., Sauret, E., Vallet, I.: Contribution to the single-point-closure Reynolds-stress modelling of inhomogeneous flow. Theor. Comp. Fluid Dyn 17(5–6), 407–431 (2004a)
Gerolymos, G.A., Sauret, E., Vallet, I.: Influence of inflow-turbulence in shock-wave/turbulent-boundary-layer interaction computations. AIAA J. 42(6), 1101–1106 (2004b)
Gerolymos, G.A., Sauret, E., Vallet, I.: Oblique-shock-wave/boundary-layer interaction using near-wall Reynolds-stress models. AIAA J. 42(6), 1089–1100 (2004c)
Gerolymos, G.A., Sénéchal, D., Vallet, I.: Wall effects on pressure fluctuations in turbulent channel flow. J. Fluid Mech 720, 15–65 (2013). doi: 10.1017/jfm.2012.633
Gerolymos, G.A., Tsanga, G.: Biharmonic 3-D grid generation for axial turbomachinery with tip-clearance. J. Prop. Power 15(3), 476–479 (1999)
Gerolymos, G.A., Vallet, I.: Implicit computation of the 3-D compressible Navier-Stokes equations using k−ε turbulence closure. AIAA J. 34(7), 1321–1330 (1996)
Gerolymos, G.A., Vallet, I.: Wall-normal-free near-wall Reynolds-stress closure for 3-D compressible separated flows. AIAA J. 39(10), 1833–1842 (2001)
Gerolymos, G.A., Vallet, I.: Mean-flow-multigrid for implicit reynolds-stress-model computations. AIAA J. 43(9), 1887–1898 (2005)
Gerolymos, G.A., Vallet, I.: Implicit mean-flow-multigrid algorithms for Reynolds-stress-model computations of 3-D anisotropy-driven and compressible flows. Int. J. Num. Meth. Fluids 61(2), 185–219 (2009). doi:10.1002/fld.1945
Gerolymos, G.A., Vallet, I.: Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow. J. Fluid Mech. 757, 701–746 (2014). doi:10.1017/jfm.2014.431
Gessner, F.B., Emery, A.F.: The numerical prediction of developing turbulent flow in rectangular ducts. ASME J. Fluids Eng 103, 445–455 (1981). doi: 10.1080/10618562.2013.772984
Gessner, F.B., Jones, J.B.: On some aspects of fully-develped turbulent flow in rectangular channels. J. Fluid Mech. 23, 689–713 (1965)
Gessner, F.B., Po, J.K., Emery, A.F.: Measurements of developing turbulent flow in a square duct. In: Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds.) Turbulent Shear Flows I — Selected Papers from the 1. International Symposium on Turbulent Shear Flows, The Pennsylvania State University, University Park, Pennsylvania, USA, April 18–20, 1977, pp. 119–136 Springer, Berlin [DEU] (1979)
Gibson, M.M., Launder, B.E.: Ground effects on pressure fluctuations in the atmospheric boundary-layer. J. Fluid Mech. 86, 491–511 (1978)
Girimaji, S.S.: Partially-averaged navier-stokes model for turbulence: a reynolds-averaged navier-stokes to direct numerical simulation bridging method. ASME J. Appl. Mech. 73, 422–429 (2006)
Girimaji, S.S., Jeong, E., Srinivasan, R.: Partially-averaged navier-stokes method for turbulence: fixed point analysis and comparison with unsteady partially averagde navier-stokes. ASME J. Appl. Mech. 73, 413–421 (2006)
Hanjalić, K.: Advanced turbulence closure models: A view of current status and future prospects. Int. J. Heat Fluid Flow 15, 178–203 (1994)
Hanjalić, K., Launder, B.E.: Contribution towards a Reynolds-stress closure for low-reynolds-number turbulence. J. Fluid Mech 74, 593–610 (1976)
Harloff, G.J., Smith, C.F., Bruns, J.E., DeBonis, J.R.: Navier-Stokes analysis of three-dimensional s-ducts. J. Aircraft 30(4), 526–533 (1993)
Jakirlić, S., Maduta, R.: Extending the bounds of steady rans closures: Toward an instability-sensitive reynolds-stress model. Int. J. Heat Fluid Flow 51, 175–194 (2015)
Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes. J. Comp. Phys. 126, 202–228 (1996)
Kovasznay, L.S.G., Kibens, V., Blackwelder, R.F.: Large-scale motion in the intermittent region of a turbulent boundary-layer. J. Fluid Mech. 41, 283–325 (1970)
Launder, B.E., Sharma, B.I.: Application of the energy dissipation model of turbulence to the calculation of flows near a spinning disk. Lett. Heat Mass Transfer 1, 131–138 (1974)
Launder, B.E., Shima, N.: 2-moment closure for the near-wall sublayer: Development and application. AIAA J. 27(10), 1319–1325 (1989)
Leschziner, M.A.: Turbulence modelling for separating flows with anisotropy-resolving closures. Phil. Trans. Roy. Soc. London A 358, 3247–3277 (2000)
Lien, F.S., Leschziner, M.A.: Second moment closure for 3-D turbulent flow around and within complex geometries. Comp. Fluids 25, 237–262 (1996)
Lumley, J.L.: Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176 (1978)
Lumley, J.L., Yang, Z., Shih, T.H.: A length-scale equation. Flow Turb. Comb. 63, 1–21 (1999)
Mansour, N.N., Kim, J., Moin, P.: Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech 194, 15–44 (1988)
Menter, F.R., Egorov, Y.: The scale-adaptive simulation method for unsteady turbulent flow predictions — i — theory and model description. Flow Turb. Comb. 85, 113–138 (2010)
Olsen, M.E., Coakley, T.J.: The lag model, a turbulence model for nonequilibrium flows. AIAA Paper, 2001–2564 (2001)
Österlund, J.M., Johansson, A.V., Nagib, H.M., Hites, M.H.: A note on the overlap region in turbulent boundary-layers. Phys. Fluids 12(1), 1–4 (2000)
Po, J.K.: Developing turbulent flow in the entrance region of a square duct. MSc, Washington University, Seattle (1975)
Reichert, B.A.: A study of high-speed flows in an aircraft transition duct. PhD, Iowa State University, Ames (1991). (also NASA–TM–104449)
Reif, B.P., Andersson, H.I.: Prediction of turbulence-generated secondary mean flow in a square duct. Flow Turb. Comb 68, 41–61 (2002)
Rumsey, C.L.: Apparent transition behavior of widely-used turbulence models. Int. J. Heat Fluid Flow 28, 1460–1471 (2007)
Rumsey, C.L.: Consistency, verification, and validation of turbulence models for reynolds-averaged navier-stokes applications. IMechE J. Aerosp. Eng. 224(11), 1211–1218 (2010)
Sauret, E., Vallet, I.: Near-wall turbulent pressure diffusion modelling and influence in 3-D secondary flows. ASME J. Fluids Eng. 129(5), 634–642 (2007)
Schiestel, R., Dejoan, A.: Towards a new partially integrated transport model for coarse grid unsteady turbulent flow simulations. Theor. Comp. Fluid Dyn. 18, 443–468 (2005)
Shima, N.: Prediction of turbulent boundary-layer flows with a 2-moment closure — Part 1 — Effects of periodic pressure gradient, wall transpiration, and free-stream turbulence. ASME J. Fluids Eng. 115, 56–63 (1993)
Simpson, R.L.: Turbulent boundary-layer separation. Ann. Rev. Fluid Mech. 21, 205–234 (1989)
Smits, A.J., Young, S.T.B., Bradshaw, P.: The effect of high surface curvature on turbulent boundary-layers. J. Fluid Mech. 94, 209–242 (1979)
So, R.M.C., Mellor, G.L.: Turbulent boundary-layers with large stramline curvature effects. J. Appl. Math. Phys. 29, 54–74 (1978)
So, R.M.C., Yuan, S.P.: A geometry independent near-wall Reynolds-stress closure. Int. J. Eng. Sci. 37, 33–57 (1999)
Sotiropoulos, F., Patel, V.C.: Prediction of turbulent flow through a transition duct using a 2-moment closure. AIAA J. 32(11), 2194–2204 (1994)
Sotiropoulos, F., Patel, V.C.: Application of Reynolds-stress transport models to stern and wake flows. J. Ship Res. 39(4), 263–283 (1995)
Sotiropoulos, F., Patel, V.C.: Turbulence anisotropy and near-wall modeling in predicting 3-D shear flows. AIAA J. 33(3), 504–514 (1995)
Speziale, C.G.: Turbulence modeling for time-dependent RANS and VLES: A review. AIAA J. 36(2), 173–184 (1998)
Vallet, I.: Reynolds-stress modelling of 3-D secondary flows with emphasis on turbulent diffusion closure. ASME J. Appl. Mech. 74(6), 1142–1156 (2007)
Vallet, I.: Reynolds-stress modelling of M = 2.25 shock-wave/turbulent-boundary-layer interaction. Int. J. Num. Meth. Fluids 56(5), 525–555 (2008)
Wellborn, S.R., Okiishi, T.H., Reichert, B.A.: A study of compressible flow through a diffusing S-duct. In: Techenical Mem. NASA–TM–1993–106411, NASA, Lewis Research Center, Cleveland [OH, USA] (1993)
Wellborn, S.R., Reichert, B.A., Okiishi, T.H.: Study of the compressible flow in a diffusing S-duct. J. Prop. Power 10(5), 668–675 (1994)
White, M.F.: Viscous Fluid Flow, 2nd edn. McGraw-Hill, New York (1991)
Wilcox, D.C.: Turbulence Modelling for CFD, 2nd edn. DCW Industries, California, USA (1998)
Yakinthos, K., Vlahostergios, Z., Goulas, A.: Modeling the flow in a 90 ∘ rectangular duct using 1 Reynolds-stress and 2 eddy-viscosity models. Int. J. Heat Fluid Flow 29, 35–47 (2008)
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Gerolymos, G.A., Vallet, I. Reynolds-Stress Model Prediction of 3-D Duct Flows. Flow Turbulence Combust 96, 45–93 (2016). https://doi.org/10.1007/s10494-015-9648-7
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DOI: https://doi.org/10.1007/s10494-015-9648-7