Skip to main content

The Computation of Turbulent Engineering Flows with Turbulence-Transport Closures

  • Conference paper
Advanced Turbulent Flow Computations

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 395))

Abstract

The paper discusses aspects of modelling complex turbulent flows, placing particular emphasis on second-moment closure and non-linear eddy-viscosity formulations. Principal features of turbulence, viewed mainly in statistical terms, are highlighted first. This is followed by considerations directed, principally, towards processes which arise from the interaction between the Reynolds stresses and mean-flow features. Attention focuses, in particular, on the interaction, as expressed through the exact Reynolds-stress generation terms, between turbulence and curvature, normal straining, system rotation, body forces and heat transfer. This exposition provides the background against which the use of anisotropy-resolving closures is advocated. Following a review of simpler approaches, based on the isotropic eddy-viscosity concept, the current status of second-moment and non-linear eddy-viscosity modelling is summarised. Consideration is then given to the performance of alternative models by reference to computational solutions for eight flows, both twodimensional and three-dimensional, some incompressible and others compressible. In presenting and discussing representative results, emphasis is placed on fundamental flow features and on assessing the predictive capabilities of alternative models by reference to experimental data. The results are argued to offer support for the use of anisotropy-resolving closure, but also serve to highlight model weaknesses and uncertainties which require further research.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bradshaw, P., 1994, Turbulence: the chief outstanding difficulty of our subject, Exp. Fluids, 16, pp. 203–216.

    Google Scholar 

  2. Leschziner, M.A. and Launder, B.E. (Eds.), 1993, Proc. 2nd ERCOFTAC/IAHR Workshop on Round Normally Impinging Turbulent Jet and Turbulent Flow through Tube Bank Sub-Channel, UMIST, Manchester.

    Google Scholar 

  3. Batten, P., Loyau, H. and Leschziner, M.A. (Eds.), 1997, Proc. of ERCOFTAC Workshop on Shock-Wave/Boundary-Layer Interaction, UMIST, Manchester.

    Google Scholar 

  4. Moin, P. and Kim, J., 1997, Tackling turbulence with supercomputers, Scientific American, 276, pp. 62–68.

    ADS  Google Scholar 

  5. Moin, P. and Mahesh, K., 1998, Direct numerical simulation: A tool in turbulence Research, Annu. Rev. Fluid Mech., 30, pp. 539–578.

    ADS  MathSciNet  Google Scholar 

  6. Franke, R. and Rodi, W., 1991, Calculation of vortex shedding past a square cylinder with various turbulence models, Proc. 8th Shear Flows Symp., Munich, 1991, pp. 20.1.1–20. 1. 6.

    Google Scholar 

  7. Archambeau, F., Leschziner, M.A. and Laurence, D., 1995, Contribution of UMIST to vortex shedding behind a square prism at Re=21,400, Proc. of Workshop on Large Eddy Simulation of Flows past Bluff Bodies (W.Rodi and J. Ferziger, Eds.), Tegernsee, Germany.

    Google Scholar 

  8. Lesieur, M. and Metais, 0., 1996, New trends in Large Eddy Simulations of turbulence, Annu. Rev. Fluid Mech., 28, pp. 45–82.

    Google Scholar 

  9. Lardat, R., 1997, Simulations numériques d’écoulements externes instationnaires décolls autour d’une aile avec des modèles de sous maille, Ph. D. Thesis, University Paris 6.

    Google Scholar 

  10. Schiestel, R., 1987, Multiple time scale modelling of turbulent flows in one point closures, Phys. Fluids, 30, pp. 722.

    ADS  MATH  Google Scholar 

  11. Wilcox, D.C., 1988, Multi-scale model for turbulent flows, AIAA J., 26, pp. 1311–1320.

    ADS  MathSciNet  Google Scholar 

  12. Reynolds, W.C. and Kassinos, S.C., 1994, One-point modelling of rapidly deformed homogeneous turbulence, Proc. Osborne Reynolds Centenary Symposium, Manchester, Proc. The Royal Society of London, Series A, 451, pp. 87–104.

    MathSciNet  Google Scholar 

  13. Hussain, A.K.M.F. and Reynolds, W.C., 1972, The mechanics of an organized wave in turbulent shear flow: Part 3: Theoretical models and comparisons with experiment, J. Fluid Mech., 54, pp. 263–287.

    ADS  Google Scholar 

  14. Drikakis, D., 1998, The equations for the coherent structure dynamics in turbulent flows, Proc. FEDSM ‘88, Washington DC.

    Google Scholar 

  15. Ha Minh, H. and Kourta, A., 1994, Semi-deterministic turbulence modelling for flows dominated by strong organised structures, 9th Symp. on Turbulent Shear Flows, Kyoto, pp. 10.5.1–10. 5. 6.

    Google Scholar 

  16. Baldwin, B.S. and Lomax, H., 1978, Thin-layer approximation algebraic model for separated turbulent flows, AIAA Paper 78–0257.

    Google Scholar 

  17. Abu-Ghannam, B.J. and Shaw, R., 1980, Natural transition of boundary layers–the effects of turbulence, pressure gradient and flow histrory, J. Mechanical Engineering Science, 22, pp. 213–228.

    ADS  Google Scholar 

  18. Hytopoulos, E., Schetz, J.A. and Simpson, R.L., 1997, Turbulence model for steady and unsteady boundary layers in strong pressure gradients“, J. Fluids Engrg., 119, pp. 541–549.

    Google Scholar 

  19. Johnson, D.A. and King, L.S., 1985, A mathematical simple turbulence closure model for attached and separated turbulent boundary layers, AIAA Paper 84–0175.

    Google Scholar 

  20. Wolfshtein, M., 1969, The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient, Int. J. Heat Mass Transfer, 12, pp. 139–163.

    Google Scholar 

  21. Norris, L.H. and Reynolds, W.C., 1975, Turbulence channel flow with a moving wavy boundary, Rep. FM-10, Dept. of Mech. Engrg., Stanford University.

    Google Scholar 

  22. Baldwin, B.W. and Barth, T.A., 1991, One-equation turbulence transport model for high Reynolds number wall-bounded flows, AIAA Paper 91–0610.

    Google Scholar 

  23. Spalart P.R. and Allmaras, S.R., 1992, A one-equation turbulence model for aerodynamic flows, AIAA Paper 92–0439.

    Google Scholar 

  24. Cho, H.-H., Liu, X., Rodi, W. and Schönung, B., 1993, Calculation of wake-induced unsteady flow in a turbine cascade, J. Turbomachinery, 115, pp. 675–686.

    Google Scholar 

  25. Leschziner, M.A., Dimitriadis, K.P. and Page, G., 1993, Computational modelling of shock wave/boundary layer interaction with a cell-vertex scheme and transport models of turbulence, The Aeronautical Journal, 97, 1993, pp. 43–61.

    Google Scholar 

  26. Lien, F.S. and Leschziner, M.A., 1993, A pressure-velocity solution strategy for compressible flow and its application to shock/boundary-layer interaction using second-moment turbulence closure, J. Fluids Engrg, 115, pp. 717–725.

    Google Scholar 

  27. Lien, F-S, and Leschziner, M.A., 1993, Modelling 2D and 3D separation from curved surfaces with variants of second-moment closure combined with low-Re near-wall formulations, Proc. 9th Symposium Turbulent Shear Flows, Kyoto, pp. 13.1.1–13. 1. 6.

    Google Scholar 

  28. Apsley, D., Chen, W.L., Leschziner, M.A. and Lien, F.S., 1998, Non-linear eddy-viscosity modelling of separated flows, IAHR J. of Hydraulic Research, 35, pp. 723–748.

    Google Scholar 

  29. Jones, W.P. and Launder, B.E., 1972, The prediction of laminarization with a two-equation model of turbulence, Int. J. Heat and Mass Transfer, 15, pp. 301–314.

    Google Scholar 

  30. Launder, B.E. and Sharma, B.I., 1974, Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Letters in Heat and Mass Transfer, 1, pp. 131–138.

    ADS  Google Scholar 

  31. Lam, C.K.G. and Bremhorst, K., 1981, A modified form of the k-E model for predicting wall turbulence, J. Fluids Engrg., 103, pp. 456–459.

    Google Scholar 

  32. Chien, K.Y., 1982, Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model, AIAA J., 20, 1, pp. 33–38.

    ADS  MATH  MathSciNet  Google Scholar 

  33. Myong, H.K. and Kasagi, N., 1990, A new approach to the improvement of k-E turbulence model for wall bounded shear flows, Japanese Society of Mechanical Engineering Int. J., Series II, 33, pp. 63–72.

    Google Scholar 

  34. Nagano, Y. and Hishida, M., 1987, Improved form of the k-E model for turbulent shear flows“, Trans. of ASME, 109, pp. 156–160.

    Google Scholar 

  35. Orzag, S.A., Yakhot, V., Flannery, W.S., Boysan, F., Choudhury, D., Maruzewski, J. and Patel, B., 1993, Renormalisation group modelling and turbulence simulations“, Near-Wall Turbulent Flows (R.M.C. So, C.G. Speziale and B.E. Launder, Eds. ), Elsevier, pp. 1031–1046.

    Google Scholar 

  36. Lien, F.S. and Leschziner, M.A., 1994, Modelling the flow in a transition duct with a non-orthogonal FV procedure and low-Re turbulence-transport models, ASME Summer Meeting, Symposium on Advances in Computational Methods in Fluid Dynamics, pp. 93–106.

    Google Scholar 

  37. Lien, F.S. and Leschziner, M.A., 1995, Second-moment closure for three-dimensional turbulent flow around and within complex geometries, Computers and Fluids, 25, pp. 237–262.

    Google Scholar 

  38. Kalitzin, G., Gould, A.R.B., Benton, J.J., 1996, Application of two-equation turbulence models in aircraft design, AIAA Paper 96–0327.

    Google Scholar 

  39. Wilcox, D.C., 1988, Reassessment of the scale-determining equation for advanced turbulence models, AIAA J., 26, pp. 1299–1310.

    ADS  MATH  MathSciNet  Google Scholar 

  40. Wilcox, D.C., 1994, Simulation transition with a two-equation turbulence model, AIAA J., 32, pp. 247–255.

    ADS  MATH  Google Scholar 

  41. Goldberg, U.C., 1994, Towards a pointwise turbulence model for wall-bounded and free shear flows, J. Fluids Engrg, 116, pp. 72–76.

    Google Scholar 

  42. Gibson, M.M. and Dafa’Alla, A.A., 1994, “The q-Ç model for turbulent wall flow”, Fluid Dynamics Division, American Physical Society, Proc. 47th Annual Meeting, Atlanta, Georgia.

    Google Scholar 

  43. Menter, F. R., 1994, Two equation eddy viscosity turbulence models for engineering applications, AIAA J., 32, pp. 1598–1605.

    ADS  Google Scholar 

  44. Patel, C.V., Rodi, W. and Scheuerer, G., 1985, “Turbulence models for near-wall and low Reynolds number flows: A review”, AIAA J., 23, pp. 1308–1319.

    ADS  MathSciNet  Google Scholar 

  45. Henkes, R.A.W.M., van Hest, B.F.A. and Passchier, D.M., 1995, Natural and by-pass transition with applications in aeronautics, ERCOFTAC Bulletin 24, pp. 34–36.

    Google Scholar 

  46. Ramaprian, B.R. and Tu, S.W., 1982, Study of periodic turbulent pipe flow, Inst. of Hydr. Res., University of Iowa Report IJHR 238.

    Google Scholar 

  47. Jackson, J.D. and He, S., 1995, Simulations of transient turbulent flow using various two-equation low-reynolds number turbulence models, Proc. 10th Symp. on Turbulent Shear Flows, Penn-State University, pp. 11. 19–11. 24.

    Google Scholar 

  48. Fan, S., Lakshminarayana, B. and Barnett, M., 1993, Low-Reynolds-number k-E model for unsteady turbulent boundary-layer flows, AIAA J., 31, pp. 1777–1784.

    ADS  MATH  Google Scholar 

  49. Fan, S. and Lakshminarayana, B., 1996, Computation and simulation of wake-generated unsteady pressure and boundary layers in cascades: Part 1–Description of the approach and validation, J. Turbomachinery, 118, pp. 96–112.

    Google Scholar 

  50. Spalart, P.R. and Baldwin, B.S., 1989, Direct numerical simulation of a turbulent oscillating boundary layer, Turbulent Shear Flows 6 (J.C. André et al, Eds. ), Springer, pp. 417–440.

    Google Scholar 

  51. Jensen, B.L., Sumer, B.M., Fredsoe, J., 1989, Turbulent oscillatory boundary layers at high Reynolds numbers, J. Fluid Mech., 206, pp. 265–297.

    ADS  Google Scholar 

  52. Justesen, P. and Spalart, P.R., 1990, Two-equation turbulence modelling of oscillatory boundary layers, AIAA Paper 90–0496.

    Google Scholar 

  53. Ha Minh, H., Viegas, J.R., Rubesin, M.W., Vandromme, D.D. and Spalart, P., 1989, Physical analysis and second-order modelling of an unsteady turbulent flow: The oscillating boundary layer on a flat plate, Proc. 7th Symp. on Turbulent Shear Flows, Stanford, pp. 11.5.1–11. 5. 6.

    Google Scholar 

  54. Shima, N., 1993, Prediction of turbulent boundary layers with a second-moment closure: Part I–effects of periodic pressure gradient, wall transpiration and free-stream turbulence, J. Fluids Engrg, 115, pp. 56–69.

    Google Scholar 

  55. Jakirlic, S., 1997, Reynolds-spannungs-modellierung komplexer turbulenter Stroemungen, Ph.D. Thesis, University of Erlangen-Nuernberg.

    Google Scholar 

  56. Guilmineau, E., Piquet, J. and Queutey, P., 1997, Unsteady two-dimensional turbulent viscous flow past aerofoils, Int. J. Num. Meths. in Fluids, 25, pp. 315–366.

    Google Scholar 

  57. Barakos, G. and Drikakis D, 1997, Simulation of unsteady aerodynamic flows using low-Re wall-distance-free turbulence models, ASME paper FEDSM97–3651.

    Google Scholar 

  58. Wu, J.-C., Huff, D.L. and Sankar, L.N., 1990, Evaluation of three turbulence models in static air loads and dynamic stall predictions“, J. Aircraft, 27, pp. 382–384.

    Google Scholar 

  59. Srinivasan, G.R., Ekaterinaris, J.A. and McCroskey, W.J., 1995. “Evaluation of turbulence models for unsteady flows of an oscillating airfoil”, Computers and Fluids, 24, pp. 883–861.

    Google Scholar 

  60. Ekaterinaris, J.A. and Menter, F.R., 1994, “Computation of separated and unsteady flows with one-and two-equation turbulence models”, AIAA J., 32, pp. 2359–2365.

    ADS  Google Scholar 

  61. Piziali, R.A., 1993, An experimental investigation of 2D and 3D osciallating wing aerodynamics for a range of angle of attach including stall, NASA Technical Memorandum 4632.

    Google Scholar 

  62. Launder, B.E. and Tselepidakis, D.P., 1993, Contribution to the modelling of near-wall turbulence, Turbulent Shear Flows 8, (F. Durst et al, Eds.) Springer-Verlag, pp. 81–96.

    Google Scholar 

  63. Archambeau, F. and Laurence, D., 1993, Description of numerical methodology for tube bank“, Proc. 2nd ERCOFTAC-IAHR Workshop on Refined Flow Modelling, 15–16 June 1993, UMIST, Manchester.

    Google Scholar 

  64. Jones, W.P. and Manners, A., 1989, The calculation of the flow through a two-dimensional faired diffuser, Turbulent Shear Flows 6 P.C. André et al, Eds. ), Springer, pp. 18–31.

    Google Scholar 

  65. Spalart, P.R., 1988, Direct numerical simulation of a turbulent boundary layer up to R =1410, J. Fluid Mech., 187, pp. 61–98.

    ADS  MATH  Google Scholar 

  66. Kim, J., Moin, P. and Moser, R., 1987, Turbulence statistics in fully-developed channel flow at low Reynolds number, J. Fluid Mech., 177, pp. 133–166.

    ADS  MATH  Google Scholar 

  67. Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. and Nieuwstadt, F.T.M., 1994, Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment, J. Fluid Mech., 268, pp. 175–209.

    ADS  Google Scholar 

  68. Le, H. and Moin, P., 1994, Direct numerical simulation of turbulent flow over a backward-facing step, Report No. TF-58, Dept. of Mech. Eng., Stanford University.

    Google Scholar 

  69. Daly, B.J. and Harlow, F.H., 1970, Transport equations in turbulence, Phys. Fluids, 13, pp. 2634–2649.

    ADS  Google Scholar 

  70. Lumley, J.L., 1978, Computational modelling of turbulent flows, Adv. Appl. Mech., 18, pp. 123–176.

    MATH  MathSciNet  Google Scholar 

  71. Craft T.J., Kidger J.W. and Launder B.E., 1997, Importance of third-moment modelling in horizontal, stably-stratified flows, Proc. 11th Shear Flows Symposium, Grenoble, pp. 20. 13–20. 18.

    Google Scholar 

  72. Craft, T.J. and Launder, B.E., 1996, A Reynolds stress closure designed for complex geometries, Int. J. Heat Fluid Flow, 17, pp. 245–254.

    Google Scholar 

  73. Launder, B.E. and Reynolds, W.C., 1983, Asymptotic near wall stress dissipation rates in a turbulent flow, Phys. Fluids, 26, pp. 1157–1158.

    ADS  MATH  Google Scholar 

  74. Hanjalic, K. and Jakirlic S., 1993, A model of stress dissipation in second moment closures, Appl. Scientific Research, 51, pp. 513–518.

    Google Scholar 

  75. Rotta, J.C., 1951, Statistische Theory nichhomogener Turbulenz, Zeitschrift der Physik, 129, pp. 547–572.

    ADS  MATH  MathSciNet  Google Scholar 

  76. Gibson, M.M. and Launder, B.E., 1978, Ground effects on pressure fluctuations in the atmospheric boundary layer“, J. Fluid Mech., 86, pp. 491–511.

    ADS  MATH  Google Scholar 

  77. Fu, S., Leschziner, M.A. and Launder, B.E., 1987, Modelling strongly swirling recirculating jet flow with Reynolds-stress transport closure, Proc. 6th Symposium on Turbulent Shear Flow, Toulouse, pp. 17.6.1–17. 6. 6.

    Google Scholar 

  78. Shir, C.C., 1973, A preliminary numerical study of atmospheric turbulent flows in the idealised planetary boundary layer“, J. Atmos. Sci., 30, pp. 1327–1333.

    ADS  Google Scholar 

  79. Craft, T.J. and Launder, B.E., 1992, New wall-reflection model applied to the turbulent impinging jet, AIAA J., 30, pp. 2970–2972.

    ADS  Google Scholar 

  80. So, R.M.C., Lai Y.G., Zhang, H.S. and Hwang, B.C., 1991, Second-order near-wall turbulence closures: A review, AIAA J., 29, pp. 1819–1835.

    ADS  MATH  Google Scholar 

  81. Shima, N., 1995, A Reynolds-stress redistribution model applicable up to the wall, Proc. Int. Symp. on Mathematical Modelling of Turbulent Flows, Tokyo, pp. 309–314.

    Google Scholar 

  82. Ince, N.Z., Betts, P.L and Launder, B.E., 1994, Low Reynolds number modelling of turbulent buoyant flows, Proc. EUROTHERM Seminar 22, Turbulent Natural Convection in Cavities, Delft, Editions européenes Thermique et Industrie, Paris, (R.A.W.M. Henkes and C.J. Hoogendoorn, Eds. ), pp. 76–87.

    Google Scholar 

  83. Jakirlic, S. and Hanjalic, K., 1995, A second-moment closure for non-equilibrium and separating high-and low-Re-number flows, Proc. 10th Symp. on Turbulent Shear Flows, Pennsylvania State University, pp. 23. 25–23. 30.

    Google Scholar 

  84. Durbin, P.A., 1993, A Reynolds stress model for near-wall turbulence, J Fluid Mech., 249, pp. 465–498.

    ADS  Google Scholar 

  85. Shih, T.H. and Lumley, J.L., 1985, Modelling of pressure correlation terms in Reynolds-stress and scalar-flux equations, Report FDA-85–3, Sibley School of Mech. and Aerospace Eng, Cornell University.

    Google Scholar 

  86. Fu, S., Launder, B.E. and Tselepidakis, D.P., 1987, Accommodating the effects of high strain rates in modelling the pressure-strain correlation, Report TFD/87/5, Mechanical Engineering Dept., UMIST, Manchester.

    Google Scholar 

  87. Speziale, C.G., Sarkar, S. and Gatski, T.B., 1991, Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach, J. Fluid Mech., 227, pp. 245–272.

    ADS  MATH  Google Scholar 

  88. Craft, T.J., Graham, L.J.W. and Launder, B.E., 1993, Impinging jet studies for turbulence model assessment–II. An examination of the performance of four turbulence models, Int. J. Heat Mass Transfer, 36, pp. 2685–2697.

    Google Scholar 

  89. Batten, P., Craft, T.J, Leschziner, M.A. anf Loyau, H., 1998, Reynolds-stress-transport modelling for compressible aerodynamic flows, Report TFD/98/02, Mechanical Engineering Dept., UMIST, (to appear AIAA J., 1999 ).

    Google Scholar 

  90. Haroutunian, V., Ince, N. and Launder, B.E., 1988, A new proposal for the c equation, Proc. 3rd UMIST CFD Colloquium, UMIST, Manchester, Paper 1. 3.

    Google Scholar 

  91. Yap, C.R., 1987, Turbulent heat and momentum transfer in recirculating and impinging flows, PhD. Thesis, University of Manchester.

    Google Scholar 

  92. Craft, T.J., 1998, Development in low-Reynolds-number second-moment closure and its application to separating and reattaching flows, Int. J. Heat Fluid Flow (in press).

    Google Scholar 

  93. Hanjalic, K, Jakirlic, S and Hadzic, I., 1995, Computation of oscillating turbulent flows at transitional Re-numbers, Turbulent Shear Flows 9 (F. Durst et al, Eds. ), Springer, pp. 323–342.

    Google Scholar 

  94. Pope, S.B., 1975, A more general effective-viscosity hypothesis, J. Fluid Mech., 72, pp. 331–340.

    ADS  MATH  Google Scholar 

  95. Rodi, W., 1976, A new algebraic relation for calculating the Reynolds stresses, Z. Angew. Math. Mech., 56, pp. 219–221.

    MathSciNet  Google Scholar 

  96. Launder, B.E., Reece, G.J. and Rodi, W., 1975, Progress in the development of Reynolds-stress turbulence closure, J. Fluid Mech., 68, pp. 537–566.

    ADS  MATH  Google Scholar 

  97. Speziale, C.G., 1987, On nonlinear K-Q and K-c models of turbulence, J. Fluid Mech., 178, pp. 459–475.

    ADS  MATH  Google Scholar 

  98. Yoshizawa, A., 1987, Statistical analysis of the derivation of the Reynolds stress from its eddy-viscosity representation, Phys. Fluids, 27, pp. 1377–1387.

    ADS  Google Scholar 

  99. Shih, T-h., Zhu, J. and Lumley, J.L., 1993, A realisable Reynolds stress algebraic equation model, NASA TM105993.

    Google Scholar 

  100. Rubinstein, R. and Barton, J.M., 1990, Non-linear Reynolds stress models and the renormalisation group, Phys. Fluids A, 2, pp. 1472–1476.

    ADS  MATH  Google Scholar 

  101. Gatski, T.B. and Speziale, C.G., 1993, On explicit algebraic stress models for complex turbulent flows, J. Fluid Mech, 254, pp. 59–78.

    ADS  MATH  MathSciNet  Google Scholar 

  102. Craft, T.J., Launder, B.E. and Suga, K., 1995, “A non-linear eddy-viscosity model including sensitivity to stress anisotropy”, Proc. 10th Symp. on Turbulent Shear Flows, Pennstate, Vol 3, pp. 23. 19–23. 24.

    Google Scholar 

  103. Craft, T.J., Launder, B.E. and Suga, K., 1997b, Prediction of turbulent transitional phenomena with a nonlinear eddy-viscosity model, Int. J. Heat Fluid Flow, 18, p. 15.

    Google Scholar 

  104. Lien, F.S. and Durbin, P.A., 1996, Non-linear k-E-v2 modelling with application to high-lift, Proc. Summer Prog., Centre For Turbulence Research, Stanford University, pp. 5–22.

    Google Scholar 

  105. Lien, F.S., Chen, W.L., and Leschziner, M.A., 1996, Low-Reynolds-number eddy-viscosity modelling based on non-linear stress-strain/vorticity relations, Engineering Turbulence Modelling and Measurements–3 ( W. Rodi and G Bergeles, Eds. ), Elsevier, pp. 91–100.

    Google Scholar 

  106. Taulbee, D.B., Sonnenmeier, J.R. and Wall, K.M., 1993, Application of a new non-linear stress-strain model to axisymmetric turbulent swirling flows, Engineering Turbulence Modelling and Experiments 2 ( W. Rodi and F.; Martelli, Eds. ), Elsevier, pp. 103–112.

    Google Scholar 

  107. Apsley, A.D. and Leschziner, M.A., 1997, A new low-Re non-linear two-Equation turbulence model for complex flows, Int. J. Heat Fluid Flow, 19, pp. 209–222.

    Google Scholar 

  108. Ellis, L.B. and Joubert, P.N., 1974, Turbulent shear flow in a curved duct, J. Fluid Mech, 62, pp. 65–84.

    ADS  Google Scholar 

  109. Hogg, S. and Leschziner, M.A., 1989, Computation of highly swirling confined flow with a Reynolds-stress turbulence model, AIAA J., 27, pp. 57–67.

    ADS  Google Scholar 

  110. Cresswell, R., Haroutunian, V., Ince, N.Z., Launder, B.E. and Szczepura, R.T., 1989, Measurement and modelling of buoyancy-modified, elliptic turbulent shear flows, Proc. 7th Symp. on Turbulent Shear Flows, Stanford, pp. 12. 41–12. 46.

    Google Scholar 

  111. Bo T. and Iacovides, H., 1996, Numerical study of the effects of rotational buoyancy on fully-developed flow in rotating rectangular ducts, Int. J. Num. Meths. Heat Fluid Flow, Vol 6, pp. 47–62.

    MATH  Google Scholar 

  112. Obi, S. Aoki, K. and Masuda, S. 1993, “Experimental and computational study of turbulent separated flow in an asymmetric diffuser, Proc. 9th Symp. on Turbulent Shear Flows, Kyoto, 3, p. 305.

    Google Scholar 

  113. Piccin, O. and Cassoudesalle, D., 1987, Etude dans la soufflerie F1 des profils AS239 et AS240, ONERA Technical Report, PV 73/1685 AYG.

    Google Scholar 

  114. Zierke, W.C. and Deutsch, S., 1989, The measurement of boundary layers on a compressor blade in a cascade, NASA CR-185118.

    Google Scholar 

  115. Cooper, D., Jackson, D.C., Launder, B.E. and Liao, G.X., 1993, Impinging jet studies for turbulence model assessment, Part 1: Flow-field experiments, Int. J. Heat and Mass Transfer, 36, pp. 2675–2684.

    Google Scholar 

  116. Kreplin, H.P., Vollmers, H. and Meier, H.U., 1985, Wall shear stress measurements on an inclined prolate spheroid in the DFVLR 3mx3m low speed wind tunnel, Goettingen, DFVLR Report IB 222–84 A 33.

    Google Scholar 

  117. Meier, H.U., Kreplin, H.P., Landhauser, A. and Baumgarten D., 1984, Mean velocity distribution in 3D boundary layers developing on a 1:6 prolate spheroid with artificial transition, DFVLR Report IB 222–84 All.

    Google Scholar 

  118. Davis, D.O. and Gessner, F., 1990, Experimental investigation of turbulent flow through a circular-to-rectangular duct, AIAA Paper 90–1505.

    Google Scholar 

  119. Delery, J., 1981, Investigation of strong shock turbulent boundary-layer interaction in 2D flows with emphasis on turbulence phenomena“, AIAA Paper 81–1245.

    Google Scholar 

  120. Barberis, D. and Molton, P., 1992, Shock wave-turbulent boundary layer interaction in a three dimensional flow - laser velocimeter results, Technical Report, ONERA TR.31/7252AY.

    Google Scholar 

  121. Barberis, D. and Molton, P., 1995, Shock wave-turbulent boundary layer interaction in a three dimensional flow, AIAA Paper 95–0227, Reno, Nevada.

    Google Scholar 

  122. Lien, F-S. and Leschziner, M.A., 1994, A general non-orthogonal finite volume algorithm for turbulent flow at all speeds incorporating second-moment closure, Part 1: numerical implementation, Comp. Meths. Appl. Mech. Engrg., 114, pp. 123–148.

    ADS  MathSciNet  Google Scholar 

  123. Lien F-S. and Leschziner, M.A., 1994, Upstream monotonic interpolation for scalar transport with application to complex turbulent flows, Int. J. Num. Meths. in Fluids, 19, pp. 527–548.

    Google Scholar 

  124. Leonard, B.P., 1979, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp. Meths. Appl. Mech. Engrg., 19, pp. 59–67.

    ADS  MATH  Google Scholar 

  125. Batten, P., Leschziner, M.A. and Goldberg, U.C., 1997, Average state Jacobians and implicit methods for compressible viscous and turbulent flows, J. Comput. Phys., 137, pp. 38–78.

    ADS  MATH  MathSciNet  Google Scholar 

  126. Lien, F.S. and Leschziner, M.A., 1995, Modelling 2D separation from high-lift aerofoils with a non-linear eddy-viscosity model and second-moment closure, The Aeronautical Journal, 99, pp. 125–144.

    Google Scholar 

  127. Chen, W.L., Lien, F.S. and Leschziner, M.A., 1997, Computational prediction of flow around highly-loaded compressor-cascade blades with non-linear eddy-viscosity models, Int. J Heat Fluid Flow, 19, pp. 307–319.

    Google Scholar 

  128. Chen, W.L., Lien, F.S. and Leschziner, M.A., 1997, Proc. 11th Symp. on Turbulent Shear Flows, Grenoble, pp. 1. 13–1. 19

    Google Scholar 

  129. Menter, F.R., 1993, Zonal two equation k-oo turbulence models for aerodynamic flows, AIAA Paper 93–2906.

    Google Scholar 

  130. Hanjalic, K., 1994, Advanced turbulence closure models: a view of current status and future prospects, Int. J Heat Fluid Flow, 15, pp. 178–203.

    Google Scholar 

  131. Haase, W., Chaput, E., Elsholz, E., Leschziner, M.A. and Müller, U.R., (Eds) 1996, ECARP: European Computational Aerodynamics Research Project. II: Validation of CFD Codes and Assessment of Turbulent Models, Notes on Numerical Fluid Mechanics, Vieweg Verlag, 58.

    Google Scholar 

  132. Haase, W., Brandsma, F., Elsholz, E., Leschziner, M.A. and Schwamborn, D. (Eds.), 1993, EUROVAL - A European Initiative on Validation of CFD Codes - Results of the EC/BRITE-EURAM Project EUROVAL, 1990–1992, Notes on Numerical Fluid Mechanics,Vieweg Verlag, 42.

    Google Scholar 

  133. Loyau, H. and Vandromme, D., 1998, TC5 Workshop Synthesis, Computation and Comparison of Efficient Turbulence Models for Aeronautics–European Research Project ETMA, (A. Dervieux, M. Braza, J.-P. Dussauge, Eds), Notes on Numerical Fluid Mechanics, Vieweg, 65, pp. 456–471.

    Google Scholar 

  134. Loyau, H., Batten, P. and Leschziner, M.A., 1998, Modelling shock/boundary-layer interaction with non-linear eddy-viscosity closures, Report TFD/98/01, Mechanical Engineering Dept., UMIST, Manchester, (to appear J. Flow, Turbulence and Combustion, 1999 ).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Wien

About this paper

Cite this paper

Leschziner, M.A. (2000). The Computation of Turbulent Engineering Flows with Turbulence-Transport Closures. In: Peyret, R., Krause, E. (eds) Advanced Turbulent Flow Computations. International Centre for Mechanical Sciences, vol 395. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2590-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2590-8_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83324-7

  • Online ISBN: 978-3-7091-2590-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics