Robust implicit multigrid reynolds-stress model computation of 3-D turbomachinery flows

Proceedings of the ASME Turbo Expo

Volumn 6 PART B, Issue , 2006, Pages 1591-1614

  Gerolymos, G A ^a   Vallet, I ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW EQUATIONS; MULTIBLOCK GRIDS; REYNOLDS STRESS TRANSPORT MODELS; TURBOMACHINERY FLOWS;

COMPUTATIONAL METHODS; MATHEMATICAL MODELS; NUMERICAL METHODS; REYNOLDS NUMBER; TRANSPORT PROPERTIES; TURBULENCE;

TURBOMACHINERY;

EID: 33750856351     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/GT2006-91324     Document Type: Conference Paper

References (123)

1. Hah, C. and Krain, H., 1990. "Secondary flows and vortex motion in a high-efficiency backswept impeller at design and off-design conditions". ASME J. Turbom., 112(1), Jan., pp. 7-13.
2. Sieverding. C. H., 1985. "Recent progress in the understanding of basic aspects of secondary flows in turbine blade passages". ASME J. Eng. Gas Turb. Power. 107, pp. 248-257.
3. Reid, L., and Moore, R. D., 1978. Design and overall performance of 4 highly loaded, high-speed inlet stages for an advanced high-pressure-ratio core compressor. Tech. Paper TP-1337, NASA, Lewis Research Center, Cleveland (OH, USA], Oct.
4. Hah, C., and Loellbach, J., 1999. "Development of hub corner stall and its influence on the performance of axial compressor blade rows". ASME J. Turbom., 121(1), pp. 67-77.
5. Volino, R. J., 2002. "Separated flow transition under simulated low-pressure turbine airfoil conditions - part 1: Mean-flow and turbulence statistics". ASME J. Turbom., 124, Oct., pp. 645-655.
6. Volino, R. J., 2002. "Separated flow transition under simulated low-pressure turbine airfoil conditions - part 2: Turbulence spectra". ASME J. Turbom., 124, Oct., pp. 656-664.
7. Copenhaver, W. W., Puterbaugh, S. L., and Hah, C., 1997. "Unsteady flow and shock motion in a transonic compressor rotor". J. Prop. Power, 13(1), pp. 17-23.
8. Dunn, M. G., 2001. "Convective heat transfer and aerodynamics in axial flow turbines". ASME J. Turbom., 123, Oct., pp. 637-686.
9. Volino, R. J., 1998. "A new model for freestream turbulence effects on boundary layers". ASME J. Turbom., 120, pp. 613-620.
10. Speziale, C. G., 1998. "Turbulence modeling for time-dependent RANS and VLES: A review". AIAA J., 36(2), Feb., pp. 173-184.
11. Suzen, Y. B., and Huang, P. G., 2000. "Modeling of flow transition using an intermittency transport equation". ASME J. fluids Eng., 122, June, pp. 273-284.
12. Steelant, J., and Dick, E., 2001. "Modelling of laminar-turbulent transition for high freestream-turbulence". ASME J. Fluids Eng., 123, Mar., pp. 22-30.
13. Suzen, Y. B., Xiong, G., and Huang, P. G., 2002. "Predictions of transitional flows in low-pressure turbines using intermittency transport equation". AIAA J., 40(2), Feb., pp. 254-266.
14. Walters, D. K., and Leylek, J. H., 2004. "A new model for boundarylayer transition using a single-point RANS approach". ASME J. Turbom., 126(1), Jan., pp. 193-202.
15. Gerolymos, G. A., and Vallet, I., 2002. "Wall-normal-free Reynolds-stress model for rotating flows applied to turbomachinery". AIAA J., 40(2), Feb., pp. 199-208.
16. Gerolymos, G. A., Neubauer, J., Sharma, V. C., and Vallet, I., 2002. "Improved prediction of turbomachinery flows using near-wall Reynolds-stress model". ASME J. Turbom., 124(1), Jan., pp. 86-99.
17. Gerolymos, G. A., Sauret, E., and Vallet, I., 2004. "Contribution to the single-point-closure Reynolds-stress modelling of inhomogeneous flow". Theor. Comp. Fluid Dyn., 17(5-6), Sept., pp. 407-431.
18. Scholz, N., ed., 1977. Aerodynamics of Cascades. No. AGARD-AG-220 in AGARDograph. AGARD, Neuilly-sur-Seine [FRA]. (translated and revised by A. Klein from the original german Aerodynamik der Schaufelgitter).
19. Gerolymos, G. A., Sauret, E., and Vallet, I., 2004. "Influence of inflow-turbulence in shock-wave/turbulent-boundary-layer interaction computations". AIAA J., 42(6), June, pp. 1101-1106.
20. Vandromme, D., and Minh, H. H., 1986. "About the coupling of turbulence closure models with averaged Navier-Stokes equations". J. Comp. Phys. 65, pp. 386-409.
21. Morrison, J. H., 1992. A compressible Navier-Stokes solver with 2-equation and Reynolds-stress turbulence closure models. Contr. Rep. CR-4440, NASA, May. (also AIAA Paper 90-5251, 1990).
22. 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 closure". ASME J. Fluids Eng., 115, Dec., pp. 717-725.
23. Chuang, C. C., and Chieng, C. C., 1995. "Comparison of varients of the bi-conjugate gradient method for compressible Navier-Stokes with 2-moment closure". Int. J. Num. Meth. Fluids, 20, pp. 233-253.
24. Davidson, L., 1995. "Reynolds-stress transport modelling of shockinduced separated flow". Comp. Fluids, 24(3), pp. 253-268.
25. Leschziner, M. A., 1995. "Computation of aerodynamic flows with turbulence-transport models based on 2-moment closure". Comp. Fluids, 24, pp. 377-392.
26. Ladeinde, F., 1995. "Supersonic flux-split procedure for second moments of turbulence". AIAA J., 33(7), July, pp. 1185-1195.
27. Zha, G. C., and Knight, D. D., 1996. "3-D shock/boundary-layer interaction using Reynolds stress equation turbulence model". AIAA J., 34(7), July, pp. 1313-1320.
28. Gerolymos, G. A., and Vallet, I., 1997. "Near-wall Reynolds-stress 3-D transonic flows computation". AIAA J., 35(2), Feb., pp. 228-236.
29. Chenault, C. F., Beran, P. S., and Bowersox, R. D. W., 1999. "Numerical investigation of supersonic injection using a Reynolds-stress turbulence model". AIAA J., 37(10), Oct., pp. 1257-1269.
30. Batten, P., Craft, T. J., Leschziner, M. A., and Loyau, H., 1999. "Reynolds-stress-transport modeling for compressible aerodynamics applications". AIAA J., 37(7), July, pp. 785-797.
31. Chassaing, J. C., Gerolymos, G. A., and Vallet, I., 2003. "Efficient and robust Reynolds-stress model computation of 3-D compressible flows". AIAA J., 41(5), May, pp. 763-773.
32. Gerolymos, G. A., and Vallet, I., 2005. "Mean-flow-multigrid for implicit Reynolds-stress-inodel computations". AIAA J., 43(9), Sept., pp. 1887-1898.
33. Hah, C., Bryans, A. C., Moussa, Z., and Tomsho, M. E., 1988. "Application of viscous flow computations for the aerodynamic performance of a backswept impeller at various operating coditions". ASME J. Turbom., 110, pp. 303-311.
34. Copenhaver, W. W., Hah, C., and Puterbaugh, S. L., 1993. "3-D flow phenomena in a transonic, high-throughflow, axial-flow compressor stage". ASME J. Turbom., 115. pp. 240-248.
35. Kunz, R. F., and Lakshminarayana, B., 1992. "3-D Navier-Stokcs computation of turbomachinery flows using an explicit numerical procedure and a coupled k - ε model". ASME J. Turbom., 114(3), pp. 627-642.
36. Kunz, R. F., Basson, A. H., and Lakshminarayana, B., 1993. "Investigation of tip-clearance phenomena in an axial compressor cascade using Euler and Navier-Stokes procedures". ASME J. Turbom., 115(3), pp. 453-467.
37. Dawes, W. N., 1992. "Toward improved throughflow capability: The use of 3-D viscous flow solvers in a multistage environment". ASME J. Turbom., 114, pp. 8-17.
38. Dawes, W. N., 1993. "The extension of a solutions-adaptive 3-D Navier-Stokes solver toward geometries of arbitrary complexity". ASME J. Turbom., 115, pp. 283-295.
39. Turner, M. G., and Jennions, I. K., 1993. "An investigation of turbulence modeling in transonic fans including a novel implementation of an implicit k - ε turbulence model". ASME J. Turbom., 115(2), pp. 249-260.
40. Jennions, I. K., and Turner, M. G., 1993. "3-D Navier-Stokes computations of transonic fan flow using an explicit flow solver and an implicit k - ε turbulence model". ASME J. Turbom., 115(2), pp. 261-272.
41. Langowsky, C., and Vogel, D. T., 1997. "Influence of film-cooling on the secondary flow in a turbine nozzle". AIAA J., 35, pp. 111-118.
42. Hildebrandt, T., and Fottner, L., 1999. "A numerical study of the influence of grid refinement and turbulence modeling on the flow field inside a highly loaded turbine cascade". ASME J. Turbom., 121, pp. 709-716.
43. Ameri, A. A., Steinthorsson. E., and Rigby, D. L., 1998. "Effect of squealer tip on rotor heat tranfer and efficiency". ASME J. Turbom., 120, pp. 753-759.
44. Ameri, A. A., Steinthorsson, E., and Rigby, D. L., 1999. "Effects of tipclearance and casing recess on heat transfer and stage efficiency in axial turbines". ASME J. Turbom., 121. pp. 683-693.
45. Rhie, C. M., Gleixner, A. J., Spear, D. A., Fischberg, C. J., and Zacharias, R. M., 1998. "Development and application of a multistage Navier-Stokes solver: Part 1 - multistage modeling using bodyforces and deterministic stresses". ASME J. Turbom., 120, pp. 205-214.
46. LeJambre, C. R., Zacharias, R. M., Biederman, B. P., Gleixner, A. J., and Yetka, C. J., 1998. "Development and application of a multistage Navier-Stokes solver: Part II - application to a high-pressure compressor design". ASME J. Turbom., 120, pp. 215-223.
47. Arima, T., Sonoda, T., Shirotori, M., Tamura, A., and Kikuchi, K., 1999. "A numerical investigation of transonic axial compressor rotor flow using a low-Reynolds-number k - ε turbulence model". ASME J. Turbom., 121, pp. 44-58.
48. Hoeger, M., Fritsch, G., and Bauer, D., 1999. "Numerical simulation of the shock/tip-leakage-vortex interaction in a HPC front stage". ASME J. Turbom., 121, pp. 456-468.
49. Fritsch, G., Hoeger, M., Blaha, C., and Bauer, D., 2000. "Viscous 3-D simulation of transonic compressor stage on parallel hardware". J. Prop. Power. 16, pp. 388-396.
50. Gerolymos, G. A., Tsanga, G., and Vallet, I., 1998. "Near-wall k - ε computation of 3-D transonic turbomachinery flows with tip-clearance". AIAA J., 36(10), Oct., pp. 1769-1777.
51. Gerolymos, G. A., and Hanisch, C., 1999. "Multistage 3-D Navier-Stokes computation of off-design operation of a 4-stuge turbine". IMechE J. Power Energy, 213, pp. 243-261.
52. Demon, J. D., 1993. "Loss mechanisms in turbomachines". ASME J. Turbom., 115(4), pp. 621-656.
53. Adamczyk, J. J., 2000. "Aerodynamic analysis of multistage turbomachinery flows in support of aerodynamic design". ASME J. Turbom., 122, pp. 189-217.
54. Gier, J., Stubert, Brouillet, B., and de Vito, L., 2005. "Interaction of shroud leakage flow and main flow in a 3-stage LPturbine". ASME J. Turbom., 127(4), Oct., pp. 649-658.
55. Gerolymos,G. A., and Vallet, I., 2001. "Wall-normal-free near-wall Reynolds-stress closure for 3-D compressible separated flows". AIAA J., 39(10), Oct., pp. 1833-1842.
56. Chassaing, J. C., Gerolymos, G. A., and Vallet. I., 2003. "Reynolds-stress model dual-time-siepping computation of unsteady 3-D flows". AIAA J., 41(10), Oct., pp. 1882-1894.
57. Gerolymos, G. A., Neubauer, J., and Michon, G. J., 2002. "Analysis and application of chorochronic periodicity for turbomachinery rotor/stator in-teraction computations". J. Prop. Power. 18(2), Nov., pp. 1139-1152.
58. Rautaheimo, P. P., Salminen, E. J., and Sikonen, T. L., 2003. "Numerical simulation of the flow in the NASA low-speed centrifugal compressor". Int. J. Turbo Jet Eng., 20, pp. 155-170.
59. Chriss, R. M., Hathaway, M. D., and Wood, J. R., 1996. "Experimental and computational results from the NASA Lewis low-speed centrifugal impeller at design and part-flow conditions". ASME. J Turbom., 118(1), Jan., pp. 55-65.
60. 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.
61. Shima, N., 1988. "A Reynolds-stress model for near-wall and low-Reynolds-number regions". ASME J. Fluids Eng., 110, pp. 38-44.
62. Patel. V. G., Rodi, W., and Scheuerer, G., 1985. "Turbulence models for near-wall and low-Reynolds-number flows: A review". AIAA J., 23, pp. 1308-1319.
63. Jones, W. P., and Launder, B. E., 1972. "The prediction of laminarization with a 2-equation model of turbulence". Int. J. Heat Mass Transf., 15(15), pp. 301-314.
64. Sauret, E., and Vallet, I., 2005. "Near-wall turbulent pressure diffusion modelling and influence in 3-D secondary flows". In Proceedings of the 4. International Symposium on Turbulence and Shear Flow Phenomena, 27-29 jun 2005, Williamsburg [VA, USA], J. A. C. Humphrey, T. B. Gatski, J. K. Eaton, R. Friedrich, N. Kasagi, and M. A. Leschziner, eds., Vol. 1, TSFP, pp. 141-146.
65. Launder. B. E., and Sharma, B. I., 1974. "Application of the energy dissipation model of turbulence 10 the calculation of s near a spinning disk". Lett. Heat Mass Transf., 1, pp. 131-138.
66. Gerolymos, G. A., 1990. "Implicit multiple-grid solution of the compressible Navier-Stokes equations using k - ε turbulence closure". AIAA J., 28(10), Oct., pp. 1707-1717.
67. Gerolymos, G. A., and Vallei, I., 1996. "Implicit computation of the 3-D compressible Navier-Stokes equations using k - ε turbulence closure". AIAA J., 34(7), July, pp. 1321-1330.
68. Wilcox, D. C., 1998. Turbulence Modelling for CFD, 2. ed. DCW Industries, La Can̄ada [CA, USA].
69. Sarkar, S., Erlebacher, G., Hussaini, M. Y. and Kreiss, H. O., 1991. "The analysis and modelling of dilataiional terms in compressible turbulence". J. Fluid Mech., 227, pp. 473-493.
70. So, R. M. C., Gatski, T. B., and Sommer, T. P., 1998. "Morkovin hypothesis and the modeling of wall-bounded compressible turbulent flows". AIAA J., 36(9), Sept., pp. 1583-1592.
71. Pantano, C., and Sarkar, S., 2002. "A study of compressibility effects in the high-speed turbulent shear layer using direct simulation". J. Fluid Mech., 451, pp. 329-371.
72. Foysi, H., Sarkar, S., and Friedrich, R., 2004. "Compressibility effects and turbulence scalings in supersonic channel flow". J. Fluid Mech., 509, pp. 207-216.
73. 60". J. Aircraft. 37(3), May, pp. 361-367.
74. Rogers, S. E., Roth, K., Cao, H. V., Slotnick, J. P., Whitlock, M., Nash, S. M., and Baker, M. D., 2001. "Compulation of viscous flow for a Boeing 777 aircraft in landing configuration". J. Aircraft, 30(6), Nov., pp. 1060-1068.
75. Basso, E., Antunes, A. P., and Azevedo, J. L. F., 2003. "Chimera simulations of supersonic flows over a complex satellite launcher configuralion". J. Spacecraft Rockets. 40(3), May. pp. 345-355.
76. Fares, E., and Sehröder, W., 2002. "A differential equation for approximate wall-distance". Int. J. Num. Meth. Fluids. 39, pp. 743-762.
77. Tucker, P. G., 2003. "Differential-equation-based wall-distance computation in DES and RANS". J. Comp. Phys., 190, pp. 229-248.
78. Coles, D., 1956. "The law of the wake in a turbulent boundary layer". J. Fluid Mech., 1, pp. 191-226.
79. Tennekes, H., and Lumley, J. L., 1972. A First Course in Turbulence. MIT Press, Cambridge [MA, USA].
80. Simpson, R. L., 1983. "A model for the backflow mean-velocity profile". AIAA J., 21, pp. 142-143.
81. Launder, B. E., 1984. "Numerical computation of convective heat transfer in complex turbulent flows: Time to abandon wall-functions?", Int. J. Heat Mass Transf., 27, pp. 1485-1491.
82. Durbin, P. A., 1993. "A Reynolds-stress model for near-wall turbulence". J. Fluid Mech., 249, pp. 465-498.
83. Launder. B. E., and Li, S. P., 1994. "On the elimination of walltopography parameters from 2-moment closure". Phys. Fluids, 6. pp. 999-1006.
84. Craft, T. J., and Launder, B., 1996. "A Reynolds-stress model designed for complex geometries". Int. J. Heat Fluid Flow. 17, pp. 245-254.
85. Djenidi. I., and Antonia. R. A., 1997. "Modeling of the Reynolds-stress transport equation". AIAA J., 35, pp. 450-455.
86. Shima, N., 1998. "Low-Reynolds-number second-moment closure without wall-reflection redistribution terms". Int. J. Heat Fluid Flow, 19, pp. 549-555.
87. Craft, T. J., 1998. "Developments in a low-Reynolds-number second-moment closure and its application to separating and reattaching flows". Int. J. Heat Fluid Flow. 19, pp. 541-548.
88. So, R. M. C. and Yuan, S. P., 1999. "A geometry independent near-wall Reynolds-stress closure". Int. J. Eng. Sci., 37, pp. 33-57.
89. Manceau, R., and Hanjalić, K., 2002. "Elliptic blending model: A new near-wall Reynolds-stress turbulence closure". Phys. fluids, 14(2), Feb., pp. 609-638.
90. Lumley, J. L., 1978. "Computational modeling of turbulent flows". Adv. Appl. Much., 18, pp. 123-176.
91. Launder, B. E., and Shima, N., 1989. "2-moment closure for the near-wall sublayer: Development and application", AIAA J., 27(10), Oct., pp. 1319-1325.
92. Rotta, J., 1951. "Statistische Theorie nichthomogener Turbulenz - 1. Mitteilung". Z. Phys., 129, pp. 547-572.
93. Naot, D., Shavit, A., and Wolfshtein, M., 1973. "2-point-correlalion model and the redistribution of Reynolds-stresses". Phys. Fluids. 16(6), June, pp. 738-743.
94. 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.
95. Hanjalić, K., and Launder, B. E., 1972. "A Reynolds stress model of turbulence and its application to thin shear flows". J. Fluid Mech., 52, pp. 609-638.
96. Gerolymos, G. A., Sauret, E., and Vallet, I., 2004. "Oblique-shock- wave/boundary-layer interaction using near-wall Reynolds-stress models". AIAA J., 42(6), June, pp. 1089-1100.
97. Vallet, I., 1995, "Aérodynamique numérique 3-D instationnaire avec fermeture bas-Reynolds au second ordre". Doctorat, Université Pierre-et-Marie-Curie, Paris [F], Dec.
98. Suder, K. L., 1998. "Blockage development in a transonic axial compressor rotor". ASME J. Turbom., 120, pp. 465-476.
99. Gerolymos, G. A., and Tsanga, G., 1999. "Biharmonic 3-D grid generation for axial turbomachinery with tip-clearance". J. Prop. Power. 15(3), May, pp. 476-479.
100. Gerolymos, G. A., and Vallet, I., 1999. "Tip-clearance and secondary flows in a transonic compressor rotor". ASME J. Turbom., 121(4), Oct., pp. 751-762.
101. Anderson, W. K., Thomas, J. L., and Van Leer, B., 1986. "Comparison of finite-volume flux-vector-splittings for the Euler equations". AIAA J., 24(9), Sept., pp. 1453-1460.
102. Anderson, W.K., Thomas, J.L., and Rumsey,C.L., 1989. "Extension and application of flux-vector-splitting to calculations on dynamic meshes". AIAA J., 27(6), June, pp. 673-674.
103. (also AIAA Paper 87-1152, 1987).
104. Amone, A., 1994. "Viscous analysis of 3-D rotor flow using a multigrid method". ASME J. Turbom., 116, pp. 435-445.
105. Schumann, U., 1977. "Realizability of Reynolds-stress turbulence models". Phys. Fluids. 20, pp. 721-725.
106. Mottura, L., Vigevano, L., and Zaccanti, M., 2000. "Factorized implicit upwind methods applied to inviscid flows at high mach number". AIAA J., 38(10), Oct., pp. 1846-1852.
107. Chakravarthy, S. R., 1983. "Euler equations - implicit schemes and boundary conditions". AIAA J., 21(5), May, pp. 699-706.
108. MacCormack, R. W., 1982. "A numerical method for solving the equations of compressible viscous flow". AIAA J., 20(9), Sept., pp. 1275-1281.
109. Davis, R. L., Delaney, R. A., Denton, J. D., Giles, M. B., Strazisar, A. J., and Wisler, D. C., 1993. CFD code assessment in turbomachinery - author's information package. ASME Turbomachinery Committee. ASME-IGTI, Atlanta [GA, USA].
110. Strazisar, A. J., 1994. Data report and data diskette for NASA transonic compressor rotor 37. NASA, Lewis Research Center, Cleveland (OH, USA[, Nov.
111. Cumpsty, N. A., and Horlock, J. H., 2006. "Averaging nonuniform flow for a purpose". ASME J. Turbom., 128, pp. 120-129.
112. Giles, M. B., 1990. "Nonreflecting boundary conditions for Euler equation calculations". AIAA J., 28(12), Dec., pp. 2050-2058.
113. Leclercq, M. P., and Stoufflet, P. L., 1993. "Characteristic multigrid method application to solve the Euler equations with unstructured and unnested grids". J Comp. Phys., 104, pp. 329-346.
114. Jameson, A., 1983, "Solution of the Euler equations for 2-D transonic flow by a multigrid method". Appl. Math. Comp., 13, pp. 327-355.
115. Ni, R. H., 1986. "Multigrid convergence acceleration techniques for explicit Euler solvers and applications to Navier-Stokes calculations". In Numerical Techniques for Viscous Flow Calculations in Turbomachinery Bindings, no. LS-1986-02 in Led. Series. VKI, jan.
116. Touyeras, A., and Villain, M., 2004. Aerodynamic design and test result analysis of a 3-stage research compressor. ASME Paper GT2004-53940, June.
117. Shabbir, A., Celestina, M. L., Adamczyk, J. J., and Strazisar, A. J., 1997. The effect of hub leakage on 2 high speed axial flow compressor rotors. ASME Paper 97-GT-346, June.
118. Toro, E. F., 1997. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer Verlag, Berlin [D].
119. Gerolymos, G. A., and Vallet, I., 2004. "Efficient and robust implicit multigrid Reynolds-stress-model computation of 3-D compressible flows". In ECCOMAS 2004 - CD-Rom Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, 24-28 jul 2004, Jyväskylä [FIN], P. Neittaanmäki, T. Rossi, S. Korotov, E. O. nate, J. Périaux, and D. Knörzer, eds., ECCOMAS, University of Jyväskylä, Department of Mathematical Information Technology, (paper 262).
120. Demon, J. D., 1992. "The calculation of 3-D viscous flow through multistage turbomachines". ASME J. Turbom., 114, pp. 18-26.
121. van de Wall, A. G., Kadambi, J. R., and Adamczyk, J. J., 2000. "A transport model for the deterministic stresses associated with turbomachinery blade-row interactions". ASME J. Turbom., 122(4), Oct., pp. 593-603.
122. Hanjalić K., 2005. "Will RANS survive LES? a view of perspectives". ASME J. Fluids Eng., 127, Sept., pp. 831-839.
123. Chaouat, B., and Schiestel, R., 2005. "A new partially integrated transport model for suhgrid-scale stresses and dissipation rates for turbulent developing flows". Phys. Fluids. 17(6), June, pp. 065106.1-065106.19.