Compressible turbulent flows: Aspects of prediction and analysis [Ludwig Prandtl Memorial lecture presented at the 77th Annual GAMM Conference, Berlin, 27 March 2006]

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 87, Issue 3, 2007, Pages 189-211

  Friedrich, Rainer ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

ADM; Channel and pipe flows; DNS; Green function of pressure fluctuations; LES; Pressure strain correlation; Temporal inert and reacting mixing layers

Indexed keywords

EID: 33947510734     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200610312     Document Type: Article

References (86)

1. L. Prandtl, Zur Theorie des Verdichtungsstoßes, Z. Ges. Turbinenwesen, 3, 241-245 (1906).
2. L. Prandtl, Neue Untersuchungen über die strömende Bewegung der Gase und Dämpfe, Phys. Z. 8, 23-30 (1907).
3. H. Glauert, The effect of compressibility on the lift of an airfoil, Proc. Roy. Soc. London Ser. A 118, 113-119 (1927).
4. A. Busemann, Drücke auf kegelförmige Spitzen in Bewegung mit Überschallgeschwindigkeiten, ZAMM 9, 496-498 (1929).
5. J. Nikuradse, Gesetzmäßigkeiten der turbulenten Strömung in glatten Rohren, VDI-Forschung Heft 356 (1932).
6. J. Nikuradse, Strömungsgesetze in rauhen Rohren, VDI-Forschung Heft 361 (1933).
7. W. Frössel, Strömungen in glatten und rauhen Rohren mit Über- und Unterschallgeschwindigkeit, Forschung Ing.-Wesen 7, 75-84 (1936).
8. K. Oswatitsch, Kondensationserscheinungen in Überschalldüsen, ZAMM 22, 1-44 (1942).
9. K. Oswatitsch, Der Druckwiedergewinn bei Geschossen mit Rückstoßantrieb bei hohen Überschallgeschwindigkeiten, KWI-Bericht (1944). Also: Pressure recovery for missiles with reaction propulsion at high supersonic speed. NACA TM 1140 (1947).
10. K. Oswatitsch and K. Wieghardt, Ludwig Prandtl and his Kaiser-Wilhelm-Institut, Ann. Rev. Fluid Mech. 19, 1-25 (1987).
11. J.C. Rotta, Ludwig Prandtl und die Turbulenz, in: Ludwig Prandtl, ein Führer in der Strömungslehre, edited by G.E.A. Meier (Vieweg Verlag, Braunschweig, 2000), pp. 53-124.
12. L. Prandtl, Bemerkungen zur Entstehung der Turbulenz, ZAMM 1, 431-436 (1921),
13. Also: Phys. Bd. 23, 19-25 (1921).
14. L. Prandtl, Bericht über Untersuchungen zur ausgebildeten Turbulenz, ZAMM 5, 136-139 (1925).
15. L. Prandtl, Über den Reibungswiderstand strömender Luft. Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen, III. Lieferung (Oldenburg, München, Berlin, 1927), pp. 1-5 (1927).
16. L. Prandtl, Zur turbulenten Strömung in Rohren und längs Platten. Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen, IV. Lieferung (Oldenbourg, München, Berlin, 1932), pp. 18-29.
17. Th. v. Kármán, Mechanische Ähnlichkeit und Turbulenz, Proc. 3rd Int. Congress of Applied Mechanics, Stockholm (1930).
18. L. Prandtl and H. Schlichting, Das Widerstandsgesetz rauher Platten. Werft Reed. Hafen 15. Jahrgang (1934).
19. L. Prandtl, Turbulent friction layers in accelerated and retarded flows, in: Aerodynamic Theory, edited by W.F. Durand, Vol. III (Julius Springer, Berlin, 1935). pp. 155-162.
20. L. Prandtl, Betrachtungen zur Mechanik der freien Atmosphäre. Abhandlungen d. Ges. Wiss. Göttingen, Math.-phys. Kl., III. Folge, H. 18, pp. 75-84 (1938).
21. L. Prandtl, Bemerkungen zur Theorie der freien Turbulenz, ZAMM 22, 241-243 (1942).
22. H. Görtler, Berechnung von Aufgaben der freien Turbulenz, ZAMM 22, 244 (1942).
23. L. Prandtl, Über ein neues Formelsystem für die ausgebildete Turbulenz. Nachr. Akad. Wiss., Göttingen, Math. Phys. Klasse, 6-19 (1945).
24. J.C. Rotta, Statistische Theorie nichthomogener Turbulenz, Z. Phys. 129, 547-572;
25. 131, 51-77 (1951).
26. A. M. Yaglom, Homogeneous and isotropic turbulence in viscous compressible fluids, Izv. Akad. Nauk SSSR. Ser. Geograf. Geofiz. 12(6), 501-522 (1948).
27. L. S. G. Kovasznay, Turbulence in supersonic flow. J. Aeronaut. Sci. 20, 657-674 (1953).
28. L. S. G. Kovasznay, The hot-wire anemometer in supersonic flow. J. Aeronaut. Sci. 17, 565-584 (1950).
29. M. V. Morkovin, Effects of compressibility on turbulent flows, in: Mecanique de la Turbulence, edited by A. Favre (CNRS, Paris, 1961), pp. 367-380.
30. H. S. Ribner, Shock-turbulence interaction and the generation of noise. NACA TN-3255 (1954).
31. P. Bradshaw, Compressible turbulent shear layers, Annu. Rev. Fluid Mech. 9, 33-54 (1977).
32. A. J. Smits, Turbulent boundary-layer structure in supersonic flow. Phil. Trans. R. Soc. London Ser. A 336, 81-93 (1991).
33. S. K. Lele, Compressibility effects on turbulence, Annu. Rev. Fluid Mech. 26, 211-254 (1994).
34. H.H. Fernholz and P. J. Finley, A critical compilation of compressible turbulent boundary layer data. AGARDograph AG 223 (1977)
35. and: A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers. AGARDograph AG 253 (1980).
36. J.-P. Dussauge and A. J. Smits, Turbulent shear layers in supersonic flow (AIP Press, New York, 1996).
37. P. Chassaing, R.A, Antonia, F. Anselmet, L. Joly, and S. Sarkar, Variable Density Fluid Turbulence, Fluid Mechanics and its Applications, Vol. 69 (Kluwer Academic Publishers, Dordrecht, 2002).
38. W. J. Feiereisen, W. C. Reynolds, and J. H. Ferziger, Numerical simulation of a compressible homogeneous turbulent shear flow. Rep. TF-13, Thermosci. Div., Dept. Mech. Eng., Stanford University (1981).
39. G. Erlebacher, M. Y. Hussaini, H. O. Kreiss, and S. Sarkar, The analysis and simulation of compressible turbulence, Theor. Comp. Fluid Dyn. 2, 73-95 (1990).
40. G. A. Blaisdell, N. N, Mansour, and W. C. Reynolds, Compressibility effects on the growth and structure of homogeneous turbulent shear flow, J. Fluid Mech. 256, 443-485 (1993).
41. S. Sarkar, G. Erlebacher, M.Y. Hussaini, and H.O. Kreiss, The analysis and modeling of dilatational terms in compressible turbulence, J. Fluid Mech. 227, 473-493 (1991).
42. S. Lee, S. K. Lele, and P. Moin, Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533-562 (1993), Corrigendum in 264, 373-374 (1993).
43. R. Hannappel and R. Friedrich, Direct numerical simulation of a Mach 2 schock interacting with isotropic turbulence, Appl. Sci. Res. 54, 205-221 (1995).
44. K. Mahesh, S. K. Lele, and P. Moin, The influence of entropy fluctuations on the interaction of turbulence with a shock wave. J. Fluid Mech. 334, 353-379 (1997).
45. A.W. Vreman, N.D. Sandham, and K.H. Luo, Compressible mixing layer growth rate and turbulence characteristics, J. Fluid Mech. 320, 235-258 (1996).
46. J. B. Freund, S. K, Lele, and P. Moin, Compressibility effects in a turbulent annular mixing layer. Part 1. Turbulence and growth rate, J. Fluid Mech. 421, 229-267 (2000).
47. C. Pantano and S. Sarkar, A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329-371 (2002).
48. T. A. Manning and S. K. Lele, A numerical investigation of sound generation in supersonic jet screech. AIAA/CEAS Paper 2000-2081.
49. M. M. Rai, T. B. Gatski, and G. Erlebacher, Direct simulation of spatially evolving compressible turbulent boundary layers. AIAA pap. 95-0583 (1995).
50. T. Maeder, N. A. Adams, and L. Kleiser, Direct simulation of turbulent supersonic boundary layers by extended temporal approach, J. Fluid Mech. 429, 187-216 (2001).
51. G. N. Coleman, J. Kim, and R. D. Moser, A numerical study of turbulent supersonic isothermal-wall channel flow, J. Fluid Mech. 305, 159-183 (1995).
52. R. Lechner, J. Sesterhenn, and R. Friedrich, Turbulent supersonic channel flow, J. Turbulence 2, 1-25 (2001).
53. N. A. Adams, Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Re = 1685, J. Fluid Mech. 420, 47-83 (2000).
54. M.-M. MacLow and R.S. Klessen, Control of star formation by supersonic turbulence, Rev. Mod. Phys. 76, 125-194 (2004).
55. P. Moin and K. Mahesh, Direct numerical simulation: A tool in turbulence research, Annu. Rev. Fluid Mech. 30, 539-578 (1998).
56. S. K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comp. Phys. 103, 16-42 (1992).
57. K.W. Thompson, Time dependent boundary conditions for hyperbolic systems II, J. Comp. Phys. 89, 439-461 (1990).
58. C. K. Q. Tam and Z. Dong, Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow, CEAS/AIAA Paper 95-007 (1995).
59. T. Colonius, S. K. Lele, and P. Moin, Boundary conditions for direct computation of aerodynamic sound generation, AIAA J. 31, 1174-1582 (1993).
60. S. K. Lele, Direct numerical simulations of compressible turbulent flows: Fundamentals and Applications, in: Transition, Turbulence and Combustion Modelling, edited by A. Hanifi et al. (Kluwer Academic Publishers, Dordrecht, 1999), pp. 421-488.
61. P. Sagaut, Large eddy simulation for incompressible flows, 3rd edn (Springer, Berlin, 2006).
62. J. A. Domaradzki and N. A. Adams, Direct modelling of subgrid scales of turbulence in large-eddy simulation, J. Turbulence 3, 024 (2003).
63. S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11, 1699-1701 (1999).
64. A. Leonard, Energy cascade in large-eddy simulations of turbulent fluid flows, Adv. Geophys. A 18, 237-248 (1974).
65. P.H. van Cittert, Z. Physik 69, 298 (1931).
66. B. Geurts, Inverse modelling for large-eddy simulations, Phys. Fluids 9, 3585 (1997).
67. J. Bardina, J. H. Ferziger, and W. C. Reynolds, Improved turbulence models based on large-eddy simulation of homogeneous, incompressible, turbulent flows. Technical Report TF-19. Dept. of Mechanical Engineering, Stanford University (1983).
68. S. Stolz, N. A. Adams, and L. Kleiser, The approximate deconvolution model for LES of compressible flows and its application to shock-turbulent- boundary-layer interaction, Phys. Fluids 13, 2985-3001 (2001).
69. J. Mathew, R. Lechner, H. Foysi, J. Sesterhenn, and R. Friedrich, An explicit filtering method for large-eddy simulation of compressible flows, Phys. Fluids 15, 2279-2289 (2003).
70. J. Mathew, H. Foysi, and R. Friedrich, A new approach to LES based on explicit filtering, Int. J. Heat Fluid Flow 27, 594-602 (2006).
71. P. G. Huang, G. N. Coleman, and P. Bradshaw, Compressible turbulent channel flows: DNS results and modelling, J. Fluid Mech. 305, 185-218 (1995).
72. H. Foysi, S. Sarkar, and R. Friedrich, Compressibility effects and turbulence scalings in supersonic channel flow, J. Fluid Mech. 509, 207-216 (2004).
73. H. Foysi, Transport passiver Skalare in wandgebundener und isotroper kompressibler Turbulenz. Dissertation, TU Munchen, Fakultät für Maschinenwesen, 10. Februar, 2005.
74. τ = 590, Phys. Fluids 9, 943-945 (1999).
75. W. D. Thacker, S. Sarkar, and T. B. Gatski, Analyzing the influence of compressibility and shear on the rapid pressure-strain rate correlation. To appear: Theoretical and Computational Fluid Dynamics (2007).
76. J. Kim, On the structure of pressure fluctuations in simulated turbulent channel flow, J. Fuid Mech. 205, 421-451 (1989).
77. K. Mohseni and T. Colonius, Numerical treatment of polar coordinate singularities, J. Comp. Phys. 157, 787 (2000).
78. S. Stolz, Large-eddy simulation of complex shear flows using an approximate deconvolution model. PhD thesis, ETH Zürich (2000).
79. S. Ghosh, J. Sesterhenn, and R. Friedrich, DNS and LES of compressible turbulent pipe flow with isothermal wall, in: Direct and Large-Eddy Simulation IV (Springer, Dordrecht, 2006), pp. 721-728.
80. A. Ern and V. Giovangigli, Fast and accurate multi-component transport property evaluation, J. Comp. Phys. 120, 105-116 (1995).
81. W. Gardiner, Combustion Chemistry (Springer, New York, 1984).
82. N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 2000).
83. C. Pantano, S. Sarkar, and FA. Williams, Mixing of a conserved scalar in a turbulent reacting shear layer, J. Fluid Mech. 481, 291-328 (2003).
84. I. Mahle, J. Sesterhenn, and R. Friedrich, Turbulent mixing in temporal compressible shear layers involving detailed diffusion processes. J. Turbulence, in press (2007).
85. S. Sarkar, The high-speed turbulent shear layer, in: Variable Density Fluid Turbulence, edited by P. Chassaing et al., Fluid Mechanics and its Applications, Vol. 69 (Kluwer Academic Publishers, Dordrecht, 2002), Chapter 9, pp. 235-259.
86. J. Kreuzinger, R. Friedrich, and T. B. Gatski, Compressibility effects in the solenoidal dissipation rate equation: A priori assessment and modeling, Int. J. Heat Fluid Flow 27, 696-706 (2006).