1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
f
Modal and transient dynamics of jet flows
Rent:
Rent this article for
Access full text Article
/content/aip/journal/pof2/25/4/10.1063/1.4801751
1.
1. D. Barkley, “Linear analysis of the cylinder wake mean flow,” Europhys. Lett. 75, 750756 (2006).
http://dx.doi.org/10.1209/epl/i2006-10168-7
2.
2. S. Bagheri, P. Schlatter, P. Schmid, and D. Henningson, “Global stability of a jet in crossflow,” J. Fluid Mech. 624, 33 (2009).
http://dx.doi.org/10.1017/S0022112009006053
3.
3. U. Ehrenstein and F. Gallaire, “Two-dimensional global low-frequency oscillations in a separating boundary-layer flow,” J. Fluid Mech. 614, 315 (2008).
http://dx.doi.org/10.1017/S0022112008003285
4.
4. P. Meliga, J. Chomaz, and D. Sipp, “Global mode interaction and pattern selection in the wake of a disk: A weakly nonlinear expansion,” J. Fluid Mech. 633, 159 (2009).
http://dx.doi.org/10.1017/S0022112009007290
5.
5. M. Navarro, L. Witkowski, L. Tuckerman, and P. L. Quéré, “Building a reduced model for nonlinear dynamics in Rayleigh-Bénard convection with counter-rotating disks,” Phys. Rev. E 81, 036323 (2010).
http://dx.doi.org/10.1103/PhysRevE.81.036323
6.
6. O. Marquet, D. Sipp, and L. Jacquin, “Sensitivity analysis and passive control of cylinder flow,” J. Fluid Mech. 615, 221252 (2008).
http://dx.doi.org/10.1017/S0022112008003662
7.
7. E. Akervik, J. Hoepffner, U. Ehrenstein, and D. Henningson, “Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes,” J. Fluid Mech. 579, 305 (2007).
http://dx.doi.org/10.1017/S0022112007005496
8.
8. A. Barbagallo, D. Sipp, and P. Schmid, “Inputoutput measures for model reduction and closed-loop control: Application to global modes,” J. Fluid Mech. 685, 2353 (2011).
http://dx.doi.org/10.1017/jfm.2011.271
9.
9. P. Huerre and P. Monkewitz, “Local and global instabilities in spatially developing flows,” Annu. Rev. Fluid Mech. 22, 473537 (1990).
http://dx.doi.org/10.1146/annurev.fl.22.010190.002353
10.
10. J. Chomaz, “Global instabilities in spatially developing flows: Non-normality and nonlinearity,” Annu. Rev. Fluid Mech. 37, 357392 (2005).
http://dx.doi.org/10.1146/annurev.fluid.37.061903.175810
11.
11. L. Lesshafft, P. Huerre, P. Sagaut, and M. Terracol, “Nonlinear global modes in hot jets,” J. Fluid Mech. 554, 393409 (2006).
http://dx.doi.org/10.1017/S0022112006008974
12.
12. L. Lesshafft, P. Huerre, and P. Sagaut, “Frequency selection in globally unstable round jets,” Phys. Fluids 19, 054108 (2007).
http://dx.doi.org/10.1063/1.2732247
13.
13. S. Crow and F. Champagne, “Orderly structure in jet turbulence,” J. Fluid Mech. 48, 547 (1971).
http://dx.doi.org/10.1017/S0022112071001745
14.
14. D. Bodony and S. Lele, “On using large-eddy simulation for the prediction of noise from cold and heated turbulent jets,” Phys. Fluids 17, 085103 (2005).
http://dx.doi.org/10.1063/1.2001689
15.
15. A. Cooper and D. Crighton, “Global modes and superdirective acoustic radiation in low-speed axisymmetric jets,” Eur. J. Mech. B/Fluids 19, 559574 (2000).
http://dx.doi.org/10.1016/S0997-7546(00)90101-8
16.
16. C. Moore, “The role of shear-layer instability waves in jet exhaust noise,” J. Fluid Mech. 80, 321 (1977).
http://dx.doi.org/10.1017/S0022112077001700
17.
17. J. Nichols and S. Lele, “Non-normal global modes of high-speed jets,” Int. J. Spray Combust. Dyn. 3, 285302 (2011).
http://dx.doi.org/10.1260/1756-8277.3.4.285
18.
18. J. Nichols and S. Lele, “Global mode analysis of turbulent high-speed jets,” Annual Research Briefs 2010 (Center for Turbulence Research, 2010).
19.
19. D. Barkley, M. Gomes, and R. Henderson, “Three-dimensional instability in flow over a backward-facing step,” J. Fluid Mech. 473, 167 (2002).
http://dx.doi.org/10.1017/S002211200200232X
20.
20. O. Tammisola, “Linear stability of plane wakes and liquid jets: Global and local approach,” Ph.D. dissertation (KTH Mechanics, 2009).
21.
21. O. Tammisola, F. Lundell, and L. Soderberg, “Effect of surface tension on global modes of confined wake flows,” Phys. Fluids 23, 014108 (2011).
http://dx.doi.org/10.1063/1.3540686
22.
22. U. Ehrenstein and F. Gallaire, “On two-dimensional temporal modes in spatially evolving open flows: The flat-plate boundary layer,” J. Fluid Mech. 536, 209218 (2005).
http://dx.doi.org/10.1017/S0022112005005112
23.
23. C. Heaton, J. Nichols, and P. Schmid, “Global linear stability of the non-parallel batchelor vortex,” J. Fluid Mech. 629, 139 (2009).
http://dx.doi.org/10.1017/S0022112009006399
24.
24. L. Trefethen, A. Trefethen, S. Reddy, and T. Driscoll, “Hydrodynamic stability without eigenvalues,” Science 261, 578584 (1993).
http://dx.doi.org/10.1126/science.261.5121.578
25.
25. P. Schmid, “Nonmodal stability theory,” Annu. Rev. Fluid Mech. 39, 129162 (2007).
http://dx.doi.org/10.1146/annurev.fluid.38.050304.092139
26.
26. E. Akervik, U. Ehrenstein, F. Gallaire, and D. Henningson, “Global two-dimensional stability measures of the flat plate boundary-layer flow,” Eur. J. Mech. B/Fluids 27, 501513 (2008).
http://dx.doi.org/10.1016/j.euromechflu.2007.09.004
27.
27. B. Farrell and A. Moore, “An adjoint method for obtaining the most rapidly growing perturbation to oceanic flows,” J. Phys. Oceanogr. 22, 338349 (1992).
http://dx.doi.org/10.1175/1520-0485(1992)022<0338:AAMFOT>2.0.CO;2
28.
28. K. Butler and B. Farrell, “Three-dimensional optimal perturbations in viscous shear flow,” Phys. Fluids A 4, 1637 (1992).
http://dx.doi.org/10.1063/1.858386
29.
29. S. Reddy and L. Trefethen, “Pseudospectra of the convection-diffusion operator,” SIAM J. Appl. Math. 54, 1634 (1994).
http://dx.doi.org/10.1137/S0036139993246982
30.
30. C. Cossu and J. Chomaz, “Global measures of local convective instabilities,” Phys. Rev. Lett. 78, 43874390 (1997).
http://dx.doi.org/10.1103/PhysRevLett.78.4387
31.
31. P. Huerre and P. Monkewitz, “Absolute and convective instabilities in free shear layers,” J. Fluid Mech. 159, 151168 (1985).
http://dx.doi.org/10.1017/S0022112085003147
32.
32. S. Reddy and D. Henningson, “Energy growth in viscous channel flows,” J. Fluid Mech. 252, 209238 (1993).
http://dx.doi.org/10.1017/S0022112093003738
33.
33. E. Dick, “Introduction to finite element methods in computational fluid dynamics,” in Computational Fluid Dynamics, edited by J. Wendt (Springer, Berlin, 2009), pp. 235274.
34.
34. T. Matsushima and P. Marcus, “A spectral method for polar coordinates,” J. Comput. Phys. 120, 365374 (1995).
http://dx.doi.org/10.1006/jcph.1995.1171
35.
35. C. Bogey and C. Bailly, “Three-dimensional non-reflective boundary conditions for acoustic simulations: Far field formulation and validation test cases,” Acta Acust. 88, 463471 (2002).
36.
36. P. Monkewitz and K. Sohn, “Absolute instability in hot jets,” AIAA J. 26, 911916 (1988).
http://dx.doi.org/10.2514/3.9990
37.
37. X. Garnaud, L. Lesshafft, and P. Huerre, “Global linear stability of a model subsonic jet,” AIAA Paper No. 2011-3608 2011.
38.
38. W. Reynolds and A. Hussain, “The mechanics of an organized wave in turbulent shear flow. Part 3. theoretical models and comparisons with experiments,” J. Fluid Mech. 54, 263 (1972).
http://dx.doi.org/10.1017/S0022112072000679
39.
39. V. Kitsios, L. Cordier, J. Bonnet, A. Ooi, and J. Soria, “Development of a nonlinear eddy-viscosity closure for the triple-decomposition stability analysis of a turbulent channel,” J. Fluid Mech. 664, 74107 (2010).
http://dx.doi.org/10.1017/S0022112010003617
40.
40. J. Crouch, A. Garbaruk, and D. Magidov, “Predicting the onset of flow unsteadiness based on global instability,” J. Comput. Phys. 224, 924940 (2007).
http://dx.doi.org/10.1016/j.jcp.2006.10.035
41.
41. D. Crighton and M. Gaster, “Stability of slowly diverging jet flow,” J. Fluid Mech. 77, 397 (1976).
http://dx.doi.org/10.1017/S0022112076002176
42.
42. K. Gudmundsson and T. Colonius, “Instability wave models for the near-field fluctuations of turbulent jets,” J. Fluid Mech. 689, 97128 (2011).
http://dx.doi.org/10.1017/jfm.2011.401
43.
43. F. Hecht, “Freefem++ manual, third edition, version 3.16-1,” Technical Report (Université Pierre et Marie Curie, Paris, France, 2011).
44.
44. P. Amestoy, I. Duff, and J.-Y. L'Excellent, “Multifrontal parallel distributed symmetric and unsymmetric solvers,” Comput. Methods Appl. Math. 184, 501520 (2000).
http://dx.doi.org/10.1016/S0045-7825(99)00242-X
45.
45. S. Balay, K. Buschelman, V. Eijkhout, W. Gropp, D. Kaushik, M. Knepley, L. C. McInnes, B. Smith, and H. Zhang, “PETSc users manual,” Technical Report ANL-95/11, Revision 3.0.0 (Mathematics and Computer Science Division, Argonne National Laboratory, 2008).
46.
46. V. Hernandez, J. Roman, and V. Vidal, “SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems,” ACM Trans. Math. Softw. 31, 351362 (2005).
http://dx.doi.org/10.1145/1089014.1089019
47.
47. R. Lehoucq, D. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, 1998).
48.
48. C. Bogey and C. Bailly, “A family of low dispersive and low dissipative explicit schemes for flow and noise computations,” J. Comput. Phys. 194, 194214 (2004).
http://dx.doi.org/10.1016/j.jcp.2003.09.003
49.
49. C. Mack and P. Schmid, “A preconditioned krylov technique for global hydrodynamic stability analysis of large-scale compressible flows,” J. Comput. Phys. 229, 541560 (2010).
http://dx.doi.org/10.1016/j.jcp.2009.09.019
50.
50. X. Garnaud, L. Lesshafft, P. Schmid, and J. Chomaz, “A relaxation method for large eigenvalue problems, with an application to flow stability analysis,” J. Comput. Phys. 231, 3912 (2012).
http://dx.doi.org/10.1016/j.jcp.2012.01.038
51.
51. M. Fosas de Pando, D. Sipp, and P. Schmid, “Efficient evaluation of the direct and adjoint linearized dynamics from compressible flow solvers,” J. Comput. Phys. 231, 77397755 (2012).
http://dx.doi.org/10.1016/j.jcp.2012.06.038
52.
52. A. Hanifi, P. Schmid, and D. Henningson, “Transient growth in compressible boundary layer flow,” Phys. Fluids 8, 826837 (1996).
http://dx.doi.org/10.1063/1.868864
53.
53. A. Michalke, “Survey on jet instability theory,” Prog. Aerosp. Sci. 21, 159199 (1984).
http://dx.doi.org/10.1016/0376-0421(84)90005-8
54.
54. M. Landahl, “A note on an algebraic instability of inviscid parallel shear flows,” J. Fluid Mech. 98, 243 (1980).
http://dx.doi.org/10.1017/S0022112080000122
55.
55. D. Jones and J. Morgan, “The instability of a vortex sheet on a subsonic stream under acoustic radiation,” Math. Proc. Cambridge Philos. Soc. 72, 465 (1972).
http://dx.doi.org/10.1017/S0305004100047320
56.
56. D. Crighton and F. Leppington, “Radiation properties of the semi-infinite vortex sheet: The initial-value problem,” J. Fluid Mech. 64, 393 (1974).
http://dx.doi.org/10.1017/S0022112074002461
57.
57. M. Barone and S. Lele, “Receptivity of the compressible mixing layer,” J. Fluid Mech. 540, 301335 (2005).
http://dx.doi.org/10.1017/S0022112005005884
58.
58. L. Lesshafft, P. Huerre, and P. Sagaut, “Aerodynamic sound generation by global modes in hot jets,” J. Fluid Mech. 647, 473489 (2010).
http://dx.doi.org/10.1017/S0022112009993612
59.
59. P. Schmid and D. Henningson, Stability and Transition in Shear Flows (Springer, New York, 2001).
60.
60. I. Orlanski, “A simple boundary condition for unbounded hyperbolic flows,” J. Comput. Phys. 21, 251269 (1976).
http://dx.doi.org/10.1016/0021-9991(76)90023-1
61.
61. W. Criminale, T. Jackson, and R. Joslin, Theory and Computation of Hydrodynamic Stability (Cambridge University Press, Cambridge, England, 2003).
62.
62.For m = 0 the linearized Navier–Stokes operator is real, so only eigenvalues with ωr ⩾ 0 need to be considered.
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801751
Loading
/content/aip/journal/pof2/25/4/10.1063/1.4801751
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/pof2/25/4/10.1063/1.4801751
2013-04-16
2014-11-27

Abstract

The linear stability dynamics of incompressible and compressible isothermal jets are investigated by means of their optimal initial perturbations and of their temporal eigenmodes. The transient growth analysis of optimal perturbations is robust and allows physical interpretation of the salient instability mechanisms. In contrast, the modal representation appears to be inadequate, as neither the computed eigenvalue spectrum nor the eigenmode shapes allow a characterization of the flow dynamics in these settings. More surprisingly, numerical issues also prevent the reconstruction of the dynamics from a basis of computed eigenmodes. An investigation of simple model problems reveals inherent problems of this modal approach in the context of a stable convection-dominated configuration. In particular, eigenmodes may exhibit an exponential growth in the streamwise direction even in regions where the flow is locally stable.

Loading

Full text loading...

/deliver/fulltext/aip/journal/pof2/25/4/1.4801751.html;jsessionid=m5jqlx8qw9pn.x-aip-live-02?itemId=/content/aip/journal/pof2/25/4/10.1063/1.4801751&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/pof2
true
true
This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Modal and transient dynamics of jet flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/4/10.1063/1.4801751
10.1063/1.4801751
SEARCH_EXPAND_ITEM