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Dependence of radiated sound frequency on vortex core dynamics in multiple vortex interactions

Published online by Cambridge University Press:  03 February 2016

Z. C. Zheng  and
W. Li
Z. C. Zheng
Affiliation:
[email protected], Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, Kansas, USA
W. Li
Affiliation:
[email protected], Department of Mechanical and Nuclear Engineering, Kansas State University, Manhattan, Kansas, USA
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Abstract

With both theoretical analysis and measurement data, it has been identified previously that there exists a robust sound emission from a pair of counter-rotating aircraft wake vortices at the frequency of unsteady vortex core rotation. In a vortex system with multiple vortices, the sound emission frequency can be subjected to change because of interactions among the vortices. The behaviour of the influence, indicated by the ratio between the core size and the distance of the vortices and the underlining vortex core dynamic mechanisms, is investigated in this study. A vortex particle method is used to simulate the vortex core dynamics in two-dimensional, inviscid and incompressible flow. The flow field, in the form of vorticity, is employed as the source in the far-field acoustic calculation using a vortex sound formula. Cases of co-rotating vortices and a multiple-vortex system composed of two counter-rotating vortex pairs are studied for applications to aircraft wake vortex sound. The study shows, without vortex merging, individual frequencies can be clearly identified that are due each to core rotation (self induction) and co-rotating motion of a vortex centre around the other (mutual induction). The ratio of the core size and the distance between vortices does not seem to significantly influence the frequency of vortex core rotation. With vortex merging, a single frequency due to the merged vortex core is generated.

Type
Research Article
Information
The Aeronautical Journal , Volume 113 , Issue 1142 , April 2009 , pp. 233 - 242
Copyright
Copyright © Royal Aeronautical Society 2009 

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References

1. Zheng, Z.C., Li, W., Wang, F.Y. and Wassaf, H., Influence of vortex core on wake vortex sound emission, J Aircr, 2007, 44, (4), pp 1369–1377.Google Scholar
2. Hardin, J.C. and Wang, F.Y., Sound generation by aircraft wake vortices, December 2003, NASA/CR-2003-212674.Google Scholar
3. Ash, R.L. and Zheng, Z.C., Numerical simulations of commercial aircraft wakes subjected to airport surface weather conditions, J Aircr, 1998, 35, (1), pp 18–26.Google Scholar
4. Han, J., Lin, Y., Arya, S.P. and Proctor, F.H., Numerical study of wake vortex decay and descent in homogeneous atmospheric turbulence, AIAA J, 2000, 38, (4), pp 643–656.Google Scholar
5. Zheng, Z.C., The Betz invariants and generalization of vorticity moment invariants, AIAA J, 2001, 39, (3), pp 431–437.Google Scholar
6. Zheng, Z.C. and Ash, R.L., A study of aircraft wake vortex behavior near the ground, AIAA J, 1996, 34, (3), pp 580–589.Google Scholar
7. Zheng, Z.C. and Baek, K., Inviscid interactions between wake vortices and shear layers, J Aircr, 1999, 36, (2), pp 477–480.Google Scholar
8. Zheng, Z.C. and Lim, S.H., Validation and operation of a vortex-wake/shear interaction model, J Aircr, 2000, 37, (6), pp 1073–1078.Google Scholar
9. Howe, M.S., Theory of Vortex Sound, 2003, Cambridge University Press, Cambridge, UK.Google Scholar
10. Tang, S.K. and Ko, N.W.M., Basic sound generation mechanisms in inviscid vortex interactions at low Mach number, J Sound and Vibration, 2003, 262, pp 87–115.Google Scholar
11. Tang, S.K. and Ko, N.W.M., Sound sources in the interactions of two inviscid two-dimensional vortex pairs, J Fluid Mech, 2000, 419, pp 177–201.Google Scholar
12. Pozrikidis, C., The nonlinear instability of Hill’s vortex, J Fluid Mechanics, 1986, 168, pp 337–367.Google Scholar
13. Zabusky, N.J., Hughes, M.H. and Roberts, K.V., Contour dynamics for the Euler equations in two dimensions, J Computational Physics, 1979, 30, pp 96–106.Google Scholar
14. Crow, S.C., Stability theory for a pair of trailing vortices, AIAA J, 1970, 8, pp 2172–2179.Google Scholar
15. Crouch, J.D., Instability and transient growth for two trailing-vortex pairs, J Fluid Mech, 1997, 350, pp 311–330.Google Scholar
16. Mokry, M., The vortex merger factor in aircraft wake turbulence, Aeronaut J, January 2005, 109, (1091), pp 13–22.Google Scholar
17. Orlandi, P., Two-dimensional and three dimensional direct numerical simulation of co-rotating vortices, Physics of Fluids, 2007, 19, pp 013101-1-013101-18.Google Scholar
18. Cottet, G.-H. and Koumoutsakos, P., Vortex Methods, Theory and Practice, 2000, Cambridge University Press.Google Scholar
19. Mohring, W., On vortex sound at low Mach number, J Fluid Mech, 1978, 85, pp 685–691.Google Scholar
20. Mohring, W., Modelling low Mach number noise, Mechanics of Sound Generation in Flows, 1979, Muller, E.-A. (Ed), Springer.Google Scholar
21. Kambe, T., Minota, T. and Takaoka, T., Oblique collision of two vortex rings and its acoustic emission, Physical Review E, 1993, 48, pp 1866–1881.Google Scholar
22. Knio, O.M., Colorec, L. and Juve, D., Numerical study of sound emission by 2D regular and chaotic vortex configurations, J Computational Physics, 1995, 116, pp 226–246.Google Scholar
23. Mitchell, B.E., Lele, S. and Moin, P., Direct computation of the sound from a compressible co-rotating vortex pair, J Fluid Mech, 1995, 285, pp 181–202.Google Scholar
24. Muller, B., On sound generation by the Kirchhoff vortex, October 1998, Report No 209/1998, Department of Scientific Computing, Uppsala University.Google Scholar
25. Norbury, J., A family of steady vortex rings, J Fluid Mech, 1973, 57, pp 417–431.Google Scholar
26. Pierrehumert, R.T., A family of steady, translating vortex pairs with distributed vorticity, J Fluid Mech, 1980, 99, pp 129–144.Google Scholar
27. Eldredge, J.D., The dynamics and acoustics of two-dimensional leapfrogging vortices, J Sound and Vibration, May 2007, 301, (1-2), pp 74–92.Google Scholar
28. Beale, J.T. and Majda, A., Vortex methods II: high order accuracy in 2 and 3 dimensions, Math Comput, 1982, 32, pp 29–52.Google Scholar
29. Eldredge, J.D., Colonius, T. and Leonard, A., A Vortex particle method for two-dimensional compressible flow, J Comp Physics, 2002, 179, pp 371–399.Google Scholar
30. Kao, H.C., Body-vortex interaction, sound generation, and destructive interference, AIAA J, 2002, 40, (4), pp 652–660.Google Scholar
31. Zheng, Z.C., Far-field acoustic pressure from a system of discrete vortices with time-varying circulation, 2005, AIAA Paper 2005-3005, 11th AIAA/CEAS Aeroacoustics Conference, 23-25 May 2005, Monterey, CA.Google Scholar
32. Melander, M.V., Zabusky, N.J. and Mcwilliams, J.C., Symmetric vortex merger in two dimensions: causes and conditions, J Fluid Mech, 1988, 195, pp 303–340.Google Scholar
33. Waugh, D.W., The efficiency of symmetric vortex merger, Physics of Fluids A, 1992, 4, (4), pp 1745–1758.Google Scholar
34. Saffman, P.G. and Szeto, R., Equilibrium shapes of a pair of equal uniform vortices, Physics of Fluids, 1980, 23, pp 2339–2342.Google Scholar
35. Meunier, P., Ehrenstein, U., Leweke, T. and Rossi, M., A merging criterion for two-dimensional co-rotating vortices, Physics of Fluids, 2002, 14, pp 2757–2766.Google Scholar
36. Tsuboi, K. and Oshima, Y., Merging of two dimensional vortices by the discrete vortex method, J Physical Society of Japan, 1985, 54, (6), pp 2137–2145.Google Scholar
37. Bertenyi, T. and Graham, W.R., Experimental observations of the merger of co-rotating wake vortices, J Fluid Mech, 2007, 586, pp 397–422.Google Scholar