Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T06:31:05.023Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

Published online by Cambridge University Press:  26 April 2006

R. J. Bodonyi ,
W. J. C. Welch ,
P. W. Duck  and
M. Tadjfar
R. J. Bodonyi
Affiliation:
Department of Aeronautical & Astronautical Engineering, The Ohio State University, 2036 Neil Ave. Mall, Columbus, OH 43210, USA
W. J. C. Welch
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
P. W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
M. Tadjfar
Affiliation:
Department of Aeronautical & Astronautical Engineering, The Ohio State University, 2036 Neil Ave. Mall, Columbus, OH 43210, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 285 - 308
Copyright
© 1989 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aizin, L. B. & Polyakov, N. F. 1979 (in Russian) Preprint 17, Akad. Nauk USSR, Siberian Div., Inst. Theor. Appl. Mech., Novosibirsk. (See also Nishioka, M. & Morkovin, M. V. 1986 J. Fluid Mech. 171, 219).
Bodonyi, R. J. & Duck, P. W. 1988 Computers Fluids 16, 279.
Bodonyi, R. J., Smith, F. T. & Gajjar, J. 1983 IMA J. Appl. Maths 30, 1.
Burggraf, O. R. & Duck, P. W. 1981 In Numerical and Physical Aspects of Aerodynamic Flows (ed. T. Cebeci). Springer.
Cooley, J. W. & Tukey, J. W. 1965 Math. Comp. 19, 297.
Duck, P. W. 1984 Q. J. Mech. Appl. Maths 37, 57.
Duck, P. W. 1985 J. Fluid Mech. 160, 465.
Duck, P. W. 1988 J. Fluid Mech. 197, 254.
Duck, P. W. 1989 Computers Fluids (to appear).
Duck, P. W. & Burggraf, O. R. 1986 J. Fluid Mech. 162, 1.
Gedney, C. J. 1983 Phys. Fluids 26, 1158.
Goldstein, M. E. 1983 J. Fluid Mech. 127, 59.
Goldstein, M. E. 1984 J. Fluid Mech. 145, 71.
Goldstein, M. E. 1985 J. Fluid Mech. 154, 509.
Goldstein, M. E. & Hultgren, L. S. 1987 J. Fluid Mech. 181, 519.
Goldstein, M. E., Leib, S. J. & Cowley, S. J. 1987 J. Fluid Mech. 181, 485.
Goldstein, M. E., Sockol, P. M. & Sanz, J. 1983 J. Fluid Mech. 129, 443.
Leehey, P. & Shapiro, P. 1979 In Laminar-Turbulent Transition (ed. R. Eppler & H. Fasel), p. 321. Springer.
Morkovin, M. V. 1969 Rep. AFFDL-TR-68-149. Air Force Flight Dyn. Lab, Wright-Paterson AFB, Ohio.
Murdock, J. W. 1980 Proc. R. Soc. Lond. A 372, 517.
Reshotko, E. 1976 In Ann. Rev. Fluid Mech. 8, 311.
Smith, F. T. 1973 J. Fluid Mech. 57, 803.
Smith, F. T. 1985 Rept. UTRC85-36, United Technologies Research Center.
Smith, F. T. & Bodonyi, R. J. 1982 J. Fluid Mech. 118, 165.
Smith, F. T. & Bodonyi, R. J. 1985 Aeronaut. J. 89, 205.
Smith, F. T. & Bodonyi, R. J. 1987 Stud. Appl. Maths 77, 129.
Smith, F. T. & Brighton, P. W. M., Jackson, P. S. & Hunt, J. C. R. 1981 J. Fluid Mech. 113, 123.
Smith, F. T. & Burggraf, O. R. 1985 Proc. R. Soc. Lond. A 399, 25.
Stewartson, K. 1969 Mathematika 16, 106.
Stewartson, K. 1970 Q. J. Mech. Appl. Maths 23, 137.
Stewartson, K. 1971 Q. J. Mech. Appl. Maths 24, 387.
Tutty, O. R. & Cowley, S. J. 1986 J. Fluid Mech. 168, 431.
Veldman, A. E. P. 1979 Rep. NLR-TR-79023. Dutch Nat. Aerosp. Lab., the Netherlands.