Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-25T08:20:25.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculations of self-excited impinging jet flow

Published online by Cambridge University Press:  21 April 2006

Samuel Ohring
Samuel Ohring
Affiliation:
David W. Taylor Naval Ship Research and Development Center, Bethesda, Maryland 20084
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents numerical calculations of the self-excited oscillations of an incompressible planar jet impinging upon a wedge for a Reynolds-number range of 250–650. For this Reynolds-number range these flows are experimentally observed to be two-dimensional and laminar. A finite-difference vorticity/stream-function formulation of the Navier-Stokes equations is employed. The self-sustained flow oscillations result in not just one but several well-defined flow frequency components due to nonlinear interaction of two primary components: the most unstable frequency (β) of the jet shear layer and a low-frequency modulating component ($\frac{1}{3}\beta $). The modulating component results from vortex-vortex interaction at the impingement edge of both like and counter-rotating vortices. Although the interaction pattern varies through the Reynolds-number range studied, the pattern adjusts itself to maintain the modulating component $\frac{1}{3}\beta $ which has a strong upstream influence. The numerical results, in agreement with experimental results, strongly suggest the occurrence of such phenomena as frequency jumps and hysteresis. Pressure at the wedge surface has been calculated and compared with experimental results. Numerical results for wedge torque and lift, which have not been experimentally measured, have also been obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 69 - 98
Copyright
© 1986 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

Goldstein, S. 1938 Modern Developments in Fluid Dynamics, vol. 1. Clarendon.
Kaykayoglu, R. & Rockwell, D. 1986 Unstable jet-edge interaction. Part II: Multiple frequency pressure fields. J. Fluid Mech. (to appear).Google Scholar
Lucas, M. & Rockwell, D. 1984 Self-excited jet: upstream modulation and multiple frequencies. J. Fluid Mech. 147, 333–352.Google Scholar
Lugt, H. J. & Ohring, S. 1975 Laminar flow behavior under slip-boundary conditions. Phys. Fluids 18, 1–8.Google Scholar
Mehta, U. B. & Lavan, Z. 1975 Starting vortex, separation bubbles and stall: A numerical study of laminar, unsteady flow around an airfoil. J. Fluid Mech. 67, 227–256.Google Scholar
Newland, D. E. 1975 An Introduction to Random Vibrations and Spectral Analysis. Longman.
Ohring, S. 1983 Numerical solution of an impinging jet flow problem. Proc. Fifth GAMM Conf. Rome 1983 Vieweg, pp. 267–274.
Plant, T. J. 1977 An exact velocity potential solution of steady, compressible flow over arbitrary, two-dimensional and axisymmetric bodies in simply connected fields. AFFDL-TR-77–116, Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base.
Powell, A. 1961 On the edgetone. J. Acoust. Soc. Am. 33, 395–409.Google Scholar
Rockwell, D. 1983 Oscillations of impinging shear layers. AIAA J. 21, no. 5, 645–664.Google Scholar
Sood, D. R. & Elrod, H. G. 1974 Numerical solution of the incompressible Navier-Stokes equations in doubly-connected regions. AIAA J. 12, 636–641.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn., McGraw Hill.
Thompson, J. F., Warsi, Z. A. U. & Mastin, C. W. 1982 Boundary-fitted coordinate systems for numerical solution of partial differential equations — a review. J. Comp. Phys. 47, 1–108.Google Scholar
Thompson, J. F., Thames, F. C., Mastin, C. W. & Shanks, S. P. 1975 Use of numerically generated body-fitted coordinate systems for solution of the Navier—Stokes equations. AIAA Second Comp. Fluid Dyn. Conf., Hartford, Conn. 19–20 June.