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Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing

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Abstract

A modal spectrum technique was used to study coherent instability modes (both axisymmetric and azimuthal) triggered by naturally occurring disturbances in a circular jet. This technique was applied to a high Reynolds number (400,000) jet for both untripped (transitional) and tripped (turbulent) nozzle exit boundary layers, with both cases having a core turbulence level of 0.15%. The region up to the end of the potential core was dominated by the axisymmetric mode, with the azimuthal modes dominating further downstream. The growth of the azimuthal modes was observed closer to the nozzle exit for the jet with a transitional boundary layer. Whether for locally parallel flow or slowly diverging flow, even at low levels of acoustic forcing, the inviscid linear theory is seen to be inadequate for predicting the amplitude of the forced mode. In contrast, the energy integral approach reasonably predicts the evolution of the forced mode.

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Abbreviations

a o a m b m :

constants

A, B :

constants

D :

nozzle diameter

d :

azimuthal probe separation

F :

velocity cross-corrélation function

f :

frequency

k :

azimuthal wave number

M :

Mach number

m :

azimuthal mode number

R :

nozzle radius

Re :

Reynolds number

r :

radial distance

St :

Strouhal numberSt(D)=f D/U j St(θ)=f (θ)/Uj

t:

time

U:

mean velocity

ũ:

coherent comportent of velocity

u′:

fluctuating comportent of velocity

Y :

transverse location

x :

axial distance

δ*:

displacement thickness

θ:

momentum thickness

ϕ:

phase difference

ψ:

azimuthal angle Subscripts

CL :

jet centerline

D :

value based on nozzle diameter

e, o :

jet exit

f :

at frequencyf

B :

value based on momentum thickness

w :

nozzle Wall

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Authors and Affiliations

  1. NYMA Inc., Experimental Fluid Dynamics Section, NASA Lewis Research Center Group, 44142, Brook Park, OH, USA

    G. Raman

  2. National Aeronautics and Space Administration, Lewis Research Center, 44135, Cleveland, OH, USA

    E. J. Rice

  3. Mechanical and Aerospace Engineering, Case Western Reserve University, 44106, Cleveland, OH, USA

    E. Reshotko

Authors
  1. G. Raman
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  2. E. J. Rice
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  3. E. Reshotko
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Additional information

The authors thank Dr R.R. Mankbadi for many helpful discussions and for his guidance in obtaining theoretical estimates for comparison with data. Dr K. Dugas provided useful comments and suggestions to improve the presentation

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Raman, G., Rice, E.J. & Reshotko, E. Mode spectra of natural disturbances in a circular jet and the effect of acoustic forcing. Experiments in Fluids 17, 415–426 (1994). https://doi.org/10.1007/BF01877044

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  • DOI: https://doi.org/10.1007/BF01877044

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