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Self-similar properties of decelerating turbulent jets

  • Dong-hyuk Shin (a1), A. J. Aspden (a2) and Edward S. Richardson (a3)

Abstract

The flow in a decelerating turbulent round jet is investigated using direct numerical simulation. The simulations are initialised with a flow field from a statistically stationary turbulent jet. Upon stopping the inflow, a deceleration wave passes through the jet, behind which the velocity field evolves towards a new statistically unsteady self-similar state. Assumption of unsteady self-similar behaviour leads to analytical relations concerning the evolution of the centreline mean axial velocity and the shapes of the radial profiles of the velocity statistics. Consistency between these predictions and the simulation data supports the use of the assumption of self-similarity. The mean radial velocity is predicted to reverse in direction near to the jet centreline as the deceleration wave passes, contributing to an approximately threefold increase in the normalised mass entrainment rate. The shape of the mean axial velocity profile undergoes a relatively small change across the deceleration transient, and this observation provides direct evidence in support of previous models that have assumed that the mean axial velocity profile, and in some cases also the jet spreading angle, remain approximately constant within unsteady jets.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: D.Shin@ed.ac.uk

References

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JFM classification

Type Description Title
VIDEO
Movies

Shin et al. supplementary movie 1
Time evolution of the centreline axial velocity over x of the decelerating jet. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the modelled profile (in a red dashed line) are added.

 Video (1.7 MB)
1.7 MB
VIDEO
Supplementary materials

Shin et al. supplementary movie 1
Time evolution of the centreline axial velocity over x of the decelerating jet. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the modelled profile (in a red dashed line) are added.

 Video (15.0 MB)
15.0 MB
VIDEO
Movies

Shin et al. supplementary movie 2
Time evolution of the radial profile of the scaled axial velocity of the decelerating jet at x/D=10. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a blue line) are added.

 Video (714 KB)
714 KB
VIDEO
Supplementary materials

Shin et al. supplementary movie 2
Time evolution of the radial profile of the scaled axial velocity of the decelerating jet at x/D=10. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a blue line) are added.

 Video (8.8 MB)
8.8 MB
VIDEO
Movies

Shin et al. supplementary movie 3
Time evolution of the radial profile of the scaled axial velocity of the decelerating jet at x/D=18. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a blue line) are added.

 Video (688 KB)
688 KB
VIDEO
Supplementary materials

Shin et al. supplementary movie 3
Time evolution of the radial profile of the scaled axial velocity of the decelerating jet at x/D=18. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a blue line) are added.

 Video (8.3 MB)
8.3 MB
VIDEO
Movies

Shin et al. supplementary movie 4
Time evolution of the radial profile of the scaled radial velocity of the decelerating jet at x/D=10. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added.

 Video (1.3 MB)
1.3 MB
VIDEO
Supplementary materials

Shin et al. supplementary movie 4
Time evolution of the radial profile of the scaled radial velocity of the decelerating jet at x/D=10. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added.

 Video (11.7 MB)
11.7 MB
VIDEO
Movies

Shin et al. supplementary movie 5
Time evolution of the radial profile of the scaled radial velocity of the decelerating jet at x/D=18. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added

 Video (1.2 MB)
1.2 MB
VIDEO
Supplementary materials

Shin et al. supplementary movie 5
Time evolution of the radial profile of the scaled radial velocity of the decelerating jet at x/D=18. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added

 Video (11.7 MB)
11.7 MB
VIDEO
Movies

Shin et al. supplementary movie 6
Time evolution of the radial profile of the scaled u'v' of the decelerating jet at x/D=10. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added.

 Video (1.2 MB)
1.2 MB
VIDEO
Supplementary materials

Shin et al. supplementary movie 6
Time evolution of the radial profile of the scaled u'v' of the decelerating jet at x/D=10. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added.

 Video (11.9 MB)
11.9 MB
VIDEO
Movies

Shin et al. supplementary movie 7
Time evolution of the radial profile of the scaled u'v' of the decelerating jet at x/D=18. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added.

 Video (1.2 MB)
1.2 MB
VIDEO
Supplementary materials

Shin et al. supplementary movie 7
Time evolution of the radial profile of the scaled u'v' of the decelerating jet at x/D=18. The jet inflow is arrested at t=0. For reference, the steady jet profile (in a solid black line) and the averaged profile over t=50-69 tau (in a solid blue line) are added.

 Video (11.2 MB)
11.2 MB
PDF
Supplementary materials

Shin et al. supplementary material
Shin et al. supplementary material

 PDF (3.0 MB)
3.0 MB

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