Chapter 3. Instability of the free plane and near – wall plane
jet
Multimedia files Nos. 3.1 – 3.13
The results of researches presented in presentation are published in the following
main articles:
1. M.V. Litvinenko On the formation and role of the longitudinal structures during the laminar breakdown process in jets.
// Thesis for the degree of licentiate in engineering, 2003, Chalmers University of Technology, Göteborg, Sweden, P. 101
2. V.V. Kozlov, G.R. Grek, L. Löfdahl, V.G. Chernorai, M.V. Litvinenko Role of Localized Streamwise Structures in the Process
of Transition to Turbulence in Boundary Layers and Jets (Review) // J. Appl. Mech. Tech. Phys. 2002 Vol. 43, No. 2, pp. 224-236
3. V.G. Chernorai, M.V. Litvinenko, Yu.A. Litvinenko, V.V. Kozlov, E.E. Cherednichenko Longitudinal structures in the near
field of a plane wall jet // Thermophysics and Aeromechanics, 2007, Vol. 14, No. 4, pp. 515-523
Free plane jet
Scheme of the experimental set - up
Settling chamber (1); grids (2); nozzle (3); potential jet core (4); Kelvin-Helmholtz vortices (5);
shear layer (6); laser sheet (7); loudspeaker (8); laser (9); traversing mechanism (10);
sound generator (11); phase shifter (12); roughness elements (13); video camera (14)
General view of the free plane jet
Video file No. 3.1
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Cross section of the free plane jet
Video file No. 3.2
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Free plane jet with top – hat mean velocity profile at the
nozzle exit, U0 = 3 m/s, without acoustic synchronization
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Video file No. 3.3
Free plane jet with top – hat mean velocity profile at the
nozzle exit, U0 = 3 m/s, with acoustic effect (F = 30 Hz)
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Video file No. 3.4
Free plane jet with top – hat mean velocity profile at the
nozzle exit, U0 = 3 m/s, with acoustic effect (F = 30 Hz)
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Video file No. 3.5
Free plane jet cross section
(roughness elements located on one nozzle side)
Roughness elements
Video file No. 3.6
Nozzle outlet
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Three independent one from other instability regions arise in the free plane jet with
top – hat mean velocity profile at the nozzle exit:
1. Two independent one from other narrow regions (two shear layers) near the
nozzle.
2. Region with parabolic shape of velocity gradient – far downstream from the
nozzle.
Conclusions:
1.
Streaky structures in a plane jet can be generated by means of roughness elements
placed at the nozzle exit.
2.
Interaction between streaky structures and Kelvin-Helmholtz ring vortices result in
3D distortion of flow accompanied mushroom – structures origin.
3.
Intensive process of a jet mixing and ambient air takes place in region of the streaky
structures development.
4.
Sixfold increase of a jet Reynolds number (with Re  1.3 × 103 up to 8 × 103)
intensifies of mixing process without qualitative change of observable processes.
Near – wall plane jet
Scheme of the experimental set - up
Near - wall plane jet with natural streaky structures under
acoustic effect (F = 30 Hz) U0 = 3 m/s
General view of the near - wall plane jet
Video file No. 3.7
Cross section of the near - wall plane jet
Video file No. 3.8
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Mean velocity profiles for the boundary layer and
free shear layer
Free shear layer
Boundary layer
Spatio – temporal hot – wire anemometer visualization of the
near – wall plane jet with roughness elements at the nozzle
exit
Streaky structures in a free shear layer (a) and in a boundary layer (b) are shown by
isosurfaces of mean velocity defect - ± 6%U0, (velocity excess and defect are shown
by blue and red colour (on the left) and yellow and blue colour (on the right),
respectively).
Disturbances evolution in the near - wall plane jet
Video file No. 3.9
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Streaky structures (different periodicity) excited by the
roughness elements in a free shear layer
U0 = 8 m/s
U0=15 m/s
Growth of different streak scales at 8 m/s (left) and at 15 m/s
(right). Streaks wavelength: 5 (○), 10 (□), 15 (), 20 (◊), 25
(∆) mm.
1.8
0.8
1.6
0.7
1.4
0.6
, m/s
rms
0.5
1
3D
3D
rms
, m/s
1.2
0.4
0.8
0.3
0.6
0.2
0.4
0.1
0.2
0
10
20
30
40
X, mm
50
60
70
0
10
20
30
X, mm
40
50
60
Near - wall plane jet with forced streaky structures under
acoustic effect, F = 200 Hz - on the left and F = 700 Hz - on
the right (free shear layer section)
Video file No. 3.10
Video file No. 3.11
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Spatio – temporal hot – wire anemometer visualization of the
near – wall plane jet. Acoustic field with frequency 200 Hz,
U0 = 8 m/s. Isosurface level – 0.3 u’max.
x =21mm
x = 31mm
x = 41mm
x = 51mm
Spatio – temporal hot – wire anemometer visualization of the
near – wall plane jet. Acoustic field with frequency 700 Hz, U0
= 8 m/s. Isosurface level – 0.3 – 0.4 u’max.
0.4
x = 6 mm
0.4
x = 10.5 mm
0.3
x = 16.5 mm
0.4
x = 21mm
Near - wall plane jet with the roughness elements under
acoustic effect, F = 700 Hz (jet cross section)
Video file No. 3.12
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Near - wall plane jet with the roughness elements under
acoustic effect, F = 700 Hz (jet streamwise section)
Video file No. 3.13
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PIV- measurements of near - wall plane jet
Smoke visualization pattern of jet cross section (left) and corresponding to it:
isolines of U – velocity component (on the right above) and vector field of V and
W – velocity components (on the right below), x = 120 mm.
PIV- measurements of near - wall plane jet
Isolines of U – velocity component (on the left) and vector field of V and W –
velocity components (on the right), x = 154 mm.
Three – dimensional visualization of the nonlinear
interaction between the optimal streak and the two –
dimensional wave as obtained from DNS (it is taken from
Levin et al., 2005).
KEY POINTS:
The dynamics of a near - wall plane jet is studied using both calculations and
experiments. It is found that an arbitrary laminar wall jet can be successfully described
by the solution of the boundary-layer equations and its solution is valid in the close
downsream field of a nozzle. Afterwards, linear stability of the jet is investigated
experimentally and theoretically. Comparison of the results of linear stability
calculations with experiments shows that the theory is able to predict the most amplified
frequency of the periodical waves and the most amplified scale of the streaks. These
spatiotemporal scales are dominating in experiments with unforced jet. Furthermore,
linear stability theory demonstrates rather high instability of the flow to non – modal
streaks and it seems that this mechanism is responsible for generation of initial of three –
dimensionality of the jet breakdown. Additional support of this conclusion is the
excellent agreement between the calculated and measured amplitude functions of the
streak. The calculations indicate that the optimal disturbance represents streamwise
vortices, which cause the formation of streaks by the so-called lift-up effect. Finally,
experimental studies of nonlinear stage of the laminar flow breakdown are supported by
direct numerical simulation (DNS). Three – dimensional simulation with random and
coherent forcing are provided and both simulations clearly demonstrated that growing
streaks are important for the breakdown process. As experiments and simulations show,
very strong amplification of streaks occurs at the stage of non – linear interaction
between streaks and two – dimensional waves.