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

Scheme of the experimental set - up 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 Double click here The free plane jet with top - hat mean velocity profile at the nozzle exit is realized. It is possible to observe development of the Kelvin-Helmholtz instability on a jet plan view .

Cross section of the free plane jet Double click here Video file No. 3.2 It is shown in a jet cross section, that streaky structures generated on top and lower lip of the nozzle penetrate of a jet core.

Free plane jet with top – hat mean velocity profile at the nozzle exit, U0 = 3 m/s, without acoustic synchronization Double click here 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) Double click here 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) Double click here Video file No. 3.5

Free plane jet cross section (roughness elements located on one nozzle side) Video file No. 3.6 Double click here Roughness elements Nozzle outlet On the right nozzle lip the roughness elements are pasted, on the left nozzle lip they are not present. It is shown, that development of streaky structures occurs on the right side more intensively, i.e. there is no penetration of disturbances on the opposite side.

Three independent one from other instability regions arise in the free plane jet with top – hat mean velocity profile at the nozzle exit: Two independent one from other narrow regions (two shear layers) near the nozzle. Region with parabolic shape of velocity gradient – far downstream from the nozzle.

Conclusions: Streaky structures in a plane jet can be generated by means of roughness elements placed at the nozzle exit. Interaction between streaky structures and Kelvin-Helmholtz ring vortices result in 3D distortion of flow accompanied mushroom – structures origin. Intensive process of a jet mixing and ambient air takes place in region of the streaky structures development. 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.

Scheme of the experimental set - up Near – wall plane jet Scheme of the experimental set - up Near - wall plane jet developed along a horizontal plate in length of 2.1 m and width of 3.2 m. Nozzle height of h = 11 mm and width of l = 500 mm.

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 Cross section of the near - wall plane jet Video file No. 3.7 Video file No. 3.8 Natural streaky structures origin and downstream development with the imposed acoustic field are shown. Occurrence of the streaky structures has irregular character. It is shown that longitudinal streaky structures develop both in near wall region and in a mixing layer. Double click here Double click here

Mean velocity profiles for the boundary layer and free shear layer The boundary layer develops directly on a plate, the mixing layer is located above. Mean velocity profiles well agree with calculated Blasius profiles .

Spatio – temporal hot – wire anemometer visualization of the near – wall plane jet with roughness elements at the nozzle exit Spatio - temporal hot - wire anemometric visualization of the jet flow: a - disturbances in a free shear layer, b - disturbances in a boundary layer. That fact, that the cross size of the longitudinal streaky structures developing in a boundary layer in two times more than similar structures in a free shear layer is very interesting. Difference of colors shows difference of the disturbances phases . 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 Double click here Video file No. 3.9 Development of the Kelvin-Helmholtz instability in a free shear layer is shown.

Streaky structures (different periodicity) excited by the roughness elements in a free shear layer U0 = 8 m/s U0=15 m/s Isosurfaces of the mean velocity defect are shown by blue color, excess by red color. It is shown that the most amplifying vortex structures develop behind of large roughnesses (10 and 12.5 mm) with preferable calculated transverse wave length is of 20 - 25 mm. Further downstream from x = 30 mm the 2D Kelvin-Helmholtz vortices intensively grow resulting to changes of characteristic scales of 3D streaky structures aside their reduction.

Growth of different streak scales at 8 m/s (left) and at 15 m/s (right). Streaks wavelength: 5 (○), 10 (□), 15 (), 20 (◊), 25 (∆) mm. It is shown, that the most intensive growth is characteristic for long-wave disturbances with wave length of 25 mm.

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 It is found, that development of the Kelvin-Helmholtz instability is typical of rather low acoustic effect frequencies ~100 - 200 Hz (at the left). At high frequencies there is a suppression of the Kelvin-Helmholtz instability by active development of longitudinal streaky structures (at the right). Double click here Double click here

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 It is shown, that at rather low frequencies Kelvin-Helmholtz instability prevails. Formation of the longitudinal streaky structures is delayed. 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 0.4 x = 6 mm x = 10.5 mm 0.3 0.4 x = 16.5 mm At high frequencies of acoustic effect, 2D Kelvin-Helmholtz instability is suppressed. Longitudinal streaky structures are developed. x = 21mm

Near - wall plane jet with the roughness elements under acoustic effect, F = 700 Hz (jet cross section) Video file No. 3.12 Double click here

Near - wall plane jet with the roughness elements under acoustic effect, F = 700 Hz (jet streamwise section) Video file No. 3.13 The longitudinal horizontal section of the jet is scanned by a light sheet. Strips of 2D waves are observed in near - wall region. Above, the 2D waves are broken by longitudinal streaky structures. Double click here

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.