International Journal of Fluid Dynamics (1999), Vol. 3, Article 1
 
Turbulence control in wall jets: a visualisation study
 
M. SCHOBER, F. GREWE and H.H. FERNHOLZ
 
Hermann-Föttinger-Institut für Strömungsmechanik
Technische Universität Berlin
Straße des 17. Juni 135
10623 Berlin, Federal Republic of Germany
 
(Received 25 Feb 1999 and in Revised Form 31 March 1999; Publication Date April 14 1999)


 Abstract

A new method for the control of the mixing of a plane turbulent wall jet has been investigated. A thin wire, mounted in the vicinity of the wall-jet nozzle, changes the formation of the shear-layer structures in the early stages of the development of the wall jet. The wire is operated in two ways: (1) A still wire inhibits the natural shear layer roll-up and reduces the size of the turbulent structures and thereby the mixing; (2) A self-excited oscillating wire introduces large coherent structures and thereby enhances the mixing. The size of these structures does not depend on the shear-layer instability but rather on the wire frequency.

Flow visualisations with paraffin vapour have been performed for these cases. The Reynolds number based on the slot width was in the range of 2500$ \le$Rej $ \le$10000.


1.    Introduction

A plane wall jet is a flow configuration obtained by injecting fluid along a wall at a velocity higher than in the ambient flow. It has features of both a boundary layer and a free shear layer. Main applications are turbine blade cooling and air-foils in high-lift configurations. In the former case it is desirable to prevent the cooling fluid from mixing with the ambient flow in order to sustain the protective layer as far downstream as possible. In the latter case the stimulation of mixing of the wall jet with the ambient flow is desirable in order to supply momentum to a boundary layer threatened, for example, by separation.

Zhou et al. (1996) were able to reduce the skin friction and to increase the spreading in a wall jet by forcing it acoustically. They showed, that the exchange of energy and momentum of the wall jet with its surrounding fluid depends primarily on the large, coherent structures. It is thus important to prevent or to strengthen the formation of these large structures in order to control the mixing of the wall jet with the ambient flow.

Excitation of instabilities is an effective means for flow control. Especially transitional flows are sensitive to the control by excitation of instabilities. A wall jet has two regions which are subject to instabilities; The ``boundary-layer'' region, ranging from the wall up to the point of the local maximum velocity, and the ''shear-layer'' region, ranging from the point of the local maximum velocity to the ambient flow.

Bajura & Catalano (1975) investigated the transition of a two-dimensional plane wall jet at Rej $ \le$600. They found that the Kelvin-Helmholtz instability of the shear layer was responsible for the transition of the whole wall jet. The stages of natural transition were described as the formation of discrete shear-layer vortices, coalescence of adjacent vortices, eruption of these vortices into the ambient fluid and the dispersion of these vortex-patterns into three-dimensional turbulent motion.

In a recent experimental investigation of transition in a wall jet at Rej = 1450, Gogineni & Shih (1997) found dipolar structures. The dipoles were formed by eddies originating from the shear layer and the boundary layer. The dipoles detached from the wall, inducing local reverse flow. These findings are, however, in sharp contrast to the results of Bajura & Catalano (1975), who did not observe flow reversal.

Therefore, we study transition in a wall jet in section 3.1.

Tong & Warhaft (1994) placed a fine circular ring close to the exit of an axisymmetric jet. They achieved a reduction of the spreading rate and of the turbulence intensity. Projected to a plane wall jet, a thin wire placed behind the wall-jet nozzle should enhance the effectiveness of turbine-blade cooling. The effect of such a wire on the wall jet is studied in section 3.2.

Vandsburger & Ding (1995) used an oscillating wire to maximise the spreading of a free shear layer. The wire was placed in the shear layer and performed self-excited oscillations. The oscillating wire led to the formation of large vortical structures. Projected to a plane wall jet, this manipulation should enhance the effectiveness of high-lift air foils or flaps. The effects of an oscillating wire are therefore studied in section 3.3.

The present investigation focuses on the change of the turbulent structures in the vicinity of the wall jet nozzle. It should be noted, however, that although this paper is mainly about transition in a wall jet, the Reynolds number was sufficiently high to ensure a well developed turbulent wall jet at streamwise distances x/b$ \ge$40, where the position x in the streamwise direction is normalised with the slot width b of the wall-jet nozzle. A more detailed comparison of the turbulence characteristics in the self-similar region with recent investigations, i.e. Wygnanski et al. (1992), Abrahamsson et al. (1994) and Eriksson et al. (1998), is given in Schober (1999).

 2.    Experimental facility

Experiments have been carried out in a plane two-dimensional wall-jet shown in Figure 1. The wall jet was driven by a centrifugal fan, allowing for exit velocities uj up to 55 m/s. The Reynolds number based on the jet exit velocity uj and the slot width b = 8 mm ranged from Rej = 2500 to Rej = 10000. At Re $ \ge$ 10000 the turbulent wall jet is self-preserving in the region of 40 $ \leq$ x/b $ \leq$ 150 with respect to the mean and turbulence quantities, as shown, for instance, by Abrahamsson et al. (1994) and Schober (1999). The slot width b of the wall jet was adjustable, but was kept constant at 8 mm throughout the experiments presented in this paper. The jet exit was mounted flush with the test section wall. The slot spanned the whole test section, which had a width of 490 mm.

A thin steel wire with a diameter of d = 0.4 mm was stretched parallel to the wall-jet exit to manipulate the shear layer originating at the nozzle (see figure 1). Strain gauges, mounted on the support prongs, enabled the determination of the wire frequency. By varying the tension of the wire the eigenfrequency could be changed. For the case of the still wire, the tension was adjusted as high as possible, limited only by the wire strength. This was necessary to obtain high eigenfrequencies and avoid the self-excited oscillations. For the case of the oscillating wire, the tension was significantly lowered to obtain eigenfrequencies at fw $ \approx$ 175 Hz.

Figure 1: Wall-jet unit.
\includegraphics[width=0.7\textwidth]{wjskizze-e.eps} 
 
 An electrically heated constantan wire was placed in the settling chamber of the wall jet (see figure 2). Paraffin oil droplets along the wire produced a sheet of oil vapour in the settling chamber. The position of the smoke wire in the settling chamber, where the velocities are small, allowed flow visualisation at the comparably high exit velocity of uj $ \approx$ 10 m/s.
Figure 2: Smoke wire setup
\includegraphics[width=0.7\textwidth]{wjskizze-sicht.eps} 
 
 The positions of the camera and the light source are shown in figure 2. The background was covered with black velvet to reduce light reflections. A stroboscopic lamp was used to freeze the motions of the vortices.

3.     Results

In this section we first investigate transition in an unforced wall jet at Reynolds numbers in the range of
2500$ \le$Rej $ \le$10000 . We then focus on one Reynolds number ( Rej = 5000) and study the effects of the still and the oscillating wire.
 

 3.1    The unforced wall jet

Figure 3 shows smoke visualisations for the unforced wall jet at three different Reynolds numbers, Rej = 2500, 5000, 10000, respectively. At all Reynolds numbers, the smoke filament leaves the nozzle as a nearly straight line, indicating that the flow is laminar. The Kelvin-Helmholtz instability leads to the formation of shear-layer vortices, which subsequently undergo one or more stages of vortex pairing. With increasing Reynolds number, the shear-layer instability and roll-up move upstream. The breakdown of the shear-layer vortices results in large-scale turbulent structures.

At Rej = 2500, two separate shear-layer vortices can be seen at x/b $ \approx$ 5. At x/b $ \approx$ 8, a pairing process takes place, and at x/b $ \approx$ 12, a vortex after the first stage of pairing can be observed.

At Rej = 5000, the processes are the same but take place closer to the wall jet nozzle. The first pairing process occurs at x/b $ \approx$ 5, a second pairing at x/b $ \approx$ 10, and the third pairing process at x/b $ \approx$ 15.

At Rej = 10000, the individual shear-layer vortices cannot be distinguished anymore, since the pairing processes had taken place too rapidly. The resulting coherent structures can, however, still be seen clearly.
 

Figure 3: Visualisation of shear layer structures (unforced) ( $ \leq$ x/b $ \leq$ 17): a) Rej = 2500; b) Rej = 5000; c) Rej = 10000.
\includegraphics[width=\textwidth]{smoke25-10-od.eps} 
 
It has been shown by Wygnanski et al. (1992) that a ``certain'' threshold Reynolds number has to be reached to ensure that the wall jet is self-similar with respect to the mean and fluctuating velocities. A Reynolds number of Rej = 5000 is about the lower limit at which this self similarity can be reached. Abrahamsson et al. (1994) showed that a Reynolds number of Rej = 10000 is well above this threshold. Since the flow visualisation becomes more and more difficult towards higher exit velocities, Rej = 5000 was chosen as a compromise between physical requirements and experimental constraints.

For a better understanding of the dynamics of the shear-layer roll-up and the pairing processes, figure 4 shows a flow-visualisation movie at Rej = 5000. The frequency of the natural shear-layer roll-up is $ \approx$ 1000 Hz.
 

Figure 4: Visualisation of shear layer structures (unforced) (movie 850kB).
\includegraphics[width=0.9\textwidth]{smoke50nowire.eps} 
 
Since the unforced shear-layer roll-up is affected by background disturbances, the process is not perfectly periodic. Therefore, the pairing processes cannot be observed very clearly.

In order to facilitate the observation of the shear-layer roll-up, the wall jet was exposed to a slight acoustical forcing by a loudspeaker located approximately one meter away from the test section. The excitation frequency was about four times the video framing frequency (fe = 100 Hz).
 

Figure 5: Visualisation of shear layer structures (slight acoustical forcing) (movie 500kB).
\includegraphics[width=0.9\textwidth]{smoke50acoustic.eps} 
 The stages of transition are more easily observed in figure 5, which shows a movie of the acoustical forced wall jet. Due to the forcing, the shear-layer roll-up moves upstream. The formation and subsequent pairing of the shear-layer vortices is now clearly visible.

The present results are in good agreement with Bajura & Catalano (1975), although their Reynolds numbers did not exceed Rej = 600. They describe the process of transition as: (1) the formation of discrete shear-layer vortices; (2) the coalescence of adjacent vortices; (3) the eruption of the wall jet into the ambient fluid; and (4) the dispersion of these vortex-patterns into three-dimensional turbulent structures.

We cannot confirm the occurence of dipolar structures observed by Gogineni & Shih (1997) at Rej = 1450. The reason is probably the different velocity profiles at the nozzle of the wall jet. Gogineni & Shih (1997) had a channel flow with a parabolic velocity profile at the exit. The vorticity in the boundary layer and the shear layer region are thus of equal strength but of opposite sign, allowing the formation of dipoles out of one shear layer and one boundary layer vortex. In the present investigation, the shear layer at the nozzle was separated from the boundary layer by a thick potential core, as described in detail by Schober (1999). This potential core inhibits interaction between the boundary layer and the shear-layer region in the early stages of the wall-jet development.

We conclude therefore, that in a wall jet emanating with a thick potential core, laminar to turbulent transition of the wall jet is driven by the growth, pairing and decay of the shear-layer vortices. The boundary layer region plays no important role at these early stages.

 3.2    The wall jet manipulated by a still wire

A simple and effective means of turbulence suppression is to introduce a small obstacle, such as a thin cylinder or wire, into the shear layer. Strykowski & Sreenivasan (1990) suppressed the Kármán vortex street behind a cylinder by placing a small control cylinder into one of the main cylinder shear layers. Tong & Warhaft (1994) suppressed the spreading and the turbulence in an axisymmetric jet by placing a thin ring behind the nozzle, and Rajagopalan & Antonia (1998) reduced the turbulence in a mixing layer with a small cylinder. In all these investigations the shear layer is essentially disturbed by the wake generated by the wire.
 
Figure 6: Visualisation of shear layer structures (still wire) (movie 300kB).
\includegraphics[width=0.9\textwidth]{smoke50stillwire.eps} 
 
Figure 6 shows a visualisation of the shear layer perturbed by the presence of a still wire with a diameter of d = 0.4 mm 1. The formation of shear-layer vortices is inhibited. Similar to a Kármán vortex street, vortex pairing does not occur. Laminar-turbulent transition takes place immediately behind the wire. The structure of turbulence is of a much finer scale than in the unforced case. The spreading rate of the smoke is much smaller than for the unforced case, indicating that the mixing of the wall jet with the ambient fluid decreased.

The wire has to be placed upstream of the position of natural shear-layer roll-up, since the wire can only inhibit the formation of shear-layer vortices, but cannot destroy vortices already formed.
 


Footnote

... mm 1

As already pointed out by Tong & Warhaft (1994), the diameter of the wire is of almost no importance to the effect. 

3.3    The wall jet manipulated by an oscillating wire

During the experiments with the still wire we noticed that under certain conditions the wire performed self-excited oscillations and a high wire tension was necessary to inhibit these oscillations. When the tension was lowered with the wire positioned in the shear layer, the oscillations started. Vandsburger & Ding (1995) reported a similar phenomenom in a mixing layer, where an oscillating ''music'' wire greatly enhanced the mixing.
 
Figure 7: Visualisation of shear layer structures (oscillating wire) (movie 500kB).
\includegraphics[width=0.9\textwidth]{smoke50oscwire.eps} 
 

Figure 7 shows a visualisation of the shear layer structures generated by the oscillating wire. The wire frequency was fw $ \approx$ 175 Hz and thus approximately six times smaller than the natural shear layer instability frequency. The very large coherent structures generated by the wire are clearly visible. Also, several stages of vortex pairing can be observed.

The wire sheds a vortex every time it traverses through the shear layer, thus generating two vortices per cycle. The first vortex, generated when the wire traversed into the potential core, is very small and convects downstream at almost the speed of the wire. It is produced by transporting fluid particles with low kinetic energy into a region with high kinetic energy. The second vortex, generated when the wire moved out of the potential core, is larger than the first one. This second vortex is produced by transporting fluid particles with high kinetic energy into a region with low kinetic energy. Since the sign of the vorticity of both vortices is the same and since they are very close together, pairing takes place immediately at x/b $ \approx$ 4. The next stage of vortex pairing occurs at x/b $ \approx$ 9. The spreading rate of the wall jet is largely enhanced by the oscillating wire.

The vortex shedding frequency solely depends on the oscillation frequency of the wire and the Kelvin-Helmholtz instability is unimportant for the vortex shedding. The wire frequency can be adjusted by varying the wire parameters, most conveniently by changing the wire tension. Choosing low oscillation frequencies results in small vortex shedding frequencies and thus leads to large vortices. Since low frequencies are accomplished by a small wire tension, the amplitude of the wire becomes larger. Since the wire must not touch the nozzle, the amplitude is limited by the distance between the wire and the nozzle. The peak to peak amplitude of the oscillating wire shown in figure 7 was 12 mm. 2 Although the forcing by the oscillating wire is essentially three dimensional due to the variation of the amplitude of the wire along the spanwise direction, the generated structures remain two dimensional within the centre part -0.25 $ \leq$ z/Bk $ \leq$ 0.25. z/Bk denotes the spanwise position normalised by the tunnel width Bk = 490 mm.
 


Footnote

... 12 mm.2
The amplitude of the wire varies along the spanwise direction. It is zero at the support prongs and largest at the centreline of the test section.

3.4    Comparison of the spreading rates

Figure 8 compares the growth of the momentum deficit thickness of the shear layer obtained from hot-wire measurements (Schober 1999) for the three cases.

For the unforced case, $ \delta_{2}^{}$/b remains almost constant for x/b $ \leq$ 1 and rapidly grows for x/b > 1 due to the shear-layer roll-up.

With the still wire inserted, the shear layer is initially thickened by the wake of the wire. But due to the suppression of the shear-layer roll-up the growth rate is reduced, such that for x/b $ \geq$ 2 the manipulated shear layer is smaller than the unforced.

The oscillating wire dramatically increases the shear layer thickness throughout the entire investigated region.
 

Figure 8: Evolution of the shear layer momentum deficit thickness ( Rej = 10000).
\includegraphics[angle=270,width=0.9\textwidth]{d2-x-eng.eps} 

 4.    Conclusions

For the unforced wall jet, which emanates laminar from the wall-jet nozzle, the Kelvin-Helmholtz instability leads to the formation of shear-layer vortices. These vortices undergo several stages of pairing processes leading to relatively large-scale turbulent structures.

Figure 9 compares the structures without, with a still, and with an oscillating wire. The arrows at the right-hand side are of equal length and represent the spreading of the smoke for the unforced case.
 

Figure 9: Comparison of shear layer structures
\includegraphics[width=0.9\textwidth]{smoke50mod4fer.eps} 
 
 A thin wire, placed directly behind the nozzle into the shear layer prevents the shear-layer roll-up. Pairing processes can no longer be observed. The wire significantly reduces the size of the turbulent structures. Both the spreading of the wall jet and the mixing with the ambient fluid are reduced.

A self-excited oscillating wire introduces structures which do not depend upon the shear-layer properties but on the wire frequency. Choosing low oscillation frequencies leads to the formation of large vortices, which increase in size over several stages of vortex pairing. The spreading rate and the mixing is dramatically increased.

Acknowledgements

The authors gratefully acknowledge the financial support by the Deutsche Forschungsgemeinschaft (DFG).

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