Flow visualisations with paraffin vapour have been performed for these
cases. The Reynolds number based on the slot width was in the range of 2500Rej 10000.
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 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/b40, 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).
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 175 Hz.
At Rej = 2500, two separate shear-layer vortices can be seen at x/b 5. At x/b 8, a pairing process takes place, and at x/b 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 5, a second pairing at x/b 10, and the third pairing process at x/b 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.
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
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).
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.
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.
Figure 7 shows a visualisation of the shear layer structures generated by the oscillating wire. The wire frequency was fw 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 4. The next stage of vortex pairing occurs at x/b 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
0.25. z/Bk denotes the spanwise position normalised
by the tunnel width Bk = 490 mm.
For the unforced case, /b remains almost constant for x/b 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 2 the manipulated shear layer is smaller than the unforced.
The oscillating wire dramatically increases the shear layer thickness
throughout the entire investigated region.
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.
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.