Jet Flapping Control with Acoustic Excitation

The dynamics of flapping motion of a rectangular jet under acoustic excitation is studied experimentally by means of hot-wire measurement and flow visualization with smoke method. The excitation sufficiently enables“phase-lock”, which permitted us to extract the organized wave motion from a background field of finite turbulent fluctuations. The mean and fluctuation velocity are investigated and focused on the excitation frequency and the Reynolds number. As the excitation frequency decreases, it was found that the jet flapping and the jet spread were enhanced. The excitation with sub-harmonic frequency has significant effects on the rectangular jet behavior. The maximum value of the periodic velocity fluctuation strongly depends on the excitation frequency.

• Jet Control; Rectangular Jet; Vortex; Hot Wire; Visualization

1. Introduction

The development of a large coherent structure in a mixing layer of jet flow is responsible for some of the most fascinating aspects of fluid dynamics, such as mixing, transport and instability, etc. In the fields of engineering, jet flows have been extensively investigated because of their widespread applications. The pioneering works on coherent structures in turbulent flow were first confirmed by Crow and Champagne [1] and Brown and Roshko [2]. A lot of researches have been carried out concerning the mechanism and role of coherent structures in jet flows [3-9]. Previous experimental observations by Sato [10] revealed that the jet had sensitivity to external sound, and different initial modes of evolution could lead to distinct growth rates of mixing layers. Ho [11] proposed that the fundamental and sub-harmonic instabilities were significant effects on the vortex formation and merging processes. Ho and Gutmark [12] found that a free jet could be effectively excited by acoustic disturbances in its inherent frequency to obtain more upstream position of a vortex roll-up and more localized, organized and higher energy containing coherent structures. Goldschmidt and Bradshaw [13] originally suggested the flapping motion based on the quasi-periodic negative cross-correlation between the fluctuating longitudinal velocities on either side of the jet centerline. Gortari and Goldshmidt [14] suggested an inviscid mechanism for the flapping motion. Atassi and Lueptow [15] assessed the flapping motion using the linear inviscid analysis and the nonlinear finite-amplitude analysis. Acoustic excitation in this study is one of a zero net mass flux control method. Recently, synthetic jet actuators, which is a net zero mass flux jet, have been shown to be a useful tool for flow control, especially flow vectoring [16] and mixing [17,18]. Jet flow characteristics strongly depend on a forcing condition.

The main objective of the present paper is to examine experimentally the effect of excitation Strouhal number based on the excitation frequency and a mean jet velocity on the jet flapping motion. We conducted flow visualization with smoke method and a velocity measurement to clarify flapping phenomena of the acoustically controlled jet. The flow visualization focused on a development in space of coherent structure evolution in the excited rectangular jet. In order to circumstantially grasp the effects of acoustic excitation on the jet flapping, a concept of phase average was applied to a hot-wire measurement [19]. Since the coherent structure signature and the flapping motion were visually and quantitatively evaluated.

2. Experimental Apparatus and Procedure

A schematic illustration of an experimental setup is shown in Figure 1. The test section including a wind tunnel and a nozzle are set in a sound proof chamber to attenuate perturbations such as noises from outside. Dimensions of the chamber are 2000 mm in height, 1800 mm in width and 2700 mm in length. The inner wall of the chamber is covered with several pieces of glass wool mat of 50 mm thickness except for the floor. A ceiling of the chamber has a socket to mount of the wind tunnel consisted of a silent duct and a flow-rectifying device such as a honeycomb and wire screens. A contraction nozzle is mounted of the tunnel exit. The side wall of the chamber has an exhaust opening to connect through another silent duct to a blower settling outside of the chamber. The blower generates negative pressure by sucking up air in the chamber, then the jet issues from the nozzle exit. The jet velocity is regulated with a variable speed motor attached to the blower. In this experiment, the background noise is 57.9 dB for the blower stopping.

The detailed illustration around a test section is shown in Figure 2. The coordinate system is fixed at the nozzle center, the origin is located at the center of the jet exit, the x-axis is along the jet flow direction, the y-axis is in the horizontal direction perpendicular to the flow, and the z-axis is in the spanwise direction of the nozzle. The tunnel has a rectangular cross section nozzle. Dimensions of the nozzle are 10 mm in width, w, 150 mm in length, h, the aspect ratio (h/w) of 15, and the contraction ratio is 10.0. A honeycomb and fine screens are installed in the tunnel for further managing the flow quality. The flow velocity at the origin was set equal to U₀ = 10, 20, 30 m/s which correspond to Reynolds numbers of 6.7 × 10³, 1.3 × 10⁴, 2.0 × 10⁴. The flow velocity, U₀, is calculated from measured pressure drop across the nozzle. The flow

temperature is kept constant by an air conditioner and a ceiling fan positioned outside the chamber.

Acoustic disturbance is inserted locally through a pair of slot devices which set at the nozzle exit in the spanwise direction of the nozzle. Excitation amplitude is defined as u_prms that the root mean square value of fluctuating velocity at the slot exit. u_prms/U₀ is set at 2.0%. It was confirmed that vortex shedding timing is synchronized with an excitation period at u_prms/U₀ ≥ 0.1%. In particular, u_prms/U₀ = 2% is the most effective condition for jet flapping control. It is noted that streamwise turbulence intensity at the nozzle exit was about 0.4% of U₀ = 10 m/s. The excitation frequency, f_p, was set from 50 to 900 Hz at 50 Hz interval. The jet is excited with the asymmetrical perturbation. The details of the slot structure are shown in a blow up in Figure 2. An opening gap of the slot tip is 0.5 mm and the slot meets the nozzle exit plane at an angle of 30˚. The slot device is shown in Figure 3. The slot is partitioned into eight cells by thin Plexiglas plates shown as Figure 3, and it is therefore possible to impose either symmetric or asymmetric excitation on the jet exit. The slot is connected to a loudspeaker by vinyl pipes having an inner diameter of 9.5 mm. Power of the loudspeaker is 300 watts and the diameter is 300 mm.

The velocity measurement was performed by using a constant temperature anemometer and a hot-wire probe that consisted of a 2.5 μm platinum wire with a length of 1 mm. The hot wire is calibrated by a high-precision pressure transducer and Pitot-tube measurements according to the King’s law. A 16-bit A/D converter is connected to a personal computer for data acquisition. The probe is inserted into a flow from a downstream position by a handmade support to attenuate a flow disturbance. The sensing probe is facilitated by a three-dimensional traversing system that is driven by stepping motors under the personal computer controlled.

Flow visualization was performed by making an alcohol mist suck with the inlet air from the upstream of the tunnel. Photographic recordings of the flow visualization were obtained by employing a six-megapixel camera positioned outside the flow. The smoke was illuminated by flashlight through a slit of 1.5 mm width.

3. Phase Average Technique

The eduction of the coherent structure as well as interpretation of the data requires introduction of the concept of phase average as suggested by Hussain and Reynolds [20]. In this experiment we used the cyclic position of the speaker signal as a clock for selective sampling, which permitted us to extract the organized wave motion from a background field of finite turbulent fluctuations. We decomposed the fluctuating velocity u(x, t) as

U is the streamwise mean velocity, is the periodic (phase average) velocity and is the turbulence velocity. We also used the definition of the phase average velocity at a particular time in the period T of the periodic perturbation, then

The difference between the instantaneous signal and the phase average represents the background random fluctuation, and the difference between the phase average and the time average denotes the (periodic) coherent component. Thus, knowing the period of the induced perturbation, the mean, coherent and random components of the velocity signal can be extracted from the instantaneous total velocity signal.

4. Result and Discussion

4.1. Jet Flow Visualization

Initial conditions of a jet are important to development of the coherent structures in a shear layer and to investigate the flapping motion. The fundamental frequency, f₀, was first measured from frequency spectra along the jet axis to estimate the excitation frequency, f_p, at U₀ = 10 m/s. The power spectra of the velocity fluctuation measured along the jet centerline are shown in Figure 4. The dominant frequency was observed after x/w = 3.5, its value was f₀ = 300 Hz, and reached the peak at x/w = 5, and then decreased. The sub-harmonic frequency was observed in the range x/w > 4.5. The Strouhal number based on the natural vortex shedding frequency and the nozzle width is St = 0.30. The sub-harmonic frequency was gradually appeared at x/w = 4.5, and reached the peak at x/w = 6.0, and observed broader band. In the range of 4.5

< x/w < 5.5, the both frequency components were clearly appeared. The frequency of a large-scale vortex shedding agrees well with the fundamental frequency, f₀, of the spectrum. The velocity spectrum enables us to exactly determine the excitation frequency, so the excitation frequency, f_p, was set to 150 (=f₀/2), 300 (=f₀), 550 Hz. The corresponding Strouhal number for excitation is St_p = 0.15, 0.30, 0.55.

The flow visualization was performed to grasp flow patterns of the excited jet. The jet mean velocity was fixed at U₀ = 10 m/s. The corresponding Reynolds number is Re = 6700. Figures 5(a) to (d) show the photographing images with the each excitation frequency by smoke method. The jet flows from the left to the right. Left images are looked into the vortex structures in the near field of the jet, and the visualization images in the far field are showed in right images. The typical vortex formations in the non-excited jet are shown in Figure 5(a). A shear layer separated from the nozzle lip (y/w = ±0.5) and rolled up into the vortex at about x/w = 3.5 with regular spacing. The non-excited vortex shedding frequency was 300 Hz, it corresponds to f₀. The vortices showed the symmetric alignment which is known as varicose mode. The pair vortex rolled up respect to the jet axis. Then the pair vortex grew up and broke down in the range 3.5 < x/w < 7. The vortex merging process and the jet flapping motion were not observed. Vortex formation in the excited jet is displayed in Figures 5(b)-(d). When the jet was excited at St_p = 0.15, asymmetric alignment of vortices which is known as sinuous mode was clearly observed. The excitation led to the formation switching from the symmetric mode to the asymmetric mode. In this case, it is clearly observed that the jet col-

umn moved laterally. Hence the jet flapping is enhanced with the sub-harmonic and asymmetric excitation. The vortex size is larger than those occurring in the non-excited jet. The roll-up position of vortex was at approximately x/w = 1.5, and the streamwise interval between the vortices was shorter than that of the non-excited jet.

The vortex could still be observed even at the far downstream region. In the right image, it was found that the jet spreading angle after x/w > 4 is approximately two times that of the non-excited jet, which implies enhancement of entrainment. For St_p = 0.30, this Strouhal number is the same as St, the vortex alignment shows sinuous mode, it was close to that for St_p = 0.15. Although the vortex formation was not clear at this excitation frequency, it was found that the roll-up position of vortex shifts upstream than that for St_p = 0.15. The streamwise distance between the vortices was diminished, and the jet spreading rate was decreased in comparison with the result for St_p = 0.15. For St_p = 0.55 as shown in Figure 5(d), the jet spread rate did not change significantly with the excitation. It was almost the same as that in the non-excited jet. These results show that the sub-harmonic excitation is the most effective frequency on the jet flapping motion.

4.2. Velocity Measurement

To investigate the relationship between the velocity distribution and the jet flapping motion, the streamwise mean velocity distribution along the jet axis is measured and shown in Figure 6(a). The potential core region was observed in x/w < 4 without excitation. The velocity decay started at x/w = 4, then the velocity decreased monotonically in the downstream region after x/w = 8. This centerline velocity was proportional to minus one-half power of the x. For the excited jet, on the other hand, the potential core region became shorter. For St_p = 0.15, it was different from the non-excited jet that the velocity decayed slowly from x/w = 10, then rapid decreasing was observed from x/w = 20. The jet has the axsymmetric profile because that the centerline velocity was proportional to minus one power of x. This result shows that the velocity decay decelerating in the region of 10 < x/w < 20 depends on the jet shrinkage to the nozzle spanwise direction. As increasing the forcing Strouhal number, this tendency becomes weak.

Next the distribution of the fluctuating velocity along the jet centerline is plotted in Figure 6(b). Solid marks and open marks show the root mean square value of the periodic velocity, , and the non-periodic velocity, , respectively only for the excited jet. The solid line is the turbulence velocity without excitation, , which includes of periodic velocity, since the velocity decomposition could not be applied to the non-excited jet. The value of grows slowly when the value of St_p is

small, but the peak of is high. This fact supports the relationship, which was revealed by the flow visualization shown in Figure 5, between the flapping motion and the value of St_p. As increasing the value of St_p, a ‘neck’ which is the portion of flapping motion begins to appear shifts upstream, and the flapping amplitude becomes small. For St_p = 0.15, in the downstream region, the value of was still high compared with that the other excitation conditions. When the jet is excited with higher value of St_p, on the contrast, it is found that the grows from more upstream region, and the peak value of becomes smaller. For St_p = 0.15, the distribution of corresponds that of in the upstream region of x/w = 3, but as the value of St_p increases, the value of grows rapidly compared to the nonexcited jet. This tendency is the same as that of. The maximum value of increases with St_p.

The contour maps of the mean velocity U and root mean square value of the velocity fluctuation are shown in Figures 7(a) and (b). The white area in the maps is outside the hot wire measurement. These results indicate only the positive range of y, because of that the jet behavior was symmetry respect to the jet centerline. The high velocity regions are observed near the jet exit in Figure 7(a). It is clearly observed that the streamwiselength of this region is shortened with the excitation, and the jet spreads wider than that for St_p = 0.00. These trends were conspicuous in particular for St_p = 0.15, and were corresponding with the visualization results shown in Figure 5.

In the contour map of the shown in Figure 7(b), the value of fluctuating velocity is high in the shear layer, the region around y/w = 0.5. For St_p = 0.3, this area spreads widely and extends to the downstream direction. For St_p = 0.15, distribution patterns of the value of is completely different from the other excitation conditions. Additionally it should be noted that a high value area of was also observed at x/w = 6 on the jet centerline. This is due to the influence of the large-scale vortex which rolls up in the shear layer reaches to the jet centerline (see Figure 5).

In order to understand the flapping mode oscillation from the instantaneous flow field under the excitation, the contour maps of the velocity for St_p = 0.15, 0.30, 0.55 are shown in Figures 8(a) to (c). The images were extracted at an interval one-fourth of the excitation period T.

Tracking the large-scale cluster of high value of, it is recognized that the jet flaps laterally in the nozzle width direction for all conditions, and the amplitude of the flapping motion is different with the excitation condition. When the value of St_p = 0.15, the jet column strongly flapped laterally, and asymmetrically distributed high-velocity region were observed in the downstream. The spread width of the jet was remarkably enhanced in the region of x/w > 7, associated with the distinctive shedding of the large-scale vortex. For St_p = 0.30, the jet flapping is also observed up to x/w = 7, and the amplitude decays along the jet axis. The flapping frequency was synchronized with that of the excitation, thus the wave length of the flapping for St_p = 0.30 becomes half of that for St_p = 0.15.

A weak flapping motion (oscillation) was observed for St_p = 0.55 of x/w < 2, the oscillation decreased in downstream region as shown in Figure 8(c).

Figure 9 presents distributions of the jet half width plotted against St_p at x/w = 5, 10 and 20. The maximum value of b_y/w occurs for St_p = 0.15 at x/w = 5 and 10, then b_z/w has the minimum value. Also, in comparison between b_y/w and b_z/w, axis switching occurs in the excitation of St_p < 0.35 at x/w = 20. The jet half width of b_y/w decreased with increasing of St_p.

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