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.
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 [
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 [
A schematic illustration of an experimental setup is shown in
The detailed illustration around a test section is shown in
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 uprms that the root mean square value of fluctuating velocity at the slot exit. uprms/U0 is set at 2.0%. It was confirmed that vortex shedding timing is synchronized with an excitation period at uprms/U0 ≥ 0.1%. In particular, uprms/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, fp, 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
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.
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 [
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.
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, fp, at U0 = 10 m/s. The power spectra of the velocity fluctuation measured along the jet centerline are shown in
< 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, fp, was set to 150 (=f0/2), 300 (=f0), 550 Hz. The corresponding Strouhal number for excitation is Stp = 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
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 Stp = 0.30, this Strouhal number is the same as St, the vortex alignment shows sinuous mode, it was close to that for Stp = 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 Stp = 0.15. The streamwise distance between the vortices was diminished, and the jet spreading rate was decreased in comparison with the result for Stp = 0.15. For Stp = 0.55 as shown in
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
Next the distribution of the fluctuating velocity along the jet centerline is plotted in
small, but the peak of is high. This fact supports the relationship, which was revealed by the flow visualization shown in
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
In the contour map of the shown in
In order to understand the flapping mode oscillation from the instantaneous flow field under the excitation, the contour maps of the velocity for Stp = 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 Stp = 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 Stp = 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 Stp = 0.30 becomes half of that for Stp = 0.15.
A weak flapping motion (oscillation) was observed for Stp = 0.55 of x/w < 2, the oscillation decreased in downstream region as shown in