Internal jet interactions in a fluidic oscillator at low flow rate
This study focuses on the internal jet interactions and the oscillation mechanism of the feedback-free fluidic oscillator at low flow rate, corresponding to a Reynolds number of 1,350 (based on exit nozzle width and average exit velocity). Particle image velocimetry (PIV) was used in this study with a refractive index-matched fluid to minimize reflections that would otherwise occur at the fluid-acrylic interface in the test setup. A simple microphone-tube sensor configuration generated a reference signal, with a phase-averaging method based on each quarter period for velocity time history reconstruction. PIV results revealed the existence of a vortex of fluctuating size, shape, and strength on each side of the oscillator; and two transient vortices that are formed in the dome region of the oscillator by each of the jets once per period. The dome vortices periodically bifurcate each of the jets and transfer some of the kinetic energy of that jet to the opposing jet. This kinetic energy transfer mechanism dictates the dominance of either jet at the exit, and this mechanism repeats itself to sustain the oscillations created by the fluidic oscillator. At this flow rate, the two jets form a continuous mutual collision, and the jets are never completely cut off from the exit. The oscillatory behavior at this flow rate is due to a complex combination of jet interactions and bifurcations, vortex–shear layer interactions, vortex–wall interactions, and saddle point formations.
Characterization of fluidic oscillators is crucial since fluidic oscillators are promising devices for various engineering applications, and there is an increased interest in flow control community to use them as flow control actuators. Wall-attachment-type and jet interaction-type fluidic oscillators are the two main types of the fluidic oscillators (Raghu 2013; Gregory and Tomac 2013). Wall-attachment fluidic oscillators have been extensively studied since the 1960s (e.g., Booth 1962; Spyropoulos 1964; Lush 1968; Gaylord and Carter 1969; Tesař and Bandalusena 2011; Bobusch et al. 2013; Tesař et al. 2013). However, jet interaction fluidic oscillators are relatively new, and more study is required in order to characterize and understand the operating mechanism of this type of fluidic oscillator. These fluidic oscillators are a very special case in the fluidic oscillator family, and its mode of operation is quite different from the standard wall-attachment-type fluidic oscillators with feedback channels. However, absence of diffusers inhibits a reasonable pressure recovery for the jet interaction fluidic oscillators and constricts their usage to applications in which efficiency is not the primary objective.
2 Experimental setup and data analysis
The feedback-free fluidic oscillator creates an oscillating jet as a result of fluid jet interactions in the dome-shaped internal chamber solely based on fluid dynamic principles. A refractive index-matched PIV technique together with a custom microphone-tube sensor setup was used to extract the phase-resolved internal velocity field of the oscillator. A phase-averaging method based on each quarter period is also discussed in detail.
2.1 Fluidic oscillator model
2.2 Refractive index-matched PIV technique
The PIV technique is an optical and non-intrusive experimental technique that provides instantaneous 2D or 3D velocity vectors of a flow field. Most PIV measurements are performed to obtain the external velocity fields over streamlined (i.e., airfoils) or bluff bodies (i.e., cylinders, spheres, etc.). In this present study, the PIV technique was used to extract the internal 2D velocity field of a fluidic oscillator.
Unpreventable reflections due to laser illumination dictated the use of a refractive index-matching fluid. A detailed list of refractive index-matching fluids used in experiments was tabulated by Budwig (1994). Out of all of the refractive index-matched fluids considered, a sodium iodide (NaI) solution was selected for this study. A 60 % NaI solution (by weight) was made with 5.5 kg of NaI added to 3.66 kg of distilled water to yield 5.5 L of solution with a density of 1,730 kg/m3. This solution has a refractive index around 1.5, very close to that of acrylic. The NaI solution was treated with the method suggested by Uzol et al. (2002) and kept in a dark and oxygen-free container. Hollow glass spheres with density of 1,200 kg/m3 and mean particle size of 10 μm were added as tracer particles to the NaI solution. The maximum velocity error induced due to the density difference was calculated to be on the order of 10−4 m/s; thus, any errors due to particle buoyancy are neglected in this study. In refractive index-matched PIV and frequency measurements, the uncertainty due to the effect of temperature on frequency measurements was calculated to be as high as ±3.59 % per °C change. In order to account for the effect of temperature in the calculations of density and viscosity of the NaI solution, temperature-based density and viscosity equations were obtained by polynomial fitting of the values provided by Zaytsev and Aseyev (1992).
PIV measurements were performed with a 200 mJ double-pulsed Nd:YAG 532 nm laser (Quantel Evergreen 200) with a beam diameter less than 6.35 mm, a CCD camera (Cooke Corp. PCO 1600) with a macro lens (Sigma 105 mm, 1:2.8D), a programmable timing unit (LaVison External PTU V. 9.0), and laser sheet-forming optics (a spherical lens and a cylindrical lens) with a pinhole plate. The pinhole plate with 0.8-mm-diameter hole was used to reduce the laser sheet thickness to less than 1 mm since the depth of the fluidic oscillator is 1.5 mm. As shown in Fig. 3, fluidic oscillator was submerged and oriented in a vertical position, such that the exiting jet centerline was parallel to the ground and the cavity was perpendicular to the camera. For the flow rate discussed in this paper (2.8 mL/s), an inter-pulse delay (Δt) of 340 µs was used. For this low flow rate, the pump was placed in a small container in the enclosure, and two holes were drilled on top of this small container allowing NaI to flow down into the container via these holes. By doing this, only surface fluid was allowed to flow into the container, and the surface level difference between the NaI solution enclosure and NaI solution container enhanced mixing. This simple setup increased the amount of hollow glass spheres observed in the interaction chamber of the fluidic oscillator.
LaVision’s Davis 7.2 software was used for data acquisition and post-processing, in conjunction with LabView 8.6 and MATLAB R2011b. In Davis, each image pair was cross-correlated with multi-pass processing (64 × 64 and 32 × 32 window size) with 50 % overlap with the neighboring window and post-processed with the help of a median filter to remove spurious vectors. Furthermore, a 3 × 3 Gaussian smoothing filter applied to the velocity vector fields. Simultaneous PIV and frequency measurements were made possible by externally triggering the Davis software, with the PIV recording controlled by a LabView Virtual Instrument (i.e., whenever the recording was started in LabView, a TTL trigger signal was sent to the Davis software from LabView to start PIV recording simultaneously). The microphone-tube sensor and flow meter were sampled at 5 kHz, and 600 PIV images were simultaneously captured at a rate of 3.75 Hz, yielding 160 s of total recording time. However, due to the fluctuations in flow rate and thus fluctuations in frequency, real-time readings from the microphone-tube sensor were not suitable for phase-locking, and a quarter period-based phase-averaging method was used to solve this problem (to be discussed in Sect. 2.4).
2.3 Microphone-tube sensor setup for frequency measurements in NaI solution
2.4 Quarter period-based method for PIV phase-averaging
The feedback-free fluidic oscillator creates an oscillating jet in a periodic manner. An important step to extract the internal flow field of the oscillator with the PIV technique is to phase-average the velocity fields throughout one period of the oscillation. However, unavoidable flow rate fluctuations complicated the PIV phase-averaging. The flow rate fluctuations in this study were approximately 1 %, leading to concomitant frequency fluctuations as high as 5 % since the frequency of the oscillator depends on the flow rate. To determine the cause of these fluctuations, the flow meter was removed from the main supply line and connected to one of the inlets of the fluidic oscillator to monitor the spectral properties of the signal at one of the inlets. The frequency of the oscillator was found to be measurable from the flow meter signal; however, the peak amplitude was very low and the peak dropped out intermittently. This indicates that not only the pumping system is the cause of the flow rate fluctuations, but the fluidic oscillator itself also has an effect on the fluctuations. Therefore, fluctuations were observed to occur due to the unsteady flow field and a non-ideal fluid supply system. The microphone-tube signal showed a continuously varying amplitude and period due to these fluctuations. Furthermore, even quarter periods were different from one another within a single period. A review of literature indicated that many phase-averaging methods were employed to address turbulent flows and periodic unsteady flows. Alfredsson and Johansson (1984) described some phase-averaging methods such as visual, band-pass filtering, short-time autocorrelation, pattern recognition, and various variable-interval time-averaging (VITA) techniques based on u velocity, v velocity or temperature. These are based on evaluation of the probe signal and were used especially in turbulence production to detect the frequency of occurrence of bursting. Furthermore, phase-averaging can also be obtained by conditional sampling, frequency filtering, and cycle-by-cycle smoothing, with these methods mainly being used to decompose a measured time-varying signal into a mean part and a fluctuating part in periodic unsteady flows (Wernert and Favier 1999).
Summary of main flow physics for the first half of the oscillation
Phase angle (°)
Summary of main flow physics
Upper jet’s core is connected to the exiting jet while the lower jet is bifurcated
Dome region branch of the bifurcated lower jet transfers its kinetic energy to the upper jet
A small lower dome vortex is created by the lower jet left shear layer
Lower side vortex is larger and stronger than the upper side vortex
Size of the lower dome vortex grows as it is fed by the lower jet left shear layer
As the lower dome vortex grows, it moves toward the upper jet and constricts the bifurcated branch of the lower jet in the dome region between itself and the upper jet
Lower dome vortex reaches the upper jet and starts bifurcating it
A saddle point is formed and indicates that the jet bifurcation process is taking place
The bifurcation process changes the flow direction in the dome region from the upper jet to the lower jet in contrast to the previous phase angle
Lower dome vortex collides with the saddle point, and the saddle point disappears indicating that the lower dome vortex had burst
The upper jet is still bifurcated and transferring some of its kinetic energy to the lower jet
The core of the upper jet is no longer connected to the exiting jet
The lower jet’s core is connected to the exiting jet
This time, a small dome vortex is being created by the upper jet
The upper jet is still bifurcated and transferring some of its kinetic energy to the lower jet
Half of the oscillation is completed
Upper dome vortex is growing stronger and larger
The core of the lower jet is still connected to the exiting jet
Upper side vortex is larger and stronger than the lower side vortex
In this study, the internal jet interactions and oscillation mechanism of a feedback-free fluidic oscillator in the low flow rate region were extracted by using a refractive index-matched PIV technique along with a custom made microphone-tube sensor configuration, and a quarter period-based PIV phase-averaging method. It was observed that two jets continuously collide with each other in the low flow rate region; however, jet bifurcation still takes place as the main kinetic energy transfer method between the jets. Phase-averaged PIV results also showed the existence of four main vortices (two dome and two side vortices) created by the shear layers of the two jets. Dome vortices were found to be mainly responsible for the jet bifurcation, and they were observed to appear and vanish throughout the period. Nevertheless, side vortices never vanished; instead, they exhibited continuous changes in size, shape, and strength. While the side vortices went through these changes, they trigger the creation of the dome vortices, push the jets to change their flow direction at the exit, and increase the vorticity of negative sign over the walls. Oscillatory behavior in the low flow rate region is a result of many interesting fluid mechanics phenomena such as jet interactions and bifurcations, vortex–shear layer interactions, vortex–wall interactions, and saddle point formations.
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