Experimental and numerical study of a fluidic oscillator frequency domain characteristics

Fluidic oscillators are fluid devices that provide steady flow at the inlet while generating unsteady flow at the outlet. This paper aims to investigate the frequency domain characteristics of internal pressure fluctuations in a specific type of fluidic oscillator to gain a deeper understanding of its dynamic behavior. The following conclusions were drawn: (1) Within a certain range, as the inlet-to-outlet pressure ratio increases, the oscillation frequency of the fluidic oscillator continuously rises, and the oscillation amplitude strengthens. (2) As the jet nozzle velocity increases within a certain range, the jet oscillation frequency exhibits a linear upward trend. These research findings provide essential academic and engineering guidance for designing and applying fluidic oscillators, assisting engineers in better understanding and controlling the device’s performance to meet the requirements of various application domains.


Introduction
Flow control technology has always been a focal point in the aerospace industry and is also considered an important pathway to enhancing future aircraft performance.
Flow control methods can primarily be divided into two categories: passive control and active control.Passive control involves altering the flow field structure by installing passive flow control devices to eliminate or reduce flow separation, such as installing deflectors, vortex generators, etc.However, the effectiveness of passive control is susceptible to changes in flow conditions, and its control effectiveness may be limited when the flow field deviates from the design stage.
In contrast, active flow control injects minute amounts of external energy into localized regions of the flow field through various actuators to couple with the main flow, thereby achieving effective control over the global flow field.These actuators include synthetic jet actuators, plasma actuators, and others.
Nevertheless, these active flow control methods also have their limitations.For instance, synthetic jet actuators consist of external moving components and control devices, making them structurally complex.At times, substantial energy input is required to achieve the objectives of lift enhancement and drag reduction, limiting their flexibility and efficiency in some applications.
Fluidic oscillators represent an efficient type of active flow control actuator.Their operation is based on the Coanda effect [1], generating unsteady pulsating jets at the exit without needing external moving parts.This simplicity in device design allows for a wide range of exit pulsation frequencies based on variations in inlet pressure, flow rate, and geometric dimensions.Notably, fluidic oscillators can operate reliably even in highly complex external environments.The simplicity, frequency domain characteristics, and robust environmental adaptability of these oscillators are unmatched by other active control IOP Publishing doi:10.1088/1742-6596/2764/1/012018 2 actuators.Consequently, fluidic oscillators are gaining increasing attention and widespread favor in aerospace and other engineering applications.Fluidic oscillators can be categorized into two main types based on the type of jet they produce.The first type is the single-exit sweeping type [2], characterized by constant velocity at the exit but oscillating jet direction within a certain angular range at a specific frequency, creating a sweeping jet.The second type is the dual-exit oscillatory type [3], where the flow through the nozzle undergoes deflection and gradually flows toward one exit.Simultaneously, the primary jet undergoes deflection under controlled flow and flows toward the other exit, causing periodic oscillatory jet formation.
Extensive research on fluidic oscillators has been conducted both domestically and internationally.For instance, Tesar et al. [4] investigated a novel type of feedback-free fluidic oscillator, with one end of the control nozzle connected to the atmosphere and the other completely sealed.They proposed a correlation between the jet oscillation frequency and the propagation rate of pressure pulsations within the sealed end.
Feikema et al. [5] introduced the momentum flux ratio between the control-end jet and the inlet flow to study the switching characteristics of fluidic oscillators.They pointed out that excessively high or low values of this ratio could adversely affect the switching performance of fluidic oscillators.They recommended keeping it within the numerical range of approximately 0.25 for optimal switching effects.
Simoes et al. [6] established a relationship between jet deflection time, jet velocity, and the distance from the jet nozzle to the splitter in controlling and measuring fluidic oscillators, which holds significant importance.
Tesar et al. [7] proposed a method of serially connecting two fluidic oscillators of different sizes, where the smaller oscillator generates high-frequency oscillating airflow to control the larger oscillator, producing oscillating jet flows with high flow rates.
Wang et al. [8] utilized computational fluid dynamics to simulate the flow process of jet switching inside fluidic oscillators.They emphasized the influence of the upstream inflow position on the controlled flow.
Zhou et al. [9] designed a new type of high-speed, high-frequency fluidic oscillator.They established a relationship between the oscillation period/frequency and internal dimensions, thus verifying the pressure propagation and reflection mechanisms within the oscillator.
Wang et al. [10] designed a single-exit fluidic oscillator device.They emphasized that the oscillatory jet velocity is close to the average velocity, enabling the outlet airflow to possess significant kinetic energy, effectively controlling a larger flow field area.
Based on the above analysis, this paper introduces a dual-outlet high-frequency fluidic oscillator and conducts experimental and simulation studies of its internal flow field structure.Firstly, a detailed investigation of the internal pressure fluctuations of the designed fluidic oscillator was carried out through experiments.Subsequently, a CFD analysis of the internal flow structure of the fluidic oscillator was performed to obtain its internal frequency domain characteristics.These research findings provide valuable insights and design concepts for the future development of fluidic oscillators suitable for various flow conditions.

Experimental model
A typical fluidic oscillator consists of structures such as the jet nozzle, control nozzle, splitter, and feedback loop.By designing the structural form and parameters reasonably, it is possible to effectively achieve the wall-attachment effect and periodic oscillation of the jet.The fluidic oscillator described in this paper and its key structural dimensions are shown in Figure 1.In the figure, ○ 1 represents the main jet inlet, ○ 2 represents the jet nozzle, ○ 3 represents the splitter, ○ 4 and ○ 5 represent the jet outlets, ○ 6  represents the feedback loop, and ○ 7 represents the control nozzle.To simplify the experimental model, we have adopted a top and bottom cover plate-clamped fluidic oscillator design scheme.The two-dimensional structure of the top cover plate is detailed in Figure 2. To measure the jet nozzle, feedback loop, and jet pressure at the outlet separately, we have designed pressure sensor mounting holes at the corresponding positions on the top cover plate, as shown in Positions 2, 3, and 4 in Figure 2. Through these mounting holes, we can accurately measure the jet pressure at different locations in the experiment, further delving into the performance characteristics of the fluidic oscillator.The physical form of the entire fluidic oscillator is depicted in Figure 3.

Introduction to the experimental system
The experimental system consists of three main components: the pressure measurement system, the flow measurement system, and the high pressure air source.The pressure measurement system includes pressure probes, high-frequency dynamic pressure sensors with model XTL-190, data acquisition cards, 4 etc.The flow measurement system comprises a float flowmeter with model LZM-15 and a precision pressure regulating valve with model SMC.The high-pressure air source is supplied from a compressed gas cylinder pressurized to 12 MPa, and the high-pressure gas pressure is regulated to the required level for the experiment using a pressure-reducing valve to ensure the stability of air supply pressure and velocity.The entire experimental system is depicted in Figure 4.

Test process description
We open the valve of the high-pressure gas cylinder and adjust it using the precise pressure regulating valve knob to ensure a stable flow of gas into the fluid oscillator.We record the pressure values at the inlet, outlet, and feedback loop of the fluid oscillator at this moment and monitor the air inflow rate indicated by the float flowmeter.In the end, we obtained the inlet-to-outlet pressure ratio Ps/PO and the corresponding volumetric flow rate values, as shown in Table 1.Here, Ps represents the inlet total pressure, and PO represents the ambient pressure.Periodic analysis of pressure changes By adjusting the knob of the precision pressure regulating valve, the inlet total pressure of the fluidic oscillator is modified, and the pressure at the feedback loop is measured using the pressure collection system.Figure 5 shows the variation of the measurement results with time when Ps/PO is 1.55.

Computational model and numerical methods
The numerical computational model of the fluidic oscillator is depicted in Figure 7.In the model, 'S' represents the inlet, while 'O1' and 'O2' are the two outlets.This model possesses specific geometric features, where 'l' and 'w' respectively denote the length and width of the feedback loop.The inlet diameter is 11.2 mm, and the nozzle width is B=2 mm.The feedback loop has a length of l=66 mm and a width of w=5 mm.The overall geometric structure model has a length of 130 mm and a width of 95 mm.We employed grid generation software ICEM to create a non-structured mesh for modeling and meshing the fluidic oscillator.During the mesh generation process, we locally refined the mesh in the near-wall region and the vicinity of the nozzle to enhance the simulation's accuracy and precision.Following mesh independence testing, we obtained a mesh consisting of approximately 100,000 elements.The entire fluidic oscillator grid generation is shown in Figure 8.For the numerical solution of the two-dimensional compressible flow field of the fluidic oscillator, we utilized computational fluid dynamics software Fluent 15.0.We employed the Navier-Stokes equations (N-S equations) for numerical computations in the simulation process.The fluid medium was assumed to be an ideal gas, and the turbulence model selected was the To simulate the flow conditions of the fluidic oscillator, we imposed a no-slip boundary condition on the walls to maintain their smooth characteristics.The inlet boundary condition was set as a pressure inlet to control the pressure conditions within the flow field.Conversely, the outlet boundary was set to represent environmental pressure, simulating the interaction between the fluid and the environment at the exit.

Numerical calculation verification and comparison
To validate the accuracy of our numerical simulations, we conducted a detailed comparison between the numerical results and the experimental data mentioned earlier.As depicted in Figure 9, we present the jet oscillation frequency variation curve with respect to the Ps/PO.
By comparing the graphical data, we can observe the remarkable consistency between the numerical calculations and the experimental results.The presence of this consistency enhances our confidence in the numerical simulation, further ensuring the scientific rigor and reliability of our study.

3.2.2
Oscillation frequency-inlet/outlet pressure ratio We analyze the relationship between oscillation frequency and the Ps/PO, keeping the pressures at both outlets of the oscillator constant, as shown in Figure 10.The graph shows that as Ps/PO increases from 1.1 to 3, the oscillation frequency increases from 300 Hz to 1100 Hz.Specifically, when Ps/PO is less than 3, the oscillation frequency increases with an increase in Ps/PO, but the rate of increase gradually diminishes.However, after Ps/PO reaches 3, the oscillation frequency no longer exhibits significant changes with further increases in the inlet-to-outlet pressure ratio.Instead, it stabilizes.This entire process can be approximated by a polynomial fit represented as y=7574x-4810x 2 +1540x 3 -244.5x 4+15.2x 5 -3825.6,where y represents the oscillation frequency and x represents Ps/PO.
The fundamental reason for this phenomenon lies in the velocity changes at the throat of the oscillator.As shown in the diagram below, with an increase in Ps/PO, the Mach number (Ma) at the throat gradually increases.When Ps/PO reaches 3, the Mach number equals 1, indicating that the velocity at the throat has reached the speed of sound.Consequently, the oscillation frequency no longer increases with further increases in Ps/PO.This further underscores that for a feedback-type fluidic oscillator with fixed geometric dimensions, there exists an upper limit to the outlet jet oscillation frequency, closely related to the velocity at the jet nozzle of the fluidic oscillator.As show in figure 11.

3.2.3
Oscillation frequency-inlet velocity As previously discussed, the oscillation frequency of the outlet jet in a fluidic oscillator is closely related to the velocity at the jet nozzle.The geometric structure of the fluidic oscillator also influences it.There exists an upper limit to the oscillation frequency.Below, we will analyze the specific relationship between the jet oscillation frequency and the velocity at the jet nozzle.By varying Ps/PO, we can obtain different velocities at the jet nozzle and plot the relationship between the oscillation jet frequency and the velocity at the jet nozzle, as shown in the graph below figure 12.The graph shows that as the velocity at the jet nozzle increases from 86 m/s to 330 m/s, the oscillation frequency of the outlet jet increases from 300 Hz to 1100 Hz.Furthermore, this increasing trend appears to be approximately linear and can be represented by a polynomial fit as y=3.38x+40.31,where y represents the oscillation frequency and x represents Ps/PO.Subsequently, as the velocity at the jet nozzle further increases, the oscillation frequency reaches its upper limit and remains constant.

Conclusion
Through experiments and numerical simulations, the frequency domain characteristics of internal pressure fluctuations in a certain type of fluidic oscillator have been investigated, providing an in-depth understanding of the dynamic behavior of this oscillator.The study has yielded several research conclusions of significant academic and engineering importance: 1) Within a certain range, as the inlet-to-outlet pressure ratio increases, the jet oscillation frequency of the fluidic oscillator continues to rise, and the oscillation amplitude gradually strengthens.This indicates that adjusting the inlet-to-outlet pressure ratio can effectively control the oscillation frequency and amplitude of the jet oscillator.This result is significant for applications requiring precise oscillation frequency control, such as flow control systems.
2) Within a certain range, an increase in the jet nozzle velocity leads to a linear increase in the jet oscillation frequency of the fluidic oscillator.This linear relationship provides engineers with a convenient means of frequency control, enabling the achievement of the desired oscillation frequency by adjusting the jet nozzle velocity.This is particularly valuable for applications requiring adjustable frequencies, such as communication equipment.

Figure 1 .
Figure 1.Structure diagram of a fluidic oscillator.To simplify the experimental model, we have adopted a top and bottom cover plate-clamped fluidic oscillator design scheme.The two-dimensional structure of the top cover plate is detailed in Figure2.To measure the jet nozzle, feedback loop, and jet pressure at the outlet separately, we have designed pressure sensor mounting holes at the corresponding positions on the top cover plate, as shown in Positions 2, 3, and 4 in Figure2.Through these mounting holes, we can accurately measure the jet pressure at different locations in the experiment, further delving into the performance characteristics of the fluidic oscillator.The physical form of the entire fluidic oscillator is depicted in Figure3.

Figure 2 .
Figure 2. Upper cover plate of a fluidic oscillator.

Figure 3 .
Figure 3. Physical drawing of a fluidic oscillator.

Figure 4 .
Figure 4. Schematic diagram of the test system.

Figure 5 .
Figure 5. Feedback loop pressure changes with time (Ps/PO=1.55).From the graph above, it can be observed that the pressure at the feedback loop of the fluidic oscillator exhibits a periodic oscillation characteristic.To quantify the intensity of pressure oscillations, we define the pressure amplitude ratio p  as (Pmax-Pmin)/Pavg, where Pmax is the maximum pressure, Pmin is the minimum pressure, and Pavg is the average pressure over one time cycle.The variation of the pressure amplitude ratio p  with the Ps/PO is shown in Figure 6.It can be observed that as the Ps/PO increases, the pressure amplitude ratio

Figure 6 .
Figure 6.Variation curve of pressure amplitude ratio with Ps/PO.

Figure 7 .
Figure 7. Numerical model of a fluidic oscillator.We employed grid generation software ICEM to create a non-structured mesh for modeling and meshing the fluidic oscillator.During the mesh generation process, we locally refined the mesh in the near-wall region and the vicinity of the nozzle to enhance the simulation's accuracy and precision.Following mesh independence testing, we obtained a mesh consisting of approximately 100,000 elements.The entire fluidic oscillator grid generation is shown in Figure8.

Figure 8 .
Figure 8. Mesh generation of a fluidic oscillator.For the numerical solution of the two-dimensional compressible flow field of the fluidic oscillator, we utilized computational fluid dynamics software Fluent 15.0.We employed the Navier-Stokes equations (N-S equations) for numerical computations in the simulation process.The fluid medium was

Figure 9 .
Figure 9. Variation curve of jet oscillation frequency with inlet and outlet pressure ratio.

Figure 10 .
Figure 10.Variation curve of oscillation frequency with Ps/PO.The graph shows that as Ps/PO increases from 1.1 to 3, the oscillation frequency increases from 300 Hz to 1100 Hz.Specifically, when Ps/PO is less than 3, the oscillation frequency increases with an increase in Ps/PO, but the rate of increase gradually diminishes.However, after Ps/PO reaches 3, the oscillation frequency no longer exhibits significant changes with further increases in the inlet-to-outlet pressure ratio.Instead, it stabilizes.This entire process can be approximated by a polynomial fit represented as y=7574x-4810x 2 +1540x 3 -244.5x 4+15.2x 5 -3825.6,where y represents the oscillation frequency and x represents Ps/PO.The fundamental reason for this phenomenon lies in the velocity changes at the throat of the oscillator.As shown in the diagram below, with an increase in Ps/PO, the Mach number (Ma) at the throat gradually increases.When Ps/PO reaches 3, the Mach number equals 1, indicating that the velocity at the throat has reached the speed of sound.Consequently, the oscillation frequency no longer increases with further increases in Ps/PO.This further underscores that for a feedback-type fluidic oscillator with fixed geometric dimensions, there exists an upper limit to the outlet jet oscillation frequency, closely related to the velocity at the jet nozzle of the fluidic oscillator.As show in figure11.

Figure 11 .
Figure 11.Variation curve of throat velocity and mach number with Ps/PO.

Figure 12 .
Figure 12.Variation curve of jet oscillation frequency with jet nozzle velocity.The graph shows that as the velocity at the jet nozzle increases from 86 m/s to 330 m/s, the oscillation frequency of the outlet jet increases from 300 Hz to 1100 Hz.Furthermore, this increasing trend appears to be approximately linear and can be represented by a polynomial fit as y=3.38x+40.31,where y represents the oscillation frequency and x represents Ps/PO.Subsequently, as the velocity at the jet nozzle further increases, the oscillation frequency reaches its upper limit and remains constant.

Table 1 .
Experimental data on inlet and outlet pressure ratio and volumetric flow rate.