Microplasma Actuator for Active Flow Control : Experiment and Simulation

Dielectric Barrier Discharge microplasma actuator energized at low discharge voltage at about 1.4 kV was applied for flow modification. Due to the microplasma generation, the flow velocity showed different characteristics at various duty ratios of the applied voltage. The observation with the high speed camera showed at various time intervals the modification of the flow due to the microplasma. The numerical simulation of the flow was carried out using Suzen model which is assuming that the electric potential of plasma actuator potential can be split in the potential due to the external electric field and potential due to the charge density of plasma.


Introduction
For active flow control applications, dielectric barrier discharge (DBD) plasma actuators offer the advantages of lack of moving parts, fast response due to the electric field and simple construction.Traditionally plasma actuators are energized at voltages of tens of kV [1][2][3].Such high voltages are hard to insulate and requires a large size power supply.It is known that electrohydrodynamic (EHD) phenomenon occurred through the momentum transfer from ions accelerated by electric field to neutral molecules by collision [1][2][3][4][5][6][7][8][9].Our study was carried out to investigate a micro scale plasma actuator energized at 1.4 kV [10][11][12][13][14][15][16][17][18].Some researchers have investigated that the flow direction could be changed by altering the amplitude of the applied voltage [19,20].However, it is difficult to control the amplitude of the voltage continuously.Therefore, in this study the flow direction was changed by controlling the duty ratio of the applied voltage.Reference 21 has shown that synthetic jets applied to modify a flow field have the ability to vector thrust, mix, and reduce noise or thermal signatures.Therefore, it is expected that the diagonal jets induced by microplasma actuators are also effective to the flow modification.
The numerical simulation of the flow modification was carried out using Suzen model [22,23], which was assuming that the electric potential of plasma actuator potential can be split in the potential due to the external electric field and potential due to the charge density of plasma.By calculating these two potentials the body-force could be determined.Furthermore the body force was implemented in the Navier-Stokes equations and the flow is obtained [24].Numerical simulations were carried out also by other researchers [23][24][25][26][27][28][29][30].

Experimental Setup
Fig. 1 shows a schematic image of DBD microplasma actuator [13].Alternating stripe like electrodes (top-side electrode) are placed above a plate like electrode (bottom-side electrode) having a dielectric layer of 25 µm thicknesses in between.The stripe's width was 200 µm and thickness was 16 µm.The number of stripe like electrodes was 20.The active electrodes from the left part of actuator were HV1 and the active electrodes from the right part of the actuator were HV2 as shown in Figure 1.Copper was used for electrodes and resin film was used for dielectric layer.Due to the microscale gap, a high electric field (10 7 ~10 8 V/m) could be obtained at the top-side electrode by applying only 1.4 kV.Flow was visualized by the Particle Tracking Velocimetry (PTV) [31].Sub-micron incense smoke was used for tracer particle.Nd YVO4 532 nm laser was utilized to visualize the flow.The phenomena induced by the microplasma actuator, was measured with a high-speed camera.
The duty ratio D of the actuator was defined as 100% from which the duty ratio of HV2 electrodes was subtracted.Thus if HV2 electrodes were energized at a duty ratio of 20% the HV1 electrodes were energized at 80% and the duty ratio of actuator was considered D = 80%.Figure 2 shows the waveform of applied voltage when D was 50 %.The original applied voltage was AC with the voltage of 1.4 kV and the frequency of 20 kHz.Burst frequency was 4 kHz.

Experimental Results
In the initial part of the discharge the HV1 electrodes were energized at a voltage having duty ratio 70% and HV2 electrodes were energized at a voltage having a duty ratio of 30% (D = 70 %).A diagonal flow was obtained as shown in Fig. 3(a).After achieving a steady state the duty ratio of the voltage applied to HV1 electrodes was increased to 80% and the duty ratio of the voltage applied to HV2 electrodes was decreased to 20% (D = 80%).The angle of the diagonal flow changed and after 50 ms it was achieved a steady state as shown in Fig. 3(b).In the case of D = 70% and 80%, the angles of the diagonal flow were 135° and 145°, respectively.

Simulation
The numerical simulation results showed similar results with the experimental ones.When duty ratio was D = 70% the diagonal flow was obtained as shown in Fig. 3(a).The HV1 electrodes generated counter clockwise flow with higher flow velocity and HV2 electrodes generated clockwise flow with lower flow speed.The duty ratio of D = 80% generated a diagonal flow at an angle that positioned the flow more above the HV2 electrodes as shown in Fig. 3(b).The velocity of the flow generated by the HV1 electrodes is higher at D = 80%.
The simulation was carried out using Suzen model [20,21].The electrohydrodynamic force is: where f is the body force per unit volume, ρc is the net charge density and E is the intensity of the electric field.The magnetic forces where neglected.The electric field is: ⃗⃗ = −∇ (2) where V is the potential.According to Gauss' law: ∇( •  ⃗⃗ ) =   (3) and furthermore: ∇( • ∇) = −  (4) where ε is permittivity that can be expressed as the product of relative permittivity εr and the permittivity of free space ε0.The charge density can be expressed in terms of the potential V and the Debye length λD: Thus the body force can be calculated using equations ( 1) and ( 5).Suzen model considers that because the gas particles are weakly ionized the potential V can be decoupled in a potential due to the external electric field ø, and a potential due to the net charge density φ:  = ∅ +  (6) It results two independent equations: Considering: we can write equation ( 8):

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Furthermore the body force is calculated by:  ⃗ =   •  ⃗⃗ =   (−∇∅) (11) The permittivity between dielectric and air was considered as the harmonic mean between dielectric permittivity taken as εrd=2.7 and air permittivity εrair=1 in order to conserve the electric field [22].The outer boundary conditions for equation (7): The outer boundary conditions for equation (10): The charge distribution over the encapsulated electrode was calculated from equation (10) after considering the covered electrodes as the charge.The value of the source charge was considered same as Suzen [23] ρc =0.00750 C/m 3 .The value of Debye length was λD =0.00017 m for the air and λD = ∞ for the dielectric.
After obtaining the body force from equation ( 11) the Navier-Stokes equations were used to simulate the plasma actuator as shown in ( 14), ( 15) and ( 16 where u and v are the components of the flow velocity on x and y, ρ is the fluid density, p is the pressure and υ is the kinematic viscosity.The dynamic viscosity μ is: Due to the fact that simulating high number of electrodes will increase the mesh dimensions and simulation time, in this study only 8 exposed electrodes and 4 covered electrodes were considered.The exposed electrodes HV1 and HV2 were energized at 1 kV.The experiments were carried out by energizing the exposed electrodes at an AC waveform having amplitude 1.4 kV and 4 kHz.The signal was modulated thus duty ratio of 20%, 30%, 70% and 80% was obtained.For computational simplicity we have considered for the simulation positive pulse signal with peak value of 1 kV since the effective value of 1.4 kV peak AC voltage is about 1 kV.The positive pulse had 20%, 30%, 70% and 80% duty ratio as shown in Figure 5. Equations ( 7), ( 10) and (11) were solved to obtain the potential due to the external electric field ø, the potential due to the net charge density φ, and furthermore the body force.These were computed before solving the Navier-Stokes as shown in Figure 6.The highest intensity of body force was obtained near the active exposed electrodes HV1 and HV2 above the grounded electrodes.Python was used for all the simulations [32].The potential as shown in Figure 6 was calculated by superimposing the potential of the left half part and the potential of the right half part.Thus in the numerical simulation code each part could be independently varied in time.The values shown in Figures 6 correspond to a moment in time when all the active electrodes were energized.This could be also seen in Figure 5 where is shown how the electrodes were energized.From Figure 5 we could observed that there are 4 cases of potential and furthermore body force distribution: first one as mentioned when both HV1 and HV2 electrodes where energized; second one when only the HV1 electrodes were energized and HV2 electrodes not; third one when the HV2 electrodes were energized and HV1 not and fourth case when no electrode is energized.The Navier-Stokes equations were solved using projection method in primitive variables on a collocated mesh.In the simulation two cases were considered: the HV1 electrodes were energized at a voltage having duty ratio 70% and HV2 electrodes were energized at a voltage having a duty ratio of 30% (D = 70 %), and second case when after achieving a steady state the duty ratio of the voltage applied to HV1 electrodes was increased to 80% and the duty ratio of the voltage applied to HV2 electrodes was decreased to 20% (D = 80%).The angle of the diagonal flow changed and after 50 ms it was achieved a steady state as shown in Fig. 7.The diagonal flow with the angle of 136° in the case of D = 70% and 142° in the case of D = 80% was obtained.This simulation results are similar with the experimental results shown in Fig. 3.The highest value of the flow was obtained above near the active electrodes.In the case of D = 70% the maximum flow was 0.92 m/s and in the case of D = 80% the maximum flow was 1.07 m/s.

Conclusion
Microplasma actuator for flow control is a simple and efficient solution for flow control.Due to its size and structure it can be easily integrated in other components.The experimental results showed that the flow could be changed in different directions by modifying the duty ratio of the voltage which energizes different parts of the actuator.When the HV1 electrodes were energized at a voltage having duty ratio 70% and HV2 electrodes were energized at a voltage having a duty ratio of 30%, the angle of generated flow was 135°.On the other hand, when a voltage having duty ratio

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80% was applied to the HV1 electrodes and a voltage having a duty ratio of 20% was applied to the HV2 electrodes, the diagonal flow with the angle of 145° was induced.The larger the duty ratio of applied voltage was, the faster the generated flow was.Therefore, the diagonal flow with the different angle was induced.The numerical simulation using Suzen model and Navier-Stokes equation was carried out.When D = 70% and D = 80%, the angles of obtained flow were 136° and 142°, respectively.This simulation results were similar with the experimental one.However, for simplicity the positive pulse signal was used as the applied voltage in the simulation while the AC voltage was applied to the electrode in the experiments.This caused some differences between experimental and simulation results such as intensity of induced flow.In near future, the conditions of the numerical simulations will be more close to those of the experiments.

Fig. 2 .
Fig. 2. The waveform of applied voltage.Duty ratio is the ratio of the time in which the voltage is on to the sum of the time on and time off.
17) We have considered the values for the air density ρ=1.177 kg/m 3 and for the kinematic viscosity υ=1.57*10 -5 m 2 /s thus dynamic viscosity μ=1.8*10 -5 kg/m s.The outer boundary conditions for u = 0 and v = 0 thus it was considered a closed box.The computational geometry is shown in Figure4.The dimensions of the grid are 11 x 11 mm.The simulation conditions were chosen to be close to the experimental one already shown in Figs. 1 to 3. In the series of experiments shown in previous chapter the plasma actuator had 20 line type exposed electrodes.

Fig. 4 .
Fig. 4. Computational geometry.Upper electrodes at extremities HV1 and HV2 are energized and rest of the electrodes are grounded.

Fig. 6 .
Fig. 6.Electric potential, charge density and body force: Exposed electrodes HV1 and HV2 =1000V; Covered electrode= 0 V. Higher values of body force were obtained near the active electrodes HV1 and HV2.

Fig. 7 .
Fig. 7. Flow: Electrodes HV1 energized by a duty ratio of 70% and HV2 are energized by a voltage the duty ratio of 30%: initial vortexes appeared (2.5 ms); vortexes increase in size (10 ms); diagonal flow towards the right part of the actuator (30 ms); steady state (85 ms); after 85 ms electrodes HV1 were energized by a duty ratio of 80% and HV2 by a voltage with the duty ratio of 20%: diagonal flow towards the right part of the actuator at a different angle than before 85 ms conditions (100 ms); steady state (135 ms). ):