# Mixing Enhancement Downstream of an Active Square-Mesh Grid Using Plasma Actuation

Tom Fridlender, Nicolas Bénard, Jean-Paul Bonnet, Éric Moreau

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## To cite this version:

Tom Fridlender, Nicolas Bénard, Jean-Paul Bonnet, Éric Moreau. Mixing Enhancement Downstream of an Active Square-Mesh Grid Using Plasma Actuation. AIAA Journal, 2024, 62 (8), pp.1-5. 10.2514/1.J063712. hal-04778465

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Submitted on 15 May 2025

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# Mixing enhancement downstream of an active square-mesh grid using plasma actuation

T. Fridlender<fnref n="1" />, N. Benard<fnref n="2" />, J.P. Bonnet<fnref n="3" /> and E. Moreau<fnref n="4" />

Institut PPRIME - UPR 3346 - CNRS - Université de Poitiers - ISAE/ENSMA, SP2MI Téléport 2
Bd Marie & Pierre Curie BP 30179, 86962 Futuroscope Chasseneuil Cedex, France

## I. Introduction

Square-mesh grids are used to study canonical transition from large scale motion to homogeneous and isotropic turbulence. Shear layers form behind regularly spaced square rods, leading to the buildup of Turbulent Kinetic Energy (TKE) as large eddies emerge and grow. TKE peaks where shear layers interact, followed by decay and dissipation into smaller eddies along the wake. Simmons and Salter's work aroused interest by being the first laboratory experiment indicating “completely diffused turbulent motion” 15 mesh lengths away from their grid [1]. From there onwards, a wave of experiments focused on passively enhancing transition to isotropy and homogeneity by studying multiple grid arrangements [2], modifying initial free-stream conditions [2], [3] or the grid geometry [5], [6]. Other experimenters shed light on a different approach: active grids. Although little-studied, they have been used to recreate large scale turbulence in small laboratory wind-tunnels [7] or to influence the TKE decay exponent through different magnitudes of a constant momentum injection [8] among other applications. Active grids, while effective, present structural drawbacks due to moving parts prone to wear and jets introducing discrete momentum, potentially delaying transition to homogeneous turbulence. Additionally, they lack excitation across a wide range of frequencies.

Here, a novel square-mesh active grid equipped with plasma dielectric barrier discharge (DBD) is presented. The plasma technology used in this experimental research is similar to typical linear plasma DBD constituted of a dielectric layer separating one grounded electrode from an exposed conductor supplied with a high AC voltage [9, 10]. As for motorized active grid, the presented plasma grid is intended as a local active mixing enhancer but with the ability to excite a broad band of frequencies going from shear layer modes to small-scale actuation as a final goal [11].

## II. Experimental apparatus and procedure

### A. Grid geometry, power supply and electrical measurement systems

The grid is composed of a thin multi-layer ceramic (total thickness of 1 mm) perforated to create 64 rounded-edge square holes (see Fig. 1a). The mesh size (distance between the center of two adjacent rods) is M = 12.24 mm, with 7 regularly spaced square rods in the y and z directions. The rod thickness is e = 2.09 mm, resulting in a relatively low solidity of $\sigma = 0.31$.

The discharge initiates by supplying the air-exposed electrode with a high alternating voltage and connecting the encapsulated electrode to the ground. The active electrode is supplied with a high VAC amplitude and high fAC frequency sinusoidal voltage output by a TREK model 30 kV/40 mA amplifier. The electric field near the edges of the exposed electrode periodically can exceed the breakdown voltage of surrounding air. The plasma discharge then develops on the surface of the dielectric barrier along the 400 µm horizontal gap and appears to extend further around the rods (see Fig. 1b). The setup for measuring current and electrical charge involves utilizing a 100 Ω non-inductive shunt resistor and a 47 nF capacitor. Voltage signals are captured using a voltage probe (Lecroy PPO18) connected to a Teledyne HDO6054 - 500 MHz oscilloscope. The electrical power consumption of the grid (Pelec) is determined by

<footnote n="1">¹ PhD candidate, AIAA student member.</footnote>

<footnote n="2">² Associate professor, nicolas.benard@univ-poitiers.fr, AIAA senior member.</footnote>

<footnote n="3">³ Emeritus Director of Research, CNRS.</footnote>

<footnote n="4">⁴ Full Professor.</footnote>
integrating voltage/charge curves, while mean and standard deviation values are computed over 60 AC cycles through a LabView program.

<figure><img src="image_3.png" /><figcaption>Fig. 1 **A REFAIRE** Plasma grid (a) front face sketch with zoomed discharge photography stacking approximately 15 consecutive AC cycles at V<sub>AC</sub> = 5 kV - f<sub>AC</sub> = 1 kHz and (b) rod cross section [dimensions in mm].</figcaption></figure>

## B. Particle image velocimetry setup for the DBD induced flow

The electromechanical transfer within the plasma induces a flow known as the ionic wind, whose velocity fluctuates at the f<sub>AC</sub> frequency of the alternating voltage supplied to the exposed electrode [9, 10]. In order to quantitatively characterize the ionic wind, two-dimensional Particle Image Velocimetry system (2D-PIV) is used. A 1 mm thin laser plane is generated using two aligned Nd-YAG Big Sky Lasers (λ = 532 nm).

A LaVision Imager LX camera (16 MP - 12 bits) equipped with a Nikon ED 200 mm lens (1:4D) is positioned facing the laser plane to capture grayscale particle images of the seeding particle (atomized Ondina 15 dielectric oil). The laser beams operate at a frequency of 4.4 Hz with an adjustable inter-frame delay Δt to precisely control particle displacement which is kept constant at 10 Px (Δt ranges from 70 to 110 μs°. A Davis 10.2 cross-correlation algorithm is applied to pairs of images to determine instantaneous fields of the most probable displacements, from which velocity fields are computed. Each acquisition comprises 500 instantaneous fields and begins 10 seconds after the discharge initiation for an accurate statistical description of the established induced flow.

## C. Experimental setup for preliminary assessment of mixing-enhancement

The grid is placed and held between the contraction and the test-section (10 by 10 cm square inner transparent cross-section to run optical diagnostics) using an inhouse made piece. The wind-tunnel fan is set for an empty free stream velocity of U<sub>0</sub> = 5 m/s. The measured free stream turbulent intensities u'/U<sub>0</sub> and v'/U<sub>0</sub> are respectively in the order of 1.2% and 1%. The corresponding flow Reynolds number is Re<sub>M</sub> = 4·10<sup>3</sup>. The same laser, seeding and camera, although with a 105 mm lens, are utilized to set and characterize the flow field without and with the grid. Mean and standard deviation velocity fields are calculated from 500 instantaneous fields.

# III. Results

## A. Electrical characteristics of the plasma grid

The instantaneous current over one operating cycle is shown in Figure 3a for a discharge powered by a sinusoidal voltage with V<sub>AC</sub> = 5.5 kV and f<sub>AC</sub> = 1 kHz. A capacitive current in the form of a cosine wave with an amplitude of
20 mA is observed. It respectively carries positive and negative current peaks during the first and second half-cycles of the voltage wave. The capacitive current is notably high due to the grid's geometry involving overlaid electrodes, resulting in a geometrical capacitance of $C_0 = 500$ pF. However, the discharge current traces are similar to the reference linear surface DBD case when the capacitive current is subtracted from measured instantaneous current (Figure 3b). During the positive half-cycle of the voltage wave, positive current peaks with an amplitude ranging from 20 to 40 mA are observed, carried by a positive synchronous current. During the negative half-cycle, the current peaks are negative with an amplitude ranging from -5 to -15 mA, carried by a negative synchronous current. These correspond to a streamer-like filamentary regime followed by a Trichel regime, separated by so-called dark periods [9, 10], but with low amplitude peaks due to the dielectric barrier's reduced dimensions respective to canonical DBD.

<figure><img src="image_4.png" /><figcaption>**Fig. 2** Time-series – applied discharge voltage (blue) and measured current (orange) at $V_{AC} = 5.5$ kV and $f_{AC} = 1$ kHz featuring (a) full current and (b) current without the capacitive component.</figcaption></figure>

The mean energy consumed per AC cycle is obtained through the integration of the voltage-charge curves [9]. The linear relation between mean power consumption and AC frequency $P_{elec} = a \cdot f_{AC}$ [9] fits data on Figure 4a within a global root mean square error (RMSE) of 0.2 W. Additionally, mean power consumption versus voltage amplitude relations shown on Figure 4b match trends previously observed on thin-dielectric linear DBD's. In fact, the $P_{elec} = c \cdot V_{AC}^n$ power law fits within a mean RMSE of 0.16 W among all 6 $f_{AC}$ exposed curves. The maximum electrical power consumption does not exceed 16 W. When scaled using the total length of plasma discharge derived from images taken by a long-exposure time camera, the power consumption is lower than 6 W/m.

<figure><img src="image_5.png" /><figcaption>**Fig. 3** Mean power consumption with standard deviation bars over 60 AC cycles plotted versus (a) applied voltage frequency with linear fits and (b) applied voltage amplitude with power-law fits.</figcaption></figure>

## B. Qualitative and quantitative mean forcing conditions

In this section, the mean flow induced by the discharge into stagnant air is studied to gain a better understanding of the spatial distribution of the forcing that results from the electromechanical transfer within the plasma region.
Firstly, a mesh-centered (x, y) plane of measurement covering 4 horizontal rods in height is investigated to assess the uniformity of the forcing conditions in the wake of the rods (Figure 5). The induced flow in the wake of the different rods must be uniform to maintain an even development of shear layers. Otherwise, the transition of the flow to a turbulent state could result in a less uniform and less isotropic distribution of turbulence in the wake of the grid. Subsequently, a zoomed plane of measurement provides a clear description of the induced flow's origin as well as its development around the horizontal rods. The contours highlight two wall jets on either side of each rod at x/M = 0.12. Their maximum velocity reaches 1 m/s in these supplying conditions. They appear to converge and merge into a single jet per rod at x/M = 0.4 on average. Indeed, a pressure deficit in the wake of each rod seems to entrain both jets, similar to the "Twin Jets" configurations [12]. The resulting jets are straight, do not interact, and their mean velocity decreases along the wake of the rods. This flow topology and localized flow acceleration corroborates that the discharge finds its way around rods thereby accelerating initially stagnant air inside the mesh which is crucial for targeting shear layers as intended.

<figure><img src="image_6.png" /><figcaption>Fig. 4 Wide central PIV plane. Mean velocity magnitude contours for $V_{AC} = 5.5$ kV and $f_{AC} = 1.75$ kHz (rods and exposed electrodes respectively drawn in light and dark grey [not to scale])</figcaption></figure>

One advantage of plasma actuators is the ability to adjust the mean forcing intensity by modifying the electrical command, such as AC frequency and voltage amplitude. Mean induced velocity can be calculated from profiles extracted from the PIV measurements as the one shown in Figure 5. Here, the velocity is extracted at x/M = 0.5 and a spatial average is calculated over the y direction. The results presented in Figure 6 confirm that the mean input velocity increases as voltage amplitude rises because of the way the electromechanical transfer works. A higher voltage amplitude leads to a stronger electric field. The latter results in more ionisation which generates more momentum. Secondly, an AC frequency increase causes nearby air to be pushed more often per unit of time. As a consequence the flow has less time to decelerate between consecutive pushes and mean input velocity increases. Finally, it is also interesting to note the linear relations between mean induced velocity and mean power consumption on Figure 6c (linear coefficients of 0.04 m/(W·s)). All things considered, it is important to clarify that results on Figure 6 are only indicative due to EHD forcing being three-dimensional at the corners.
<figure><img src="image_7.png" /><figcaption>Fig. 6: 5 PLOT A REFAIRE SANS Close to rod Mean axial velocity induced along one mesh calculated at x/M = 0.5 in both zoomed planes of measurement versus (a) applied voltage amplitude at f<sub>AC</sub> = 1.75 kHz, (b) applied frequency at V<sub>AC</sub> = 5.5 kV and (c) versus mean power consumption with linear fittings (as dashed black lines).</figcaption></figure>

C. Influence of the plasma actuation on isotropy

This section examines the impact of the active grid on mixing, drawing from data obtained in wind-tunnel experiments. In this context, the actuation is in counter-flow mode, where the excitation is anticipated to enhance the velocity fluctuations inputted into the counter-flowing freestream. This mode is also expected to strengthen the inflectional velocity profiles, which are crucial for the development of shear layers behind the rods. All experiments are conducted using a driven signal at f<sub>AC</sub> = 1.8 kHz and V<sub>AC</sub> = 5.5 kV to optimize input momentum. Two properties of turbulent motion are studied to characterize mixing. The homogeneity of its distribution, which tells how invariant turbulent motion is in space. Secondly, its isotropy accounts for how unchanged it is in every direction. Part of the isotropic character can be estimated with equation (2). This indicator has been used in [2] and is suited to data in two-dimensional planes. It is worth mentioning that a similar indicator should be used in transverse planes in order to get the full isotropic character of turbulence.

$$I = \sqrt{\frac{\langle u'u' \rangle}{\langle v'v' \rangle}} \qquad (2)$$
Mean isotropy factor contours are represented in Figure 13 for the baseline flow and with the DBD driven at $f_{AC} = 1.8$ kHz at $V_{AC} = 5.5$ kV. Turbulent motion in the plane of measurement is considered isotropic when $(u'/v') \approx 1$. On average, the flow starts from an anisotropic state with a mixture of dark and bright spots as it is expected in zones with mean shear. It then evolves in the wake becoming brighter as the distribution of I along the y axis also evens out. The discharge seems to improve the distribution of the isotropy factor in the whole plane of measurement. In fact, the difference between both cases is better perceived when the I indicator is averaged along the vertical direction within the core flow at every x/M position (see Figure 15). Here, an empirical law detailed on equation (3) is also used to highlight the discharge's authority.

<figure><img src="image_8.png" /><figcaption>Fig. 6 A REFAIRE SANS LA BOITE BLEUE Mean isotropy factor contours of the baseline flow (left) and with DBD on at $f_{AC} = 1.8$ kHz and $V_{AC} = 5.5$ kV (right).</figcaption></figure>

The empirical law fits data within a global RMSE of 0.01 which represents 1 % of the expected fully isotropic state of turbulent motion. Indeed, the idea behind this law is that the averaged isotropy indicator $\bar{I}_y$ decays from a virtual origin $x_0$ following an inverse law that tends towards an asymptotic value of 1 in the very far-field. Here, all fitting coefficients are determined by fitting equation (3) to each scatter plot using a Levenberg-Marquardt algorithm. Both curves on Figure 8a start from a similar value and decrease at different rates. According to our results, averaged isotropy tends faster towards 1 when the DBD is turned on. The difference between both fitted curves is represented in Figure 14b. It starts close to zero at x/M = 6, reaches a maximum value close to 2.5 % just after x/M = 9 and then decreases. This suggests that turbulence isotropy is not highly affected by the discharge in the near-wake. The input perturbation's effect on isotropy seems greater on average at the end of the TKE production zone. Downstream of that location, the difference will gradually decrease until reaching zero as both curves share the same asymptotic fully isotropic state according to theory.

$$ \bar{I}_y = \frac{a - x_0}{x - x_0} + 1 \qquad (3) $$
<figure><img src="image_9.png" /><figcaption>Fig. 8 Average isotropy factor along the test-section's height for the baseline flow (blue), for the DBD on at $f_{AC} = 1.8$ kHz and $V_{AC} = 5.5$ kV (red) and associated fitting functions (dashed black line) (a) and difference between both fitted curves along the wake (b).</figcaption></figure>

## IV. Concluding remarks

A novel square-mesh grid equipped with a DBD has been surveyed. The discharge current traces have the form of peaks carried by a high amplitude capacitive current. The reference current traces of a streamer discharge and a glow regime appear as soon as it is subtracted from the total current. Moreover, power measurements with applied repeatable empirical fittings match bibliographical elements related to linear thin dielectric DBD.

An AC frequency value of $f_{AC} = 1.75$ kHz is chosen for the characterization of the DBD's electromechanical conversion as it inputs the most momentum among the acquired cases. The mean induced flow highlights localized and uniform forcing of the shear layers that develop when a flow passes through the grid. Its distribution appears to be conducive to flow control experiments. Its amplitude and frequency can also be adjusted through electrical power parameters.

Finally, preliminary wind-tunnel experiments are conducted in order to first characterize the unforced flow in the wake of the grid at $Re_M = 4 \cdot 10^3$. Mean quantities are not significantly modified in presence of the actuation, however the analysis of the turbulent motion isotropy indicates that the DBD improves isotropy in the far field of the grid. A fitted empirical law shows that the mean isotropy factor averaged along the test-section's height approaches more rapidly an asymptotic value of 1 when the DBD is turned on. It is worth noting that this change occurs at a surprisingly low mean power consumption of 0.6 W per meter of discharge.

## Acknowledgments

A part of the experimental equipment used in this work was funded by the French Government program Investissements d'Avenir (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01 as well as EUR INTREE, reference ANR-18-EURE-001).

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