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# Effect of Humidity on the Ionic Wind and the Ozone Produced by a DC Positive Corona Discharge: Numerical Simulations and Experimental Validation

Toufik Khattara, Jean-Maxime Orlac'H, Pierre Guitton, Christophe O Laux

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Toufik Khattara, Jean-Maxime Orlac'H, Pierre Guitton, Christophe O Laux. Effect of Humidity on the Ionic Wind and the Ozone Produced by a DC Positive Corona Discharge: Numerical Simulations and Experimental Validation. AIAA SCITECH 2025 Forum, Jan 2025, Orlando, United States. pp.AIAA 2025-1592, 10.2514/6.2025-1592. hal-04923452

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# Numerical Simulations of a DC Corona Discharge in Humid Air with Experimental Validation

T. Khattara¹,², J. -M. Orlac'h³, P. Guitton¹ and C O. Laux²

¹Teqoya, Villandraut, 33730, France

²Laboratoire EM2C, CNRS, CentraleSupelec, Université Paris Saclay, 91192 Gif-sur-Yvette, France

³DAAA, ONERA, Institut Polytechnique de Paris, 92320 Châtillon, France

The present study is dedicated to the 2D steady state simulation of the ionic wind and the ozone produced by a DC corona discharge between two parallel wires in ambient humid air at atmospheric pressure. The kinetic model includes a mechanism of humid air chemistry to simulate the spatial production of ozone and charged species. The model also predicts the ionic wind velocity, in dry and humid air. The results of the 2D simulations conducted with the model are compared with measurements. In humid air, H₃O⁺(H₂O)ₙ ions are identified as the dominant ions, as opposed to O₄⁺ ions in pure dry air. A significant reduction of the ozone production rate is observed as the humidity increases, accompanied by a slight decrease in the velocity of the ionic wind.

## I. Nomenclature

<table><tr><td>V</td><td>=</td><td>electric potential</td></tr><tr><td>&#x20D7;</td><td>=</td><td>electric field</td></tr><tr><td>e</td><td>=</td><td>elementary charge</td></tr><tr><td>&epsilon;<sub>0</sub></td><td>=</td><td>vacuum permittivity</td></tr><tr><td>n<sub>e</sub>, n<sub>+</sub>, n<sub>-</sub>, n<sub>n</sub></td><td>=</td><td>number density of electrons, positive ions, negative ions, and neutrals, respectively</td></tr><tr><td>&mu;<sub>e</sub>, &mu;<sub>+</sub>, &mu;<sub>-</sub></td><td>=</td><td>mobility of electrons, positive ions, and negative ions, respectively</td></tr><tr><td>D<sub>e</sub>, D<sub>+</sub>, D<sub>-</sub>, D<sub>n</sub></td><td>=</td><td>diffusivity of electrons, positive ions, negative ions, and neutrals, respectively</td></tr><tr><td>S<sub>ion</sub></td><td>=</td><td>electron-impact ionization rate</td></tr><tr><td>S<sub>att</sub></td><td>=</td><td>electron-attachment rate</td></tr><tr><td>S<sub>det</sub></td><td>=</td><td>electron-detachment rate</td></tr><tr><td>S<sub>e/+</sub></td><td>=</td><td>electron-ion recombination rate</td></tr><tr><td>S<sub>+/-</sub></td><td>=</td><td>ion-ion recombination rate</td></tr><tr><td>S<sub>cx</sub></td><td>=</td><td>charge-exchange rate</td></tr><tr><td>S<sub>prod</sub></td><td>=</td><td>species production rate</td></tr><tr><td>S<sub>loss</sub></td><td>=</td><td>species depletion rate</td></tr><tr><td>&#x20D7;</td><td>=</td><td>fluid velocity</td></tr><tr><td>&rho;</td><td>=</td><td>air density</td></tr><tr><td>&tau;</td><td>=</td><td>viscosity tensor</td></tr><tr><td>&gamma;</td><td>=</td><td>secondary electron emission coefficient</td></tr><tr><td>&#x20D7;</td><td>=</td><td>unit vector normal to boundary</td></tr></table>
## II. Introduction

Corona discharge, a phenomenon characterized by the ionization of the gas surrounding a conductor at high voltage, plays a crucial role in various industrial and environmental applications. One such application is in air flow control [1,2], where this technology is employed to reduce drag and control the transition to turbulence, thus enhancing aerodynamic performance. The characteristics of corona discharges can be influenced by various factors, including the applied voltage, the electrode configuration, and the air conditions. Air humidity, a crucial factor, has a significant impact on the behavior of positive corona discharges [3,4].

Additionally, corona discharges are utilized in electrostatic precipitation, affording an effective method for air purification. However, for indoor air cleaners, corona discharges in air can produce highly toxic gases, particularly ozone, which pose significant risks to human health [5,6].

The objective of this study is to deepen our understanding of how the relative humidity (RH) influences electrical properties, ionic wind velocity, and ozone generation in wire-wire positive corona discharges. Additionally, the study presents a 2D steady-state drift-diffusion model that integrates detailed chemical kinetics to predict the production of ozone and ionic wind under both dry and humid air conditions. The modeling results are then compared with experimental data.

## III. Experimental Setup

The experimental setup is shown in Fig. 1. It comprises two parallel cylindrical wires separated by a 9 mm gap distance. The thin electrode (anode) is 0.2 mm in diameter and is connected to a high positive DC potential produced with a *FUG 140-20000 power supply* and varying from 8 kV to 11 kV. The other electrode (cathode) is 2 mm in diameter and is connected to the ground. The flow velocity is measured in the median plane behind the cathode using a *hotwire anemometer MG-TA440*. UV absorption spectroscopy with a *2B Technologies Model 202 Ozone Monitor* is used to measure the concentration of ozone generated by the discharge. The present study aims to investigate discharge phenomena under ambient air conditions. Furthermore, a controlled atmosphere chamber with a volume of approximately 1 m³ will be utilized, facilitating precise control of relative humidity levels from 10% to 90%.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Schematic of the experimental setup (not to scale)</figcaption></figure>

## IV. Numerical Model

The computational domain (10 × 6 cm²) for the two parallel cylindrical wire geometry is shown in Fig. 2. The two electrodes are 9.0 mm apart. The simulations are made over a half-domain because of the symmetry of the system and the boundary conditions (BCs). A structured quadrilateral mesh is used near the two electrodes, and an unstructured triangular mesh is used in the rest of the domain allowing a homogeneous growth of the meshes up to the limits of the domain. A mesh convergence study was performed to obtain the optimal balance between accuracy and runtime. The present model is a continuation of the work of Bérard et al. [7].
<figure><img src="image_4.png" /><figcaption>Fig. 2. Computational domain. The HV electrode is biased at a positive potential.</figcaption></figure>

The electric potential in the presence of charged species is computed with the Poisson equation (1). The steady state drift-diffusion equations for electrons (2), positive ions (3), and negative ions (4), as well as the continuity equation for neutrals (5) are solved simultaneously. A second order implicit scheme is used for all computations. The numerical simulations are made with the commercial software ANSYS Fluent CFD [8].

$$ \Delta V = - \frac{e(n_{+} - n_{-} - n_{e})}{\varepsilon_{0}} \qquad (1) $$

$$ \nabla \cdot (\mu_e n_e \vec{E} - D_e \vec{\nabla} n_e) = S_{ion} + S_{det} - S_{att} - S_{e/+} \qquad (2) $$

$$ \nabla \cdot (\mu_{+} n_{+} \vec{E} - D_{+} \vec{\nabla} n_{+}) = S_{ion} \pm S_{cx} - S_{e/+} - S_{-/+} \qquad (3) $$

$$ \nabla \cdot (\mu_{-} n_{-} \vec{E} - D_{-} \vec{\nabla} n_{-}) = S_{att} - S_{det} - S_{-/+} \qquad (4) $$

$$ \nabla \cdot (n_n \vec{u} - D_n \vec{\nabla} n_n) = S_{prod} - S_{loss} \qquad (5) $$

$$ \nabla \cdot (\rho \vec{u} \vec{u}) = -\vec{\nabla} P + e(n_{+} - n_{-} - n_{e}) \vec{E} + \nabla \cdot \boldsymbol{\tau} \qquad (6) $$

The detailed kinetic model involves 35 species, including 19 charged species and 14 neutrals, modeled with 152 reactions. It is available from the authors upon request. The rates of electron-impact ionization, electron-impact dissociation, dissociative attachment, and electron-impact excitation are calculated with Bolsig [9]. The Morgan cross-sections [10] are employed for O₂ and H₂O, whereas Siglo's cross-sections [11] are utilized for N₂. The rate constants are calculated with a simulated air-like mixture comprised of [O₂: 20%, N₂: 79% and H₂O: 1%]. Our analysis indicates that varying the relative humidity from 0 to 1.5% at T = 300 K does not change the electron-impact reaction rates by more than 4% in the simulated range of electric fields. Therefore, the influence of H₂O on the electron swarm coefficients is negligible and can be neglected when simulating the corona discharge in humid air. Sieck et al. [12] investigated the core database of ion-molecule reactions, and the deduced rate data for association reactions of clustering and inverse reactions of protonated water clusters H₃O⁺(H₂O)ₙ (n=1-6) (reactions no. 64 - 75), which are considered key to model nonthermal plasmas in humid air.

The transport properties (mobilities and diffusion coefficients) of ions in air are important data to model the discharge development and the ionic wind. The mobilities of dry air ions (oxygen and nitrogen ions) as a function of the electric field have been measured for many years [19-22] using mainly Ion Mass Spectrometry (IMS). Ellis et al. [13] reported a compilation of experimental data for the reduced mobilities of several ions in neutral gases: { O₂⁺, O₄⁺, O₂⁻, O⁻ } in O₂ and { N₂⁺, N₄⁺, HN₂⁺ } in N₂, at room temperature as a function of the reduced electric field. These mobilities are in a good agreement with the measurements of Samson [14], Lindinger [16], Dahlquist [17], and Dotan [15].

In addition, several studies [24-29] used the Monte Carlo simulation method to calculate mobility and diffusion coefficients for a variety of positive and negative ions, including H₃O⁺, H₃O⁺(H₂O), and H₃O⁺(H₂O)₂. A wide range of reduced electric field strengths, up to 1000 Td, were covered. Due to a lack of information regarding the mobility
of the remaining water cluster ions H₃O⁺(H₂O)ₙ (n=3-6), a scaling factor is applied to determine the dependency of their mobility on the electric field. This scaling factor is based on the zero-field mobilities reported by Sieck [12]

The boundary conditions are determined according to the following assumptions:

- The total number density of charged species at the domain boundaries are set to 10⁹ m⁻³, which corresponds to the typical net charge density produced by cosmic rays and natural radioactivity in ambient air [7]. The densities are distributed among electrons, O₂⁻, O₂⁺ and N₂⁺ to preserve overall charge neutrality. The initial densities of these charged species are set to the same values.

- Once the positive corona discharge is operated and under the effect of the electric field, negatively charged species (electrons and negative ions) move towards the anode while positive ions migrate to the cathode. At the surface of the electrode, a zero gradient is applied to the corresponding species density.

- At the surface of the cathode, the electron flux is assumed to be determined by secondary electron emission (SEE) under the effect of positive ion bombardment. The density of electrons is then calculated as:

$$n_e \approx (\gamma\mu_+n_+)/\mu_e \quad (7)$$

where γ represents the SEE coefficient, μ_+n_+ denotes the product of the mobility and the density of the predominant positive ion in the drift zone, and μ_e is the mobility of electrons.

- The pressure is fixed at 1 atm and the mixture velocity is assumed to be normal to the boundaries of the domain.

## V. Results and Discussion

The effect of humidity on the production of ozone by a positive corona discharge at different applied voltages and corona currents is shown in Fig. 3. Voltages of 8, 9, 10 and 11 kV are considered, leading to a lineic current density ranging from 0.06 to 2 μA/cm. The ozone production increases linearly with current density due to the increase in electron number density in the vicinity of the anode. The current of the discharge is calculated in the present model as follows:

$$I = \int_{\text{anode surface}} (e \cdot n_e \cdot \mu_e E) \, dS \quad (8)$$

A comparison of the predicted ozone production rate to the available data in the literature is presented in Fig. 3 (a). The data attributed to Boelter and Davidson [6] correspond to ozone generation rate measurements in a wire-plate geometry at a relative humidity of 42-52% at T ≈ 22 K. The data of Castle et al. [5] and Viner et al. [23] are not measured directly but are determined through empirical correlations provided by the authors. These data were obtained in wire-cylinder and wire-plate geometries, respectively, with relative humidities in the range 15-45%. There is excellent agreement between the predicted values at relative humidity ranging from 20% to 50% and the measured values at the ambient humidity mentioned earlier even though the data were obtained in different geometries. The humidity appears to play a critical role in ozone production, regardless of the discharge current density, as illustrated in Fig. 3 (b). The rate of ozone production notably decreases with increasing RH. This reduction is more pronounced at lower RH levels but is less pronounced as the RH increases.
<figure><img src="image_5.png" /><figcaption>Fig. 3. (a) Effect of current density on the rate of production of ozone at different relative humidities, the numerical results are compared to measured data. (b) Effect of relative humidity on the density of ozone calculated at 3 cm downstream of the cathode, V = 8-11 kV.</figcaption></figure>

When the thin electrode (i.e. the anode) is biased to a positive voltage, the high electric field ionizes the gaseous species surrounding the thin electrode. In the corona region (i.e. in the vicinity of the thin electrode) electron-impact ionization dominates over electron attachment, while outside the corona region, electron attachment prevails. Under the effect of the electric field, positive ions drift towards the grounded electrode, resulting in a unipolar positive region where positive ions dominate over electrons and negative ions. Fig. 4 presents density profiles of O₄⁺ and H₃O⁺(H₂O)₆, the predominant ions in dry and humid air respectively for (a) dry air (0% HR), (b) 10% HR, and (c) 100% HR. In dry air, the dominant ion species in the discharge is O₄⁺. In humid air, the hydronium ions H₃O⁺ form hydrated ion clusters even at extremely low humidities in the range of 10⁻² to 1%. As shown in Fig. 4 (b) and (c), H₃O⁺(H₂O)₆ becomes the dominant ion species in humid air over most of the inter-electrode region after being transformed according to the sequence : O₂⁺ → O₄⁺, O₂⁺(H₂O) → H₃O⁺, H₃O⁺(OH) → H₃O⁺(H₂O)₆. The higher the humidity, the faster this conversion occurs.

<figure><img src="image_6.png" /><figcaption>Fig. 4. One-dimensional density profile of dry-air predominant ion O₄⁺ and humid-air predominant ion H₃O⁺(H₂O)₆ along the inter-electrode line for (a) dry air, (b) 10% RH, and (c) 100% RH</figcaption></figure>

The two-dimensional profile of ionic wind velocity is plotted in Fig. 5 (a), calculated under ambient conditions (HR = 50% and T = 25 °C) at 9 kV. The velocity vector aligns with the electric field vector between the two electrodes given the predominance of positive ions in the drift region. Fig. 5 (b) shows good agreement between the predicted and the measured one-dimensional profiles of ionic wind velocity along the symmetry line behind the cathode. However, the simulated velocity is underestimated by up to approximately 30% within the first 3 cm downstream of the cathode. This is likely due to the interference of the hotwire anemometer with the discharge, particularly when it
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Two-dimensional profile of ionic wind velocity, RH = 50%, (b) Effect of RH on the velocity of ionic wind at 8-11 kV voltage, and (c) one-dimensional profile of ionic wind velocity calculated and measured at the symmetric line 3cm behind the cathode at 8-10 kV voltage.</figcaption></figure>

gets close to the cathode. The impact of the humidity on the ionic wind velocity calculated at 8, 9, 10 and 11 kV is presented in Fig. 5 (c). The presence of water vapor in air leads to the replacement of simple dry ions with relatively heavy water cluster ions. Due to their reduced mobility, these ions accumulate in the drift region, resulting in a decrease of the electric field. Consequently, the discharge current density and the velocity of the ionic wind decrease as the relative humidity increases. These preliminary results also demonstrate that humidity does not significantly impact the velocity. Moreover, at low voltages, the velocity is more sensitive to humidity, showing a decrease of approximately 14% from 5% to 100% RH. In contrast, at high voltages, the decrease in velocity is only around 2% for the same range of RH.

## VI. Conclusions and Future Work

In this work, a numerical model has been developed to simulate the ionic wind velocity and ozone production by a positive corona discharge in dry and humid air. The model solves the Poisson equation and the drift-diffusion equations with plasma chemistry and transport phenomena. The kinetic model involves 19 charged species and 16 neutrals, simulated through 152 reactions. Humidity is found to play a crucial role in the production of ozone by positive corona discharges. This result agrees with other works [24,25]. Additionally, preliminary results reveal that the ionic wind velocity slightly decreases with increasing humidity, with this influence becoming more pronounced at lower discharge current density.

Work is currently in progress to measure the ionic wind velocity and the ozone production over a range of relative humidity levels. The objective is to validate our model over a wide range of humidities. Furthermore, a parametric study will be conducted to explore the influence of specific coefficients on the discharge, including the secondary electron emission coefficient, the mobility of relevant species, and the rate constants of the prevailing reactions.
Acknowledgments

This work has been supported by a CIFRE Ph. D. grant (n° 2021/1779) from TEQOYA and the Agence Nationale
de la Recherche et de la Technologie (ANRT).

A CC-BY public copyright license has been applied by the authors to the present document and will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions.

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