**3.2 Discharge phase simulation**

280 Hydrodynamics – Advanced Topics

affect the charged species transport coefficients or are needed to follow the charged species chemical kinetics and energy or momentum exchange. For example, in order to calculate the macroscopic electron swarm parameters in water vapor, 21 collision cross sections must be known involving the rotational, the vibrational and the electronic excitation processes as

One of the main difficulties is to validate for each pure gas that compose the mixture the chosen set of cross sections. To do that, a first reliable set of electron-molecule and ionmolecule cross section for each individual neutral molecule in the gas mixture must be known. Then, in order to obtain the complete and coherent set of cross sections, it is necessary to adjust this first set of cross sections so as to fit experimental macroscopic coefficients with the calculated ones estimated from either a Boltzmann's equation solution or a Monte Carlo simulation. The obtained solution is certainly not unique but as the comparisons concern several kinds of swarm macroscopic parameters having different dependencies on cross sections (ionization or attachment coefficient, drift velocity, transverse or longitudinal diffusion coefficient) over a wide range of reduced electric field or mean electron energy, most of the incoherent solutions are rejected. Finally, when the sets of cross section are selected for each pure gas, they can be used to calculate with a Bolzmann's equation solution or a Monte Carlo simulation the macroscopic charged species transport and reaction parameters

Micro-discharges are characterized by the development of primary and secondary streamers. As a function of the high voltage applied on the small curvature electrode (DC or pulse), the micro-discharges show either a mono-filament or a large branching structure. The passage from multi-filaments to mono-filament structure can be observed if a sufficiently large high voltage pulse is applied. The transition can be explained through the memory effects accumulated during the previous discharge. The primary streamers propagate fast ionization waves characterized by streamer heads in which the electric field is high enough to generate high energetic electrons like in an electron gun. The streamer head propagates a high charge quantity toward the inter-electrode gap. The micro-plasmas are generated behind the streamer heads. They are small conductive channels that connect the streamer head to the electrode stressed by the high voltage. The primary streamers are then followed by a secondary streamer which is characterized by an electric field extension that ensures the transition between the displacement current and the conductive one when the primary streamer arrives on the cathode. Both primary and secondary streamers create radicals and excited species by electron-molecule impacts. The elastic and inelastic energy transfers generate a chemical activity, a thermal energy increase of the gas and a neutral gas dynamics. To better understand all these complex phenomena, a hydrodynamics model can be used based on conservation equations of charged and neutral particles coupled to

**3. Chemical and hydrodynamics activation of gases using corona micro-**

During the past two decades several studies have shown that non-thermal plasmas reactor working in ambient air are very efficient sources of active species like charged particles,

well as the ionization, the dissociative attachment and the superelastic processes.

whatever the proportion of the pure gas in the background gas mixture.

Poisson equation for the electric field calculation.

**2.6 Summary** 

**discharge** 

**3.1 Introduction** 

The simulation conditions are described in detail in reference (Eichwald et al. 2008) as well as the used numerical methods and boundary conditions. To summarize, a DC high voltage of 7.2kV is applied on the pin of a pin-to-plane reactor filled with dry air at atmospheric pressure. The inter-electrode gap is of 7mm, the pin radius is equal to 25µm and photoionisation phenomenon is taken into account in the simulation. Results in Fig. 10 and 11 are obtained by coupling equations (1) to (4) for electrons, two negative ions (O- and O2-), four positive ions (N2+, O2 +, N+ and O+) and two radical atoms (O, N) reacting following 10 selected reactions. Because of the time scale of the discharge phase (some hundred of nanoseconds), the radical atoms and the main neutral molecules (N2 and O2) are supposed to remain static during the discharge phase simulation. Fig. 10 shows the reduced electric field (E/N) expressed in Td (1Td=10-21 Vm2 so that 500Td at atmospheric pressure is equivalent to an electric field of 12MVm-1). When the high voltage is applied to the pin, some seed electrons are accelerated in the high geometric electric field around the pin. A luminous spot is observed experimentally near the pin thus indicating the formation of excited species due to a high electronic energy. On can notice that the electrons move towards the pin. Furthermore, the electrons gain sufficient energy to perform electronic

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 283

arrives at the cathode plane, a secondary streamer starts its propagation from the pin. The secondary streamer is an electric field plateau extension of value of about 100Td. This extension ensures the continuity of the total current when the total charge space transported by the streamer head is absorbed at the cathode (Eichwald et al. 2008, Bastien & Marode, 1985). The second red dashed curve follows the plateau extension. The evolution of the luminous trail left by the secondary streamer shown in Fig. 3 is due to the excited species created by the energetic electrons inside the secondary streamer expansion. Fig. 11 shows the radical O density after 150ns. The simulation indicates that about 70% of the radical O is produced inside the secondary streamer by dissociative collisions between electrons and O2 molecules in reaction e+O2 → O + O. The concentration of O radical is also high near the cathode plane due to a higher electric field magnitude inside the streamer head when it

The effect on the neutral gas dynamics induced by the micro-discharge propagation is shown in Fig. 12 and 13. Fig. 12 shows the temperature profile of the background neutral gas at 0.1µs (=100ns) and 0.3µs (=300ns). Fig. 13 shows the pressure profile from 0.1µs to 4µs. The gas temperature just on the pin reaches some thousands of Kelvin but a mean value of about 700°K is obtained around the point. This value is coherent with experimental results obtained under very similar condition (Spyrou et al., 1992). The thermal shock creates high pressure gradients (see Fig. 13 at 0.1µs) and induces the gas expansion (see Fig. 13). Due to the inertia principle, the mass density near the point decreases more gradually in a time scale greater than the temperature increase. The gas expansion is characterised by a cylindrical and a spherical shock wave (see Fig. 13 from 0.3 to 0.9µs). Indeed, the initial pressure gradients (which induced the gas motion) follow the temperature ones which are constricted along the axis and inside the micro-plasma channel. We therefore observe a cylindrical pressure wave (represented by two vertical lines in the flat pressure mappings of Fig. 13) that propagates from the streamer axis towards the whole domain. The complex

reaches the cathode.

Fig. 11. O radical profile (m-3)

avalanches and a plasma spot is created just around the pin. The plasma is a quasi neutral electric gas in which the quantity of negative and positive species is quasi similar. Nevertheless, as the mobility of electrons is much higher than those of positive ions, the electric neutrality of the initial plasma spot is perturbed just in front of the pin. Indeed, the electrons are absorbed by the positive anodic pin while the positive ions remain quasi static due to their mass inertia. A positive charged space is formed and the electric field is no more at his maximum on the pin but just in front of it. This situation can be seen at time t=20ns in the first picture of Fig. 10.

Fig. 10. Reduced electric field profile (500Td=12MVm-1) in function of time

A streamer head is created that propagates from the pin towards the plane. This streamer head can be interpreted as the propagation of a positive charge space shock wave. At each time of its propagation, new seed electrons are created in front of the streamer head by photo-ionisation processes. These electrons are accelerated in the high electric field and their energy is high enough to ionize, dissociate and excite the main molecules of the gas. When the electrons have crossed the streamer head they drift towards the pin inside a small conductive plasma channel that connects the streamer head to the pin. A micro-plasma is formed behind the streamer head and is constricted by a cylinder of space charged electric field. A quasi-homogeneous small value of electric field is maintained inside the microplasma in order to allow the drift of electrons from the streamer head to the pin that ensures the continuity of the total current density. The time laps needed for the streamer head to cross the inter-electrode gap is associated with the primary streamer propagation of the micro-discharge phase. The streamer head propagates a charge quantity which is absorbed by the cathode plane as soon as it arrives on the cathode plane. It results to the first current peak observed in Fig. 4 for a high voltage DC condition. The first red dashed curve in Fig. 10 follows the trail left by the high electric field of the streamer head. Its shape corresponds to the luminous trail observed by streak camera shown in Fig. 3. When the primary streamer arrives at the cathode plane, a secondary streamer starts its propagation from the pin. The secondary streamer is an electric field plateau extension of value of about 100Td. This extension ensures the continuity of the total current when the total charge space transported by the streamer head is absorbed at the cathode (Eichwald et al. 2008, Bastien & Marode, 1985). The second red dashed curve follows the plateau extension. The evolution of the luminous trail left by the secondary streamer shown in Fig. 3 is due to the excited species created by the energetic electrons inside the secondary streamer expansion. Fig. 11 shows the radical O density after 150ns. The simulation indicates that about 70% of the radical O is produced inside the secondary streamer by dissociative collisions between electrons and O2 molecules in reaction e+O2 → O + O. The concentration of O radical is also high near the cathode plane due to a higher electric field magnitude inside the streamer head when it reaches the cathode.

Fig. 11. O radical profile (m-3)

282 Hydrodynamics – Advanced Topics

avalanches and a plasma spot is created just around the pin. The plasma is a quasi neutral electric gas in which the quantity of negative and positive species is quasi similar. Nevertheless, as the mobility of electrons is much higher than those of positive ions, the electric neutrality of the initial plasma spot is perturbed just in front of the pin. Indeed, the electrons are absorbed by the positive anodic pin while the positive ions remain quasi static due to their mass inertia. A positive charged space is formed and the electric field is no more at his maximum on the pin but just in front of it. This situation can be seen at time t=20ns in

Fig. 10. Reduced electric field profile (500Td=12MVm-1) in function of time

A streamer head is created that propagates from the pin towards the plane. This streamer head can be interpreted as the propagation of a positive charge space shock wave. At each time of its propagation, new seed electrons are created in front of the streamer head by photo-ionisation processes. These electrons are accelerated in the high electric field and their energy is high enough to ionize, dissociate and excite the main molecules of the gas. When the electrons have crossed the streamer head they drift towards the pin inside a small conductive plasma channel that connects the streamer head to the pin. A micro-plasma is formed behind the streamer head and is constricted by a cylinder of space charged electric field. A quasi-homogeneous small value of electric field is maintained inside the microplasma in order to allow the drift of electrons from the streamer head to the pin that ensures the continuity of the total current density. The time laps needed for the streamer head to cross the inter-electrode gap is associated with the primary streamer propagation of the micro-discharge phase. The streamer head propagates a charge quantity which is absorbed by the cathode plane as soon as it arrives on the cathode plane. It results to the first current peak observed in Fig. 4 for a high voltage DC condition. The first red dashed curve in Fig. 10 follows the trail left by the high electric field of the streamer head. Its shape corresponds to the luminous trail observed by streak camera shown in Fig. 3. When the primary streamer

the first picture of Fig. 10.

The effect on the neutral gas dynamics induced by the micro-discharge propagation is shown in Fig. 12 and 13. Fig. 12 shows the temperature profile of the background neutral gas at 0.1µs (=100ns) and 0.3µs (=300ns). Fig. 13 shows the pressure profile from 0.1µs to 4µs. The gas temperature just on the pin reaches some thousands of Kelvin but a mean value of about 700°K is obtained around the point. This value is coherent with experimental results obtained under very similar condition (Spyrou et al., 1992). The thermal shock creates high pressure gradients (see Fig. 13 at 0.1µs) and induces the gas expansion (see Fig. 13). Due to the inertia principle, the mass density near the point decreases more gradually in a time scale greater than the temperature increase. The gas expansion is characterised by a cylindrical and a spherical shock wave (see Fig. 13 from 0.3 to 0.9µs). Indeed, the initial pressure gradients (which induced the gas motion) follow the temperature ones which are constricted along the axis and inside the micro-plasma channel. We therefore observe a cylindrical pressure wave (represented by two vertical lines in the flat pressure mappings of Fig. 13) that propagates from the streamer axis towards the whole domain. The complex

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 285

Fig. 13. Pressure wave (Pa) near the point (from 0.1 to 0.9µs) and in the whole domain (from

As an example, let us suppose the multi-pin reactor described in Fig. 14. The domain is divided with square structured meshes of 50µm×50µm size. A DC high voltage of 7.2kV is applied on the pins. During each discharge phase, monofilament micro-discharges are created between each pin and the plane with a natural frequency of 10kHz. The microdischarges have an effective diameter of 50µm which correspond to the size of the chosen cells. Therefore, it is possible to inject in the cells located between each pin and the plane specific profiles of active source species and energy that will correspond the micro-discharge

1 to 4µs)

effects.

Fig. 12. Gas temperature (°K) profile near the point

structure of the pressure gradients near the point induces a spherical pressure wave superimposed to the cylindrical one. Such kind of spherical pressure waves were already observed experimentally (Ono & Oda b, 2004) using the laser Schlieren method. Furthermore, the simulation shows that the spherical shock wave propagates at the speed of sound as in the case of experimental work (Ono & Oda b, 2004).

In this kind of simulation the effects of temperature and gas density variations on the streamer development are not taken into account. However, it should be in further works because if the gas density varies it will modify the reduced electric flied (E/N) and therefore the behaviour of the charged particles whose properties (like mobility, ionisation frequency,…) completely depend on the reduced electric field. Nevertheless, the previous results are able to give the initial profiles of all the source terms needed to simulate the postdischarge phase evolution.

### **3.3 Post-discharge phase simulation**

The discharge phase simulation gives very clear information on the gas dynamics and the spatio-temporal evolution of each active species of the background gas mixture. However, the time and space scales between the discharge phase and the post-discharge phase are completely different. Indeed, the micro-discharge generated micro-plasma in some hundred of nanoseconds while post-discharge phase must be considered with centimetre scale and milliseconds time laps. A complete simulation of both coupled phenomena for multi-pin reactor needs therefore adaptive meshes from micrometer to centimetre scale and also adaptive time scale from picoseconds (in order to follow the nano-scale discharge phenomena) up to fraction of milliseconds. This means a large number of discrete spatial cells and a huge computing time. In order to overcome these difficulties, on can assume that the effects of the discharges on the background gas can be simulated by locally injected inside the micro-discharge volumes and only during the discharge phase, average source terms estimated from the complete discharge phase model.

300 400 500 600

structure of the pressure gradients near the point induces a spherical pressure wave superimposed to the cylindrical one. Such kind of spherical pressure waves were already observed experimentally (Ono & Oda b, 2004) using the laser Schlieren method. Furthermore, the simulation shows that the spherical shock wave propagates at the speed of

In this kind of simulation the effects of temperature and gas density variations on the streamer development are not taken into account. However, it should be in further works because if the gas density varies it will modify the reduced electric flied (E/N) and therefore the behaviour of the charged particles whose properties (like mobility, ionisation frequency,…) completely depend on the reduced electric field. Nevertheless, the previous results are able to give the initial profiles of all the source terms needed to simulate the post-

The discharge phase simulation gives very clear information on the gas dynamics and the spatio-temporal evolution of each active species of the background gas mixture. However, the time and space scales between the discharge phase and the post-discharge phase are completely different. Indeed, the micro-discharge generated micro-plasma in some hundred of nanoseconds while post-discharge phase must be considered with centimetre scale and milliseconds time laps. A complete simulation of both coupled phenomena for multi-pin reactor needs therefore adaptive meshes from micrometer to centimetre scale and also adaptive time scale from picoseconds (in order to follow the nano-scale discharge phenomena) up to fraction of milliseconds. This means a large number of discrete spatial cells and a huge computing time. In order to overcome these difficulties, on can assume that the effects of the discharges on the background gas can be simulated by locally injected inside the micro-discharge volumes and only during the discharge phase, average source

Fig. 12. Gas temperature (°K) profile near the point

discharge phase evolution.

**3.3 Post-discharge phase simulation** 

sound as in the case of experimental work (Ono & Oda b, 2004).

terms estimated from the complete discharge phase model.

Fig. 13. Pressure wave (Pa) near the point (from 0.1 to 0.9µs) and in the whole domain (from 1 to 4µs)

As an example, let us suppose the multi-pin reactor described in Fig. 14. The domain is divided with square structured meshes of 50µm×50µm size. A DC high voltage of 7.2kV is applied on the pins. During each discharge phase, monofilament micro-discharges are created between each pin and the plane with a natural frequency of 10kHz. The microdischarges have an effective diameter of 50µm which correspond to the size of the chosen cells. Therefore, it is possible to inject in the cells located between each pin and the plane specific profiles of active source species and energy that will correspond the micro-discharge effects.

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 287

post-discharge phase, the size of discrete cells is not sufficiently small to follow the gradients of pressure wave generated by thermal shock near the point (see Fig. 13). However, pressure waves transport a part of the stored thermal energy accumulated around each pin. From 0.1µs to 0.3µs, the gas temperature on the pins decreases from about 3000°K down to about 1200°K. After this time, the temperature variation in the micro-discharge volume is less affected by the gas dynamics. The diffusive phenomena become predominant. Therefore, taken into account the mean energy source term at time td will overestimate the temperature enhancement on the pins during the post-discharge phase simulation. As a consequence, the time tp is chosen equal to 300ns i.e. after the pressure

As an example, Fig. 15 shows the temperature profile obtained at t=tp just after the first discharge phase. The results were obtained using the Fluent Sofware in the simulation conditions described in Fig. 14. As expected and just after the first discharge phase, the enhancement of the gas temperature is confined only inside the micro-plasma filaments located between each pin and the plane. The temperature profile along the inter-electrode gap is very similar to the one obtained by the complete discharge phase simulation (see Fig. 12). It is also the case for the active source terms species. Fig. 16 shows at time t=td, the axial profile of some active species that are created during the discharge phase. The curves of the discharge model represent the axial profile density averaged along the radial direction. In

Fig. 15. Gas temperature profile after the first discharge phase at t=tp = 300ns.

Fig. 16. Comparison of numerical solutions given by the completed discharge and Fluent models at td=150 ns for O, N and O2 (a1∆g) densities. The zoom box shows, as an example,

waves have left the micro-discharge volume.

the O radical profile near a pin.

Fig. 14. 2D Cartesian simulation domain of the multi-pin to plane corona discharge reactor. As an example, consider equation (5) of section 2.5 applied to O radical atoms ('i"=O).

$$\frac{\partial \rho m\_O}{\partial t} + \vec{\nabla} . \rho m\_O \vec{v} + \vec{\nabla} . \vec{J}\_O = S\_O + S\_{O\vec{\alpha}}$$

The challenge is to correctly estimate the source term SOc inside the volume of each microdischarge. As the radial extension of the micro-discharges is equal to the cell size, the source term between each pin and the plane depends only on variable z. The average source term responsible of the creation of O radical during the discharge phase is therefore expressed as follow:

$$S\_{\rm Oc}(z) = \frac{1}{r\_d} \frac{1}{t\_d} \prod\_{0 \le 0}^{r\_d} \int\_{\rm Oc} s\_{\rm Oc}(t, r, z) \, dt dr \tag{10}$$

td is the effective micro-discharge duration, rd the effective micro-discharge radius and sOc(t,r,z) the source terms (m-3s-1) of radical production during the discharge phase (i.e. k(E/N)nenO2 for reaction 2 *eO OO* + →+ where k(E/N) is the corresponding reaction coefficient). All the data in equation (10) come from the complete simulation of the discharge phase. In the present simulation conditions, specific source terms are calculated for 5 actives species that are created during the discharge phase (N2(A3∑u+), N2(a'1∑u-), O2(a1∆g), N and O).

The energy source terms in equations (8) and (9) are estimated using equations (11) and (12):

$$S\_h(z) = \rho \mathbb{C}\_p \frac{1}{r\_d} \frac{1}{t\_p^2} \prod\_{0 \le \mathbf{0}}^{r\_d} T(t\_p, r, z) \, dt dr \tag{11}$$

$$S\_v(z) = \frac{1}{r\_d} \frac{1}{t\_d} \prod\_{0 \le 0}^{r\_d} f\_v \vec{J}. \vec{E} \, dt dr \tag{12}$$

In equation (12), *j E*. is the total electron density power gained during the discharge phase and fv the fraction of this power transferred into vibrational excitation state of background gas molecules. One can notice the specificity of equation (11) related with the estimation of the direct random energy activation of the gas. In this equation, tp is the time scale of the pressure wave generation rather than the micro-discharge duration td. In fact, during the

Fig. 14. 2D Cartesian simulation domain of the multi-pin to plane corona discharge reactor.

*<sup>m</sup> mv J S S <sup>t</sup>*

The challenge is to correctly estimate the source term SOc inside the volume of each microdischarge. As the radial extension of the micro-discharges is equal to the cell size, the source term between each pin and the plane depends only on variable z. The average source term responsible of the creation of O radical during the discharge phase is therefore expressed as

> 0 0 1 1 ( ) (, , ) *d d r t*

td is the effective micro-discharge duration, rd the effective micro-discharge radius and sOc(t,r,z) the source terms (m-3s-1) of radical production during the discharge phase (i.e. k(E/N)nenO2 for reaction 2 *eO OO* + →+ where k(E/N) is the corresponding reaction coefficient). All the data in equation (10) come from the complete simulation of the discharge phase. In the present simulation conditions, specific source terms are calculated for 5 actives species that are created during the discharge phase (N2(A3∑u+), N2(a'1∑u-),

The energy source terms in equations (8) and (9) are estimated using equations (11) and (12):

2 0 0 1 1 ( ) ( ,,) *<sup>p</sup> dr t*

> 1 1 ( ) . *d d r t*

*v v d d*

0 0

and fv the fraction of this power transferred into vibrational excitation state of background gas molecules. One can notice the specificity of equation (11) related with the estimation of the direct random energy activation of the gas. In this equation, tp is the time scale of the pressure wave generation rather than the micro-discharge duration td. In fact, during the

*hp p d p S z C T t r z dtdr*

*<sup>r</sup> <sup>t</sup>* <sup>=</sup> ρ

*S z s t r z dtdr*

*Oc Oc d d*

*O O O Oc*

*r t* <sup>=</sup> (10)

(11)

*S z f J Edtdr r t* <sup>=</sup> (12)

is the total electron density power gained during the discharge phase

As an example, consider equation (5) of section 2.5 applied to O radical atoms ('i"=O).

<sup>∂</sup> +∇ +∇ = +

. . *<sup>O</sup>*

ρ

ρ

follow:

O2(a1∆g), N and O).

In equation (12), *j E*.

∂

post-discharge phase, the size of discrete cells is not sufficiently small to follow the gradients of pressure wave generated by thermal shock near the point (see Fig. 13). However, pressure waves transport a part of the stored thermal energy accumulated around each pin. From 0.1µs to 0.3µs, the gas temperature on the pins decreases from about 3000°K down to about 1200°K. After this time, the temperature variation in the micro-discharge volume is less affected by the gas dynamics. The diffusive phenomena become predominant. Therefore, taken into account the mean energy source term at time td will overestimate the temperature enhancement on the pins during the post-discharge phase simulation. As a consequence, the time tp is chosen equal to 300ns i.e. after the pressure waves have left the micro-discharge volume.

As an example, Fig. 15 shows the temperature profile obtained at t=tp just after the first discharge phase. The results were obtained using the Fluent Sofware in the simulation conditions described in Fig. 14. As expected and just after the first discharge phase, the enhancement of the gas temperature is confined only inside the micro-plasma filaments located between each pin and the plane. The temperature profile along the inter-electrode gap is very similar to the one obtained by the complete discharge phase simulation (see Fig. 12). It is also the case for the active source terms species. Fig. 16 shows at time t=td, the axial profile of some active species that are created during the discharge phase. The curves of the discharge model represent the axial profile density averaged along the radial direction. In

Fig. 15. Gas temperature profile after the first discharge phase at t=tp = 300ns.

Fig. 16. Comparison of numerical solutions given by the completed discharge and Fluent models at td=150 ns for O, N and O2 (a1∆g) densities. The zoom box shows, as an example, the O radical profile near a pin.

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 289

For more than one pin, the temperature and ozone wreaths interact each other and their superposition induce locally a rise of both the gas temperature and ozone density (see Fig. 17). The local maximum of temperature is around 325K for one pin case and increases up to

The average temperature in the whole computational domain remains quasi constant and the small variations show a linear behavior with the number of anodic pins. The same linear tendency is observed for the ozone production in Fig. 18. After 1ms, and for the four pins

1234

Number of points

The complete simulation of all the complex phenomena that are triggered by microdischarges in atmospheric non thermal plasma was found to be possible not as usually done in the literature only for 0D geometry but also in multidimensional geometry. In DC voltage conditions, a specific first order electro-hydrodynamics model was used to follow the development of the primary and secondary streamers in mono pin-to-plane reactor. The simulation results reproduce qualitatively the experimental observations and are able to give a full description of micro-discharge phases. Further works, already undertaken in small dimensions or during the first instants of the micro-discharge development (Pancheshnyi 2005, Papageorgiou et al. 2011 ), have to be achieved in 3D simulation in order to describe the complex branching structure for pulsed voltage conditions. Nevertheless, the micro-discharge phase simulation gives specific information about the active species profiles and density magnitude as well as about the energy transferred to the background gas. All these parameters were introduced as initial source terms in a more complete hydrodynamics model of the post-discharge phase. The fist obtained results show the ability of the Fluent

Fig. 18. Mean ozone density increase inside the computational domain of Fig. 14 as a

software to solve the physico-chemical activity triggered by the micro-discharges.

The present chapter was devoted to the description of the hydrodynamics generated by corona micro-discharges at atmospheric pressure. Both experimental and simulation tools have to be exploited in order to better characterise the strongly coupled behaviour of micro-

case, the mean total density inside the computational domain reaches 4x1014 cm-3.

0,8

1,6

2,4

Mean ozone density (1014cm-3

)

3,2

4,0

350K for four anodic pins.

function of the number of pins

**3.4 Summary** 

**4. Conclusion** 

the case of the O radical, the density profile of Fig. 11 was averaged along the radial direction until rd=50µm and drawn in Fig. 16 with the magenta color. The light blue color curve represents the O radical profile obtained with the Fluent Software when the specific source term profile SOc(z) is injected between a pin and the cathode plane in the simulation conditions of Fig. 14.

In the following results, the complete simulation of the successive discharge and postdischarge phases involves 10 neutral chemical species (N, O, O3, NO2, NO, O2, N2, N2 (A3∑u+), N2 (a'1∑u-) and O2 (a1∆g)) reacting following 24 selected chemical reactions. The pin electrodes are stressed by a DC high voltage of 7.2kV. Under these experimental conditions the current pulses appear each 0.1ms (i.e. with a repetition frequency of 10KHz). It means that the previous described source terms are injected every 0.1ms during laps time td or tp and only locally inside the micro-plasma filament located between each pin and the plane. The lateral air flow is fixed with a neutral gas velocity of 5m.s-1.

Pictures in Fig. 17 show the cartography of the temperature and of the ozone density after 1ms (i.e. after 10 discharge and post-discharge phases). One, two, three or four pins are stressed by the DC high voltage. Pictures (a) show that for the mono pin case, the lateral air flow and the memory effect of the previous ten discharges lead to a wreath shape of the space distribution of both the temperature and the ozone density.

Fig. 17. Temperature and ozone density profile at 1ms i.e. after ten discharge and postdischarge phases. The number of high voltage pin is respectively (a) one, (b) two, (c) three and (d) four. The lateral air flow is 5m.s-1.

The temperature and the ozone maps are very similar. Indeed, both radical and energy source terms are higher near the pin (i.e. inside the secondary streamer area expansion as it was shown in section 3.2). Furthermore, the production of ozone is obviously sensitive to the gas temperature diminution since it is mainly created by the three body reaction *OO M O M* + +→ + 2 3 (having a reaction rate inversely proportional to gas temperature). For more than one pin, the temperature and ozone wreaths interact each other and their superposition induce locally a rise of both the gas temperature and ozone density (see Fig. 17). The local maximum of temperature is around 325K for one pin case and increases up to 350K for four anodic pins.

The average temperature in the whole computational domain remains quasi constant and the small variations show a linear behavior with the number of anodic pins. The same linear tendency is observed for the ozone production in Fig. 18. After 1ms, and for the four pins case, the mean total density inside the computational domain reaches 4x1014 cm-3.

Fig. 18. Mean ozone density increase inside the computational domain of Fig. 14 as a function of the number of pins
