Physics and chemistry of plasma-assisted combustion

Abstract

There are several mechanisms that affect a gas when using discharge plasma to initiate combustion or to stabilize a flame. There are two thermal mechanisms—the homogeneous and inhomogeneous heating of the gas due to ‘hot’ atom thermalization and vibrational and electronic energy relaxation. The homogeneous heating causes the acceleration of the chemical reactions. The inhomogeneous heating generates flow perturbations, which promote increased turbulence and mixing. Non-thermal mechanisms include the ionic wind effect (the momentum transfer from an electric field to the gas due to the space charge), ion and electron drift (which can lead to additional fluxes of active radicals in the gradient flows in the electric field) and the excitation, dissociation and ionization of the gas by e-impact, which leads to non-equilibrium radical production and changes the kinetic mechanisms of ignition and combustion. These mechanisms, either together or separately, can provide additional combustion control which is necessary for ultra-lean flames, high-speed flows, cold low-pressure conditions of high-altitude gas turbine engine relight, detonation initiation in pulsed detonation engines and distributed ignition control in homogeneous charge-compression ignition engines, among others. Despite the lack of knowledge in mechanism details, non-equilibrium plasma demonstrates great potential for controlling ultra-lean, ultra-fast, low-temperature flames and is extremely promising technology for a very wide range of applications.

The use of thermally equilibrium plasma for combustion control dates back more than a hundred years to internal combustion engines and spark ignition systems. The same principles are still applied today to achieve high efficiency in different applications. Recently, the potential use of non-equilibrium plasma for ignition and combustion control has garnered increasing interest [1,2]. The reason for this interest lies in the new possibilities for ignition and flame stabilization that have been proposed for plasma-assisted approaches. During the past decade, significant progress has been made in understanding the mechanisms of plasma–chemistry interactions, energy redistribution and the non-equilibrium initiation of combustion. A wide range of different fuels have been examined using different types of discharge plasmas [3].

Reviews of recent experimental studies of non-equilibrium plasma-assisted ignition and combustion can be found in the literature [1–7]. Over the last several years, considerable progress has been made in understanding the mechanisms of plasma-assisted combustion in various mixtures, including hydrocarbon-containing mixtures [1]. This progress was recently stimulated by support from the Air Force Office of Scientific Research under the multi-university research initiative ‘Fundamental mechanisms, predictive modeling, and novel aerospace applications of plasma assisted combustion’. A significant portion of papers in this theme issue are reporting the results of this project.

The mechanisms of plasma-assisted combustion were validated by performing experiments under controlled conditions and by comparing their results with numerical simulations of the discharge and combustion processes. We consider the possibility of generating chemically active discharge plasma with desirable parameters and the effect of the non-equilibrium plasma on ignition and combustion through different mechanisms. The difficulties of these studies and some unsolved problems are discussed in the papers in this theme issue. The number of groups working in the field of plasma-assisted combustion is rapidly increasing. We have attempted to show in this theme issue the main achievements in the understanding of physics and chemistry of the process of plasma-assisted ignition and combustion, the obstacles to further progress in the use of non-equilibrium plasma in assisting and improving combustion processes, and modern diagnostic tools for investigating and analysing plasma processes.

The major difference between common combustion and plasma-assisted combustion is the extremely non-equilibrium excitation of the gas in the discharge plasma. An external electric field accelerates electrons. Energy exchange between the electrons and the translational degrees of freedom of the molecules is very slow because of the large differences in mass. This means that electron impact can only transfer energy to the internal degrees of freedom of the molecules. If the rate of internal energy relaxation is not very high, the population distribution of the excited states of the molecules will be very far from the initial Boltzmann energy distribution. The overpopulation of excited states and the dissociation and ionization of the molecules, which can lead to UV generation and additional gas heating, cause an increase in the system reactivity and facilitate ignition and flame propagation. From this point of view, the most important questions for plasma-stimulated chemistry concern how the discharge energy branches through the different degrees of freedom of the molecules, the rate of system relaxation (thermalization) and the chemically active system response to this non-equilibrium excitation.

The rate of the excited level population in the discharge depends on the electron energy. The excitation of rotational degrees of freedom requires the lowest energy electrons. A typical rotational quantum is of the order of a few degrees kelvin, and electron energy at approximately 300 K (approx. 0.03 eV) is enough for the efficient excitation of molecular rotations. A typical quantum of the vibrational degrees of freedom is in the range of 1–3 kK. This means that, for the efficient excitation of vibrations, the average electron energy should be higher (in air, it should be in the range of 0.2–2 eV). The excitation of the electronic degrees of freedom and gas dissociation require energies of 3–10 eV. If the average electron energy exceeds 10 eV, the main process occurring in the plasma is gas ionization. Thus, the potential to control the energy of electrons suggests the potential to control the direction of energy deposition and to selectively excite the different degrees of freedom of the gas.

The average electron energy in a gas discharge is determined by a reduced electric field, E/n, where E is the electric field and n is the gas density [8]. Figure 1 illustrates the deviation of the characteristic electron energy, D/μ, from the temperature of the molecules, T, for different gases. Here, D is the diffusion coefficient of electrons and μ is their mobility. The critical E/n that results in a notable difference between D/μ and T and, consequently, a non-equilibrium electron energy distribution function (EEDF) formation is close to E/n approximately 0.1 Td for atomic gases and E/n approximately 1 Td for molecular gases (1 Td=10⁻¹⁷ V cm²).

Figure 1.

Characteristic electron energy. He and Ar [9]; H₂, N₂ and CO₂ [10]. (Online version in colour.)

A non-equilibrium EEDF can be found as a solution of the Boltzmann equation. In the simplest case, one can approximate the solution by a local, steady-state function that only depends on the local electrical field [8]. Further simplification is possible using the so-called two-term approximation (the electron distribution function is presented in the form f(v)=f₀(v)+f₁(v) cos(θ) [8], where v is the electron velocity and θ is the angle between v and E) using a full set of cross sections for electron–molecule collisions. Table 1 shows self-consistent sets of electron cross sections available for plasma-assisted combustion modelling at this time.

Table 1.

Electron–molecule collisions database.

atmospheric	saturated	unsaturated	oxygenated	isomers
N2	CH4	C2H2	CO	iso-butane
O2	C2H6	C2H4	CH3OH	iso-propane
CO2	C3H8	C3H6	C2H5OH	neo-pentane
H2O	C4H10		CH3OCH3 (DME)
O3	C5H12
Ar	H2
N2O

The EEDF that is obtained can be used for calculations of the energy branching through the different degrees of freedom. Figure 2 demonstrates energy branching through the internal degrees of freedom of selected gases for different E/n values in a discharge. Rotational excitation dominates at a very low E/n, approximately 0.1 Td. Fast energy exchange between the rotational and translational degrees of freedom causes thermally equilibrium gas heating in this type of discharge. An increase in the E/n value up to 0.4 Td changes the energetic priorities.

Figure 2.

Fractional power dissipated by electrons into the different molecular degrees of freedom as a function of E/n. (a) Air; (b) methane–air stoichiometric mixtures [1]. (Online version in colour.)

Above this point, the main mechanism of electron energy loss becomes the vibrational excitation of oxygen. The most efficient mechanism of electron energy loss is the excitation of the vibrational levels of nitrogen (figure 2a) for a reduced electric field on the interval 4 Td<E/n<110 Td in air.

Under low-temperature conditions, vibrational–translational (VT) relaxation is a rather slow process, and the vibrational temperature in the discharge can be higher than the translational temperature of molecules. In the same region of E/n values, the excitation of the lowest electronic level of oxygen, the O(a¹Δ) state, occurs. The efficiency of this electronic excitation in the presence of nitrogen is very small (approx. 2%), but the low rate of singlet oxygen quenching under some conditions can lead to an increase in its concentration.

It should be noted that the electric field value of E/n approximately 120 Td is a very important threshold in air. Above this point, the electric field is strong enough to ionize the gases in the air, and the discharge can propagate in a self-sustained manner. Below this value, a discharge can exist only in the presence of an external source of ionization. At E/n values from 140 to 500 Td, the main mechanism of energy loss is the excitation of the electronic triplet states of nitrogen. Because of the high electron energy in this range of E/n (from 3 to 10 eV, respectively), the ionization of the gas in the discharge gap is very fast. Between 500 and 1000 Td, the excitation of nitrogen singlet states becomes most significant, and above an E/n of 1000 Td the main portion of the electron energy goes to the ionization of the gas.

The presence of fuel additives (figure 2b) does not change this picture dramatically. The main reason is the relatively small concentration of fuel molecules in the mixture under typical combustion conditions. Figure 2b demonstrates the effect of methane on electron energy branching. A stoichiometric mixture of H₂–air (CH₄:O₂:N₂=1:2:8) contains approximately 9.1% of methane. It is clear from the calculations that these additives only change the energy branching slightly at moderate and high E/n values, more than 20 Td. The excitation of molecular nitrogen remains the main process. The vibrational and electronic excitation and ionization of methane only change the energy branching slightly (figure 2b). At a low E/n, less than 10 Td, the influence of methane addition becomes more significant. The vibrational excitation of methane is the main mechanism of energy losses for an E/n=5–10 Td. The role of the rotational excitation of methane is also important and increases the energy flux into the rotational and translational degrees of freedom under low E/n conditions (figure 2b).

The electron multiplication process is most important for discharge development kinetics. Ionization, processes of charge transfer and recombination reactions were included in the kinetic model (figure 3).

Figure 3.

Ionization and charge transfer pathways. (Online version in colour.)

As a result of gas ionization and electron–ion recombination, we have fast gas heating, hot atom formation, electronically excited radical production and ionic chain development. These processes are not very important at high-temperature conditions but a play a key role at low temperatures. At very low temperatures, this channel becomes important because competing reactions with uncharged reagents cannot propagate at T∼300 K. For example, process is 11 orders of magnitude faster at 300 K than process O₂+H→OH+O. The processes with ions are limited by ion–ion and electron–ion recombination and formation of negative ions by electron attachment: .

Electron attachment to oxygen changes the recombination mechanism from electron–ion to ion–ion and decreases the rate of recombination by several orders of magnitude because of low mobility of heavy ions in comparison with electrons. Thus, the overall effect becomes pressure dependent because it relies on the rate of the three-body attachment process.

The difference between atomic oxygen in ground state O(³P) and electronically excited state O(¹D) becomes critical at low T. O(³P) mostly recombines at T=300 K, while O(¹D) allows reactions of chain branching (most important is O(¹D)+RH→R*+OH). Both major channels of atomic oxygen production (O₂+e→O+O+e and )) give almost equal amounts of O in the ground (³P) state and the excited (¹D) state. Thus, at low T, we need to analyse all reactions with O(¹D). At high T, O(³P) has almost the same reactivity as O(¹D) and we can consider both radicals as ‘atomic oxygen’.

This process is also pressure dependent. At low P, we have radiative depopulation of , which changes the products of the quenching reaction: . At high pressure, the radiative lifetime of N₂(C³) (37 ns) becomes too long in comparison with collisional quenching and the products are O(³P)+O(¹D) (figure 4).

Figure 4.

Electronic level excitation and quenching mechanisms. (Online version in colour.)

It is well known that the dissociation of molecules by electrons and photons goes through repulsive energy surfaces, and the excessive energy is converted into the translational motion of the products. Thus, several of the very first collisions of these products with their neighbours will take place with a huge energy (typically 1–5 eV). This energy is enough to overcome reaction thresholds for all possible channels including even direct dissociation in one collision. Thus, the reactivity of these ‘hot’ radicals increases dramatically; almost non-reactive at T=300 K O(³P) with additional kinetic energy will react with N₂, H₂, and hydrocarbons in chain-branching reactions. The influence of this effect decreases with the temperature increase because, at high temperatures, atomic oxygen has significant reactivity even without additional energy. Thus, at low-temperature conditions, we have to take into account translational non-equilibrium effects. They increase the rate of production of radicals by two to four times depending on conditions, but we can neglect their influence at high temperatures.

This process is concentration dependent. In diluted mixtures, we can expect complete thermalization of the hot atoms before they collide with possible reagents. Vice versa, in undiluted mixtures, the reaction channel will always prevail (that is probably the real reason this channel was not discovered before—in strongly diluted mixtures, its influence is negligible).

Vibrational excitation leads to the acceleration of reactions. At high temperatures, two factors decrease the role of non-equilibrium vibrational excitation: (i) increase of the reactivity of unexcited molecules and (ii) increase of the VT relaxation rates. That is why, at high temperatures, we can consider that the population of vibrational levels is in equilibrium with the translational degrees of freedom; corrections to ‘non-equilibrium’ population are rather small (figure 5).

Figure 5.

Vibrational level excitation and vibrationally activated reactions. (Online version in colour.)

At low temperatures, the reactions with the participation of unexcited molecules are too slow. Under these conditions, two major ‘vibrational’ pathways take place. Firstly, vibrational excitation of reagents accelerates chain-branching reactions. For example, hydrogen by electron impact and reaction of H₂(v) with oxygen (reaction H₂(v=1)+O→H+OH(v=1) is 3000 times faster than the same reaction with H₂(v=0) at T=300 K). Secondly, the vibrational excitation of nitrogen by electron impact accelerates the peroxide decomposition. This process has a limiting step of vibrational energy transfer from N₂(v) to which is followed by the fast decomposition of vibrationally excited HO₂ and active radical regeneration in the mixture. This mechanism can elongate the chemical chains below the self-ignition threshold by one to two orders of magnitude, and dramatically change the chemical energy release during the non-equilibrium stage of ignition.

Thus, there are several mechanisms that affect a gas when using discharge plasma to initiate combustion or to stabilize a flame. There are two thermal mechanisms—the homogeneous and inhomogeneous heating of the gas due to ‘hot’ atom thermalization and vibrational and electronic energy relaxation. The homogeneous heating causes the acceleration of the chemical reactions. The inhomogeneous heating generates flow perturbations, which promote increased turbulence and mixing.

Non-thermal mechanisms include the ionic wind effect (the momentum transfer from an electric field to the gas due to the space charge), ion and electron drift (which can lead to additional fluxes of active radicals in the gradient flows in the electric field) and the excitation, dissociation and ionization of the gas by e-impact, which leads to non-equilibrium radical production and changes the kinetic mechanisms of ignition and combustion [1].

These mechanisms, either together or separately, can provide additional combustion control which is necessary for ultra-lean flames, high-speed flows, cold low-pressure conditions of high-altitude gas turbine engine relight, detonation initiation in pulsed detonation engines and distributed ignition control in homogeneous charge-compression ignition engines, among others. Despite the lack of knowledge in mechanism details, non-equilibrium plasma demonstrates great potential for controlling ultra-lean, ultra-fast, low-temperature flames and is extremely promising technology for a very wide range of applications.

Competing interests

I declare I have no competing interests.

Funding

I received no funding for this study.