Influence of equivalence ratio on plasma assisted detonation initiation by alternating current dielectric barrier discharge under rich burn condition

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Influence of equivalence ratio on plasma assisted detonation initiation by alternating current dielectric barrier discharge under rich burn condition Siyin Zhou ∗ , Wansheng Nie, Xueke Che, Qingya Chen, Zheng Zhang

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Department of Aerospace Equipment, Equipment Academy, 101416, China

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Article history: Received 9 January 2017 Received in revised form 27 May 2017 Accepted 19 June 2017 Available online xxxx Keywords: Alternating current dielectric barrier discharge Plasma assisted detonation initiation Rich burn Equivalence ratio Active radicals

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a b s t r a c t

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In order to study the effect of different equivalence ratios on plasma assisted detonation initiation under a rich burn condition, a loosely coupled method was adopted to simulate the detonation formation by alternating current dielectric barrier discharge in a hydrogen–oxygen gas mixture with different equivalence ratios. The spatial and temporal evolution of discharge products were analyzed first. Then, the species distribution, Mach number, thrust wall pressure, and whole history of detonation formation were examined in detail. Results showed that the shapes of the temporal and spatial distribution of discharge products do not change when equivalence ratio varies in one discharge cycle. However, due to the variation of the percentage of fuel and oxidizer, and its impact on the discharge elementary reactions, the number density of every key active particle declines while the decline amplitude decreases when equivalence ratio rises. Although the magnitudes of species concentration are not altered by the plasma, the reacted region extends towards the downstream flow more quickly. The influence of equivalence ratio on plasma assisted detonation initiation becomes remarkable until late in the subsonic stage of the flowfield evolution process in the combustor under a rich burn condition. Furthermore, a larger equivalence ratio leads to a better accelerating effect of the plasma. Through analyzing the dynamic process of thrust wall pressure, it is also found that the DDT process is expedited more notably under a larger equivalence ratio, yet the magnitude of pressure is independent of the plasma. The provision of active particles for the combustion reaction by the plasma and its dilution effect on the fuel are the two intrinsic reasons for the reduction of DDT time and distance and the increase of this reduction degree, when equivalence ratio rises. © 2017 Elsevier Masson SAS. All rights reserved.

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1. Introduction

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Equilibrium plasma has been used for the ignition of internal engines for more than 150 years [1]. However, as the development of hypersonic propulsion and the higher demands for fuel utilization and emission control at the end of the 20th century, the traditional spark plug which generates equilibrium plasma no longer meets these requirements, so the idea of using nonequilibrium plasma began to attract people’s attention. The effect of gas heating by nonequilibrium plasma is not as impressive as equilibrium plasma, yet the highly thermal nonequilibrium nature of the internal particles of nonequilibrium plasma particularly makes for improving ignition and combustion efficiency. In addition, by choosing certain discharge methods, it may have several merits

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*

Corresponding author. E-mail addresses: [email protected], [email protected] (S. Zhou).

http://dx.doi.org/10.1016/j.ast.2017.06.039 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.

such as larger ignition volume, longer operation time of the electrodes, and so on [2]. As one of the best candidates for hypersonic propulsion devices, the detonation engine possesses a very high thermal cycle efficiency and releases energy fast. But it is very difficult to initiate detonation steadily and reliably under varying or off-design conditions, which blocks the practical application of detonation engines [3]. Considering the merits of nonequilibrium plasma mentioned above, a series of research aims at shortening the deflagration-todetonation (DDT) distance and time by using this kind of plasma in detonation engines recently, and it shows that the plasma do have the capability to facilitate the detonation formation [4–7]. In our previous research [8], results also proved that the DDT process is accelerated with the help of an alternating current dielectric barrier discharge (AC DBD) plasma in a stoichiometric mixed hydrogen and oxygen. However, for a realistic application, the detonation engine usually works under off-design and varying conditions, where a most important operating index—equivalence ratio, which re-

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flects the percentage of the fuel and oxidizer in a mixture, can change notably. Thus, studies on the influence of equivalence ratio on plasma assisted detonation initiation are urgently needed. The words “equivalence ratio” firstly occurs in the combustion field rather than in the gas discharge field, and the ignition time is a function of equivalence ratios. Commonly, it is the optimal value that equivalence ratio equals to 1 and it becomes difficult for a fuel–air mixture to be ignited as equivalence ratio stays away from 1. To improve a laminar lifted flame by the dielectric barrier discharge [9], an O3 plasma was added into the flame reactions, yet simulation showed that the flame speed is enhanced more for lean and rich equivalence ratios than at stoichiometric. Similar conclusions were obtained by Lefkowitz et al. [6]: they found that the ignition time is reduced more significantly near the lean and rich limits when a nanosecond repetitively pulsed discharge is adopted, especially for aviation gasoline–air mixtures. Different from the conclusions given above, Nagaraja et al. [10] pointed out that the nonequilibrium plasma action on low temperature chemistry is nearly independent of the equivalence ratio through conducting a plane-to-plane DBD simulation, where the discharge gas is composed of n-heptane and air. As for flow discharge experiments without combustion [11], under lean conditions, OH number density measured after the nanosecond pulsed discharge burst demonstrated that unlike H2 –air mixture, where OH concentration is almost independent of the equivalence ratio, OH concentration is reduced as the equivalence ratio is reduced for all the three hydrocarbon–air mixtures. Notice than this sensitivity of equivalence ratio on the fuel was also proved in ref. [12]: in the comparative study of plasma assisted ignition for C2 -hydrocarbons, it was found that the equivalence ratio ϕ action on the delay time is totally different for different fuels, only ϕ = 1 and 0.5 were considered here. Meanwhile, some researchers deem that equivalence ratio might have little effect on plasma assisted combustion: swirl-stabilized combustor experiments on the effect of plasma on nitric oxide emissions with equivalence ratios ranging from 0.6 to 0.82 showed that the NO production from nanosecond pulsed discharge is not significantly affected by the equivalence ratio at a frequency of 20 kHz [13]. Moreover, at high pressure discharge environment, Boumehdi et al. [14] found that there is no sharp difference between the productions of active species in the surface-DBD discharge for different equivalence ratios, which are between 0.3 and 1. Since most of the related studies performed under lean conditions, and the effect of equivalence ratio on plasma assisted combustion may change depending on specific conditions, it is very necessary to understand how equivalence ratio affects the AC DBD plasma assisted detonation initiation process under rich burn conditions. Based on the establishment of a plasma discharge model and a plasma-combustion model, the flowfield characteristics at certain moments, pressure history of thrust wall, and DDT time and distance are all numerically studied under different equivalence ratios.

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2. Models and numerical approaches

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2.1. Discharge simulation

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The one dimensional computational configuration of AC DBD is presented in Fig. 1. A high voltage electrode is located at y = 0 mm and a grounded electrode is located at y = 10 mm with a dielectric layer covering on its surface (the thickness of the dielectric layer is assumed to be zero). Thus, the discharge gap has a distance of dG = 10 mm. The discharge only varies along the y direction to establish a 1D model (ignore the edge effect and others, then the discharge is uniform in the x direction). The gap is filled with

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Fig. 1. Schematic of discharge simulation configuration.

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hydrogen–oxygen mixture at an initial pressure of 0.8 atm and a temperature of 500 K. The governing equations for discharge simulation incorporate the drift-diffusion equations for positively charged, negatively charged, and neutral particles, and Poisson’s equation for the electric field as follows:

∂ nk + ∇(μk nk E) − ∇ 2 ( D k nk ) = S k ∂t ∂ nk − ∇(μk nk E) − ∇ 2 ( D k nk ) = S k ∂t ∂ nk − ∇ 2 ( D k nk ) = S k ∂t ∂ 2ϕ e  =− Z k nk 2 ε0 εd ∂y

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(1)

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(2)

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(3)

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where nk is the number density of particle k; μk and D k denote the mobility and diffusion coefficient respectively, and S k is the reaction source term. ϕ , e, ε0 , and εd are the electric potential, elementary charge, permittivity of free space, and relative permittivity, respectively; εd = 3.0; nk and Z k are the number density and charge of particle k, respectively. Then, the strength of electric field is calculated by the following equation:

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E = −∇ ϕ

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+ + Positively charged particles O+ , O+ 2 , H2 , H , negatively charged − − − − − particles O , O2 , O3 , OH , H , and neutral particles O, O2 , O3 , H2 , H, OH, H2 O are taken into account. Discharge related reactions are given in Table 1. More details about the equations, reaction mechanisms, boundary and initial conditions, and numerical solving schemes can be found in ref. [8]. The DBD actuator is driven by a sinusoidal alternating current power supply with 10 kHz frequency and 14 kV peak-to-peak voltage, and the applied voltage starts from the negative peak. To study the effect of equivalence ratio on plasma assisted detonation initiation under rich burn condition, three equivalence ratios including ϕ = 1.0, 1.33, 2.0 are selected.

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2.2. Combustion simulation

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A loosely-coupled approach [8] is adopted to deal with the simulation of plasma assisted detonation initiation. In this study, the operation sequence is set as follows: the DBD actuator discharges in a defined area first, and then the mixture is ignited by a traditional spark ignition method. In this way, after simulating the AC DBD process, the spatial distributions of the key radicals and molecules at the moment when all the radicals reach their relatively high concentrations, together with a widely used traditional heat ignition (i.e. defining a high temperature domain) [3], are chosen as the initial conditions of the combustion simulation in the discharge zone. As shown in Fig. 2, the cylinder detonation combustor is 800 mm in length with an inner diameter of 23 mm. The close

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Table 1 Reactions in O2 –H2 mixture discharge [8]. Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Reaction +

e + O2 → O2 + 2e

e + O2 → O− + O+ + e e + O2 → O− + O e + O2 → 2O + e e + O2 → O+ + O + 2e e + O3 → O− + O2 e + O3 → O + O− 2 e + O → O+ + 2e + e + O2 → 2O O− + O2 → e + O3 O− + O2 → e + O2 + O O− + O → e + O2 O− + O+ 2 → 3O O− + O+ → 2O − O− 2 + O → O2 + O O− + O → O + e 3 2 − O+ 2 + O2 → 2O2 O+ + O2 → O + O+ 2 O+ + O3 → O+ 2 + O2 O + O3 → 2O2 O− + O3 → O− 3 +O + O− 3 + O2 → O3 + O2

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Rate coefficient

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e

7.2 × 10−17 T e0.5 e(−17/ T e ) 8.8 × 10−17 e(−4.4/ T e ) 7.1 × 10−15 e(−8.6/ T e ) 5.3 × 10−16 T e0.9 e(−20/ T e ) 9.3 × 10−16 T e−0.62 2.0 × 10−16 9 × 10−15 T e0.7 e(−11.6/ T e ) 6 × 10−11 T e−1.0 5 × 10−21 (300/ T g )0.5 2.4 × 10−18 1.4 × 10−16 1.0 × 10−13 2.0 × 10−13 (300/ T g )0.5 3.3 × 10−16 1.5 × 10−16 2 × 10−13 (300/ T g )0.5 2.1 × 10−17 10−17 (300/ T g )0.5 2.0 × 10−17 (300/ T g )0.5 5.3 × 10−16 (300/ T g )0.5 2.0 × 10−13 (300/ T g )0.5

+ O− 3 + O2 → O3 + 2O − O− + O 3 → O2 + O3 2 e + H2 → H+ + 2e 2 e + H2 → 2H + e e + H → H+ + 2e H2 + O− → H2 O + e H2 + O− 3 → H2 O + O2 + e − H2 + O− 2 → OH + OH O− + H2 O → OH− + OH e + H → H− e + H+ → H

1.01 × 10−13 (300/ T g )0.5 4.0 × 10−16 (300/ T g )0.5 BOLSIG+ BOLSIG+ BOLSIG+ 2.36 × 10−15 T e−0.24 10−15 10−16 × e−3100/ T g 1.4 × 10−15 3.46 × 10−22 T e−0.5 2.62 × 10−19 T e−0.5

→e+H + e + H+ 2 →H+H +e

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2e + H+

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e + H+ 2 → H + H(n = 3) H− + H → H2 + e − H + H → 2H + e H− + H2 (ν = 3) → H2 + H + e + H+ 2 + H → H + H2 H− + H+ → H(n = 3) + H H− + H+ 2 → H + H2 H− + H+ + M → 2H + M H− + H+ 2 + M → H + H2 + M

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2H → H2 3H → H2 + H

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2H + H2 → 2H2

8.8 × 10−39 T −4.5 e

5.66 × 10−14 T e−0.6 1.3 × 10−15 6 × 10−21 ( T g /300)3.5 1.6 × 10−16 6.93 × 10−16 1.8 × 10−13 ( T g /300)−0.5 2 × 10−13 ( T g /300)−0.5 2 × 10−37 ( T g /300)−2.5 2 × 10−37 ( T g /300)−2.5

6.04 × 10−39 ( T g /298)−1 6 × 10−43 ( T g /300)−1

8.1 × 10−45 ( T g /300)−0.6

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side wall, also known as the thrust wall of a detonation combustor, is on the left end of the combustor and the outlet is on the right end. To take full advantage of the cylinder tube configuration of the combustor, a rod-shaped high voltage electrode is connected to the center of the close side wall (so this electrode is coaxial to the combustor), and the combustor cylindrical wall is set as the grounded electrode directly with the dielectric layer covering its internal surface. Both electrodes have an axial length of 10 mm and the outer diameter of the central electrode is 3 mm. Thus, the discharge gap and zone both have a length of 10 mm. To compare the two cases easily, the computational configuration stays unchanged when the DBD actuator is turned off. The heat ignition is performed within the space between two electrodes for the plasma and no plasma cases. For simplicity, the discharge is assumed to be uniform along the axial and circumferential directions which is generally acceptable as reported in refs. [1,15,16], so the former discharge results can be used in the later simulation. Structural meshes are adopted in the whole computational domain. Three sub-domains are divided just along the symmetry axis to obtain a well flowfield with the least number of grids and restrict the aspect ratio of every cell to within 1–3. A mesh scheme

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Fig. 2. Computational domain and electrodes arrangement.

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that consists of 419 000 cells is chosen with the minimum grid step being 0.1 mm. An axisymmetric boundary is specified for the combustor axis. When the outflow of the combustor is subsonic, the local static pressure is set to be 0.8 atm at the outlet and all other variables are extrapolated from the upstream zone. A supersonic extrapolation condition is assumed here when the outflow is supersonic. The species is assumed to be air at the boundary. No slip and adiabatic conditions are imposed on the entire wall of the combustor. The combustor is filled with premixed quiescent hydrogen and oxygen in certain equivalence ratios with an initial temperature of 500 K and a pressure of 0.8 atm. The heat ignition zone is adjacent to the close side wall with an axial length of 10 mm and a temperature of 3000 K. The unsteady Reynolds averaged Navier–Stokes equations together with the Realizable k–ε turbulence model [17] and multispecies conservation equations are solved as reaction flow governing equations. The nonequilibrium wall function is adopted near the wall to accommodate the local gradient of pressure and nonequilibrium flow. The finite rate reaction model is used for combustion simulation, and the reaction rate is derived from the Arrhenius formula. The 6 species 7 reactions scheme is selected as the O2 –H2 chemical kinetic model [18], and related physical properties of the mixture and species are described in ref. [19]. The numerical schemes and validation of our simulation can be found in ref. [8]. 3. Results and discussion

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3.1. Temporal and spatial characteristics of discharge products

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The temporal and spatial distributions of the most important active radicals O, H, and electrons in the 4th discharge cycle for the three cases with different equivalence ratios ϕ = 1.0, 1.33, 2.0 are shown in Fig. 3 (here the vertical axis represents the discharge distance and it has the same y-direction as given in Fig. 1). The shapes of the distributions of different cases are almost identical for a certain species. For atom O, the number density decreases from high voltage electrode to the low voltage electrode, and it is higher in the latter half of the discharge cycle. For atom H, the number density increases from two electrodes to the middle of discharge gap and reaches its maximum value in the center, and the relatively high density appears in the middle stage of the cycle. Similarly to atom H, electrons have a higher density in the middle stage of the cycle, whereas the majority of electrons are produced in the vicinity of the high voltage electrode. Furthermore, there is a huge difference in the peak value of species number density. It shows that O has the highest magnitude, followed by H, and electron is the lowest, which is in accord with reality [20,21]. As equivalence ratio increases from 1.0 to 2.0, the peak value of every species density decreases. For example, the density of atom O is reduced by 45.5% and 73.0% for ϕ = 1.33 and 2.0, respectively, compared with the peak value 3.3 × 1023 m−3 at ϕ = 1.0. Also, the density of electrons is reduced by 40% and 66%, yet the density of H decreases evenly. However, considering the differences between these equivalence ratios, the conclusion is reached that although the density decreases as ϕ

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Fig. 3. Temporal and spatial distributions of discharge products at different equivalence ratios.

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rises from 1.0 to 2.0, the variation level gradually falls, meaning the influence of the equivalence ratio is weakened. The reasons for the above phenomenon are as follows: a larger equivalence ratio corresponds to a lower mass fraction of oxygen. According to the discharge reaction mechanism adopted here, atom O mainly comes from the collision reactions between electron and molecule oxygen to initiate the reactions chain, such as e + O2 → O− + O (R3), e + O2 → 2O + e (R4), e + O2 → O+ + O + 2e (R5), and O− + O2 → e + O2 + O (R11). If the mass fraction of O2 decreases, the amount of atom O produced from these key reactions will also decline. The yield of O from other reactions where O2 acts as the reactant will also decline when the mass fraction of O2 decreases. Then, consider the reactions involving the production of electron.

Because the initial number density of electrons is specified and the production of electrons is mainly through reacting with oxygen − + directly, such as e + O2 → O+ 2 + 2e (R1), e + O2 → O + O + e (R2), e + O2 → 2O + e (R4), e + O2 → O+ + O + 2e (R5), and O− + O2 → e + O3 (R10), the yield of electrons diminishes. Moreover, since another source of the electrons is through reacting with atom O, the yield also decreases. Then, the whole effect leads to the reduction of electron density. As for the source of atom H, though a larger equivalence ratio means a higher mass fraction of H, it is mainly produced from the reactions between hydrogen (or the decomposition products of hydrogen) and electrons, such as e + H2 → 2H + e (R26), and the density of electron decreases. Thus, the density of H decreases as equivalence ratio increases.

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Among all the intermediate species, radicals O, H, and OH have notably larger number density than others in the simulation results (other intermediate species are not presented here). Even for radical OH, which has the lowest concentration among the three radicals, its number density is two orders larger than other species. In addition, it has been reported that it is primarily the active species O, H, and OH that have relatively high concentration in a H2 –O2 discharge plasma, and have a large impact on ignition under the given conditions [2,21,22]. Thus, only species O, H, and OH are considered in the combustion simulation. It is easy to find that nearly all of the three radicals reach the highest concentration at about t = 0.6T (T denotes the duration of one discharge cycle) based on the temporal and spatial distributions of their density. Therefore, the concentration distributions of O, H, OH, H2 , O2 , and H2 O at t = 0.6T are selected as the initial conditions of the subsequent combustion simulation.

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3.2. Analysis of detonation formation process

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A whole DDT process for the completion of indirect detonation initiation consists of five sub-processes, which are the very slow combustion right after ignition, deflagration, over-driven detonation, decay of over-driven detonation, and propagation of selfsustained stable detonation. As three flow statuses including the static, subsonic, and supersonic exist in a whole DDT history, it is necessary to analyze both the transient flowfield inside the combustor and the ultimate results of forming the detonation.

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3.2.1. Characteristics of flowfield at different moments Three representative moments are selected based on the evolution of the ϕ = 1.0 case, to find the features of the phase before forming a shock, later phase before reaching the stable detonation, and stable propagation phase of the detonation wave.

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(1) 100 μs

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Fig. 4 shows the mass fraction profiles of reactant H2 , product H2 O, and active particle O along the combustor axis for different cases at t = 100 μs. At this moment, all the cases are still in the initial stage of the DDT process. Here, the abrupt ascending or descending of the curves reflects the boundary of the reacted and unreacted region. According to the definition of equivalence ratio and the analysis of the changes of discharge products density mentioned above, it is relatively easy to find the correspondence between the equivalence ratio and the case from the profile curves. The upstream H2 is partly consumed to produce H2 O as the reacted region expands downstream. For atom O, it is produced by the discharge at first and then develops in the later chain reactions. Because the discharge is limited within a 10 mm length zone, there is no atom O downstream of the reacted boundary. The expansion of the reacted region is expedited by the plasma, presented as a further movement of the discontinuity surface (i.e. the abrupt ascending/descending curve) under the same equivalence ratio, which is similar to the conclusion given in [8]. Notice that the reacted boundary of the ϕ = 1.33 case with actuator on has caught up with the ϕ = 1.0 case with actuator off. It can be inferred from the comparison of the maximum mass fraction of the plasma and no plasma case that the species concentration was not altered by the plasma. The movements of the reacted boundary by the plasma are almost the same under different equivalence ratios.

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(2) 130 μs

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The development degrees of the combustor flowfield will become quite different for different cases due to the plasma and

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Fig. 4. Profiles of species along the axis at t = 100 μs.

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equivalence ratio after 30 μs. To analyze the evolution of leading waves, the Mach number distributions of detonation combustor at t = 130 μs are shown in Fig. 5. As equivalence ratio rises, the maximum Mach number decreases indicating a slower evolution of flow, which is obvious as a further deviation from the stoichiometric ratio results in a harder ignition and combustion. When the actuator operates, the maximum Mach number rises sharply from 0.6 to 2.98 under the ϕ = 1.0 condition, meaning that the leading wave has transformed from the compression wave to the shock wave. A hot spot has arisen in the center of the shock wave front, thus the detonation wave has not formed yet. Except for Fig. 5(b), the leading wave of the other five cases still belongs to a compression wave. At this moment, the flowfield shape of the ϕ = 1.33 case with plasma is close to that of the ϕ = 1.0 case without plasma, which is in accord with the description of the reacted boundary at t = 100 μs. Generally, the evolution of the flowfield towards the occurrence of the detonation wave is expe-

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Fig. 5. Distribution of Mach number at t = 130 μs.

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dited when the actuator operates for different equivalence ratios. Through the comparison of the maximum Mach number of different cases, it seems that the plasma plays a weak role when ϕ = 1.33 at this moment. However, since the development degrees of flowfield are quite different for different equivalence ratios right now, and the formation of detonation is never a uniformly developing process, it is still difficult to determine the relationship between the action of plasma and equivalence ratio. (3) 200 μs The mass fraction profiles of species H2 , H2 O, and O along the combustor axis at t = 200 μs are shown in Fig. 6. The curves representing the discontinuity surfaces become steeper at this moment than they are in Fig. 4, since the leading wave develops more strongly, resulting in a sharp distinction of the species concentration of the reacted and unreacted regions. Obviously, the combustion zone extends towards the downstream unreacted region further at this moment. While all of the discontinuity surfaces of species move downstream when the actuator operates, the concentrations of these species remain unchanged, which can be confirmed from the peak values of the amount of hydrogen consumption, water production, and O production. Thus, the combustion zone extends faster with the plasma. The displacements of the discontinuity surfaces led by the plasma are 20.6 mm, 54.3 mm, and 29.3 mm for ϕ = 1.0, 1.33, and 2.0 respectively, indicating that the flowfield development in the ϕ = 1.33 case gets the best acceleration when the actuator operates, and the ϕ = 2.0 case is in the second place. Therefore, it can be inferred that the accelerating effect of plasma on the flowfield evolution increases first and then decreases as equivalence ratio rises at t = 200 μs. In addition, Fig. 6 shows that the combustion front of the ϕ = 1.33, plasma on case has caught up with it in the ϕ = 1.0, plasma off case. According to the mutual positions relationship of the combustion front of these two cases at t = 100 μs shown in Fig. 4, the effect of plasma on accelerating the DDT process continually strengthens under the ϕ = 1.33 condition.

3.2.2. Flow parameters at Ma = 1.0 The flow velocity of the combustor keeps rising with continual coupling of the compression waves. As the critical value of flow velocity, the distribution of flowfield parameters at Ma = 1.0 is capable of revealing the accumulative variation of the flowfield during the whole subsonic stage. At this moment, the maximum pressure of the combustor has substantially raised compared to its initial value. The profiles of local pressure and axial velocity (i.e., around the peak) along the combustor axis at Ma = 1.0 for the six cases are presented in Fig. 7. It is obvious that raising the equivalence ratio results in the movement of the summit of the profile curve towards the downstream flowfield, with or without plasma, as shown in Fig. 7. It means that the distance required to reach the supersonic stage increases when the equivalence ratio rises, which accords with reality. Furthermore, the distance is reduced by the plasma under different equivalence ratios, which can be confirmed from the initial positions and slopes of the main rising curves. There is a big difference in the profile curve shape between the ϕ = 2.0, without plasma case, and other cases, which could be attributed to the very weak combustion reaction led by the extremely low percentage of oxidizer in the mixture and the relatively low energy of the leading wave. The time saved to reach the supersonic flow by the plasma for ϕ = 1.0, 1.33, and 2.0 are obtained as follows: t = 9.19 μs, 18.7 μs, and 102.32 μs. Thus, the plasma has a more remarkable effect on shortening the time needed to form the shock wave in a combustor as the equivalence ratio increases. On the whole, the evolution of the flowfield is expedited by the plasma before reaching a supersonic flow in the combustor under different equivalence ratios, and the impact of equivalence ratio on the expedition becomes more remarkable at the later part of the subsonic phase—a large equivalence ratio corresponds to an evident expedition.

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3.2.3. Thrust wall pressure Due to the unsteady characteristics of the detonation combustor, the thrust wall pressure continually varies. This pressure is closely related to the performance of detonation engines and can

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Fig. 6. Profiles of species along the axis at t = 200 μs.

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exhibit the dynamic changes of the combustor internal flowfield. Thus, the history of thrust wall pressure is shown in Fig. 8. Here, the thrust wall denotes the inner close side wall of the combustor excluding the surface of the central electrode, and the magnitude of pressure is an area weighted average value. The appearance of the summits of pressure profiles is caused by the propagation of compression waves or shock waves towards the upstream flow. As the fuel runs out in the reacted region upstream of the leading wave, the profile curves of the thrust wall pressure eventually tend towards stability. First, through comparing the precedence of the occurrence of pressure summits for different cases, it shows that the summit occurs late when the equivalence ratio rises, yet it occurs earlier by the plasma for a certain equivalence ratio. It can be inferred from the pressure summit, which reflects the moment when the strongest combustion happens near the wall, that the combustion process is accelerated by the plasma. To investigate the effect of plasma on the appearance time of the pressure summit, the time

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Fig. 8. History of the average pressure of thrust wall.

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saved to reach the summit is calculated for ϕ = 1.0, 1.33, and 2.0 to be 10 μs, 23 μs, and 140 μs, respectively. Therefore, the plasma does improve the evolution more under a larger equivalence ratio. In addition, it seems that the higher equivalence ratio corresponds to a slightly larger peak value of pressure. However, the peak values of the plasma and the no plasma case are almost identical for a fixed equivalence ratio, meaning that the plasma will not alter the magnitude of the thrust wall pressure.

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3.2.4. DDT time and distance According to the axial profile of flowfield parameters when the C–J detonation wave has just formed, the DDT time and distance of different cases are obtained, as shown in Fig. 9. Obviously, the DDT time and distance are both shortened by the plasma. Under

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Fig. 9. DDT time and distance vs. equivalence ratio.

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the rich burn condition, although raising the equivalence ratio will result in an increase of DDT time and distance, the shortening effect on them caused by the plasma is also enhanced, especially for a high equivalence ratio case. For instance, when the actuator operates, the reduced DDT time and distance are about 6.4% and 3.7%, respectively, for ϕ = 1.0, yet they are up to approximately 52.6% and 42.7%, respectively, for ϕ = 2.0. Furthermore, under relatively low equivalence ratio conditions, the variation of DDT distance by the plasma are much smaller than that of DDT time, and the DDT distance is not sensitive to the change of equivalence ratio. Recently, many studies [1,2,23] have mentioned that even the addition of a very low concentration of discharge produced active particles is capable of improving the combustion. However, there is a lack of deep understanding of the correlation between environmental parameters and discharge products, and the relationship between the discharge environmental parameters and later combustion. By reviewing the influence of plasma on the reaction flow and combustion at several representative stages in the detonation combustor, it is found that the acceleration of flowfield evolution led by the plasma becomes more pronounced as the equivalence ratio rises under rich burn conditions. However, based on the temporal and spatial characteristics of discharge products distribution studied above, the number density of active species decreases as the equivalence ratio rises, in other words, a high concentration of the active species does not contribute to the plasma assisted detonation initiation. The reasons for this phenomenon can be concluded as follows: under rich burn conditions, the discharge not only provides active particles to expedite the combustion reactions, but also plays a role in diluting the fuel of the mixture. Fig. 3 shows that the density of active particles declines as the equivalence ratio rises. Take an example of the most important active species O: the peak value of its density declines 73% when ϕ rises from 1.0 to 2.0, yet atom H only declines 28.6%, indicating that atom O has a much larger change. Since atom O mainly comes from the decomposition of O2 , and atom H is mainly produced by the decomposition of H2 , the decomposing level of O2 declines compared with that of H2 . Therefore, raising the equivalence ratio amounts to increasing the concentration of O2 while decreasing that of H2 , and that results in the decline of the equivalence ratio of the whole mixture, which makes for forming a stable detonation wave quickly.

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4. Conclusion

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After receiving the simulation results of alternating current dielectric barrier discharge, a loosely coupled approach is utilized to establish a discharge-combustion model to study the effect of equivalence ratio on plasma assisted detonation initiation under

rich burn conditions numerically. The following conclusions can be drawn: (1) The shape of the temporal and spatial distribution of every discharge product is not altered when the equivalence ratio varies, yet when the equivalence ratio rises from 1.0, the number density of active species O, H, and electrons decreases while the decrease amplitude declines gradually. The changes of the percentage of fuel and oxidizer, and their effects on the discharge elementary reactions are the intrinsic causes for the variation of the density of these active species; (2) Although the species concentration is not altered when the actuator operates, the reacted region at different stages of the DDT process extends towards the downstream flow faster. Under the rich burn condition, the impact of plasma on the flowfield evolution is not sensitive to the variation of the equivalence ratio at the early stage. After that, the role of the plasma strengthens first and then weakens as the equivalence ratio rises. It is not until the late subsonic stage of the evolution process that the influence of the equivalence ratio begins to be significant, and the acceleration of the flowfield evolution by the plasma becomes more and more prominent as the equivalence ratio rises, which raises the time saving degree to form a shock wave quickly; (3) Based on the history of thrust wall pressure, plasma causes the pressure summit to occur earlier, indicating that the fuel burning process is expedited. In addition, the acceleration becomes more remarkable when raising the equivalence ratio, but the magnitude of the thrust wall pressure does not changed; (4) The AC DBD plasma is capable of shortening the DDT time and distance under rich burn conditions. Both the DDT time and distance increase as the equivalence ratio rises. Furthermore, the effect of plasma assisted detonation initiation becomes more distinct, though the variation of DDT distance caused by the plasma is not so obvious as that of DDT time under the relatively low equivalence ratios. The reasons for the influence of the equivalence ratio on plasma assisted detonation initiation are that the discharge plasma not only provides a variety of active particles to expedite the combustion reactions, but also plays a significant role in decreasing the equivalence ratio through diluting the fuel mixture under rich burn conditions.

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Conflict of interest statement

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None declared.

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Acknowledgements

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The authors would like to acknowledge the Science and Technology on Scramjet Laboratory Foundation (Grant No. CG-2014-05118) and the National Natural Science Foundation of China (Grant No. 91441123) for supporting this work. Also, special thanks to Dr. Y. Liu for his useful suggestions on detonation simulation, and Mr. Daniel R. Churchman for improving the language in this paper.

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