2.1.1. Plasma model and its configuration

By applying a high voltage across the anode and cathode, a bright plasma filament appears above the two electrodes. With the impacting of incoming flow, the plasma occurs not only between the two electrodes but also several centimeters downstream on the wall [10]. In consideration of the oscillation character of its electrical parameters and mean temperature in the discharge path, this type of discharge plasma is called "quasi-DC discharge plasma." However, it is a type of low temperature arc plasma in fact. The main properties of quasi-DC discharge plasma are described in [10–12, 15].

combustion and flame [1–3]. Whereas, it is difficult yet for the fuel to reach properly mixing within the supersonic flow by the mechanical methods [4, 5]. Moreover, it is a great challenge for matching the transverse fuel jet up with the cavity under off-design condition [4]. Furthermore, certain stagnation pressure loss will appear using the approaches. Taken all account, some new methods are imminently needed for keeping stable and highly efficient combustion in combustor

It is rather promising to adopt a discharge plasma for supersonic flow and/or combustion control in aerospace field [6–8]. It has been widely considered that plasma-assisted combustion is one of the most promising approaches for enhancing ignition and combustion in the environment of scramjet combustion [4, 6, 9]. As a further promising method, there are three advantages, that is: rapid response, less inertia, and flexibility [10]. Former studies clearly show that the quasi-DC discharge plasma can availably modify supersonic flow in a controllable manner among the discharge plasma mentioned above [8, 11], whereas the DBD plasma is commonly used in low-speed flow environment [12, 13]. If we can combine the quasi-DC discharge plasma with cavity and transverse fuel jet together, some new phenomena will

There in three primary mechanisms of the plasma effect on flow and combustion can be summarized: (1) momentum transfer, (2) fast local ohmic heating of the medium, and (3) active particles [6, 7, 14]. Ignoring the magnetic field, the mechanism of quasi-DC discharge plasma affecting a supersonic flow is mainly its fast local heating rather than the electrostatic

This chapter aims at investigating the changes of the fuel jet, cavity, and whole scramjet combustor led by the quasi-DC discharge plasma based on the dominant thermal blocking mechanism. Here, a short cavity downstream of a fuel jet orifice is considered in order to simulate the combustor flowfield more realistic. The plasma is set as a controllable heat source. The k-ω shear stress transport (SST) model together with finite rate chemical reaction model is used simulating the turbulent flow and combustion. The flow structures, equivalent ratio, product distribution, stagnation pressure, and combustion efficiency in the combustor are all obtained and analyzed using the 3D numerical simulation which can acquire some data that

By applying a high voltage across the anode and cathode, a bright plasma filament appears above the two electrodes. With the impacting of incoming flow, the plasma occurs not only between the two electrodes but also several centimeters downstream on the wall [10]. In consideration of the oscillation character of its electrical parameters and mean temperature in

surely appear, which may help in the improvement of combustor performance.

force (i.e., the momentum transfer mechanism) [10, 15, 16].

are difficult to measure in experiments.

2.1.1. Plasma model and its configuration

2.1. Numerical methods

2. Case one—effect of plasma on fuel jet

with the least penalties adding to the flowfield.

168 Plasma Science and Technology - Basic Fundamentals and Modern Applications

As depicted in Figure 1, the domain of quasi-DC discharge plasma filament is simplified as a cuboid region presented in red dashed lines for simulation based on its appearance. In Figure 1, the symmetric plotted line indicates that the cathode and anode are symmetrical for the central line of combustor wall and so does the plasma filament.

Because the quasi-DC discharge plasma releases a large amount of heat concentrated in its discharge path, the discharge path goes into very hot. This high temperature domain (i.e., the discharge path) obstructs the supersonic inflow due to a thermal blocking occurred. Hereby, the quasi-DC discharge plasma behaves as a virtual blockage in the high speed flow of scramjet combustor, which is called as "the dominant thermal blocking mechanism" [17]. On the foundation of dominant thermal blocking mechanism, the individual plasma filament can be simulated as a volumetric heat source [10, 12].

Generally speaking, the plasma input power and the effective heat power that transfers into circumambient gas are quite different. Besides, the percentage of loss commonly varies with the power supply and environment, so it is not a suitable way to use the plasma input power as the heat source value of quasi-DC discharge plasma in simulation. In order to straightforwardly describe the plasma heat strength, the average temperature of the plasma zone is acquired by using the numerical simulation here. This way is feasible when the average temperature of the plasma zone is within a reasonable range [10, 16, 18, 19]. Hence, based on the thermal blocking mechanism, a certain temperature which denotes the actuating strength (i.e., the input power) is specified for the plasma filament domain when the actuator works.

The electrodes are flush mounted and do not have influence on the main flow themselves. The length and the section dimensions of individual plasma filament heat source are 20 mm length and 3 3 mm, respectively. The plasma filament locates 40 mm upstream of the fuel orifice center. Besides, it is generated near the wall in the center of the combustor, which means the symmetric plane of plasma filament is within the symmetric xy-plane of combustor. The quasi-DC discharge plasma working under a pulsed mode shows better performance than a continuous mode [19], so a plasma control frequency F<sup>c</sup> = 8 kHz with duty cycle ratio D = 2/5 is chosen here. And Tpl = 2500 K is specified as an optimal actuating strength.

Figure 1. Computed configuration of quasi-DC discharge plasma in case one.

#### 2.1.2. Governing equations, physical models, and numerical schemes

The unsteady Reynolds averaged 3D Navier-Stokes equations (URANS) with the k-ω SST two equation turbulence model [20] and four species (H2, O2, N2, and H2O) conservation equations are used as the governing equations of flow and combustion. The thermal conductivity of every species remains as constant and the mixture thermal conductivity is calculated using ideal gas mixing law. Based on the perfect gas assumption, it can be seen that the mixing gas satisfies the local thermodynamics equilibrium hypothesis and follows the state equation:

$$P = R\_0 T \sum\_{i=1}^{N\_s} \frac{\rho\_i}{W\_i} \tag{1}$$

second-order upwind approach at same time. The viscous fluxes are evaluated by using the second-order central differential scheme. Because the transport process of multispecies and the reaction both exist in the flowfield, a modified LU-SGS implicit method [23] is adopted for

Equation Pre-exponential factor Temperature index Activity energy [J/kg�mol]

Plasma-Assisted Combustion

171

http://dx.doi.org/10.5772/intechopen.80959

H2 þ 0:5O2 \$ H2O 9.87E + 8 0 3.1E + 7

Figure 2 shows the entire computational domain which is the half of scramjet combustor together with a short cavity and a fuel jet orifice. The inlet of combustor is located at x = 0 mm, which is 33.064 mm high and 44 mm wide. The upper wall angle is set as 1� to prevent thermal block. For avoiding the interaction between multifuel jets, there is only one single fuel orifice arranged at the symmetric plane of combustor, which locates at 60 mm downstream of the inlet. The distance between the fuel orifice center and the leading edge of downstream cavity is 10 mm, which can strengthen the resisting back pressure capability. And a short cavity is adopted here with rear edge angle 45�, length 56 mm, width 44 mm, and depth 8 mm, respectively. Instead using a circular fuel orifice, a 1.772 mm � 1.772 mm square cross section orifice is adopted to acquire high-quality mesh, which has the same cross section area

The grids number is largely reduced by setting the symmetry face (xy-plane) of combustor as a symmetry boundary condition. In order to improve the quality of computational grids, the whole domain is divided into six parts to make all grids in structured type, except for the rear part of the cavity with unstructured grids. All grids aspect ratio and equisize skew are within 8 and 0.54, respectively. Grids are refined in key zones, such as the plasma domain, fuel orifice, wall, and shear layer. Besides, grids in zones with relatively large pressure gradient and the boundary layer are refined using adaptive mesh refining method based on the initial simulation

temporal integration.

Table 2. H2/O2 one-step chemical model.

2.1.3. Computational zone and boundary conditions

as a 2 mm diameter circular orifice.

Figure 2. Computational domain and grids of the combustor.

here, R<sup>0</sup> = 8.314 J/ (mol∙K) is the gas constant. The specific heat capacity cpi of species i is derived from a piecewise polynomial as follows:

$$\mathcal{L}\_{pi} = a\_{1,i} + a\_{2,i}T + a\_{3,i}T^2 + a\_{4,i}T^3 + a\_{5,i}T^4 \tag{2}$$

where the coefficients can be found in [21]. The k-ω SST two equation turbulence model is used here because of its well behave in separation flow and free shear flow. Based on the Boussinesq assumption, viscosity coefficient μ = μ<sup>l</sup> + μt, where μ<sup>l</sup> is the laminar viscosity coefficient and μ<sup>t</sup> is the turbulence viscosity coefficient. μ<sup>l</sup> can be received from the Sutherland law, whereas μ<sup>t</sup> is received from the k-ω SST model.

$$
\mu\_l = \mu\_{\text{ref}} \left( \frac{T}{T\_{\text{ref}}} \right)^{2/3} \frac{T\_{\text{ref}} + S}{T + S} \tag{3}
$$

where μref is the reference viscosity coefficient under corresponding reference temperature Tref and S is the Sutherland constant which can be got from Table 1.

Since this study focuses on the qualitative effect of plasma on the fuel jet and the scramjet combustor, the finite rate chemical model with the single step H2/O2 combustion kinetics model is applied. The reaction rate constant is derived from the Arrhenius formula. Hence, the computational time can be saved much and the well combustion flowfield can be obtained, too. The relevant parameters of H2/O2 one-step chemical model are shown in Table 2.

In order to capture the shock waves and other complex fluid structures better, the convective fluxes are evaluated using the advection upstream splitting method (AUSM) [22] with the


Table 1. Parameters in Sutherland law.


Table 2. H2/O2 one-step chemical model.

2.1.2. Governing equations, physical models, and numerical schemes

170 Plasma Science and Technology - Basic Fundamentals and Modern Applications

derived from a piecewise polynomial as follows:

received from the k-ω SST model.

Table 1. Parameters in Sutherland law.

The unsteady Reynolds averaged 3D Navier-Stokes equations (URANS) with the k-ω SST two equation turbulence model [20] and four species (H2, O2, N2, and H2O) conservation equations are used as the governing equations of flow and combustion. The thermal conductivity of every species remains as constant and the mixture thermal conductivity is calculated using ideal gas mixing law. Based on the perfect gas assumption, it can be seen that the mixing gas satisfies the local thermodynamics equilibrium hypothesis and follows the state equation:

P ¼ R0T

X Ns

ri Wi

cpi <sup>¼</sup> <sup>a</sup>1,i <sup>þ</sup> <sup>a</sup>2,iT <sup>þ</sup> <sup>a</sup>3,iT<sup>2</sup> <sup>þ</sup> <sup>a</sup>4,iT<sup>3</sup> <sup>þ</sup> <sup>a</sup>5,iT<sup>4</sup> (2)

Tref (K) S (K) μref (kg/m∙s)

<sup>T</sup> <sup>þ</sup> <sup>S</sup> (3)

(1)

i¼1

here, R<sup>0</sup> = 8.314 J/ (mol∙K) is the gas constant. The specific heat capacity cpi of species i is

where the coefficients can be found in [21]. The k-ω SST two equation turbulence model is used here because of its well behave in separation flow and free shear flow. Based on the Boussinesq assumption, viscosity coefficient μ = μ<sup>l</sup> + μt, where μ<sup>l</sup> is the laminar viscosity coefficient and μ<sup>t</sup> is the turbulence viscosity coefficient. μ<sup>l</sup> can be received from the Sutherland law, whereas μ<sup>t</sup> is

> T Tref

where μref is the reference viscosity coefficient under corresponding reference temperature Tref

Since this study focuses on the qualitative effect of plasma on the fuel jet and the scramjet combustor, the finite rate chemical model with the single step H2/O2 combustion kinetics model is applied. The reaction rate constant is derived from the Arrhenius formula. Hence, the computational time can be saved much and the well combustion flowfield can be obtained,

In order to capture the shock waves and other complex fluid structures better, the convective fluxes are evaluated using the advection upstream splitting method (AUSM) [22] with the

H2 273.11 96.67 8.411 � <sup>10</sup>�<sup>6</sup> O2 273.11 138.9 1.919 � <sup>10</sup>�<sup>5</sup> H2O 416.67 861.11 1.703 � <sup>10</sup>�<sup>5</sup> N2 273.11 106.67 1.663 � <sup>10</sup>�<sup>5</sup>

too. The relevant parameters of H2/O2 one-step chemical model are shown in Table 2.

� �<sup>2</sup>=<sup>3</sup> <sup>T</sup>ref <sup>þ</sup> <sup>S</sup>

μ<sup>l</sup> ¼ μref

and S is the Sutherland constant which can be got from Table 1.

second-order upwind approach at same time. The viscous fluxes are evaluated by using the second-order central differential scheme. Because the transport process of multispecies and the reaction both exist in the flowfield, a modified LU-SGS implicit method [23] is adopted for temporal integration.

#### 2.1.3. Computational zone and boundary conditions

Figure 2 shows the entire computational domain which is the half of scramjet combustor together with a short cavity and a fuel jet orifice. The inlet of combustor is located at x = 0 mm, which is 33.064 mm high and 44 mm wide. The upper wall angle is set as 1� to prevent thermal block. For avoiding the interaction between multifuel jets, there is only one single fuel orifice arranged at the symmetric plane of combustor, which locates at 60 mm downstream of the inlet. The distance between the fuel orifice center and the leading edge of downstream cavity is 10 mm, which can strengthen the resisting back pressure capability. And a short cavity is adopted here with rear edge angle 45�, length 56 mm, width 44 mm, and depth 8 mm, respectively. Instead using a circular fuel orifice, a 1.772 mm � 1.772 mm square cross section orifice is adopted to acquire high-quality mesh, which has the same cross section area as a 2 mm diameter circular orifice.

The grids number is largely reduced by setting the symmetry face (xy-plane) of combustor as a symmetry boundary condition. In order to improve the quality of computational grids, the whole domain is divided into six parts to make all grids in structured type, except for the rear part of the cavity with unstructured grids. All grids aspect ratio and equisize skew are within 8 and 0.54, respectively. Grids are refined in key zones, such as the plasma domain, fuel orifice, wall, and shear layer. Besides, grids in zones with relatively large pressure gradient and the boundary layer are refined using adaptive mesh refining method based on the initial simulation

Figure 2. Computational domain and grids of the combustor.

results. After comparing the results of different grids size, a mesh scheme which consists of 955,166 cells in the whole computational zone is chosen, and it can be proved when the grids size increases, the flowfield remains almost unchanged all the same.

The entire computational domain is divided into 32 subdomains, and all assignments are completed by parallel computation on HP senior workstation, which takes about 320 h to obtain a convergence result. The inflow conditions in computation are as follows: Ma = 2.2, static pressure P = 101 kPa, static temperature T = 823 K, and boundary layer thickness δ = 2.0 mm. In order to identify product water, dry air is set as the inflow (the mass fraction of oxygen and nitrogen are YO2 = 23.3%, YN2 = 76.7%, respectively). Here, hydrogen is used as fuel which is perpendicularly injected into the main flow at sonic speed. The parameters of fuel injection at the outlet of fuel orifice are given as: static pressure Pjst = 334 kPa, stagnation pressure Pj0 = 0.6 MPa, and stagnation temperature Tj0 = 290 K. At the exit boundary, the supersonic extrapolation condition is used. Besides, symmetry condition is used in central xyplane (z = 0) for decreasing the calculation cost. There is no slip and adiabatic conditions, which are specified on the upper, bottom, and lateral walls of combustor including the cavity walls.

### 2.1.4. Simulation validation

The ability of our numerical methods for simulating the multispecies reaction flow field of the scramjet combustor with a cavity has been validated and can be found in [14, 18].

#### 2.2. Results and discussion

Three representative times are selected during one plasma control cycle for comparison after computation converged. The end of the actuator duty time (t = 2/5Tc, where T<sup>c</sup> is the period of one plasma control cycle), a certain time of the actuator free time (t = 4/5Tc) and the end of a whole plasma control cycle (t = Tc) are named A, B, and C, respectively.

### 2.2.1. Temperature and wall pressure distribution of the jet flowfield

The temperature distribution on the symmetric xy-plane of combustor is shown in Figure 3. It can be seen that the relatively high temperature zone appears mainly in the cavity when there is no plasma actuator arranged. But it moves downstream with the actuator working. The local temperature of the near wall downstream and the rear part of the cavity increases distinctly, which means the combustion centrality zone moves downstream. Besides, the lower temperature zone which denotes the fuel jet flow (i.e., the deep blue zone in Figure 3) prominently shrinks as the actuator works. However, the area of the lower temperature zone extended gradually at time B and C compared with time A. The unsteady phenomena should be due to the high heat nature of quasi-DC discharge plasma, which transfers its heat to the fuel jet resulted in changing the combustion zone downstream.

move upstream from 56.6 to 52 mm due to the effect of plasma, which indicates the separation shock wave induced by the fuel jet moves upstream. And the first pressure peak decreases from 2.0 to 1.7, because of the weakening of the fuel jet induced shock on the symmetric plane. The results above are similar to the previous studies on nonreaction flow combustor [19]. More details indicate that the first pressure peak of time A is a bit higher than time B and C, but time B equals time C, which is due to the plasma control cycle too

Figure 3. Contours of temperature on the symmetric xy-plane of combustor. (a) Plasma off. (b) Plasma on, time A. (c) Plasma

Plasma-Assisted Combustion

173

http://dx.doi.org/10.5772/intechopen.80959

Figure 4. Wall pressure distribution on the symmetric plane.

on, time B. (d) Plasma on, time C.

The distribution of wall pressure near the fuel orifice on the symmetric plane of the combustor is shown in Figure 4, which is normalized by the value of the static pressure of inflow at the inlet. Compared with no plasma case, the positions that pressure starts to rise at different times

Figure 3. Contours of temperature on the symmetric xy-plane of combustor. (a) Plasma off. (b) Plasma on, time A. (c) Plasma on, time B. (d) Plasma on, time C.

Figure 4. Wall pressure distribution on the symmetric plane.

results. After comparing the results of different grids size, a mesh scheme which consists of 955,166 cells in the whole computational zone is chosen, and it can be proved when the grids

The entire computational domain is divided into 32 subdomains, and all assignments are completed by parallel computation on HP senior workstation, which takes about 320 h to obtain a convergence result. The inflow conditions in computation are as follows: Ma = 2.2, static pressure P = 101 kPa, static temperature T = 823 K, and boundary layer thickness δ = 2.0 mm. In order to identify product water, dry air is set as the inflow (the mass fraction of oxygen and nitrogen are YO2 = 23.3%, YN2 = 76.7%, respectively). Here, hydrogen is used as fuel which is perpendicularly injected into the main flow at sonic speed. The parameters of fuel injection at the outlet of fuel orifice are given as: static pressure Pjst = 334 kPa, stagnation pressure Pj0 = 0.6 MPa, and stagnation temperature Tj0 = 290 K. At the exit boundary, the supersonic extrapolation condition is used. Besides, symmetry condition is used in central xyplane (z = 0) for decreasing the calculation cost. There is no slip and adiabatic conditions, which are specified on the upper, bottom, and lateral walls of combustor including the cavity

The ability of our numerical methods for simulating the multispecies reaction flow field of the

Three representative times are selected during one plasma control cycle for comparison after computation converged. The end of the actuator duty time (t = 2/5Tc, where T<sup>c</sup> is the period of one plasma control cycle), a certain time of the actuator free time (t = 4/5Tc) and the end of a

The temperature distribution on the symmetric xy-plane of combustor is shown in Figure 3. It can be seen that the relatively high temperature zone appears mainly in the cavity when there is no plasma actuator arranged. But it moves downstream with the actuator working. The local temperature of the near wall downstream and the rear part of the cavity increases distinctly, which means the combustion centrality zone moves downstream. Besides, the lower temperature zone which denotes the fuel jet flow (i.e., the deep blue zone in Figure 3) prominently shrinks as the actuator works. However, the area of the lower temperature zone extended gradually at time B and C compared with time A. The unsteady phenomena should be due to the high heat nature of quasi-DC discharge plasma, which transfers its heat to the fuel jet

The distribution of wall pressure near the fuel orifice on the symmetric plane of the combustor is shown in Figure 4, which is normalized by the value of the static pressure of inflow at the inlet. Compared with no plasma case, the positions that pressure starts to rise at different times

scramjet combustor with a cavity has been validated and can be found in [14, 18].

whole plasma control cycle (t = Tc) are named A, B, and C, respectively.

2.2.1. Temperature and wall pressure distribution of the jet flowfield

resulted in changing the combustion zone downstream.

size increases, the flowfield remains almost unchanged all the same.

172 Plasma Science and Technology - Basic Fundamentals and Modern Applications

walls.

2.1.4. Simulation validation

2.2. Results and discussion

move upstream from 56.6 to 52 mm due to the effect of plasma, which indicates the separation shock wave induced by the fuel jet moves upstream. And the first pressure peak decreases from 2.0 to 1.7, because of the weakening of the fuel jet induced shock on the symmetric plane. The results above are similar to the previous studies on nonreaction flow combustor [19]. More details indicate that the first pressure peak of time A is a bit higher than time B and C, but time B equals time C, which is due to the plasma control cycle too short for flow response and the duty cycle ratio also comparatively large in the flow condition here. Hence, the influence of plasma on the shock will be observed a little latter due to an inertia influence. Nevertheless, the effect of plasma on the shock wave for three typical times is highly similar on the whole.

Because the separation zone upstream of the fuel orifice is primarily controlled by the separation shock wave, the size of this separation zone can be regulated by changing the location of the separation shock wave. On the one side, this zone behaves as an main ignition zone which can provide a high temperature and low flow speed environment in the scramjet combustor. On the other side, it will bring in certain pressure loss to the combustor. Hence, we can make use of the separation zone upstream of the fuel orifice by means of using the plasma with proper control parameters.
