2.2.2. Characteristics of fuel mixing and combustion

For the sake of determining the fuel mixing quality, the five cross-sectional planes distributed in equivalent ratio along the flow direction are given, as shown in Figure 5. The fuel jet arises with the actuator working, resulting in fuel decreasing near the wall including the bottom wall of the cavity. Whereas, the distribution shape of fuel in the cross-sectional planes varies from a distribution narrow and long profile into a circular profile in the upper space, which shows that the process of fuel spreading into the main supersonic flow is enhanced resulted from the plasma. Furthermore, the fuel distributions at time A are nearly the same as at time C, which is also correlated to the inertial effect mentioned above.

It can be seen that the fuel entrainment into the cavity is decreased and the combustion in cavity becomes weaker due to the plasma, as given in Figures 5 and 6.Whereas, the two figures also show that more fuel penetrates into the supersonic air flow, so the mass exchange between the inside cavity and its outside is enhanced due to the plasma. Hence, the plasma improves the fuel mixing above the cavity prominently, which can also be realized as the calculation

The stagnation pressure recovery coefficient can indicate the pressure loss in a combustor, so it is an important index. When the stagnation pressure recovery coefficient goes up, the capability of combustor outflow will be enhanced. So, it is defined as the ratio of combustor outlet stagnation pressure to inlet stagnation pressure [24]. In fact, calculating the mass flow

> <sup>¼</sup> <sup>p</sup>0\_outlet p0\_inlet

where ηp<sup>0</sup> and p<sup>0</sup> are the stagnation pressure recovery coefficient and the combustor stagnation

where u and r are the flow velocity across a certain plane and the density of selected plane,

<sup>η</sup><sup>p</sup>0,loss <sup>¼</sup> <sup>1</sup>:<sup>0</sup> � <sup>p</sup>0\_outlet

The calculated data about the stagnation pressure are given in Table 3. In order to analyze the tendency of stagnation pressure loss coefficient further, the average stagnation pressure at the

p0\_inlet

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(6)

<sup>r</sup>d<sup>y</sup> (5)

weighted mean stagnation pressure can gain the stagnation pressure in a cross section.

ηp0

p<sup>0</sup> ¼ Ð p0rudy Ð

respectively. Based on above, we get the stagnation pressure loss coefficient:

results of combustion efficiency in Section 2.2.4.

Figure 6. Iso-surfaces of product water, YH2O = 0.015. (a) Plasma off. (b) Plasma on.

2.2.3. Combustor stagnation pressure

pressure, respectively.

In Figure 6, the distribution of product water is shown. In order to distinguish the extent of product water between time A and C easily, the iso-surfaces of both are plotted by combining the half parts of them together as shown in Figure 6(b). Similar to the changes in Figure 5, more water is generated in the upper space due to plasma. Contrasted with the case without plasma actuator, the iso-surface of water expands much in its center and shrinks near the combustor wall especially downstream of cavity. These above should be attributed to the change of fuel jet spread, as given in Figure 5. Compared time A with C, the only distinction is a little more water formed at time A, which indicates that the combustion becomes weaker in the free time of a plasma control cycle.

Figure 5. Distribution of equivalent ratio in cross-sectional planes. (a) Plasma off. (b) Plasma on, time A. (c) Plasma on, time C.

Figure 6. Iso-surfaces of product water, YH2O = 0.015. (a) Plasma off. (b) Plasma on.

It can be seen that the fuel entrainment into the cavity is decreased and the combustion in cavity becomes weaker due to the plasma, as given in Figures 5 and 6.Whereas, the two figures also show that more fuel penetrates into the supersonic air flow, so the mass exchange between the inside cavity and its outside is enhanced due to the plasma. Hence, the plasma improves the fuel mixing above the cavity prominently, which can also be realized as the calculation results of combustion efficiency in Section 2.2.4.

#### 2.2.3. Combustor stagnation pressure

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

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

For the sake of determining the fuel mixing quality, the five cross-sectional planes distributed in equivalent ratio along the flow direction are given, as shown in Figure 5. The fuel jet arises with the actuator working, resulting in fuel decreasing near the wall including the bottom wall of the cavity. Whereas, the distribution shape of fuel in the cross-sectional planes varies from a distribution narrow and long profile into a circular profile in the upper space, which shows that the process of fuel spreading into the main supersonic flow is enhanced resulted from the plasma. Furthermore, the fuel distributions at time A are nearly the same as at time C, which is

In Figure 6, the distribution of product water is shown. In order to distinguish the extent of product water between time A and C easily, the iso-surfaces of both are plotted by combining the half parts of them together as shown in Figure 6(b). Similar to the changes in Figure 5, more water is generated in the upper space due to plasma. Contrasted with the case without plasma actuator, the iso-surface of water expands much in its center and shrinks near the combustor wall especially downstream of cavity. These above should be attributed to the change of fuel jet spread, as given in Figure 5. Compared time A with C, the only distinction is a little more water formed at time A, which indicates that the combustion becomes weaker in

Figure 5. Distribution of equivalent ratio in cross-sectional planes. (a) Plasma off. (b) Plasma on, time A. (c) Plasma on,

times is highly similar on the whole.

174 Plasma Science and Technology - Basic Fundamentals and Modern Applications

2.2.2. Characteristics of fuel mixing and combustion

also correlated to the inertial effect mentioned above.

the free time of a plasma control cycle.

time C.

proper control parameters.

The stagnation pressure recovery coefficient can indicate the pressure loss in a combustor, so it is an important index. When the stagnation pressure recovery coefficient goes up, the capability of combustor outflow will be enhanced. So, it is defined as the ratio of combustor outlet stagnation pressure to inlet stagnation pressure [24]. In fact, calculating the mass flow weighted mean stagnation pressure can gain the stagnation pressure in a cross section.

$$
\eta\_{p\_0} = \frac{\overline{p}\_{0\\_\text{outlet}}}{\overline{p}\_{0\\_\text{inlet}}} \tag{4}
$$

where ηp<sup>0</sup> and p<sup>0</sup> are the stagnation pressure recovery coefficient and the combustor stagnation pressure, respectively.

$$
\overline{p}\_0 = \frac{\int p\_0 \overline{\rho} u \, \mathrm{d}y}{\int \overline{\rho} \mathrm{d}y} \tag{5}
$$

where u and r are the flow velocity across a certain plane and the density of selected plane, respectively. Based on above, we get the stagnation pressure loss coefficient:

<sup>η</sup><sup>p</sup>0,loss <sup>¼</sup> <sup>1</sup>:<sup>0</sup> � <sup>p</sup>0\_outlet p0\_inlet (6)

The calculated data about the stagnation pressure are given in Table 3. In order to analyze the tendency of stagnation pressure loss coefficient further, the average stagnation pressure at the outlet is replaced by the average stagnation pressure at different positions, as shown in Figure 7. At the actuator working time or even at the free time, the stagnation pressure loss can both be increased due to the plasma, as given in Table 3. In (7), the relative change rate of ηp0 is defined to realize the variation degree of the stagnation pressure recovery coefficient.

$$
\varepsilon\_i = \left| \frac{\eta\_i - \eta\_b}{\eta\_b} \right| \times 100\% \tag{7}
$$

in three aspects: (1) the strength of separation shock upstream of the jet is changed due to plasma as mentioned above, which will affect the stagnation pressure distribution; (2) the quasi-DC discharge plasma behaves as a virtual blockage in supersonic flow resulted in new shock waves or compression waves forming. Then, the pressure loss is increased; (3) the heat release from combustion can result in the stagnation pressure decreasing. Hence, the increase of stagnation pressure loss in the combustor is correlated to all the changes in flowfield which is due to the comprehensive effect mentioned above. To ensure the maximal combustion efficiency while keeping the stagnation pressure loss as little as possible, the optimal design is important. So the calculation of combustion efficiency is essential to choose the proper plasma

The combustion efficiency η<sup>c</sup> is commonly denoted by the amount of combustion product.

<sup>η</sup><sup>c</sup> <sup>¼</sup> ð Þ <sup>m</sup>\_ H2O,<sup>X</sup> � <sup>m</sup>\_ H2O,<sup>I</sup> <sup>=</sup>WH2O m\_ H2 =WH2

where m\_ H2O,<sup>I</sup> is the mass flow rate of water at inlet cross section and m\_ H2O, <sup>x</sup> is x-direction cross section, respectively. m\_ H2 and Wi are the mass flow rate of hydrogen and the mole mass of

Figure 8 plots the distribution of combustion efficiency in x-direction. At both time A and C, the rise rates of combustion efficiency go into larger along x-direction. At the outlet, η<sup>c</sup> reaches 0.81341, 0.76008, and 0.60278 for time A, C, and no plasma case, respectively. Namely that η<sup>c</sup> at time A and C are 1.35 and 1.26 times of no plasma case. As a result, the quasi-DC plasma does obviously improve the combustion in combustor on the whole level, as shown in Figure 8, even if the most water forms in the upper space rather than in the cavity. But the η<sup>c</sup> at time A and time C are almost same. From Figure 6, the increase of combustion efficiency can also be realized, which indicates that the mixing performance of the fuel jet in scramjet combustor is

In order to define the cost to effectiveness of quasi-DC plasma, it is calculated in value E<sup>f</sup> = 0.00811 for the ratio of deposited plasma energy to the increased combustion heat release. Accordingly, for improving the combustion of scramjet combustor, the quasi-DC plasma

The main results in this section are as follows: (1) The distribution of relatively high temperature zone moves downstream prominently due to the heat release from the quasi-DC discharge plasma. The separation shock wave induced by the fuel jet is partly weakened and moves upstream due to the plasma, which can regulate the size of recirculation zone upstream of the fuel orifice. (2) The fuel jet moves upward integrally resulted from the plasma heating effect. The fuel spread wider along the spanwise and penetrates into the leading flow deeper,

specie i, respectively. And dry air is assumed at the inlet in the simulation m\_ H2O,<sup>I</sup> ¼ 0.

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actuator parameters.

2.2.4. Combustion efficiency downstream of the fuel orifice

Thus, the amount of water is employed [24]:

improved due to the quasi-DC discharge plasma.

shows good capability as costing a little.

2.3. Conclusions

where η<sup>i</sup> is the stagnation pressure recovery coefficient of a certain case and η<sup>b</sup> is the base case.

In Figure 7, the difference of stagnation pressure loss between plasma cases is shown where no plasma case enlarges along the flow direction (x-direction). At time A, B, and C, the relative change rate of stagnation pressure recovery coefficient at outlet point are 3.7, 3.1, and 3.4%, respectively, which indicates that the stagnation pressure loss varies little during a whole plasma control cycle and the loss is relatively little. The reasons resulted in these changes are


Table 3. The inlet mean stagnation pressure P0\_inlet, outlet mean stagnation pressure P0\_outlet, stagnation pressure recovery coefficient ηp0 Z, and stagnation pressure loss coefficient in the combustor.

Figure 7. Distribution of the stagnation pressure loss coefficient.

in three aspects: (1) the strength of separation shock upstream of the jet is changed due to plasma as mentioned above, which will affect the stagnation pressure distribution; (2) the quasi-DC discharge plasma behaves as a virtual blockage in supersonic flow resulted in new shock waves or compression waves forming. Then, the pressure loss is increased; (3) the heat release from combustion can result in the stagnation pressure decreasing. Hence, the increase of stagnation pressure loss in the combustor is correlated to all the changes in flowfield which is due to the comprehensive effect mentioned above. To ensure the maximal combustion efficiency while keeping the stagnation pressure loss as little as possible, the optimal design is important. So the calculation of combustion efficiency is essential to choose the proper plasma actuator parameters.
