2.2.4. Combustion efficiency downstream of the fuel orifice

The combustion efficiency η<sup>c</sup> is commonly denoted by the amount of combustion product. Thus, the amount of water is employed [24]:

$$\eta\_c = \frac{(\dot{m}\_{\text{H}\_2\text{O},\text{X}} - \dot{m}\_{\text{H}\_2\text{O},\text{I}}) / W\_{\text{H}\_2\text{O}}}{\dot{m}\_{\text{H}\_2} / W\_{\text{H}\_2}} \tag{8}$$

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

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 improved due to the quasi-DC discharge plasma.

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 shows good capability as costing a little.

### 2.3. Conclusions

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.

> 

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

Plasma off Plasma on, time A Plasma on, time B Plasma on, time C

� 100% (7)

<sup>ε</sup><sup>i</sup> <sup>¼</sup> <sup>η</sup><sup>i</sup> � <sup>η</sup><sup>b</sup> ηb

 

176 Plasma Science and Technology - Basic Fundamentals and Modern Applications

P0\_outlet /Pa 916,532 882,270 888,143 885,268 ηp<sup>0</sup> 0.83466 0.80346 0.80880 0.80619 ηp0,loss 0.16534 0.19654 0.19120 0.19381

recovery coefficient ηp0 Z, and stagnation pressure loss coefficient in the combustor.

Figure 7. Distribution of the stagnation pressure loss coefficient.

Table 3. The inlet mean stagnation pressure P0\_inlet, outlet mean stagnation pressure P0\_outlet, stagnation pressure

Index of performance Case

P0\_inlet /Pa 1,098,093

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,

Figure 8. Distribution of combustion efficiency downstream of fuel orifice.

resulting in the cross-section shape of the fuel jet varying from a narrow and long profile to a circular profile. Because of the variation of fuel mixing, in the upper space, more water forms while less appears near the wall compared with the case without plasma. (3) The stagnation pressure loss of combustor increases a little as actuator works, but the combustion efficiency in the combustor rises obviously. These above can be summarized as the comprehensive effects of flow structure changes caused by the plasma, including waves induced and heat transfer. Since it is negligible for the relative change of stagnation pressure recovery coefficient in the actuator working cases, and the ratio of deposited plasma energy to the increased combustion heat release is very little, it can be obtained that the quasi-DC discharge plasma can make more benefits than penalties for the scramjet combustor, when proper adopting control parameters of the plasma actuator.

acts as strongly oscillating and bright and looks like an inverted "L" crossing the backward wall of cavity. Since the major heat energy of the quasi-DC discharge plasma focuses on the bright filament domain [10, 25], the filament plasma domain can be established in such a simplified

Plasma-Assisted Combustion

179

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

Just like the way given in case one, every quasi-DC plasma filament is dealt as a volumetric heat source. To represent the plasma heat strength reasonably, the mean temperature of the plasma domain Tpl is specified in this simulation too. Considering the real size of the plasma filament, all the heat source is modeled with a section of dimensions 3 3 mm. the distance between the backward wall and left side of plasma filament upstream of cavity is 6 mm as depicted in Figure 9. While the distance between the backward wall and the right side of plasma filament downstream of cavity is 25.5 mm. Based on the previous research, Tpl = 3000 K is specified as the actuating strength, and five actuators work together in a pulsed mode with plasma actuation frequency F<sup>c</sup> = 5 kHz and duty cycle D = 1/5. In this case, all configurations (e.g., combustor, cavity) and simulation conditions are identical to those used in case one, except for the plasma. Therefore, the numerical methods, including physical models, numeri-

Three representative times are chosen from one plasma cycle, which consists of the later actuator free duration and the actuator working duration, for comparison after computations converged. In the simulation, the duration of one plasma cycle is T<sup>c</sup> = 200 μs. The end of an actuator working duration t = 1/5T<sup>c</sup> , t = 3/5T<sup>c</sup> , and the end of a cycle t = T<sup>c</sup> are named A, B, and C, respectively.

The Mach number distribution of local cavity flowfield on the symmetrical xy plane is shown in Figure 10. A distinct shear layer forms upon the cavity mouth and develops toward the

cal schemes, computational zone, etc., could be found in Section 2.1.

3.2.1. Typical parameters distribution of cavity flowfield

shape as given in Figure 9.

Figure 9. The schematic of plasma filaments in the cavity.

3.2. Results and discussion
