3.2.3. Analysis of pressure oscillation in cavity

In the research fields related to "sound cavity," "embedded magazine" and "flame holding cavity," the dynamic study on pressure oscillation in a cavity is always greatly valued around the world [27]. According to the cavity shear layer distribution, four monitor points are chosen to capture the dynamic pressure feature, as shown in Figure 9. F-1 is located on the front wall of cavity with z = 16 mm (refers to a lateral section of the combustor) and F-2 is located on z = 0 mm (refers to the symmetry section of the combustor), and they are 0.5 mm beneath the front edge. R-1 is located on the rear wall with z = 16 mm and R-2 is with z = 0 mm, and they are 0.71 mm away from the rear edge. To ascertain the intensity of pressure oscillations, the sound pressure level (SPL) is used to present the time averaged pressure fluctuation magnitude, with dB as its unit, which is defined as:

$$L\_{\rm sp} = 20 \log \frac{\overline{p'}}{p\_{\rm ref}} \tag{10}$$

raised due to the plasma filaments, especially for time A and C. The increase of the combustor stagnation pressure loss is caused by several factors, such as the enlargement of separation zones, the rise of back pressure induced by local combustion and the strengthening of shock waves, which is based on the analysis of cavity shear layer and wall pressure distribution.

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Considering the interesting variation of product water distribution as shown in Figure 12, the distribution of combustion efficiency in the flow direction may also vary influenced by the plasma filaments. Hence, the combustion efficiency η<sup>c</sup> is calculated. The distribution of combustion efficiency along x-direction is presented in Figure 14. Usually, the combustion efficiency goes on increasing from time A to time C due to the plasma. It can be seen the combustion efficiency of time A is little lower at most positions, but prominently higher at time B in the upstream of cavity rear wall and time C on the whole compared with the no plasma case. As involved above, the transportation ability of the spanwise reverse vortex pairs are improved by

In a word, the combustion efficiency increases downstream of the front wall of cavity in most of the time due to the plasma. It becomes lower than the no plasma case at several positions for few moments, but the decrease is comparatively small. Furthermore, during one plasma cycle, the combustion efficiency gradually increases from beginning to end, which indicates that the

The ratio of power consumption of the plasma actuator to the increased combustion heat release of the combustor is calculated in value E<sup>f</sup> = 0.0016 to depict the cost to effectiveness of quasi-DC plasma. Therefore, the assistance of plasma to the combustion process presents

The main results are as follows: (1) Because of the "cutting" effect of quasi-DC plasma filaments, the cavity shear layer becomes fluctuating and the local combustion changes which also results

the plasma, so the local combustion efficiency during certain periods increases.

Figure 13. The normalized pressure frequency spectrum, with plasma. (a) R-1. (b) R-2.

plasma performs better during actuator free period for the pulsed actuation mode.

improvements in performance that outweighs the additional cost.

3.3. Conclusions

where p<sup>0</sup> and Pref are the RMS of dynamic pressure and the reference sound pressure, respectively, and here <sup>P</sup>ref is 2 � <sup>10</sup>�<sup>5</sup> Pa.

The SPLs of F-1, F-2, R-1, and R-2 are 168, 193, 188, and 191 dB, respectively. However, at the no plasma case, their SPL values are 120, 118, 124, and 106 dB, respectively. It indicates that the SPL of all the monitor points go up sharply, and the relationship between point location and magnitude of SPL changes prominently. The points are near the mouth of cavity and the effect of plasma filaments on the cavity edges is strongest, so the SPL magnitude increases here. Moreover, through the analysis on cavity drag in Table 4, the conclusion can be obtained that the pressure disturbance on the monitor points is controlled by combustion, and the shear layer strongly affects the change of local combustion.

In Figure 13, the frequency spectrum characteristics of R-1 and R-2 by FFT are depicted. The several dominant frequencies of pressure oscillation are marked with red circles here, which show that the first dominant frequency is almost the double of the plasma actuation frequency 5 kHz. Whereas, it is barely equal to the plasma actuation frequency under nonreaction condition [19]. Furthermore, nearly every dominant frequency is an integer multiple of the plasma actuation frequency. The results above indicate that the pressure oscillation in the cavity is controlled by both local combustion flowfield and the plasma actuation frequency.

#### 3.2.4. Analysis of stagnation pressure loss and combustion efficiency

The combustor stagnation pressure recovery coefficient of time A, B, C, and the no plasma case is 0.75, 0.81, 0.65, and 0.83, respectively. And the calculated time weighted average stagnation pressure recovery coefficient is 0.73. It suggests that the overall stagnation pressure loss is

Figure 13. The normalized pressure frequency spectrum, with plasma. (a) R-1. (b) R-2.

raised due to the plasma filaments, especially for time A and C. The increase of the combustor stagnation pressure loss is caused by several factors, such as the enlargement of separation zones, the rise of back pressure induced by local combustion and the strengthening of shock waves, which is based on the analysis of cavity shear layer and wall pressure distribution.

Considering the interesting variation of product water distribution as shown in Figure 12, the distribution of combustion efficiency in the flow direction may also vary influenced by the plasma filaments. Hence, the combustion efficiency η<sup>c</sup> is calculated. The distribution of combustion efficiency along x-direction is presented in Figure 14. Usually, the combustion efficiency goes on increasing from time A to time C due to the plasma. It can be seen the combustion efficiency of time A is little lower at most positions, but prominently higher at time B in the upstream of cavity rear wall and time C on the whole compared with the no plasma case. As involved above, the transportation ability of the spanwise reverse vortex pairs are improved by the plasma, so the local combustion efficiency during certain periods increases.

In a word, the combustion efficiency increases downstream of the front wall of cavity in most of the time due to the plasma. It becomes lower than the no plasma case at several positions for few moments, but the decrease is comparatively small. Furthermore, during one plasma cycle, the combustion efficiency gradually increases from beginning to end, which indicates that the plasma performs better during actuator free period for the pulsed actuation mode.

The ratio of power consumption of the plasma actuator to the increased combustion heat release of the combustor is calculated in value E<sup>f</sup> = 0.0016 to depict the cost to effectiveness of quasi-DC plasma. Therefore, the assistance of plasma to the combustion process presents improvements in performance that outweighs the additional cost.

#### 3.3. Conclusions

3.2.3. Analysis of pressure oscillation in cavity

Table 5. Calculation results of cavity mass exchange rate, unit: g/s.

184 Plasma Science and Technology - Basic Fundamentals and Modern Applications

tude, with dB as its unit, which is defined as:

layer strongly affects the change of local combustion.

3.2.4. Analysis of stagnation pressure loss and combustion efficiency

tively, and here <sup>P</sup>ref is 2 � <sup>10</sup>�<sup>5</sup> Pa.

In the research fields related to "sound cavity," "embedded magazine" and "flame holding cavity," the dynamic study on pressure oscillation in a cavity is always greatly valued around the world [27]. According to the cavity shear layer distribution, four monitor points are chosen to capture the dynamic pressure feature, as shown in Figure 9. F-1 is located on the front wall of cavity with z = 16 mm (refers to a lateral section of the combustor) and F-2 is located on z = 0 mm (refers to the symmetry section of the combustor), and they are 0.5 mm beneath the front edge. R-1 is located on the rear wall with z = 16 mm and R-2 is with z = 0 mm, and they are 0.71 mm away from the rear edge. To ascertain the intensity of pressure oscillations, the sound pressure level (SPL) is used to present the time averaged pressure fluctuation magni-

m<sup>0</sup> 0.067 0.614 13.013 7.223

No plasma Pulse, A Pulse, B Pulse, C

<sup>L</sup>sp <sup>¼</sup> 20 log <sup>p</sup><sup>0</sup>

where p<sup>0</sup> and Pref are the RMS of dynamic pressure and the reference sound pressure, respec-

The SPLs of F-1, F-2, R-1, and R-2 are 168, 193, 188, and 191 dB, respectively. However, at the no plasma case, their SPL values are 120, 118, 124, and 106 dB, respectively. It indicates that the SPL of all the monitor points go up sharply, and the relationship between point location and magnitude of SPL changes prominently. The points are near the mouth of cavity and the effect of plasma filaments on the cavity edges is strongest, so the SPL magnitude increases here. Moreover, through the analysis on cavity drag in Table 4, the conclusion can be obtained that the pressure disturbance on the monitor points is controlled by combustion, and the shear

In Figure 13, the frequency spectrum characteristics of R-1 and R-2 by FFT are depicted. The several dominant frequencies of pressure oscillation are marked with red circles here, which show that the first dominant frequency is almost the double of the plasma actuation frequency 5 kHz. Whereas, it is barely equal to the plasma actuation frequency under nonreaction condition [19]. Furthermore, nearly every dominant frequency is an integer multiple of the plasma actuation frequency. The results above indicate that the pressure oscillation in the cavity is controlled by both local combustion flowfield and the plasma actuation frequency.

The combustor stagnation pressure recovery coefficient of time A, B, C, and the no plasma case is 0.75, 0.81, 0.65, and 0.83, respectively. And the calculated time weighted average stagnation pressure recovery coefficient is 0.73. It suggests that the overall stagnation pressure loss is

pref

(10)

The main results are as follows: (1) Because of the "cutting" effect of quasi-DC plasma filaments, the cavity shear layer becomes fluctuating and the local combustion changes which also results

Conflict of interest

Author details

References

The authors declared that they have no conflicts of interest to this work.

\*Address all correspondence to: nws1969@126.com; 286982061@qq.com

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Siyin Zhou, Haiqing Wang, Wansheng Nie\* and Xueke Che

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Figure 14. Combustion efficiency along x.

in the variation of wall pressure distribution near the cavity rear edge. On the mass fraction isosurface of product water several "branch pipes" curve structures form periodically, which can be put down to the influence of plasma on the local combustion. (2) The effect of plasma on the cavity drag is relatively perplexing and the drag coefficient value is observed to be unsteady. Nevertheless, the mass exchange rate goes up prominently due to plasma, and the magnitude change from time A to C is in agreement with the fluctuation degree of cavity shear layer. (3) The SPLs of four cavity monitor points rise, and the frequency spectrum of monitor points near the rear edge presents that the first dominant frequency is twice the plasma actuation frequency, under the effect of plasma. Hence, the pressure oscillation in the cavity is controlled by both the plasma and local combustion flowfield. (4) On the one side, the combustion efficiency is usually increased due to plasma, and on the other side, the certain pressure loss increases resulted from the changes of combustion and waves in the flowfield by the plasma. Because the ratio of deposited plasma energy to the increased combustion heat release is extraordinarily small, it is considered that if optimal actuation parameters of the actuator are chosen the quasi-DC plasma can bring more benefits than penalties for the cavity in scramjet combustor.
