Investigation of Thrust Augmentation and Acoustic Performance by Ejectors on PDE

2.1 Ejector hardware

As depicted in Figure 2, three typical ejectors are used during testing: straight ejector, divergent ejector and convergent ejector, named for their exhaust section shapes. All ejectors have the same rounded inlet diameter of 132 mm and the same ejector diameter of 280 mm which is defined as the diameter of the straight section. The lengths of the ejectors are varied by extending the straight sections, respectively. The divergent ejector sections have a 4 half-angle of divergence at a fixed length of 200 mm. The convergence ejector sections have the same half-angle and fixed length. The axial position × is the distance from the PDE tube exit plane to the ejector inlet plane. A positive axial position value means the ejector inlet being placed downstream of the PDE exit. For a negative value, the ejector is mounted upstream of the detonation tube exit.

Figure 2:

Diagram of the ejector geometry.

2.2 Evaluation parameters

The amount of PDE thrust augmentation produced by the use of an ejector is defined as follows:

where CDATA[$TEjector is the time-averaged thrust generated by the PDE with ejector, and CDATA[$TPDE is the baseline time-averaged thrust of the system with no ejector installed.

The detonation acoustic of PDE with an ejector is quantified through PSPL and OASPL, shown as follows:

where CDATA[$p0 is the reference noise pressure with value of 20 × 10⁻⁶ Pa and T is 132 ms. (The PDE cycle is 132 ms at the condition of 1 for fill fraction.)

3.1 Baseline testing of pulse detonation engine

The baseline testing is carried out in the 1,900 mm length PDE detonation tube (80 mm diameter) without an ejector. Figure 3 shows the thrust time traces and detonation noise pressure time traces at 0° direction in 3,000 mm during PDE running at the condition of 1 for fill fraction. A time-averaged thrust value of 94.28 N is measured at the PDE cycle. First, the fast rising edge that appeared in detonation noise pressure time traces represented the arrival of shock wave noise, as shown in Figure 3(b). The peak of first fast rising edge P_Impact is 8.53 kPa which is called impact noise. A series of rising edges P_JetN appeared 0.95 ms after, because vortexes which are caused by jet are formed there.

Figure 3:

Thrust time traces and detonation noise pressure time traces in the baseline PDE running. (a) Thrust time traces in the baseline testing. (b) Detonation noise pressure time traces at 0° direction in 3,000 mm.

The corresponding PSPL and OASPL values under different directivity angles are listed in Table 1 in the baseline PDE running. The maximal PSPL is obtained at 30° direction, which is 175.06 dB. It is noteworthy that the OASPL is the minimum at 30° direction, which is 148.18 dB.

3.2 Effect of ejector length on PDE performance

The effect of ejector length on PDE performance is investigated at a fixed ejector axial position, x/D_PDE = 0. The lengths of ejectors could be varied by changing the length of the straight sections as depicted in Figure 1, resulting in an increase in L_Ejector/D_Ejector from 1.18 to 4 during the experiment. As shown in Figure 4(a), the thrust augmentation generally increases with an increase in L_Ejector/D_Ejector for all ejectors, while an inflection in the curve appears which is located at the L_Ejector/D_Ejector of 2.61. The reason is that primary exhaust flow cannot entrain enough secondary flow when the ejector is too short. An extension in ejector length would lead to a fast increase in additional secondary flow, but the effect would not be obvious when the ejector is long enough.

Figure 4:

Effect of ejector length on thrust augmentation and detonation noise. (a) Effect of ejector length on thrust augmentation. (b) Effect of ejector length on PSPL. (c) Effect of ejector length on OASPL.

The effect of L_Ejector/D_Ejector on detonation acoustic features, PSPL and OASPL, continues to be a matter of great interest in PDE performance research, as shown in Figure 4(b) and (c). It can be seen that the extension in divergent ejector length exhibits an increase in PSPL at both 0° and 30°. The amplification effect is most prominent for the L_Ejector/D_Ejector of 4 at 0°, where an amplification of 4.37 dB is achieved. The multiple reflections would contribute to the intensity enhancement in the peak of detonation wave. However, the wave radial propagation at 60° may be refrained by ejector configuration, resulting in a reduction in PSPL with increasing ejector length. The maximum reduction is up to 2.63 dB at L_Ejector/D_Ejector of 4. Reductions in OASPL with increasing L_Ejector/D_Ejector are observed in the experiment for all the directions, shown in Figure 4(c). The maximum reduction, about 3.12 dB, appears with the longest divergent ejector (L_Ejector/D_Ejector = 4) at 60°. It can be seen that reductions in OASPL would not be obvious when the ejector is long enough. Based on sound attenuation and thrust augmentation, it can make a conclusion that the optimum L_Ejector/D_Ejector is 2.61 in this portion of study.

Figure 5 shows the effect of detonation noise pressure time traces with ejector at 60° and 30°. It can be observed that P_JetN which is caused by turbulence is restrained at 60° and 30° for PDE testing with ejector. These may be probably due to the decelerating effect from secondary flow by divergent ejector on detonation exhaust of high temperature. It is one reason for reductions in OASPL at 30° and 60°. As shown in Figure 6(b), a phenomenon worthy to be pointed out is that P_Jet1 is delayed at 30°. It is the other reason for reductions in OASPL at 30° and 0°.

Figure 5:

Contrast diagram of detonation noise pressure time traces. (a) Contrast diagram of detonation noise pressure time traces at 60 degree. (b) Contrast diagram of detonation noise pressure time traces at 30°.

3.3 Effect of ejector shape on PDE performance

There are three kinds of ejectors (straight, divergent and convergent ejectors) tested in this portion of study. All ejectors are mounted at an axial position of x/D_PDE = 0. As shown in Figure 4(a), it indicates that the best thrust augmentation curve is obtained for a divergent ejector at all L_Ejector/D_Ejector. Figure 6(a) shows the contrast diagram of thrust time traces at L_Ejector/D_Ejector of 2.61. Installing ejectors exhibits a reduction in the peak of thrust time traces but augmentation in the duration of thrust time traces. The maximum thrust durations is achieved for a divergent ejector. It is due to this that the diverging section appears to be that of a subsonic diffuser, reducing static pressure on divergent ejector [16], increasing secondary flow rate and thrust duration. The phenomenon of blocking caused by convergent ejector leads to the secondary flow rate and thrust duration declines.

Figure 6:

Effect of ejector shape on thrust augmentation and detonation noise. (a) Contrast diagram of thrust time traces. (b) Effect of ejector shape on PSPL. (c) Effect of ejector shape on OASPL.

The effect of ejector shape on PSPL is shown in Figure 6(b). One trend that can be observed clearly is that all of the ejectors exhibit a reduction in the PSPL at 60° but amplification at 0° and 30°. The most prominent amplification is obtained for straight ejector at 0°, where an amplification of 2.94 dB is achieved. The best reduction is obtained at 60°, where a reduction of 1.77 dB is achieved for convergent ejector.

The reduction in OASPL caused by the different ejectors is shown in Figure 6(c). It can be seen that OASPL is reduced at all angles with all ejectors. The reduction effect is most prominent at 0°, where a reduction of 3.45 dB is achieved for the convergent ejector. This behavior can be attributed to the weakest oscillation of detonation noise pressure of convergent ejector, as shown in Figure 7. The phenomenon of blocking caused by convergent ejector leads to the secondary flow rate declines. The turbulence causes oscillations of detonation noise pressure, and the deceleration of jet speed results in restrained oscillations.

Figure 7:

Contrast diagram of detonation noise pressure time traces at 0°.

3.4 Effect of ejector axial position on PDE performance

Previous work has shown that PDE performance is sensitive to the ejector axial position relative to the PDE exit [15, 16], and maximum thrust augmentation occurred with divergent ejector. Here, the effect of axial position is investigated in an installed divergent ejector with L_Ejector/D_Ejector of 2.61. A detailed mapping of PDE performance as a function of axial position is obtained and shown in Figure 8(a). The increase in thrust augmentation is obvious with the increasing x/D_PDE from −3 to 2, due to the improvement in the secondary flow restriction from limited flow area. The maximum thrust augmentation is at x/D_PDE = 2 for the divergent ejector by an augmentation of 50.15%. Obviously, this is the very critical position where the PDE performance is the best. With further movement downstream, the velocity of the primary exhaust flow suffered a serious deceleration when ejector inlet is too far away from the tube exit so the primary exhaust flow does not have enough power to entrain the secondary flow, resulting in a reduction in thrust augmentation when x/D_PDE is more than 2.

Figure 8:

Effect of axial position on thrust augmentation and detonation noise. (a) Effect of axial position on thrust augmentation. (b) Effect of axial position on PSPL. (c) Effect of axial position on OASPL.

The effect of axial position on detonation noise on PSPL is shown in Figure 8(b). For both 0° and 30°, PSPL increases at first and then decreases with increasing the axial position L_Ejector/D_Ejector from −3 to 3. Results indicate that PSPL reaches its maximum of 1.89 dB and 2.89 dB at L_Ejector/D_Ejector of 0. PSPL at 60° is decreasing with increased axial position, resulting in the highest reduction of 2.35 dB in experiments.

Generally, divergent ejector is helpful for reducing the OASPL during PDE running. The OASPL exhibits good agreement in changing trend for experimental curves at all directions, as shown in Figure 8(c). The maximum reduction appears at the x/D_PDE of 0, and movement of ejector downstream or upstream further would increase the OASPL obviously. The maximum reduction values are 2.09 dB at 0°, 6.01 dB at 30° and 5.74 dB at 60°. The time between P_Impact and P_Jet1 is increased when x/D_PDE is away from 0, as shown in Figure 9. This behavior can be attributed to the phenomenon that the secondary flow is accelerated when ejector position is away from PDE exit.

Figure 9:

Contrast diagram of detonation noise pressure time traces at different axial position.

Since previous work has shown that x/D_PDE = 2, L_Ejector/D_Ejector = 2.61 and divergent ejector provided the best performance, propagation of PDE detonation noise with those factors is analyzed in this portion of the study. The investigation of detonation noise characteristic is carried out in the range from 1,000 mm to 3,000 mm at three different angles. The divergent ejector affects PSPL change and OASPL change at 0° as shown in Figure 10. Baseline detonation noise amplitude is mapped as a function of radial distance. It is found that P_Peak and P_RMS rapidly decrease with radial distance. With increased distance, the decay rate of P_Peak and P_RMS slows down. As shown in Figure 10, the divergent ejector shows significant influence on PSPL and OASPL. It can be observed that for ejector, amplification is obtained at short distance, but reduction at long distance. The decay rate of P_Peak and P_RMS for the divergent ejector is faster than baseline.

Figure 10:

Effect of detonation noise with divergent ejector in different r. (a) P_Peak in different r. (b) P_RMS in different r.