**2. Improvement of supersonic aerodynamics using repetitive nano‐second laser pulses**

In the aspect of the supersonic aerodynamic performance, shock wave formation leads inevita‐ bly to serious problems preventing the development of high‐performance supersonic vehicle. A representative problem is sonic boom which is an impulsive noise induced by a supersonic aircraft. Wave drag force induced by shock wave is another serious problem against improve‐ mentoftheaerodynamicperformance.Thisstudyconsidersfurthertechnologytoreduceawave drag force. Wave drag reduction over a 20‐mm‐dia. cylinder with a truncated cone nose in a Mach 1.94 flow is done by depositing laser pulse energies atrepetition frequencies up to 80 kHz and average input power of 400 W at a maximum. In actual application of energy deposition scheme [1‐8] to reduce the drag, it should be taken into account both a drag coefficient and efficiency of energy deposition. The purpose of this chapteris to investigate the impacts of nose shape on supersonic drag reduction performance with repetitive energy depositions.

## **2.1. Trade‐off in truncated cone shape**

Figure 1 indicates why truncated cone shape is important to apply energy deposition scheme. In order to realize the energy depositions for improvement of drag reduction, two conditions should be satisfied. The first condition is that the magnitude of a drag force or a drag coefficient

© 2013 Sasoh; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Sasoh; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

has a lower value than the one of a baseline value, for example obtained by a conical body. Another condition is to obtain a large value of an 'efficiency of energy deposition'[1](or'power gain'), which is defined by the ratio of a saved propulsion power to a power deposited into the flow. As shown in Figure 1, with a flat‐faced cylinder body, a decrement in drag is largest although its baseline drag is largest. Without energy deposition, a conical nose leads to a smallest drag, yet the efficiency of energy deposition is worst. By truncating the cone, this tradeoff problem can be solved. Although the drag reduction performance with truncated cone model is weaker, it is easily accomplished the target drag force because its base drag force has smaller value compared to blunt body. In this case, the effective time, for which the effect of the energy deposition on a blunt body lasts, is a key parameter to know what shape of a body is suitable for obtaining a lower drag.

ed cone model decreasing, the efficiency of energy deposition is higher as the front face area is increased. A quasi‐steady state flowfield over truncated conical geometry is established with the higher repetitive frequency of pulse energy, typically higher than 50 kHz. In the quasi‐steady state flowfield, recirculation zone composed of several vortices makes a virtual

Aerospace Application 273

spike in front of the truncated cone body.

**Figure 2.** Schematic and photographs of experimental apparatus.

Sakai [8] reported that the effective time is evaluated during the interaction of the low density core created by a single laser pulse using an Nd:YAG laser with the bow shock wave over a blunt body. The evaluated effective time on a flat‐faced cylinderis longerthan on a hemisphere under the same energy deposition condition. The longer effective time for the flat‐faced cylinder is due to the fact that the recirculation zone with vortices, which are produced due to baroclinic interaction, keeps for longer time in the forebody region. This behavior results in the reduction of the drag for a longer period. He also presented that the modulated drag for the flat‐faced cylinder is nearly the same with that for the hemisphere and that the drag value is higher than that for a sharp cone with the same base diameter. It should be noted that the efficiencies for the flat‐faced cylinder are typically higher than for the hemisphere under the same energy deposition condition. Thus, it is believed that a flat‐faced geometry has a potential advantage to be used in the drag reduction with energy deposition.

**Figure 1.** Trade-off in truncated cone model for improving the drag reduction performance.

Sakai [9] then proposed to employ a truncated cone and estimated its drag reduction per‐ formance using computational fluid dynamics method with Euler equations. In accordance with his results, while the magnitude of drag force is reduced with front face area of truncat‐

ed cone model decreasing, the efficiency of energy deposition is higher as the front face area is increased. A quasi‐steady state flowfield over truncated conical geometry is established with the higher repetitive frequency of pulse energy, typically higher than 50 kHz. In the quasi‐steady state flowfield, recirculation zone composed of several vortices makes a virtual spike in front of the truncated cone body.

has a lower value than the one of a baseline value, for example obtained by a conical body. Another condition is to obtain a large value of an 'efficiency of energy deposition'[1](or'power gain'), which is defined by the ratio of a saved propulsion power to a power deposited into the flow. As shown in Figure 1, with a flat‐faced cylinder body, a decrement in drag is largest although its baseline drag is largest. Without energy deposition, a conical nose leads to a smallest drag, yet the efficiency of energy deposition is worst. By truncating the cone, this tradeoff problem can be solved. Although the drag reduction performance with truncated cone model is weaker, it is easily accomplished the target drag force because its base drag force has smaller value compared to blunt body. In this case, the effective time, for which the effect of the energy deposition on a blunt body lasts, is a key parameter to know what shape of a body

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Sakai [8] reported that the effective time is evaluated during the interaction of the low density core created by a single laser pulse using an Nd:YAG laser with the bow shock wave over a blunt body. The evaluated effective time on a flat‐faced cylinderis longerthan on a hemisphere under the same energy deposition condition. The longer effective time for the flat‐faced cylinder is due to the fact that the recirculation zone with vortices, which are produced due to baroclinic interaction, keeps for longer time in the forebody region. This behavior results in the reduction of the drag for a longer period. He also presented that the modulated drag for the flat‐faced cylinder is nearly the same with that for the hemisphere and that the drag value is higher than that for a sharp cone with the same base diameter. It should be noted that the efficiencies for the flat‐faced cylinder are typically higher than for the hemisphere under the same energy deposition condition. Thus, it is believed that a flat‐faced geometry has a potential

advantage to be used in the drag reduction with energy deposition.

**Figure 1.** Trade-off in truncated cone model for improving the drag reduction performance.

Sakai [9] then proposed to employ a truncated cone and estimated its drag reduction per‐ formance using computational fluid dynamics method with Euler equations. In accordance with his results, while the magnitude of drag force is reduced with front face area of truncat‐

is suitable for obtaining a lower drag.

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**Figure 2.** Schematic and photographs of experimental apparatus.

The data acquisition system is shown in Figure 5.

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**Figure 4.** Drag measurement system and example of calibration.

**Figure 3.** Schematic of laser optics system

#### **2.2. Apparatus**

Overall experimental apparatus is the same as of used in Ref. 6. The experimental facility comprises of a supersonic wind tunnel, laser optic system and diagnostic system. While the supersonic wind tunnel is operating, measurement system of stagnation pressure, drag force and visualization system is operated. Figure 2 shows the schematic and photographs of apparatus including the supersonic wind tunnel. Window diameterfor visualization is 90mm. Drag reduction performance with constant pulse energy is estimated as a function of laser frequency. Nd:YVO4 is used only to deposit the repetitive pulse energy. In our laser optic system (Figure 3), laser frequency can be applied up to 50 kHz under allowable pulse energy, *E*, is 7.2 mJ. Laser pulses up to 8 kHz is deposited with *E*=5.0 mJ.

The drag force is measured by using force balance system introduced in Ref. 5 (Figure 4). The flowfiled overthe model is visualized via schlieren system including two 300‐mm‐dia. concave mirrors and a circular knife edge. In a single run of the wind tunnel one hundred frames of schlieren images are captured into a high‐speed framing camera (Shimadzu HPV‐1) with a framing interval of 4 μs, 1/4 of which is an exposure period. To measure the time‐dependent stagnation pressure, a piezoelectric pressure transducer (H112A21, PCB Inc., rise time of 1 μs, sensitivity of 7.015mV/Pa) is flush‐mounted at head of the model.

The data acquisition system is shown in Figure 5.

f = -30 mm f = 60 mm

*E*, is 7.2 mJ. Laser pulses up to 8 kHz is deposited with *E*=5.0 mJ.

sensitivity of 7.015mV/Pa) is flush‐mounted at head of the model.

Laser

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**2.2. Apparatus**

**Figure 3.** Schematic of laser optics system

45° Mirror

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45° Mirror

Overall experimental apparatus is the same as of used in Ref. 6. The experimental facility comprises of a supersonic wind tunnel, laser optic system and diagnostic system. While the supersonic wind tunnel is operating, measurement system of stagnation pressure, drag force and visualization system is operated. Figure 2 shows the schematic and photographs of apparatus including the supersonic wind tunnel. Window diameterfor visualization is 90mm. Drag reduction performance with constant pulse energy is estimated as a function of laser frequency. Nd:YVO4 is used only to deposit the repetitive pulse energy. In our laser optic system (Figure 3), laser frequency can be applied up to 50 kHz under allowable pulse energy,

The drag force is measured by using force balance system introduced in Ref. 5 (Figure 4). The flowfiled overthe model is visualized via schlieren system including two 300‐mm‐dia. concave mirrors and a circular knife edge. In a single run of the wind tunnel one hundred frames of schlieren images are captured into a high‐speed framing camera (Shimadzu HPV‐1) with a framing interval of 4 μs, 1/4 of which is an exposure period. To measure the time‐dependent stagnation pressure, a piezoelectric pressure transducer (H112A21, PCB Inc., rise time of 1 μs,

f = 60 mm

15mm

BK-7 window

Wind tunnel wall

focus

**Figure 4.** Drag measurement system and example of calibration.

*d*<sup>f</sup> *d*

*d*<sup>f</sup> */ d =* 1.0

*d*<sup>f</sup> */ d =* 0.75

*d*<sup>f</sup> */ d =* 0.5

*d*<sup>f</sup> */ d =* 0

**df/ d E [mJ] f [kHz] Shape of front face**

Flat face

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Concave face

**Figure 6.** Truncated cone models for improving the drag reduction performance.

1.0 5.0 10 ~ 80

0.75 5.0 10 ~ 80 0.75 7.2 10 ~ 50 0.5 5.0 10 ~ 80 0.5 7.2 10 ~ 50 0 5.0 10 ~ 80 0 7.2 10 ~ 50 0.5 5.0 10 ~ 80

0.5 7.2 10 ~ 50 0.5 5.0 10 ~ 80 0.5 7.2 10 ~ 50

**Table 1.** Experimental conditions.

2.25*d*

#### **2.3. Drag reduction performance of flat‐faced truncated cone model**

First, the drag reduction performance with flat‐faced truncated conical body is investigated. Figures 6 shows the schematic illustration of truncated cone models used in the experiments. The base diameter of body, *d*, is 20 mm. The front face diameter is defined as *d*<sup>f</sup> . The diameter ratio, *d*<sup>f</sup> /*d,* is varied from 1.0 (cylinder model) to 0(cone model) with half apex angle of 15 degree. The stagnation pressure is measured only on 3‐types (*d*<sup>f</sup> / *d*=1.0, 0.75 and 0.5) flat‐faced truncated con model, because diameter of pressure transducer, 5.56 mm, is comparable to the nose dimension.

**Figure 6.** Truncated cone models for improving the drag reduction performance.


**Table 1.** Experimental conditions.

Oscilloscope 1

**Figure 5.** Data acquisition system.

ratio, *d*<sup>f</sup>

nose dimension.

HPV-1 High Speed Camera Flash ramp

Pressure transducer 1

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Laser

Oscilloscope 2 generator

First, the drag reduction performance with flat‐faced truncated conical body is investigated. Figures 6 shows the schematic illustration of truncated cone models used in the experiments.

degree. The stagnation pressure is measured only on 3‐types (*d*<sup>f</sup> / *d*=1.0, 0.75 and 0.5) flat‐faced truncated con model, because diameter of pressure transducer, 5.56 mm, is comparable to the

/*d,* is varied from 1.0 (cylinder model) to 0(cone model) with half apex angle of 15

Pressure transducer 2

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

Sub-chamber Vacuum

pump

Amplifier

**2.3. Drag reduction performance of flat‐faced truncated cone model**

The base diameter of body, *d*, is 20 mm. The front face diameter is defined as *d*<sup>f</sup>

Signal conditoner

Delay generator

Function

. The diameter

> The effective residence time of vortex ring [10, 11] can be seen from stagnation pressure histories in Figure 9.With *d*<sup>f</sup> / *d* = 1.0, pulse‐to‐pulse interaction is significant at*f*=10 kHz. Hence, stagnation pressure history shows the almost quasi‐steady state behavior. However, stagna‐ tion pressure decrement caused by vortex ring can be found for *d*<sup>f</sup> / *d* = 0.75. In the case of *d*<sup>f</sup> / *d* = 0.5, stagnation pressure is almostrecovered into the former state, and then affected by blast wave. Even if pulse‐to‐pulse interaction is somewhat occurred, the effect on stagnation

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Figure 10 shows examples of the time variation of the drag. Figures 11 and 12 show the drag reduction performance of flat‐faced truncated cone model as a function of *f*. When the pulse energy of 5.0 mJ is deposited, drag force almost linearly reduces with *f*. For *d*<sup>f</sup> / *d*=1.0, *∆D*/*D*<sup>0</sup> is obtained up to 21%, and the efficiency of energy deposition is nearly constant value of about 7. Under the same condition, amount of drag reduction and efficiency of energy deposition are decreased with decreasing of *d*<sup>f</sup> / *d*. With *E*=5.0mJ, propulsion energy saving is not realized

(a) *d*f / *d* = 1.0 (b) *d*f / *d* = 0.75

(c) *d*f / *d* = 0.5 (d) *d*f / *d* = 0.0

**Figure 8.** Instantaneous schlieren images at f= 80kHz, E=5.0mJ.

pressure is very weak.

if *d*<sup>f</sup> / *d* is smaller than 0.5.

**Figure 7.** Shock layer without laser pulses.

Experimental conditions are shown in Table 1. Drag reduction performance with constant pulse energy is estimated as a function of laser frequency. In our laser optic system, laser frequency can be applied up to 50 kHz under allowable pulse energy, *E*, is 7.2 mJ. On the other hand, laser pulses up to 80 kHz is deposited with *E*=5.0 mJ.

For the absence of laser pulses, the shock layer over the truncated cone model is compared with a different *d*<sup>f</sup> / *d* value in Figure 7. Although all of shock layer have bow shock shape except for the case of the conical model(*d*<sup>f</sup> / *d* = 0.0), those shock stand‐off distances are decreased with decreasing front face area; shock stand‐off distance is 0.45 *d* for *d*<sup>f</sup> / *d* = 1.0, 0.31*d* for *d*<sup>f</sup> / *d* = 0.75 and 0.25*d* for *d*<sup>f</sup> / *d* = 0.5.

Figures 8 presents schlieren images with laser pulse energy depositions (*f*=80 kHz, *E*=5.0 mJ). With energy depositions, the effective apex angle of distorted shock layer becomes smaller with *d*<sup>f</sup> /*d* increasing. In particular, shock layer shape of *d*<sup>f</sup> / *d*=1.0 is similar to oblique shock. As the residence time of vortex rings is longer, the virtual spike composed of several vortices becomes more sharply. For the *d*<sup>f</sup> / *d*=0.0, the baroclinical vortex ring is not observed because laser‐heated gas interacts with attached oblique shock wave.

The effective residence time of vortex ring [10, 11] can be seen from stagnation pressure histories in Figure 9.With *d*<sup>f</sup> / *d* = 1.0, pulse‐to‐pulse interaction is significant at*f*=10 kHz. Hence, stagnation pressure history shows the almost quasi‐steady state behavior. However, stagna‐ tion pressure decrement caused by vortex ring can be found for *d*<sup>f</sup> / *d* = 0.75. In the case of *d*<sup>f</sup> / *d* = 0.5, stagnation pressure is almostrecovered into the former state, and then affected by blast wave. Even if pulse‐to‐pulse interaction is somewhat occurred, the effect on stagnation pressure is very weak.

Figure 10 shows examples of the time variation of the drag. Figures 11 and 12 show the drag reduction performance of flat‐faced truncated cone model as a function of *f*. When the pulse energy of 5.0 mJ is deposited, drag force almost linearly reduces with *f*. For *d*<sup>f</sup> / *d*=1.0, *∆D*/*D*<sup>0</sup> is obtained up to 21%, and the efficiency of energy deposition is nearly constant value of about 7. Under the same condition, amount of drag reduction and efficiency of energy deposition are decreased with decreasing of *d*<sup>f</sup> / *d*. With *E*=5.0mJ, propulsion energy saving is not realized if *d*<sup>f</sup> / *d* is smaller than 0.5.

**Figure 8.** Instantaneous schlieren images at f= 80kHz, E=5.0mJ.

(a) *d*<sup>f</sup> /*d* =1.0 (b) *d*<sup>f</sup> /*d* =0.75

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(c) *d*<sup>f</sup> /*d* =0.5 (d) *d*<sup>f</sup> /*d* =0

Experimental conditions are shown in Table 1. Drag reduction performance with constant pulse energy is estimated as a function of laser frequency. In our laser optic system, laser frequency can be applied up to 50 kHz under allowable pulse energy, *E*, is 7.2 mJ. On the other

For the absence of laser pulses, the shock layer over the truncated cone model is compared with a different *d*<sup>f</sup> / *d* value in Figure 7. Although all of shock layer have bow shock shape except for the case of the conical model(*d*<sup>f</sup> / *d* = 0.0), those shock stand‐off distances are decreased with decreasing front face area; shock stand‐off distance is 0.45 *d* for *d*<sup>f</sup> / *d* = 1.0,

Figures 8 presents schlieren images with laser pulse energy depositions (*f*=80 kHz, *E*=5.0 mJ). With energy depositions, the effective apex angle of distorted shock layer becomes smaller

/*d* increasing. In particular, shock layer shape of *d*<sup>f</sup> / *d*=1.0 is similar to oblique shock. As the residence time of vortex rings is longer, the virtual spike composed of several vortices becomes more sharply. For the *d*<sup>f</sup> / *d*=0.0, the baroclinical vortex ring is not observed because

**Figure 7.** Shock layer without laser pulses.

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hand, laser pulses up to 80 kHz is deposited with *E*=5.0 mJ.

laser‐heated gas interacts with attached oblique shock wave.

0.31*d* for *d*<sup>f</sup> / *d* = 0.75 and 0.25*d* for *d*<sup>f</sup> / *d* = 0.5.

with *d*<sup>f</sup>


0 20 40 60 80 100 *f* [ kHz ]

Laser irradiation

50kHz

*E=*5.0mJ *d*<sup>f</sup> / *d* = 0.0 *d*<sup>f</sup> / *d* = 0.5 *d*<sup>f</sup> / *d* = 0.75 *d*<sup>f</sup> / *d* = 1.0

10kHz 25kHz

Nd:YLF Laser (E=6.6 mJ ) Nd:YVO4 Laser (E=6.2mJ)

> *f* = 1kHz 2kHz 4kHz

Aerospace Application 281

0.7

0

**Figure 11.** Efficiency of energy deposition of flat-faced truncated cone model, E=5.0mJ/pulse.

2

4

6

8

10

0.8

0.9

6kHz 8kHz

*D*

**Figure 10.** Example of drag variation

*/*

*D*0 1.0

1.1

**Figure 9.** Stagnation pressure histories, f=10kHz, E=5.0mJ.

**Figure 10.** Example of drag variation

(a)*d*<sup>f</sup> /*d* =1.0

Micro-Nano Mechatronics — New Trends in Material, Measurement, Control, Manufacturing and Their Applications in

*t*

100 s

100 s

100 s

0.8

0.8

1.1

0.8

**Figure 9.** Stagnation pressure histories, f=10kHz, E=5.0mJ.

0.9

*p*st */*

*p*st,0 1.0

0.9

*p*st */*

*p*st,0 1.0

1.1

0.9

*p*st */*

*p*st,0

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1.0

1.1

(b)*d*<sup>f</sup> /*d* =0.75

*t*

(c)*d*<sup>f</sup> /*d* =0.5

*t*

**Figure 11.** Efficiency of energy deposition of flat-faced truncated cone model, E=5.0mJ/pulse.

**Figure 12.** Variation of drag coefficient with df/d, E=5.0mJ/pulse.

The drag coefficient, *C*D, is plotted against *f* in Figure 12. As repetitive laser frequency is increased, the drag coefficient is decreased. Without energy depositions, drag coefficient of *d*<sup>f</sup> / *d*=1.0 is 1.8. Although the drag coefficient of *d*<sup>f</sup> / *d*=1.0 is decreased down to 1.46 with *f*=80 kHz and *E*=5.0 mJ, that is still higher than the base drag(=0.55) of conical model(*d*<sup>f</sup> / *d*=0.0).

0 20 40 60 80 100 *f* [ kHz ]

From the above results, it was concluded that drag reduction performance of truncated cone become poor since the effective residence time of vortices become shorter with *d*<sup>f</sup> / *d* decreasing. Therefore, concave‐faced truncated cone shape is considered to improve the drag reduction performance of truncated cone in this section. Truncated cone model with *d*<sup>f</sup> / *d*=0.5 is used,

Figure 14 presents the effect of concave radius curvature on the drag reduction performance. It is interesting that *∆D*/*D*<sup>0</sup> with concave‐faced truncated cone becomes higher comparing with flat‐faced truncated cone. *∆D*/*D*<sup>0</sup> is increased with *R*/*d*=1.0 for *E*=5.0mJ and *f*=80 kHz. As shown in Figure 10, the efficiency of energy deposition is slightly enhanced with concave‐faced truncated cone. This implies that concave‐faced truncated cone is useful to improve the drag reduction performance. From these results, it is confirmed that drag coefficient of concave‐ faced truncated cone is slightly decreased. In the case of *R*/*d*=0.5, drag reduction performance is almost same with one of *R*/*d*=1.0. However, drag coefficient of *R*/*d*=0.5 becomes higher than

Although a blunt body shape brings the better drag reduction performance due to energy depositions, a truncated cone shape has considerable advantage to satisfy the necessary

that of *R*/*d*=1.0 because small radius curvature leads to increase of base drag force.

0

**2.5. Summary of this chapter**

1

2

3

*E=*5.0mJ, *d*<sup>f</sup> / *d* = 0.5

Concave face (*R/d*=1.0) Concave face (*R/d*=0.5) Aerospace Application 283

Flat face

**Figure 14.** Power gain of concave-faced truncated cone model, df/d=0.50, E=5.0mJ/pulse.

and radius curvature (*R/d*) of concave face is varied from 0.5 to 1.0.

#### **2.4. Drag reduction performance of concave‐faced truncated cone model**

In order to improve the drag reduction performance, experimental studies are conducted on concave‐faced truncated cone models with *d*<sup>f</sup> / *d* = 0.5 as seen in Figure 13. The radius curvatures of front face are *R*/*d*= 0.5 and 1.0, respectively. All of truncated cone models have same length, and location of depositing pulse energy is 2*d* ahead of the model.

**Figure 13.** Schematic diagram of concave-faced truncated cone model with df/d = 0.5.

**Figure 14.** Power gain of concave-faced truncated cone model, df/d=0.50, E=5.0mJ/pulse.

From the above results, it was concluded that drag reduction performance of truncated cone become poor since the effective residence time of vortices become shorter with *d*<sup>f</sup> / *d* decreasing. Therefore, concave‐faced truncated cone shape is considered to improve the drag reduction performance of truncated cone in this section. Truncated cone model with *d*<sup>f</sup> / *d*=0.5 is used, and radius curvature (*R/d*) of concave face is varied from 0.5 to 1.0.

Figure 14 presents the effect of concave radius curvature on the drag reduction performance. It is interesting that *∆D*/*D*<sup>0</sup> with concave‐faced truncated cone becomes higher comparing with flat‐faced truncated cone. *∆D*/*D*<sup>0</sup> is increased with *R*/*d*=1.0 for *E*=5.0mJ and *f*=80 kHz. As shown in Figure 10, the efficiency of energy deposition is slightly enhanced with concave‐faced truncated cone. This implies that concave‐faced truncated cone is useful to improve the drag reduction performance. From these results, it is confirmed that drag coefficient of concave‐ faced truncated cone is slightly decreased. In the case of *R*/*d*=0.5, drag reduction performance is almost same with one of *R*/*d*=1.0. However, drag coefficient of *R*/*d*=0.5 becomes higher than that of *R*/*d*=1.0 because small radius curvature leads to increase of base drag force.

#### **2.5. Summary of this chapter**

0 20 40 60 80 100 *f* [ kHz ]

The drag coefficient, *C*D, is plotted against *f* in Figure 12. As repetitive laser frequency is increased, the drag coefficient is decreased. Without energy depositions, drag coefficient of *d*<sup>f</sup> / *d*=1.0 is 1.8. Although the drag coefficient of *d*<sup>f</sup> / *d*=1.0 is decreased down to 1.46 with *f*=80 kHz

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In order to improve the drag reduction performance, experimental studies are conducted on concave‐faced truncated cone models with *d*<sup>f</sup> / *d* = 0.5 as seen in Figure 13. The radius curvatures of front face are *R*/*d*= 0.5 and 1.0, respectively. All of truncated cone models have same length,

*d*<sup>f</sup> */ d =* 0.5

*d*<sup>f</sup> */ d =* 0.5

and *E*=5.0 mJ, that is still higher than the base drag(=0.55) of conical model(*d*<sup>f</sup> / *d*=0.0).

**2.4. Drag reduction performance of concave‐faced truncated cone model**

and location of depositing pulse energy is 2*d* ahead of the model.

*R* / *d* = 0.5

*R* / *d* = 1.0

**Figure 13.** Schematic diagram of concave-faced truncated cone model with df/d = 0.5.

*d*<sup>f</sup> / *d* =1.0

*E*=5.0mJ

0.75

0.50

0.0

0.0

**Figure 12.** Variation of drag coefficient with df/d, E=5.0mJ/pulse.

0.5

1.0

*C*D 1.5

2.0

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Although a blunt body shape brings the better drag reduction performance due to energy depositions, a truncated cone shape has considerable advantage to satisfy the necessary conditions in actual application of energy deposition scheme; the magnitude of drag force should be lower than the base drag force of a sharp conical body and the efficiency of energy depositions should be higher than unity. From these demands, drag reduction performance over truncated cone model was experimentally estimated.

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In the experiments, a truncated cone model with half angle of 15 degree is used. The diameter ratio of flat‐faced truncated cone is varied from 1.0 to 0.0. From the presentresults on flat‐faced truncated cone, the effective residence time of vortices resulted by laser‐heated gases interac‐ tion with shock wave plays an importantrole in drag reduction performance of truncated cone model. In order to improve the drag reduction performance of the truncated cones, the drag reduction performance of a concave‐faced truncated cone model is evaluated. In the concave‐ faced truncated cone experiments, the radius curvature of concave face is varied from 0.5 to 1.0 with diameterratio of 0.5. From the comparison with flat‐faced truncated cone,the concave‐ faced truncated cone has more effective drag reduction performance.
