4. Results and discussion

#### 4.1. Response of the hypersonic flowfield to freestream pulse wave

#### 4.1.1. Response of the hypersonic flowfield

Before analyzing, it should be pointed out that the numerical simulation method and the grid independence in present work is validated in our previous investigation [21–23], which indicates the numerical method adopted in this paper is reliable. Figure 5 shows the contours of pressure under freestream pulse wave at different times.

Figure 3(a)–(d) in the figure correspond to t = 2.0, 4.0, 6.0 and 8.0, respectively. In Figure 3, when the pulse wave enters the flow field, it first interacts with the bow-shaped shock wave. When it is encountered with the slow acoustic pulse wave, the bow-shaped shock wave is Numerical Study of Hypersonic Boundary Layer Receptivity Characteristics Due to Freestream Pulse Waves http://dx.doi.org/10.5772/intechopen.70660 27

Figure 3. Contours of pressure under freestream pulse wave at different times. (a) t=2.0, (b) ) t=4.0, (c)t=6.0, (d) ) t=8.0.

u 0 v 0 p 0 ρ 0

26 Advances in Some Hypersonic Vehicles Technologies

; <sup>k</sup> = 3.1446 � <sup>10</sup>�<sup>4</sup>

8 >><

>>:

<sup>A</sup> <sup>0</sup> � <sup>A</sup>

4.1. Response of the hypersonic flowfield to freestream pulse wave

pressure under freestream pulse wave at different times.

½ � <sup>0000</sup> <sup>T</sup> ð Þ <sup>t</sup> <sup>&</sup>lt; <sup>0</sup>

½ � <sup>0000</sup> <sup>T</sup> ð Þ <sup>t</sup> <sup>≥</sup> <sup>2</sup>

e i kx�FRe <sup>106</sup> <sup>t</sup>þ<sup>π</sup> 2 � �

ð Þ 0 ≤ t < 2

(11)

<sup>M</sup><sup>∞</sup> � AM<sup>∞</sup>

Where u', v', P<sup>0</sup> and ρ' indicate the velocity disturbance along x direction, the velocity disturbance along y direction, the pressure disturbance and the density disturbance, respectively; A indicates the amplitude, F indicates the generalized frequency, t indicates time. Here,

Before analyzing, it should be pointed out that the numerical simulation method and the grid independence in present work is validated in our previous investigation [21–23], which indicates the numerical method adopted in this paper is reliable. Figure 5 shows the contours of

Figure 3(a)–(d) in the figure correspond to t = 2.0, 4.0, 6.0 and 8.0, respectively. In Figure 3, when the pulse wave enters the flow field, it first interacts with the bow-shaped shock wave. When it is encountered with the slow acoustic pulse wave, the bow-shaped shock wave is

h i<sup>T</sup>

; F = 50π; Ma∞ = 6.

4. Results and discussion

4.1.1. Response of the hypersonic flowfield

<sup>A</sup> = 8 � <sup>10</sup>�<sup>2</sup>

Figure 2. Mesh grid.

deformed and protruded outward, and the surrounding pressure is also significantly affected. Due to the deformation of the shock wave, the pressure of outward convex region near shock wave is significantly increased, and the flowfield pressure below the bow shock wave is greatly reduced. That is to say, from Figure 3(a)–(d), it shows that the freestream disturbance waves significantly interact with the bow-shaped shock waves, which greatly changes the shock standoff distance and the distribution of flowfield pressure in the active region.

Figure 4 shows the contours of density under freestream pulse wave at different times. Figure 4(a)–(f) correspond to t = 0.0, 2.0, 4.0, 6.0, 8.0 and 10.0, respectively. Figure 5 shows the contours of temperature under freestream pulse wave at different times. Figure 5(a)–(f) correspond to t = 0.0, 2.0, 4.0, 6.0, 8.0 and 10.0, respectively. As can be seen from Figure 4, the pulse wave disturbance has a great impact on the density. The density of the flowfield changes significantly under the action of freestream pulse wave, especially in the disturbance area between the pulse wave and the bow-shaped shock wave, where the density of the region is significantly smaller. Compared with the significant changes of flowfield density around the shock wave, the pulse wave has much smaller effect on the density in the boundary layer. Meanwhile, the closer to the nasal area, the greater the density changes and the effects are after the action of pulse wave. Obviously, this is because the closer the bowshaped shock wave is to the nose area, the stronger the action is. Therefore, it can be concluded that the stronger the intensity of the shock wave is, the more intense the effect of the pulse slow acoustic wave and the bow-shaped shock wave are. As can be seen from

Figure 4. Contours of density under freestream pulse wave at different times. (a) t=0.0, (b) t=4.0, (c) t=6.0, (d) t=8.0.

Figure 5, the effect of disturbances on the temperature is pretty significant, which similar to the density. Under the action of impulse disturbances, a strip area exists in the hypersonic flowfield temperature disturbances between the boundary layer and the shock wave, which is similar to the change trend of the flowfield density's disturbances. What is worth noting is that from the upstream to the downstream, the strip area becomes longer; this is due to the fact that through the shock wave, the disturbance wave slows down. The farther it is away from the wall, the greater the flow velocity is, which leads to the disturbance wave's different spread velocity to the downstream. It also can be seen from Figure 5 that the temperature in the boundary layer is much more significantly affected by the pulse wave compared with the temperature change of the flowfield near the shock wave. That is to say, the freestream pulse wave's influence on the thermodynamic state in boundary layer is significantly greater than that on the thermodynamic state the outside boundary layer. It is known that the temperature is a characteristic parameter of the thermodynamic properties in the boundary layer. Obviously, the freestream pulse disturbance wave changes the thermal mechanism of the strong shear flow in the boundary layer, while the thermodynamic mechanism is considered to have an important effect on the stability of the boundary layer [24], so it is reasonable to believe that the pulse slow acoustic wave in freestream plays a considerable role in the stability of hypersonic boundary layer.

layer and shock wave, and the flowfield in the boundary layer change greatly. On the other hand, the velocity disturbance modes out of the boundary layer and the velocity disturbance modes near the boundary layer differ significantly. From Figure 6, there are many obvious disturbance characteristic regions in the hypersonic boundary layer under the action of freestream pulse disturbances. It can also be seen that the boundary layer's disturbance velocity is very large, which shows that there is complex interference in the boundary layer under the action of the pulse wave. It is worth mentioning that, after the disturbance wave interfering with the bow-shaped shock wave, and entering into the flowfield, a part of the

Figure 5. Contours of temperature under freestream pulse wave at different times. (a) t=0.0, (b) t=2.0, (c) t=4.0, (d) t=6.0,

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(e) t=8.0, (f) t=10.0.

Figure 6 shows the contours of velocity along axis y under freestream pulse wave at different times. From Figure 6, under the action of the pulse slow acoustic wave, the velocity in the interference area between pulse wave and shock wave, the flowfield between the boundary Numerical Study of Hypersonic Boundary Layer Receptivity Characteristics Due to Freestream Pulse Waves http://dx.doi.org/10.5772/intechopen.70660 29

Figure 5, the effect of disturbances on the temperature is pretty significant, which similar to the density. Under the action of impulse disturbances, a strip area exists in the hypersonic flowfield temperature disturbances between the boundary layer and the shock wave, which is similar to the change trend of the flowfield density's disturbances. What is worth noting is that from the upstream to the downstream, the strip area becomes longer; this is due to the fact that through the shock wave, the disturbance wave slows down. The farther it is away from the wall, the greater the flow velocity is, which leads to the disturbance wave's different spread velocity to the downstream. It also can be seen from Figure 5 that the temperature in the boundary layer is much more significantly affected by the pulse wave compared with the temperature change of the flowfield near the shock wave. That is to say, the freestream pulse wave's influence on the thermodynamic state in boundary layer is significantly greater than that on the thermodynamic state the outside boundary layer. It is known that the temperature is a characteristic parameter of the thermodynamic properties in the boundary layer. Obviously, the freestream pulse disturbance wave changes the thermal mechanism of the strong shear flow in the boundary layer, while the thermodynamic mechanism is considered to have an important effect on the stability of the boundary layer [24], so it is reasonable to believe that the pulse slow acoustic wave in freestream plays a considerable role in the

Figure 4. Contours of density under freestream pulse wave at different times. (a) t=0.0, (b) t=4.0, (c) t=6.0, (d) t=8.0.

Figure 6 shows the contours of velocity along axis y under freestream pulse wave at different times. From Figure 6, under the action of the pulse slow acoustic wave, the velocity in the interference area between pulse wave and shock wave, the flowfield between the boundary

stability of hypersonic boundary layer.

28 Advances in Some Hypersonic Vehicles Technologies

Figure 5. Contours of temperature under freestream pulse wave at different times. (a) t=0.0, (b) t=2.0, (c) t=4.0, (d) t=6.0, (e) t=8.0, (f) t=10.0.

layer and shock wave, and the flowfield in the boundary layer change greatly. On the other hand, the velocity disturbance modes out of the boundary layer and the velocity disturbance modes near the boundary layer differ significantly. From Figure 6, there are many obvious disturbance characteristic regions in the hypersonic boundary layer under the action of freestream pulse disturbances. It can also be seen that the boundary layer's disturbance velocity is very large, which shows that there is complex interference in the boundary layer under the action of the pulse wave. It is worth mentioning that, after the disturbance wave interfering with the bow-shaped shock wave, and entering into the flowfield, a part of the

Figure 6. Contours of velocity along axis y under freestream pulse wave at different times. (a)t=0.0, (b)t=4.0, (c)t=8.0, (d)t=10.0.

density, temperature and pressure disturbances on wall are similar to that of friction factor. Zhang et al. [19] studied the evolution of continuous small disturbance in hypersonic flow using direct numerical simulation (DNS), and found that, because of the normal shock wave, the forcing disturbance in freestream is enlarged. From Figure 8, it is obtained that the

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Figure 8. Comparison of the density, temperature and pressure disturbances on wall at different times (t<sup>1</sup> = 1.0,t<sup>2</sup> = 6.0, t<sup>3</sup> = 9.0).

Figure 7. Distribution of friction factor disturbance on wall under freestream pulse wave at different times.

wave will propagate from the upstream to the downstream of the flowfield and a part of the reflected wave will oscillate between the shock wave and the wall [24]. Moreover, the velocity disturbance mode in the boundary layer becomes more complicated on account of reflected waves. As shown in Figure 6(c) and (d), the disturbance characteristic regions marked with arrows are induced by the reflected waves in the flowfield.

#### 4.1.2. Response of the boundary layer

Figure 7 shows the distribution of friction factor disturbance on wall under freestream pulse wave at different times (t = 2.0, 4.0, 6.0, 8.0, 10.0). It can be seen from the figure that, when the pulse wave disturbance is through some place of the wall, the friction factor reduces at first, and after reaching a minimum value, it increases. When the pulse disturbance completely passes this point, the disturbance effect on this position is not over, and it will go through a number of processes in oscillating changes like getting bigger-smaller-bigger-smaller, until the change magnitude decreases to zero. It is clear that this oscillating decreasing phenomenon is caused by the reciprocating reflected waves between the wall and the bow shock. Most importantly, the friction factor is an important parameter for characterizing the shear flow, which indicates that the strong shear flow structure in the boundary layer under freestream pulse wave has changed.

Figure 8 shows the comparisons of the density, temperature and pressure disturbances on wall at different times. Figure 8 indicates that, under freestream pulse wave, the variations of the

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Figure 7. Distribution of friction factor disturbance on wall under freestream pulse wave at different times.

wave will propagate from the upstream to the downstream of the flowfield and a part of the reflected wave will oscillate between the shock wave and the wall [24]. Moreover, the velocity disturbance mode in the boundary layer becomes more complicated on account of reflected waves. As shown in Figure 6(c) and (d), the disturbance characteristic regions marked with

Figure 6. Contours of velocity along axis y under freestream pulse wave at different times. (a)t=0.0, (b)t=4.0, (c)t=8.0, (d)t=10.0.

Figure 7 shows the distribution of friction factor disturbance on wall under freestream pulse wave at different times (t = 2.0, 4.0, 6.0, 8.0, 10.0). It can be seen from the figure that, when the pulse wave disturbance is through some place of the wall, the friction factor reduces at first, and after reaching a minimum value, it increases. When the pulse disturbance completely passes this point, the disturbance effect on this position is not over, and it will go through a number of processes in oscillating changes like getting bigger-smaller-bigger-smaller, until the change magnitude decreases to zero. It is clear that this oscillating decreasing phenomenon is caused by the reciprocating reflected waves between the wall and the bow shock. Most importantly, the friction factor is an important parameter for characterizing the shear flow, which indicates that the strong shear flow structure in the boundary layer under freestream

Figure 8 shows the comparisons of the density, temperature and pressure disturbances on wall at different times. Figure 8 indicates that, under freestream pulse wave, the variations of the

arrows are induced by the reflected waves in the flowfield.

4.1.2. Response of the boundary layer

30 Advances in Some Hypersonic Vehicles Technologies

pulse wave has changed.

density, temperature and pressure disturbances on wall are similar to that of friction factor. Zhang et al. [19] studied the evolution of continuous small disturbance in hypersonic flow using direct numerical simulation (DNS), and found that, because of the normal shock wave, the forcing disturbance in freestream is enlarged. From Figure 8, it is obtained that the

Figure 8. Comparison of the density, temperature and pressure disturbances on wall at different times (t<sup>1</sup> = 1.0,t<sup>2</sup> = 6.0, t<sup>3</sup> = 9.0).

amplitude of parameters disturbance on the wall is enlarged sharply relative to that of initial wave in freestream. The numerical results agree with Li's results. It also shows that the disturbance amplitudes of pressure on the nose of blunt wedge are larger than that on nonnose, and the former are several times, even more than 10 times, larger than the latter; while the discrepancy is tiny for temperature and density.

boundary layer disturbance. Furthermore, the signals are expanded in frequency order to make it as a frequency function, thereby converting the time domain signal of the pressure disturbance into a frequency domain signal. Figure 10 shows the results of the Fourier frequency spectral analysis of pressure disturbance in boundary layer under freestream pulse wave at different locations. Figure 10(a)–(d) are the results of the Fourier frequency spectral analysis when x = 0.83566, x = 1.2196, x = 3.3050 and x = 5.3846, respectively. It can be seen from Figure 10(a) that, at the location of x = 0.83566, namely the nose area, the main disturbance modes in the boundary layer are distributed near f = 0.25, indicating that near the fundamental frequency, the disturbance mode component of other frequencies is relatively small, which is consistent with the results obtained by Zhang et al. [19] in studying continuous waves. It also shows that the higher the disturbance mode's frequency is, the smaller its component ratio will be. Based on Figure 10(b), at the position of x = 1.2196, the disturbance mode component ratio near the fundamental frequency decreases rapidly, the high frequency disturbance harmonic mode like the second order harmonic frequency and above significantly increase. And the main disturbance modes in the boundary layer are distributed near f = 0.5, that is near the second order harmonic frequency. The main

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Figure 10. Fourier frequency spectral analysis of pressure disturbance in boundary layer under freestream pulse wave at

different locations. (a) x=0.83566, (b)x=1.2196, (c) x=3.3050, (d) x=5.3846.

To study the evolution of the disturbance wave in boundary layer during the interaction process, the temperature disturbance on wall along the streamwise is considered. Figure 9 shows the distribution of temperature disturbance on wall along the streamwise at t = 8.6. As discussed earlier, it has been verified that the disturbance amplitude of aerothermodynamics parameters will undergo a damped oscillation during the interaction process although there is just a half sinusoidal pulse wave in freestream. Figure 9 indicates that the distance between crests as well as trough of disturbance variables changed markedly during the damped oscillation process. The distances a1-a2, a2-a3, b1-b2 and b2-b3 along the x-axis direction equal to 1.733, 2.939, 1.541 and 1.491, respectively. Hence, it is obvious that the damped oscillation is aperiodic. In other word, the waves with other frequencies are induced due to the interaction between freestream blast wave and bow shock wave as well as boundary layer. It should be noted that the evolution of the wave's modes in the blunt wedge boundary layer exerts an important impact on both boundary layer stability characteristic and laminar-turbulent transition [10, 25]. There is little research focused on the evolution of the wave's modes in the boundary layer under freestream pulse wave, and the evolution characteristic remains unclear although a host of in-depth researches is done in the evolution of the wave's modes in boundary layer under freestream continuous small disturbances in recent years.

To analyze the disturbance mode distribution in the hypersonic boundary layer and its evolution characteristics along the streamwise under the action of freestream pulse wave, the fast Fourier transformation method is used to decode the time domain signal of the

Figure 9. Temperature disturbance profile along streamwise at t = 8.6.

boundary layer disturbance. Furthermore, the signals are expanded in frequency order to make it as a frequency function, thereby converting the time domain signal of the pressure disturbance into a frequency domain signal. Figure 10 shows the results of the Fourier frequency spectral analysis of pressure disturbance in boundary layer under freestream pulse wave at different locations. Figure 10(a)–(d) are the results of the Fourier frequency spectral analysis when x = 0.83566, x = 1.2196, x = 3.3050 and x = 5.3846, respectively. It can be seen from Figure 10(a) that, at the location of x = 0.83566, namely the nose area, the main disturbance modes in the boundary layer are distributed near f = 0.25, indicating that near the fundamental frequency, the disturbance mode component of other frequencies is relatively small, which is consistent with the results obtained by Zhang et al. [19] in studying continuous waves. It also shows that the higher the disturbance mode's frequency is, the smaller its component ratio will be. Based on Figure 10(b), at the position of x = 1.2196, the disturbance mode component ratio near the fundamental frequency decreases rapidly, the high frequency disturbance harmonic mode like the second order harmonic frequency and above significantly increase. And the main disturbance modes in the boundary layer are distributed near f = 0.5, that is near the second order harmonic frequency. The main

amplitude of parameters disturbance on the wall is enlarged sharply relative to that of initial wave in freestream. The numerical results agree with Li's results. It also shows that the disturbance amplitudes of pressure on the nose of blunt wedge are larger than that on nonnose, and the former are several times, even more than 10 times, larger than the latter; while

To study the evolution of the disturbance wave in boundary layer during the interaction process, the temperature disturbance on wall along the streamwise is considered. Figure 9 shows the distribution of temperature disturbance on wall along the streamwise at t = 8.6. As discussed earlier, it has been verified that the disturbance amplitude of aerothermodynamics parameters will undergo a damped oscillation during the interaction process although there is just a half sinusoidal pulse wave in freestream. Figure 9 indicates that the distance between crests as well as trough of disturbance variables changed markedly during the damped oscillation process. The distances a1-a2, a2-a3, b1-b2 and b2-b3 along the x-axis direction equal to 1.733, 2.939, 1.541 and 1.491, respectively. Hence, it is obvious that the damped oscillation is aperiodic. In other word, the waves with other frequencies are induced due to the interaction between freestream blast wave and bow shock wave as well as boundary layer. It should be noted that the evolution of the wave's modes in the blunt wedge boundary layer exerts an important impact on both boundary layer stability characteristic and laminar-turbulent transition [10, 25]. There is little research focused on the evolution of the wave's modes in the boundary layer under freestream pulse wave, and the evolution characteristic remains unclear although a host of in-depth researches is done in the evolution of the wave's modes in boundary layer under freestream continuous small disturbances in

To analyze the disturbance mode distribution in the hypersonic boundary layer and its evolution characteristics along the streamwise under the action of freestream pulse wave, the fast Fourier transformation method is used to decode the time domain signal of the

the discrepancy is tiny for temperature and density.

32 Advances in Some Hypersonic Vehicles Technologies

Figure 9. Temperature disturbance profile along streamwise at t = 8.6.

recent years.

Figure 10. Fourier frequency spectral analysis of pressure disturbance in boundary layer under freestream pulse wave at different locations. (a) x=0.83566, (b)x=1.2196, (c) x=3.3050, (d) x=5.3846.

disturbance modes in the boundary layer migrate from the fundamental frequency to the second order harmonic frequency. In Figure 10(c), it can be seen that at the position of x = 3.3050, the disturbance mode components in the vicinity of the fundamental frequency are further reduced, and the proportion of disturbance mode components is further increased. The main disturbance modes in the boundary layer are distributed at f = 0.5–0.75, namely near the second and third order harmonic frequency. The main disturbance modes in the boundary layer are transformed from the dominant state of the second order harmonic frequency to the collective leadership state of the second order harmonic frequency and the third order harmonic frequency. According to Figure 10(d), at the position of x = 5.3846, the distribution of the boundary layer disturbance modes is similar to that at x = 3.3050. The main disturbance modes in the boundary layer are distributed near the second and third order harmonic frequency, but the frequency band of the boundary layer disturbance mode is significantly narrowed.

Figure 11 shows the evolution of different disturbance modes along streamwise in boundary layer. Figure 11(a)–(f) are the evolution of the fundamental frequency mode, the second order harmonic frequency, the third order harmonic frequency, the fourth order harmonic frequency, the fifth order harmonic frequency and the sixth order harmonic frequency, respectively. From Figure 11(a), in the nose region, the amplitude of the fundamental frequency becomes smaller. When out of the nose region, the amplitude of the fundamental frequency gradually becomes smaller and generally remains. In Figure 11(b), it can be seen that in the nose region, the amplitude of the second order harmonic frequency mode significantly becomes smaller. Out of the nose region, the amplitude of the second order harmonic frequency mode continues to increase. From Figure 11(c), it can be seen that the amplitude of the third order harmonic frequency mode becomes smaller in the nose region, and the third order harmonic frequency mode first increases and then decreases in the downstream evolution. From Figure 11(d)–(f), it shows that the evolution of the fourth order harmonic frequency mode, the fifth order harmonic frequency mode and the sixth order harmonic frequency mode along the streamwise is similar to that of the third order harmonic frequency mode. As shown in the figure, whether it is the fundamental mode or harmonic modes, in the area of the nose boundary layer, the amplitude of the disturbance significantly becomes smaller, indicating that the intensity of the bow shock in the hypersonic flowfield becomes weak, and it has significant effects on both the fundamental mode and the harmonic modes in each order. According to the figure, it also shows that except for the fundamental mode, from the nose area to the non-nose area, the amplitude of each harmonic frequency mode all increase significantly. It is believed that this phenomenon is caused by the recompression of the flowfield, which means in this region, the effect of the shock wave intensity on the harmonic frequency modes of the boundary layer is smaller than the recompression effect, and the effect of the shock wave intensity on the fundamental mode of the boundary layer is larger than the recompression effect.

#### 4.2. Effects of pulse wave type

In this section, to discuss the effects of the pulse wave types on the generation and evolution of the disturbance mode in the hypersonic boundary layer, the numerical simulations of hypersonic flowfield under the action of freestream pulse fast acoustic wave, slow acoustic wave and entropy wave were conducted. It should be noted that the wall temperature T<sup>w</sup> = 200 K, and the

Figure 11. Evolution of different disturbance modes along streamwise in boundary layer. (a) P1, (b) P2, (c) P3, (d) P4, (e) P5,

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forms of pulse fast acoustic wave and entropy wave is no longer listed in this section. Due to the fact that the wall of shear force is decided by the friction factor on wall directly which is a key

. The other computational condition is consistent with Section 4. The

amplitude <sup>A</sup> = 6 <sup>10</sup><sup>2</sup>

(f) P6.

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disturbance modes in the boundary layer migrate from the fundamental frequency to the second order harmonic frequency. In Figure 10(c), it can be seen that at the position of x = 3.3050, the disturbance mode components in the vicinity of the fundamental frequency are further reduced, and the proportion of disturbance mode components is further increased. The main disturbance modes in the boundary layer are distributed at f = 0.5–0.75, namely near the second and third order harmonic frequency. The main disturbance modes in the boundary layer are transformed from the dominant state of the second order harmonic frequency to the collective leadership state of the second order harmonic frequency and the third order harmonic frequency. According to Figure 10(d), at the position of x = 5.3846, the distribution of the boundary layer disturbance modes is similar to that at x = 3.3050. The main disturbance modes in the boundary layer are distributed near the second and third order harmonic frequency, but the frequency band of the boundary layer disturbance mode

Figure 11 shows the evolution of different disturbance modes along streamwise in boundary layer. Figure 11(a)–(f) are the evolution of the fundamental frequency mode, the second order harmonic frequency, the third order harmonic frequency, the fourth order harmonic frequency, the fifth order harmonic frequency and the sixth order harmonic frequency, respectively. From Figure 11(a), in the nose region, the amplitude of the fundamental frequency becomes smaller. When out of the nose region, the amplitude of the fundamental frequency gradually becomes smaller and generally remains. In Figure 11(b), it can be seen that in the nose region, the amplitude of the second order harmonic frequency mode significantly becomes smaller. Out of the nose region, the amplitude of the second order harmonic frequency mode continues to increase. From Figure 11(c), it can be seen that the amplitude of the third order harmonic frequency mode becomes smaller in the nose region, and the third order harmonic frequency mode first increases and then decreases in the downstream evolution. From Figure 11(d)–(f), it shows that the evolution of the fourth order harmonic frequency mode, the fifth order harmonic frequency mode and the sixth order harmonic frequency mode along the streamwise is similar to that of the third order harmonic frequency mode. As shown in the figure, whether it is the fundamental mode or harmonic modes, in the area of the nose boundary layer, the amplitude of the disturbance significantly becomes smaller, indicating that the intensity of the bow shock in the hypersonic flowfield becomes weak, and it has significant effects on both the fundamental mode and the harmonic modes in each order. According to the figure, it also shows that except for the fundamental mode, from the nose area to the non-nose area, the amplitude of each harmonic frequency mode all increase significantly. It is believed that this phenomenon is caused by the recompression of the flowfield, which means in this region, the effect of the shock wave intensity on the harmonic frequency modes of the boundary layer is smaller than the recompression effect, and the effect of the shock wave intensity on the fundamental mode of the

In this section, to discuss the effects of the pulse wave types on the generation and evolution of the disturbance mode in the hypersonic boundary layer, the numerical simulations of hypersonic flowfield under the action of freestream pulse fast acoustic wave, slow acoustic wave and

is significantly narrowed.

34 Advances in Some Hypersonic Vehicles Technologies

boundary layer is larger than the recompression effect.

4.2. Effects of pulse wave type

Figure 11. Evolution of different disturbance modes along streamwise in boundary layer. (a) P1, (b) P2, (c) P3, (d) P4, (e) P5, (f) P6.

entropy wave were conducted. It should be noted that the wall temperature T<sup>w</sup> = 200 K, and the amplitude <sup>A</sup> = 6 <sup>10</sup><sup>2</sup> . The other computational condition is consistent with Section 4. The forms of pulse fast acoustic wave and entropy wave is no longer listed in this section. Due to the fact that the wall of shear force is decided by the friction factor on wall directly which is a key parameters for representing the strong shear structure in boundary layer, the stability of the hypersonic boundary layer is the study of the stability of the strong shear structure. Figure 12 shows the distribution of friction factor disturbance on wall under different freestream pulse waves at t = 6. From Figure 12, it is obtained that, under freestream pulse waves, the mainstream disturbance wave influence on the wall friction coefficient under the pulse slow acoustic wave is opposite to that under pulse fast acoustic wave and entropy wave. There is significant difference between the disturbance amplitude of the wall friction coefficient under pulse fast acoustic wave and that under entropy wave. It also can be seen that there is a significant difference in the friction factor disturbance on wall caused by the reflected wave for these three cases, and the reflected wave has a significant effect on the friction factor. In general, different types of freestream pulse waves have different effects on the friction factor on wall, which indicates the interaction between the strong shear structure of boundary layer and different types of freestream pulse waves have different mechanisms of action. That is, the strong shear structure of boundary layer under the action of different types of freestream pulse waves reveals different stability characteristics.

Figure 13 shows the pressure disturbance in boundary layer under different freestream pulse waves. Figure 13(a) and (b) are corresponding the position s = 0.92619 and 5.90498, respectively. From Figure 13, it can be seen that the pressure disturbance in boundary layer under the action of different types of freestream pulse waves appear different changes in the time domain.

effects of different types of freestream pulse waves are significant on the distribution of modes in boundary layer and the evolution of disturbance modes along with the streamwise. From the figure, it is obtained that, s = 0.92619, the Fourier frequency spectral curve of pressure disturbance in boundary layer under different freestream pulse waves shows similar trend. Namely, the max amplitude of the disturbance modes in boundary layer are distributed near f = 0.25, and four main disturbance clusters (near f = 0.25, 1.0, 1.5 and 2.0) exist in the hypersonic boundary layer both for all cases. With evolution of disturbance waves in boundary layer along with the streamwise, at s = 3.83551, four main disturbance clusters still exist in the hypersonic boundary layer both for fast acoustic wave and entropy wave. However, the distribution of the four main disturbance clusters changes sharply, which indicates there is movement of main disturbance clusters in the boundary layer. It also can be seen that, at s = 3.83551, there is only one main disturbance cluster (near f = 0.5) in the hypersonic boundary layer for slow acoustic wave, and the other main modes have a remarkable decline. It is obtained that, at s = 8.02802, the number of main disturbance mode clusters in the boundary layer both for fast acoustic wave and entropy wave decreases

Figure 14. Fourier frequency spectral analysis of pressure disturbance in boundary layer under different freestream pulse

waves. (a) s = 0.92619, (b) s = 3.83551, (c) s = 8.02802.

Figure 13. Pressure disturbance in boundary layer under different freestream pulse waves. (a) s=0.92619, (b) s=5.90498.

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The Fourier frequency spectral analysis of pressure disturbance in boundary layer under different freestream pulse waves is shown in Figure 14. Figure 14(a)–(c) are corresponding the position s = 0.92619, s = 3.83551 and s = 8.02802, respectively. Figure 14 shows that the

Figure 12. Distribution of friction factor disturbance on wall under different freestream pulse waves at t = 6 s.

Numerical Study of Hypersonic Boundary Layer Receptivity Characteristics Due to Freestream Pulse Waves http://dx.doi.org/10.5772/intechopen.70660 37

parameters for representing the strong shear structure in boundary layer, the stability of the hypersonic boundary layer is the study of the stability of the strong shear structure. Figure 12 shows the distribution of friction factor disturbance on wall under different freestream pulse waves at t = 6. From Figure 12, it is obtained that, under freestream pulse waves, the mainstream disturbance wave influence on the wall friction coefficient under the pulse slow acoustic wave is opposite to that under pulse fast acoustic wave and entropy wave. There is significant difference between the disturbance amplitude of the wall friction coefficient under pulse fast acoustic wave and that under entropy wave. It also can be seen that there is a significant difference in the friction factor disturbance on wall caused by the reflected wave for these three cases, and the reflected wave has a significant effect on the friction factor. In general, different types of freestream pulse waves have different effects on the friction factor on wall, which indicates the interaction between the strong shear structure of boundary layer and different types of freestream pulse waves have different mechanisms of action. That is, the strong shear structure of boundary layer under the action of different types of freestream pulse waves reveals different

Figure 13 shows the pressure disturbance in boundary layer under different freestream pulse waves. Figure 13(a) and (b) are corresponding the position s = 0.92619 and 5.90498, respectively. From Figure 13, it can be seen that the pressure disturbance in boundary layer under the action of different types of freestream pulse waves appear different changes in the time domain.

The Fourier frequency spectral analysis of pressure disturbance in boundary layer under different freestream pulse waves is shown in Figure 14. Figure 14(a)–(c) are corresponding the position s = 0.92619, s = 3.83551 and s = 8.02802, respectively. Figure 14 shows that the

Figure 12. Distribution of friction factor disturbance on wall under different freestream pulse waves at t = 6 s.

stability characteristics.

36 Advances in Some Hypersonic Vehicles Technologies

Figure 13. Pressure disturbance in boundary layer under different freestream pulse waves. (a) s=0.92619, (b) s=5.90498.

effects of different types of freestream pulse waves are significant on the distribution of modes in boundary layer and the evolution of disturbance modes along with the streamwise. From the figure, it is obtained that, s = 0.92619, the Fourier frequency spectral curve of pressure disturbance in boundary layer under different freestream pulse waves shows similar trend. Namely, the max amplitude of the disturbance modes in boundary layer are distributed near f = 0.25, and four main disturbance clusters (near f = 0.25, 1.0, 1.5 and 2.0) exist in the hypersonic boundary layer both for all cases. With evolution of disturbance waves in boundary layer along with the streamwise, at s = 3.83551, four main disturbance clusters still exist in the hypersonic boundary layer both for fast acoustic wave and entropy wave. However, the distribution of the four main disturbance clusters changes sharply, which indicates there is movement of main disturbance clusters in the boundary layer. It also can be seen that, at s = 3.83551, there is only one main disturbance cluster (near f = 0.5) in the hypersonic boundary layer for slow acoustic wave, and the other main modes have a remarkable decline. It is obtained that, at s = 8.02802, the number of main disturbance mode clusters in the boundary layer both for fast acoustic wave and entropy wave decreases

Figure 14. Fourier frequency spectral analysis of pressure disturbance in boundary layer under different freestream pulse waves. (a) s = 0.92619, (b) s = 3.83551, (c) s = 8.02802.

sharply. In general, the narrowing of frequency band and the decreasing of main disturbance mode clusters exist in the boundary layer both for all cases.

Author details

\*, Juan Yu<sup>2</sup>

, Tianli Hui<sup>1</sup>

1 Beijing Spacecrafts, China Academy of Space Technology, Beijing, China

2 China Center for Information Industry Development, Beijing, China

opposing jet in hypersonic flow. AIAA Paper. 2002;2002:646

pean Journal of Mechanics - B/Fluids. 2002;21:325-340

suction. AIAA Journal. 2011;49(7):1336-1353

Computational Fluid Dynamics. 2006;20(1):41-54

Aeronautics and Astronautics, Miami, Florida; Reston, VA: 2007

ing jet. Memoirs of the Faculty of Engineering. 2006;66(1):39-54

over a parabola. Journal of Fluid Mechanics. 2001;441:315-367

free-stream acoustic waves. Journal of Fluid Mechanics. 2006;556:55-103

bances. Theoretical and Computational Fluid Dynamics. 2002;15:231-254

tions in hypersonic boundary layers. AIAA Journal. 2011;49(3):463-471

\*Address all correspondence to: tangxiaojun2214@163.com

, Fenglong Yang<sup>1</sup> and Wentao Yu1

Numerical Study of Hypersonic Boundary Layer Receptivity Characteristics Due to Freestream Pulse Waves

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Xiaojun Tang<sup>1</sup>

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