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Temporal and spatial evolution characteristics of disturbance wave in a hypersonic boundary layer due to single-frequency entropy disturbance.

Wang Z, Tang X, Lv H, Shi J - ScientificWorldJournal (2014)

Bottom Line: Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer.The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer.The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

View Article: PubMed Central - PubMed

Affiliation: College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China.

ABSTRACT
By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

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Frequency spectrum analysis of pressure disturbance at different locations in the period phase.
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Related In: Results  -  Collection


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fig8: Frequency spectrum analysis of pressure disturbance at different locations in the period phase.

Mentions: Figure 8 shows the Fourier frequency spectrum analysis of pressure disturbance at different surface locations in the period phase. It can be found that, both in the nose boundary and in the no-nose boundary layer, the Fourier amplitude of the fundamental mode is significantly larger than that of the other modes in the period phase; the fundamental mode is the dominant mode in the boundary layer. Similar to the case in the response phase, the Fourier amplitude of pressure disturbance in the nose boundary layer is considerably larger than that in the no-nose boundary layer in period phase. In the nose boundary layer, the fundamental mode is the only main disturbance mode since the Fourier amplitude of the other modes is very tiny and the effect of the other modes can be neglected. With the disturbance evolving from the upstream to the downstream, the high frequency components increase quickly and the amplitude of the fundamental mode is restrained to grow. It should be mentioned that the high frequency components are mainly distributed near harmonic frequency modes (fn, n is integer), as the mark A1 shown in Figure 8, and the Fourier amplitudes of the other high frequency modes are still tiny, as the mark A2 shown in Figure 8. It can be clearly observed that the proportion of the modes in the range from f2 to f10 appear different levels of increases when s from 0.63566 to 1.97001. When s = 4.84436, the proportion of the modes of f2–10 declines along streamwise rapidly, and the frequency range narrows. When s = 8.39659, the main disturbance modes in the boundary layer are mainly distributed near the fundamental mode and the modes in the range from f2 to f5 and the other modes are basically filtered out. This implies that (1) the disturbance waves within a certain frequency range will be generated in the transition region between the nose and no-nose boundary layer under the interaction between freestream disturbance and shock wave as well as boundary layer. (2) With the disturbance evolving from the upstream to the downstream, most of disturbance waves in the boundary layer decrease, and only special frequency ranges (f1–f5) of unstable wave exist in the downstream boundary layer, indicating mode competition exists during the disturbance wave evolution along streamwise in the boundary layer. By comparing Figure 7 with Figure 8, it can be seen that the frequency spectrum of pressure disturbance in the period phase is remarkably different from that in the response phase. The frequency range of main disturbance modes in the boundary layer in the response phase ranges from 0 to f4; while the main disturbance modes in the boundary layer are fundamental modes and the amplitudes of harmonic frequency are small in the period phase. This indicates that mode competition exists during the process of changing from response phase into period phase. In the process, the mode competition makes the fundamental mode sharply increases and the other modes slowly increase or are suppressed.


Temporal and spatial evolution characteristics of disturbance wave in a hypersonic boundary layer due to single-frequency entropy disturbance.

Wang Z, Tang X, Lv H, Shi J - ScientificWorldJournal (2014)

Frequency spectrum analysis of pressure disturbance at different locations in the period phase.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4109134&req=5

fig8: Frequency spectrum analysis of pressure disturbance at different locations in the period phase.
Mentions: Figure 8 shows the Fourier frequency spectrum analysis of pressure disturbance at different surface locations in the period phase. It can be found that, both in the nose boundary and in the no-nose boundary layer, the Fourier amplitude of the fundamental mode is significantly larger than that of the other modes in the period phase; the fundamental mode is the dominant mode in the boundary layer. Similar to the case in the response phase, the Fourier amplitude of pressure disturbance in the nose boundary layer is considerably larger than that in the no-nose boundary layer in period phase. In the nose boundary layer, the fundamental mode is the only main disturbance mode since the Fourier amplitude of the other modes is very tiny and the effect of the other modes can be neglected. With the disturbance evolving from the upstream to the downstream, the high frequency components increase quickly and the amplitude of the fundamental mode is restrained to grow. It should be mentioned that the high frequency components are mainly distributed near harmonic frequency modes (fn, n is integer), as the mark A1 shown in Figure 8, and the Fourier amplitudes of the other high frequency modes are still tiny, as the mark A2 shown in Figure 8. It can be clearly observed that the proportion of the modes in the range from f2 to f10 appear different levels of increases when s from 0.63566 to 1.97001. When s = 4.84436, the proportion of the modes of f2–10 declines along streamwise rapidly, and the frequency range narrows. When s = 8.39659, the main disturbance modes in the boundary layer are mainly distributed near the fundamental mode and the modes in the range from f2 to f5 and the other modes are basically filtered out. This implies that (1) the disturbance waves within a certain frequency range will be generated in the transition region between the nose and no-nose boundary layer under the interaction between freestream disturbance and shock wave as well as boundary layer. (2) With the disturbance evolving from the upstream to the downstream, most of disturbance waves in the boundary layer decrease, and only special frequency ranges (f1–f5) of unstable wave exist in the downstream boundary layer, indicating mode competition exists during the disturbance wave evolution along streamwise in the boundary layer. By comparing Figure 7 with Figure 8, it can be seen that the frequency spectrum of pressure disturbance in the period phase is remarkably different from that in the response phase. The frequency range of main disturbance modes in the boundary layer in the response phase ranges from 0 to f4; while the main disturbance modes in the boundary layer are fundamental modes and the amplitudes of harmonic frequency are small in the period phase. This indicates that mode competition exists during the process of changing from response phase into period phase. In the process, the mode competition makes the fundamental mode sharply increases and the other modes slowly increase or are suppressed.

Bottom Line: Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer.The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer.The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

View Article: PubMed Central - PubMed

Affiliation: College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China.

ABSTRACT
By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

Show MeSH
Related in: MedlinePlus