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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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Related in: MedlinePlus

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


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fig9: Frequency spectrum analysis of pressure disturbance at different locations in the ablation phase.

Mentions: Figure 9 shows the Fourier frequency spectrum analysis of pressure disturbance at different surface locations in the ablation phase. As discussed in Figure 8, we know the main disturbance modes in the boundary layer is fundamental mode f1 and the amplitudes of harmonic frequency (fn, n ≥ 2) are small in the period phase. However, it can be clearly observed from Figure 9 that the disturbance mode in the boundary layer is widely distributed in the range from 0 to f12 in the ablation phase. The proportion of the modes with frequency larger than 0.25 (f > 0.25) in the boundary layer will grow by a significant amount during the process of changing from the period phase into the ablation phase although all modes will finally disappear due to the loss of disturbance excitation in freestream. It indicates that, when the freestream disturbance is terminated, the mode with the amplitude of fundamental mode decreases sharply and firstly with the temporal evolution of disturbance wave in the boundary layer; the disturbance energy of fundamental mode is transferred to the modes with frequency larger than the second harmonic frequency, especially the modes in the range from f2 to f8 (f = 2.0). Meanwhile, from Figure 8, we know that, in the period phase, the disturbance waves are mainly distributed near fundamental mode and harmonic frequency modes (fn, n is integer) and the Fourier amplitudes of the other high frequency modes are still tiny. As seen in Figure 9, in the ablation phase, the disturbance waves are widely distributed in the range from f = 0 to f = 3.0. Namely, the frequency range in the boundary layer in the period phase is narrower than that in the ablation phase, which indicates that a part of the disturbance energy of fn (n is integer) is transferred to other modes. It also can be seen that, due to the transformation of disturbance energy in the boundary layer, when s < 4.84436, the dominant mode in the boundary layer is transferred from the fundamental mode to the second harmonic mode during the process of changing from period phase into ablation phase; when s > 4.84436, the dominant mode in the boundary layer is transferred from the fundamental mode to near the third harmonic mode during the process of changing from period phase into ablation phase. That is, there are the transformations of the dominant mode in both temporal and spatial evolution of disturbance wave modes in the boundary layer.


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 ablation phase.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig9: Frequency spectrum analysis of pressure disturbance at different locations in the ablation phase.
Mentions: Figure 9 shows the Fourier frequency spectrum analysis of pressure disturbance at different surface locations in the ablation phase. As discussed in Figure 8, we know the main disturbance modes in the boundary layer is fundamental mode f1 and the amplitudes of harmonic frequency (fn, n ≥ 2) are small in the period phase. However, it can be clearly observed from Figure 9 that the disturbance mode in the boundary layer is widely distributed in the range from 0 to f12 in the ablation phase. The proportion of the modes with frequency larger than 0.25 (f > 0.25) in the boundary layer will grow by a significant amount during the process of changing from the period phase into the ablation phase although all modes will finally disappear due to the loss of disturbance excitation in freestream. It indicates that, when the freestream disturbance is terminated, the mode with the amplitude of fundamental mode decreases sharply and firstly with the temporal evolution of disturbance wave in the boundary layer; the disturbance energy of fundamental mode is transferred to the modes with frequency larger than the second harmonic frequency, especially the modes in the range from f2 to f8 (f = 2.0). Meanwhile, from Figure 8, we know that, in the period phase, the disturbance waves are mainly distributed near fundamental mode and harmonic frequency modes (fn, n is integer) and the Fourier amplitudes of the other high frequency modes are still tiny. As seen in Figure 9, in the ablation phase, the disturbance waves are widely distributed in the range from f = 0 to f = 3.0. Namely, the frequency range in the boundary layer in the period phase is narrower than that in the ablation phase, which indicates that a part of the disturbance energy of fn (n is integer) is transferred to other modes. It also can be seen that, due to the transformation of disturbance energy in the boundary layer, when s < 4.84436, the dominant mode in the boundary layer is transferred from the fundamental mode to the second harmonic mode during the process of changing from period phase into ablation phase; when s > 4.84436, the dominant mode in the boundary layer is transferred from the fundamental mode to near the third harmonic mode during the process of changing from period phase into ablation phase. That is, there are the transformations of the dominant mode in both temporal and spatial evolution of disturbance wave modes in the boundary layer.

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