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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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Fourier amplitudes of pressure disturbance in boundary layer are compared with literatures [21, 23].
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fig6: Fourier amplitudes of pressure disturbance in boundary layer are compared with literatures [21, 23].

Mentions: Since the evolution of disturbance mode in boundary layer has a significant effect on boundary layer stability [1, 22, 26], the nonlinear evolution of disturbance wave in the boundary layers is investigated by analyzing the pressure disturbance on wall. Different locations on the wall surface are selected to record the disturbance value of aerothermodynamics parameter in the boundary layer and to explore the temporal and spatial evolution (streamwise evolution) of disturbance waves in the boundary layer. A fitted coordinate s corresponding to x is employed for representing the curve length from wall location to the stagnation point and the fitted coordinate is the same as that in [25]. The time domain signals of pressure disturbance at different wall locations in both the response phase, period phase, and ablation phase are transformed by Fourier series. The temporal signals of pressure disturbance are decomposed into frequency signals using Fourier transform, which makes the time domain signals into the frequency domain signals. Figure 6 shows that the distribution of the Fourier amplitudes of pressure disturbance along streamwise in the hypersonic blunt body boundary layer under freestream entropy wave in the period phase is compared with literatures [21, 23]. The computational conditions are included in the figure. Figures 6(a), 6(b), and 6(c) are Zhang et al.'s result [21], Zhong's result, and present result, respectively. As shown in the figure, the Fourier amplitudes of pressure disturbance in the three kinds of the hypersonic blunt body boundary layer under freestream entropy wave have similar change tendency along streamwise. That is to say, it sharply decreases along streamwise in the nose boundary layer and the decreasing rate becomes small in the no-nose boundary layer. However, it can be seen that there is an obvious difference among the three kinds of Fourier amplitude. By comparing Figures 6(a) and 6(c), it can be seen that there are four similar areas, as the marks R1, R2, R3, and R4 shown in the figure. In the nose boundary layer (in Figure 6(a),  x < 1; in Figure 6(c),  x < 0), namely, R1 area, the amplitude sharply decreases, the amplitude in R2 area decreases slowly and in R3 area, it increases obviously and it generally decreases in R4 area. The reason why the amplitude remains a decreasing tendency in R2 area is that there is expansion wave in the junction region (in Figure 6(a),  x = 1; in Figure 6(c),  x = 0) between the spherical nose and the straight cone which is caused by the surface curve discontinuity [25]. However, in the no-nose area, the flow will be recompressed [25]. Thus, the decreasing tendency slows. In the R3 area, the effect of the expansion waves on the pressure disturbance in the boundary layer decreases with the distance departing from the junction region. The flow recompression obviously increases the amplitude of pressure disturbance. What is worth mentioning is that there is small fluctuation of the amplitude of pressure disturbance in Figure 6(c)'s R4 area. It can be believed that the phenomenon is due to the nonlinearity of disturbance evolution caused by the fact that the amplitude of freestream disturbance in this paper is significantly larger than that in literature [21].


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)

Fourier amplitudes of pressure disturbance in boundary layer are compared with literatures [21, 23].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig6: Fourier amplitudes of pressure disturbance in boundary layer are compared with literatures [21, 23].
Mentions: Since the evolution of disturbance mode in boundary layer has a significant effect on boundary layer stability [1, 22, 26], the nonlinear evolution of disturbance wave in the boundary layers is investigated by analyzing the pressure disturbance on wall. Different locations on the wall surface are selected to record the disturbance value of aerothermodynamics parameter in the boundary layer and to explore the temporal and spatial evolution (streamwise evolution) of disturbance waves in the boundary layer. A fitted coordinate s corresponding to x is employed for representing the curve length from wall location to the stagnation point and the fitted coordinate is the same as that in [25]. The time domain signals of pressure disturbance at different wall locations in both the response phase, period phase, and ablation phase are transformed by Fourier series. The temporal signals of pressure disturbance are decomposed into frequency signals using Fourier transform, which makes the time domain signals into the frequency domain signals. Figure 6 shows that the distribution of the Fourier amplitudes of pressure disturbance along streamwise in the hypersonic blunt body boundary layer under freestream entropy wave in the period phase is compared with literatures [21, 23]. The computational conditions are included in the figure. Figures 6(a), 6(b), and 6(c) are Zhang et al.'s result [21], Zhong's result, and present result, respectively. As shown in the figure, the Fourier amplitudes of pressure disturbance in the three kinds of the hypersonic blunt body boundary layer under freestream entropy wave have similar change tendency along streamwise. That is to say, it sharply decreases along streamwise in the nose boundary layer and the decreasing rate becomes small in the no-nose boundary layer. However, it can be seen that there is an obvious difference among the three kinds of Fourier amplitude. By comparing Figures 6(a) and 6(c), it can be seen that there are four similar areas, as the marks R1, R2, R3, and R4 shown in the figure. In the nose boundary layer (in Figure 6(a),  x < 1; in Figure 6(c),  x < 0), namely, R1 area, the amplitude sharply decreases, the amplitude in R2 area decreases slowly and in R3 area, it increases obviously and it generally decreases in R4 area. The reason why the amplitude remains a decreasing tendency in R2 area is that there is expansion wave in the junction region (in Figure 6(a),  x = 1; in Figure 6(c),  x = 0) between the spherical nose and the straight cone which is caused by the surface curve discontinuity [25]. However, in the no-nose area, the flow will be recompressed [25]. Thus, the decreasing tendency slows. In the R3 area, the effect of the expansion waves on the pressure disturbance in the boundary layer decreases with the distance departing from the junction region. The flow recompression obviously increases the amplitude of pressure disturbance. What is worth mentioning is that there is small fluctuation of the amplitude of pressure disturbance in Figure 6(c)'s R4 area. It can be believed that the phenomenon is due to the nonlinearity of disturbance evolution caused by the fact that the amplitude of freestream disturbance in this paper is significantly larger than that in literature [21].

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