Limits...
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.

Show MeSH

Related in: MedlinePlus

Growth of different frequency disturbances in the boundary layer along streamwise in 3 phases.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4109134&req=5

fig11: Growth of different frequency disturbances in the boundary layer along streamwise in 3 phases.

Mentions: Figure 11 shows the growth rate of different frequency disturbances in the boundary layer along streamwise in the three phases, namely, response phase, period phase, and ablation phase, respectively. It can be seen that (1) the main disturbance modes in the nose boundary layer (s = 0.63566) decay along streamwise in all the three phases. It is believed that because the bow shock wave changed from the normal shock in nose region to the oblique shock in no-nose region, the former is stronger than the latter. It implies that the disturbance evolution in the nose boundary layer is significantly affected by the shock wave. However, it can be found that the growth of many disturbance modes along streamwise in the no-nose boundary layer is larger than 0. Namely, these modes in the no-nose boundary layer have an increasing trend in the disturbance's evolution along streamwise, indicating that the bow shock no longer plays a leading role in the evolution of the disturbance. (2) When s = 2.60247, the modes with the frequency less than 1.0 decrease along streamwise and some modes within the range of f ≥ 1.0 increase slowly in the response phase; all the modes except the second harmonic mode and the fifth harmonic mode decrease or basically remain stable along streamwise in the period phase; the fundamental mode, the second harmonic mode, sixth harmonic mode, and the seventh harmonic mode increase along streamwise and the other modes decrease or basically remain stable along streamwise in the ablation phase. This means different phases have different unstable modes in the boundary layer. Namely, the unstable mode in the boundary layer changes with the temporal evolution of disturbance wave in the boundary layer. (3) The growth rate of some modes in the range of frequency f > 0.5 in the ablation phase is larger than that in the period and response phase, as the rectangular mark shown in Figure 11. For instance, the growth rate of the modes near f = 0.75 and f = 1.75 at s = 5.38530 in the ablation phase is larger than that in the other two phase. This also means that some modes in the boundary layer are suppressed during response and period phase; mode competition between these modes and the main disturbance modes exists in the temporal evolution of boundary layer disturbance wave, which can change the characteristics of nonlinear evolution of the unstable waves in the boundary layer. (4) In the period phase, in both the nose boundary and the no-nose boundary, the attenuation rates of fundamental mode are significantly higher than that of other modes; in no-nose boundary, the second harmonic mode becomes the mode with the highest growth rate, which is the most unstable mode. It is also seen that, in the downstream boundary layer (s = 5.38530, 8.39659), the attenuation rates of the most unstable mode are significantly higher than that of other modes when the boundary layer state changes from period phase to ablation phase. This shows that 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.


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)

Growth of different frequency disturbances in the boundary layer along streamwise in 3 phases.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig11: Growth of different frequency disturbances in the boundary layer along streamwise in 3 phases.
Mentions: Figure 11 shows the growth rate of different frequency disturbances in the boundary layer along streamwise in the three phases, namely, response phase, period phase, and ablation phase, respectively. It can be seen that (1) the main disturbance modes in the nose boundary layer (s = 0.63566) decay along streamwise in all the three phases. It is believed that because the bow shock wave changed from the normal shock in nose region to the oblique shock in no-nose region, the former is stronger than the latter. It implies that the disturbance evolution in the nose boundary layer is significantly affected by the shock wave. However, it can be found that the growth of many disturbance modes along streamwise in the no-nose boundary layer is larger than 0. Namely, these modes in the no-nose boundary layer have an increasing trend in the disturbance's evolution along streamwise, indicating that the bow shock no longer plays a leading role in the evolution of the disturbance. (2) When s = 2.60247, the modes with the frequency less than 1.0 decrease along streamwise and some modes within the range of f ≥ 1.0 increase slowly in the response phase; all the modes except the second harmonic mode and the fifth harmonic mode decrease or basically remain stable along streamwise in the period phase; the fundamental mode, the second harmonic mode, sixth harmonic mode, and the seventh harmonic mode increase along streamwise and the other modes decrease or basically remain stable along streamwise in the ablation phase. This means different phases have different unstable modes in the boundary layer. Namely, the unstable mode in the boundary layer changes with the temporal evolution of disturbance wave in the boundary layer. (3) The growth rate of some modes in the range of frequency f > 0.5 in the ablation phase is larger than that in the period and response phase, as the rectangular mark shown in Figure 11. For instance, the growth rate of the modes near f = 0.75 and f = 1.75 at s = 5.38530 in the ablation phase is larger than that in the other two phase. This also means that some modes in the boundary layer are suppressed during response and period phase; mode competition between these modes and the main disturbance modes exists in the temporal evolution of boundary layer disturbance wave, which can change the characteristics of nonlinear evolution of the unstable waves in the boundary layer. (4) In the period phase, in both the nose boundary and the no-nose boundary, the attenuation rates of fundamental mode are significantly higher than that of other modes; in no-nose boundary, the second harmonic mode becomes the mode with the highest growth rate, which is the most unstable mode. It is also seen that, in the downstream boundary layer (s = 5.38530, 8.39659), the attenuation rates of the most unstable mode are significantly higher than that of other modes when the boundary layer state changes from period phase to ablation phase. This shows that 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.

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