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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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The pressure disturbance mode obtained under two grid conditions.
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fig3: The pressure disturbance mode obtained under two grid conditions.

Mentions: After the steady flowfield without disturbance is computed, the entropy disturbance with single mode is introduced to the upstream boundary from t = 0 to t = 48. The entropy disturbances [21, 23] that impinge on the upstream boundary are taken to(5)[u′v′p′ρ′]T  =[000AMa]Tei(βx−(γ·Re/106)t+(π/2)),where the variables u′, v′, P′, and ρ′ are the disturbance values of the velocity along axis x, and velocity along axis y, pressure and density, respectively; A, β, γ, Ma, and Re are amplitude, wave number, generalized frequency freestream Mach number, and Reynolds number, respectively. The superscripts “′” that used in the follow denote disturbance values which are obtained by the variables value of instantaneous flow minus the variables value of the local steady base flow. The computational conditions and flow parameters for the model are shown in Figure 2 and Table 1. The variable η is the angle of attack. A 300 × 120 grid is used for the steady and unsteady calculations. The grid lines stretching method is used in wall-normal directions to cluster more points inside the boundary layer where strong shear flow exists. The grid lines are also stretched in the streamwise for maintaining a good resolution in strong shock wave regions. The mesh grid density which introduces the present computations matches that in the investigations with similar computational model conducted by Duan et al. [18], Zhang et al. [21], and Prakash et al. [24]. It should be pointed out that the stretching method is employed in the numerical calculation of Figure 1. Since the amplitudes of disturbance in the boundary layer obtained by the stretching method agree well with Zhang et al's result [21], it can be believed that the stretching method is available. Meanwhile, to evaluate the reliability of the grid density, the simulations with two kinds of grid (300 × 120 and 450 × 180) are conducted under the condition employed in this paper. The pressure disturbance mode in boundary layer obtained under the two conditions is shown in Figure 3. From Figure 3, it can be seen the difference of the pressure disturbance mode in boundary layer under the two conditions is tiny, which indicates the grid density in this paper, especially the one in the vicinity of the boundary layer (near the wall) is reliable.


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)

The pressure disturbance mode obtained under two grid conditions.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig3: The pressure disturbance mode obtained under two grid conditions.
Mentions: After the steady flowfield without disturbance is computed, the entropy disturbance with single mode is introduced to the upstream boundary from t = 0 to t = 48. The entropy disturbances [21, 23] that impinge on the upstream boundary are taken to(5)[u′v′p′ρ′]T  =[000AMa]Tei(βx−(γ·Re/106)t+(π/2)),where the variables u′, v′, P′, and ρ′ are the disturbance values of the velocity along axis x, and velocity along axis y, pressure and density, respectively; A, β, γ, Ma, and Re are amplitude, wave number, generalized frequency freestream Mach number, and Reynolds number, respectively. The superscripts “′” that used in the follow denote disturbance values which are obtained by the variables value of instantaneous flow minus the variables value of the local steady base flow. The computational conditions and flow parameters for the model are shown in Figure 2 and Table 1. The variable η is the angle of attack. A 300 × 120 grid is used for the steady and unsteady calculations. The grid lines stretching method is used in wall-normal directions to cluster more points inside the boundary layer where strong shear flow exists. The grid lines are also stretched in the streamwise for maintaining a good resolution in strong shock wave regions. The mesh grid density which introduces the present computations matches that in the investigations with similar computational model conducted by Duan et al. [18], Zhang et al. [21], and Prakash et al. [24]. It should be pointed out that the stretching method is employed in the numerical calculation of Figure 1. Since the amplitudes of disturbance in the boundary layer obtained by the stretching method agree well with Zhang et al's result [21], it can be believed that the stretching method is available. Meanwhile, to evaluate the reliability of the grid density, the simulations with two kinds of grid (300 × 120 and 450 × 180) are conducted under the condition employed in this paper. The pressure disturbance mode in boundary layer obtained under the two conditions is shown in Figure 3. From Figure 3, it can be seen the difference of the pressure disturbance mode in boundary layer under the two conditions is tiny, which indicates the grid density in this paper, especially the one in the vicinity of the boundary layer (near the wall) is reliable.

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