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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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Amplitudes of the second harmonic mode of pressure disturbance in the boundary layer are compared with Zhang et al.'s result [21, 22].
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fig1: Amplitudes of the second harmonic mode of pressure disturbance in the boundary layer are compared with Zhang et al.'s result [21, 22].

Mentions: Since finite difference method can be easily applied to the simulations of flowfiled existing complex geometries, it has been widely employed in the DNS of unsteady flows, especially compressible unsteady flows [15–18]. Because central difference schemes only introduce phase errors but no dissipative errors in numerical solutions, the schemes have been widely implemented in direct numerical simulation [15]. However, they are not robust enough in the simulations of convection dominated flow [18]. To provide adequate accuracy level for DNS, high-order schemes are required. However, the higher-order numerical scheme generally introduces the numerical oscillatory behavior near the discontinuity [19], while weighted essentially nonoscillatory (WENO) scheme [20] can be used to suppress the oscillatory behavior near the discontinuities or high gradient regions. In addition, upwind schemes show strong robustness in hypersonic flow simulation even when they are made high-order accurate [18]. Therefore, the governing equations are solved by using the 6th order center difference scheme and 5th order upwind WENO scheme for viscous flux terms and convection terms, respectively. Meanwhile, to maintain adequate time accuracy, a third-order, total variation diminishing Runge-Kutta scheme [19] is used for time integration. To validate the numerical program employed in this paper, a hypersonic unsteady flow over a blunt wedge with 5° half-wedge-angle (Zhang et al's numerical model [21]) under the action of freestream disturbance wave is solved in our previous investigation [22]. The amplitudes of the second harmonic mode of pressure disturbance in the boundary layer are compared with Zhang et al.'s result [21], as shown in Figure 1. Figure 1 shows that the numerical program 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)

Amplitudes of the second harmonic mode of pressure disturbance in the boundary layer are compared with Zhang et al.'s result [21, 22].
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig1: Amplitudes of the second harmonic mode of pressure disturbance in the boundary layer are compared with Zhang et al.'s result [21, 22].
Mentions: Since finite difference method can be easily applied to the simulations of flowfiled existing complex geometries, it has been widely employed in the DNS of unsteady flows, especially compressible unsteady flows [15–18]. Because central difference schemes only introduce phase errors but no dissipative errors in numerical solutions, the schemes have been widely implemented in direct numerical simulation [15]. However, they are not robust enough in the simulations of convection dominated flow [18]. To provide adequate accuracy level for DNS, high-order schemes are required. However, the higher-order numerical scheme generally introduces the numerical oscillatory behavior near the discontinuity [19], while weighted essentially nonoscillatory (WENO) scheme [20] can be used to suppress the oscillatory behavior near the discontinuities or high gradient regions. In addition, upwind schemes show strong robustness in hypersonic flow simulation even when they are made high-order accurate [18]. Therefore, the governing equations are solved by using the 6th order center difference scheme and 5th order upwind WENO scheme for viscous flux terms and convection terms, respectively. Meanwhile, to maintain adequate time accuracy, a third-order, total variation diminishing Runge-Kutta scheme [19] is used for time integration. To validate the numerical program employed in this paper, a hypersonic unsteady flow over a blunt wedge with 5° half-wedge-angle (Zhang et al's numerical model [21]) under the action of freestream disturbance wave is solved in our previous investigation [22]. The amplitudes of the second harmonic mode of pressure disturbance in the boundary layer are compared with Zhang et al.'s result [21], as shown in Figure 1. Figure 1 shows that the numerical program 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