DIRECT NUMERICAL SIMULATION OF HYPERSONIC SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTIONS 1)

doi:10.6052/0459-1879-17-239

Abstract

Abstract:

The peak of local thermal load might be severe due to the interactions of hypersonic shock wave and turbulent boundary layer. It has significant effect on the aerodynamic performance and flight safety of vehicle. Most previous studies on the interaction in hypersonic condition were based on the Reynolds-averaged methods, the corresponding direct numerical simulation is relatively scarce. The direct numerical analysis of hypersonic shock wave and turbulent boundary layer interaction are helpful to the understanding of the relevant mechanisms and the improvement of existing turbulent modes and sub-grid stress models. Numerical analysis of hypersonic shock wave and turbulent boundary layer interactions in a 34° compression ramp are carried out by means of direct numerical simulation for a free-stream Mach number $M ∞ = 6.0$ . Based on the Reynolds stress anisotropy tensor, the evolution of turbulent boundary layer along the compression ramp is analyzed. The compressibility effects on turbulent kinetic energy and its transport mechanism are studied through item by item analysis of transport equation. Using dynamic mode decomposition method, the characteristic of unsteadiness in the interaction region is investigated. It is found that along the flow developing downstream, the turbulent state in the near wall region is gradually turned into two-component turbulence from two-component axisymmetric state. The turbulence in outer region approaches the isotropic state from axisymmetric expansion. The results exhibit that there exist significant compressibility effects in the interaction region. The pressure-dilation correlation in turbulent kinetic energy budgets is enhanced significantly. However, it has little effect on the dilatational dissipation. The low-frequency oscillation in hypersonic compression ramp is characterized by the breathing motion of separation bubble. According to the spatial structure of low frequency dynamic modes, the unsteadiness is strongly associated with the separated shear layer.

Key words: hypersonic, shock wave and turbulent boundary layer interactions, direct numerical simulation, turbulent kinetic energy, low-frequency oscillation

CLC Number:

Tong Fulin, Li Xin, Yu Changping, Li Xinliang. DIRECT NUMERICAL SIMULATION OF HYPERSONIC SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTIONS ¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 197-208.

Figures/Tables 21

Fig. 1 Schematic of computational grid

Table 1 Selected streamwise positions

Symbol	$Streamwise position / mm$	Comment
E1	$- 50$	reference point
E2	$- 30$	mean-flow separation
E3	0	separation bubble
E4	55	reattachment region

Table 1 Selected streamwise positions

Symbol	$Streamwise position / mm$	Comment
E1	$- 50$	reference point
E2	$- 30$	mean-flow separation
E3	0	separation bubble
E4	55	reattachment region

Table 2 Boundary layer parameters at E1

$δ$ /mm	$δ *$ /mm	$θ$ /mm	$H$
.2	5.1	0.56	2.58

Table 2 Boundary layer parameters at E1

$δ$ /mm	$δ *$ /mm	$θ$ /mm	$H$
.2	5.1	0.56	2.58

Fig. 2 Profiles of mean velocity and root-mean square

Fig. 3 Distribution of two-point correlations in the spanwise direction

Fig. 4 Distribution of wall pressure and skin-friction coefficient

Fig. 4 Distribution of wall pressure and skin-friction coefficient (continued)

Fig. 5 Iso-contours of instantaneous streamwise velocity

Fig. 6 Iso-surface of instantaneous coherent vortex structure colored by the wall-normal distance

Fig. 7 Anisotropy invariant maps of the Reynolds stress tensor

Fig. 8 Distribution of turbulent kinetic energy

Fig. 9 Distribution of turbulent Mach number

Fig. 10 Transport of turbulent kinetic energy

Fig. 10 Transport of turbulent kinetic energy (continued)

Fig. 11 Turbulent viscous dissipation decomposition

Fig. 12 Comparison of pressure-dilatation and dilatational dissipation

Fig. 13 Power spectral density of wall pressure fluctuations

Fig. 14 Relationships between mode energy and frequencies

Fig. 15 Time series of the variable Ms at various streamwise location

Fig. 16 Reconstruction of the flow field based on the low frequency modes 1~4

Fig. 17 The real part of low frequency mode 1

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DIRECT NUMERICAL SIMULATION OF HYPERSONIC SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTIONS ¹⁾

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