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Response of a hypersonic blunt cone boundary layer to slow acoustic waves with assessment of various routes of receptivity

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Abstract

The hypersonic boundary-layer receptivity to slow acoustic waves is investigated for the Mach 6 flow over a 5-degree half-angle blunt cone with the nose radius of 5.08 mm. The plane acoustic wave interacts with the bow shock, and generates all types of disturbances behind the shock, which may take various routes to generate the boundary-layer unstable mode. In this paper, two routes of receptivity are investigated in detail. One is through the disturbance in the entropy layer. The other is through the slow acoustic wave transmitted downstream the bow shock, which can excite the boundary-layer mode due to the synchronization mechanism. The results show that, for a low frequency slow acoustic wave, the latter route plays a leading role. The entropy-layer instability wave is able to excite the first mode near the neutral point, but its receptivity efficiency is much lower.

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Abbreviations

Ma :

Mach number

Re 1 :

unit Reynolds number

Re :

Reynolds number

ρ :

density

u :

stream-wise velocity

v :

normal velocity

T :

temperature

p :

pressure

φ :

cone half-angle

γ :

specific heat ratio

Pr :

Prandtl number

t :

time

x,y :

axial and radial coordinates

ξ,η :

stream and normal coordinates

s :

cone surface location

U :

vector of the flow variable

E :

convective flux in the axial direction

F :

convective flux in the radial direction

E v :

viscous heat conduction flux in the axial di-rection

F v :

viscous heat conduction flux in the radial-direction

M :

source term

τ ij :

shear stress

q i :

heat flux

e s :

total internal energy

μ :

viscosity coefficient

κ :

heat conductivity coefficient

A :

amplitude

α :

stream-wise wavenumber

ω :

angular frequency

i:

imaginary unit

c.c.:

conjugate complex

∞:

free stream

w:

wall

′:

disturbance

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Acknowledgements

The first author and the third author are grateful to Prof.Heng ZHOU of Tianjin University for the stimulating discussion and tremendous support on this work. The third author would like to thank Prof.Xuesong WU of Imperial College for his continuous encouragement and inspiring discussion. Special thanks to Dr. Lei ZHAO from Tianjin University for generously providing his DNS codes for the current computations.

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Authors and Affiliations

  1. Laboratory for High-Speed Aerodynamics, School of Mechanical Engineering, Tianjin University, Tianjin, 300072, China

    Bingbing Wan, Jisheng Luo & Caihong Su

Authors
  1. Bingbing Wan
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  2. Jisheng Luo
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  3. Caihong Su
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Corresponding author

Correspondence to Caihong Su.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11472188 and 11332007) and the National Key Research and Development Program of China (No. 2016YFA0401200)

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Wan, B., Luo, J. & Su, C. Response of a hypersonic blunt cone boundary layer to slow acoustic waves with assessment of various routes of receptivity. Appl. Math. Mech.-Engl. Ed. 39, 1643–1660 (2018). https://doi.org/10.1007/s10483-018-2391-6

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