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Direct numerical simulation of conical shock wave–turbulent boundary layer interaction

Published online by Cambridge University Press:  19 August 2019

Feng-Yuan Zuo Open the ORCID record for Feng-Yuan Zuo [Opens in a new window] ,
Antonio Memmolo ,
Guo-ping Huang  and
Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window]
Feng-Yuan Zuo*
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, PR China Dipartimento di Meccanica e Aerospaziale, Sapienza Università e di Roma, Via Eudossiana 18, 00184 Roma, Italy
Antonio Memmolo
Affiliation:
Dipartimento di Meccanica e Aerospaziale, Sapienza Università e di Roma, Via Eudossiana 18, 00184 Roma, Italy
Guo-ping Huang
Affiliation:
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, PR China
Sergio Pirozzoli*
Affiliation:
Dipartimento di Meccanica e Aerospaziale, Sapienza Università e di Roma, Via Eudossiana 18, 00184 Roma, Italy
*
†Email addresses for correspondence: zuofy@nuaa.edu.cn, sergio.pirozzoli@uniroma1.it
†Email addresses for correspondence: zuofy@nuaa.edu.cn, sergio.pirozzoli@uniroma1.it
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Abstract

Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Compressible boundary layers Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 167 - 195
Copyright
© 2019 Cambridge University Press 

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Zuo et al. supplementary movie 1

Overall structure of the CSBLI. The cone geometry is blanked, and shock waves are shown by means of numerical schlieren, defined through the magnitude of the density gradient ( ). Contours range , from black to white.

Download Zuo et al. supplementary movie 1(Video)
Video 9.9 MB

Zuo et al. supplementary movie 2

Three-dimensional view of CSBLI. The shock structure is educed through the pressure iso-surface . Streamwise velocity contours are shown for (color scale from blue to red) in a near-wall plane at y+=10.5. Pressure contours are shown in a side plane for (color scale from blue to red).

Download Zuo et al. supplementary movie 2(Video)
Video 9.8 MB

Zuo et al. supplementary movie 3

Vortical structures in CSBLI. Vortices are educed through the iso-surface of the swirling strength ( ), and colored with the wall-normal velocity ( , color scale from blue to red).

Download Zuo et al. supplementary movie 3(Video)
Video 9.6 MB