Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

AbstractIn this paper, direct numerical simulation (DNS) is presented for spatially evolving turbulent boundary layer over an isothermal flat-plate atMa∞= 2.25,5,6,8. WhenMa∞= 8, two cases with the ratio of wall-to-reference temperatureTω/T∞= 1.9 and 10.03 are considered respectively. The wall temperature approaches recovery temperatures for other cases. The characteristics of compressible turbulent boundary layer (CTBL) affected by freestream Mach number and wall temperature are investigated. It focuses on assessing compressibility effects and the validity of Morkovin's hypothesis through computing and analyzing the mean velocity profile, turbulent intensity, the strong Reynolds analogy (SRA) and possibility density function of dilatation term. The results show that, when the wall temperature approaches recovery temperature, the effects of Mach number on compressibility is insignificant. As a result, the compressibility effect is very weak and the Morkovin's hypothesis is still valid for Mach number even up to 8. However, when Mach number equal to 8, the wall temperature effect on the compressibility is sensitive. In this case, whenTω/T∞= 1.9, the Morkovin's hypothesis is not fully valid. The validity of classical SRA depends on wall temperature directly. A new modified SRA is proposed to eliminate such negative factor in near wall region. Finally the effects of Mach number and wall temperature on streaks are also studied.

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Direct numerical simulation of thermally-stratified turbulent boundary layer subjected to adverse pressure gradient

International Journal of Heat and Fluid Flow ◽

10.1016/j.ijheatfluidflow.2016.05.020 ◽

2016 ◽

Vol 61 ◽

pp. 213-228

Author(s):

Hirofumi Hattori ◽

Amane Kono ◽

Tomoya Houra

Keyword(s):

Numerical Simulation ◽

Boundary Layer ◽

Turbulent Boundary Layer ◽

Direct Numerical Simulation ◽

Pressure Gradient ◽

Adverse Pressure Gradient

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314 Direct Numerical Simulation of the Effects of External Turbulence on Turbulence Structure and Heat Transfer in a Turbulent Boundary Layer

The Proceedings of Conference of Tokai Branch ◽

10.1299/jsmetokai.2008.57.211 ◽

2008 ◽

Vol 2008.57 (0) ◽

pp. 211-212

Author(s):

Hiroki SUZUKI ◽

Kouji NAGATA ◽

Yasuhiko SAKAI ◽

Toshiyuki HAYASE ◽

Takashi KUBO

Keyword(s):

Heat Transfer ◽

Numerical Simulation ◽

Boundary Layer ◽

Turbulent Boundary Layer ◽

Direct Numerical Simulation ◽

Turbulence Structure ◽

External Turbulence

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

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.558 ◽

2019 ◽

Vol 877 ◽

pp. 167-195 ◽

Cited By ~ 2

Author(s):

Feng-Yuan Zuo ◽

Antonio Memmolo ◽

Guo-ping Huang ◽

Sergio Pirozzoli

Keyword(s):

Numerical Simulation ◽

Boundary Layer ◽

Shock Wave ◽

Turbulent Boundary Layer ◽

Direct Numerical Simulation ◽

Pressure Gradient ◽

Stokes Equations ◽

Shear Stresses ◽

Mean Flow ◽

Conical Shock

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.

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