Reynolds number and wall cooling effects on correlations between the thermodynamic variables in hypersonic turbulent boundary layers

In this paper, direct numerical simulations in hypersonic turbulent boundary layers over a $24^{\circ }$ compression ramp at Mach 6.0 are performed. The wall skin friction and its spanwise non-homogeneity in the interaction region are analysed via the spectral analysis and drag decomposition method. On the compression ramp, the premultiplied spanwise energy spectrum of wall shear stress $\tau _{w}$ reveals two energetic spanwise length scales. One occurs in the region of $x/\delta _{ref}=0\unicode{x2013}3$ ( $x=0$ lies in the compression corner; $\delta _{ref}$ is the boundary layer thickness upstream of the interaction region) and is consistent with that of the large-scale streamwise vortices, indicating that the fluctuation intensity of $\tau _{w}$ is associated with the Görtler-type structures. The other one is observed downstream of $x/\delta _{ref}=3.0$ and corresponds to the regenerated elongated streaky structures. The fluctuation intensity of $\tau _{w}$ peaks at $x/\delta _{ref}=3.0$ , where both the above energetic length scales are observed. The drag decomposition method proposed by Li et al. (J. Fluid Mech., vol. 875, 2019, pp. 101–123) is extended to include the effects of spanwise non-homogeneity so that it can be used in the interaction region where the mean flow field and the mean skin friction $C_f$ exhibit an obvious spanwise heterogeneity. The results reveal that, in the upstream turbulent boundary layer, the drag contribution arising from the spanwise heterogeneity can be neglected, while this value on the compression ramp is up to 20.7 % of $C_f$ , resulting from the Görtler-type vortices. With the aid of the drag decomposition method, it is found that the main flow features that contribute positively to the amplification of $C_f$ and its rapid increase on the compression ramp includes: the density increase across the shock, the high mean shear stress and turbulence amplification around the detached shear layer and the Favre-averaged downward velocity towards the ramp wall. Compared with the spanwise-averaged value, $C_f$ and its components at the spanwise station where the downwash and upwash of the Görtler-type vortices occur reveal a spanwise variation exceeding 10 %.

Section: Numerical Schemementioning

confidence: 99%

Wall skin friction analysis in a hypersonic turbulent boundary layer over a compression ramp

Guo,

Zhang,

Zhu

et al. 2024

Effect of bulk viscosity on the hypersonic compressible turbulent boundary layer

Zheng,

Feng,

Zheng

2024

The impact of bulk viscosity is unclear with considering the increased dilatational dissipation and compressibility effects in hypersonic turbulence flows. In this study, we employ direct numerical simulations to conduct comprehensive analysis of the effect of bulk viscosity on hypersonic turbulent boundary layer flow over a flat plate. The results demonstrate that the scaling relations remain valid even when accounting for large bulk viscosity. However, the wall-normal velocity fluctuations $v_{rms}^{\prime \prime }$ decrease significantly in the viscous sublayer due to the enhanced bulk dilatational dissipation. The intensity of travelling-wave-like alternating positive and negative structures of instantaneous pressure fluctuations $p_{rms}^{\prime }$ in the near-wall region decreases distinctly after considering the bulk viscosity, which is attributed mainly to the reduction of compressible pressure fluctuations $p_{c,rms}^{+}$ . Furthermore, the velocity divergence $\partial u_{i} / \partial x_{i}$ undergoes a significant decrease by bulk viscosity. In short, our results indicate that bulk viscosity can weaken the compressibility of the hypersonic turbulent boundary layer and becomes more significant as the Mach number increases and the wall temperature decreases. Notably, when the bulk-to-shear viscosity ratio of the gas reaches a few hundred levels ( $\mu _b/\mu =O(10^2)$ ), and mechanical behaviour of the near-wall region ( $\kern 0.06em y^+\le 30$ ) is of greater interest, the impact of bulk viscosity on the hypersonic cold-wall turbulent boundary layer may not be negligible.

Investigations on the turbulentnon-turbulent interface in supersonic compressible plate turbulent boundary layer

Su,

Long,

Wang

et al. 2024

The turbulent boundary layer (TBL) is a widely existing flow phenomenon in nature and engineering applications. Its strong mixing effect can achieve more sufficient material mixing, heat transport, etc. The understanding of the entrainment process and mechanism of irrotational fluids entering the turbulent region can be promoted by studying the geometric and dynamic characteristics of turbulent ${/}$ non-turbulent interfaces (TNTI). In compressible flow, it is unclear whether the properties of TNTI will change and whether the entrainment will show different features due to the influence of compressibility. Based on the direct numerical simulation results of supersonic compressible plate TBLs with Mach number of 2.9, the geometric and dynamic characteristics of TNTI are investigated in this paper. The interface is identified by the enstrophy method, and the height, thickness, fractal dimension, enstrophy transportation and entrainment characteristics of the interface are investigated. It is found that for the enstrophy transportation in a TBL, the contribution of compressibility-related terms accounts for approximately 13.4 % of the total enstrophy transportation, which tends to transfer the enstrophy of turbulence near the interface to both directions vertical to the interface. This promotes the expansion of the turbulent region towards the non-turbulent region, and the mean height, thickness and entrainment velocity are increased by approximately 3.7 %, 7.0 % and 8.5 %, respectively, while the fractal dimension is basically unaffected. Different from the incompressible flow, the contribution of the compressibility-related terms to the entrainment velocity is independent of the local curvature, and the intense entrainment process is more likely to occur on a highly curved concave surface.