“…In the turbulent region, and are almost superposed, differently from what observed by Passiatore et al. (2021) where the former was shown to be predominant. Such a discrepancy can be ascribed to the much larger friction Reynolds numbers reached in the current configuration, leading to an increased turbulent contribution (Fan, Li & Pirozzoli 2019).…”
Section: Resultscontrasting
confidence: 75%
“…Neither chemical activity nor thermal relaxation process should substantially alter the validity of the transformation since a certain degree of decoupling is observed between the thermochemical and turbulent activities, as previously noticed by Passiatore et al. (2021) and Di Renzo & Urzay (2021). Figure 4.Wall-normal profiles of ( a ) the van Driest-transformed streamwise velocity, ( b ) Trettel & Larsson's transformation and ( c ) comparison between Trettel & Larsson transformation and total-stress-based scaling of Griffin et al.…”
Section: Resultsmentioning
confidence: 66%
“…The former scaling has been shown to work reasonably well for adiabatic boundary layers, even at high speeds (Passiatore et al. 2021). On the other hand, it becomes inaccurate when highly cooled configurations are considered, whether they be boundary layers (Zhang et al.…”
Section: Resultsmentioning
confidence: 96%
“…The interaction of finite-rate chemistry with transitional and turbulent spatially developing boundary layers was recently investigated by Passiatore et al. (2021) and Di Renzo & Urzay (2021), who isolated the effects of chemical non-equilibrium on pseudo-adiabatic and cooled TBLs, respectively. In both studies, the effect of thermal non-equilibrium was neglected since the selected edge conditions were not expected to promote significant vibrational relaxation phenomena.…”
A hypersonic, spatially evolving turbulent boundary layer at Mach 12.48 with a cooled wall is analysed by means of direct numerical simulations. At the selected conditions, massive kinetic-to-internal energy conversion triggers thermal and chemical non-equilibrium phenomena. Air is assumed to behave as a five-species reacting mixture, and a two-temperature model is adopted to account for vibrational non-equilibrium. Wall cooling partly counteracts the effects of friction heating, and the temperature rise in the boundary layer excites vibrational energy modes while inducing mild chemical dissociation of oxygen. Vibrational non-equilibrium is mostly driven by molecular nitrogen, characterized by slower relaxation rates than the other molecules in the mixture. The results reveal that thermal non-equilibrium is sustained by turbulent mixing: sweep and ejection events efficiently redistribute the gas, contributing to the generation of a vibrationally under-excited state close to the wall, and an over-excited state in the outer region of the boundary layer. The tight coupling between turbulence and thermal effects is quantified by defining an interaction indicator. A modelling strategy for the vibrational energy turbulent flux is proposed, based on the definition of a vibrational turbulent Prandtl number. The validity of the strong Reynolds analogy under thermal non-equilibrium is also evaluated. Strong compressibility effects promote the translational–vibrational energy exchange, but no preferential correlation was detected between expansions/compressions and vibrational over-/under-excitation, as opposed to what has been observed for unconfined turbulent configurations.
“…In the turbulent region, and are almost superposed, differently from what observed by Passiatore et al. (2021) where the former was shown to be predominant. Such a discrepancy can be ascribed to the much larger friction Reynolds numbers reached in the current configuration, leading to an increased turbulent contribution (Fan, Li & Pirozzoli 2019).…”
Section: Resultscontrasting
confidence: 75%
“…Neither chemical activity nor thermal relaxation process should substantially alter the validity of the transformation since a certain degree of decoupling is observed between the thermochemical and turbulent activities, as previously noticed by Passiatore et al. (2021) and Di Renzo & Urzay (2021). Figure 4.Wall-normal profiles of ( a ) the van Driest-transformed streamwise velocity, ( b ) Trettel & Larsson's transformation and ( c ) comparison between Trettel & Larsson transformation and total-stress-based scaling of Griffin et al.…”
Section: Resultsmentioning
confidence: 66%
“…The former scaling has been shown to work reasonably well for adiabatic boundary layers, even at high speeds (Passiatore et al. 2021). On the other hand, it becomes inaccurate when highly cooled configurations are considered, whether they be boundary layers (Zhang et al.…”
Section: Resultsmentioning
confidence: 96%
“…The interaction of finite-rate chemistry with transitional and turbulent spatially developing boundary layers was recently investigated by Passiatore et al. (2021) and Di Renzo & Urzay (2021), who isolated the effects of chemical non-equilibrium on pseudo-adiabatic and cooled TBLs, respectively. In both studies, the effect of thermal non-equilibrium was neglected since the selected edge conditions were not expected to promote significant vibrational relaxation phenomena.…”
A hypersonic, spatially evolving turbulent boundary layer at Mach 12.48 with a cooled wall is analysed by means of direct numerical simulations. At the selected conditions, massive kinetic-to-internal energy conversion triggers thermal and chemical non-equilibrium phenomena. Air is assumed to behave as a five-species reacting mixture, and a two-temperature model is adopted to account for vibrational non-equilibrium. Wall cooling partly counteracts the effects of friction heating, and the temperature rise in the boundary layer excites vibrational energy modes while inducing mild chemical dissociation of oxygen. Vibrational non-equilibrium is mostly driven by molecular nitrogen, characterized by slower relaxation rates than the other molecules in the mixture. The results reveal that thermal non-equilibrium is sustained by turbulent mixing: sweep and ejection events efficiently redistribute the gas, contributing to the generation of a vibrationally under-excited state close to the wall, and an over-excited state in the outer region of the boundary layer. The tight coupling between turbulence and thermal effects is quantified by defining an interaction indicator. A modelling strategy for the vibrational energy turbulent flux is proposed, based on the definition of a vibrational turbulent Prandtl number. The validity of the strong Reynolds analogy under thermal non-equilibrium is also evaluated. Strong compressibility effects promote the translational–vibrational energy exchange, but no preferential correlation was detected between expansions/compressions and vibrational over-/under-excitation, as opposed to what has been observed for unconfined turbulent configurations.
“…Furthermore, the RD relation was used to quantify the effects of finite-rate chemistry in hypersonic turbulent boundary layers by Passiatore et al. (2021), and similarly to the FIK relation, has been used to quantify the effects of control methodologies on skin friction generation in supersonic turbulent boundary layers by Liu et al. (2021).…”
Turbulence enhances the wall shear stress in boundary layers, significantly increasing the drag on streamlined bodies. Other flow features such as free stream pressure gradients and streamwise boundary layer growth also strongly influence the local skin friction. In this paper, an angular momentum integral (AMI) equation is introduced to quantify these effects by representing them as torques that alter the shape of the mean velocity profile. This approach uniquely isolates the skin friction of a Blasius boundary layer in a single term that depends only on the Reynolds number most relevant to the flow's engineering context, so that other torques are interpreted as augmentations relative to the laminar case having the same Reynolds number. The AMI equation for external flows shares this key property with the so-called FIK relation for internal flows (Fukagata et al., Phys. Fluids, vol. 14, 2002, pp. L73–L76). Without a geometrically imposed boundary layer thickness, the length scale in the Reynolds number for the AMI equation may be chosen freely. After a brief demonstration using Falkner–Skan boundary layers, the AMI equation is applied as a diagnostic tool on four transitional and turbulent boundary layer direct numerical simulation datasets. Regions of negative wall-normal velocity are shown to play a key role in limiting the peak skin friction during the late stages of transition, and the relative strengths of terms in the AMI equation become independent of the transition mechanism a very short distance into the fully turbulent regime. The AMI equation establishes an intuitive, extensible framework for interpreting the impact of turbulence and flow control strategies on boundary layer skin friction.
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