Numerical tripping of high-speed turbulent boundary layers

Abstract

The influence of turbulence inflow generation on direct numerical simulations (DNS) of high-speed turbulent boundary layers at Mach numbers of 2 and 5.84 is investigated. Two main classes of inflow conditions are considered, based on the recycling/rescaling (RR) and the digital filtering (DF) approach, along with suitably modified versions. A series of DNS using very long streamwise domains is first carried out to provide reliable data for the subsequent investigation. A set of diagnostic parameters is then selected to verify achievement of an equilibrium state, and correlation laws for those quantities are obtained based on benchmark cases. Simulations using shorter domains, with extent comparable with that used in the current literature, are then carried out and compared with the benchmark data. Significant deviations from equilibrium conditions are found, to a different extent for the various flow properties, and depending on the inflow turbulence seeding. We find that the RR method yields superior performance in the evaluation of the inner-scaled wall pressure fluctuations and the turbulent shear stress. DF methods instead yield quicker adjustment and better accuracy in the prediction of wall friction and of the streamwise Reynolds stress in supersonic cases. Unrealistically high values of the wall pressure variance are obtained by the baseline DF method, while the proposed DF alternatives recover a closer agreement with respect to the benchmark. The hypersonic test case highlights that similar distribution of wall friction and heat transfer are obtained by both RR and DF baseline methods. Graphical abstract

Compressibility effects in supersonic and hypersonic turbulent boundary layers subject to wall disturbances

“…After a preliminary examination, we found that the turbulence reaches a quasi-equilibrium state that is free from the synthetic turbulent inlet downstream of x ≈ 60δ in , where the growth rate of the boundary layer thickness and the shape factors retain approximately constant values (Lee, Sung & Krogstad 2011). Ceci et al (2022) found that it takes a streamwise extent of (10 ∼ 25)δ in for supersonic and (55 ∼ 75)δ in for hypersonic turbulent boundary layers to achieve the mean momentum balance with the synthetic turbulent inlet. Therefore, from hereon in, we only choose the subdomain of interest within the streamwise region x = (70 ∼ 90)δ in for the cases at M ∞ = 2 and x = (100 ∼ 120)δ in for cases at M ∞ = 4 and 6, a region sufficiently away from the synthetic turbulent inlet and the outlet to reduce the possibly existing numerical errors that contaminate the results.…”

“…Ceci et al. (2022) found that it takes a streamwise extent of for supersonic and for hypersonic turbulent boundary layers to achieve the mean momentum balance with the synthetic turbulent inlet. Therefore, from hereon in, we only choose the subdomain of interest within the streamwise region for the cases at and for cases at and , a region sufficiently away from the synthetic turbulent inlet and the outlet to reduce the possibly existing numerical errors that contaminate the results.…”

On low-frequency unsteadiness in swept shock wave–boundary layer interactions

“…The recycling–rescaling procedure is used to generate the target flow at the inflow, as described by Ceci et al. (2022). The impinging shock is generated through local enforcement of the Rankine–Hugoniot jump relations at the top boundary, and periodic boundary conditions are applied to the spanwise boundaries.…”

“…Numerical boundary conditions at the far-field boundaries are managed according to a characteristic relaxation strategy (Pirozzoli & Colonius 2013). The recycling-rescaling procedure is used to generate the target flow at the inflow, as described by Ceci et al (2022). The impinging shock is generated through local enforcement of the Rankine-Hugoniot jump relations at the top boundary, and periodic boundary conditions are applied to the spanwise boundaries.…”

On the generation of near-wall dilatational motions in hypersonic turbulent boundary layers

“…Hypersonic turbulent boundary layers have become a topic of great interest amongst researchers in the fluid dynamics community due to their significant engineering applications (Gatski & Bonnet 2013;Theofilis, Pirozzoli & Martin 2022). With the aid of advanced experimental equipment and apparatus, and powerful computational resources, abundant databases have been established for the purpose of accurate predictions of the aerodynamic performance of high-speed vehicles (Roy & Blottner 2006;Tichenor, Humble & Bowersox 2013;Williams et al 2018;Ceci et al 2022;Huang, Duan & Choudhari 2022). Compared with incompressible flows, a crucial aspect that complicates the modelling and prediction of hypersonic turbulence is the compressibility effects (Smits & Dussauge 2006;Duan, Beekman & Martin 2010, 2011, encompassing the influences caused by the variation of mean fluid properties (density and viscosity, for instance) due to aerodynamic heating, and the fluctuations of density and velocity divergence related to compression and expansion of the fluid elements (Gatski & Bonnet 2013).…”