We investigate the control effects of spanwise heterogeneous roughness on shockwave/turbulent boundary-layer interactions (STBLIs) using wall-resolved large-eddy simulations. The roughness extends over the entire computational domain and consists of streamwise-aligned sinusoidal ridges alternating with flat valleys. The baseline case is a Mach 2.0 impinging STBLI flow with a 40^◦ impinging-shock angle, for which we consider incoming turbulent boundary layers at two friction Reynolds numbers, Re_τ ≈ 350 and 1200. Multiple roughness configurations are analysed, which maintain consistent geometric characteristics under either inner or outer scaling. The results show that the rough-wall configurations introduce a moderate increase in mean drag, while substantially modifying the dynamics of the interaction. The wall-pressure fluctuations near the separation-shock foot consist of two components: low-frequency fluctuations associated with large-scale shock excursions and high-frequency fluctuations linked to amplified turbulence. We find that both spectral components can be significantly attenuated by the investigated wall roughness. At low Reynolds number, the attenuation of low- and high-frequency components contributes comparably to the overall reduction. At high Reynolds number, an overall stronger reduction of the pressure fluctuation peak is observed and is mainly attributed to the effective suppression of the low-frequency component. Cross-correlation analyses support downstream mechanisms for the low-frequency dynamics in the current strong interaction regime, where large-scale shock excursions are mainly driven by the breathing of the reverse-flow bubble. Large-scale Görtler-like vortices are identified around the reattachment location in all cases. They appear largely unaffected by roughness geometry and contribute to the flow dynamics over a wide range of frequencies.

The nacelle of aircraft engines is coated with acoustic liners to reduce engine noise emissions. An undesirable side effect of acoustic liners is that they increase aerodynamic drag. For the first time, the authors study this drag penalty through pore-resolved direct numerical simulation (DNS) of a flat-plate zero pressure gradient turbulent boundary layer at friction Reynolds number Re_τ ≈ 850–2600, which is high enough to be representative of liners in operating conditions. In the configuration under scrutiny, the turbulent boundary layer experiences a step change in surface topography passing from a smooth wall to an acoustic liner array, allowing one to study the streamwise adaptation length of the boundary layer. It is found that the mean velocity profile adjusts to the new surface condition in a nearly negligible distance (less than 10 local boundary-layer thicknesses), whereas turbulent fluctuations take much longer. DNS is also performed with external acoustic noise in the form of planar monocromatic waves grazing the boundary layer with an amplitude of 150 dB. In agreement with some earlier studies, it is found that sound waves do not affect aerodynamic drag at these flow conditions.

Exascale High Performance Computing (HPC) represents a tremendous opportunity to push the boundaries of Computational Fluid Dynamics (CFD), but despite the consolidated trend towards the use of Graphics Processing Units (GPUs), programmability is still an issue. STREAmS-2 (Bernardini et al. Comput. Phys. Commun. 285 (2023) 108644) is a compressible solver for canonical wall-bounded turbulent flows capable of harvesting the potential of NVIDIA GPUs. Here we extend the already available CUDA Fortran backend with a novel HIP backend targeting AMD GPU architectures. The main implementation strategies are discussed along with a novel Python tool that can generate the HIP and CPU code versions allowing developers to focus their attention only on the CUDA Fortran backend. Single GPU performance is analyzed focusing on NVIDIA A100 and AMD MI250x cards which are currently at the core of several HPC clusters. The gap between peak GPU performance and STREAmS-2 performance is found to be generally smaller for NVIDIA cards. Roofline analysis allows tracing this behavior to unexpectedly different computational intensities of the same kernel using the two cards. Additional single-GPU comparisons are performed to assess the impact of grid size, number of parallelized loops, thread masking and thread divergence. Parallel performance is measured on the two largest EuroHPC pre-exascale systems, LUMI (AMD GPUs) and Leonardo (NVIDIA GPUs). Strong scalability reveals more than 80% efficiency up to 16 nodes for Leonardo and up to 32 for LUMI. Weak scalability shows an impressive efficiency of over 95% up to the maximum number of nodes tested (256 for LUMI and 512 for Leonardo). This analysis shows that STREAmS-2 is the perfect candidate to fully exploit the power of current pre-exascale HPC systems in Europe, allowing users to simulate flows with over a trillion mesh points, thus reducing the gap between the Reynolds numbers achievable in high-fidelity simulations and those of real engineering applications.

We develop a theoretical framework for predicting friction and heat transfer coefficients in variable-properties forced-air convection, as typical of turbine blade cooling. To do this, we borrow concepts from high-speed wall turbulence, also featuring large temperature and density variations. Using the mean momentum balance and mean thermal balance equations we develop integral transformations that account for the effect of the variable fluid properties, and apply the inverse transformations to calculate the friction and heat transfer coefficients. The proposed theory is validated using a direct numerical simulation dataset spanning both heating and cooling conditions, and the predicted friction and heat transfer coefficients match DNS data with 1–2% accuracy.

We derive explicit formulas for the mean profiles of temperature (modeled as a passive scalar) in forced turbulent convection, as a function of the Reynolds and Prandtl numbers. The derivation leverages on the observed universality of the inner-layer thermal eddy diffusivity with respect to Reynolds and Prandtl number variations and across different flows, and on universality of the passive scalar defect in the core flow. Matching of the inner- and outer-layer expression yields a smooth compound mean temperature profile. We find excellent agreement of the analytical profile with data from direct numerical simulations of pipe and channel flows under various thermal forcing conditions, and over a wide range of Reynolds and Prandtl numbers.

A novel passive flow-control method for shock-wave/turbulent boundary-layer interactions (STBLI) is investigated. The method relies on a structured roughness pattern constituted by streamwise-aligned ridges. Its effectiveness is assessed with wall-resolved large-eddy simulations of the interaction of a Mach 2 turbulent boundary layer flow with an oblique impinging shock with shock angle 40^∘. The structured roughness pattern, which is fully resolved by a cut-cell based immersed boundary method, covers the entire computational domain. Results show that this rough surface induces large-scale secondary streamwise vortices, which energize the boundary layer by transporting high-speed fluid closer to the wall. A parametric study is performed to investigate the effect of the spacing between the ridges. This investigation is further substantiated through spectral analysis and sparsity-promoting dynamic mode decomposition. We find that ridges with small spacing effectively mitigate the low-frequency unsteadiness of STBLI and slightly reduce total-pressure loss.

We investigate the impact of a single miniature Helmholtz resonator on wall-bounded turbulence using time-resolved planar particle image velocimetry. A particular aim is to explain the mechanism by which a resonator alters the turbulent velocity fluctuations of different scales. A grazing flow configuration is studied in which the resonator is embedded in the wall beneath a turbulent boundary layer at a friction Reynolds number of Reτ≈2300; the resonator is designed so that its resonance frequency matches the peak frequency of the wall-pressure spectrum. It is found that the resonator amplifies velocity fluctuations near its resonance frequency, while it attenuates the energy of subresonance scales. Underlying mechanisms responsible for these changes in energy are discussed in view of the resonator's local impedance condition. It is posited that large-scale velocity fluctuations in the wall-normal velocity, at temporal frequencies below resonance, are subject to a phase-opposed wall-normal velocity perturbation when the TBL flow convects over the resonator's orifice. This yields a decrease of large-scale energy in u′u′¯,-u′v′¯, and v′v′¯. In addition, modifications of the wall-shear stress field downstream of the resonator are addressed. Insights from this research will contribute to the development of surface designs for passive skin-friction control using arrays of miniature resonators.

We carry out direct numerical simulations (DNS) of turbulent flow and heat transfer in pressure-driven plane channels, by considering cases with heating on both walls, as well as asymmetric heating limited to one of the channel walls. Friction Reynolds numbers up to are considered, and Prandtl numbers from to, the temperature field being regarded as a passive scalar. Whereas cases with symmetric heating show close similarity between the temperature and the streamwise velocity fields, with turbulent structures confined to either half of the channel, in the presence of one-sided heating the temperature field exhibits larger regions with coherent fluctuations extending beyond the channel centreline. Validity of the logarithmic law for the mean temperature is confirmed, as well as universality of the associated von Kármán constant, which we estimate to be. Deviations from the logarithmic behaviour are much clearer in cases with one-sided heating, which feature a wide outer region with parabolic mean temperature profile. The DNS data are exploited to construct a predictive formula for the heat transfer coefficient as a function of both Reynolds and Prandtl number. We find that the reduction of the thermal efficiency in the one-sided case is approximately at unit Prandtl number; however, it can become much more significant at low Prandtl number.

Microvortex generators are passive control devices smaller than the boundary layer thickness that energise the boundary layer to prevent flow separation with limited induced drag. In this work, we use direct numerical simulations (DNS) to investigate the effect of the Reynolds number in a supersonic turbulent boundary layer over a microramp vortex generator. Three friction Reynolds numbers are considered, up to, for fixed free stream Mach number and fixed relative height of the ramp with respect to the boundary layer thickness. The high-fidelity data set sheds light on the instantaneous and highly three-dimensional organisation of both the wake and the shock waves induced by the microramp. The full access to the flow field provided by DNS allows us to develop a qualitative model of the near wake, explaining the internal convolution of the Kelvin-Helmholtz vortices around the low-momentum region behind the ramp. The overall analysis shows that numerical results agree excellently with recent experimental measurements in similar operating conditions and confirms that microramps effectively induce a significantly fuller boundary layer even far downstream of the ramp. Moreover, results highlight significant Reynolds number effects, which in general do not scale with the ramp height. Increasing Reynolds number leads to enhanced coherence of the typical vortical structures in the field, faster and stronger development of the momentum deficit region, increased upwash between the primary vortices from the sides of the ramp - and thus increased lift-up of the wake - and faster transfer of momentum towards the wall.

The nacelle of aircraft engines is coated with acoustic liners to reduce engine noise. An undesirable effect of these liners is that they increase aerodynamic drag. We study this drag penalty by performing Direct Numerical Simulations of a turbulent boundary layer over an acoustic liner array at friction Reynolds number, Re _τ ≈ 850–2500. We use this simulation to confirm several findings that we recently brought forward using a simpler channel flow setup [1]. We show that acoustic liners lead to high wall-normal velocity fluctuations that can be directly correlated with a modulation of the classical near-wall cycle and to an increase in drag. We also confirm that the acoustic liners act as permeable surface roughness and the non-linear Forchheimer coefficient is the relevant permeability parameter for scaling the drag increase.

This paper is associated with a video winner of a 2022 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion (GFM) Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2022.GFM.V0037

We present pore-resolved compressible direct numerical simulations of turbulent flows grazing over perforated plates, that closely resemble the acoustic liners found on aircraft engines. Our direct numerical simulations explore a large parameter space including the effects of porosity, thickness and viscous-scaled diameter of the perforated plates, at friction Reynolds numbers, which allows us to develop a robust theory for estimating the added drag induced by acoustic liners. We find that acoustic liners can be regarded as porous surfaces with a wall-normal permeability and that the relevant length scale characterizing their added drag is the inverse of the wall-normal Forchheimer coefficient. Unlike other types of porous surfaces featuring Darcian velocities inside the pores, the flow inside the orifices of acoustic liners is fully turbulent, with a magnitude of the wall-normal velocity fluctuations comparable to the peak in the near-wall cycle. We provide clear evidence of a fully rough regime for acoustic liners, also confirmed by the increasing relevance of pressure drag. Once the fully rough asymptote is reached, canonical acoustic liners provide an added drag comparable to that of sand-grain roughness with viscous-scaled height matching the inverse of the viscous-scaled Forchheimer permeability of the plate.

We study turbulent flow in open channels with a free surface and rectangular cross-section, for various Reynolds numbers and duct aspect ratios. Direct numerical simulations are used to obtain accurate characterization of the secondary motions, which are found to be more intense than in closed ducts, and to scale with the bulk, rather than with the friction velocity. A notable feature of open-duct flows is the presence of a velocity dip, namely the peak velocity is achieved at some depth underneath the free surface. We find that the depth of the velocity peak increases with the Reynolds number, and correspondingly the flow becomes more symmetric with respect to the horizontal midplane. This is also confirmed from the change of the topology of the secondary motions, which exhibit a strong corner circulation at the free-surface/wall corners at low Reynolds number, which, however, weakens at higher. The structure of the mean velocity field is such that the log law applies with good approximation in the direction normal to the nearest wall, which allows us to explain why predictive friction formulae based on the hydraulic diameter concept are successful. Additional analysis shows that the secondary motions account for a large fraction of the frictional drag (up to %).

We carry out direct numerical simulation (DNS) of forced thermal convection in one-sided heated square ducts and compare the global heat transfer to the idealized case of uniformly heated walls, and also to the case of plane channel flow with one-sided heating. DNS results reveal a reduction of global heat transfer of about 10% at unit Prandtl number and friction Reynolds number Re_τ ≈ 2000, which is consistent with the values reported in early experiments. The global heat transfer of square ducts matches very well the one of plane channel flow with the same boundary conditions, at matched bulk Reynolds number based on the effective diameter.

We present STREAmS-2.0, an updated version of the flow solver STREAmS, first introduced in Bernardini et al. (2021) [1]. STREAmS-2.0 has an object-oriented design which separates the physics equations from the specific back-end, making the code more suitable for future expansions, such as porting to novel computing architectures or implementation of additional flow physics. Similarly to the previous version, STREAmS-2.0 supports NVIDIA-GPU and CPU back-ends. Additionally, this version features improvements of the input/output data management, new energy and entropy preserving schemes for the discretization of the convective fluxes, recycling/rescaling inflow boundary condition, and a model for thermally perfect gases with variable specific heats. New version program summary: Program Title: STREAmS CPC Library link to program files: https://doi.org/10.17632/hdcgjpzr3y.2 Developer's repository link: https://github.com/STREAmS-CFD/STREAmS-2 Licensing provisions: GPLv3 Programming language: Fortran, CUDA Journal reference of previous version: M. Bernardini, D. Modesti, F. Salvadore, and S. Pirozzoli. STREAmS: a high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows. Comput. Phys. Commun. 263 (2021) 107906. Does the new version supersede the previous version?: Yes. Reasons for the new version: New code structure and release of new features. Summary of revisions: • The original solver [1] has been rewritten following an object-oriented design implemented through Fortran derived types that include variables and type bound procedures. The new software architecture has been designed to increase modularity and extensibility of the code, allowing users to add new back-ends and physics equations while maintaining the same code structure. This allows users to reuse portions of the code that are independent of the physics equations, the back-end, or both. The layer of computing procedures maintains a lean structure that can be highly optimized with respect to the implemented back-end. • Input handling is now based on the classic.ini format improving both user readability and input data management. • A family of new kinetic energy and entropy preserving schemes (KEEP) are now available and can be selected for stable, non-dissipative and accurate spatial discretization of the convective terms of the Navier–Stokes equations in smooth flow regions [2]. Concerning the shock-capturing flux, the improved low-dissipative WENO-Z scheme proposed by [3] is now available. • New inflow boundary conditions based on the recycling/rescale approach [4] have been implemented for the simulation of spatially evolving compressible turbulent boundary layers. Moreover, a new inflow condition based on the solution of the compressible Blasius equation is available to take into account the case of laminar boundary layers. • The constitutive relations have been generalized to take into account thermally perfect gases with variable specific heats, approximated with polynomial functions of the temperature that can be specified by the user [5]. • A new stretching function has been implemented to improve the distribution of grid nodes for the computation of wall-bounded turbulent flows. The formulation blends uniform near-wall spacing with uniform resolution in terms of Kolmogorov units in the outer wall layer, guaranteeing accuracy with higher computational efficiency [6]. Nature of problem: The code solves the compressible Navier–Stokes equations in Cartesian coordinates for a thermally perfect gas. The solver is designed for direct numerical simulation (DNS) of compressible supersonic turbulent boundary layers and various canonical configurations are supported, including turbulent channel flow, laminar and turbulent boundary layer and shock-wave/boundary layer interaction. Solution method: The equations are discretized using high-order finite difference approximations with hybrid low-dissipative/shock-capturing capabilities and the time advancement is performed using a Runge–Kutta scheme. References: [1] M. Bernardini, D. Modesti, F. Salvadore, S. Pirozzoli, STREAmS: A high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows, Comput. Phys. Commun. 263 (2021) 107906. [2] Y. Tamaki, Y. Kuya, S. Kawai, Comprehensive analysis of entropy conservation property of non-dissipative schemes for compressible flows: KEEP scheme redefined, J. Comput. Phys. 468 (2022) 111494. [3] R. Borges, M. Carmona, B. Costa, W. Don, An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys. 227 (6) (2008) 3191–3211, https://doi.org/10.1016/j.jcp.2007.11.038 [4] S. Pirozzoli, M. Bernardini, F. Grasso, Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation, J. Fluid Mech. 657 (2010) 361–393. [5] B. J. McBride, M. J. Zehe, S. Gordon, NASA Glenn coefficients for calculating thermodynamic properties of individual species, NASA/TP 211556, NASA, 2002. [6] S. Pirozzoli, P. Orlandi, Natural grid stretching for DNS of wall-bounded flows, J. Comput. Phys. 439 (2021) 110408.

We carry out direct numerical simulation (DNS) of flow in a turbulent square duct by focusing on heat transfer effects, considering the case of unit Prandtl number. Reynolds numbers up to Re_τ ≈ 2000 are considered which are much higher than in previous studies, and which yield clear scale separation between inner- and outer-layer dynamics. Close similarity between the behavior of the temperature and the streamwise velocity fields is confirmed as in previous studies related to plane channels and pipes. We find good agreement between the Nusselt number of square duct and circular pipe flow when the Reynolds number based on the hydraulic diameter is used, thus corroborating the common engineering practice. Popular engineering correlations for the heat transfer reveal deviations up to 5% with respect to DNS data, which are nicely fitted by a power law.

We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers -, both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature-velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating.

We perform direct numerical simulations of turbulent flow at friction Reynolds number Re_τ≈ 500 - 2000 grazing over perforates plates with moderate viscous-scaled orifice diameter d⁺≈ 40 - 160 and analyse the relation between permeability and added drag. Unlike previous studies of turbulent flows over permeable surfaces, we find that the flow inside the orifices is dominated by inertial effects, and that the relevant permeability is the Forchheimer and not the Darcy one. We find evidence of a fully rough regime where the relevant length scale is the inverse of the Forchheimer coefficient, which can be regarded as the resistance experienced by the wall-normal flow. Moreover, we show that, for low porosities, the Forchheimer coefficient can be estimated with good accuracy using a simple analytical relation.