arXiv subjects

Sergio Pirozzoli

Publications and source records attributed to Sergio Pirozzoli.

At least 37 records · Page 2Linked to original sources

arXiv2023

Estimating mean profiles and fluxes in high-speed turbulent boundary layers using inner/outer-layer transformations

Accurately predicting drag and heat transfer for compressible high-speed flows is of utmost importance for a range of engineering applications. This requires the precise knowledge of the entire velocity and temperature profiles. A common approach is to use compressible velocity scaling laws (transformation), that inverse transform the velocity profile of an incompressible flow, together with a temperature-velocity relation. In this Note, we use distinct velocity transformations for the inner and outer layers. In the inner layer, we utilize a recently proposed scaling law that appropriately incorporates variable property and intrinsic compressibility effects, while the outer layer profile is inverse-transformed with the well-known Van Driest transformation. The result is an analytical expression for the mean shear valid in the entire boundary layer, which combined with a temperature-velocity relationship, provides predictions of mean velocity and temperature profiles at unprecedented accuracy. Using these profiles, drag and heat transfer is evaluated with an accuracy of +/-4% and +/-8%, respectively, for a wide range of compressible turbulent boundary layers up to Mach numbers of 14.

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arXiv2023

High-speed turbulent flows towards the exascale: STREAmS-2 porting and performance

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 HIPFort backend targeting AMD GPU architectures. The main implementation strategies are discussed along with a novel Python tool that can generate the HIPFort and CPU code versions allowing developers to focus their attention only on the CUDA Fortran backend. Single GPU performance is analysed 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. 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.

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arXiv2022

Drag reduction on a transonic airfoil

Flow control for turbulent skin-friction drag reduction is applied to a transonic airfoil to improve its aerodynamic performance. The study is based on direct numerical simulations (with up to 1.8 billions cells) of the compressible turbulent flow around a supercritical airfoil, at Reynolds and Mach numbers of $Re_\infty= 3 \times 10^5$ and $M_\infty =0.7$. Control via spanwise forcing is applied over a fraction of the suction side of the airfoil. Besides locally reducing friction, the control modifies the shock wave and significantly improves the aerodynamic efficiency of the airfoil by increasing lift and decreasing drag. Hence, the airfoil can achieve the required lift at a lower angle of attack and with a lower drag. Estimates at the aircraft level indicate that substantial savings are possible; when control is active, its energy cost becomes negligible thanks to the small application area. We suggest that skin-friction drag reduction should be considered not only as a goal, but also as a tool to improve the global aerodynamics of complex flows.

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arXiv2022

Direct numerical simulation of forced thermal convection in square ducts up to $Re_τ\approx 2000$

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 $Re_τ\approx 2000$ 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. Just like the mean velocity, the mean temperature is found to exhibit logarithmic layers as a function of the nearest wall, however with a different slope. The most important practical implication is the validity of the traditional hydraulic diameter as the correct reference length for reporting heat transfer data, as we rigorously show here. Temperature and velocity fluctuations also have similar behavior, but apparently logarithmic growth of their inner-scaled peak variances is not observed here unlike in canonical wall-bounded flows. Analysis of the split contributions to the heat transfer coefficient shows that mean cross-stream convection associated with secondary motions is responsible for about $5\%$ of the total. Finally, we use the DNS database to highlight shortcomings of traditional linear closures for the turbulent heat flux, and show that substantial modeling improvement may be in principle obtained by retaining at least the three terms in the vector polynomial integrity basis expansion.

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arXiv2021

One-point statistics for turbulent pipe flow up to $Re_τ \approx 6000$

We study turbulent flows in a smooth straight pipe of circular cross--section up to $Re_τ \approx 6000$ using direct--numerical-simulation (DNS) of the Navier--Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to about $2\%$, which would extrapolate to about $4\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$, which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centerline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at $Re_τ \gtrsim 10^4$, as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

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arXiv2021

Natural grid stretching for DNS of wall-bounded flows

We propose a natural stretching function for DNS of wall-bounded flows, which blends uniform near-wall spacing with uniform resolution in terms of Kolmogorov units in the outer wall layer. Numerical simulations of pipe flow are used to educe optimal value of the blending parameter and of the wall grid spacing which guarantee accuracy and computational efficiency as a results of maximization of the allowed time step. Conclusions are supported by DNS carried out at sufficiently high Reynolds number that a near logarithmic layer is the mean velocity profile is present. Given a target Reynolds number, we provide a definite prescription for the number of grid points and grid clustering needed to achieve accurate results with optimal exploitation of resources.

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arXiv2021

Scaling turbulence in the near-wall region

A new velocity scale is derived that yields a Reynolds number independent profile for the streamwise turbulent fluctuations in the near-wall region of wall bounded flows for $y^+<25$. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence distribution.

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arXiv2020

STREAmS: a high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flow

We present STREAmS, an in-house high-fidelity solver for large-scale, massively parallel direct numerical simulations (DNS) of compressible turbulent flows on graphical processing units (GPUs). STREAmS is written in the Fortran 90 language and it is tailored to carry out DNS of canonical compressible wall-bounded flows, namely turbulent plane channel, zero-pressure gradient turbulent boundary layer and supersonic oblique shock-wave/boundary layer interactions. The solver incorporates state-of-the-art numerical algorithms, specifically designed to cope with the challenging problems associated with the solution of high-speed turbulent flows and can be used across a wide range of Mach numbers, extending from the low subsonic up to the hypersonic regime. The use of cuf automatic kernels allowed an easy and efficient porting on the GPU architecture minimizing the changes to the original CPU code, which is also maintained. We discuss a memory allocation strategy based on duplicated arrays for host and device which carefully minimizes the memory usage making the solver suitable for large scale computations on the latest GPU cards. Comparison between different CPUs and GPUs architectures strongly favor the latter, and executing the solver on a single NVIDIA Tesla P100 corresponds to using approximately 330 Intel Knights Landing CPU cores. STREAmS shows very good strong scalability and essentially ideal weak scalability up to 2048 GPUs, paving the way to simulations in the genuine high-Reynolds number regime, possibly at friction Reynolds number $Re_τ > 10^4$. The solver is released open source under GPLv3 license and is available at https://github.com/matteobernardini/STREAmS.

physics.comp-ph↗

arXiv2019

DNS of transitional and turbulent flows in rectangular ducts

We carry out Direct Numerical Simulation (DNS) of flows in closed rectangular ducts with several aspect ratios. The Navier-Stokes equations are discretized through a second-order finite difference scheme, with non-uniform grids in two directions. The duct cross-sectional area is maintained constant as well as the flow rate, which allows to investigate which is the appropriate length scale in the Reynolds number for a good scaling in the laminar and in the fully turbulent regimes. We find that the Reynolds number based on the half length of the short side leads to a critical Reynolds number which is independent on the aspect ratio (AR), for ducts with AR>1. The mean and rms wall-normal velocity profiles are found to scale with the local value of the friction velocity. At high friction Reynolds numbers, the Reynolds number dependence is similar to that in turbulent plane channels, hence flows in rectangular ducts allow to investigate the Reynolds number dependency through a reduced number of simulations. At low Re the profiles of the statistics differ from those in the two-dimensional channel due to the interaction of flow structures of different size. The projection of the velocity vector and of the Reynolds stress tensor along the eigenvectors of the strain-rate tensor yields reduced Reynolds stress anisotropy, and simple turbulent kinetic energy budgets.

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arXiv2019

On algebraic TVD-VOF methods for tracking material interfaces

We revisit simple algebraic VOF methods for advection of material interfaces based of the well established TVD paradigm. We show that greatly improved representation of contact discontinuities is obtained through use of a novel CFL-dependent limiter whereby the classical TVD bounds are exceeded. Perfectly crisp numerical interfaces are obtained with very limited numerical atomization (flotsam and jetsam) as compared to previous SLIC schemes. Comparison of the algorithm with accurate geometrical VOF shows larger error at given mesh resolution, but comparable efficiency when the reduced computational cost is accounted for.

physics.comp-ph↗

arXiv2018

Direct numerical simulation of supersonic pipe flow at moderate Reynolds number

We study compressible turbulent flow in a circular pipe, at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies.Regarding velocity statistics, we find that Huang's transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny ($\Rey_τ \approx 1000$), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et Al.(2014). The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear.

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arXiv2018

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

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 $Re_θ\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $θ_c = 25^\circ$. 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 behavior is strongly affected by the imposed pressure gradient, with streaks which are locally suppressed in adverse pressure gradient (APG) zones, and which suddenly reform in the downstream region with favourable pressure gradient (FPG). Three-dimensional mean flow separation is only observed in the first APG region associated with 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 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 isotropic state in APG regions, and to a two-component anisotropic state in FPG.

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arXiv2018

Direct numerical simulation of developed compressible flow in square ducts

We carry out direct numerical simulation of compressible square duct flow in the range of bulk Mach numbers M_b = 0.2-3, and up to friction Reynolds number Re_τ = 500. The effects of flow compressibility on the secondary motions are found to be negligible, as the typical Mach number associated with the cross-stream flow is always less than 0.1. As in the incompressible case, we find that the wall law for the mean streamwise velocity applies with good approximation with respect to the nearest wall, upon suitable compressibility transformation. The same conclusion also applies to a passive scalar field, whereas the mean temperature does not exhibit inertial layers because of nonuniformity of the aerodynamic heating. We further find that the same temperature/velocity relation that holds for planar channels is applicable with good approximation for square ducts, and develop a similar relation between temperature and passive scalars.

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arXiv2018

Numerically stable formulations of convective terms for turbulent compressible flows

A systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the compressible Navier-Stokes equations is reported. A general triple splitting of the nonlinear convective terms is considered, and energy-preserving formulations are fully characterized by deriving a two-parameter family of split forms. Previously developed formulations reported in literature are shown to be particular members of this family; novel splittings are introduced and discussed as well. Furthermore, the conservation properties yielded by different choices for the energy equation (i.e. total and internal energy, entropy) are analyzed thoroughly. It is shown that additional preserved quantities can be obtained through a suitable adaptive selection of the split form within the derived family. Local conservation of primary invariants, which is a fundamental property to build high-fidelity shock-capturing methods, is also discussed in the paper. Numerical tests performed for the Taylor-Green Vortex at zero viscosity fully confirm the theoretical findings, and show that a careful choice of both the splitting and the energy formulation can provide remarkably robust and accurate results.

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arXiv2018

On turbulent friction in straight ducts with complex cross section: the wall law and the hydraulic diameter

We develop predictive formulas for friction resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress nonuniformities. The traditional hydraulic diameter naturally emerges from the analysis as the controlling length scale for common duct shapes as triangles and regular polygons. The analysis also suggests that a new effective diameter should be used in more general cases, yielding corrections of a few percent to friction estimates based on the traditional hydraulic diameter. Fair but consistent predictive improvement is shown for duct geometries of practical relevance, including rectangular and annular ducts, and circular rod bundles.

physics.flu-dyn↗

arXiv2018

On the role of secondary motions in turbulent square duct flow

We use a direct numerical simulations (DNS) database for turbulent flow in a square duct up to bulk Reynolds number $\Rey_b=40000$, to quantitatively analyze the role of secondary motions on the mean flow structure. For that purpose we derive a generalized form of the identity of Fukagata, Iwamoto and Kasagi (FIK), which allows to quantify the effect of cross-stream convection on the mean streamwise velocity, wall shear stress and bulk friction coefficient. Secondary motions are found to contribute for about $6\%$ of total friction, and to act as a self-regulating mechanism of turbulence whereby wall shear stress nonuniformities induced by corners are equalized, and universality of the wall-normal velocity profiles is established. We also carry out numerical experiments whereby the secondary motions are artificially suppressed, in which case their equalizing role is partially taken by the turbulent stresses.

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arXiv2017

Transitional natural convection with conjugate heat transfer over smooth and rough walls

We study turbulent natural convection in enclosures with conjugate heat transfer. The simplest way to increase the heat transfer in this flow is through rough surfaces. In numerical simulations often the constant temperature is assigned at the walls in contact with the fluid, which is unrealistic in laboratory experiments. The DNS (Direct Numerical Simulation), to be of help to experimentalists, should consider the heat conduction in the solid walls together with the turbulent flow between the hot and the cold walls. Here the cold wall, $0.5h$ thick (where $h$ is the channel half-height) is smooth, and the hot wall has two- and three-dimensional elements of thickness $0.2h$ above a solid layer $0.3h$ thick. The independence of the results on the box size has been verified. A bi-periodic domain $4h$ wide allows to have a sufficient resolution with a limited number of grid points. It has been found that, among the different kind of surfaces at a Rayleigh number $Ra \approx 2 \cdot 10^6$, the one with staggered wedges has the highest heat transfer. A large number of simulations varying the $Ra$ from $10^3$ to $10^7$ were performed to find the different ranges of the Nusselt number ($Nu$) relationship as a function of $Ra$. Flow visualizations allow to explain the differences in the $Nu(Ra)$ relationship. Two values of the thermal conductivity were chosen, one corresponding to copper and the other ten times higher. It has been found that the Nusselt number behaves as $Nu=αRa^γ$, with $α$ and $γ$ independent on the solid conductivity, and dependent on the roughness shape.

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arXiv2016

A high-fidelity solver for turbulent compressible flows on unstructured meshes

We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of the convective terms in the Navier-Stokes equations relies on a robust energy-preserving numerical flux, and numerical diffusion inherited from the AUSM scheme is added limited to the vicinity of shock waves, or wherever spurious numerical oscillations are sensed. The solver is capable of conserving the total kinetic energy in the inviscid limit, and it bears sensibly less numerical diffusion than typical industrial solvers, with incurred greater predictive power, as demonstrated through a series of test cases including DNS, LES and URANS of turbulent flows. Simplicity of implementation in existing popular solvers such as OpenFOAM is also highlighted.

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