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  • 1.
    Atzori, Marco
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Köpp, Wiebke
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Chien, Wei Der
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Mallor, Fermin
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Rezaei, Mohamad
    PDC Center for High Performance Computing, KTH Royal Institute of Technology.
    Jansson, Niclas
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Markidis, Stefano
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Laure, Erwin
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Weinkauf, Tino
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    In-situ visualization of large-scale turbulence simulations in Nek5000 with ParaView Catalyst2021Report (Other academic)
    Abstract [en]

    In-situ visualization on HPC systems allows us to analyze simulation results that would otherwise be impossible, given the size of the simulation data sets and offline post-processing execution time. We design and develop in-situ visualization with Paraview Catalyst in Nek5000, a massively parallel Fortran and C code for computational fluid dynamics applications. We perform strong scalability tests up to 2,048 cores on KTH's Beskow Cray XC40 supercomputer and assess in-situ visualization's impact on the Nek5000 performance. In our study case, a high-fidelity simulation of turbulent flow, we observe that in-situ operations significantly limit the strong scalability of the code, reducing the relative parallel efficiency to only ~21\% on 2,048 cores (the relative efficiency of Nek5000 without in-situ operations is ~99\%). Through profiling with Arm MAP, we identified a bottleneck in the image composition step (that uses Radix-kr algorithm) where a majority of the time is spent on MPI communication. We also identified an imbalance of in-situ processing time between rank 0 and all other ranks. Better scaling and load-balancing in the parallel image composition would considerably improve the performance and scalability of Nek5000 with in-situ capabilities in large-scale simulation.

  • 2.
    Atzori, Marco
    et al.
    KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Köpp, Wiebke
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Chien, Wei Der
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS. KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Mallor, Fermin
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Rezaei, Mohammadtaghi
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for High Performance Computing, PDC.
    Jansson, Niclas
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Markidis, Stefano
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Vinuesa, Ricardo
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Laure, E.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Weinkauf, Tino
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    In situ visualization of large-scale turbulence simulations in Nek5000 with ParaView Catalyst2022In: Journal of Supercomputing, ISSN 0920-8542, E-ISSN 1573-0484, Vol. 78, no 3, p. 3605-3620Article in journal (Refereed)
    Abstract [en]

    In situ visualization on high-performance computing systems allows us to analyze simulation results that would otherwise be impossible, given the size of the simulation data sets and offline post-processing execution time. We develop an in situ adaptor for Paraview Catalyst and Nek5000, a massively parallel Fortran and C code for computational fluid dynamics. We perform a strong scalability test up to 2048 cores on KTH’s Beskow Cray XC40 supercomputer and assess in situ visualization’s impact on the Nek5000 performance. In our study case, a high-fidelity simulation of turbulent flow, we observe that in situ operations significantly limit the strong scalability of the code, reducing the relative parallel efficiency to only ≈ 21 % on 2048 cores (the relative efficiency of Nek5000 without in situ operations is ≈ 99 %). Through profiling with Arm MAP, we identified a bottleneck in the image composition step (that uses the Radix-kr algorithm) where a majority of the time is spent on MPI communication. We also identified an imbalance of in situ processing time between rank 0 and all other ranks. In our case, better scaling and load-balancing in the parallel image composition would considerably improve the performance of Nek5000 with in situ capabilities. In general, the result of this study highlights the technical challenges posed by the integration of high-performance simulation codes and data-analysis libraries and their practical use in complex cases, even when efficient algorithms already exist for a certain application scenario.

  • 3.
    Coelho Leite Fava, Thales
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Fluid Physics.
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Fluid Physics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Fluid Physics.
    Henningson, Dan S.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Fluid Physics.
    Hanifi, Ardeshir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Fluid Physics.
    Transition to turbulence on a rotating wind turbine blade at 𝑅𝑒𝑐 = 3 x 105Manuscript (preprint) (Other academic)
    Abstract [en]

    The stability of the boundary layer over a section of a rotating wind turbine blade at Rec = 300,000 is studied with direct numerical simulations and linear stability analyses.The results indicate that the transition location is not significantly affected by rotation in the outboard region of the blade for low rotation numbers Roc = Ω𝑐/𝑈. The relative insensitivity to rotation is due to a laminar separation bubble (LSB) near the leading edge, significantly spanwise-deformed by a primary self-excited instability, leading to the secondary absolute instability of the Kelvin-Helmholtz (KH) vortices and rapid transition. Moderate increases in the rotation rates and moving towards lower radii promote a stabilising effect due to the counteraction of the adverse pressure gradient (APG) in the attached flow region. This leads to the downstream displacement of theseparation point. Furthermore, competition with crossflow modes may also reduce the growth rates of KH waves. Higher increases in the rotation rate lead to a temporary transition delay in the blade inboard region. Nevertheless, stationary and travelling crossflow modes are triggered, spanwise modulating the KH rolls in the LSB and shifting the transition to the leading edge. Crossflow velocities as high as 50% of the free-stream velocity directed towards the blade tip are reached at the transition location. Considering a lower rotation number based on the radius 𝑅𝑜𝑟 = Ω𝑟/𝑈, crossflow transition is also triggered inside the LSB. However, due to the stabilisation of the attached flow by rotation, the transition point is more downstream than the non-rotating case.

  • 4.
    Karp, Martin
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST). Division of Computational Science and Technology, EECS, KTH Royal Institute of Technology, Stockholm, Sweden.
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. SimEx/FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden.
    Jansson, Niclas
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for High Performance Computing, PDC. PDC Centre for High Performance Computing, EECS, KTH Royal Institute of Technology, Stockholm, Sweden.
    Hart, Alistair
    Hewlett Packard Enterpise (HPE), UK.
    Wahlgren, Jacob
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST). Division of Computational Science and Technology, EECS, KTH Royal Institute of Technology, Stockholm, Sweden.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. SimEx/FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden.
    Markidis, Stefano
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST). Division of Computational Science and Technology, EECS, KTH Royal Institute of Technology, Stockholm, Sweden.
    Large-scale direct numerical simulations of turbulence using GPUs and modern Fortran2023In: The international journal of high performance computing applications, ISSN 1094-3420, E-ISSN 1741-2846Article in journal (Refereed)
    Abstract [en]

    We present our approach to making direct numerical simulations of turbulence with applications in sustainable shipping. We use modern Fortran and the spectral element method to leverage and scale on supercomputers powered by the Nvidia A100 and the recent AMD Instinct MI250X GPUs, while still providing support for user software developed in Fortran. We demonstrate the efficiency of our approach by performing the world’s first direct numerical simulation of the flow around a Flettner rotor at Re = 30,000 and its interaction with a turbulent boundary layer. We present a performance comparison between the AMD Instinct MI250X and Nvidia A100 GPUs for scalable computational fluid dynamics. Our results show that one MI250X offers performance on par with two A100 GPUs and has a similar power efficiency based on readings from on-chip energy sensors.

  • 5.
    Lupi, Valerio
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Institute of Fluid Mechanics (LSTM), Friedrich--Alexander--Universität (FAU) Erlangen--Nürnberg, Erlangen 91058, Germany.
    Swirl switching in spatially developing bent pipesManuscript (preprint) (Other academic)
  • 6.
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Space-adaptive simulation of transition and turbulence in shear flows2024Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Transitional and turbulent shear flows are ubiquitous, from the boundary layer developing on an aeroplane wing to the flow within the aortic arch. In this thesis, we study wall-bounded and free shear flows through direct numerical simulations. To control numerical errors and represent every flow structure, we implement the adaptive mesh refinement (AMR) technique within a spectral element method code. Using data-driven methods and causality metrics, we explore the fundamental physical mechanisms in various shear flows.

    The adaptive mesh refinement technique necessitates a precise evaluation of the committed error. Thus, we compare the local spectral error indicator with the dual-weighted adjoint error estimator. The former ensures a more homogeneous refinement, targeting regions with a high-velocity gradient, while the latter is goal-oriented. However, the adjoint error estimator fails in turbulent flows due to the exponential sensitivity of the adjoint linear solution to any perturbation. Alternatively, we introduce a causality-based error indicator that employs the Shannon transfer entropy, i.e. a causality metric arising from information theory, to establish causal relations between the local solution and a specified quantity of interest.

    Using information-theoretic causality, linear global stability analysis and modal decomposition, we investigate transitional and turbulent coherent structures. In turbulent straight pipe flows, the proper orthogonal decomposition is integrated with the Voronoi diagram to automatically discern between wall-attached and detached eddies. In spatially developing bent pipe flows, we employ the proper orthogonal decomposition to examine the swirl switching phenomenon, the origins of which continue to be a topic of debate. In the context of external flows around a cylinder, we explore two configurations: the Flettner rotor, a rotating cylinder in a wall-bounded shear flow, and the stepped cylinder, namely two cylinders of different diameters joined at one extremity. In the first configuration, we analyse the large-scale motion at the base of the rotor and the local vortex shedding suppression. In the second, we provide an in-depth look at structures arising on the junction surface and in the wake. Additionally, we conduct a global stability analysis with a novel AMR-based approach for some of the aforementioned cases.

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  • 7.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Karp, Martin
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Jansson, Niclas
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, Centre for High Performance Computing, PDC.
    Markidis, Stefano
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Computational Science and Technology (CST).
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. Institute of Fluid Mechanics (LSTM), Friedrich--Alexander--Universität (FAU) Erlangen--Nürnberg, Erlangen 91058, Germany.
    Direct numerical simulation of the turbulent flow around a Flettner rotor2024In: Scientific Reports, E-ISSN 2045-2322, Vol. 14, no 1, article id 3004Article in journal (Refereed)
    Abstract [en]

    The three-dimensional turbulent flow around a Flettner rotor, i.e. an engine-driven rotating cylinder in an atmospheric boundary layer, is studied via direct numerical simulations (DNS) for three different rotation speeds (α). This technology offers a sustainable alternative mainly for marine propulsion, underscoring the critical importance of comprehending the characteristics of such flow. In this study, we evaluate the aerodynamic loads produced by the rotor of height h, with a specific focus on the changes in lift and drag force along the vertical axis of the cylinder. Correspondingly, we observe that vortex shedding is inhibited at the highest α values investigated. However, in the case of intermediate α, vortices continue to be shed in the upper section of the cylinder (y/h>0.3). As the cylinder begins to rotate, a large-scale motion becomes apparent on the high-pressure side, close to the bottom wall. We offer both a qualitative and quantitative description of this motion, outlining its impact on the wake deflection. This finding is significant as it influences the rotor wake to an extent of approximately one hundred diameters downstream. In practical applications, this phenomenon could influence the performance of subsequent boats and have an impact on the cylinder drag, affecting its fuel consumption. This fundamental study, which investigates a limited yet significant (for DNS) Reynolds number and explores various spinning ratios, provides valuable insights into the complex flow around a Flettner rotor. The simulations were performed using a modern GPU-based spectral element method, leveraging the power of modern supercomputers towards fundamental engineering problems.

  • 8.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Lupi, Valerio
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Institute of Fluid Mechanics (LSTM), Friedrich--Alexander--Universität (FAU) Erlangen--Nürnberg, Erlangen 91058, Germany.
    Adaptive mesh refinement for global stability analysis of transitional flowsManuscript (preprint) (Other academic)
  • 9.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lupi, Valerio
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. Institute of Fluid Mechanics (LSTM), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91058, Germany.
    Global stability of 180-bend pipe flow with mesh adaptivity2023In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 8, no 11, article id 113903Article in journal (Refereed)
    Abstract [en]

    The global stability of the flow in a spatially developing 180∘-bend pipe with curvature δ=R/Rc=1/3 is investigated by performing direct numerical simulations to understand the underlying transitional mechanism. A unique application of the adaptive mesh refinement technique is used during the stability analysis for minimizing the interpolation and quadrature errors. Independent meshes are created for the direct and adjoint solutions, as well as for the base flow extracted via selective frequency damping. The spectrum of the linearized Navier-Stokes operator reveals a pair of complex conjugate eigenvalues, with frequency f≈0.233. Therefore, the transition is attributed to a Hopf bifurcation that takes place at Reb,cr=2528. A structural sensitivity analysis is performed by extracting the wavemaker. We identify the primary source of instability located on the outer wall, θ≈15 downstream of the bend inlet. This region corresponds to the separation bubble on the outer wall. We thus conclude that the instability is caused by the strong shear resulting from the backflow, similar to the 90-bend pipe flow. We believe that understanding the stability mechanism and characterizing the base flow in bent pipes is crucial for studying various biological flows, like blood vessels. Hence, this paper aims to close the knowledge gap between a 90-bend and toroidal pipes by investigating the transition nature in a 18-bend pipe flow.

  • 10.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Lupi, Valerio
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    On the global stability of 180°-bend pipe flow with mesh adaptivityManuscript (preprint) (Other academic)
  • 11.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. Department of Aerospace Sciences and Technologies, Politecnico di Milano, via La Masa 34 20156 Milano, Italy.
    Martinelli, Fulvio
    Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytecnique, F-91128 Palaiseau, France.
    Schmid, Peter
    Department of Mechanical Engineering, PSE Division, KAUST, 23955 Thuwal, Saudi Arabia.
    Quadrio, Maurizio
    Department of Aerospace Sciences and Technologies, Politecnico di Milano, via La Masa 34 20156 Milano, Italy.
    Linear stability of Poiseuille flow over a steady spanwise Stokes layer2023In: Physical Review Fluids, E-ISSN 2469-990X, Vol. 8, no 10, article id 103902Article in journal (Refereed)
    Abstract [en]

    The temporal linear stability of plane Poiseuille flow modified by spanwise forcing applied at the walls is considered. The forcing consists of a stationary streamwise distribution of spanwise velocity that generates a steady transversal Stokes layer, known to reduce skin-friction drag in a turbulent flow with little energetic cost. A large numerical study is carried out, where the effects of both the physical and the discretization parameters are thoroughly explored, for three representative subcritical values of the Reynolds number Re. Results show that the spanwise Stokes layer significantly affects the linear stability of the system. For example, at Re=2000 the wall forcing is found to more than double the negative real part of the least-stable eigenvalue, and to decrease by nearly a factor of 4 the maximum transient growth of perturbation energy. These observations are Re dependent and further improve at higher Re. Comments on the physical implications of the obtained results are provided, suggesting that spanwise forcing might be effective to obtain at the same time a delayed transition to turbulence and a reduced turbulent friction.

  • 12.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics. Friedrich Alexander Univ, Inst Fluid Mech, Erlangen, Germany..
    Coherent structures in the turbulent stepped cylinder flow at ReD=50002023In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 102, p. 109144-, article id 109144Article in journal (Refereed)
    Abstract [en]

    The coherent structures arising in the turbulent flow around a three-dimensional stepped (or step) cylinder are studied through direct numerical simulation. This geometry is widespread in many applications and the junction substantially modifies the wake behaviour, generating three main cells. The mechanisms of vortex connections on the junction are difficult to be captured and interpreted. We thus use a high-order spectral -element methodology (SEM), and the adaptive mesh refinement technique (AMR) to adequately resolve each region of the domain, capturing the smallest turbulent scales. In this way, we can analyse the vortical interactions on the junction via the A2-criterion and understand the evolution of the train of hairpins, which appears only when the cylinder shear layer gets unstable. Together with the hairpins, four horseshoe and edge vortices coexist on the flat junction surface. A complete picture of the vortices' evolution in time is provided. To extract the large-scale, and most energetic, structures in the wake we perform a three-dimensional proper orthogonal decomposition (POD) of the flow. The first six POD modes correspond to three travelling modes which identify the large (L), the small (S) and the modulation (N) cells. The ReD trend shows that these cells persist at higher Reynolds numbers with a larger separation between the vortex shedding frequencies fN and fL. At the same time, the downwash POD mode gets less strong with a more intense and localised modulation region which affects a more extended portion of the large cylinder wake.

  • 13.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Direct Numerical Simulation of Turbulent Flow Around 3D Stepped Cylinder wth Adaptive Mesh Refinement2022In: 12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022, International Symposium on Turbulence and Shear Flow Phenomena, TSFP , 2022Conference paper (Refereed)
    Abstract [en]

    In the present study, we investigate the turbulent three-dimensional flow around a stepped cylinder, namely two cylinders of different diameters joint at one extremity. We perform a direct numerical simulation with the spectral element code Nek5000 that uses a high order spatial discretisation (the polynomial order is p = 7). The adaptive mesh refinement technique is employed in the error-driven meshing procedure, allowing an adequately refined mesh everywhere. We consider the Reynolds number ReD = 1000, based on the large cylinder diameter and the uniform inflow velocity. We compare our results with the previous experimental campaign by Morton & Yarusevych (2014b). The results agree very well and we can identify the three main wake regions: the S, N and L cell with a Strouhal number StS = 0.408, StN = 0.188 and StL = 0.201 respectively. The instantaneous mean flow properties are studied showing that the junction dynamics is more similar to the previous laminar studies at ReD = 150 rather than at higher ReD = 3900. Moreover, proper orthogonal decomposition is used to detect the most energetic coherent structures, that resemble the three wake cells.

  • 14.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Interface Discontinuities in Spectral-Element Simulations with Adaptive Mesh Refinement2023In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 - Selected Papers from the ICOSAHOM Conference 2021, Springer Nature , 2023, p. 375-386Conference paper (Refereed)
    Abstract [en]

    We investigate the discontinuities arising at non-conforming (or non-conformal) interfaces in spectral element method (SEM) simulations. The derivate terms are by definition discontinuous and interface instabilities are usually not visible with a conformal mesh and sufficient resolution. Using the adaptive mesh refinement (AMR) technique the initial coarse mesh is progressively refined according to an error indicator or estimator. In our case, the spectral error indicator (SEI) is adopted. This leads to non-conformal interfaces, where hanging nodes are introduced through h-refinement implemented in the SEM code Nek5000. We consider the flow in a three-dimensional periodic straight pipe and use the turbulent kinetic energy budget as an indicator for assessing discontinuities (wiggles). They involve first and second-order derivatives and represent a fixed point in the statistical analysis of this canonical flow. Looking at the results, we observe that our AMR implementation does not affect the interface discontinuities. The jumps in derivatives are uniquely related to an inadequately resolved mesh. Relying on an error-driven approach, the SEI produces a mesh that allows computing the TKE budgets in excellent agreement with the literature and ensures saving in grid points by a factor of 2.

  • 15.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. Institute of Fluid Mechanics, Friedrich-Alexander-Universität Erlangen-NÜrnberg, DE-91058 Erlangen, Germany.
    The flow around a stepped cylinder with turbulent wake and stable shear layer2023In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 977, article id A3Article in journal (Refereed)
    Abstract [en]

    The turbulent external flow around a three-dimensional stepped cylinder is studied by means of direct numerical simulations with the adaptive mesh refinement technique. We give a broad perspective of the flow regimes from laminar to turbulent wake at, which is the highest ever considered for this flow case. In particular, we focus on the intermediate Reynolds number that reveals a turbulent wake coupled with a stable cylinder shear layer (subcritical regime). This flow shows a junction dynamics similar to the laminar, where no hairpin vortex appears around the edges, and just two horseshoe vortices are visible. A new stable vortex in the form of a ring, which coils around the rear area, is also identified. In the turbulent wake, the presence of three wake cells is pointed out: the large and small cylinder cells together with the modulation region. However, the modulation dynamics varies between the subcritical and turbulent regimes. A time-averaged, three-dimensional set of statistics is computed, and spatially coherent structures are extracted via proper orthogonal decomposition (POD). The POD identifies the (long-debated) connection between the N-cell and the downwash behind the junction. Furthermore, as the Reynolds number increases, the downwash phenomenon becomes less prominent. Eventually, a reduced-order reconstruction with the most energetically relevant modes is defined to explain the wake vortex interactions. This also serves as a valuable starting point for simulating the stepped cylinder wake behaviour within complex frameworks, e.g. fluid-structure interaction.

  • 16.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Stanly, Ronith
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Mirzareza, Shahab
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Trondheim NO-7491, Norway.
    Lupi, Valerio
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Xiang, Yan
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. SimEx/FLOW, Engineering Mechanics, KTH Royal Institute of Technology, Stockholm 100 44, Sweden.
    Schlatter, Philip
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    A comprehensive framework to enhance numerical simulations in the spectral-element code Nek50002024In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 302, article id 109249Article in journal (Refereed)
    Abstract [en]

    A framework is presented for the spectral-element code Nek5000, which has been, and still is, widely used in the computational fluid dynamics (CFD) community to perform high-fidelity numerical simulations of transitional and high Reynolds number flows. Despite the widespread usage, there is a deficiency in having a comprehensive set of tools specifically designed for conducting simulations using Nek5000. To address this issue, we have created a unique framework that allows, inter alia, to perform stability analysis and compute statistics of a turbulent flow. The framework encapsulates modules that provide tools, run-time parameters and memory structures, defining interfaces and performing different tasks. First, the framework architecture is described, showing its non-intrusive approach. Then, the modules are presented, explaining the main tools that have been implemented and describing some of the test cases. The code is open-source and available online, with proper documentation, to-run instructions and related examples.

  • 17.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Rezaeiravesh, Saleh
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. Department of Fluids and Environment/MACE, The University of Manchester, Manchester, M139PL, UK.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics. Institute of Fluid Mechanics (LSTM), Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Erlangen, 91058, Germany.
    On the potential of transfer entropy in turbulent dynamical systems2023In: Scientific Reports, E-ISSN 2045-2322, Vol. 13, no 1, article id 22344Article in journal (Refereed)
    Abstract [en]

    Information theory (IT) provides tools to estimate causality between events, in various scientific domains. Here, we explore the potential of IT-based causality estimation in turbulent (i.e. chaotic) dynamical systems and investigate the impact of various hyperparameters on the outcomes. The influence of Markovian orders, i.e. the time lags, on the computation of the transfer entropy (TE) has been mostly overlooked in the literature. We show that the history effect remarkably affects the TE estimation, especially for turbulent signals. In a turbulent channel flow, we compare the TE with standard measures such as auto- and cross-correlation, showing that the TE has a dominant direction, i.e. from the walls towards the core of the flow. In addition, we found that, in generic low-order vector auto-regressive models (VAR), the causality time scale is determined from the order of the VAR, rather than the integral time scale. Eventually, we propose a novel application of TE as a sensitivity measure for controlling computational errors in numerical simulations with adaptive mesh refinement. The introduced indicator is fully data-driven, no solution of adjoint equations is required, with an improved convergence to the accurate function of interest. In summary, we demonstrate the potential of TE for turbulence, where other measures may only provide partial information.

  • 18.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Institute of Fluid Mechanics (LSTM), Friedrich--Alexander--Universität (FAU) Erlangen--Nürnberg, Erlangen 91058, Germany.
    Global stability of the flow past a stepped cylinderManuscript (preprint) (Other academic)
  • 19.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics. Institute of Fluid Mechanics (LSTM), Friedrich-Alexander-Universität (FAU) Erlangen-NÜrnberg, DE-91058 Erlangen, Germany.
    Global stability of the flow past a stepped cylinder2024In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 988, article id A1Article in journal (Refereed)
    Abstract [en]

    We investigate the global instability mechanism of the flow past a three-dimensional stepped cylinder. A comprehensive study is performed for different diameter ratios of the two joined cylinders ranging from to. Independently of, the spectrum of the linearised Navier-Stokes operator reveals a pair of complex conjugate eigenvalues, with Strouhal number. The initial transition is triggered by a two-dimensional mechanism of the larger cylinder only, not affected by the presence of the junction and the smaller cylinder . The structural sensitivity analysis is used to identify where the instability mechanism acts. The onset of transition is solely localised in the large cylinder wake (L cell), where the wavemaker has two symmetric lobes across the separation bubble. When the Reynolds number increases, a second and a third unstable pair of complex conjugate eigenvalues appears. They are localised in the small cylinder (S) wake and modulation (N) region. For any, the appearance of unstable eigenmodes resembling the three cells S-N-L in the wake is observed. The nonlinear simulation results support this finding, in contrast with the previous classification of the laminar vortex shedding in direct (L-S) and indirect (L-N-S) modes interaction Lewis & Gharib (Phys. Fluids, vol. 4, 1992, pp. 104-117). This result indicates that each cell undergoes a supercritical Hopf bifurcation for any. As approaches, the modal linear stability results also show an unstable eigenmode in the wake of the small cylinder resembling a new modulation cell, named N2, similar to the N cell but mirrored with respect to the junction plane.

  • 20.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics.
    Yao, J.
    Advanced Research Institute of Multidisciplinary Sciences, Beijing Institute of Technology, Beijing 100081, China; Department of Mechanical Engineering, Texas Tech University, Lubbock 79409, Texas, USA.
    Rezaeiravesh, S.
    Department of Fluids and Environment/MACE, The University of Manchester M139PL, Manchester, UK.
    Hussain, F.
    Department of Mechanical Engineering, Texas Tech University, Lubbock 79409, Texas, USA.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics. Institute of Fluid Mechanics (LSTM), Friedrich-Alexander-Universität (FAU) Erlangen-Nürnberg, Erlangen 91058, Germany.
    Karhunen-Loéve decomposition of high Reynolds number turbulent pipe flows: A Voronoi analysis2024In: Journal of Physics: Conference Series, IOP Publishing , 2024, Vol. 2753, p. 012018-, article id 012018Conference paper (Refereed)
    Abstract [en]

    We perform the Karhunen-Loéve decomposition of the data from direct numerical simulations pertaining to incompressible turbulent pipe flow at various Reynolds numbers, in order to identify large-scale coherent structures. A novel approach based on the Voronoi diagram is introduced to estimate the energy distribution along the radial direction as a function of the geometrical properties of the modes. In contrast to previous classifications, no user-defined criterion, threshold or ad-hoc separation of the eddies is required since the two most energetic branches are inherently present as the Reynolds number increases. Details about the Voronoi analysis are provided, together with a comprehensive validation and comparison with previous classifications at low Reynolds numbers. We discuss the results and potential of the presented approach at Reτ = 180 and 5200, commenting on the two classes of coherent structures with a varying and constant size in the radial direction appearing at Reτ = 5200.

  • 21.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Yao, Jie
    Advanced Research Institute of Multidisciplinary Sciences, Beijing Institute of Technology, Beijing 100081, China.
    Rezaeiravesh, Saleh
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Department of Fluids and Environment/MACE, The University of Manchester, Manchester M139PL, UK.
    Hussain, Fazle
    Department of Mechanical Engineering, Texas Tech University, Lubbock 79409, Texas, USA.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Institute of Fluid Mechanics (LSTM), Friedrich--Alexander--Universität (FAU) Erlangen--Nürnberg, Erlangen 91058, Germany.
    Energy-based characterisation of large-scale coherent structures in turbulent pipe flowsManuscript (preprint) (Other academic)
  • 22.
    Massaro, Daniele
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory.
    Yao, Jie
    Advanced Research Institute of Multidisciplinary Sciences, Beijing Institute of Technology, Beijing 100081, China.
    Rezaeiravesh, Saleh
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Department of Fluids and Environment/MACE, The University of Manchester, Manchester M139PL, UK.
    Hussain, Fazle
    Department of Mechanical Engineering, Texas Tech University, Lubbock 79409, Texas, USA.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics, Turbulent simulations laboratory. Institute of Fluid Mechanics (LSTM), Friedrich--Alexander--Universität (FAU) Erlangen--Nürnberg, Erlangen 91058, Germany.
    Karhunen-Loève decomposition of high Reynolds number turbulent pipe flows: a Voronoi analysis2024Manuscript (preprint) (Other academic)
  • 23.
    Offermans, Nicolas
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Massaro, Daniele
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Peplinski, Adam
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Schlatter, Philipp
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Error-driven adaptive mesh refinement for unsteady turbulent flows in spectral-element simulations2023In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 251, p. 105736-, article id 105736Article in journal (Refereed)
    Abstract [en]

    The simulation of turbulent flows requires high spatial resolution in potentially a priori unknown, solution -dependent locations. To achieve adaptive refinement of the mesh, we rely on error indicators. We assess the differences between an error measure relying on the local convergence properties of the numerical solution and a goal-oriented error measure based on the computation of an adjoint problem. The latter method aims at optimizing the mesh for the calculation of a predefined integral quantity, or functional of interest. This work follows on from a previous study conducted on steady flows in Offermans et al. (2020) and we extend the use of the so-called adjoint error estimator to three-dimensional, turbulent flows. They both represent a way to achieve error control and automatic mesh refinement (AMR) for the numerical approximation of the Navier-Stokes equations, with a spectral element method discretization and non-conforming h-refinement.The current study consists of running the same physical flow case on gradually finer meshes, starting from a coarse initial grid, and to compare the results and mesh refinement patterns when using both error measures. As a flow case, we consider the turbulent flow in a constricted, periodic channel, also known as the periodic hill flow, at four different Reynolds numbers: Re = 700, Re = 1400, Re = 2800 and Re = 5600. Our results show that both error measures allow for effective control of the error, but they adjust the mesh differently. Well-resolved simulations are achieved by automatically focusing refinement on the most critical regions of the domain, while significant saving in the overall number of elements is attained, compared to statically generated meshes. At all Reynolds numbers, we show that relevant physical quantities, such as mean velocity profiles and reattachment/separation points, converge well to reference literature data. At the highest Reynolds number achieved (Re = 5600), relevant quantities, i.e. reattachment and separation locations, are estimated with the same level of accuracy as the reference data while only using one-third of the degrees of freedom of the reference. Moreover, we observe distinct mesh refinement patterns for both error measures. With the spectral error indicator, the mesh resolution is more uniform and turbulent structures are more resolved within the whole domain. On the other hand, the adjoint error estimator tends to focus the refinement within a localized zone in the domain, dependent on the functional of interest, leaving large parts of the domain marginally resolved.

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