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Rinaldi, E., Schlatter, P. & Bagheri, S. (2018). Edge state modulation by mean viscosity gradients. Journal of Fluid Mechanics, 838, 379-403
Open this publication in new window or tab >>Edge state modulation by mean viscosity gradients
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 838, p. 379-403Article in journal (Refereed) Published
Abstract [en]

Motivated by the relevance of edge state solutions as mediators of transition, we use direct numerical simulations to study the effect of spatially non-uniform viscosity on their energy and stability in minimal channel flows. What we seek is a theoretical support rooted in a fully nonlinear framework that explains the modified threshold for transition to turbulence in flows with temperature-dependent viscosity. Consistently over a range of subcritical Reynolds numbers, we find that decreasing viscosity away from the walls weakens the streamwise streaks and the vortical structures responsible for their regeneration. The entire self-sustained cycle of the edge state is maintained on a lower kinetic energy level with a smaller driving force, compared to a flow with constant viscosity. Increasing viscosity away from the walls has the opposite effect. In both cases, the effect is proportional to the strength of the viscosity gradient. The results presented highlight a local shift in the state space of the position of the edge state relative to the laminar attractor with the consequent modulation of its basin of attraction in the proximity of the edge state and of the surrounding manifold. The implication is that the threshold for transition is reduced for perturbations evolving in the neighbourhood of the edge state in the case that viscosity decreases away from the walls, and vice versa.

Place, publisher, year, edition, pages
Cambridge University Press, 2018
Keyword
nonlinear dynamical systems, nonlinear instability, transition to turbulence
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-222027 (URN)10.1017/jfm.2017.921 (DOI)2-s2.0-85040834445 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20180131

Available from: 2018-01-31 Created: 2018-01-31 Last updated: 2018-01-31Bibliographically approved
Offermans, N., Peplinski, A., Marin, O. & Schlatter, P. (2017). Adjoint error estimators and adaptive mesh refinement in Nek5000.
Open this publication in new window or tab >>Adjoint error estimators and adaptive mesh refinement in Nek5000
2017 (English)Report (Other academic)
Abstract [en]

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. In this report, we describe recent developments that have been made to enable adaptive mesh refinement in Nek5000 and we validate the method on simple, two-dimensional, steady test cases.We start by describing the modifications brought to Nek5000 that enable the presence of hanging nodes in the mesh. Thanks to this new feature, we can use the h-refinement technique for mesh adaptation, where selected elements are split via quadtree (2D) or octree (3D) structures. Then, two methods are considered to estimate and control the error. The first method is local and based on the spectral properties of the solution on each element. The second method is goal-oriented and takes into account both the local properties of the solution and the global dependence of the error in the solution via the resolution of an adjoint problem. Finally, the use of automatic mesh refinement is demonstrated in Nek5000 on two test cases: the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. Both error estimation methods are compared andare shown to efficiently reduce the number of degrees of freedom required to reach a given tolerance on the solution compared to conforming refinement. Moreover, the gains in terms of mesh generation, accuracy and computational cost are discussed by analysing the convergence of some functional of interest and the evolution of the mesh as refinement proceeds.

Keyword
Error estimators; mesh refinement; adaptivity; spectral element method
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-217498 (URN)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20171123

Available from: 2017-11-13 Created: 2017-11-13 Last updated: 2017-11-23Bibliographically approved
Saglietti, C., Schlatter, P., Monokrousos, A. & Henningson, D. S. (2017). Adjoint optimization of natural convection problems: differentially heated cavity. Theoretical and Computational Fluid Dynamics, 31(5-6), 537-553
Open this publication in new window or tab >>Adjoint optimization of natural convection problems: differentially heated cavity
2017 (English)In: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250, Vol. 31, no 5-6, p. 537-553Article in journal (Refereed) Published
Abstract [en]

Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr= 0.15 - 7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors’ knowledge, this behavior is illustrated here for the first time.

Place, publisher, year, edition, pages
Springer, 2017
Keyword
Adjoint optimization, Arnoldi method, Differentially heated cavity, Natural convection, Power iterations
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-218117 (URN)10.1007/s00162-016-0398-5 (DOI)000414941500006 ()2-s2.0-85033476369 (Scopus ID)
Note

QC 20171124

Available from: 2017-11-24 Created: 2017-11-24 Last updated: 2017-11-24Bibliographically approved
Sanmiguel Vila, C., Örlü, R., Vinuesa, R., Schlatter, P., Ianiro, A. & Discetti, S. (2017). Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization. Flow Turbulence and Combustion, 99(3-4), 589-612
Open this publication in new window or tab >>Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization
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2017 (English)In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 99, no 3-4, p. 589-612Article in journal (Refereed) Published
Abstract [en]

This manuscripts presents a study on adverse-pressure-gradient turbulent boundary layers under different Reynolds-number and pressure-gradient conditions. In this work we performed Particle Image Velocimetry (PIV) measurements supplemented with Large-Eddy Simulations in order to have a dataset covering a range of displacement-thickness-based Reynolds-number 2300 34000 and values of the Clauser pressure-gradient parameter beta up to 2.4. The spatial resolution limits of PIV for the estimation of turbulence statistics have been overcome via ensemble-based approaches. A comparison between ensemble-correlation and ensemble Particle Tracking Velocimetry was carried out to assess the uncertainty of the two methods. The effects of beta, R e and of the pressure-gradient history on turbulence statistics were assessed. A modal analysis via Proper Orthogonal Decomposition was carried out on the flow fields and showed that about 20% of the energy contribution corresponds to the first mode, while 40% of the turbulent kinetic energy corresponds to the first four modes with no appreciable dependence on beta and R e within the investigated range. The topology of the spatial modes shows a dependence on the Reynolds number and on the pressure-gradient strength, in line with the results obtained from the analysis of the turbulence statistics. The contribution of the modes to the Reynolds stresses and the turbulence production was assessed using a truncated low-order reconstruction with progressively larger number of modes. It is shown that the outer peaks in the Reynolds-stress profiles are mostly due to large-scale structures in the outer part of the boundary layer.

Place, publisher, year, edition, pages
Springer, 2017
Keyword
Wall turbulence, PTV, PIV, POD
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-220479 (URN)10.1007/s10494-017-9869-z (DOI)000416838200004 ()2-s2.0-85033499999 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20180104

Available from: 2018-01-04 Created: 2018-01-04 Last updated: 2018-01-04Bibliographically approved
Sanmiguel Vila, C., Örlü, R., Vinuesa, R., Schlatter, P., Ianiro, A. & Discetti, S. (2017). Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization. Flow Turbulence and Combustion, 99(3-4), 589-612
Open this publication in new window or tab >>Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization
Show others...
2017 (English)In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 99, no 3-4, p. 589-612Article in journal (Refereed) Published
Abstract [en]

This manuscripts presents a study on adverse-pressure-gradient turbulent boundary layers under different Reynolds-number and pressure-gradient conditions. In this work we performed Particle Image Velocimetry (PIV) measurements supplemented with Large-Eddy Simulations in order to have a dataset covering a range of displacement-thickness-based Reynolds-number 2300 34000 and values of the Clauser pressure-gradient parameter beta up to 2.4. The spatial resolution limits of PIV for the estimation of turbulence statistics have been overcome via ensemble-based approaches. A comparison between ensemble-correlation and ensemble Particle Tracking Velocimetry was carried out to assess the uncertainty of the two methods. The effects of beta, R e and of the pressure-gradient history on turbulence statistics were assessed. A modal analysis via Proper Orthogonal Decomposition was carried out on the flow fields and showed that about 20% of the energy contribution corresponds to the first mode, while 40% of the turbulent kinetic energy corresponds to the first four modes with no appreciable dependence on beta and R e within the investigated range. The topology of the spatial modes shows a dependence on the Reynolds number and on the pressure-gradient strength, in line with the results obtained from the analysis of the turbulence statistics. The contribution of the modes to the Reynolds stresses and the turbulence production was assessed using a truncated low-order reconstruction with progressively larger number of modes. It is shown that the outer peaks in the Reynolds-stress profiles are mostly due to large-scale structures in the outer part of the boundary layer.

Keyword
Wall turbulence, PTV, PIV, POD
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-220259 (URN)10.1007/s10494-017-9869-z (DOI)000416838200004 ()2-s2.0-85033499999 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationEU, European Research CouncilEuropean Regional Development Fund (ERDF)
Note

QC 20180112

Available from: 2018-01-12 Created: 2018-01-12 Last updated: 2018-01-12Bibliographically approved
Vinuesa, R., Örlü, R. & Schlatter, P. (2017). Characterisation of backflow events over a wing section. Journal of turbulence, 18(2), 170-185
Open this publication in new window or tab >>Characterisation of backflow events over a wing section
2017 (English)In: Journal of turbulence, ISSN 1468-5248, E-ISSN 1468-5248, Vol. 18, no 2, p. 170-185Article in journal (Refereed) Published
Abstract [en]

Rare backflow (negative wall-shear stress) events have recently been found and quantified in the near-wall region of canonical wall-bounded turbulent flows. Although their existence and correlation with large-scale events have been established beyond numerical and measurement technique uncertainties, their occurrence at numerically high Reynolds numbers is still rare (less than 1 per thousand and 1 per million at the wall and beyond the viscous sublayer, respectively). To better quantify these rare events, the turbulent boundary layer developing over the suction side of a wing section, experiencing an increasing adverse pressure gradient (APG) without separation along its chord c, is considered in the present work. We find that the backflow level of 0.06% documented in turbulent channels and zero-pressure-gradient (ZPG) turbulent boundary layers is already exceeded on the suction side for x/c > 0.3, at friction Reynolds numbers three times lower, while close to the trailing edge the backflow level reaches 30%. Conditional analysis of extreme events indicates that for increasing Clauser pressure-gradient parameters (reaching β ≃ 35), the flow reaches a state in which the extreme events are more likely aligned with or against the freestream, and that the otherwise strong spanwise component of the wall-shear stress reduces towards the vicinity of the trailing edge. Backflow events subjected to moderate up to strong APG conditions (0.6 < β < 4.1) exhibit an average width of Δz+ ≃ 20, and an average lifetime of Δt+ ≃ 2. This directly connects with the findings by Lenaers et al., and implies that there is a connection between high-Re ZPG and strong APG conditions. 

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keyword
adverse pressure gradient, backflow, separation, Turbulent boundary layers, wings
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-202210 (URN)10.1080/14685248.2016.1259626 (DOI)000394422100004 ()2-s2.0-84997235696 (Scopus ID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation
Note

QC 20170320

Available from: 2017-03-20 Created: 2017-03-20 Last updated: 2017-11-29Bibliographically approved
Brynjell-Rahkola, M., Tuckerman, L. S., Schlatter, P. & Henningson, D. S. (2017). Computing Optimal Forcing Using Laplace Preconditioning. Communications in Computational Physics, 22(5), 1508-1532
Open this publication in new window or tab >>Computing Optimal Forcing Using Laplace Preconditioning
2017 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 22, no 5, p. 1508-1532Article in journal (Refereed) Published
Abstract [en]

For problems governed by a non-normal operator, the leading eigenvalue of the operator is of limited interest and a more relevant measure of the stability is obtained by considering the harmonic forcing causing the largest system response. Various methods for determining this so-called optimal forcing exist, but they all suffer from great computational expense and are hence not practical for large-scale problems. In the present paper a new method is presented, which is applicable to problems of arbitrary size. The method does not rely on timestepping, but on the solution of linear systems, in which the inverse Laplacian acts as a preconditioner. By formulating the search for the optimal forcing as an eigenvalue problem based on the resolvent operator, repeated system solves amount to power iterations, in which the dominant eigenvalue is seen to correspond to the energy amplification in a system for a given frequency, and the eigenfunction to the corresponding forcing function. Implementation of the method requires only minor modifications of an existing timestepping code, and is applicable to any partial differential equation containing the Laplacian, such as the Navier-Stokes equations. We discuss the method, first, in the context of the linear Ginzburg-Landau equation and then, the two-dimensional lid-driven cavity flow governed by the Navier-Stokes equations. Most importantly, we demonstrate that for the lid-driven cavity, the optimal forcing can be computed using a factor of up to 500 times fewer operator evaluations than the standard method based on exponential timestepping.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-214476 (URN)10.4208/cicp.OA-2016-0070 (DOI)000408436300012 ()
Note

QC 20171011

Available from: 2017-10-11 Created: 2017-10-11 Last updated: 2017-11-23Bibliographically approved
Vinuesa, R., Negi, P. S., Hanifi, A., Henningson, D. S. & Schlatter, P. (2017). High-fidelity simulations of the flow around wings at high reynolds numbers. In: 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017: . Paper presented at 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017, Swissotel Chicago, United States, 6 July 2017 through 9 July 2017. , 2
Open this publication in new window or tab >>High-fidelity simulations of the flow around wings at high reynolds numbers
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2017 (English)In: 10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017, 2017, Vol. 2Conference paper (Refereed)
Abstract [en]

Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we conducted a well-resolved large-eddy simulation of the turbulent flow around the NACA4412 airfoil at a Reynolds number based on freestream velocity and chord length of Rec = 1;000;000, with 5° angle of attack. The results of this simulation are used, together with the direct numerical simulation by Hosseini et al. (Int. J. Heat Fluid Flow 61, 2016) of the same wing section at Rec = 400;000, to characterize the effect of Reynolds number on APG TBLs subjected to the same pressure-gradient distribution (defined by the Caluser pressure-gradient parameter β). Our results indicate that the increase in inner-scaled edge velocity U+e, and the decrease in shape factor H, is lower in the APG on the wing than in zero-pressure-gradient (ZPG) TBLs over the same Reynolds-number range. This indicates that the lower-Re boundary layer is more sensitive to the effect of the APG, a conclusion that is supported by the larger values in the outer region of the tangential velocity fluctuation profile in the Rec = 400;000 wing. Future extensions of the present work will be aimed at studying the differences in the outer-region energizing mechanisms due to APGs and increasing Reynolds number.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-218452 (URN)2-s2.0-85033231950 (Scopus ID)
Conference
10th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2017, Swissotel Chicago, United States, 6 July 2017 through 9 July 2017
Note

QC 20171128

Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2017-11-28Bibliographically approved
Kleusberg, E., Mikkelsen, R. F., Schlatter, P., Ivanell, S. & Henningson, D. S. (2017). High-Order Numerical Simulations of Wind Turbine Wakes. Paper presented at 30 May 2017 through 1 June 2017. Journal of Physics, Conference Series, 854(1), Article ID 012025.
Open this publication in new window or tab >>High-Order Numerical Simulations of Wind Turbine Wakes
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2017 (English)In: Journal of Physics, Conference Series, ISSN 1742-6588, E-ISSN 1742-6596, Vol. 854, no 1, article id 012025Article in journal (Refereed) Published
Abstract [en]

Previous attempts to describe the structure of wind turbine wakes and their mutual interaction were mostly limited to large-eddy and Reynolds-averaged Navier-Stokes simulations using finite-volume solvers. We employ the higher-order spectral-element code Nek5000 to study the influence of numerical aspects on the prediction of the wind turbine wake structure and the wake interaction between two turbines. The spectral-element method enables an accurate representation of the vortical structures, with lower numerical dissipation than the more commonly used finite-volume codes. The wind-turbine blades are modeled as body forces using the actuator-line method (ACL) in the incompressible Navier-Stokes equations. Both tower and nacelle are represented with appropriate body forces. An inflow boundary condition is used which emulates homogeneous isotropic turbulence of wind-tunnel flows. We validate the implementation with results from experimental campaigns undertaken at the Norwegian University of Science and Technology (NTNU Blind Tests), investigate parametric influences and compare computational aspects with existing numerical simulations. In general the results show good agreement between the experiments and the numerical simulations both for a single-turbine setup as well as a two-turbine setup where the turbines are offset in the spanwise direction. A shift in the wake center caused by the tower wake is detected similar to experiments. The additional velocity deficit caused by the tower agrees well with the experimental data. The wake is captured well by Nek5000 in comparison with experiments both for the single wind turbine and in the two-turbine setup. The blade loading however shows large discrepancies for the high-turbulence, two-turbine case. While the experiments predicted higher thrust for the downstream turbine than for the upstream turbine, the opposite case was observed in Nek5000.

Place, publisher, year, edition, pages
Institute of Physics Publishing, 2017
Keyword
Incompressible flow, Navier Stokes equations, Numerical methods, Numerical models, Turbomachine blades, Turbulence, Vortex flow, Wakes, Wind turbines, Comparison with experiments, Homogeneous isotropic turbulence, Incompressible Navier Stokes equations, Inflow boundary conditions, Numerical dissipation, Reynolds-averaged navier-stokes simulations, Science and Technology, Spectral element method, Turbine components
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-216460 (URN)10.1088/1742-6596/854/1/012025 (DOI)2-s2.0-85023600314 (Scopus ID)
Conference
30 May 2017 through 1 June 2017
Note

QC 20171205

Available from: 2017-12-05 Created: 2017-12-05 Last updated: 2017-12-05Bibliographically approved
Bobke, A., Vinuesa, R., Örlü, R. & Schlatter, P. (2017). History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers. Journal of Fluid Mechanics, 820, 667-692
Open this publication in new window or tab >>History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers
2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 820, p. 667-692Article in journal (Refereed) Published
Abstract [en]

Turbulent boundary layers under adverse pressure gradients are studied using well-resolved large-eddy simulations (LES) with the goal of assessing the influence of the streamwise pressure-gradient development. Near-equilibrium boundary layers were characterized through the Clauser pressure-gradient parameter β. In order to fulfil the near-equilibrium conditions, the free stream velocity was prescribed such that it followed a power-law distribution. The turbulence statistics pertaining to cases with a constant value of β (extending up to approximately 40 boundary-layer thicknesses) were compared with cases with non-constant β distributions at matched values of β and friction Reynolds number Reδ∗. An additional case at matched Reynolds number based on displacement thickness Reδ∗ was also considered. It was noticed that non-constant β cases appear to approach the conditions of equivalent constant β cases after long streamwise distances (approximately 7 boundary-layer thicknesses). The relevance of the constant β cases lies in the fact that they define a 'canonical' state of the boundary layer, uniquely characterized by β and Re. The investigations on the flat plate were extended to the flow around a wing section overlapping in terms of β and Re. Comparisons with the flat-plate cases at matched values of β and Re revealed that the different development history of the turbulent boundary layer on the wing section leads to a less pronounced wake in the mean velocity as well as a weaker second peak in the Reynolds stresses. This is due to the weaker accumulated effect of the β history. Furthermore, a scaling law suggested by Kitsios et al. (Intl J. Heat Fluid Flow, vol. 61, 2016, pp. 129-136), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adverse-pressure-gradient turbulent boundary layers and highlights the fact that the values of the Clauser pressure-gradient parameter and the Reynolds number are not sufficient to characterize the state of the boundary layer.

Place, publisher, year, edition, pages
Cambridge University Press, 2017
Keyword
turbulent boundary layers, turbulent flows, Atmospheric thermodynamics, Boundary layer flow, Flow of fluids, Large eddy simulation, Pressure gradient, Reynolds number, Turbulence, Turbulent flow, Velocity, Adverse pressure gradient, Constant pressure gradient, Displacement thickness, Equilibrium boundaries, Equilibrium conditions, Power law distribution, Pressure-gradient parameters, Boundary layers
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-216464 (URN)10.1017/jfm.2017.236 (DOI)2-s2.0-85019182537 (Scopus ID)
Note

QC 20171205

Available from: 2017-12-05 Created: 2017-12-05 Last updated: 2017-12-05Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9627-5903

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