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Procedia Structural (2017) 370–379 Structural IntegrityIntegrity Procedia300 (2016) 000–000

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XXIV Italian Group of Fracture Conference, 1-3 March 2017, Urbino, Italy

Megastructures: use of CFD turbulence models for the evaluation of wind-induced fatigue loads Thermo-mechanical modeling of Antonello a high pressure turbine blade of an a* a b Alberto Lorenzon , Marco , Filippo Berto airplane gas turbine engine University of Padua, Department of Management and Engineering, Stradella S.Nicola 3, Vicenza 36100, Italy

XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal

a

b

NTNU, Department of Engineering Design and Materials, Richard Birkelands bei 2b, 7491 Trondheim, Norway

P. Brandãoa, V. Infanteb, A.M. Deusc*

a

Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal Thec determination of time dependent wind actions on large civil steel structures by means of turbulence models for CFD allows CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, an improved evaluation of the fatigue load spectrum. Portugal

Abstract b

The purpose of this paper is to identify, from literature review, the flow characteristics required to conduct a proper assessment of a fatigue load spectrum, given that practical cases determine which are the properties of the flow to be relevant. Subsequently, some CFD turbulence models are presented in order to investigate their ability to provide the required outputs with an appropriate Abstract level of detail. The computational cost of the models is also considered. During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, Copyright © 2017 The Authors. Published by Elsevier B.V.Such This isconditions an open access BY-NC-ND license the high pressure turbine (HPT) blades. causearticle theseunder partsthe to CC undergo different types of time-dependent © especially 2017 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Peer-review under responsibility of the Scientific Committee of IGF Ex-Co. Peer-review under responsibility of the Scientific Committee of IGF Ex-Co. the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used Turbulence; to obtain thermal and Steel mechanical data for three different flight cycles. In order to create the 3D model Keywords: CFD; Fatigue; Wind, Large Structures. needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The 1. Introduction overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

In recent decades, there has been an increasing use of metal structures, such as bridges, skyscrapers and stadium characterized byPublished large size highB.V. slenderness. This phenomenon is motivated by the ever-larger social and roofs © 2016 The Authors. by and Elsevier economic needs and is supported byScientific various Committee factors such as the constant increase in computational capacity, the Peer-review under responsibility of the of PCF 2016. development of software that enables the optimization of all aspects of the design, scientific progress and the Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.

*

Corresponding author. Tel.: +39-0444-998711 Fax: +39-0444-998888 E-mail address: [email protected]

2452-3216 © 2017 The Authors. Published by Elsevier B.V.

Peer-review underauthor. responsibility the Scientific Committee of IGF Ex-Co. * Corresponding Tel.: +351of 218419991. E-mail address: [email protected]

2452-3216 © 2016 The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the Scientific Committee of PCF 2016.

Copyright © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of IGF Ex-Co. 10.1016/j.prostr.2017.04.038

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availability of high resistance materials. However, the increase in the size of civil structures makes them more subject to fatigue and to wind action. Major international standards such as EN 1993-1-1:2005+A1:2014, Annex C have recently reinforced the request to consider the fatigue phenomenon for the design of large steel structures. The size of the structure it is implicitly part of the concept of Consequence Class and the large size almost automatically leads to fatigue calculations. In order to obtain the local stress in correspondence of a joint of a large structure, FEM model reduction techniques such as Guyan or Craig-Bampton methods (Bampton and Craig, JR. (1968)) need to be used - even if not many structural software implement superelements sub-modeling efficiently. Whereas an order of magnitude of approximately 5000 tons of steel for a large steel structure, the number of welds can be estimated roughly at a ratio 1-10, and then a number of welds equal to about 50000 can be expected. As shown in Colussi et al. (2017), a complete nominal stress based fatigue analysis all around a welding would require 20 checks, each of which could potentially be characterized by a different load spectrum, so this type of calculation easily becomes computationally demanding. The size of the structure also dramatically affects the potential number of imperfection as shown in Davidenkov et al. (1946). In order to guarantee the safety of a structure with respect to the fatigue phenomenon it is, in the end of the process of fabrication, necessary to perform inspection on the welds in workshop, where the inspection class is function of the fatigue utilization factor of each weld, as indicated by prEN 1090-2:2016, Annex L, Table L.1, and the utilization factor is based of fatigue calculations. The inspection may, eventually, lead to repair as explained in Jonsson et al. (2016), Thus, although the calculation of fatigue of large steel structures a has been a widely studied topic, there are still present several challenges to the industry, especially when the size of the structures becomes a relevant factor. Moreover, as the fluctuating nature of wind load generates the fluctuating stresses in structures, it becomes necessary to consider the phenomenon of wind-induced fatigue in the design of steel and aluminum structures. The introduction of fluctuating action of the wind introduction represents a very complex challenge because, as reported by many authors, (Holmes (2002)) the treatment of the damage under the dynamic loading of wind is still a not sufficiently developed subject. This consideration is true both from the scientific point of view, and from the regulatory point of view. In fact, a practical tool which enables to determine wind loads for the fatigue analyses of large steel structures, is not yet available to the engineering community. Among the (few) tools provided by Eurocode it should be noted the EN 1991-1-4 Annex B, Clause B.3 where an equation is provided an equation that calculates the number of cycles of an effect of wind during a period 50 years. Such equation does not, however, take into account any information about wind features and structural response (except for the effect Sk due to a 50 years return period wind action). Some approaches have been proposed for a more accurate evaluation of wind-induced fatigue loading of steel structures and many of these methods makes use of wind tunnels to evaluate relevant features of the flow. Recently many Computational Fluid Dynamic (CFD) methods for the simulation of turbulence have gained appreciation for their ability to correctly represent flow characteristics with reduced cost in comparison to wind tunnels. Therefore, their use could potentially be extended to conduct fatigue analyses of steel structures exposed to dynamic wind action. Following a literature search, no cases of use of turbulence models for CFD to conduct fatigue analyses have been found by the authors. It is therefore of interest of this paper make a first step to link the topic of fatigue calculations of large steel structures to the subject of CFD. A brief review of the turbulence models for CFD that have been successfully applied to civil applications is here provided. These models are presented from the perspective of their use in place (or in combination) of the wind tunnel in order to perform fatigue analysis of the structure. To conduct this evaluation, we mention some studies in the scientific literature in which a test in the wind tunnel have been performed in order to calculate features of the flow that lead to the wind-induced fatigue spectrum. Consequently, we observe the key flow properties that a CFD model needs to grasp in order to use them for this purpose. The purpose of this paper is not therefore to carry out a comprehensive review of the turbulence models for CFD. The description of the turbulence models is reduced to the essential and the same applies to the methods for the assessment of the fatigue spectrum.

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2. Methods 2.1. Turbulence models for CFD Many commercial and open source programs are currently available to perform CFD analysis. In this review, only CFD methods currently implemented within these codes (or easily implementable) will be presented, in order to focus on a set of tools that are already available for the assessment of wind effects on large steel structures. The solution to the Navier-Stokes equations provides all information regarding every aspect of a turbulent flow. Considering a homogeneous incompressible fluid of constant viscosity, in general Navier-Stokes equations can be expressed as: v 1  ( v   ) v   p   2 v t 

(1)

 v 0

(2)

As shown by many (see Speziale (1991), Hanjalić (2004), Argyropoulos and Markatos (2015)) limitations in computer capacity make it impossible –for now and the foreseeable future – to directly solve these equations in the complex turbulent flows of engineering interest. This is essentially due to the nature of turbulence, which is, by definition, an irregular condition of flow, characterized by strong non-linearity and large amplitude in the scales of length, time and velocity. However, for most engineering purposes, it is not necessary to identify every feature of the flow. In fact, in many relevant civil applications, as shown theoretically by POD and other similar decomposition (see, for example Romanowski (1996) and Dowell and Hall (2001)) that only eddies with the higher energy are responsible for dynamic effects on structures. Use of mathematical models to simulate the physics of turbulence is thus an obvious and reasonable choice. The various approaches to turbulence modeling differ essentially on the portion of turbulence, which is solved analytically against the portion that is instead simulated. The three major classes of models are: 1. DNS (Direct Numerical Simulation): Navier-Stokes equations are numerically simulated at all length and at all scales and there is therefore no need of any turbulence model. This class of models has provided significant contribution in turbulence research as it allows for the most accurate results. The need to model the largest scale of turbulence while also providing a fine enough grid resolution that allow to capture the dissipation length scale (Kolmogorov micro-scale) makes, however, its computational demand too high for any relevant industrial application. 2. RANS (Reynolds Averaged Navier-Stokes): the entire flow is averaged and the turbulence is modeled using various approaches. 3. LES (Large Eddy Simulation): only the major vortices are numerically solved while sub-grid eddies are modeled. RANS and LES models are further described below. Between these classes are also present many other models that aim to realize improvements in the description of the physics while obtaining reduction in computational cost. An ample review of hybrid RANS-LES models has been provided in Fröhlich and von Terzi (2008). Some of the most successful hybrid models are: - VLES (Very Large Eddy Simulation), see Johansen et al. (2004); - DES (Detached Eddy Simulation), see Spalart (2009); - PANS (Partially-Averaged Navier-Stokes), see Girimaji (2006). In recent years, many alternative approaches to “traditional” CFD implementation have been proposed. One of the most attracting for the industry may be represented by the Lattice Boltzmann method, which is a mesoscopic particle-based approach to CFD which eventually promises to remove the complexity introduced by the grid generation (see Holman et al. (2012)).

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2.1.1. RANS models RANS models have been for many years the only tool available to calculate the features of a turbulent flow in relevant, complex applications (Hanjalic (2005)) The fundamental concept of RANS methods lies in Reynolds decomposition of Navier-Stokes equations: turbulent flow is described as a random variation around a mean value. The Reynolds-averaged Navier-Stokes equations can be written as Wilcox (2006):



U i U i P  (2 S ji   u 'j ui' )  U j    t x j xi x j

(3)

while time-averaged mass-conservation is identical to the instantaneous: U i 0 xi

(4)

where Ui is the time-averaged velocity, ui’ is the fluctuating velocity, µ is molecular viscosity, Sij is the deformation tensor. In RANS equation the quantity  u 'j ui' is known as the Reynolds Stress tensor,  u 'j ui'   ij . The unknowns are 10: one pressure, three velocity components, six Reynolds stress tensor components, while the equations are four. In order to solve the prolem it is necessary to introduce more equations. This is called the “closure problem” and many models have been proposed, most of which are part of the two-equation models family. The most popular two-equation model is the Standard k   model and is based to the physical hypothesis that the production of dissipation should be proportional to the production of turbulent kinetic energy. The following equations define a standard k   model:  u i u j   x j xi 

2 3

 ij  K  ij  t 

 t  C

K2



 ,  

(5)

(6)

,

K K u i   ui  ij   t xi x j xi

  T K  2     K ,  x   K i

  u i   2    T   2  ui C 1  ij  C 2       , t xi K x j K xi    xi 

(7)

(8)

Where K is the turbulent kinetic energy, ε is the turbulent dissipation rate,  T is the eddy viscosity, u i is the mean velocity vector,  is the kinematic viscosity of the fluid and the constants assume the following approximate values of C  0.09 ,  K  1.0 ,    1.3 , C 1  1.44 , C 1  1.92 . Many improvements have been done over the years to the standard k-ε model. Other closure models differ essentially by the choice of the modeled equations along with the equation of turbulent kinetic energy. At the moment, one of the RANS model that has proven to be more efficient is v2-f proposed in Durbin (1991), which is based on the elliptic relaxation concept and uses two additional equations, one for the velocity scale and one for the elliptic relaxation function. This model improved the modeling in proximity of the wall.


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2.1.2. LES models In LES, the large eddies are fully resolved and the smallest, subgrid-scale eddies are modeled. Instead of timeaveraging, the resolved (large-eddy) field is separated from the small-eddy (sub-grid) field by using a spatial filtering and providing the following governing equations:  u i    u i 1 P      ij  ui u j   t x j  xi x j  x j 





(9)

where  

1 3

 

  Qij  Qkk  ij   ij 

(10)

1 P p   Qkk  ij 3

(11)

Q Rij  Cij ij

(12)

where Cij is the cross term stress tensor, Rij and Qij are Sub-Grid Scales (SGS) Reynolds stress tensors. Smagorinsky developed a model for the SGS stresses assuming that they follow a gradient-diffusion process similar to molecular motion, whose governing equations are:

 ij  2 T S ij , Sij

1  u i u j   2  x j xi

   

(13)

where Sij is the resolved strain rate, νT is the Smagorinsky eddy viscosity

 (Cs )2 Sij Sij T

(14)

and Cs is the Smagorinsky coefficient. The accuracy of LES is much dependent on the use of an accurate SGS stress model and in the correct representation of boundary conditions. In alternative to Smagorinsky’s model, Wall Adapting Eddy Viscosity model has been proposed in Ducros et al. (1998), which improves the prediction of the wall stress rate, as well as turbulent intensities.

2.1.3. PANS models Partially Averaged Navier-Stokes model allows for a smooth variation from RANS equations to Navier-Stokes equations, depending on the values of the filter-width control parameters defined in Girimaji (2006): fk 

 Ku , f  u  K

(15)

where fk is the ratio of the unresolved (Ku) to total (K) kinetic energy, fε is the ratio of resolved (εu) to total (ε) dissipation. These models have shown good preliminary results, with results comparable to even the most computationally expensive LES models but have not yet been used extensively in the field of civil engineering.

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2.2. Calculation of wind-induced fatigue damage Two main approaches have been proposed: - Frequency domain-based methods developed from Davenport’s work. These methods calculate the total damage by considering the probability of the fluctuating stress related to different values of mean wind velocity (see Petrov (1998)). As pointed out in Repetto and Solari (2002) these methods are able to provide efficient results but are difficult to use in complex applications; moreover, the link between the stochastic characteristics of excitations and those of the structural response is easily determinable only when the structural model is linear (see Cluni et al. (2007)). In Repetto and Solari (2002) and Holmes (2002) a closed form formulations to assess the wind-induced fatigue damage in narrow band response hypothesis has been proposed. - Time domain-based methods calculate the total damage by applying deterministic methods, such as the rain-flow counting algorithm, to time series. Time series of turbulent flows can be obtained by performing Monte Carlo simulations or through wind tunnel test. This approach is easier to use but requires higher computational or experimental effort. Nevertheless, as pointed out in Repetto and Torrielli (2017), rainflow cycles counting of long time series is the approach that is most widely used in different fields and standard codes and is part of the framework of classical fatigue theory. As for the calculation of fatigue, some local approaches such as Strain Energy Density (SED) criterion (see Colussi et al. (2017); Lazzarin and Zambardi (2001)) have emerged which, coupled with the usual nominal stress method, are capable of conducting massive amounts of computations while guaranteeing robustness and affordable computational cost for not requiring an extremely fine mesh. 3. Literature review of wind-induced fatigue analysis of steel structures In literature, some analyses have been presented where an assessment of fatigue behavior of structures exposed to wind has been performed. A certain number of papers are here referred and described with the aim of identifying the key flow properties that were necessary for the studies.

3.1. High-rise, slender buildings Repetto and Solari extensively analyzed the fatigue behavior of slender steel structures in Repetto et al. (2014); Repetto and Solari (2002) and formulated a mathematical model in frequency domain in order to obtain the accumulated fatigue damage in closed form for slender vertical structures subjected to alongwind, crosswind and directional gust-excited vibrations. This is done by taking into account the probability distribution of in-site mean velocity and determining the histogram of the stress cycles by applying a probabilistic counting method of the cycles to an analytical solution of the dynamic response. Another approach used by the authors as a benchmark is based on a time-domain analysis based on the cycle counting of synthetic time series produced using Monte Carlo simulations. These approaches need a previous knowledge of the aerodynamic parameters of the structure.

3.2. Long span bridges In Cluni et al. (2007) an investigation of wind-induced cable fatigue has been performed. The fatigue damage was calculated in time domain. Wind tunnel experimental analyses were performed in order to evaluate the drag coefficient of the cable CD . The drag coefficient was then used to calculate the generic i-th component of the vector of nodal wind drag forces: 1 FDi (t )  CD  a Ai U i (t ) U i (t ) 2

(16)


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Where U(t) is the vector of wind velocities at the nodal position, CD is the drag coefficient, ρa is the air density and Ai is the area of influence for each node. The vector of wind velocities can be written as the sum of a mean and a turbulent component. While the mean component is assumed to be constant in space and time, the turbulent component is simulated as a mono-dimensional zero-mean Gaussian stochastic process whose spectrum well approximates the theoretical one. A series of numerical simulations were then performed using a tridimensional geometric nonlinear finite element model and the stress cycles histograms for each simulation were evaluated using rain-flow cycle-counting methods.

3.3. Large roofs and stadiums In Flamand et al. (1996), the authors performed fatigue analyses for the design of a large steel stadium exposed to wind. The fatigue damage was calculated in time domain. A boundary layer wind tunnel provided the time series of the pressures on a 1:200 scaled fixed model of a steel stadium. Using a FEM model, the calculation of stress time series due to quasi-static and resonant wind components was then performed. A rain-flow counting method was then used to build the fatigue load spectrum and the total damage was evaluated using Miners law. In order to calculate the number of cycles for each stress group, the authors used site wind data measured over 30 years to calculate the probability of occurrence of every wind speed. 4. CFD applications to civil structures in literature On the basis of literature research on fatigue analysis of steel structures invested by the wind, it is clear that the wind tunnels are often used to obtain information on the effect of the wind on the structure. Such information consists on the aerodynamic and aeroelastic parameters in the case of analysis based in the frequency domain and in the case of analysis based in the time domain with a synthetic time series. In case of analysis based in the time domain with “real” time histories they consist in the time series of the pressures acting on the scaled model. Reported below are some examples from (the very numerous) CFD simulations in literature regarding large steel structures with the aim of observing whether such methods are able to provide the information necessary to perform fatigue analysis with one of the methods above.

4.1. High-rise, slender buildings -

-

-

In Huang et al. (2007) the authors conducted a comprehensive numerical study of wind effects on CAARC standard tall building. The study used many different CFD turbulence models such as LES, RANS (many RANS closure models were used). The most advanced RANS model used in this test (namely the MMK model) was able to provide a good estimate of all pressure coefficients in most of the cases. The LES method gave results adherent to the results of experimental tests in the wind tunnel as well. It is noted in addition that the LES method is able to capture all effects of the irregular flow while the MMK model is not able to predict a part of the irregular motion. The difference between the two time histories is visible in Figure 1. The authors also provided information about CPU time showing that LES analyses required far more computational resources than RANS. In Elshaer et al. (2016) the authors investigated the aerodynamic response of the on CAARC standard tall building using LES. In addition to the study of Huang and Li et al., a flow generator was implemented that allowed the introduction of an inflow boundary condition that satisfies the proper turbulence spectra and coherency. The pressures are in very good agreement with those from wind tunnels. The power spectral density obtained from the LES using the time history base moments match reasonably with the experimental measurements. In Tominaga et al. (2008) the authors compared CFD results using various RANS and LES models applied to a high-rise building. Among the RANS models, Durbin’s v2-f has shown the best agreement with the experiment. LES model provided better results but the authors remark the influence of the inflow turbulence on the quality of the results.

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Figure 1 - Time histories of CD (Huang et al. (2007))

4.2. Long span bridges -

In Mannini et al. (2016), (2010) the authors have performed 2D Unsteady RANS of the flow field around a trapezoidal box-girder bridge section. Even if these models show some limit, it has been shown that they are able to predict correctly most complex flow features, while requiring low computing resource. In Sarwar et al. (2008) and in Watanabe and Fumoto (2008) the authors conducted LES analyses of box girder bridge sections. Both analyses have shown a very good agreement with experimental data. In Scotta et al. (2016) the authors proposed an engineering procedure that uses numerical analyses based on CFD models to bypass wind-tunnel tests in order to calculate aerodynamic and aeroelastic parameters of bridges subject to wind. The authors were able to obtain a good estimate of many parameters of primary importance (cp, cD, c’L, c’M St) and evaluated the numerical procedure to be suitable as an alternative to wind tunnel tests for bridge design, at least in its initial phase.

4.3. Large roofs -

In Lu et al. (2012) the flow field around a large roof was studied and the authors reported that LES models correctly predict mean and RMS pressure coefficients. The ability to conduct LES analyses for full-scale size model, to use large Reynolds numbers and to capture high pressure gradients in small areas makes this method particularly attractive also in comparison to wind tunnel tests.

5. Discussion and conclusions The analysis of published results have shown that CFD methods are able to provide an adequate estimate of the aerodynamic and aeroelastic parameters in many cases of civil engineering interest and therefore they could be used in place of wind tunnels within the frequency domain-based methods for the calculation of the accumulation of wind-induced fatigue damage. Regarding the use of CFD methods with models for the calculation of wind-induced fatigue damage in the time domain, it is outlined that the CFD models could be used as a basis for the definition of synthetic time series generated by stochastic Monte Carlo methods. Moreover, the cycle counting carried out directly from the time series of pressures obtained as a result from CFD analyses may be developed in analogy to what has been done in Flamand et al. (1996) (ensuring that the spectral resonant components of wind action are correctly identified). Because of the

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large amount of data provided by CFD, a scaling procedure on the basis of climatic data of a fatigue load spectrum evaluated from a reference mean wind velocity (see Flamand et al. (1996); Repetto and Torrielli (2017)) could allow a reduction of computational effort. In the framework of time-domain approach, it is opinion of the authors that the use of a turbulence model that allows to resolve only the most dynamically important fluctuating scales without the need to resolve inertial scales could provide optimal results. This is possible, for example by means of hybrid models such as PANS model by tuning the ratios of the unresolved-to-total kinetic energy and dissipation parameters. Further studies could therefore be carried out to assess the application of hybrid models like PANS models to structures of interest for civil engineering. Another possible future development could be the calculation of fatigue damage based on the time-domain cycle counting of stress cycles obtained from time series from CFD models with different approaches (LES and RANS). In fact, as shown above, both models are able to capture the flow irregularities, and although the LES method provides the most accurate results they are also much more computationally expensive, and their ability to capture more irregularities could be of little significance for the purpose of the accumulation of damage. In conclusion, on the basis of the results of the present review, it is possible to assume that the CFD methods can be successfully used for the purpose of fatigue calculations of steel structures subject to fluctuating wind action. Their use could allow a reduction of the costs of analysis by avoiding, at least in a preliminary phase, the use of expensive models in the wind tunnel. Finally, the authors wish to emphasize the fact that the latest requirements from standards in terms of fatigue safety make it necessary to thicken the links between different engineering disciplines. In fact, CFD or wind tunnel analyses and consequent fatigue analyses have not only an impact on the project but also on the production and quality control phases. Acknowledgement The authors wish to thank Dr Alessandro Catanzano, for kindly providing us his valuable industrial perspective, and Dr Marco Colussi for the useful observation and suggestions. References Argyropoulos, C.D., Markatos, N.C., 2015. Recent advances on the numerical modelling of turbulent flows. Appl. Math. Model. 39, 693–732. doi:10.1016/j.apm.2014.07.001 Bampton, M.C.C., Craig, JR., R.R., 1968. Coupling of substructures for dynamic analyses. AIAA J. 6, 1313–1319. doi:10.2514/3.4741 Cluni, F., Gusella, V., Ubertini, F., 2007. A parametric investigation of wind-induced cable fatigue. Eng. Struct. 29, 3094–3105. doi:10.1016/j.engstruct.2007.02.010 Colussi, M., Berto, F., Meneghetti, G., 2017. Fatigue assessment of welded joints in large steel structures: a modified nominal stress definition, in: Proceedings of the International Fatigue Conference - Fatigue 2017, Downing College, Cambridge, UK July 2017. Davidenkov, N.N., Shevandin, E., Wittmann, F., 1946. The Influence of Size on the Brittle Strength of Steel. Int. J. Appl. Mech. 68. Dowell, E.H., Hall, K.C., 2001. Modeling of fluid-structure interaction. Annu. Rev. Fluid Mech. 33, 445–490. doi:10.1146/annurev.fluid.33.1.445 Ducros, F., Nicoud, F., Poinsot, T., 1998. Wall-adapting local eddy-viscosity models for simulations in complex geometries. Conf. Numer. Methods Fluid Dyn. 1–7. Durbin, P.A., 1991. Near-wall turbulence closure modeling without “damping functions.” Theor. Comput. Fluid Dyn. 3, 1–13. doi:10.1007/BF00271513 Elshaer, A., Aboshosha, H., Bitsuamlak, G., El Damatty, A., Dagnew, A., 2016. LES evaluation of wind-induced responses for an isolated and a surrounded tall building. Eng. Struct. 115, 179–195. doi:10.1016/j.engstruct.2016.02.026 Flamand, O., Bietry, J., Barre, C., Germain, E., Bourcier, P., 1996. Fatigue calculation on the roof sustaining cables of a large stadium in Paris. J. Wind Eng. Ind. Aerodyn. 64, 127–134. doi:10.1016/S0167-6105(96)00087-6 Fröhlich, J., von Terzi, D., 2008. Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44, 349–377. doi:10.1016/j.paerosci.2008.05.001 Girimaji, S.S., 2006. Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method. J. Appl. Mech. 73, 413. doi:10.1115/1.2151207 Hanjalic, K., 2005. Will RANS Survive LES? A View of Perspectives. J. Fluids Eng. 127, 831. doi:10.1115/1.2037084 Hanjalić, K., 2004. Closure models for incompressible turbulent flows. Lect. Notes Von Kármán Inst. 1–75. Holman, D.M., Brionnaud, R.M., Abiza, Z., 2012. Solution to industry benchmarck problems with the Lattice-Boltzmann code XFlow. Eur. Congr. Comput. Methods Appl. Sci. Eng. (ECCOMAS 2012) 22.

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