The introduction of cracks into loaded versus unloaded components has a significant effect on the apparent fracture toughness within finite element modelling. The history effects of crack introduction can be beneficial to defect assessment procedures that do not consider prior plasticity specifically from crack introduction. It is assumed that as strain energy is released due to plastic deformation during crack formation a reduction in the energy available for crack propagation under fracture conditions is experienced. This can be characterized by the formation of a plastic wake behind the crack tip and leads to significant increases in load at critical J and other crack growth parameters for modelling situations. However experimental evidence validating this apparent fracture toughness increase are needed. A beneficial increase in apparent fracture toughness can prolong the life of components that might be taken out of service prematurely if history effects are not considered. This paper discusses a series of experimental and modelling approaches that have been taken to assess the magnitude of the benefit in increase of apparent fracture toughness by the manipulation of crack introduction history effects. An initial parametric study of material properties on the effect of introducing cracks into loaded and unloaded components indicates that most benefit be derived from high hardness, high yield materials such as Aluminum 7000 series alloys. Further work has been carried out with experimental C(T) specimens of Aluminum Alloy 7475 T7351. Cracks were introduced by fatigue into the samples. One set of specimens was fatigued with a low mean load and the other with a high mean load, this was achieved by keeping a consistent ΔK I between specimens and changing the load ratio one set of specimens. Fracture test results indicate that the influence of prior plasticity on fracture initiation is much subtler in experimental trials than in the finite element model. Crack growth resistance curves and neutron diffraction results measuring the residual stress created ahead of the crack tip by this method are be discussed and contrasted with the parametric study and finite element modelling of the two different crack introduction scenarios.

In order to elucidate the temperature dependence of hydrogen-assisted fatigue crack growth (HAFCG), the fatigue crack growth (FCG) test was performed on low-carbon steel JIS-SM490B according to ASTM E647 using compact tension (CT) specimen under 0.7 MPa (≈ 0.1 ksi) hydrogen-gas at room temperature (RT: 298 K (≈ 77 °F)) and 423 K (≈ 302 °F) at stress intensity factor range of Δ K = 30 MPa m 1/2 (≈ 27 ksi in 1/2 ). Electron backscatter diffraction (EBSD) observation was performed on the mid-thick section of CT specimen in order to investigate change in plasticity around the crack wake in gaseous hydrogen environment and how it changes due to temperature elevation. The obtained results showed the higher temperature, the lower intense of HAFCG as reported in our previous article. Plasticity around the crack wake became less in gaseous hydrogen environment, especially tested at 298 K. The propensity of the results obtained at higher temperature (423 K) can be separated into two cases: (i) intense plasticity occurs like tested in air, (ii) crack propagates straighter accompanying less plasticity like tested in gaseous hydrogen environment at 298 K. This implies macroscopic FCG rate is determined by combination of microscopic FCG rate in the case (i) and case (ii).

As the most dangerous flow-induced vibration (FIV) mechanism, fluid-elastic instability is always accompanied by the wake shedding. If both of the two FIV mechanisms are considered, fluid forces in this condition can be quite complex. In this paper, a time-domain model based on unsteady flow theory was used to investigate the fluid-elastic instability in a rotated triangular tube array. The vortex shedding forces were simplified as harmonic forces. Computational fluid dynamics (CFD) was used to get the fluid force coefficients with vortex shedding. The model was established by a finite element code with MATLAB software and simulation results agreed with the experiment results. The results showed the critical instability velocity can be influenced by vortex shedding forces, and double peaks can be found in the frequency spectrum of displacements of tubes. The time-domain displacements showed the phases had been impacted by the shedding and periodic characteristic was found in the displacements results. The model can also be adopted in fluid-elastic instability analysis in other tube arrangements and flow conditions.

Environmentally Assisted Fatigue (EAF) is receiving nowadays an increased level of attention for existing Nuclear Power Plants (NPPs) as utilities are now working to extend their life. In the wake of numerous experimental fatigue tests carried out in air and also in a PWR environment, the French RCC-M code [1] has recently been amended (in its 2016 edition) with two Rules in Probatory Phase (RPP), equivalent to ASME code-cases, “RPP-2” and “RPP-3” [2] [3]. RPP-2 consists of an update of the design fatigue curve in air for stainless steels (SSs) and nickel-based alloys, and is also associated with RPP-3 which provides guidelines for incorporating the environmental penalty “Fen” factor in fatigue usage factor calculations. Alongside this codification effort, an EAF screening has recently been carried out within EDF DT [4] on various areas of the primary circuit of the 900 MWe plants of the EDF fleet. This screening led to the identification of a list of 35 “sentinel locations” which are defined as areas most prone to EAF degradation process. These locations will be subjected to detailed EAF analysis in the stress report calculations (according to the above-mentioned RCC-M code cases) for the fourth decennial inspection of the 900 MWe (VD4 900 MWe) power plants. The potential impact of EAF on the secondary circuit components is another question to address in anticipation of the VD4 900 MWe, as they may be considered as class 1 or class 2 equipment for RCC-M application according to the equipment specification. This paper presents the approach proposed by EDF towards an exemption of environmental effects consideration for secondary circuit components. The argument is first based on a review of experimental campaigns led in Japan and France (respectively on fatigue test specimens and at the component scale) which indicate a Dissolved Oxygen (DO) content threshold below which environmental effects are almost inexistent. The (conservative) value of 40 ppb has been selected consistently with NUREG/CR-6909 revision 0 [5]. The second part of the argument is built, on the one hand, on the analysis of the EDF Technical Specifications for Operation (STE) which narrows the scope of the study only to unit outages, and, on the other hand, on the analysis of 5 years of operations of all 900 MWe plants of the EDF fleet (equivalent to 170 reactor-years). It has been shown that the DO content rarely exceeded the 40 ppb threshold in the secondary coolant, and that in this case, the considered locations were not submitted to any fatigue loading.

Hydrogen effect on fatigue performance of commercially pure BCC iron has been studied with a combination of various electron microscopy techniques. The fatigue crack growth (FCG) in gaseous hydrogen was found to consist of two regimes corresponding to a slightly accelerated regime at relatively low stress intensity factor range, Δ K , (Stage I) and the highly accelerated regime at relatively high Δ K (Stage II). These regimes were manifested by the intergranular and quasicleavage types of fractures respectively. Scanning electron microscopy (SEM) observations demonstrated an increase in plastic deformation around the crack wake in the Stage I, but considerably lower amount of plasticity around the crack path in the Stage II. Transmission electron microscopy (TEM) results identified dislocation cell structure immediately beneath the fracture surface of the Stage I sample, and dislocation tangles in the Stage II sample corresponding to fracture at high and low plastic strain amplitudes respectively.

If a crack is introduced progressively into an elastic-plastic material containing a residual stress field, the incremental relaxation of the residual stress field causes the formation of a plastic wake along the crack boundaries. This leads to the reduction in the J parameter for a crack of a given size, compared to a crack with the same dimensions which has been introduced instantaneously, having the crack faces released simultaneously along the whole length, a 40% reduction is observed in the current analysis. This reduction in J is due to the dissipation of strain energy which is otherwise available for further crack extension, as in the instantaneously introduced crack. This is important for the current J-based fracture assessment common in the nuclear and petrochemical industries such as EDF Energy’s R6 and BS7910:2013 as they currently assume instantaneous insertion of cracks as this is inherently more conservative. Although many studies demonstrating this effect in FE are available, there is little experimental evidence for this phenomenon. Especially those including rigorous comparisons with specimens that have been ‘instantaneously’ cracked. This may be due to the difficulty inherent in manufacturing such a specimen as manufacturing processes rely on the incremental removal of material. The aim of this paper is to detail analysis of a novel method of crack introduction that aims to replicate the deformation behavior of an instantaneously introduced crack tip in a model that has had the nodes released in a progressive manner. This will allow specimens to be machined in a way that replicates ‘instantaneous’ cracking allowing for experimental techniques to be developed to display the difference between instantaneous and progressively introduced cracks.

Hydrophobic surfaces, enabling flow slip past a solid boundary, can be effective for suppressing flow unsteadiness, as well as for heat transfer enhancement; both are important for heat exchanger applications. In the present work, a computational investigation of forced convection heat transfer in cross-flow past a hydrophobic circular cylinder is performed at a Reynolds number value of 300, for which flow past a non-hydrophobic cylinder is three-dimensional. Here, the cylinder surface is maintained at a constant temperature, whereas a Prandtl number of unity is considered. Surface hydrophobicity is modelled based on the Navier model. In a first step, slip conditions are implemented on the entire cylinder surface (full slip), for a nondimensional slip length b* = b/D = 0.20, b being the slip length and D the cylinder diameter. This results in a suppression of flow unsteadiness, as well as in a simultaneous heat transfer enhancement; the latter is quantified by the increase of the mean Nusselt number. Next, in order to reduce the extent of the hydrophobic region, and thus the associated cost, a partial slip setup is considered. This setup consists of alternating hydrophobic and non-hydrophobic strips along the spanwise direction, the width of which is selected considering the spanwise wavelength, λ z , of three-dimensional flow. Further, following recent studies of the authors on two-dimensional flow, a non-hydrophobic region is considered around the average rear stagnation point (in the circumferential direction), for all hydrophobic strips. It is shown that the present setup can result in values of mean Nusselt number comparable to those attained with full slip. Overall, the present results illustrate that a proper implementation of partial hydrophobicity on the cylinder surface, along the circumferential and the spanwise direction, results in a suppression of wake unsteadiness and fluctuating forces, as well as in a simultaneous enhancement of heat transfer rates.

This paper investigates the phase characteristics of vortex shedding from tube banks on acoustic resonance. We measured the time variation of a phase between surface pressures related to the lift force on a tube and acoustic pressure on a side wall related to the acoustic particle velocity when acoustic resonance occurred in in-line tube banks. The measured tube was installed at the second rows in the tube banks. As the peak level of spectrum of surface pressure fluctuations increased, the coherence between vortex shedding and wall acoustic pressure in the tube banks also increased. The phase delay between the lift force and acoustic pressure on the side wall was calculated by using a proposed modeling method. In addition, we discuss the verification of the synchronization feedback for a coupling condition between a sound field and wake oscillator.

Fatigue curves are receiving nowadays an increased level of attention in the wake of experimental campaigns showing that the original ASME III mean air curve, also known as the Langer curve [1], does not represent accurately part of the recently obtained laboratory data. EDF, VTT and E.ON have been working towards a relevant fatigue assessment strategy. The three organizations recently exchanged HCF databases, providing a common benchmark to test and compare the various analysis methods. Following the 2014 PVP paper [2], several statistical approaches are being investigated. A special focus is given to methods able to properly account for run-out data points, which do not have the same statistical significance as failed data points. Besides, it has to be noted that only a limited number of material grades are used in NPP primary loop components and in each case, the material batches are identified and specified in detail. Therefore, a more accurate and relevant fatigue assessment might be obtained by splitting large datasets that generally mix various testing conditions and material grades. A comparison is made between a “mixed” approach and a “separated” one, in which the fatigue assessment is performed successively for two or more subsets, e.g. associated with two testing temperature ranges and/or steel grades. Both “mixed” and “separated” strategies are applied to the EDF and the E.ON databases containing fatigue data in different temperatures for non-stabilized and stabilized austenitic stainless steels. The resulting data scatters are compared and the significance of these statistical approaches to fatigue assessment is discussed.

Hydrophobic surfaces, enabling flow slip past a solid boundary, can potentially be effective for heat transfer enhancement in heat exchanger applications. The scope of the present work is the computational study of forced convection heat transfer in flow past a hydrophobic cylinder, maintained at constant surface temperature. Hydrophobic surfaces are applied in flow control applications, since they enable flow slip past a solid boundary; as a result, they can contribute to flow stabilization. At the same time, hydrophobic surfaces are a potential means for heat transfer enhancement. In the present study, a computational investigation of forced convection heat transfer in cross-flow past a circular hydrophobic cylinder is performed by means of Computational Fluid Dynamics; the effects of hydrophobicity on flow stability and forces are also quantified. Here, low Reynolds number values, Re , are considered, whereas the Prandtl number, Pr , is maintained constant, equal to unity. Hydrophobicity is modelled by means of the Navier model. For slip conditions applied on the entire cylinder surface, the present results demonstrate that the stabilizing effect of increasing the non-dimensional slip length, b * = b/D , b being the slip length and D the cylinder diameter, is accompanied by a simultaneous enhancement of heat transfer. In particular, the time-averaged mean Nusselt number, Nu m , is found to be an increasing function of both b * and Re . Further, it is shown that, for the same levels of b * , an equivalent heat transfer rate can be achieved by substantially reducing the extent of the hydrophobic region, in particular by excluding the rear stagnation point region, i.e. at a significantly reduced cost. Overall, the present results illustrate that implementing partial hydrophobicity results in a substantial enhancement of heat transfer rates and a simultaneous (partial or full) suppression of the wake unsteadiness.

Vortex shedding over a cylinder is strongly affected by the cylinder oscillation. The dynamics of the cylinder wake subjected to harmonic forced excitation in the inline direction at Re = 200 is investigated in this work. Two dominant modes of the transverse velocity field are considered to model and predict the nonlinear interaction of 2D vortex shedding. The normal form symmetries have the main role in the pattern formation. The interaction of two steady modes in the presence of O (2) × S 1 symmetry is described by equivariant theory. Considering the symmetries, the amplitude equations are developed with the frequency saturation information included by the addition of complex coefficients. The reduced model is expanded up to 7 th order, in order to include the spatio-temporal effects. The coefficients of the model are obtained from 2D simulations of the cylinder wake flow. The physical significance of the inline amplitude oscillation on the wake dynamics is captured by the variation of the two linear coefficients of the low order model. Similarly to the numerical results, as the amplitude of oscillation increases, two limit cycles undergo the symmetry-breaking bifurcation leading to a quasi-periodic state. The existence of the second frequency in addition to the natural shedding frequency is manifested as the small amplitude oscillation in the quasi-periodic state. For a forcing amplitude A/D = 0.5, the quasi-periodic state undergoes a torus doubling bifurcation. The dominant frequency of the bifurcated S mode matches the lift coefficient shedding frequency at A/D = 0.5 obtained from the numerical computation. The lift coefficient signal is not absolutely periodic due to the presence of the other peaks in addition to the dominant one at St = 0.1 representing the quasi-periodic flow pattern. The modulated travelling waves bifurcated from the low order model have mode S as the basic v-velocity mode which verifies the symmetric torus-doubled transverse velocity pattern observed in CFD simulation. Thus the proposed low order model can predict, with reasonable accuracy, the bifurcation sequence of the forced cylinder wake dynamic transitions observed in the numerical computation results.

In the wake of numerous experimental tests carried out in air and also in a PWR environment, both abroad and in France, an update of the current thermal fatigue codification is underway in France. Proposals are currently being integrated in the RCC-M code [1]. In parallel, it is necessary to evaluate the impact of codification evolution on the RCS components. In the USA, such evaluations have already been implemented for license renewal to operate power plants beyond their initial 40 years of operation. In order to reduce the scope of the calculations to perform, a preliminary screening was carried out on the various areas of the primary system components: this screening is detailed in an EPRI report [2]. The output of this screening process is a list of locations that are most prone to EAF degradation process and it is on these zones only that detailed EAF calculations are carried out. In France, a similar approach was defined in the perspective of the fourth ten-year visit of the 900 MWe plants (VD4 900 MWe) so as to map out all the locations that are most impacted by EAF and hence concentrate the calculation effort on these specific areas for the VD4 900 MWe. In that respect, a specific methodology to evaluate the factor to account for environmental effects or F en [3] based on correlations [4] for hot and cold shocks was established. These correlations use data that is readily accessible in transient description documents and stress reports such as temperature change, heat transfer coefficients, ramp duration and geometry. The need for these correlations is specific to the French context due to a need for a preliminary and yet precise idea of the overall impact of the modifications brought to the RCC-M code in fatigue before the VD4 900 MWe. This paper presents the results of the screening method that was applied to the whole RCS of the 900 MWe NPP fleet.

Threshold stress intensity factor K ih would be an appropriate index parameter for the cut-off limit in fatigue crack growth analysis in order to prevent hydrogen storage tanks from suffering brittle fractures at hydrogen stations. The K ih factors were evaluated using rising load and constant displacement tests conducted in high-pressure gaseous hydrogen. The following results were obtained: 1. K ih measured under rising load was less than K ih measured under constant displacement. 2. The difference of K ih increased as tensile strength decreased. 3. The difference of K ih may be attributed to the plastic wake of propagating cracks. Hydrogen diffusion behavior at crack tips was also estimated by a finite difference method analysis.

DNS results are presented for three-dimensional flow past a circular cylinder forced to oscillate both in the transverse and in-line direction with respect to a uniform stream, at Reynolds number equal to 400, and are compared against simulation results for two-dimensional flow. The cylinder follows a figure-eight motion, traversed either counter-clockwise or clockwise in the upper half-plane for a flow stream from left to right. The transverse oscillation frequency is equal to the natural frequency of the Kármán vortex street. The Navier-Stokes equations are solved using a spectral element code, and the forces acting on the cylinder are computed for both three- and two-dimensional flow. The results demonstrate that the effect of cylinder oscillation on the flow structure and forces differs substantially between the counter-clockwise and the clockwise oscillation mode. For the counter-clockwise mode, forcing at low amplitude decreases the flow three-dimensionality, with the wake becoming increasingly three-dimensional for transverse oscillation amplitudes higher than 0.25–0.30 cylinder diameters, with corresponding discrepancies in forces with respect to two-dimensional flow. For the case of clockwise mode, a strong stabilizing effect is found: the wake becomes two-dimensional for a transverse oscillation amplitude of 0.20 cylinder diameters, and remains so at higher amplitudes, resulting in nearly equal values of the force coefficients for three- and two-dimensional flow.

In this paper, the flow-excited acoustic resonance of an in-line row of cylinders ranging from one to five is investigated. Cylinders of three different diameters of 12.7 mm, 19.1 mm, and 25.4 mm are tested in cross flow with flow speeds up to 160 m/s. Two different tube lengths of 76.2 mm and 127 mm are used to investigate the effect of the cylinder’s aspect ratio at a given diameter on the excitation mechanism of acoustic resonance. A fixed spacing ratio of L/D = 2 is used for all cases. For more than one cylinder of the larger diameter, the self-excitation of resonance occurs at two discrete flow velocity regions that are generally wider than the case of a single cylinder. A larger diameter does not only trigger the excitation of the pre-coincidence resonance region, but also increases the normalized acoustic pressure of this pre-coincidence resonance. On the contrary, the cylinder’s aspect ratio does not have a similar effect on the pre-coincidence and coincidence resonance regions. Therefore, it is important that the effect of diameter should be included in formulas predicting the occurrence of resonance for in-line tube bundles. In addition, the Strouhal number related to the coincidence resonance decreases with the increase in the number of cylinders. The coincidence resonance is related to the vortex shedding in the wake of the last cylinder, while the pre-coincidence resonance is related to the shear layer in the gap between successive cylinders.

A simplified model of a landing gear is tested in a wind tunnel to investigate the effect of the landing light orientation on the resulting noise generation. Examination of the near-field pressure fluctuations, combined with phase-locked stereoscopic particle imaging velocimetry (SPIV) of the unsteady wake identified two distinct sources of pressure fluctuations. The higher frequency source has a wide frequency band and is situated in the outer regions of the wake near the lights. However, the lower frequency source is found to be stronger, has a narrower frequency band, and is developed further downstream in the wake, closer to the wake centerline. The lower frequency source is observed to be rather robust as it is hardly affected by the orientation of the landing lights, whereas the higher frequency source becomes weaker as the distance between the lights is reduced. The effect of a splitter plate positioned downstream of the strut is also investigated as a means of disrupting the lower frequency pressure fluctuations. Although the lower frequency source is considerably reduced by the splitter plate, substantial enhancement of the higher frequency source is observed.

In the wake of numerous experimental tests carried out in air and also in a PWR environment, both abroad and in France, an update of the current fatigue codification is underway. Proposals are currently being formulated in France [1] [2] and discussions are taking place in the frame of a French working group involving EDF, AREVA and CEA. In parallel with these worldwide modification efforts, it is necessary to evaluate their impact on the NSSS components. In the USA, many such evaluations have already been implemented for license renewal to operate power plants beyond their initial 40 years of operation. In order to reduce the scope of the calculations to perform, a preliminary screening was carried out on the various areas of the primary loop: this screening is detailed in an EPRI report [3]. The output of this screening process is a list of locations that are most prone to EAF degradation process and it is on these zones only that detailed EAF calculations are carried out. In France, with the approaching fourth decennial inspection of the 900 MWe (VD4 900 MWe) power plants, EDF needs also to map out the impact of these updates to the RCC-M code before initiating detailed calculation efforts. The EPRI report was not applicable as such to the French plants due to domestic specificities and more particularly, a need for a more detailed F en estimation. A method was therefore developed by EDF, peer-reviewed by SI with the main innovation being the introduction of correlations enabling the calculation of F en on the basis of the geometrical dimensions and the information available in the transient document. This paper presents how these correlations were built and proposes to benchmark them with some existing sample case problems.

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Four square prisms of aspect ratios AR = 9, 7, 5 and 3 were tested at a Reynolds number of Re = 7.4×10 4 . The relative thickness of the boundary layer on the ground plane was δ/D = 1.5 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths were varied from L/D = 1 to 7. Measurements of the mean drag force were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-sensor hot-wire probe. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR ≤ 5) when long splitter plates (of L/D ≥ 5) were used. In contrast, a splitter plate of length L/D = 3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression.

Many technologies based on fluid-structure interaction mechanisms are being developed to harvest energy from geo-physical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using VIV of cables is addressed in this paper, through the case of a hanging cable with a harvester at its upper extremity. An experimental analysis of the vortex-induced vibrations of a hanging cable with variable tension along its length is first presented. It is shown that standing waves develop and that the extracted mode shapes are self-similar. This self-similar behaviour of the spatial distribution of the vibrations along the hanging string is explained theoretically by performing a linear stability analysis of an adapted wake-oscillator model. The hanging cable is then combined with a localized harvester and its dynamics is measured. An appropriate reduced-order wake-oscillator model is also used to perform parametric studies of the impact of the harvesting parameters on the efficiency. An optimal set of parameters is identified and it is shown that the maximum efficiency is close to the value reached with an elastically-mounted rigid cylinder. The efficiency is found to be essentially driven by the occurrence of traveling wave vibrations.

The mean wake of two identical surface-mounted finite-height circular cylinders arranged in a tandem configuration was investigated in a low-speed wind tunnel using a seven-hole pressure probe. The Reynolds number was Re = 2.4×10 4 , the cylinder aspect ratio was AR = 9, and the boundary layer thickness on the ground plane relative to the cylinder height was δ/H ≈ 0.4. Three centre-to-centre longitudinal pitch ratios of L/D = 1.125, 2, and 5 were examined, corresponding to the extended-body, reattachment, and co-shedding flow regimes, respectively. Reference measurements were also made in the wake of a single finite circular cylinder of AR = 9. For the tandem configurations, velocity measurements were made behind the downstream cylinder in two orthogonal vertical planes. Compared to the wake of the single surface-mounted finite-height circular cylinder, the mean downwash and upwash flows for the tandem cylinders, behind the downstream cylinder, were weaker, the mean recirculation zone behind the downstream cylinder was shorter, and the mean wake extended higher above the ground plane, for all three pitch ratios. Marked changes were also observed in the mean streamwise wake vortex structures, compared to the case of the single finite cylinder. For the extended-body and reattachment flow regimes, the tip vortex structures became elongated in the wall-normal direction. In the co-shedding regime, two sets of tip vortices were observed, with the second set possibly originating from the upstream cylinder.