Jordan Barras
email: jordan.barras@cea.fr

Nicolas Leymarie

Delphine Landois

Alexandre Imperiale

Edouard Demaldent

Philippe Bredif

Orland Guedes

Hiroshi Hori

Roel Van Os

Roel Van Os

Custom transient finite element for the modelling of ultrasonic testing methods for downhole well integrity

Introduction

Ultrasonic measurements are one of the nondestructive testing (NDT) methods used with oil and gas well tubulars to ensure the safe hydrocarbon production from subsurface reservoirs. Ultrasonic transducers are deployed downhole to evaluate the thickness of tubulars and acoustic impedance (AI) of material outside the tubulars, respectively for tubular corrosion and well cement quality evaluation. The transducers excite wide-band frequency signals below 1 MHz to excite signals near the fundamental thickness resonance of tubulars in acoustically attenuative downhole environment. Semi-analytical methods are very popular in the NDT industry thanks to relatively low calculation times compared to finite element methods (FEM). This is the case of the models implemented in the CIVA platform: CIVA-UT provides an accurate estimation of the ultrasonic field radiated by an ultrasonic transducer in a propagation media that can be fluidic, elastic or a combination of several materials in a structure of which geometries are much larger than the elastic wavelength, which is often the case in the NDT industry. The semi-analytic modelling software URAI, developed at SLB, uses a similar approach in terms of transducer signal modelling, but is based on an analytical elastic response of a cylindrically layered structure to a very wide band excitation. Near the frequency of the fundamental thickness mode resonance of the tubular, strong compressional and shear-coupled modes are excited. This coupling invalidates the CIVA software model that uncouples the longitudinal and the transversal calculations. A simulation of the cylindrical geometry has been carried out by CIVA-UT as a test, and it shows such a discrepancy in the results. One of the limits of the URAI model appears when the geometry of the inspected part is not a cylinder, includes a defect or exhibits some other irregularity. In this case the formulation of the analytical elastic response is insufficient.

The main way to accurately simulate such geometries is in the use of FEM software, such as OnScale. Calculation times, however, are much higher than those for semianalytic methods. One of the strengths of the CIVA software lies in the combination of several models to solve the ultrasonic propagation. One of them is using standard CIVA-UT models in a wide propagation zone, combined with a finite element domain that is defined only around a zone of interest, here the elastic cylinder. The result is a compromise between a shorter calculation time offered by the CIVA-UT module and the accuracy of the FEM zone. In the current commercial version of CIVA, only a defect can be included in the FEM area. In the method described in this paper, this principle has been extended, such that the part itself can be included.

Evaluation of the well integrity

In the past decades, the oil & gas industry has invested considerably in the well integrity domain. One of the key aspects is to provide a good cement quality behind a steel casing that ensures the sealing of hydrocarbons from the reservoirs to the different zones of the well. SLB offers a solution involving ultrasonic technology to evaluate the acoustic impedance behind a steel casing [START_REF] Hayman | High Resolution Cementation and Corrosion Imaging by Ultrasound[END_REF] [2] [START_REF] Thierry | New-Generation Ultrasonic Measurements for Quantitative Cement Evaluation in Heavy Muds and Thick-Wall Casings[END_REF]. A commercial downhole ultrasonic imager uses an ultrasonic transducer mounted on a rotor that enables an azimuthal scan from the interior of a well. Such tool is deployed downhole at the end of a logging cable to transmit measured data while running into or pulling out of a well. The transducer is excited at the central frequency of 500 kHz and the received signal is processed using the T 3 algorithm [1] dedicated to obtaining the thickness of the casing and the acoustic impedance behind the casing in real time.

State of the art of simulation tools for the SLB case study

Figure 1 shows a schematized cross-section of a wellbore with a single casing. The fluid inside the casing is often referred to as 'mud'. The casing itself is typically made of carbon-steel. The annular space behind the casing is typically filled with a cement. The acoustic impedance of material behind casing may vary in the range from about 0 to 10 MRayl, respectively from gas to high-density well cement. Table 1 shows three typical materials to be discriminated during the control that is simulated for this case study. If cement is compromised in quality, inclusions or entire connected paths of water or gas may be present in the cement. The downhole ultrasonic imager can distinguish between the different acoustic impedances and discriminate cement from water and gas.

As such, it provides a response of the integrity of the cement.

Simulation using OnScale FEM

The modelling of ultrasonic wave-propagation is well defined by finite element codes. In this study, OnScale [START_REF] Onscale | Simulation of Ultrasonic Borehole Imaging[END_REF] is used to provide reference FEM results. The code uses an explicit scheme that allows a parallelization of the calculation. The OnScale platform sends the tasks to cloud computing servers to speed up the computation process.

Simulation using CIVA

The computation of ultrasonic fields and inspections in CIVA is performed with two different models.

The first one, implemented in the historical CIVA-UT module, is a semi-analytic and under high-frequency assumption formulation [START_REF] Gengembre | Pencil Method in Elastodynamics: Application to Ultrasonic Field Computation[END_REF] of the main bulk waves usually interfering in the NDT applications (namely longitudinal and transverse waves in the solids). A relatively restricted number of interactions with the specimen boundary is computed, taking into account all possible wave conversions. Defects of dimension above the wavelength can also be treated through analytic diffraction models or more generically by FEM boxes englobing the defect [START_REF] Imperiale | Coupling Strategies Between Asymptotic and Numerical Models with Application to Ultrasonic Non-Destructive Testing of Surface Flaws[END_REF]. A custom CIVA module, that is currently under development, integrates an in-house finite element solver that relies on transient spectral element method (SEM). The latter is usually coupled to the semi-analytical model, which sets the loading source on well-chosen coupling boundaries. The resolution is performed following a domain decomposition approach: the topology of the scene is described by a macro mesh that allows solving separately an acoustic problem in fluid zones and an elastodynamic problem in solid zones. The transfer conditions between two neighboring macro elements are realized by mortar elements [START_REF] Imperiale | A macro-element strategy based upon spectral finite elements and mortar elements for transient wave propagation modeling. Application to ultrasonic testing of laminate composite materials[END_REF]. The high-order micro mesh, which is used for the SEM computation, is generated automatically according to the considered minimum wavelength.

Dedicated hybrid simulation chain

A fully integrated simulation procedure is set in place. It begins with the specimen generation, done by a built-in plugin implemented in C++ and Python. Parameters that define the nominal casing are controlled with a dedicated graphical interface (see Figure 2). This interface can be completed in the future to describe damaged casings. The FEM mesh is automatically generated. Then, the specimen can be used either for CIVA-UT or for hybrid simulations. This framework not specific to the actual study case and can be easily derived for other applications [START_REF] Demaldent | Custom Transient Finite Element Method and Ray Tracing Hybridization Strategies for Ultrasonic Testing Modelling[END_REF].

Figure 2. View of the specimen generation plugin graphical user interface.

Calibration procedure

The calibration part is a simple steel tube with an external diameter of 139.7 mm and a thickness of 2 mm. It is filled with water and the inspection is done, in immersion, on the internal surface. The external surface is left free. The macro mesh of the complete specimen is thus a triple ring extruded along its axis. The three layers are the part itself, a fluid layer and a fluid perfectly matched layer (PML) that is settled in the inner side (see Figure 3). The CIVA user starts by defining a region of interest (ROI) in the CAD view provided by the specimen generator plugin. Such region has a geometry surrounding the piece or solely the coupling region, with a part in the mud. The ROI is meshed, and the calculation is performed with the boundary conditions defined above.

Figure 3. Macro scene of a calibration configuration using the ROI subdivision.

To be able to quantitatively compare the simulation with the experimental measurements, a calibration procedure is deployed based on the measurement of the experimental A-Scan 𝑉 (𝑐𝑎𝑙) obtained with the calibration part.

Because of the resonant character of this configuration, a simple calibration on the amplitude gain is not sufficient.

The objective is to obtain the reference signal 𝑠 (𝑟𝑒𝑓) which, if used as an excitation signal during the simulation, returns the experimental A-Scan on the calibration part. We thus have:

𝑉 (𝑐𝑎𝑙) (𝜔) = 𝐻 (𝑐𝑎𝑙) (𝜔) • 𝑠 (𝑟𝑒𝑓) (𝜔), (1)
where 𝐻 (𝑐𝑎𝑙) is the simulated transfer function. To obtain the reference signal, it is first necessary to characterize this transfer function over the frequency band over which 𝑉 (𝑐𝑎𝑙) is non-zero. This is done by performing a first simulation, denoted by (0), on the calibration part and taking an excitation signal 𝑠 (0) whose spectrum encompasses the target bandwidth of the probe. We can summarize this simulation by writing:

𝑉 (0) (𝜔) = 𝐻 (𝑐𝑎𝑙) (𝜔) • 𝑠 (0) (𝜔). (2)
Hence the term 𝐻 (𝑐𝑎𝑙) can be made to disappear by dividing the two previous equalities member by member. The reference signal is expressed as a function of the experimental A-Scan measured on the calibration part and the preliminary simulation data as:

𝑠 (𝑟𝑒𝑓) (𝜔) = 𝑉 (𝑐𝑎𝑙) (𝜔) 𝑉 (0) (𝜔) • 𝑠 (0) (𝜔). (3)
Finally, the introduction of a factor ϵ≪1 regularizes the spectral division for near zero values of 𝑉 (0) :

𝑠 (𝑟𝑒𝑓) (𝑡) = ℱ -1 ( 𝑉 (𝑐𝑎𝑙) • (𝑉 (0) ) * |𝑉 (0) | 2 + 𝜖 • 𝑠 (0) ) (𝑡). (4)
This calibration procedure uses a rather basic deconvolution method of the experimental calibration signal. Its implementation has been done using a web app framework integrated in this custom CIVA version (see Figure 4) providing the new reference signal to use in the .civa file of the preliminary simulation. To verify the correct operation of the procedure, we compare the experimental A-Scan with the simulated A-Scan obtained from this calibrated reference signal.

According to Figure 5, we observe a very good agreement, except for the noise filtering. The calibration procedure thus meets the specifications.

Figure 5. Validation of the calibration procedure by reproducing the experimental signal, using the reference signal as an input to the calibration simulation.

Simulation of a casing

Now we aim to model the situation presented in Figure 1.

The difference with the calibration specimen is that the metallic tube does not have free outer boundary conditions. Instead, a cement layer must be added. Wave reflections at the outer cement radius are not of interest to the current simulation. Therefore, only a thin cement layer needs to be meshed (~ 1 or 2 wavelengths) and surrounded by a solid PML. The ROI can still be applied, as shown in Figure 6.

Figure 6. Macro scene of a casing configuration using the ROI subdivision.

Results and Discussion

Four modeled time-domain signals from the aforementioned methods are presented in Figure 7. The signals are bandpass-filtered in 400 ± 50 kHz frequency range and scaled to better visualize the match among the four simulations. The signals are inverted to the casing thickness and annular AI using T 3 processing excluding the correction for nonplanar geometry [START_REF] Hayman | High Resolution Cementation and Corrosion Imaging by Ultrasound[END_REF]. Inverted AI and casing thickness values are presented in comparison to the model input AI values, respectively in Figure 8 and Figure 9. Figure 9 presents the inverted resonance frequencies, normalized by a reference frequency, i.e., inverse two-way traveling time of the compressional wave in casing thickness. The resonant frequency is negligibly dependent on annular impedance. Relatively large deviation of CIVA-UT results from other models indicates its limited applicability to simulation of the casing resonance in this example case. Indeed, CIVA-UT is a propagation model that is not designed to deal with resonance problems (contrarily to the URAI model) and is usually applied to more classical bulk waves inspections.

Conclusions

After the confirmation that the CIVA-UT module was not adapted for low-frequency well inspection, a dedicated semi-analytic / FEM simulation tool is implemented. Every useful option is accessible using the CIVA graphical user interface. A simple and easy-to-use frequency calibration method is also made accessible using an add-in framework.

Results of the hybrid method are compared with results from a commercial FEM code and with results from the URAI analytical model. It confirms the validity of the proposed dedicated tool. Further developments will consist of adding reference defects as supplementary options of the specimen generator plugin and to study their influence on the extracted acoustic impedance. Such defects include canonic holes made on purpose to qualify the inspection method with the calibration part. Finally, the goal is to detect and characterize real defects, in particular thickness losses due to corrosion, channeling in the cement layer and so-called micro-annuli (thin fluid or gas inclusions between the metallic casing that hamper the interpretation of the cement integrity).

Figure 1 :

 1 Figure 1: Ultrasonic signal simulation in a water-filled casing surrounded by annular material.

3. 1 .

 1 Simulation using URAIThe model used by SLB is based on the resolution of acoustic wave scattering through reciprocity relations. These developments led to the simulation of the response of ultrasonic transducers interacting with fluid-loaded cylindrically layered elastic structures[START_REF] Randall | Mathematical model for internal ultrasonic inspection of cylindrically layered structures[END_REF] [5][START_REF] Zeroug | Spectral Integral Formulae for the Response of Acoustic Transducers in Cylindrically Curved Configurations[END_REF].

Figure 4 .

 4 Figure 4. Graphic user interface of the calibration app.

Figure 7 :

 7 Figure 7: Simulated time-domain signals, 400 ± 50 kHz bandpass-filtered.

Figure 8 :

 8 Figure 8: Inverted annular acoustic impedance.

Table 1 :

 1 Material parameters of the annulus

	Material	VL	VT	ρ	ZL
		(m/s)	(m/s)	(g/cm 3 )	(MRayls)
	Water	1500	/	1.01	1.52
	Cement 1	3600	2000	1.90	6.84
	Cement 2	3000	1600	1.70	5.10


Perla Alnajjar

Déborah Martin

Claire Soligot-Hognon

Delphine Muselet

Hussein Kanso

Stéphane Pacaud

Cyril Feidt

Pierre-Loïc Saaidi

Yves Le Roux

Evaluation of the biodegradability of chlordecone during mesophilic and thermophilic organic waste treatment via anaerobic digestion

Anaerobic digestion (AD) has long been studied as an effective treatment strategy for organic wastes contaminated with recalcitrant pollutants. The bioremediation potential of AD was tested on digestates supplemented with chlordecone (CLD, C10Cl10H2O2), a persistent organic pollutant that has been applied in the French West Indies (1972Indies ( -1993) ) against the banana black weevil Cosmopolites sordidus. Its application has resulted in an extensive longterm environmental contamination; concentrations between 0.03-24.2 mg.kg -1 of soils are still recorded 1 . CLD has been shown to accumulate in the food chain 2 triggering harmful acute and chronic toxicities in humans 3 . Anaerobic digestates from animal and plant origins were spiked with 20 mg.L -1 of CLD and incubated, in batch mode, under mesophilic (37.5°C) and thermophilic (55°C) conditions, respectively. This concentration was chosen to facilitate the detection and/or quantification of transformation products (TPs) at early stages as well as the quantification of CLD after 40 incubation days. A sacrificial approach was followed in which the bottles were stopped at different incubation days (0, 5, 20, and 40), extracted with a developed QuEChERS 4 protocol, and analyzed with a combined GC-MS and LC-HRMS approach.

The Biochemical Methane Potential (BMP), followed throughout the entire experiment, showed that a concentration of CLD as high as 20 mg.L -1 did not alter the production of biogas, as evidenced by the absence of a statistically significant difference between the bottles filled with CLD-treated digestates and the control bottles. Moreover, a redox potential lower than -350mV was maintained, providing thus sufficient reducing conditions reported to be needed for efficient CLD degradation 5 . Indeed, a significant reduction of around 87 +/-4% of CLD under thermophilic conditions, after 40 days, was observed. Under mesophilic conditions, the reduction of CLD was rather moderate with a decrease in CLD concentration of 32 +/-7%.

Various TPs, with a similar profile to that obtained with previous microbiological degradation studies 6,7 , appeared in a concomitant manner with CLD's removal. Hydrochlordecones (C10Cl10-nO2H2+n , n=1,2), arising from reductive dechlorination, as well as polychloroindenes (C9Cl6-nH2+n , n=1,2), formed after ring-opening, were quantified. Polychloroindenecarboxylic acids (C10Cl5-nH3+nO2 , n=1,2) were also detected.

The anaerobic digestion, in our experimental conditions, has therefore provided the adequate conditions needed not only to dechlorinate CLD but also to open its ring structure which is partially responsible for its persistence in the environment. AD could thus possibly be considered as an effective treatment technique for CLD-contaminated organic wastes. The fate of the obtained TPs as well as their possible toxicity will be explored in subsequent works. Laquitaine, L., Rambinaising, S., Flick, R., Starostine, A., Jean-Marius, C., Edwards, E. A., & Gaspard, S. (2020). Evidence for extensive anaerobic dechlorination and transformation of the pesticide chlordecone (C10Cl10O) by indigenous microbes in microcosms from Guadeloupe soil. PloS One, 15(4), e0231219.

  Crabit, A., Cattan, P., Colin, F., & Voltz, M. (2016). Soil and river contamination patterns of chlordecone in a tropical volcanic catchment in the French West Indies (Guadeloupe). Environmental Pollution, 212, 615-626. https://doi.org/10.1016/j.envpol.2016.02.055 2:Dubuisson, C., Héraud, F., Leblanc, J.-C., Gallotti, S., Flamand, C., Blateau, A., Quenel, P., & Volatier, J.-L. (2007). Impact of subsistence production on the management options to reduce the food exposure of the Martinican population to Chlordecone. Regulatory Toxicology and Pharmacology: RTP, 49(1), 5-16. https://doi.org/10.1016/j.yrtph.2007.04.008 3: Maudouit, M., & Rochoy, M. (2019). [Systematic review of the impact of chlordecone on human health doi.org/10.1016/j.therap.2019.01.010 4: Déborah Martin, Delphine Muselet, Perla Alnajjar, Stéphane Pacaud, Yves Le Roux, Sébastien Bristeau, Jennifer Hellal, Cyril Feidt et Pierre-Loïc Saaidi. Protocole d'extraction QuEChERS pour l'analyse de la chlordécone et ses produits de transformation dans des procédés de (bio)remédiation et des échantillons de sol. Poster présenté dans le cadre du « GFP 2022 », 18-20 Mai 2022, Namur, Belgique. 5: Dictor M.C., Mercier A., Lereau L., Amalric L., Bristeau S., Mouvet C., avec la collaboration de Auger P., Béchu E., Breeze D., Touzelet S., Tris H. et Henry B. (2011). Décontamination de sols pollués par la chlordécone. Validation de procédés de dépollution physico-chimique et biologique, étude des produits de dégradation et amélioration de la sensibilité analytique pour la chlordécone dans les sols. Rapport final. BRGM/RP-59481-FR, 201p., 70 fig., 42 tabl., 6 ann. 6: Chevallier, M. L., Della-Negra, O., Chaussonnerie, S., Barbance, A., Muselet, D., Lagarde, F., Darii,E., Ugarte, E., Lescop, E., Fonknechten, N., Weissenbach, J., Woignier, T., Gallard, J.-F., Vuilleumier, S., Imfeld, G., Le Paslier, D., & Saaidi, P.-L. (2019

  ). Natural Chlordecone Degradation Revealed by Numerous Transformation Products Characterized in Key French West Indies Environmental Compartments.

	Environmental	Science	&	Technology,	53(11),	6133-6143.
	https://doi.org/10.1021/acs.est.8b06305
	7: Lomheim, L.,


domain: spi nlin

text:
Wen Yang

Ivan Delbende

Yann Fraigneau

Laurent Martin Witkowski

Laurent Martin

Witkowski Structures

Structures in a rotating flow with free surface: simulations and experiments

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Structures in a rotating flow with free surface: simulations and experiments.

Wen Yang 1,2 , Ivan Delbende 3,4 , Yann Fraigneau 4 , Laurent Martin Witkowski 3,4

1 Sorbonne Université, Collège Doctoral, F-75005 Paris, France The intermediate Reynolds number regime has been investigated using several numerical techniques -computations of steady solutions, mean unsteady two-dimensional and threedimensional direct simulations -as well as Laser-Doppler Velocimetry measurements. Simulations reveal the structure of a toroidal flow located at the periphery of a central solid body rotation region. This flow cell is found bordered by four layers in the meridional plane, a bottom layer on the disk, a side layer along the wall, a core layer separating the solid body rotation (discussed also in [START_REF] Iga | Axisymmetric flow in a cylindrical tank over a rotating bottom. Part I. Analysis of boundary layers and vertical circulation[END_REF]) and a layer at the free surface. The Froude number that quantifies surface deformation and the Reynolds number are shown to have little effect on the flow structure when the Reynolds number is sufficiently large. By increasing the aspect ratio, we find that the toroidal flow is composed of an upper sub-region with sinuous core layer and a mostly z-independent lower region. The mean flow and the rms of fluctuations in 3D simulations obtained through space and time averaging are compared with LDV measurements. A fair agreement is obtained for azimuthal and axial velocity distributions, except some local discrepancies.

Preliminary experiments show that the modal structure at intermediate Reynolds number is robust over a large range of f d as long as the free surface does not touch the bottom disk. The spectrum shown in figure 1(c) indicates that this instability is observed always at a frequency close to 2f d before moving abruptly to 1.13f d when the rotating triangle occurs. Yet, the transition between the two regimes seems complex and depends on the protocol used to increase the disk speed [START_REF] Mougel | Ondes et instabilités dans les écoulements tournants à surface libre[END_REF].

2

  FAST, UMR 7608, Parc-Club Orsay Université, F-91405 Orsay Cedex, France 3 Sorbonne Université, Faculté des Sciences et Ingénierie, UFR d'Ingénierie, F-75005 Paris, France 4 LIMSI, CNRS, Bât. 507, rue du Belvédère, F-91405 Orsay Cedex, FranceWe are interested in the free surface rotating flow driven by the rotation of the bottom in an open cylinder with radius R. Given an initial filling depth H, increasing the rotation disk frequency f d breaks the flow axisymmetry. Two kinds of instability patterns can be observed: a modal structure with almost no free surface deformation (Fig.1a) similar to those observed in[START_REF] Poncet | Shear-layer instability in a rotating system[END_REF] at intermediate Reynolds number values; a pattern of rotating polygons at high Reynolds numbers (Fig.1b) with large free surface deformations[START_REF] Vatistas | A note on liquid vortex sloshing and Kelvins equilibria[END_REF]. In the present work, we carry out a detailed study of the flow structure for the intermediate Reynolds number regime by characterizing the influence of Froude number, aspect ratio and Reynolds number. The ultimate goal is to understand if the structures prevailing in the two regimes are related.

Figure 1 :

 1 Figure 1: (a)-(b) Top view of the experiment using kalliroscope to visualise the flow structure (H = 26 mm, R = 140 mm). (a): azimuthal mode m = 3 for f d = 14.6 rpm (no surface deformation is observed). (b): rotating triangle with a dry core at f d = 139 rpm. (c): typical spectrum of the azimuthal velocity component [probe location (r, z) = (112, 13) mm].


Samir F Matar

Vladimir Solozhenko
email: vladimir.solozhenko@univ-paris13.fr

Keywords: diamond polytypes, hybridization, DFT, hardness, phonons, electronic structure

Novel ultrahard carbon allotropes from crystal chemistry and first principles: rhombohedral ene-C21 and yne-C24

Introduction

Diamond, known mainly in the cubic form, has a less common hexagonal form called lonsdaleite.

Such structures are also observed in binary SiC, and the different phases are called polytypes, which are distinguished by the stacking of layers, usually labeled A/B/C: AB in 2H (2 layers; hexagonal system), ABC in 3C (3 layers; cubic system), ABCB in 4H (4 layers; hexagonal system), etc. [START_REF]Comprehensive Semiconductor Science and Technology[END_REF].

Silicon and carbon are isoelectronic with respect to the valence shell, and diamond has analogous polytypes, with the best known being 3C, which corresponds to cubic diamond, and 2H, which corresponds to lonsdaleite. Other diamond polytypes: 4H, 8H, 9R to 21R (R for rhombohedral) have been identified with calculated X-ray diffraction data published by Ownby et al. in 1992 [2].

Recently, it has been shown that a novel class of machine-learning-based interatomic potentials can be used for random structure search and readily predicts several hitherto unknown carbon allotropes [START_REF] Deringer | Extracting crystal chemistry from amorphous carbon structures[END_REF], allowing them to be identified with topology labels such as dia (diamond), lon (lonsdaleite), and for polytypes: cfc for 4H diamond, cfe for rhombohedral 9R. In view of the enormous number of carbon allotropes, experimentally found and theoretically predicted, a database "SACADA" has been created to store them with topologies and identifiers; 9R allotrope (hRC 18 in Pearson notation) studied here and classified with cfe topology and database code: 447 [START_REF] Hoffmann | Homo Citans and carbon allotropes: For an ethics of citation[END_REF].

In 3C and 2H diamond, as well as in the extended lattice polytypes, the valence 4 electrons (2s 2 , 2p 2 ) arrange in tetrahedra with sp 3 -like hybridization; note that this term, as well as other carbon hybridizations (sp 2 and sp 1 ), are common in organic chemistry, and less so in the solid state chemistry; nevertheless, they are useful for establishing the chemical description of the bonding and the resulting physical and chemical properties.

For applications such as electronics, the physical properties of diamond can be modified by introducing trigonal C(sp 2 ) -double C=C bonds as in ethene -and linear C(sp 1 ) -triple CC bonds as in acetylene -on the one hand, and by working on the particle size as in nanodiamonds, on the other hand. Indeed, recent works have shown that nanodiamonds with mixed C(sp 2 )-C(sp 3 ) hybridization play an important role in designing advanced electronic materials [START_REF] Lin | Catalysis by hybrid sp 2 /sp 3 nanodiamonds and their role in the design of advanced nanocarbon materials[END_REF]. Zhai et al. highlighted electrochemical applications of hybrid diamond/sp 2 -C nanostructures [START_REF] Zhai | Progress in electrochemistry of hybrid diamond/sp 2 -C nanostructures[END_REF]. Furthermore, regarding other mixed carbon hybridizations, sp 3 -sp 1 were recently identified in superhard so-called "ynediamond", which is classified as semi-metallic [START_REF] Hu | Superhard and high-strength yne-diamond semimetals[END_REF].

In this context, we considered the reduction of the sp 2 /sp 3 extended stoichiometries allotropes, and C 10 , C 14 and C 18 were proposed as derived respectively from 4H, 6H and 8H diamond polytypes, respectively, and also characterized by ultrahardness close to diamond, and semi-metallic electronic structure due to the presence of C(sp 2 ) [START_REF] Matar | Novel ultrahard extended hexagonal C 10 , C 14 and C 18 allotropes with mixed sp 2 /sp 3 hybridizations: Crystal chemistry and ab initio investigations[END_REF]. The purpose of the present work was to study the changes in the mechanical and electronic properties of cfe 9R (hRC 18 ) allotrope, referred to as C 18 in the present work, by the insertion of sp 2 and sp 1 carbon atoms in two stoichiometries, based on crystal chemistry rationale and subsequent first-principles ground state energy calculations of stable structures and derived quantities within the well-established quantum mechanics framework of the density functional theory DFT [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF]. The two novel allotropes: ene-C 21 with sp 3 -sp 2 mixed hybridizations and yne-C 24 with sp 3 -sp 1 mixed hybridizations retain the same cfe topology of the original C 18 . ene-C 21 and yne-C 24 were found unique from the CCDC curation and provided with corresponding DOI references [START_REF] Matar | eneC 21 -166[END_REF][START_REF] Matar | yneC 24 -166[END_REF].

Brief presentation of the computational framework

The methodology was developed in earlier work (cf. [START_REF] Matar | Novel ultrahard extended hexagonal C 10 , C 14 and C 18 allotropes with mixed sp 2 /sp 3 hybridizations: Crystal chemistry and ab initio investigations[END_REF] and the papers cited therein). Essentially, the search for the ground state structures with minimal energies was performed with unconstrained geometry optimizations within the DFT-based plane-wave Vienna Ab initio Simulation Package (VASP) [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] using the projector augmented wave (PAW) method for potentials [START_REF] Blöchl | Projector augmented wave method[END_REF]. Within the DFT, the effects of exchange and correlation (XC) were treated using Generalized Gradient Approximation (GGA) scheme [START_REF] Perdew | The Generalized Gradient Approximation made simple[END_REF]. Investigation of the mechanical properties was based on the calculations of the elastic properties by performing finite distortions of the lattice and deriving the elastic constants from the strain-stress relationship. The calculated elastic constants C ij were then used to obtain the bulk (B) and the shear (G) moduli using the Voigt averaging method [START_REF] Voigt | Über die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper[END_REF] based on uniform strain. Besides the mechanical properties, the dynamic stability was determined from the calculations of the phonons and illustrated with the corresponding band structures in the reciprocal space (Brillouin zone) using the "Phonopy" interface code based on the Python language [START_REF] Togo | First principles phonon calculations in materials science[END_REF]. The structures were plotted using the VESTA graphical program [START_REF] Momma | VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data[END_REF]. For the evaluation of the electronic properties, the band structures were obtained with the all-electrons augmented spherical wave method ASW [START_REF] Eyert | Basic notions and applications of the augmented spherical wave method[END_REF].

Crystal chemistry results

The 9R diamond polytype (hRC 18 ; space group R-3m No. 166) is shown in Fig. 1a, in two representations: ball and stick (left) and tetrahedral stacking (right). C4 tetrahedra are corner sharing within 9 layers like 9-layered SiC polytype. Table 1 listes To create the carbon allotrope with CC bonds, the (3a) 0,0,0 position of ene-C 21 was changed to (6c) 0,0,z resulting in a C 24 stoichiometry. Following the same geometry relaxation protocol as above, the final structure with zero strains is shown in Fig. 1c and the lattice parameters are given in Table 1,

Mechanical properties

The evaluation of the mechanical properties was carried out by calculating the elastic properties by performing finite distortions of the lattice. The elastic constants C ij were then derived from the strainstress relationship, assuming statistically isotropic solid on a large scale. The C ij were then used to obtain the bulk (B) and shear (G) moduli using the Voigt averaging method [START_REF] Voigt | Über die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper[END_REF].

The calculated sets of elastic constants are given in The bulk (B) and shear (G) moduli were calculated from elastic tensors within the Voigt averaging scheme using ELATE software [START_REF] Gaillac | ELATE: an open-source online application for analysis and visualization of elastic tensors[END_REF]. Diamond-like C 18 has the largest B V and G V close to the accepted values for diamond (B V = 445 GPa and G V = 550 GPa [START_REF] Brazhkin | Myths about new ultrahard phases: Why materials that are significantly superior to diamond in elastic moduli and hardness are impossible[END_REF]). For hybrid C 21 , large B V and G V are obtained but they are of smaller magnitudes compared to the original polytype. The trend of smaller B V and G V is confirmed for C 24 . The two hybrid systems with lower densities are increasingly more compressible.

Vickers hardness (H V ) has been predicted using four modern theoretical models. The thermodynamic (T) model [START_REF] Mukhanov | The interrelation between hardness and compressibility of substances and their structure and thermodynamic properties[END_REF], which is based on thermodynamic properties and crystal structure, shows surprising agreement with available experimental data [START_REF] Matar | Crystal chemistry and ab initio prediction of ultrahard rhombohedral B 2 N 2 and BC 2[END_REF] and is therefore recommended for hardness evaluation of superhard and ultrahard phases [START_REF] Solozhenko | Prediction of novel ultrahard phases in the B-C-N system from first principles: Progress and problems[END_REF]. The Lyakhov-Oganov (LO) approach [START_REF] Lyakhov | Evolutionary search for superhard materials: Methodology and applications to forms of carbon and TiO 2[END_REF] takes into account the topology of the crystal structure, the strength of covalent bonding, the degree of ionicity and directionality; however, in the case of ultrahard phases of light elements, this model gives underestimated hardness values [START_REF] Matar | Crystal chemistry and ab initio prediction of ultrahard rhombohedral B 2 N 2 and BC 2[END_REF][START_REF] Solozhenko | Prediction of novel ultrahard phases in the B-C-N system from first principles: Progress and problems[END_REF]. Two empirical models, Mazhnik-Oganov (MO) [START_REF] Mazhnik | A model of hardness and fracture toughness of solids[END_REF] and Chen-Niu (CN) [START_REF] Chen | Modeling hardness of polycrystalline materials and bulk metallic glasses[END_REF], use the elastic properties. Fracture toughness (K Ic ) has been evaluated within the Mazhnik-Oganov model [START_REF] Mazhnik | A model of hardness and fracture toughness of solids[END_REF]. The results for the currently proposed hexagonal carbon allotropes and others from the literature are summarized in Tables 3 and4.

Table 3 shows the crystal parameters, density and Vickers hardness obtained from the thermodynamic model.

Dynamic properties from the phonons

Other stability criteria, namely dynamic stability, were obtained by studying phonons, defined as quanta of vibrations. The phonon energy is quantized by the Planck constant h multiplied by the frequency ω, giving the phonon energy E = (h/2π)ω. The calculations of the phonons for C 18 , ene-C 21 and yne-C 24 are illustrated with the corresponding band structures shown in Fig. 3. In all three panels all frequencies are positive signaling stable systems. Marked differences between the three carbon allotropes are observed for the highest frequencies of the optical modes. In C 18 they culminate at ω ~ 40 THz, a magnitude observed for diamond by Raman spectroscopy [START_REF] Krishnan | Raman spectrum of diamond[END_REF]. In ene-C 21 they culminate at ω max ~ 42 THz, a magnitude also observed for ene-like C 10 , C 14 [START_REF] Matar | Novel ultrahard extended hexagonal C 10 , C 14 and C 18 allotropes with mixed sp 2 /sp 3 hybridizations: Crystal chemistry and ab initio investigations[END_REF], as well as in tetragonal C 6 with 3 tetrahedral and 3 trigonal carbons, where the flat band was attributed to antisymmetric C-C-C stretching in the allene (propadiene) molecule [START_REF] Matar | Crystal chemistry rationale and DFT investigations of novel hard tetragonal C 6 built from tetrahedral C(sp 3 ) lattice embedding allene-like sp 2 linear tricarbon[END_REF]. The phonon band structure of yne-C 24 , exhibits flat bands at 70 THz, which can be assigned to CC characterized by much shorter distance than in ene-C 21 .

Electronic band structures

The electronic band structures shown in Fig. 4 were obtained using the ASW method [START_REF] Togo | First principles phonon calculations in materials science[END_REF] with crystal inputs of the calculated crystal parameters from Table 1. The bands develop along the main directions of the primitive rhombohedral Brillouin zone. For the diamond-like 9R C 18 , Fig. 4a shows an insulating behavior with a large band gap ~5eV separating the filled valence band VB from the empty conduction band CB. The energy level along the vertical line is with respect to the top of the valence band (VB), E V . In contrast, ene-C 21 is metallic-like with a band that crosses the Fermi level E F , and the energy is now with respect to E F . Such behavior can be explained by the delocalized nature of the π electrons resulting from the C=C bonds. Finally, yne-C 24 , shows a semiconducting behavior and the zero energy is with respect to E V . The localization of the charge at the triple CC bond can explain the semiconducting behavior.

Conclusions

The Atomic position C1 (6c) 0, 0, 0.0635(0.1806) C2 (6c) 0, 0, 0.0635(0.2644) C3 (6c) 0, 0, 0.0635(0.9588) C1 (6c) 0, 0, 0.0635 C2 (6c) 0, 0, 0.1782 C3 (6c) 0, 0, 0.24579 C4 (3a) 0, 0, 0 C1 (6c) 0, 0, 0.02267 C2 (6c) 0, 0, 0.0774 C3 (6c) 0, 0, 0.1766 C4 (6c) 0, 0, 0.2358

  the structural parameters showing agreement between literature and presently calculated values of the lattice constants and the z values of three (6c) 0,0,z sites. The shortest C-C separations have two d(C-C) values: 1.54 Å and 1.56 Å, in contrast to diamond with a unique d(C-C) =1.54 Å. Nevertheless, the close relationship to diamond is established by the identical cohesive energy of E coh = 2.479 eV/atom. The introduction of a trigonal sp 2 carbon was achieved by inserting of a 4 th carbon at the (3a) 0,0,0 site resulting in a C 21 stoichiometry. The resulting constrained structure with short C-C distances was relaxed along successive cycles of geometry optimization until reaching the ground state configuration whose parameters are shown in

  3 rd column. As expected, the structure is now characterized by a very short C-C distance of 1.21 Å, close to that observed in the acetylene molecule. The more open structure in Fig.1c, with a different arrangement of the C4 tetrahedra, has a low density ρ = 3.13 g/cm3 . The cohesive energy is reduced by an order of magnitude E coh /atom = -1.923 eV. The two novel ene-C 21 and yne-C 24 allotropes have been identified with cfe topology like original C 18 .Charge density projectionsA further qualitative illustration of the different types of hybridization is obtained from the projections of the charge densities. Figs 2a, 2b and 2c, which reproduce the crystal structure sketches of Fig.1, highlight the volumes shown in yellow. In diamond-like C 18 (Fig.2a), the sp 3 -type hybridization is clearly observed from the tetrahedral volumes around the C atoms. Like diamond, the rhombohedral 9R polytype is a perfectly covalent system with similar physical properties (mechanical, dynamic, etc.) and electronic structure as shown below. Changes are observed in the hybrid ene-C 21 (Fig.2b), where the sp3 -type hybridization is now accompanied by the sp 2 -type one observed with the yellow volumes along the C-C-C unit aligned along the vertical hexagonal cdirection. In Fig. 2c, representing the projections in yne-C 24 , besides the sp 3 tetrahedral shapes, a remarkable charge density is observed along the aligned C-C-C-C unit with strong localization for the middle C-C clearly featuring the CC triple bond. Therefore, the mixed hybridized novel allotropes are further illustrated by the charge density projections.

  For pristine C 18 , the values of density (ρ), hardness (H V ) and bulk modulus (B 0 ) have magnitudes close to those of diamond and lonsdaleite. This is quite expected since 9R carbon is considered to be a diamond polytype. The two hybrid allotropes show lower values closer to C 18 . Table 4 displays the hardness values along the different models in addition to the thermodynamic model presented above. Again, the trends of decreasing values along the series are observed, with the highest value obtained for C 18 . However, the Pugh modulus ratio (G/B) for all three allotropes is almost the same (~1.15). The fracture toughness of C 18 (6.3 MPa•m ½ ) is between the corresponding values for diamond and lonsdaleite, while two hybrid allotropes show lower values, i.e. 5.7 and 4.4 MPa•m ½ for ene-C 21 and yne-C 24 . Similar trends are also observed for Young's modulus (E) and Poisson's ratio (). These trends in mechanical properties are consistent with the decrease in density and increase in openness of the structure upon introduction of C=C and CC bonds in ene-C 21 and yne-C 24 respectively.

Fig. 1

 1 Fig. 1 Ball-and-stick (left) and tetrahedral (right) representations of crystal structures of C 18 (a), ene-C 21 (b) and yne-C 24 (c).

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 2. Charge density projections (yellow volumes) in C 18 (a), ene-C 21 (b) and yne-C 24 (c).

Table 1 ,

 1 2 nd column, characterized by the shortest 18 to 3.39 g/cm 3 in C 21 . Note that the configuration of sp 2 carbon in the present ene-C 21 with C-C-C motifs is closer to the propadiene C 3 H 4 molecule, H 2 C=C=CH 2 .

distance: 1.46 Å assigned to the C=C bond, larger by 0.11 Å than that in the ethylene molecule (~1.35 Å). The perturbation of the 9R diamond polytype (hRC 18 ) leads to a decrease of the cohesive energy E coh = 2.061 eV/atom. The structure shown in Fig.

1b

exhibits a different stacking of tetrahedra and a less compact structure quantified by the decrease in density from ρ = 3.52 g/cm 3 in C

Table 2

 2

	. All C ij values are positive, and their

Table 1

 1 aim of this work was to give diamond new properties by introducing additional carbon atoms forming C=C and CC bonds into the rhombohedral 9R polytype C 18 . The resulting new structures were geometry-optimized to the ground state and found to be cohesive, though less than pristine 9R diamond polytype. Like 9R C 18 , ene-C 21 and yne-C 24 belong to the cfe topology characterizing layered SiC polytypes. From mechanical characterization, the two hybrid allotropes have been identified as ultrahard and dynamically stable. They exhibit high-frequency vibrational phonon modes close to the molecular C=C and CC bonds characteristic of as allene and acetylene molecules, respectively. The electronic band structures are indicative of the insulating C 18 , metallic ene-C 21 and semiconducting yne-C 24 . It is suggested that such model systems are likely to help improve experimental studies of nanodiamonds for electronic and other applications. Crystal structure parameters of carbon allotropes with cfc topology. Values for cfe C 18 are calculated for the C 18 structure proposed by Deringer et al.[START_REF] Deringer | Extracting crystal chemistry from amorphous carbon structures[END_REF].

	Space group	cfe C 18	cfe ene-C 21	cfe yne-C 24
	R-3m (No 166)	SACADA Database Code: 447
	a, Å	2.510	2.4922	2.5935
	c, Å	18.672	22.988	26.290
	V cell , Å 3	101.91	123.65	153.14
	<V atom > Å 3	5.66	5.97	6.38
	Density, (g/cm 3 )	3.52	3.39	3.13
	Shortest bonds, Å 1.54, 1.56	1.46, 1.54, 1.55	1.21, 1.56, 1.59

Table 2

 2 Elastic constants C ij and Voigt values of bulk (B V ) and shear (G V ) moduli (all values are in GPa) of carbon allotropes with cfc topology.

		C C 1 11 1	C C 1 12 2	C C 1 13 3	C C 3 33 3	C C 4 44 4	C C 6 66 6	B B V V	G G V V
	cfe C 18	1168	131	30	1288	518	459	445	516
	cfe ene-C 21	1009	89	33	1423	460	420	417	479
	cfe yne-C 24	794	76	21	1406	359	380	359	415

Table 3

 3 Vickers hardness (H V ) and bulk moduli (B 0 ) of cfe carbon allotropes calculated within the framework of the thermodynamic model of hardness[START_REF] Mukhanov | The interrelation between hardness and compressibility of substances and their structure and thermodynamic properties[END_REF] Ref. 2 ‡ Ref. 28 † Ref.[START_REF] Brazhkin | Myths about new ultrahard phases: Why materials that are significantly superior to diamond in elastic moduli and hardness are impossible[END_REF]

				S Sp pa ac ce e g gr ro ou up p	a a = = b b ( (Å Å) )	c c ( (Å Å) )	ρ ρ ( (g g/ /c cm m 3 3 ) )	H H V V ( (G GP Pa a) )	B B 0 0 ( (G GP Pa a) )
	C 18	#166	R-3m	2.5104	18.672	3.523	98	444
	ene-C 21	#166	R-3m	2.4922	22.987	3.387	94	427
	yne-C 24	#166	R-3m	2.5935	26.290	3.126	87	394
	Lonsdaleite	P6 3 /mmc	2.5221 *	4.1186 ‡	3.516	97	443
	Diamond	Fd-3m	3.56661 ‡	3.517	98	445 †

*

Table 4

 4 Mechanical properties of cfe carbon allotropes: Vickers hardness (H V ), bulk modulus (B), shear modulus (G), Young's modulus (E), Poisson's ratio () and fracture toughness (K Ic )

				T T * *	L LO O † †	H H V V	M MO O ‡ ‡	C CN N § §	B B 0 0 * *	B B	B V B V	G G V V	E E * ** *	  * ** *	K K I Ic c ‡ ‡
								GPa					MPa•m ½
	C 18	#166	98	90		97	89	444		445	516	1117	0.082	6.3
	ene-C 21	#166	94	73		89	84	427		417	479	1039	0.084	5.7
	yne-C 24	#166	87	69		77	78	394		359	415	899	0.082	4.4
	Lonsdaleite	97	90		99	94	443		432	521	1115	0.070	6.2
	Diamond	98	90		100	93		445 † † † †		530 † † † †	1138	0.074	6.4

* Thermodynamic model

[22]

† Lyakhov-Oganov model

[25]

‡ Mazhnik-Oganov model

[26]

§ Chen-Niu model

[START_REF] Chen | Modeling hardness of polycrystalline materials and bulk metallic glasses[END_REF]

** E and  values calculated using isotropic approximation † † Ref.

[START_REF] Brazhkin | Myths about new ultrahard phases: Why materials that are significantly superior to diamond in elastic moduli and hardness are impossible[END_REF]


text:
Wen Yang

Ivan Delbende

Yann Fraigneau

Laurent Martin Witkowski

Laurent Martin

Witkowski Rotating

Rotating polygons : Numerical and experimental study of the base flow

come   L'archive ouverte pluridisciplinaire

Numerical results averaged in time and space reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found bordered by four layers, in particular by a layer at the free surface leading to a better understanding of the complete flow structure. The Froude number associated to surface deformation and the Reynolds number if sufficiently large are shown to have little effect on the flow structure. Experimental measurements corroborate the azimuthal velocity distribution used in the simplified models. But experimental and numerical results also reveal a large robust modal structure as seen in Fig. 1 (left) with the same azimuthal wave number as the corners' number of the rotating polygon. This structure is observed while the free surface remains almost axisymmetric and thus before the rotating polygon settles in.

  Rotating polygons : Numerical and experimental study of the base flow W. Yang * † , I. Delbende ‡ § , Y. Fraigneau § and L. Martin Witkowski ‡ § Rotating polygons, as shown in Fig. 1 (right), have challenged the curiosity of various research groups 12 . The flow is induced by a disk rotating at the bottom of a cylindrical tank partially filled with a working fluid. The polygons appear above a threshold that breaks the symmetry of the base flow initially axisymmetric. Instability mechanisms have been proposed based on simplified base flow model 3 . The aim of our study is to characterize in details the base flow using numerical techniques -computation of steady solutions or mean unsteady two-dimensional and three-dimensional direct simulations -as well as Laser-Doppler Velocimetry measurements.

Figure 1 :

 1 Figure 1: (Left) Visualization with kalliroscope of a mode 3 below threshold for the rotating polygon, (Right) Rotating polygon once it is settled.


Fabrice Foucher
email: fabrice.foucher@extende.com

Sébastien Lonne

Gwénaël Toullelan
email: gwenael.toullelan@cea.fr

Steve Mahaut
email: steve.mahaut@cea.fr

Sylvain Chatillon
email: sylvain.chatillon@cea.fr

Erica Schumacher
email: erica.schumacher@extende.com

VALIDATION OF THE SIMULATION SOFTWARE CIVA UT IN SEPARATED TRANSMIT/RECEIVE CONFIGURATIONS

Numerical modelling is widely used in the framework of inspection qualification processes, since it offers the capability to study a wide scope of configurations and at a lower cost compared to a full experimental campaign. In this context, the reliability of simulation models is of the highest importance. In order to evaluate this reliability and determine the field of application of CIVA simulation tools, a long-range collaborative work has been engaged between the CEA-LIST & EXTENDE. This is based on comparisons between experimental results and CIVA predictions on configurations representative of industrial NDT applications. After an overview of the validation works initiated, this paper focuses on the presentation of results obtained in tandem mode, a UT technique commonly used for the detection of side wall weld defects, such as in the zonal discrimination method. In this configuration, a pair of single element transducers located one after the other scans the part, one being the transmitter and the other being the receiver. This technique can also use a phased-array probe with two separate groups of elements. The comparisons between experimental and simulated results obtained on such configurations are presented in this paper.

Introduction

The Ultrasounds Testing module of CIVA [1] uses ray-based beam computation models and interaction algorithms to compute the beam scattered by a defect or by the specimen boundaries. These models are mainly based on semi-analytical formulations and numeric integrals [START_REF] Darmon | Main Features of a Complete Ultrasonic Measurement Model: Formal Aspects of Modeling of Both Transducers Radiation and Ultrasonic Flaws Responses[END_REF]. In order to evaluate their reliability, an experimental characterization procedure of these models is followed [START_REF] Calmon | Recommendations for the use and validation of NDT simulation, V, IIW Best practice document[END_REF], which includes: Defining and performing experiments, precisely describing the relevant and corresponding input parameters in CIVA, and conducting the simulations with CIVA, and comparing the simulated results with experimental ones.

In this paper some results obtained in separate Transmit/Receive configurations widely used industrially are described, weld UT inspections for instance. For each presented case, a depiction of how to properly describe input parameters is provided. Most of the presented results are publicly available on the EXTENDE website [4]. You will also find many other experimental validation results there such as: side drilled hole and flat bottom hole (FBH) responses in various calibration blocks and for various inspection techniques (immersion, contact), corner echoes obtained with pressure waves and shear waves, TOFD configurations, phased-array UT cases, geometrical echoes studies, multi skips inspection configurations, etc. Some validation results with the Eddy Current module of CIVA are also available on the website.

Dual Element probe characterization

A Dual Element probe uses two crystals, one for beam transmission and one for reception, separated by an acoustic barrier. This type of transducer is quite commonly used in order to inspect strongly attenuating materials, or to detect near surface defects, thanks to the natural ability of such probes to remove the entry surface echo.

In this experimental characterization study, FBH reflectors are used. The transducer used is a 4MHz transducer on a Plexiglas wedge designed to generate a 45° longitudinal wave in stainless steel.

Description of the Dual Element probe and of the CIVA simulation configuration

For such probes, the necessary input data for the simulation is often difficult to obtain, especially because of the lack of information from the manufacturer, and also the lack of standardization of the data provided from one manufacturer to another. This applies mostly for the wedge various angles (roof and incidence angle) but also regarding the T and R crystal separation distance or the acoustic properties of the wedge itself. For all these reasons, it is sometimes necessary to do Radiographic or Computed Tomography acquisitions and analysis on such probes to find out the relevant values. On the following images, a picture of such a probe can be seen as well as its 3D view in CIVA after entering the right parameters. As some of the angles are very sensitive to the results, another very efficient approach which facilitates overcoming the uncertainties of the input data can be used. This process is based on a reverse engineering applied on the DAC curves analysis and is presented in [5].

Figure 1. Dual Element Transducer and its description in CIVA.

The transducer response has been evaluated on a calibration block made of ferritic steel and where several FBHs have been inserted. To simulate FBH echoes, the KIRCHHOFF model has been used.

Two simulations have been performed:

 One computation with a plane wave approximation used for the incident beam description (mentioned as « KIR » in the following part of the paper).  One computation with a more precise description of the acoustic beam, the « Full wave » option, now available in CIVA. Results obtained with this model will be written down as « KIR COMPLETE BEAM» in this paper.

Acquisitions

Comparison of simulation/experimental results

The « Depth -Amplitude » curves obtained experimentally and in the CIVA simulation are presented below for both models « KIR » and « KIR COMPLETE BEAM ». Both predictions give a fairly good agreement with the measurements, the discrepancy being generally lower than 2dB, except for the 10mm depth where it reaches 3dB. A slight improvement can be noticed of the agreement with the « KIR_COMPLETE » model for the larger depths and for the near field zone. It confirms the very good agreement between CIVA and the experiment, also on the signal shapes (versus time or versus scanning position). In addition to this, it is also possible to identify the part of the signal associated with the slight discrepancy seen at a depth of 10 mm. However, it's important to note that these discrepancies are in the same order of magnitude as the experimental uncertainty evaluated at +/-3 dB.

Tandem configuration

Tandem is an inspection technique commonly used for weld inspections, especially with the zonal discrimination approach [START_REF] Chapuis | Simulation Supported POD Curves for Automated Ultrasonic Testing of Pipeline Girth Welds[END_REF].

Description of the configuration

The tested tandem configuration involves a linear phased-array (PA) probe of 64 elements, working at 5 MHz and mounted on a S45° Plexiglas wedge. The linear array parameters have been obtained from the manufacturer while the properties of the wedge have been measured (geometry, velocity, angle).

To create the tandem configuration with the PA probe, a group of elements is enabled to transmit the beam while other elements are active in reception. In this case, the transmission pattern is performed with 20 active & fixed elements while the reception mode is created with 10 elements working in electronic scanning. This reception mode generates a dynamic change of the shear waves crossing points in transmission and reception, from 32.5 mm to 50 mm in depth. The 7 sequences (seq) created are illustrated on the sketch below.

A delay law is applied to the transmission group creating a focusing along the beam axis (at 45 mm depth with a 45° angle). No delay laws are applied in reception. These focal laws have been imported from the acquisition files (note that CIVA can also compute focal laws). A specific mock-up of 50 mm wall thickness in ferritic steel has been made in order to have available some embedded planar defects, necessary to predict the performance of CIVA in such a tandem configuration. It is made of 5 EDM notches of 5mm height initiated from the side of the specimen. For calibration, FBHs placed at different depths from the end of the block have been machined so that they are oriented horizontally. Notches and FBHs are at the same depths (depths referenced at the center of the notches and the axis of the FBHs).

Defects are located each 5 mm in depth. Then, the defects' depths change from 27.5 to 47.5mm (or from 20mm to 5mm if you consider their ligament, that is to say the distance between the defect bottom and the back wall).

Figure 7. Mock-up used to evaluate CIVA performance for tandem configuration.

Acquisitions performed

C-scan acquisitions have been performed and the indirect signals obtained have been recorded, corresponding to the « TrbTdT » sound paths (« T » corresponds to T wave path, « rb » to the back wall reflection and « d » to the defect interaction). An example of experimental B-scans obtained for sequences 1 to 7 is shown in Figure 8. The whole set of curves showing the obtained amplitudes versus the ligament of the notches is then presented for all the relevant sequences where a signal amplitude can be measured (sequences 1 to 6). Amplitudes are normalized in comparison to the signal amplitude obtained with the FBH at a depth of 32.5 mm and detected with sequence #1. This variation shows the ability of the tandem mode to detect embedded defects with a similar sensitivity for various thicknesses and depth ranges.

Comparison of simulation/experimental results

The Amplitude/Ligament curves obtained by the simulation (KIR model) and experimentally are superimposed and shown on the following Figure 10, for a few of the electronic sequences (number #1, #3, #4 and #5). Regardless of notch depth, CIVA predicts signal amplitudes with a very good accuracy. A slight overestimation is observed for the sequence #1, but is only about 2dB, less than the measurement uncertainty estimated at 3dB. For most of the other cases, the amplitude differences are lower than 2 dB. The superimposition of echodynamic curves obtained on these notches is presented for a few sequences on the following Figure 11. Again it confirms a very good agreement between CIVA and the experiment on the signal shapes. Amplitudes are normalized with reference to the maximum amplitude obtained on each sequence.

Conclusion

This paper presents comparisons between experimental acquisitions and simulations for different configurations using separate Transmission/Reception modes in the CIVA software.

In the first part, a dual element transducer is used. It is often very challenging to validate this type of probe due to the input parameters which are often difficult to know with sufficient accuracy (roof or incidence angles for instance). It is sometimes necessary to use radiography or to use reverse engineering methodologies to get the relevant information. The obtained simulation results are in a good agreement with the experimental results in regards to both the signal amplitudes and signal shapes versus time or scanning position, considering the experimental uncertainty (3dB).

In the second part, a tandem mode has been used to study echoes obtained on various notches embedded in a planar block and located at different depths. This configuration involves a 64 elements contact probe generating shear waves at 45°. An electronic scanning technique is applied to transmission and reception elements to cover various ranges of depths in the block. More precisely, 7 sequences are enabled successively to change the crossing point depth of shear waves from 32.5mm to 50mm in depth. The agreement with the experimental data is very good in terms of amplitudes (differences lower than 2dB) but also in terms of echo shapes for the different sequences considered.

You will find more information on these test cases as well as many other validation cases on the EXTENDE website [4].

  performed C-scan acquisitions have been performed and the direct signals obtained from the FBHs have been recorded. You can see the experimental C-scans obtained on both series of FBHs on the following figure. Group #1 corresponds to FBHs located between 5 & 150 mm in depth while Group #2 corresponds to FBHs located between 10 & 60 mm in depth. The experimental echodynamic curves obtained are superimposed below. The maximum amplitude is obtained at a depth of 15mm.

Figure 2 .

 2 Figure 2. Experimental C-scans & echodynamic curves obtained for both groups of FBHs.

Figure 3 .

 3 Figure 3. Image of the transmitted beam computation in a steel block. Comparison of « Depth-Amplitude » curves obtained by simulation (model « KIR » & « COMPLETE KIR ») and experimentally. Amplitude reference on a SDHØ2mm, 16 mm depth.The superimposition of echodynamic curves and A-scans is presented on the following figure.It confirms the very good agreement between CIVA and the experiment, also on the signal shapes (versus time or versus scanning position). In addition to this, it is also possible to identify the part of the signal associated with the slight discrepancy seen at a depth of 10 mm. However, it's important to note that these discrepancies are in the same order of magnitude as the experimental uncertainty evaluated at +/-3 dB.

Figure 4 .

 4 Figure 4. Comparison of echodynamic curves (along the scanning axis) and the A-scan signals obtained on the different FBHs (experiments in black, KIR and KIR COMPLETE models respectively in red and blue). Normalized amplitudes.

Figure 5 .

 5 Figure 5. Tandem Configuration with a PA probe mounted on a S45° wedge. The following figure shows an example of the radiated beam in Transmission/Reception for sequences 1 & 5, corresponding to shear wave axis crossing points around 32.5 mm & 44 mm in depth. The beam spot obtained has a size (along the vertical axis) of 9.5mm for sequence #1 and 10.8 mm for sequence #5, at -6dB.

Figure 6 .

 6 Figure 6. Ultrasonic field in the ferritic steel block. PA probe 64 elements 5MHz, sequences #1 & #5, shear wave at 45°, tandem mode.

Figure 8 .

 8 Figure 8. Experimental results obtained on notches. PA probes 5MHz, S45°, sequence #1 and #7, tandem mode.

Figure 9 .

 9 Figure 9. Amplitude/Ligament curves for notches and for sequences #1 to #6. Amplitude reference taken on a FBH Ø3mm at 32.5 mm depth (i.e. 15 mm ligament) detected with sequence #1. PA probes 5MHz, S45°, tandem mode.

Figure 10 .

 10 Figure 10. Comparison of Amplitude/Ligament (~depth) curves obtained with the simulation model (KIR) and experimentally on the notches. PA probe, 5MHz, S45°, Tandem mode.

Figure 11 .

 11 Figure 11. Comparison of echodynamic curves (along the scanning axis) obtained on the different notches (experiments in black, KIR model in red). Normalized amplitudes. PA probe, 5MHz, S45°, Tandem mode.