Juhi Sharma
email: juhi.sharma@mines-paristech.fr

Alexis Nicolaÿ
email: alexis.nicolay@mines-paristech.fr

Marc De Graef

Nathalie Bozzolo
email: nathalie.bozzolo@mines-paristech.fr

Phase discrimination between δ and η phases in the new nickel-based superalloy VDM Alloy 780 using EBSD

Keywords: EBSD, Phase Discrimination, Dictionary Indexing

VDM Alloy 780 is a new nickel-based superalloy developed for higher service temperatures up to 750°C. In addition to fine γ′-Ni3(Al,Ti) strengthening precipitates, grain boundary precipitates resembling δ-Ni3Nb and/or η-Ni3Ti phases are observed in this alloy. Previous studies on Alloy 718Plus, with chemical composition close to VDM Alloy 780, revealed that phase discrimination between δ and η particles is not straightforward and requires the use of high-resolution characterization techniques such as HRTEM. This work aims at evaluating the use of EBSD technique with regards to phase identification of these plateshaped precipitates. Classical indexing of diffraction patterns based on Kikuchi band detection in Hough space fails to differentiate between the two phases. However approaches based on the comparison of experimental and simulated patterns, at least partly, could overcome this issue. The advanced dictionarybased approach that involves the simulation of dynamic electron scattering events identified η phase as the main component of these grain boundary precipitates, consistent with the recently published HRTEM investigation on VDM Alloy 780. Refinement of the classical indexing method under kinematic assumptions implemented in the "Refined Accuracy" mode on the Oxford AZtec software package also led to appreciable improvement.

Introduction

Electron backscattered diffraction (EBSD) is a widely used technique for microstructure and micro-texture characterization. Classical EBSD pattern indexing is based on the angles measured between the Kikuchi bands (that is a gnomonic projection of the angles between the diffracting planes onto the EBSD detector screen) after detecting the band positions in the Hough transform of the pattern. Conventional EBSD can be used efficiently for phase discrimination provided the considered phases have significant differences in their crystal structures and consequently differences in the detected interplanar angles.

The design of polycrystalline nickel-based superalloys is usually adjusted to promote the precipitation of (i) hardening phases and (ii) particles to pin grain boundaries and control grain sizes. Depending on the various alloying elements and the associated chemical composition, different phases can be found in superalloys. There are several examples in these materials where EBSD fails to distinguish between two phases. The γ-γ′ alloy system is one such example which presents a well-known challenge of discrimination between the disordered FCC matrix phase and the ordered L12 precipitated phase. The lattice parameters of γ and γ′ are often quite close, differing by less than 0.5% [START_REF] El-Dasher | Application of electron backscatter diffraction to phase Identification[END_REF]. Due to structural similarities, the two phases exhibit very similar diffraction patterns. The weak additional diffracted intensities resulting from the ordered γ′ structure are not sufficient to be detected and used to discriminate between the two phases by EBSD. This problem was overcome in a γ-γ′ nickel-based superalloy by coupling EBSD with Energy dispersive X-ray spectroscopy (EDS) which also allows taking into account the chemical composition of the phases [START_REF] Charpagne | Evidence of multimicrometric coherent γ′ precipitates in a hot-forged γ-γ′ nickel-based superalloy[END_REF]. Only primary γ′ precipitates were large enough to be separated from the matrix based on the EDS signal, EDS spatial resolution being in the range of 1 μm. Another method that could successfully solve this phase discrimination issue in a γ-γ′ nickel-based superalloy [START_REF] Vernier | iCHORD-SI combination as an alternative to EDS-EBSD coupling for the characterization of γ-γ′ nickel-based superalloy microstructures[END_REF] was based on the chemical contrast of Secondary ion (SI) images correlated with the crystallographic orientations obtained by the i-CHORD technique [START_REF] Langlois | Crystal orientation mapping via ion channeling: An alternative to EBSD[END_REF]. The spatial resolution of SI images allowed for identification of γ′ particles as small as 150 nm. This article deals with another problem of phase discrimination, between δ and η phases, in nickel-based superalloys where none of the aforementioned approaches work. The crystallographic description and the lattice parameters of the generic compounds of both phases are given in Table 1 [START_REF] Villars | Pearson's Handbook: Desk Edition : Crystallographic Data for Intermetallic Phases[END_REF]. Theoretically, δ phase exists as Ni3Nb with an orthorhombic structure whereas η-Ni3Ti has a hexagonal structure as shown in Fig. 1. Owing to their different crystal structures and chemical compositions, δ and η phases seem a priori to be easily differentiable; which is actually not true as detailed below.

Table 1

Crystallographic information of δ and η phases [START_REF] Villars | Pearson's Handbook: Desk Edition : Crystallographic Data for Intermetallic Phases[END_REF].

Phase δ η

Generic compound Ni3Nb Ni3Ti

Unit Both δ and η phases precipitate discontinuously at the grain boundaries and result in serrated boundaries [START_REF] Pickering | Grain-boundary precipitation in Allvac 718Plus[END_REF]. The two phases usually display similar needle/plate-type morphology. These phases are characterized by a γ′-precipitate depleted zone around them as a result of local variation in the alloying element contents as observed in Alloy 718Plus [START_REF] Pickering | Grain-boundary precipitation in Allvac 718Plus[END_REF][START_REF] Löhnert | Microstructure evolution in the nickel base superalloy Allvac®718Plus TM[END_REF] and in VDM Alloy 780 (Fig. 2). Topologically, both phases resemble each other. Moreover, they can actually exist with similar compositions by substituting the elements present in their generic structure compounds which make the use of chemical information insufficient to recognize their precise nature. TEM/EDS (Transmission electron microscope coupled with Energy dispersive X-ray spectroscopy) indeed revealed the presence of a plate-like phase Ni3Al0.5Nb0.5 with a hexagonal structure similar to that of η-Ni3Ti but rich in Nb and Al and not Ti [START_REF] Xie | Structure stability study on a newly developed nickel-base superalloy-Allvac® 718plus TM[END_REF]. In another study, the same technique showed affinity of Nb, Al and Ti towards η phase and η-Ni6AlNb was seen to form with its majority of Ti sites replaced by Al and Nb while conserving the hexagonal structure [START_REF] Pickering | Grain-boundary precipitation in Allvac 718Plus[END_REF]. TEM/EDS analysis on the same alloy discussed presence of δ phase which deviated from the generic Ni3Nb stoichiometry and contained Nb, Al and Ti [START_REF] Löhnert | Microstructure evolution in the nickel base superalloy Allvac®718Plus TM[END_REF]. Because of the common forming elements (Nb, Al and Ti) in the two phases, chemical composition cannot really help to distinguish between δ and η phases. In addition, it is worth mentioning that SEM/EDS (EDS in a Scanning electron microscope) should anyway be avoided in such phase identification issues as the thickness of these lamellar particles is usually below the spatial resolution of SEM/EDS.

Therefore, crystallographic information has to be taken into consideration in this context. Precipitation of δ-Ni3Nb phase in Inconel 718 is well-known and has been demonstrated in the literature using TEM with an orientation relationship to the γ matrix: 111 // 010 and 〈11 0〉 // [100] [START_REF] Sundararaman | Precipitation of the δ-Ni3Nb phase in two nickel base superalloys[END_REF][START_REF] Cozar | Morphology of γ′ and γ′′ precipitates and thermal stability of Inconel 718 type alloys[END_REF][START_REF] Kirman | The precipitation of Ni3Nb phases in a Ni-Fe-Cr-Nb alloy[END_REF][START_REF] Dehmas | TEM study of high-temperature precipitation of delta phase in Inconel 718 alloy[END_REF]. HRTEM (High resolution transmission electron microscopy) study on Inconel 718 has also revealed presence of a local stacking fault of type (ABACAB…) within δ (ABCABC…) structure [START_REF] Niang | Contribution à l'étude de la précipitation des phases intermétalliques dans l'alliage 718[END_REF]. This kind of stacking fault can also be seen as a local η layer but concerning only three atomic planes. No example of thicker η layer defects observed in the δ phase of Inconel 718 could be found in the literature.

However, in case of more recently developed alloys such as Alloy 718Plus and VDM Alloy 780, phase identification of the grain boundary precipitates has posed challenges. X-ray diffraction (XRD) diagrams showed that the peaks corresponding to the grain boundary precipitates could be assigned to either δ phase, η phase or Ni3Al0.5Nb0.5 phase in Alloy 718Plus [START_REF] Xie | Structure stability study on a newly developed nickel-base superalloy-Allvac® 718plus TM[END_REF] and in VDM Alloy 780 [START_REF] Solís | In situ characterization at elevated temperatures of a new Ni-based superalloy VDM-780 Premium[END_REF]. TEM selected-area electron diffraction patterns (SADPs) of the lamellar precipitates in Alloy 718Plus matched the η-Ni3Ti D024 hexagonal structure [START_REF] Pickering | Grain-boundary precipitation in Allvac 718Plus[END_REF]. This phase was referred as Ni6AlNb and was found to have a crystallographic orientation relationship with the γ matrix: 111 // 0001 and 〈11 0〉 // 〈21 1 0〉 with lattice parameters similar to those of η-Ni3Ti. Another study on Alloy 718Plus described the presence of fine δ atomic layers as faults in the local stacking sequence of the η structure using HAADF-STEM (High angle annular dark field imaging in a Scanning transmission electron microscope) [START_REF] Messé | On the precipitation of delta phase in Allvac®718Plus[END_REF]. A more recent study on VDM Alloy 780 using HRTEM also showed that the plate-shaped particles are composed of alternating layers of η and δ phases following the crystallographic orientation relationship: 0001 // 010 , 101 0 // 001 , 〈21 1 0〉 // [100] [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF]. This study analyzed samples from two types of heat treatments to generate different microstructures. The first sample was heat treated at 1000°C followed by another heating of 975°C for 16 hours. The other sample was exposed to multiple step ageing treatments at relatively lower temperatures starting from 900°C for 11 hours, then to 955°C for 1 hour followed by ageing at 800°C and 650°C for 8 hours respectively [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF]. Both the samples revealed η phase as the principle phase, almost twice that of δ, although both η and δ phases co-existed in all the analyzed particles. Formation of δ phase at the interface of the plate-shaped particle was also observed in the sample exposed to the multiple step ageing treatments at lower temperatures. Relatively thicker δ phase stripes (20-50 nm) were encountered in this study as compared to that in Alloy 718Plus where δ stripes were narrower [START_REF] Messé | On the precipitation of delta phase in Allvac®718Plus[END_REF].

The effect of chemical composition on the formation of δ and η phases has been demonstrated by considering different experimental alloys [START_REF] Antonov | Precipitate phase stability and compositional dependence on alloying additions in γ-γ′-δ-η Ni-base superalloys[END_REF]. It was empirically shown that the tendency of an alloy to form δ and/or η phases can be influenced by the atomic ratio of (Nb+Ta) / (Al+Ti) [START_REF] Antonov | Precipitate phase stability and compositional dependence on alloying additions in γ-γ′-δ-η Ni-base superalloys[END_REF]. According to this study, a ratio of less than 1 favors η phase, a ratio well above 1 ensures δ phase, whereas a ratio close to 1 generates a microstructure with both δ and η phases. For Alloy 718, this ratio is 1.55 and indeed exhibits presence of δ phase [START_REF] Antonov | Precipitate phase stability and compositional dependence on alloying additions in γ-γ′-δ-η Ni-base superalloys[END_REF]. This ratio is 0.86 for Alloy 718Plus [START_REF] Antonov | Precipitate phase stability and compositional dependence on alloying additions in γ-γ′-δ-η Ni-base superalloys[END_REF] and 0.87 for VDM Alloy 780 [START_REF] Solís | In situ characterization at elevated temperatures of a new Ni-based superalloy VDM-780 Premium[END_REF]. Hence both the alloys lie in the η phase domain yet close to δ/η limit. From this compositional tendency, η phase seems more likely to be present in VDM Alloy 780. This is consistent with the HRTEM investigation which showed the main phase in this alloy as η phase [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF].

TEM based techniques were thus able to identify the precise nature of these grain boundary precipitates in Alloy 718Plus and VDM Alloy 780 but involved preparation of thin foils and hence are more time intensive, in addition to having the drawback of limited statistics regarding the number of analyzed particles which is inherent to TEM investigations. This article focusses on the issue of phase identification between δ and η phases using EBSD technique, thus with simpler sample preparation and potential for better statistics, in VDM Alloy 780. However, since conventional EBSD indexing could not discriminate between both the phases, advanced indexing methods that rely on the comparison of experimental and simulated patterns were evaluated and will be shown below to be able to identify the major component of these plate-shaped particles.

Material: VDM Alloy 780

The use of nickel-based superalloys in the aerospace industry is extensive owing to their excellent properties at elevated temperatures. The need and demand to increase the maximum operating temperature to reduce emission levels has motivated the development of new superalloys. With this objective, VDM Alloy 780 was developed to achieve improved microstructural stability and service temperature up to 750°C [START_REF] Fedorova | Development of a new 718-type Ni-Co superalloy family for high temperature applications at 750[END_REF][START_REF] Rösler | On the development concept for a new 718-type superalloy with improved temperature capability[END_REF]. The chemical composition in Table 2 ensures the microstructure to be predominantly strengthened by γ′ precipitates. Another phase that resembles δ (orthorhombic D0a) and/or η (hexagonal D024) was observed mainly at the grain boundaries (Fig. 3a). The analyzed sample was taken from a VDM Alloy 780 pancake forged from a billet at 1000°C and then heat treated at 980°C for 48 hours. This is comparable to one of the heat treatments applied in the previously reported HRTEM study [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF]. This particular heat treatment was chosen in order to obtain a microstructure with considerable amount of such grain boundary precipitates. The three-dimensional shape of these grain boundary precipitates is reconstructed using FIB nano-tomography in Fig. 3b. software from Bruker). Both systems led to the same conclusion: an experimental pattern (Fig. 4b) could be successfully indexed using crystallographic data of δ-Ni3Nb and of η-Ni3Ti phases, as shown in Fig. 4c and Fig. 4d respectively.

Both solutions appear similar even though minute differences exist (marked by yellow lines on Fig. 4c) which suggest that the pattern more likely corresponds to η-Ni3Ti phase. However these differences are too subtle to help in phase discrimination in an automatic Hough transform-based indexing procedure. The mean angular deviation (MAD) which measures the misfit between the detected bands and those of the proposed solutions are very close in both cases. Using the Oxford AZtec software package, the MAD of the example shown in Fig. 4 was calculated as 0.19° considering δ-Ni3Nb and 0.17° when considering η-Ni3Ti with 12 identified bands in both cases. This similarity between the diffraction patterns of δ and η phases can actually be understood when looking at the crystal structures plotted in Fig. 1. Crystal lattices are aligned according to the misorientation between δ and η phase in accordance to the pattern indexing shown in Fig. 4 which is also consistent with the previously reported orientation relationship:

// , // , 〈 〉 // [ ] [16].
Both structures look similar in terms of arrangement of atoms and differ only by slight distortions which make them fall into either orthorhombic or hexagonal crystallographic system. Diffracting planes in both these phases form almost the same angles between them. The difference in those angles in one phase compared to the other is likely to be within the tolerance that must be admitted in the classical EBSD indexing procedure. This explains why conventional EBSD fails in discriminating between δ and η phases. orthorhombic δ-Ni3Nb data with 〈 〉 zone axis at the center of the particle, and d) Experimental pattern indexed using η-Ni3Ti crystallographic data with 〈 〉 zone axis at the center. Yellow lines on c) highlight missing lines as compared to d).

Comparison of conventional and more advanced EBSD indexing methods

A sample of VDM Alloy 780 (annealed at 980°C for 48 hours, same as in Fig. 3) was analyzed by EBSD using a Tescan FERA3 Field emission gun scanning electron microscope (FEG-SEM) equipped with an Oxford EBSD system comprising a C-Nano detector and AZtec software package. The settings used for the analyses are given in Table 3. Two different indexing modes available on the Oxford AZtec software package were used: (i) Optimized indexing mode based on classical Hough transform and (ii) "Refined Accuracy" mode. The same sets of patterns were analyzed using the Dictionary Indexing method implemented in the open source EMsoft software package. All these three approaches are further described below. Step size 0.1 μm

Conventional Hough transform based indexing

Conventional EBSD uses the Hough transform of the pattern to detect the position of Kikuchi bands and determine the angles between each pair of bands. From the list of measured angles and assuming a given crystal structure, the software determines the possible crystal orientation giving rise to the recorded band configuration. The accurate identification of the phase and orientation of the crystal depends mostly on the precise detection of these band positions. This, in turn, depends on the resolution of the Hough space and on the mask-filter used for band detection in the Hough space in addition to the contrast, sharpness and resolution of the pattern image itself.

Dictionary Indexing (DI)

Contrary to the classical Hough transform approach that only aims at detecting bands, the DI method uses all the available pixels rather than only linear aspects of the diffraction pattern image [START_REF] Callahan | Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations[END_REF][START_REF] Singh | Dictionary Indexing of Electron Channeling Patterns[END_REF][START_REF] Chen | A Dictionary Approach to Electron Backscatter Diffraction Indexing[END_REF]. DI uses a library of precomputed simulated patterns to index the experimental diffraction patterns with best match from the dictionary. For this purpose, a normalized dot product between the experimental patterns and dictionary elements is used to determine the best match and the orientation of the corresponding dictionary element. A physics-based forward model is used for computation of the dynamic electron-scattering events in the form of a master Kikuchi pattern. The individual diffraction patterns are obtained using bilinear interpolation of these master patterns [START_REF] Callahan | Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations[END_REF]. The master patterns of δ and η phases in Fig. 5 confirm the similarity of both phases with regards to diffraction signals. Slight relative intensity modulations and fine differences in the angles between bands exist between these phases which can barely be detected by simple visual inspection.

"Refined Accuracy" method offered by the Oxford system

Within the Oxford AZtec software package, the orientation measurement accuracy can be improved by using the so-called "Refined Accuracy" mode that also uses simulated Kikuchi patterns but calculated under kinematical assumptions [START_REF] Thomsen | Improving the Accuracy of Orientation Measurements using EBSD[END_REF]. In the "Refined Accuracy" mode, an experimental pattern is first indexed using a variant of the classical Hough transform. Band detection in Hough space is performed with a sub-pixel resolution allowing to detect the position of the bands with a precision which is slightly improved compared to the classical Hough transform indexing. This first solution is then used to model, under kinematical assumption, the expected band edge positions taking into consideration their hyperbolic shape. The refined solution is then determined as the best fit between the simulated and the original experimental pattern [START_REF] Penman | Method of electron beam diffraction analysis[END_REF]. This corresponds to the so-called refinement step that enables better determination of the band positions and hence can be used to discriminate between some phases with similar crystal structures [START_REF]Developments in EBSD[END_REF][START_REF] Nicolaÿ | Discrimination of dynamically and post-dynamically recrystallized grains based on EBSD data: application to Inconel 718[END_REF].

Results and Discussion

Conventional EBSD based on classical Hough transform could not differentiate between δ and η phases as seen from Fig. 6b where most of the particles contain pixels corresponding to both δ and η phases with poor spatial correlation. It is worth noting that both δ and η phases can be indexed using the crystallographic information in Table 1 even though their actual chemical composition deviates from the generic compounds. The pole figures in Fig. 6c indicate that points indexed as η and δ phases follow the aforementioned orientation relationship (section 1) with γ-matrix, which is also summarized in Table 4. A set of diffraction patterns acquired with the Oxford C-Nano detector on a region involving δ/η particles (white box in Fig. 7a) were saved and analyzed using the Dictionary Indexing method. Conventional EBSD generated a phase map given in Fig. 7b with mixed δ/η indexing. The points near the matrix/particle interface seem to have a higher mixed-indexing rate. Fig. 7c shows the phase map obtained using Dictionary Indexing. Firstly, indexing has been performed for one phase at a time. A line profile map (see Fig. 7d) for the same region displays the maximum refined dot product values for δ, η and γ phases. This normalized dot product determines the best match and orientation for the experimental pattern; it is systematically higher for η phase as compared to δ phase. Fig. 7c was generated by considering all the three phases for each pixel and selecting the phase with the highest value of this refined dot product. Contrary to the classical indexing technique, Dictionary Indexing showed that all the points in particles of the analyzed area are most likely to be η phase. The result from DI method is consistent with the chemical composition criterion leading to the occurrence of η phase mentioned in section 1 [START_REF] Antonov | Precipitate phase stability and compositional dependence on alloying additions in γ-γ′-δ-η Ni-base superalloys[END_REF] and with the HRTEM investigations which identified η as the major phase in VDM Alloy 780 [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF]. However, the presence of thin layers of another phase precisely observed by the HRTEM studies could not be resolved using EBSD, despite the fact that the analyzed area was chosen to get the best possible spatial resolution through the thickness of the plates (i.e. with the long dimension of the particle aligned with the Y direction of the map). The typical spatial resolution of EBSD in a FEG-SEM is indeed better, in the order of 30 nm along the X direction parallel to the tilt axis and about three times lower, about 100 nm, in the Y direction [START_REF] Zaefferer | On the formation mechanisms, spatial resolution and intensity of backscatter Kikuchi patterns[END_REF] because of the geometric configuration with the analyzed surface tilted by 70°.

In Alloy 718Plus, the stacking defects of δ phase observed within η structure were only few tens of nanometers in thickness [START_REF] Messé | On the precipitation of delta phase in Allvac®718Plus[END_REF]. For VDM Alloy 780, these δ layers had a thickness of 20-50 nm inside η [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF], about the expected EBSD spatial resolution along the X direction. There is thus only a slight possibility that the thin δ phase layers could be resolved, which would require them to be lying perpendicular to the scanned surface. Such thin δ layers could actually not be revealed using the DI method in the analyzed region.

The two different EBSD indexing modes available on the Oxford AZtec software package described in section 4 were compared to Dictionary Indexing results on another area as shown in Fig. 8a. DI again revealed the analyzed particles as η phase (see Fig. 8b), except the particle marked as A which was obviously too thin to be resolved under the actual settings. Conventional EBSD settings generated the phase map in Fig. 8c with mixed indexed points of δ and η phases; with higher proportion of δ phase in particle B, higher proportion of η phase in particle C, a core of η surrounded by δ in particle D. Analyzing the same area using "Refined Accuracy" mode (Fig. 8d) significantly changed the results. The lamellar particles (see Fig. 8d) now appear more likely to be η phase although a number of (sparse) points, notably close to the matrix/particle interfaces, are still indexed as δ phase. Noteworthily, few points at grain or twin boundaries of the matrix are also misindexed as either η or δ phase. A possible explanation for points indexed as δ phase at the interface between the particle and the matrix could be the actual presence of a δ interfacial layer, as earlier reported by the HRTEM analyses on VDM Alloy 780 sample submitted to multiple heat treatment steps at lower temperatures (900°C for 11 hours, then to 955°C for 1 hour followed by ageing at 800°C and 650°C for 8 hours respectively) [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF], and in an Alloy 7180Plus sample heat treated at 840°C for 72 hours [START_REF] Messé | On the precipitation of delta phase in Allvac®718Plus[END_REF]. But this explanation most probably is not suitable in the present case since DI method with the exact same set of diffraction patterns did not return such interfacial δ phase points or internal thin defect layers. It is thus more likely that these points are actually misindexed as a result of poorer diffraction pattern quality as a result of a combination of diffraction intensities coming from both particle and matrix. Pattern overlapping would also explain the misindexed η or δ phase points at the grain and twin boundaries.

In order to check the latter hypothesis, the "Refined Accuracy" mode on the Oxford system was also used to analyze a sample of Inconel 718. Presence of δ phase in Inconel 718 is well-known and has been reported in several studies [START_REF] Sundararaman | Precipitation of the δ-Ni3Nb phase in two nickel base superalloys[END_REF][START_REF] Cozar | Morphology of γ′ and γ′′ precipitates and thermal stability of Inconel 718 type alloys[END_REF][START_REF] Kirman | The precipitation of Ni3Nb phases in a Ni-Fe-Cr-Nb alloy[END_REF][START_REF] Dehmas | TEM study of high-temperature precipitation of delta phase in Inconel 718 alloy[END_REF]. In the δ phase of this alloy, the presence of stacking faults of η type has been reported however their thickness is far below the spatial resolution of EBSD. One of the possible solutions to handle overlapping diffraction patterns at the particle/matrix interface or due to the lack of spatial resolution of the thin layers of a phase within another, could be to use the DI method with a combination of overlapping master patterns as done in the case of α and β phases in titanium alloy [START_REF] Lenthe | Spherical indexing of overlap EBSD patterns for orientation-related phases-application to titanium[END_REF]. The same principle could be applied here since the orientation relationships between the involved δ, η and γ phases are known and well-defined and could thus be used to produce suitable overlapping master patterns. This is a perspective to the work presented here.

Conclusion

δ and η phases cannot be easily distinguished in nickel-based superalloys based on their shape or chemical composition alone. Despite their different crystallographic systems (orthorhombic for δ phase and hexagonal for η phase), conventional EBSD fails to discriminate between δ and η phases. This is due to the underlying similarities in terms of atomic arrangements and associated diffraction signals.

HRTEM study on this alloy has revealed that these plate-shaped particles are actually composed of alternating layers of δ phase within η phase, with η almost twice that of δ phase [START_REF] Ghica | HRTEM analysis of the high-temperature phases of the newly developed high-temperature Ni-base superalloy VDM 780 Premium[END_REF]. The present work attempts to solve the issue of phase identification using advanced EBSD indexing methods. In this context, the advanced Dictionary Indexing technique appeared to be able to index all the analyzed particles as η phase in VDM Alloy 780. The "Refined Accuracy" indexing mode available on the Oxford AZtec software was also able to identify the particles as η phase, except for the points close to the grain boundaries.

However, these advanced indexing techniques were able to identify only the major component (η phase) of the grain boundary precipitates in this alloy. The very possible presence of fine layers of δ phase within η phase, reported in the literature using HRTEM, could not be resolved using these techniques. The use of DI method with overlapping master patterns could potentially allow overcoming this drawback. Nevertheless, the possibility of discriminating between η and δ phases in superalloys without requiring TEM based techniques is by itself a step forward, avoiding complex preparation of thin foils, opening the route for better statistics in terms of the number of analyzed particles and being less time-intensive.

Authors wish to thank VDM Metals GmbH for funding this work and providing the material for this study. MDG acknowledges funding from a DoD Vannevar-Bush Faculty Fellowship (N00014-16-1-2821), as well as the computational facilities of the Materials Characterization Facility at CMU under grant # MCF-677785.

Data availability: Raw/processed EBSD data can be made available on request.

Fig. 1 .

 1 Fig. 1. Crystal structures of a) δ-Ni3Nb and b) η-Ni3Ti where [010]δ ∥ [0001]η.

Fig. 2 .

 2 Fig. 2. Backscattered electron image (BSE) showing γ′-depleted zone around needle/plate-shaped particle in VDM Alloy 780 heat treated at 960°C for 10 hours.

Fig. 3 a

 3 Fig. 3 a) Microstructure of VDM Alloy 780 after a heat treatment at 980°C for 48 hours showing presence of γ′ (spheroid-shaped) and δ/η precipitates (plate-shaped), BSE image of a mirror polished sample and b) Three-dimensional view of the plate-shaped particles obtained using Plasma-FIB nano-tomography (in a Tescan FERA3 microscope) on a volume of 17.5x17.5x17.5 μm 3 with a cubic voxel size of 100 nm.3. Reason why conventional EBSD fails in δ/η phase discriminationThe experimental electron backscattered pattern (EBSP) of a δ/η particle (arrowed on Fig.4a) is shown in Fig.4b. This pattern could be indexed "classically" based on the angles measured between the Kikuchi bands detected in the Hough transform of the pattern, using the crystallographic data of either orthorhombic δ-Ni3Nb or hexagonal η-Ni3Ti phase. Two commercial EBSD systems have been tested (C-Nano detector coupled with AZtec software from Oxford and e-Flash detector coupled with Esprit

Fig. 4 .

 4 Fig. 4. a) Forward scattered electron (FSE) image showing the δ/η particle (white arrow) under investigation, b) Experimental EBSD pattern of the particle, c) Experimental pattern indexed using

Fig. 5 .

 5 Fig. 5. Master patterns at 20 kV for a) δ-Ni3Nb with orthorhombic [010] axis in the middle of the pattern and b) η-Ni3Ti with [0001] axis in the middle of the pattern consistent with the alignment of the crystal structures in Fig. 1 and that arising from pattern indexing in Fig. 4.

Fig. 6 .

 6 Fig. 6. a) Band contrast image of the area indexed using conventional Hough transform based indexing, b) associated phase map, and c) Pole figures for γ, η and δ phases corresponding to the region (black box) shown in a). The colors aim at highlighting alignment of different poles of corresponding phases.

Fig. 7 .

 7 Fig. 7. a) FSE image showing the analyzed area (white box), b) Phase map obtained with conventional Hough transform based indexing, c) Phase map obtained using DI technique, and d) Line profile through the particles (dotted line on c) showing refined dot product values for δ, η and γ phases.

Fig. 8 .

 8 Fig. 8. a) FSE image of the analyzed particles, b) Phase map using DI, c) Phase map using conventional indexing mode, and d) Phase map using "Refined Accuracy" mode.

FigFig. 9 .

 9 Fig. 9. a) Band contrast image of Inconel 718 and b) Phase map using "Refined Accuracy" mode.

Table 2

 2 Nominal chemical composition (wt.%) of VDM Alloy 780, Alloy 718Plus and Alloy 718.

	Alloy	Al	Ti	Cr	Fe	Co	W	Nb	Mo	Ni
	VDM Alloy 780	2	0.3	18.0	<3	25.0	--	5	3.0	Bal.
	Alloy 718Plus	1.45 0.75 18.0	9.5	9.1	1.0	5.4	2.7	Bal.
	Alloy 718	0.6	0.9	19.0 18.5	--	--	5.15	3.0	Bal.

Table 3

 3 Parameters used in phase identification using EBSD.

	Parameter	Value
	Working distance	23.2 mm
	Accelerating voltage	15 kV
	Sample tilt	70°
	EBSD detector gain	1
	EBSP size	311×256 pixels
	Integration time per frame	8 ms

Table 4

 4 Aligned crystallographic planes and directions of γ, η and δ phases from pole figures in Fig.6c.

	Phase	Planes Aligned	Direction Aligned	Symbol
	γ phase	{111}		<110>		circle
	η phase	(0001)	112 0	<112 0>	<101 0>	triangle
	δ phase	(010)	(100)	[100], [102]	[001]	star

Acknowledgements


A J Wang

B Manescau

K Chetehouna

C De Izarra

S Rudz

Experimental investigation of the confinement effect on a flame impinging a ceiling in an enclosure

Keywords: Confinement level, Impinging flame, Temperature distribution, Equivalence ratio, Fire safety

This experimental study highlights the confinement effects on a flame impinging a ceiling in confined or semi-confined environment. The enclosure used in this study represents a 1:10 scale model of a student compartment with two possible openings: a door and a window. It is developed based on the conservation of the Froude number based on the scaling law. The objective of this work is to provide explanations in terms of fire safety on thermal phenomena that can occur during fires in closed environments, for example in a room of a university residence, regarding eight heat rates release of fuel and five confinement levels. A flame oscillation modelling of propane-air flame is proposed and is verified by the experimental results. It is shown both by theoretical modeling and experimental results that the confinement of a compartment has an effect on period time of flame oscillation. Moreover, experimental results show that the confinement level of compartment is a key parameter to characterize vertical temperature evolution both in the center (impinging zone) and near the wall in the enclosure. The correlations for normalized gas temperature rise near the wall are proposed and these temperature evolutions are bounded by the ventilation conditions of the five configurations. Indeed, under condition of equivalence ratio greater than 1, the maximum gas temperature near the wall of a certain heat release rate decreases dramatically with the increasing of confinement level of configurations, which is associated to the decrease in flame intensity by lack of oxygen with a great criterion of under ventilation.

Introduction

In a burning enclosure, flame can extend along a ceiling that contributed to the dramatically increase of heat flux and temperature on the ceiling [START_REF] Heskestad | Ceiling jets of strong fire plumes[END_REF][START_REF] You | An investigation of fire impingement on a horizontal ceiling[END_REF]. With the heat transfer through the ceiling, fire can spread from one room to another: unacceptable situation for fire safety engineering [START_REF] Alpert | Calculation of response time of ceiling-mounted fire detectors[END_REF]. Consequently, the behavior of flames impinging ceilings and thermal gradients observed in closed or semi-closed environments are of great interest to fire safety engineering [START_REF] Hinkley | The contribution of flames under ceilings to fire spread in compartments[END_REF][START_REF] Karlsson | Enclosure fire dynamics[END_REF].

The flame-wall interaction in an open or semi-confined environment has been studied earlier [START_REF] Alpert | Calculation of response time of ceiling-mounted fire detectors[END_REF][START_REF] Mccaffrey | Purely buoyant diffusion flames: Some experimental results[END_REF][START_REF] Alpert | Turbulent ceiling-jet induced by large-scale fires[END_REF][START_REF] Gross | Measurement of flame lengths under ceilings[END_REF] and was also an ongoing topic over the last decades [START_REF] Zhang | Experimental study on flame morphologic characteristics of wall attached non-premixed buoyancy driven turbulent flames[END_REF][START_REF] Mann | Transient flame-wall interactions: Experimental analysis using spectroscopic temperature and CO concentration measurements[END_REF][START_REF] Zhen | The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires[END_REF][START_REF] Ji | Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under the tunnel ceiling[END_REF][START_REF] Gao | Experimental study on longitudinal and transverse temperature distribution of sidewall confined ceiling jet plume[END_REF][START_REF] Newale | Quantitative infrared imaging of impinging turbulent buoyant diffusion flames[END_REF][START_REF] Tian | Full-scale tunnel fire experimental study of fire-induced smoke temperature profiles with methanol-gasoline blends[END_REF][START_REF] Zhang | Flame extension length and temperature profile in thermal impinging flow of buoyant round jet upon a horizontal plate[END_REF][START_REF] Wan | Experimental study on horizontal gas temperature distribution of two propane diffusion flames impinging on an unconfined ceiling[END_REF]. In the objective to characterize the behavior of flame impinging a ceiling in open environment, several models for predicting physical parameters such as the temperature profile under the ceiling have developed by many works [START_REF] Alpert | Calculation of response time of ceiling-mounted fire detectors[END_REF][START_REF] Mccaffrey | Purely buoyant diffusion flames: Some experimental results[END_REF][START_REF] Alpert | Turbulent ceiling-jet induced by large-scale fires[END_REF][START_REF] Gross | Measurement of flame lengths under ceilings[END_REF]. Among these models, McCaffrey [START_REF] Mccaffrey | Purely buoyant diffusion flames: Some experimental results[END_REF] proposed that the vertical temperature profile of buoyant turbulent flame could be divided into three regions: continuous flame region, intermittent flame region and plume region. The relations for each region were developed and validated by the experimental results. In the same context, Heskestad and Hamada [START_REF] Heskestad | Ceiling jets of strong fire plumes[END_REF] developed a correlation for temperature rise under ceiling which was caused by the impinging plume of a solid fuel. Alpert [START_REF] Alpert | Turbulent ceiling-jet induced by large-scale fires[END_REF] predicted the major characteristics of the turbulent ceiling-jet fire as functions of heat release rates and distance beneath the ceiling, which were in consideration of the air entrainment model. This correlation was then improved by Li et al. [START_REF] Zhen | The maximum temperature of buoyancy-driven smoke flow beneath the ceiling in tunnel fires[END_REF] and Ji et al. [START_REF] Ji | Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under the tunnel ceiling[END_REF] for flame impinging on a confined ceiling. Ji et al. [START_REF] Ji | Experimental investigation on influence of different transverse fire locations on maximum smoke temperature under the tunnel ceiling[END_REF] carried out series of experiments in a small-scale (1:6) urban road tunnel with fire located in different distances to the sidewall and found that the maximum smoke temperature under the ceiling in the tunnel larger than in the unconfined space, owing to the restriction effect. In consideration of multiple fire sources, Wan et al. [START_REF] Wan | Experimental study on horizontal gas temperature distribution of two propane diffusion flames impinging on an unconfined ceiling[END_REF] investigated gas temperature distribution under unconfined ceiling impinged by two fire sources. They showed that the interaction between multiple flames might lead to flames tilt to each other and even merge together with small spacings, resulting in different ceiling gas temperature distribution in comparison with the case of a flame. Furthermore, it was shown that the behavior of flame impinging a ceiling is greatly influenced by the geometry of walls (corridor, corner…) [START_REF] Gao | Experimental study of tunnel sidewall effect on flame characteristics and air entrainment factor of methanol pool fires[END_REF][START_REF] Poreh | A Study of wall and corner fire plumes[END_REF][START_REF] Tao | The investigation of flame length of buoyancy-controlled gas fire bounded by wall and ceiling[END_REF][START_REF] Gao | Experimental investigation on transverse ceiling flame length and temperature distribution of sidewall confined tunnel fire[END_REF][START_REF] Raksmey | Temperature profile of thermal flow underneath an inclined ceiling induced by a wall-attached fire[END_REF][START_REF] Fan | Experimental study on thermal smoke backlayering length with an impinging flame under the tunnel ceiling[END_REF][START_REF] Ji | Experimental study of non-monotonous sidewall effect on flame characteristics and burning rate of n-heptane pool fires[END_REF][START_REF] Zhao | Impact of openings on fire properties in the confined corridors[END_REF]. For this reason, Gao et al. [START_REF] Gao | Experimental investigation on transverse ceiling flame length and temperature distribution of sidewall confined tunnel fire[END_REF] carried out a series of experiments in the 1/6 scale tunnel model, of which fire source was located near the sidewall. Similar to the free plume [START_REF] Mccaffrey | Purely buoyant diffusion flames: Some experimental results[END_REF], the centerline ceiling temperature was also can be divided into three regions but the ceiling temperature was closely in relation to the effective heat release rate not the total heat release rate. Different from the horizontal ceiling, Zhang et al. [START_REF] Raksmey | Temperature profile of thermal flow underneath an inclined ceiling induced by a wall-attached fire[END_REF] performed experiments of a wall confined flame impinging on an inclined ceiling. They found that the inclination angle of ceiling didn't affect remarkably on the maximum temperature rise under the ceiling in the flame impingement region and a new relation was proposed to predict the temperature decay profiles by taking the ceiling angle into account. In addition, Zhao et al. [START_REF] Zhao | Impact of openings on fire properties in the confined corridors[END_REF] studied the effects of openings on fire properties of the ceiling-jet in a confined reduced-scale corridor using both experimental and numerical methods. With the varying of the size and position of opening, the mass lose and temperature field were measured and compared to Delichatsios's model and previous studies while the influence mechanism of openings wasn't revealed.

In the works cited above, the major part studied the behaviour of the impinging flame in a completely open environment and minor works presented the behaviour of impinging flame in a semi-closed condition. However, there is rarely work that focuses on the effect of the confinement level of the configurations on impinging flame [START_REF] Zhao | Impact of openings on fire properties in the confined corridors[END_REF], for example flame impinging a ceiling of compartments. Indeed, in consideration of the windows and doors of a compartment, it is possible to produce different confinement levels. Thus, the fire dynamics and thermal behaviour of a flame impinging a ceiling will strongly depend on the confinement level of the compartment. In order to provide explanations related to this subject, this work studies the confinement effects on the temperature distribution and flame oscillation in a burning enclosure. The experimental device used is a small-scale compartment (1:10) representing a student compartment model in the university residence. The design of this model was carried out by conserving the Froude number based on the scaling law. The experimental tests were carried out for five configurations with eight heat release rates. By coupling the different openings conditions with the heat capacities used in this study, confinement levels are connected to the equivalence ratio in the compartment. In addition, the results in this work can be used as a mean of evaluating thermal effects which can contribute to the fire spread in compartments.

Experimental details

Experimental setup

The experimental setup used in this study is presented in Fig. 1. It is a compartment at small-scale (1:10), whose dimensions are 0.6 m (length) × 0.4 m (width) × 0.24 m (height) with one door and one window. Based on a survey of the single room in France, England, Australia and other countries, it is found that, generally, the area of single room in different countries is in the range of 15-30 m 2 . For this, the area of the large-scale compartment is equal to 24 m 2 and it particularly represents a student room in university residence. The smallscale compartment was then developed according to the scaling law based on the conservation of the Froude number [26]. The dimensions of the window are 0.15 m (height) × 0.15 m (width) and the dimensions of the door are 0.20 m (height) × 0.09 m (width). The sidewalls of the enclosure are made of fireproofing concrete plate with a thickness of 2 cm and the ceiling is made in steel plate. Their thermal properties are presented in Table 1: m of the target with an emissivity and a transmission of 1. It measured the temperature field on the ceiling. Two columns of K-type stainless thermocouples were placed in the center and near sidewall from floor to ceiling, respectively. Flame videos were recorded by a digital camera (DV) with a frequency of 25 frames per second, that was set 1 m in front of the target. The flame videos were further processed by the image processing method, which included three consecutive steps: direct linear transformation (DLT), fire segmentation and flame length computation. More details on this methodology are presented in a previous work [START_REF] Pettersson | Fire engineering design of steel structures[END_REF]. The uncertainty of the measurements was mainly attributed to the error due to thermocouple radiation and the error related to measurement repeatability. Each test was conducted three times to ensure reproducible results within permitted error ranges.

In this work, the Froude number modeling was applied to build up the physical scale model. With the conservation of Froude number, the scaling law between reduced-scale and full-scale model can be obtained.

Based on the geometric scale, temperature scale and heat release scale, physical parameters such as geometry , temperature , and heat release rate can be scaled with the following Eqs. (1)(2)(3):

= (1) = (2) = = (3)
where the subscript 'R' and 'F' denote the reduced-scale model and full-scale model respectively.

Test series

In order to highlight the confinement effect, five different configurations were used with the different opening conditions of door and window (Ref. Table 2). Thus, the confined factor, of each configuration can be calculated based on the opening factor proposed by Pettersson et al. [START_REF] Pettersson | Fire engineering design of steel structures[END_REF]:

1 o o c t t A H A H δ = - (4)
where represents the confined factor, is the area of opening, is the area of the total compartment, is the height of the compartment, is the height of the opening. For Conf. 2, = ! + # and

= ! ℎ ! + # ℎ # / [27].
In this work, Conf. 5 is assumed completely confined with the neglection of leakages. Thus, the experimental configurations with the confined factor are summarized in Table 2. It can be seen that the confinement level increases from Conf. 1 to Conf. 5.

ϕ -- = = -- (5)
The calculation of this parameter is based on the ratio between the quantity of fuel (propane) which reacts with the oxidizer (air) illustrated in Eq. [START_REF] Karlsson | Enclosure fire dynamics[END_REF]. In this study, it was possible to determine the quantity of fuel (propane) released into the enclosure after a test period (120 s). Concerning the estimation of the quantity of air which reacted, this was determined by the quantity of air contained in the volume of the enclosure. For the calculation of the equivalence ratio, configuration 5 which represents the completely closed enclosure was used as a reference to calculate this parameter. Additionally, based on the measurements of the O2 concentration remaining after each test, it was found that only about half of the oxygen reacted in the study scenarios. The calculation of the equivalence ratio was carried out by considering the quantity of fuel released after 120 s and half quantity of air present in the enclosure. Moreover, the combustion of the propane was carried out in good condition with the minimum oxygen concentration of 10.5 %, representing half of the oxygen concentration in air. For that, the calculation of the equivalence ratio is made using the half amount of air calculated from the volume of the enclosure.

The equivalence ratio of the complete confined configuration, i.e. Conf. 5, is used as the reference equivalence ratio. From the calculations, equivalence ratio φ of Conf. 5 with eight HRRs is shown in Table 3. It can be seen that, equivalence ratio is between 0.12 and 4.70, and the equivalence ratio is larger than 1 for heat release rate larger than 4.6 kW.

Flame oscillation modeling of a propane-air diffusion flame

In Refs. [START_REF] Joulin | Flame oscillations induced by conductive losses to a flat burner[END_REF][START_REF] Niu | Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear[END_REF][START_REF] Grier | Combustion: Types of reactions, fundamental processes and advanced technologies[END_REF][START_REF] Korpela | Appendix B: Thermodynamic Tables[END_REF], the evaluation level of the oscillation of a diffusion flame can be obtained from the mass flow rate of the fuel. In the current study, the fuel is the propane.

It is possible to define two typical time scales that give rise to flame oscillations: the convection time scale and the diffusion time scale [START_REF] Kitahata | Oscillation and synchronization in the combustion of candles[END_REF]. From the typical flame radius & and the gas diffusion coefficient ' ( , it is possible to evaluate the typical diffusion time ) !( of the flame oscillations by the following relation [START_REF] Rasbash | handbook of fire protection engineering[END_REF]:

2 f diff iff R D τ = (6)
The typical convection time ) *+ is given by the following relation:

0 f conv L u τ = (7)
where Lf is the flame length and , -is the speed of the flame jet. Knowing that, the temporal fluctuations observed are of the order of ten seconds, we decide to take into account only the diffusion phenomenon, with a differential delay equation [START_REF] Niu | Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear[END_REF].

In order to dissociate from the complex phenomena, present in the reaction zone of the flame, only the zone of the flame where there is no combustion will be considered. With this assumption, the typical times of chemical reactions are much lower than the typical times of diffusion. We will therefore consider oxygen as the diffusion gas. We define the variation in oxygen concentration using the following relationship (Fick's law):

( )

0 2 ( ) iff f D dx x x t dt R = - (9)
where ( ) x t is the oxygen concentration at time t, ' ( is the oxygen diffusion coefficient, & is the flame radius and 5 -is the oxygen concentration outside of the flame.

Since the diffusion of oxygen is not instantaneous, we introduce a delay ) in the previous differential equation [START_REF] Niu | Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear[END_REF], that becomes:

( ) 0 2 ( ) iff f D dx x x t dt R τ = - - (10)
and using the 2 nd order approximation of Taylor expansion of ( )

x t τ -: ( ) ( ) ( ) ( ) 2 2 ( ) 2 0 ... ! 1! 2! k k k dx d x x t x t x t k dt dt τ τ τ τ ∞ = - -= ≈ - + + ∑ (11)
It is deduced:

2 2 0 2 2 2 2 2 2 2 2 1 f iff iff f R D x d x dx x dt D R dt τ τ τ τ   + - ⋅ + =       (12)
From the flame fluctuations observed experimentally, we will hypothesize that the problem is reduced to that of a harmonic oscillator with:

2 2 0 0 2 2 2 2 x d x dx x dt dt λ ω τ + + = (13)
In this context, we decide to put the friction term

f iff f iff f iff R D R D R D τ τ τ   ⋅ - = ⇒ =       (14)
In addition, the third term = -= 2 ) ⁄ of the Eq. ( 13) can be associated with the frequency of oscillation of the flame, so we can determine the frequency by the following relationship:

2 0 0 2 2 2 ω ω τ τ = ⇒ = (15)
Since = -is linked to the period of flame oscillation > , we have:

0 2 2 2 2 os os T T π π τ π τ ω ⋅ = ⇒ = = ⋅ ⋅ (16)
At the last, using Eq. ( 14):

2 2 f os iff R T D π = ⋅ ⋅ (17)
This expression represents the oscillation period of the flame. As gas diffusion coefficient ' ( depends on the temperature, so that flame oscillation is related to the temperature in the compartment. In order to apply Eq. ( 17), that gives the period from the differential equation delay model, the diffusion coefficient must be evaluated more precisely. The kinetic theory of gases establishes that ' ( varies as a function of temperature according to ' ( ∝ [START_REF] Rasbash | handbook of fire protection engineering[END_REF]. Considering flame temperature between 600°C and 800°C, the diffusion coefficient of oxygen in propane is of the order of ' ( ≈ 0.5 4 ⁄ . The application of Eq. ( 17), gives an oscillation period = 8.9 , which is agreement with the measurements obtained in the current work. However, it can be seen from Fig. 3 (b), flame oscillation time varies greatly with the confinement level of the configurations. When HRR=18.6 kW, the equivalence ratio of each configuration is greater than 1. In this condition, flame temperature decreases with the decrease in flame intensity due to the lack of oxygen in the enclosure. For it, the more the confinement level increases, the more the flame temperature decreases, even leading to the extinction of the flame.

Results and discussion

Flame oscillations in confined compartment

Confinement effect on vertical temperature distribution in impinging zone

The fire plume in open space is conventionally divided into three zones: continuous flame zone, intermittent flame zone and buoyant plume zone [START_REF] Mccaffrey | Purely buoyant diffusion flames: Some experimental results[END_REF]. For flame impinging a ceiling, Gao et al. [START_REF] Gao | Experimental study on longitudinal and transverse temperature distribution of sidewall confined ceiling jet plume[END_REF] has pointed that the ceiling excess temperature of 400 K and 600 K can be considered as two critical values to evaluate the impinging condition under the ceiling. For ∆ < 400 , 400 < ∆ < 600 and ∆ > 600 , they represent buoyant plume, intermittent flame and continuous flame respectively. For a strong plume, Ji et al. [START_REF] Ji | Experimental study on behavior of sidewall fires at varying height in a corridor-like structure[END_REF] proposed a correlation for predicting the ∆ HI< under a confined ceiling: 0.267 , 10.9

2.9, 10.9

Q Q T H H T Q H ∞  <  ∆  =   ≥   & & & (18)
In Eq. ( 18), the two parts are consistent with the intermittent and continuous impinging flames respectively.

As discussed above, the impinging plumes in this work are considered to be strong plumes with intermittent and continuous impinging flames under the ceiling. Thus, an equation for predicting maximum temperature rise in impinging zone ∆ HI< for Conf.

Q Q T H H T Q H ∞  + <  ∆  =   ≥   & & & (19)
The experimental data and fitted curve for nondimensional maximum temperature rise in impinging zone for Conf. 1 are presented in Fig. 5.

Fig. 5. The experimental data and fitted curve for nondimensional maximum temperature rise in impinging zone

Confinement effect on vertical temperature distribution near the wall

Fig. 6 shows the vertical gas temperature near the wall for eight HRRs. On reading these graphs, it is shown that for HRRs less than 4.6 kW, the vertical temperature evolution under the ceiling is similar for all configurations while the maximum temperature under the ceiling for confined configuration (i.e. Conf. 2 to Conf. 5) are higher than the flame impinging a ceiling in open environment (i.e. Conf. 1) owing to the heat accumulation in the compartment.

However, they show differences for the heat release rates of 9.3 kW, 14.0 kW, 16.3 kW and 18.6 kW (Fig.

6 (e)(f)(g)(h)), which corresponds to equivalence ratio larger than 1. At a certain HRR, for example HRR=14.0 kW, the maximum gas temperature of configuration decreases when the confinement level of configuration increases. It is noted that these maximum temperatures decrease to converge towards the values of temperature in the lower part of the room. Indeed, the more the confinement level increases, the more the accumulation of smoke rich in unburnt gases. These smoke layers thicken from the ceiling to the ground, promoting temperature uniformity in the room when the flame intensity decreases due to the lack of oxygen in the compartment. For HRRs larger than 9.3 kW (equivalence ratio larger than 1) (Fig. 6 (f)(g)(h)), the temperature evolutions are similar considering the presence of flame fluctuation. 7 shows maximum gas temperature rise under ceiling (∆ HI< ) against . It is clear that the maximum temperature rise under ceiling of Conf. 1 increases with the increasing of . For heat release rates less than 4.6 kW, the ∆ HI< presents nearly unchanged for all configurations. The HRR of 4.6 kW presents a turning point of the maximum temperature rise in five configurations (Conf. 1 to Conf. 5). For heat release rates larger than 4.6 kW, which is corresponding to equivalence ratio larger than 1, the maximum temperature gap between Conf. 1 and Conf. 5 increases dramatically with the increasing of heat release rate, from 87 K to 369 K. That is associated to the decrease in flame intensity by lack of oxygen with the increasing in confinement level of configurations. Thus, from the results presented in this study, it is shown that the flame intensity decreases as a function of the compartment's confinement level. Fig. 7. Maximum gas temperature rise near the wall (∆ HI< ) against Fig. 8 shows relationships between normalized temperature rise and normalized HRR for five configurations, which are obtained by the fitting of experimental data. It can be seen that with the increasing of normalized HRR, normalized temperature rise increases for all five configurations. Indeed, at a certain * , especially for * larger than 2.2 × 10 , which corresponds to the equivalence ratio larger than 1, normalized temperature rise decreases with the increasing of confinement level. These temperature evolutions are bounded by the ventilation conditions of the five configurations. Correlations of normalized temperature rise for five configurations are listed in Table 4. Note that in Conf. 5, the temperature decays slightly along the transverse radius of ceiling for larger HRRs (HRR > 9.3 kW, φ >1). This can be caused by the incomplete combustion in the enclosure so that the total enclosure is filled with the unburn gas and smoke. The dangerous accidents such as backdraft and flashover may occur if a window or door is broken manually or automatically in these conditions.

Q Q T - - ∞ ∆ = -× + × + & & (

Conclusions

The aim of this work is to investigate the confinement effects on fire dynamics and heat transfer for impinging flame in the enclosure. For obtaining this object, a small-scale (1:10) compartment model has developed. A systematic experimental study is performed using five configurations with eight heat release rates, on the temperature distributions of impinging zone, smoke layer and ceiling's surface, as well as flame oscillation. The major findings include:

(1) A flame oscillation modelling of a propane-air flame is proposed and is verified by the experimental results. It is shown both by theoretical modeling and experimental results that confinement level of a compartment has an effect on period time of flame oscillation.

(2) Considering vertical temperature in smoke layer (near the wall), the temperature evolutions vary greatly with the level of confinement. In fact, for the same HRR, especailly for HRRs larger than 4.6 kW, in corresponding to equivalence ratio greater than 1, the greater the confinement level is, the lower the temperatures close to the ceiling presents. This variation is associated to the combustion process for different configurations. Besides, correlations of normalized temperature rise for five configurations are proposed.

(3) The higher the confinement level is, the more the area of impinging zone on the ceiling decreases. The maximum ceiling temperature is at the flame impinging point and decreases along the transverse radius of ceiling.

The results in this study may help to design fire detectors on the ceiling and better understand fire behavior and heat transfer during fire disasters in compartments. The hot temperature of unburned gases and a supply of fresh air being the sources of a backdraft, it is desirable to check the temperature level in the enclosure to avoid the fire progress to a backdraft.

In future, the effect of the fire source's position will be studied and the investigation on the full-scale model will be carried out.

Fig. 1 .

 1 Fig. 1. Schematic of the experimental set up

  One of our typical experimental conditions are as follows: mass flow rate of propane = 0.1 / , -= 2.1 / , flame radius R=1 cm, flame length = 46 4 and the diffusion coefficient is ' ( = 0.1 4 / . With these values, typical diffusion and convection times are:

Fig. 2

 2 Fig. 2 depicts the experimental measurements of the mean flame length over time for Conf. 2, i.e. impinging flame in compartment of open door and window, with HRR=4.6 kW. It can be seen that flame fluctuates with a period time about the order of 10 seconds. These measurements were obtained from video recordings that lasted approximately 120 seconds (see Fig.2).

Fig. 2 .

 2 Fig. 2. Mean flame length over time for Conf. 2 with HRR=4.6 kW

Fig. 3 .

 3 Fig. 3. Mean flame length over time for five configurations with: (a) HRR=1.2 kW; (b) HRR=18.6 kW Fig. 3 shows the experimental measurements of mean flame length over time for five configurations with HRR=1.2 kW and HRR=18.6 kW, which are respectively the minimum and maximum HRRs in this study. It is shown that in Fig. 3 (a), the confinement level of the configurations has a little effect on the flame oscillation time as the equivalence ratios of five configuration are smaller than 1.

Fig. 4 Fig. 4 .

 44 Fig.4shows the vertical temperature distribution in impinging zone for five configurations with the varying eight heat release rates from 0.5 kW to 18.6 kW. It can be seen that for Conf. 1, i.e. flame impinging a ceiling in open environment, the vertical excess temperature ∆ increases with the height above fire source, owing to the flame progress with the increasing of burning rate. It should be noted that for Conf. 1, even the excess temperature near the ceiling is greater than 600 K in condition of all eight heat release rates, which means that the flame is continuous under the ceiling. Furthermore, for Conf. 1, the ceiling is impinged by a strong plume with all heat release rates of the gas burner from 0.5 kW to 18.6 kW. Specially, the plume under the ceiling is in the first zone of plume: continuous flame zone, such that it's called impinging flame in this work.

Fig. 6 .

 6 Fig. 6. Vertical gas temperature distribution near the wall for eight HRRs Fig. 7 shows maximum gas temperature rise under ceiling (∆ HI< ) against . It is clear that the maximum

Fig. 8 .

 8 Fig. 8. Relationships between normalized gas temperature rise and normalized HRR for five configurations

Fig. 9 .

 9 Fig. 9 shows temperature fields on the ceiling for different confinement levels at HRR of 9.3 kW, obtained by IR camera which can represent the flame impinging zone on the ceiling. The imping zones are almost symmetrical because the conditions of fire in enclosure are near symmetrical even through the confinement levels are relatively high. It is possible to observe the confinement effects by the yellow area impinged by the flame and the red area impinged by the plume. It is clearly visible that the flame impinging area decreases and the plume impinging area increases with the increasing of configurations' confinement level, i.e. from Conf. 2 to Conf. 5.

Fig. 10 .

 10 Fig. 10. Temperature distribution along the transverse radius of ceiling

Table 1 .

 1 Thermal parameters of aerated concrete and steel

	Thermal parameters		Aerated concrete	Steel
	Density ( / )		870	7850
	Conductivity ( /	)	0.175	46
	Specific heat ( / • )	0.92	0.5
	In this work, the fire source was provided by a gas burner with the nozzle's diameter of 5 mm, which was
	placed in the center of the compartment. The fuel used was the propane (C3H8) with a heat of combustion of
	46.45 ⁄ . The mass flow rate of fuel was controlled by a Bronkhorst Coriolis mass flow meter with a range of
	0-1.00 ⁄ with an accuracy of 0.05 ⁄ . The used instrumentations were an infrared camera, K-type
	thermocouples and a digital camera. The infrared camera (IR) was a FLIR A655sc which can record field
	temperature from -45 °C to 2000 °C with a frequency of 35 frames per second. It was set above the ceiling at 2

Table 2 .

 2 The experimental configurations with the confined factor

	Configurations	Condition of openings Window Door	o A	H	o	δ	c
		Conf. 1	Flame impinging a ceiling in open environment	∞	-	0
		Conf. 2	Open					Open	0.0405	0.415	0.964
		Conf. 3	Open					Closed	0.0225	0.387	0.981
		Conf. 4	Closed					Open	0.0180	0.447	0.983
		Conf. 5	Closed					Closed	≈0	-	≈1
	In each series of experiments, eight different heat release rates (HRRs) have been used: HRRs = {0.5, 1.2,
		fuel to oxidizer	ratio			m	fuel	/	ox m
	(	fuel to oxidizer	ratio)	st	(	m	fuel	/	) ox st m

2.3, 4.6, 9.3, 14.0, 16.3, 18.6} kW. These HRRs represent the different heat capacities that it is possible to get in the experiments, set up in relation to the compartment in real scale.

In order to study the confinement effects on the behavior of the flame impinging the ceiling, the equivalence ratio is used. This makes it possible that depending on its value, to indicate the confinement level related to the mass flow rates of the fuel released. The equivalence ratio is defined as following:

Table 3 .

 3 Equivalence ratio φ of Conf. 5 under eight HRRs

	HRR (kW)	0.5	1.2	2.3	4.6	9.3	14.0	16.3	18.6
	%	0.12	0.29	0.59	1.17	2.35	3.52	4.11	4.70

  1, i.e. flame impinging a ceiling in open environment, is

	proposed:
	2 5	2 5
	0.06	2.4,	12.7
	max
	2 5
	3.1,	12.7

Table 4 .

 4 Correlations of normalized temperature rise for five configurations

	Configuration			Correlations
	Conf. 1	max T ∞ T ∆	8 *2 Q -2.4 10 = -× &	4 * Q -4.6 10 + × &	+	0.2	(20)

Acknowledgements

The authors thank the reviewers for their valuable comments on the initial version of this paper.