Anna Shvarts
email: a.y.shvarts@uu.nl

Theory, methodology and design as an insightful bundle: a case of dual eye-tracking student-tutor collaboration on an embodied mathematical task

Keywords: Eye movements, research methodology, epistemology

While the importance of reflection on methodological dimension for the networking theories was already stated (e.g. Bikner-Ahsbahs & Prediger 2014), here we claim that educational design is another essential dimension in distinguishing a phenomenon that might be unattainable as far as it has not been lit by a particular theory-methodology-design bundle. In this poster, we explore a bundle of a culture-historical approach, dual eye-tracking (DUET) method, and action-based interactive design; we argue that these three aspects being taken together form a lens that manifests in the teaching/learning process a perception-action system that is distributed between the tutor and student. The argument is based on multimodal data from student-tutor collaboration on interactive activity, where a student was required to discover a parabola in an embodied way as a set of points equidistant from the focus and directrix (Shvarts & Abrahamson, 2018).

Theory-methodology coupling. A culture-historical approach provides us both with the theory and methodology for investigating the psyche's development, and yet they are interconnected. Vygotsky proposes an "experimental-genetic method" that aims to restore the development process and to expose the higher psychic functions in the form of moving, "flowing flood" (Vygotsky, 1978). This method involves the active participation of a researcher in interaction with a pupil that, unlikely to natural science, do not distort the data, but on the contrary allow the genesis of mathematical functions to emerge. A theoretical presumption here is the social nature of psychological functions that emerge in intersubjective interactions. In our study, an experimenter interacts with the student as a tutor, and later interaction is reproduced between the just-instructed participant and a new pupil. DUET appears to be a perfect way to investigate this collaboration: while often eyemovements are interpreted with the presumption of the eye-mind hypothesis, the data from DUET might be perceived as evidence of a psychic function as distributed between a student and a tutor. Then joint attention is not a result of initiation or response by single participants, but a functional end that emerges from "the multiple pathways" (Yu & Smith, 2016, p. 18) within their system.

Theory-design coupling. Traditionally from Vygotsky's point of view, communication between a student and a teacher is considered as mediated by some cultural artifacts, signs. However, Roth argues that in his late writing Vygotsky departures from the mediation as a primary mechanism that serves communication (Roth, 2018). This embodied character of collaboration is particularly accessible in an activity which is deliberately designed so that introduction of mathematical notations is postponed to the moment when a student has experienced mathematical concepts in an embodied way (Abrahamson, Shayan, Bakker, & van der Schaaf, 2015). The involvement of a student and a tutor in a motor problem that required formation of a new sensory-motor coordination allowed us to trace this function as socially distributed.

Method-design coupling. As eye-tracking let us observe oculomotor spatially articulated activity, we shall involve the participants in the design that benefits from an eye-tracking observation. The embodied action-based design is particularly suitable as it provides an opportunity for the learner to elaborate mathematical knowledge at first in the form of sensory-motor coordination. It is through eye-tracking we may gather empirical evidence of attentional anchorsthe perceptual aspects of sensory-motor coordination that serves the efficiency of movement (Abrahamson et al., 2015).

Theory-methodology-design bundle. A combination of all three couplings let some phenomena surface; we present the one phenomenon that seems to be of great importance for educational science. While the students' eye-movements manifested emerging attentional anchors, the same was found in the tutors' oculomotor behavior, whether they were a researcher or an instructed participant. Thus, we obtained evidence of embodied coupling between the student and tutor: The tutor's perception is as if it regulates the student's action. While de facto it is the student who conducts the movements, the tutor enacts these movements in their imagination thus anticipating student's progress in learning and sensing her micro-zone of proximal development. This coordination between student's action and tutor's perception allows us introducing intersubjectively distributed perception-action system that evolves in the teaching/learning process.

Shall this be a local phenomenon of particular activity under the particular lens? We argue that this theory-methodology-design bundle does not limit generalization of the findings: The phenomenon of an intersubjectively distributed perception-action system is made spatially articulated due to the design settings, visible through dual eye-tracking methodology and understood under the light of Vygotsky's theory of irreducibly collaborative teaching/learning. Finally, it becomes influential far beyond particular experimental settings just like the phenomenon of diffraction of light and its dual wave-particle nature goes far beyond the settings in which it was spotted.

  Shvarts, A., & Abrahamson, D. (2019). Dual-eye-tracking Vygotsky: A microgenetic account of a teaching/learning collaboration in an embodied-interaction technological tutorial for mathematics. Learning,Culture and Social Interaction, 22, doi.org/10.1016/j.lcsi.2019.05.003 Vygotsky, L. S. (1978). Mind in society: the development of higher psychological processes. Oxford, England: Harvard University Press.

	Abrahamson, D., Shayan, S., Bakker, A., & van der Schaaf, M. (2015). Eye-Tracking Piaget:
	Capturing the Emergence of Attentional Anchors in the Coordination of Proportional Motor
	Action. Human Development, 58(4-5), 218-244.
	Bikner-Ahsbahs, A., & Prediger, S. (2014). Networking as research practices: Methodological
	lessons learnt from the case studies. In Networking of theories as a research ractice in
	mathematics education (pp. 235-247). Cham, Switzerland: Springer International Publishing.
	Roth, W.-M. (2018). Birth of Signs: A (Spinozist-Marxian) Materialist Approach. In N. Presmeg, L.
	Radford, W.-M. Roth, & G. Kadunz (Eds.), Signs of signification: Semiotics in mathematics
	education research (pp. 37-53). Cham, Switzerland: Springer International Publishing.

Yu, C., & Smith, L. B. (2016)

. Multiple sensory-motor pathways lead to coordinated visual attention. Cognitive Science, 41, 1-27.


Mireille Lefèvre

Sylvain Cros

Yves-Marie Saint-Drenan

Jan Fokke Meirink

Marion Schroedter-Homscheidt

Hartwig Deneke

Martin Stengel

Applying the Heliosat-4 method to three different cloud properties databases for the estimation of the surface downwelling shortwave irradiance

There is a clear sensitivity of HS-4 output product to the COD and CT from the different sources, and from their temporal evolution (APOLLO bias is unusually higher in 2016).

(

  -4 SW irradiance for 56 stations: Year 2016: a CAMS-RAD anomaly in the Netherlands investigated with a comparison of different cloud properties databases Conclusion  Heliosat-4 method is simple to use and to implement with different databases of cloud properties  There are significant differences among existing cloud properties databases that have a noticeable effect on SW irradiance from Heliosat-4  This work demonstrated the relevance of inter-comparison of cloud properties databases Applying the Heliosat-4 method to three different cloud properties databases for the estimation of the surface downwelling shortwave irradiance EMS -Copenhagen, Denmark (11/09/2019) Sensitivity of HS-4 to the cloud properties for the 37 northern stations Armel Oumbe, Philippe Blanc, Bella Espinar, Gerhard Gesell, et al.. Fast radiative transfer parameterisation for assessing the surface solar irradiance: The Heliosat-4 method. Meteorologische Zeitschrift, Berlin: A. Asher & Co., 2017, 26 (1), pp.33-57.  Marked differences between the different datasets  APOLLO is relatively non-discriminatory for the low COD mainly considered as null  SICLONE presents a more uniform distribution of low COD  Over-representation of high irradiations and under-representation of low values  APOLLO-HS4 farther from measurements than the two others

  A Model Output Statistics is implemented for KNMI on Dutch stations and CAMS-RAD on BSRN stations. (a, d) http://msgcpp.knmi.nl/ (b, e) http://www.soda-pro.com/web-services/radiation/cams-radiation-service (c) http://reuniwatt.com/en/applications/atmospheric-sciences


Heather Lynn Johnson
email: 1heather.johnson@ucdenver.edu

Evan Mcclintock
email: evan.mcclintock@ucdenver.edu

Amber Gardner
email: amber.gardner@ucdenver.edu

Locally integrating theories to investigate students' transfer of mathematical reasoning

Keywords: Transfer of learning, reasoning, learning theories, instructional design

To theorize the study of students' transfer of mathematical reasoning, we integrate Lobato's theory of actor-oriented transfer, Thompson's theory of quantitative reasoning, and Marton's variation theory. Linking theory and method, we argue for an expansion of design possibilities for researchers' investigations of students' transfer of reasoning. To bolster our argument, we provide empirical data of a secondary student's transfer of a particular form of reasoning-covariational reasoning. Our research has implications for researchers' development of new theoretical and methodological approaches to investigate complex phenomena, such as students' mathematical reasoning.

Integrating theories to investigate students' transfer of covariational reasoning

Task designers, teachers, and researchers share a goal of promoting students' mathematical reasoning. While mathematical reasoning comprises students' mental activity, in our view, it is impossible to separate students' mental activity from their embodied experiences [START_REF] English | Analogies, metaphors, and images: Vehicles for mathematical reasoning[END_REF]. Interacting with mathematical tasks can provide students opportunities to engage in mathematical reasoning. By mathematical task, we mean something more than a problem statement. From our perspective, tasks encompass the intentions of a task designer, the implementation of a task by a teacher/researcher, students' interaction with the task, and physical materials associated with the task [START_REF] Johnson | Mathematical tasks and the student: Navigating "tensions of intentions" between designers, teachers, and students[END_REF]. Ideally, when students develop a form of mathematical reasoning, they could engage in that form of reasoning on subsequent tasks and in different situations.

We aim to infer students' reasoning based on their observable behavior. In our view, students are experts in their own mathematical reasoning, and our role is to elicit and explain that reasoning. Our stance on students' reasoning influences our assumptions about the viability of their reasoning. First, we do not assume that students working on a task will share our goals for the task (e.g., [START_REF] Johnson | Mathematical tasks and the student: Navigating "tensions of intentions" between designers, teachers, and students[END_REF]. Second, we acknowledge that students may engage in mathematical reasoning that is different from the reasoning we intend. Third, we assume students' different forms of reasoning to be viable and productive. Hence, we do not seek to "fix" students' reasoning. Rather, we seek to understand and engender students' mathematical reasoning, in its myriad forms.

Employing a transfer lens, researchers can investigate how students might engage in different forms of mathematical reasoning across a range of tasks and situations. Yet, researchers' perspectives on transfer impact what researchers may construe as evidence of students' transfer of reasoning [START_REF] Lobato | How design experiments can inform a rethinking of transfer and vice versa[END_REF][START_REF] Lobato | Research methods for alternative approachers to transfer. Implications for design experiments[END_REF][START_REF] Marton | Sameness and Difference in Transfer[END_REF]. To address the problem of investigating transfer of students' reasoning, we employ an actor-oriented transfer perspective [START_REF] Lobato | How design experiments can inform a rethinking of transfer and vice versa[END_REF][START_REF] Lobato | Research methods for alternative approachers to transfer. Implications for design experiments[END_REF], because it affords researchers the opportunity to gather evidence of transfer of reasoning beyond forms of reasoning that a researcher may intend.

From an actor-oriented transfer perspective, transfer is generalization, rather than application [START_REF] Lobato | How design experiments can inform a rethinking of transfer and vice versa[END_REF][START_REF] Lobato | Research methods for alternative approachers to transfer. Implications for design experiments[END_REF]. Meaning, students who generalize some form of reasoning from one task to another would engage in transfer, even if they do not apply a particular solution method. Hence, an actor-oriented transfer perspective broadens the scope of what is possible for students to transfer. Furthermore, a researcher's theoretical perspective on transfer impacts methods used to gather evidence of students' transfer. Researchers employing an actor-oriented transfer perspective examine students' constructions of similarities across tasks, rather than students' task performance [START_REF] Lobato | How design experiments can inform a rethinking of transfer and vice versa[END_REF][START_REF] Lobato | Research methods for alternative approachers to transfer. Implications for design experiments[END_REF]. Because students' mathematical reasoning is not the same as task performance, an actor-oriented transfer perspective is a productive theoretical lens to use to investigate students' reasoning.

We focus on students' engagement in and transfer of a particular form of reasoning-covariational reasoning-which is critical for students' development of a conception of function [START_REF] Thompson | Variation, covariation and functions: Foundational ways of mathematical thinking[END_REF]. We draw on Thompson's theory of quantitative reasoning [START_REF] Thompson | Quantitative reasoning and mathematical modeling[END_REF][START_REF] Thompson | Variation, covariation and functions: Foundational ways of mathematical thinking[END_REF] to explain our perspective on covariational reasoning. When students engage in covariational reasoning, they form and interpret relationships between attributes they conceive of as capable of varying and possible to measure. For example, consider a situation involving a toy car moving around a track. A student engaging in covariational reasoning could form and interpret relationships between different attributes, such as the toy car's distance traveled around the track and its distance from some stationary object. Because an actor-oriented transfer perspective focuses on students' generalization rather than performance, it is a useful theoretical lens to explain invariance in students' engagement in quantitative (and covariational) reasoning across tasks and situations [START_REF] Thompson | Quantitative reasoning and mathematical modeling[END_REF].

Researchers employing a variation theory perspective [START_REF] Kullberg | What is made possible to learn when using the variation theory of learning in teaching mathematics?[END_REF][START_REF] Marton | Sameness and Difference in Transfer[END_REF][START_REF] Marton | Necessary conditions of learning[END_REF] consider critical aspects of objects of learning (intended objects of learning), problematize ways in which to provide students opportunities to experience those critical aspects (enacted objects of learning), and acknowledge the viability of learning that students actually demonstrate (lived objects of learning). Although we focus on a particular form of reasoningcovariational reasoning-we acknowledge that students may engage in or transfer forms of reasoning other than what we intend. From a variation theory perspective, students discern the similar (and generalize) because they discern difference, and consequently, designers should design opportunities for students to experience difference. Simply put, variation (in terms of difference) is a necessary condition for students to experience discernment.

Networking theories is useful for addressing complexities inherent in investigations of students' mathematical reasoning. For example, our investigation of students' transfer of covariational reasoning is intertwined with students' creation and interpretation of dynamic graphs in a Cartesian coordinate system. Drawing on Variation Theory, we considered critical aspects to include the types of attributes that students would encounter (e.g., length measures), the motion of objects in physical space (e.g., up/down, left/right, curving paths), and the representation of those attributes in a Cartesian coordinate system. Accordingly, we varied those critical aspects to provide opportunities for students to engage in covariational reasoning.

Networking (coordinating) Thompson's theory of quantitative reasoning and Marton's variation theory of learning, [START_REF] Johnson | When a critical aspect is a conception: Using multiple theories to design dynamic computer environments and tasks to promote secondary students' discernment of covariation[END_REF] explained how researchers could design learning experiences to engender students' discernment of critical aspects of covariation. We extend this research in two ways. First, we connect the investigation of students' transfer of reasoning, employing an actor-oriented transfer perspective on transfer. Second, we build from coordinating theories to locally integrating theories, to contribute to theory development.

Extending design possibilities for actor-oriented transfer

Lobato (2014) identified four criteria on which researchers should base claims of actor-oriented transfer. We summarize these claims, centering students' mathematical reasoning, which is our focus. First, students should demonstrate a change in reasoning on transfer tasks, from a preinterview to a post-interview. Second, students should demonstrate the new reasoning during interview tasks occurring between the pre-and post-interviews. Third, researchers should provide evidence that students' reasoning during the interview tasks influenced their reasoning on the post-interview tasks. Fourth, researchers should provide evidence that changes in students' reasoning in a post-interview occurred as a result of their work on the interview tasks, and was not just a spontaneous occurrence.

We posit an extension of design possibilities for researchers employing an actor-oriented transfer perspective. From our perspective, inherent in [START_REF] Lobato | Research methods for alternative approachers to transfer. Implications for design experiments[END_REF] design criteria is an assumption that researchers design transfer tasks that are separate from interview tasks. We argue that by leveraging Variation Theory in task design, researchers can investigate students' transfer by analyzing students' reasoning on subsequent tasks across a set of interviews. In making this argument, we follow [START_REF] Cobb | Putting philosophy to work: Coping with multiple theoretical perspectives[END_REF] recommendation for theory expansion rather than replacement. In particular, we aim to expand design possibilities, rather than to replace one design type with another design type.

An empirical example: A task sequence and a student's work

To illustrate how we locally integrated theories, we provide an example from the work of a 9 th grade student, Aisha, during three individual, task-based interviews, conducted by Johnson. Task sequences in each interview had a different background (first a Ferris Wheel, second a Cannon Man, and finally a Toy Car), given by a computer animation. Aisha worked on a tablet (an iPad), with pencil and paper available. In each task sequence, Aisha sketched and/or interpreted different Cartesian graphs to represent a relationship between attributes in a situation given in an animation.

The Cannon Man and Toy Car task sequences were more involved than the Ferris Wheel task sequence. For the Ferris Wheel, Aisha needed to sketch only one graph. For the Cannon Man and Toy Car, Aisha explored change in individual attributes, manipulating dynamic segments located on the horizontal and vertical axes. Next, Aisha sketched a graph representing a relationship between both attributes. Then, Aisha repeated the process for a second graph with attributes represented on different axes. After sketching each graph, Aisha viewed a computer-generated graph. Transcripts that follow are from each interview. Figure 1 shows graphs that Aisha drew in each interview. The Cannon Man and Toy Car graphs shown in Figure 1 (middle, right) are the second Cartesian graph that Aisha drew during each interview.

Ferris Wheel

Johnson asked Aisha to sketch a graph relating a Ferris wheel cart's height from the ground and total distance traveled, around one revolution of the Ferris wheel. While sketching the graph shown in Figure 1, left, Aisha explained why she drew the graph the way that she did.

Aisha:

I feel like the height would be more like the line (sketches a line, Figure 1, left). Distance would be more like the rise and run of the situation (sketches small segments, Figure 1, left). Cause you're using the rise and run to find the line, and you need to use the distance to find the height.

Cannon Man

Johnson asked Aisha to sketch a graph relating a Cannon Man's height from the ground and total distance traveled, with the height on the horizontal axis and the distance on the vertical axis. After Aisha sketched the graph shown in Figure 1, middle, Johnson asked her to explain how her graph showed Cannon Man's height and distance.

Johnson:

Can you show me how you see the height increasing and decreasing in this purple graph? (Points to the curved graph Aisha drew, Figure 1, middle)

Aisha: It's (the height's) increasing here, since it's (the graph's) backwards in my opinion (Sketches green dots, beginning on bottom left near the vertical axis, then moving outward, Figure 1, middle). Decreasing here. (Continues to sketch green dots, until getting close to the vertical axis, adding arrows after sketching dots, Figure 1, middle)

Johnson: How is the distance changing?

Aisha:

(Turns iPad so that vertical axis is horizontal. Draws arrow parallel to vertical axis, Figure 1, middle.) That way. Continues to get bigger.

Toy Car

Prior to sketching the graph shown in Figure 1, right, Aisha stated, without prompting from Johnson, that distance traveled was the "same as the Cannon Man." Johnson asked Aisha to clarify.

Johnson: So, you said the total distance traveled is like the Cannon Man. Why is that like the Cannon Man again? Cause Cannon Man goes up and down, and this one moves around. How are those things the same?

Aisha: Just because Cannon Man is coming back down, doesn't mean his distance is going down. His distance is still rising.

To explore change in each of the individual attributes, Aisha manipulated dynamic segments located on the horizontal and vertical axes. For the total distance, Aisha began at the origin, continually moving the segment up, along the vertical axis. She explained: "I moved it up. It continuously went up, because the distance doesn't decrease. The total distance traveled doesn't decrease." For the distance from the shrub, Aisha began to the right of the origin, initially moving the segment to the left, and then to the right. She explained: "I moved it (the segment) to the left, because it (the Toy Car) was getting closer to the shrub. Then, when it (the Toy Car) started to turn, I started to moved it (the segment) back up to the right, because it (the Toy Car) was getting closer to the shrub." Next, Aisha sketched the graph shown in Figure 1, right. After viewing the computergenerated graph, Aisha explained what she thought the curved graph represented. Aisha stated: "This (moving her finger from left to right along the horizontal axis) is tracking the distance from the shrub, and this (moving her finger along the curved graph, beginning near the horizontal axis) is also tracking the distance."

Employing individual theories as analytic lenses

We explain how we draw on individual theories to analyze Aisha's transfer of covariational reasoning. While we present the accounts separately, we conceive of these accounts as something more than complementary. In our view, each theoretical lens is like one of the intertwined strands of a braid or cord.

Thompson's theory of quantitative reasoning

In our task design, we made strategic choices about the kinds of attributes that students would represent in graphs. In particular, we selected length attributes (e.g., height, distance) because we anticipated it would be less difficult for students to conceive of measuring length attributes than for other kinds of attributes, such as area or volume. During clinical interviews, Johnson asked students to represent ways in which individual attributes were varying (e.g., increasing and/or decreasing), and to explain how graphs they sketched represented different attributes.

For the Cannon Man and Toy Car, Aisha provided evidence of engaging in an early form of covariational reasoning. In contrast, for the Ferris wheel, Aisha attempted to show how one might obtain one value given another value. For the Cannon Man and Toy Car, Aisha conceived of both attributes as possible to measure and capable of varying. Her graphs (Figure 1, middle, right) represented both attributes, one varying in a single direction (increasing), and another varying in different directions (increasing and decreasing).

Marton's Variation Theory

For the Cannon Man and Toy Car task sequences, we incorporated patterns of variation and invariance to provide opportunities for Aisha to discern critical aspects of covariation (intended object of learning). First, Aisha could vary each attribute individually, then both attributes together. Second, Aisha repeated the process for a new Cartesian graph with the same attributes represented on different axes. We designed each of the first two elements against a background of invariance (e.g., the Cannon Man). Next, we repeated the first two elements against a new background (e.g., the Toy Car). When creating a new background, we varied different elements while keeping other elements the same. In particular, we varied the motion of the object (e.g., the Toy Car moved in a curved line; Cannon Man moved up and down), while keeping the kinds of attributes (length measures) invariant.

When Aisha interacted with the Cannon Man task sequence, she discerned differences between the motion of the Cannon Man (up/down) and the total distance traveled (enacted object of learning).

After interacting with both the Cannon Man and Toy Car task sequences, Aisha discerned that the differences in the motion of the Cannon Man and the Toy Car did not impact the total distance traveled, which still increased in both situations (lived object of learning). We argue that the opportunity to experience difference in the motion of objects for the Cannon Man and Toy Car contributed, in part, to Aisha's transfer of covariational reasoning.

Lobato's theory of actor-oriented transfer

We adapted Lobato's (2014) criteria to align with Aisha's work during the task sequence we reported. We analyzed for evidence of the following: (1) Aisha's change in reasoning from the first interview (Ferris Wheel) to the third interview (Toy Car); (2) Aisha's engagement in covariational reasoning during the second interview;

(3) Influence of Aisha's reasoning during the second interview on her reasoning during the third interview; and (4) Attribution of Aisha's changed reasoning to the interview tasks, rather than to a spontaneous occurrence.

For the Ferris Wheel, Aisha provided evidence that she was doing something other than engaging in covariational reasoning (1). We interpret that Aisha was conceiving of how she might use a formula or rule to determine one amount (height), given another amount (distance). For the Cannon Man, Aisha demonstrated evidence of engaging in covariational reasoning (2). Rather than attempting to show how one might obtain one value given another value, she conceived of both attributes as possible to measure and capable of varying. Aisha's explanations provide evidence of how she construed similarities in an attribute (total distance), common to the Toy Car and the Cannon Man (3). We interpret Aisha's reasoning for the Toy Car to be influenced by her reasoning for the Cannon Man (4). First, Aisha identified a common attribute across both the Toy Car and the Cannon Man (total distance). Second, Aisha related the toy car's total distance traveled and its distance from the shrub. Third, Aisha's substantial change from the Ferris Wheel to the Toy Car strongly suggests that her reasoning for the Cannon Man influenced her reasoning for the Toy Car.

Locally integrating theories to theorize the "tension of intentions" in task design

In integrating these theories, we aim to theorize the "tension of intentions" when researching task design to account for the student perspective. We aim to position students' perspectives as being just as viable as the perspectives of designers, teachers, and researchers. Accordingly, we aim not to place one theory as hierarchically superior to another, but rather to weave together the theories into a new form. In so doing, we bring together different assumptions: Students' reasoning depends on their conceptions of attributes as being possible to measure and capable of varying (Thompson's theory of quantitative reasoning), students discern difference, rather than sameness (Marton's Variation Theory); and transfer depends on the student perspective (Lobato's theory of actororiented transfer).

To claim that we can integrate theories, we need to address their epistemological roots (Bikner-Ahsbahs & Prediger, 2010). Lobato's and Thompson's theories have roots in students' conceptions, which makes integrating those theories more straightforward. In contrast, Marton's theory has roots in students' experience. We argue that both students' conceptions and experiences are central to their learning opportunities. For example, in our research, students' experiences with Cartesian graphs and students' conceptions of attributes were both central to their covariational reasoning. Through centering the student perspective, we integrate these different theories.

Conclusion: Rethinking design possibilities for transfer studies

We view a reflexive relationship between theoretical perspectives and research methods. Employing alternative transfer perspectives, such as an actor-oriented transfer perspective, can result in innovations in methods to investigate transfer. A variation theory lens afforded us novel opportunities to design for and investigate students' transfer of covariational reasoning. Rather than designing a set of pre-and post-tasks, that in our view were structurally similar, we designed task sequences that incorporated difference within and across backgrounds of invariance. Analyzing across students' work on the task sequences, we gathered evidence of students' transfer of reasoning from an actor-oriented transfer perspective. Overall, we acknowledge that the perspectives of designers, teachers, and researchers can impact students' opportunities to engage in mathematical reasoning. In theorizing, we aim to address this tension of intention, by centering the student perspective.

Figure 1 :

 1 Figure 1: Aisha's Ferris Wheel, Cannon Man, and Toy Car graphs, respectively

Acknowledgment. The development of the digital task sequences was supported by a US National Science Foundation Grant (DUE-1709903). Opinions, findings, and conclusions are the authors.


Nicole L Fonger
email: nfonger@syr.edu

Muhammed Amy Ellis
email: amyellis@uga.edu

F Dogan

Muhammed F Dogan

Epistemological and methodological foundations of creating a learning trajectory of children's mathematics

Keywords: Learning trajectory, constructivism, cognition, learning theories, epistemology

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Learning trajectories in mathematics education

Attention to learning trajectories and progressions remains a prominent strand of research in mathematics education (e.g., [START_REF] Clements | Learning trajectories in mathematics education[END_REF]. The influence of this domain of research is evident in the development of mathematics standards (e.g., National Governor's Association Center for Best Practices, 2010; UK Department of Education, 2009), funding priorities, topics conferences (e.g., the Third International Realistic Mathematics Education Conference), and special reports (e.g., [START_REF] Daro | Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction[END_REF]. Given the relatively wide-spread promulgation of trajectories and progressions in our discourse in research and practice, there is a need to articulate theoretical and methodological foundations of learning and teaching [START_REF] Simon | The need for theories of conceptual learning and teaching of mathematics[END_REF]. This paper argues for the importance of creating learning trajectories as research-based models of teaching and learning that take seriously a commitment to understanding and supporting students' mathematics.

The notion of a learning trajectory has different meanings among mathematics education researchers. [START_REF] Simon | Reconstructing mathematics pedagogy from a constructivist perspective[END_REF] original discussion offered a description of a hypothetical learning trajectory (HLT) consisting of "the learning goal, the learning activities, and the thinking and learning in which students might engage" (p. 133). An HLT constitutes a starting point for task design, and is then modified into a learning trajectory based on empirical data, often in the form of a teaching experiment. [START_REF] Clements | Learning trajectories in mathematics education[END_REF] described a learning trajectory as an elaboration of children's thinking and learning in a specific mathematical domain, connected to a conjectured route through a set of tasks. These definitions emphasize the construct as a tool for hypothesizing what students might understand about a particular mathematical topic and how that understanding may change over time in interaction with carefully designed tasks and teaching actions.

Building on this body of work, we argue that the main purpose of a learning trajectory is to effectively convey the relationships between teaching, task-design, and shifts in student conceptions. We advocate for a stance that articulates an integrated system of ways of bringing about conceptual change in the mathematics of students in relation to theory-driven instructional support. Thus, in order to create learning trajectories, we need mutually informing theories of learning and teaching. This paper elaborates two such theories, the radical constructivist theory of learning and Duality, Necessity, and Repeated Reasoning-based instruction, and identifies how these two related theories influence our methodological approach to building learning trajectories. We provide an example situated in a rate of change approach to quadratic function.

Theoretical and epistemological framing A theory of learning mathematics

In discussing the theory that guides our approach to crafting learning trajectories, we address three major issues: (a) distinguishing students' mathematics from the mathematics of students, (b) leveraging the epistemic student, and (c) leveraging a model of learning. Theory of instructional design is treated in the next section.

Learning trajectories articulate students' evolving conceptions within a particular instructional context. In order to do this, we distinguish from our own mathematics as researchers and teachers, our students' mathematics, and the models we create of our students' mathematics. The need to distinguish our own mathematics from students' mathematics is borne out of our epistemological stance. We consider mathematical knowledge to develop as part of a process in which children gradually construct and then experience a reality as external to themselves [START_REF] Von Glasersfeld | Radical constructivism: A way of knowing and learning[END_REF][START_REF] Piaget | Studies in reflecting abstraction[END_REF]. From this perspective, knowledge is considered viable if it stands up to experience, enables one to make predictions, and allows for the enactment of desired objectives.

The term students' mathematics refers to the models students construct to organize, comprehend, and control their experiencesi.e., students' knowledge. The mathematics of students is the set of models we construct of our students' knowledge [START_REF] Steffe | Children's fractional knowledge[END_REF]. Often there is little distinction between these two notions in curricula or in standards documents. We believe, however, that the mathematical knowledge we attribute to students in the creation of a learning trajectory must be viewed as different from our own knowledge. Our goal is to determine how to engender and explain students' productive thinking. By distinguishing our mathematics from the students' mathematics, we recognize that students bring significant knowledge to bear when engaging in school mathematics, and we position students as logical, coherent thinkers and doers of mathematics. The job of establishing a learning trajectory then becomes one of explaining students' thinking in a way that portrays it as coherent and internally consistent [START_REF] Steffe | On the construction of learning trajectories of children: The case of commensurate fractions[END_REF].

Individual students differ in their personal backgrounds, knowledge, and dispositions. A learning trajectory should depict not one particular student or group of students, but rather the epistemic student. An epistemic student is an organization of schemes that researchers build to explain students' characteristic mathematical activity and how that activity changes in the context of teaching [START_REF] Steffe | Epistemic algebraic students: Emerging models of students' algebraic knowing[END_REF]. Researchers construct epistemic students through teaching interactions with specific students, but epistemic students are not specific to those particular interactions. Instead we conceive them to be useful models of students' schemes that one can leverage to describe, explain, and predict the mathematical actions of similar students who may be operating at the same level. Formulating an explanation of changes in students' concepts and operations is not merely an empirical matter. We also bring to bear a set of conceptual tools in order to interpret students' activity and problem solving. These tools have their origins in the radical constructivist (RC) model of knowing [START_REF] Von Glasersfeld | Radical constructivism: A way of knowing and learning[END_REF][START_REF] Piaget | Studies in reflecting abstraction[END_REF]. For the purposes of learning trajectory construction, we rely particularly on the constructs of mental operation, scheme, assimilation and accommodation, and abstraction. A mental operation is an internalized, reversible mental action that is an element of a larger structure, such as a scheme, constituted by the coordination of operations. A scheme is an organization of actions or operations which enables anticipation of results without having to engage in mental activity. As an example, [START_REF] Piaget | Studies in reflecting abstraction[END_REF] described the mental operation of combining objects (such as addition). Several successive additions are the equivalent of a single addition (so one can compose additions), and they can be inverted into the operation of taking away, or subtraction.

Treating new material as something already known is an act of assimilation. When assimilating, one encounters an experience and incorporates it into a scheme. When the enactment of a scheme results in an unexpected outcome, a learner may experience perturbation or disequilibrium. One response can be a change in the learner's recognition, in effect spurring a reorganization of one's scheme. This reorganization is accommodation, which many consider to be the source of conceptual change.

DNR-based instructional design

The theory of DNR-based instruction (Duality, Necessity, and Repeated Reasoning; Harel, 2008a;2008b) informs our instructional design principles. Drawing on the RC theory of knowing, Harel (2008b) noted that "any observations humans claim to have made is due to what their mental structure attributes to their environment" (p. 894). He emphasized that researchers' observations are merely models of students' conceptions; using our language, these are models of the mathematics of students [START_REF] Harel | Intellectual need[END_REF]. Drawing on the mechanisms of assimilation and accommodation, [START_REF] Harel | Intellectual need[END_REF] characterized knowing as a developmental process that proceeds through a back-and-forth between the two in order to reach equilibrium.

The duality principle addresses two forms of knowledge, Ways of Understanding (WoU) and Ways of Thinking (WoT). WoU can be thought of as subject matter, consisting of students' definitions, theorems, proofs, problems, and their solutions (Harel, 2008a). WoT are students' conceptual tools, such as deductive reasoning, heuristics, and beliefs about mathematics [START_REF] Harel | Intellectual need[END_REF]. The Duality Principle states that students develop WoT through the production of WoU, and, conversely, the WoU they produce are afforded and constrained by their WoT (Harel, 2008a). We contend that the mathematical content of a learning trajectory must be formulated in terms of both WoU and WoT.

The necessity principle states that in order for students to learn the mathematics we intend to teach them, they must have an intellectual need for it (Harel, 2008b). We can engender intellectual need through problematic situations that necessitate the creation of new knowledge in order to be resolved. Finally, the repeated reasoning principle addresses the need for teachers to ensure that their students internalize, retain, and organize knowledge (Harel, 2008a). Repeated reasoning should not be confused with drill and practice of routine problems. Rather, it is an instructional principle that advocates providing students with sequences of problems that require thinking through puzzling situations and solutions; the problems must respond to students' intellectual need.

Methodological approach and rationale

Our methodological approach to establishing learning trajectories is a direct consequence of our theoretical and epistemological framing. We elaborate how our networked theories (RC, DNRbased instruction) informed our methodologies. We describe three aspects: (a) leveraging theory to create an HLT, (b) ongoing refinement of an HLT into an LT through enacting a teaching experiment, and (c) finalization of an LT through retrospective analysis.

Creation of an HLT

We enact a form of design-based research to simultaneously engender and study innovative forms of learning [START_REF] Cobb | Experimenting to support and understand learning processes[END_REF]. The planning phase involves creating an HLT [START_REF] Simon | Reconstructing mathematics pedagogy from a constructivist perspective[END_REF] informed by the networking of the RC theory of learning and the theory of DNR-based instruction. Our HLT was a tentative progression of student concepts and associated tasks that we hypothesized would necessitate a WoU that quadratic functions represent a constantly-changing rate of change between two covarying quantities. Simultaneously, our aim was to support a WoT that functions can be representations of covariation and can be explored and understood through a covariational lens [START_REF] Thompson | Variation, covariation, and functions: Foundational ways of thinking mathematically[END_REF]. Consequently, we devised a dynamic representation of proportionally-growing rectangles in which students could investigate situations that, to us, entailed the three continuously covarying quantities, height, length, and area (Figure 1). The relationship between height, h, and area, A, can be expressed as A = ah 2 where a is the ratio of length to height. We wanted the students to develop the following specific WoUs: (a) the rate of change of a rectangle's area grows at a constantly-changing rate for each same-unit increase in height (or length); (b) the rate of the rate of change of the rectangle's area is constant for same-unit height (or length) increases; (c) given a height h, the rectangle's area could be determined by ah 2 ; and (d) the rate of the rate of change of area is dependent on the change in height. In order to engender these WoUs, we devised tasks in which students had to predict the nature of growth, determine areas for specific height values and vice versa, and decide whether given tables of values represented rectangles that grew in proportion to one another or not. See [START_REF] Ellis | Generalizing-promoting actions: How classroom collaborations can support students' mathematical generalizations[END_REF] for an elaboration of the mathematics. Drawing from the theories we networked, we engaged in an in-depth, 15-day teaching experiment following the method of [START_REF] Steffe | Teaching experiment methodology: Underlying principles and essential elements[END_REF]. We taught 15 lessons to a group of 6 middle-grades students (ages 1314) who were enrolled in pre-algebra (3 students), algebra (2 students), and geometry (1 student). The second author was the teacher-researcher (TR). One purpose of a teaching experiment is to gain direct experience with students' mathematical reasoning, which affords the creation and testing of hypotheses about the mathematics of students in real time. This means that our mathematical tasks were not wholly predetermined, but instead were created and revised on a daily basis in response to hypothesized models of students' mathematics. Because our problem context relied on area models, it was important to first identify the students' existing schemes and operations for area. After conducting pre-interviews and developing an initial model of the mathematics of students, we created new tasks to necessitate more robust constructions of area as not dependent on whole-unit iterations. During and between each session, we engaged in an iterative cycle of (a) teaching actions, (b) assessment and model building of students' thinking, and (c) task revision and creation on an ongoing basis. In this manner, during each session, we continually revised our HLT into a tentative, empirically based LT.

Retrospective analyses: Finalizing an LT

In addition to our ongoing analysis, we relied on retrospective analysis to inform the development of a learning trajectory as a model of the mathematics of students [START_REF] Steffe | Teaching experiment methodology: Underlying principles and essential elements[END_REF]. One purpose of retrospective analysis is to build a model of the epistemic student and to characterize students' changing WoU and WoT throughout the course of the teaching experiment. A secondary purpose, for us, was to contextualize and explain changes in students' schemes and operations with respect to the tasks and teaching actions they encountered. We aimed to elaborate features of tasks, teacher moves, questioning, and socio-mathematical norms that supported the students' scheme accommodation. Our inclusion of instructional supports into a learning trajectory relied both on our analyses of empirical data and on our understandings of the local instructional theories grounding our design and enactment of the teaching experiment. Figure 2 identifies the goals, tools and constructs we leveraged in order to create a learning trajectory. Notice how the primary and secondary aims are linked to a coordination of RC and DNR-based instructional design theories.

An excerpt of a learning trajectory for quadratic function

In our previous work, we identified WoT and WoU in students' learning of quadratic function from a rates of change perspective [START_REF] Fonger | Students' clusters of concepts of quadratic functions[END_REF]. Below, we provide an example of a link between goal-directed instructional supports and a shift in student thinking (i.e., an excerpt of a LT). We focus on one shift from a student's WoU that (a) the rate of the rate of change of the rectangle's area is constant with ∆x implicit, to (b) the rate of the rate of change of area is dependent on ∆x, which is explicit. In the excerpt, the students had already created well-ordered tables for the growing rectangles (Figure 3). They had also attended to the constantly changing rate of change of area as determined by finding area increases for same-unit increases in, but there was a lack of coordination of change in area with change in height. Prompted to explain the growth in area of a 2 cm by 3 cm rectangle (Task A), one student said, "It goes 4.5 and then 7.5 and then 10.5 and then…just keeps going." In this manner, the students attended to the area's growth, but did not coordinate it with growth in height or length. In response, the TR prompted the students to draw diagrams of the growing area, predicting that the act of drawing would necessitate a coordination of height and area. The students' drawing activity did necessitate a coordination, but many students kept the change in height implicit, as evidenced by their language "every time." For instance, Jim drew a picture of a growing 2 cm by 3 cm rectangle and explained the rate of change of area as "how many new squares it's gaining every time it grows."

In an attempt to further encourage an explicit coordination of the rate of area with a quantified change in height, the TR asked the students to create a table for a 2 cm x 5 cm growing rectangle (Task B), anticipating that the students would make tables with different height increments. This did occur: For instance, Jim created a table in which ∆x was 1 cm, and Daeshim created a table with ∆x as 2 cm (Figure 3). The different tables resulted in a conflict about whether the constantly-changing rate of change of area should be 5 cm 2 or 20 cm 2 until one student, Jim, realized that the rate depended on ∆x: "I'm going up by1's and they're going up by evens." After a class discussion in which the students agreed that the rate could legitimately be either 5 cm 2 or 20 cm 2 , depending on ∆x, Jim exclaimed, "Your rate of growth can change no matter what!" In subsequent days the TR encouraged the students to think about other proportionally-growing rectangles, and, ultimately, to draw diagrams relating changes in area to the rectangles' dimensions. These diagrams further emphasized explicit attention to all three quantities, height, length, and area, and enabled the students to explicitly link the change in area to the change in height. For instance, Daeshim determined that the rate of the rate of change of area would be twice the area of the original rectangle; Jim found that it would be equivalent to twice the length for any 1 cm by L cm rectangle. We propose that a learning trajectory should include not only an articulation of particular WoUs and the shifts between them, but also a hypothesized connection between these shifts and specific instructional supports. Although space constraints limit an in-depth discussion of all of the instructional supports in play, we see that the instructional move to prompt diagram drawing necessitated a functional accommodation: students began to attend to and then coordinate increases in height and length, not just area. In addition, the open structure of the task to determine rates of change of area for a 2 cm by 5 cm rectangle further encouraged explicit attention to ∆x.

Discussion

In the domain of research on learning trajectories, attention to a theory of instructional design is lacking. Moreover, methodological approaches to creating learning trajectories as a retrospective practice are scant in the literature. In this research we networked RC and DNR-based theories to inform our methods of task development, pedagogical actions, and retrospective analyses. This approach and the resulting product (i.e., an empirical LT for quadratic growth) are novel and not elaborated in the literature thus far.

This paper contributes to an understanding of how a networking of theoretical assumptions can guide methodological choices in establishing learning trajectories. Specifically, we argue for learning trajectories research to be guided by theoretical lenses on the mathematics of students as well as on a theory of instructional design. In this domain of research, there is a need for researchers to move beyond a focus on creating hypothetical learning trajectories, attending to their methods of creating learning trajectories.

This paper makes explicit the theoretical perspectives undergirding our approach to learning trajectories research. One challenge we see is leveraging learning trajectories as a way to not only frame a study (e.g., in creating hypothetical learning trajectories), but to also retrospectively create and share learning trajectories in ways that are consistent with the theories undergirding their creation. This research illustrates one approach for addressing the challenge of creating learning trajectories as empirically based models of an interweaving of shifts in students' mathematical understandings and goal-directed, theoretically grounded instructional practices.

Figure 1 :

 1 Figure 1: A growing rectangle and associated table of height-area values Teaching experiment: Ongoing refinement of an HLT into a tentative LT

Figure 2 :

 2 Figure 2: Analytic aims, goals, tools, and constructs for creating a learning trajectory

Figure 3 :

 3 Figure 3: Jim and Deashim's well-ordered tables for a 2x5 growing rectangle


C Fluhrer

S Journeau

Z Bechta

D Hozer

Pd Manara

M Bottomley

T Kiselova

G Keim

Langrock

A Miassoedov
email: alexei.miassoedov@kit.edu

B Fluhrer

C Journeau

S Bechta

Z Hózer

D Manara

P D Bottomley

M Kiselova

T Keim

G Langrock

F Belloni

M Schyns

The SAFEST project: towards pan-European Lab on Corium Behavior in Severe Accidents. Main Objectives and R&D priorities

Keywords: LWR, severe accidents, corium, experimental facilities

The SAFEST project towards pan-European Lab on Corium Behavior in Severe Accidents. Main Objectives and RetD priorities.

Introduction

After the TMI-2 and Chernobyl-4 accidents R&D programmes have been launched worldwide to study severe accidents and to propose means to mitigate their consequences for the populations and to the environment. In the European Union, these national research efforts have been shared in EC-funded projects starting at least in the 4 th Euratom Framework Programme. The SARNET2 network [START_REF] Van Dorsselaere | Recent severe accident research synthesis of the major outcomes from the SARNET network[END_REF] has been co-ordinating research on these issues and is currently pursuing this task as a dedicated Technical Area on severe accidents under Nuclear Generation II and III Association (NUGENIA) [START_REF]NUGENIA Association[END_REF].

The efficiency of cooling reactor core structures and materials during severe accidents either in the core region, in the vessel lower head or in the reactor cavity is a key issue to limit the progression of the accident. This can be achieved either by ensuring corium retention within the reactor pressure vessel (RPV) or at least by limiting the corium progression and, consequently, the rate of corium release into the reactor cavity in case of RPV failure. These issues are covered within the scope of accident management for existing reactors and within the scope of design and safety evaluation of future reactors. The specific objectives addressed creation of a database on coolability of degraded core, debris formation, debris coolability and corium behaviour in the lower head, development and validation of models and computer codes for simulation of in-vessel debris bed and melt pool behaviour, performance of reactor scale analysis for in-vessel corium coolability and assessment of the influence of severe accident management measures on in-vessel coolability. In-vessel corium and debris coolability, paper 517

Currently available data on degraded core reflooding are summarised in the reflood map developed at KIT, which is being constantly updated to include findings from previous and currently running programs on the coolability of the reactor core, taking into account available coolant mass flow rates and the core damage state. Substantial knowledge and understanding of the phenomena governing the coolability of intact rod-like reactor core geometry was obtained in numerous national and international projects. However, major gaps in knowledge still exist in the areas of debris and molten pool behaviour.

There is a significant progress on simulation of in-vessel core coolability, with 2D and 3D simulation codes, focusing on the enhanced coolability of debris beds by lateral and/or bottom water inflow [START_REF] Leininger | Experimental investigation on reflooding of debris beds[END_REF], [START_REF] Bürger | Coolability of particulate beds in severe accidents: Status and remaining uncertainties[END_REF]. These phenomena are being investigated in a number of experimental programs including study of multi-dimensional effects on debris bed coolability, e.g. PRELUDE/PEARL at IRSN [START_REF] Repetto | Experimental program on debris reflooding (PEARL) -Results on PRELUDE facility[END_REF] and DEFOR at KTH [START_REF] Kudinov | Agglomeration and size distribution of debris in DEFOR-A experiments with Bi 2 O 3 -WO 3 corium simulant melt[END_REF]. Many experiments are currently being performed in this domain in several international projects, e.g. in the frame of SARNET within NUGENIA. They are accompanied by numerous efforts on modelling in simulation codes and benchmarking activities among these codes (e.g. OECD/NEA BSAF 1 and 2 benchmarks on Fukushima-Daiichi accidents).

For the ex-vessel situation, significant progress has been made in R&D activities started after TMI-2 and Chernobyl accidents. Many experiments are currently performed in this domain in international projects, either in SARNET frame or in the PLINIUS experimental platform at CEA. They are accompanied by large efforts on modelling in simulation codes and benchmarking activities among these codes. Other R&D efforts are based on ANL (USA) CCI experiments on molten corium-concrete interaction. Concerning Fuel Coolant Interaction (FCI), the OECD/NEA project SERENA2 has provided a large amount of experimental data on steam explosion, including advanced visualization of premixing (the explosion initial conditions).

As corium molten pool delivers a significant part of the decay heat to the RPV lower head, there is little chance to arrest melt progression without cooling. It is nevertheless necessary to study concrete ablation and molten pool configuration in the cavity, as means to verify that there is no risk of early basement melt-through, and to provide the initial conditions for corium cooling phase or transfer to a core catcher. At present, international R&D is mostly performed in the frame of the NUGENIA TA2/SARNET network, mainly on the basis of the VULCANO (CEA) [START_REF] Journeau | Contributions of the VULCANO experimental programme to the understanding of MCCI phenomena[END_REF], MOCKA (KIT) [START_REF] Foit | MCCI of a Metal and Oxide Melt With Reinforced Siliceous Concrete in MOCKA Experiments[END_REF], HECLA (UJV) [START_REF] Sevón | MCCI with Hematite-containing Concrete: HECLA and VULCANO Experiments[END_REF] and SICOPS (AREVA NP GmbH) experiments [START_REF] Foit | Experiments on MCCI with oxide and steel[END_REF]. OECD/NEA/CSNI state-of-the report on molten corium-concrete interaction (MCCI) is also in progress with a significant contribution by the SARNET network. Current 2D oxidic pool MCCI experimental programmes have shown that limestone-rich concretes are almost isotropically ablated while for silica-rich concretes lateral ablation was much larger than vertical ablation. This reproducible behaviour is not yet understood so application of the obtained results to reactor scale or to other concrete compositions (e.g. basaltic) should be done with caution [START_REF] Cranga | Towards an European consensus on possible causes of MCCI ablation anisotropy in an oxidic pool[END_REF]. Furthermore, recent experiments with oxidic and metallic pools have shown phase repartitions which are different from simple-layers assumptions considered in MCCI codes (emulsion or gravity stratification, effect of steel reinforcement).

Globally, an important database exists on the phenomena occurring in non-mitigated ex-vessel situations (steam explosion, direct containment heating, corium spreading and molten core concrete interaction, debris bed formation and coolability) and for the support of commercially available core catchers. Nevertheless, there are some remaining uncertainties on application of the results obtained in experiments to reactor conditions. Moreover, since most of previous severe accident research topics were focused on PWR design and majority of severe accident codes and models were developed for PWRs, only some special experimental series were focused on BWR-type reactors. It was in agreement with the fact that most of the operating light water reactors (LWR) are of PWR type. However, large number of BWR reactors is operated worldwide and in Europe as well.

The Fukushima Daiichi accident demonstrated that some BWR specific design features can play a very important role in severe accident progression. For example, the penetrations for control rods through the lower head most probably affected release and behaviour of molten core in the reactor cavity; however, this phenomenon has to be confirmed after defueling of Fukushima Daiichi plants.

Additionally, the stress tests of nuclear power plants in the European Union pointed out that some BWR special features may have an impact on severe accidents, e.g. the flooding of lower drywell may stabilise exvessel molten corium progression. The planned or implemented safety improvements included also some BWRspecific topics. For example, in Germany the development of accident management measures was proposed to protect the building structure surrounding the spent fuel pool in BWRs, which is located outside the containment, against hydrogen combustions or to prevent them. In Finland, the installation of additional emergency diesel In-vessel corium and debris coolability, paper 517 generators and of diverse and independent ways of pumping water to the RPV via fire-fighting diesel driven pumps is foreseen in BWR units. Other specific features of BWR design which require further detailed analysis include:

larger vessel dimensions and mass of water, deeper cavity, channels and bypasses in the core, separated by the canisters of fuel assemblies which can influence melt relocation and oxidation of Zircaloy, control rod and instrumentation guide tubes in the vessel lower head which can influence formation of in-vessel debris beds, RPV failure mode and timing, possible limitation of flow-rate of releasing melt, mass and composition of the releasing corium, nitrogen inertisation of primary containment which may have a significant impact on early core degradation.

All these facts emphasise that the severe accident research for BWR needs further efforts aiming at improvement and optimization of BWR-specific models and validation of them against future experiments, which will be one of the main objectives of the SAFEST project.

SAFEST experimental facilities are unique in providing the possibility to perform experiments in specific fields of research on corium behaviour in severe accidents in main types of light water reactors including BWRs. There are less than ten currently operating prototypic corium facilities in the world and three of them are located in Europe and belong to the SAFEST consortium. The facilities are operated by a team of experts who have long and recognised experience in the nuclear safety research. The SAFEST project will contribute significantly to establishment of an integrated pan-European laboratory for severe accident research able to address and successfully resolve the variety of the remaining issues related to the corium behaviour in severe accidents. The way towards the establishment of a pan-European laboratory will clearly depend on conclusions of the roadmap activities planned in the project. This unique consortium will be a valuable asset for the fulfilment of the severe accident R&D programmes that are being set up after Fukushima Daiichi accidents and the subsequent European stress tests, addressing both national and European objectives, in collaboration with major international stakeholders.

In particular, the following topics, all belonging to high-priority issues identified by the SARP group of SARNET [START_REF] Klein-Heßling | Conclusions on severe accident research priorities[END_REF] and confirmed in the NUGENIA R&D roadmap, are addressed in the SAFEST project, contributing considerably towards understanding and perhaps even closure of these issues:

-Formation and cooling of debris beds and molten corium pools in the reactor core in order to demonstrate effective cooling modes and rates, and coolability limits. The specific R&D objectives are to create and enhance the database on debris formation, debris coolability and corium pool behaviour in the lower head, to develop and validate the models and computer codes for simulation of in-vessel debris bed and melt pool behaviour. -Influence of control rod and instrumentation guide on debris bed formation and cooling and corium pool coolability for BWRs. -Though the behaviour of pure oxidic pool in the vessel lower head is quite well understood, the efforts will be focused on scenarios with a large pool of molten corium: heat flux to metal layer in a layered molten pool configuration, including possible 3-layer configuration (observed in OECD/NEA MASCA experiments [START_REF]Main Results of the MASCA-1 and MASCA-2 Projects. Integrated application report[END_REF]). An important point is the thickness of the metallic layer. This is of high priority because it can influence strongly the strategy for in-vessel retention concepts in some of the existing (e.g. VVER-440) and new plant designs. -Corium behaviour inside BWR-type lower heads including corium relocation into a deep lower head filled with water, significant thermo-mechanical loads on the vessel structures during debris re-heating and re-melting, and high fraction of Zr in the core. -Database on critical heat flux and external cooling conditions in order to evaluate and design SAM measures for external vessel cooling. Influence of BWR lower head penetrations on melt cooling and its influence on the external convection. -Location of RPV failure for BWRs, failure timing and modes.

-New phenomena related to the in-vessel retention by cavity flooding (pressurized molten corium jets directly entering water, corium concrete interaction starting underwater) that were not considered previously in experimental and analytical R&D programmes. -Interaction of corium jets with water in the cavity pool (deep pools for BWRs) after a failed in-vessel retention, focusing on jet fragmentation to provide reliable initial conditions for the steam explosion phase and to determine the characteristics of the formed debris bed (particle size distribution, geometrical repartition, chemical state) that are necessary inputs for debris bed coolability issues. In-vessel corium and debris coolability, paper 517

-MCCI for concrete compositions that have not been yet studied earlier (e.g. basaltic concrete mainly used in Japan and in the USA) focusing on 2D convective heat transfer distribution. -Two-dimensional concrete ablation caused by oxidic melt as well as by stratified oxide-metal melt in presence of steel reinforcing bars, focusing on metal oxidation during MCCI. -Long-term MCCI (i.e. longer than 1 day after start of interaction) characterised by high concrete fraction and reduced heat fluxes to the concrete interface. -Criteria and scaling approaches for extrapolation of the results obtained in small to medium scale experiments to reactor case.

To resolve these issues the partners of the SAFEST project perform experiments, develop and validate numerical models aiming at adequate description of the investigated phenomena and upgrade the SAFEST facilities to be able to address the future research needs. As an important part of the project, the SAFEST experimental platforms and facilities are offered for access to external user groups.

Project activities

Coordinated by KIT, the SAFEST consortium is small and consists of five research centres (CEA, MTA EK, JRC-ITU, SCK-CEN and UJV), two universities (KIT and KTH), and one industrial partner (AREVA) and forms a balanced mix of expertise in state-of-the-art severe accident management and experimental research. Complementarity and synergy between partners is maximized by identifying overlapping roles in this project and exploiting them by choosing the partner best suited to the identified tasks. The involvement of the industry is beneficial in providing a balanced approach between research and industrial needs. The description of some of the SAFEST activities are given below.

Development of research roadmaps

The general objective is to develop a common vision and experimental research roadmaps for the next years, and the management structure to achieve these objectives. Safety research roadmap for Gen IV plant safety is also under development taking advantage of the knowledge and expertise obtained for existing reactors as well as on specific safety characteristics of considered Gen IV designs.

The draft of the European corium experimental research roadmap was completed in 2016 with the help of many contributors from the various SAFEST partners [START_REF] Journeau | SAFEST roadmap for corium experimental research in Europe[END_REF]. It is based on the research priorities determined by SARNET SARP group as well as those from the NUGENIA Technical Area 2 on severe accidents. It also takes into account issues identified in the analysis of the European stress tests and from the interpretation of the Fukushima-Daiichi accident. The roadmap takes advantage of the current and developing European corium infrastructures and, if necessary, recommends its adaptation.

Following the Fukushima-Daiichi accident, JAEA experts have contacted European counterparts in order to promote joint R&D activities as well as to solicit scientific and technical support from EU to Japan. As a consequence, a series of meetings between the SAFEST consortium and Japanese organizations were held aiming at assessing long-term goals and proposing experimental support needed for proper understanding and interpretation of Fukushima-Daiichi accident, analysis of collected debris in European and Japanese laboratories and even eventual processing of molten cores.

Experiments in the SAFEST distributed research infrastructure

Being one of the most important activities of the project, the experimental facilities of the SAFEST partners are integrated into a pan-European laboratory for severe accident and corium studies and are offered to external organizations who are interested in performing the tests. The activities of the SAFEST distributed research infrastructure are divided into three groups, each one addressing a specific topic:

-In-vessel corium and debris behaviour; -Ex-vessel corium and debris behaviour; -Corium properties.

After publishing the rules of access to the SAFEST facilities in October 2014, two calls for proposals were announced attracting the interested users to specify the experimental requirements and conditions. Following each call, the user selection panel with the help of independent international experts evaluated the proposals and selected a short-list of user groups. Together with facility operators the user groups prepare, perform, analyse and document the experiments. Total of 16 experiments have been selected to be performed in the SAFEST In-vessel corium and debris coolability, paper 517 SES, have already been successfully performed. A short summary of objectives of the planned experiments and results obtained up to know is given below.

QUENCH experiment at KIT

The main objective of the test will be study of high temperature degradation of BWR assembly mock-up. The bundle containing the fuel rod simulators and the BWR absorber blade will be heated up to the onset of degradation and flooded with water from the bottom. Data on clad oxidation and hydrogen generation and release, material degradation and relocation (including melting and relocation of control blade materials) will be measured during the test and obtained in the post-test material analysis. These data will be used for severe accident model development and code validation. The bundle cross-section is presented in Figure 1

LIVE experiment at KIT

The purpose of this test is to assess the characteristic time of convection development in a homogeneous melt pool in the 1:5 scaled 3D RPV lower head after a rapid change in boundary conditions. There are indications that this transient phase may need to be accounted for in the integral codes through some adjustment of the heat flux correlations; this may increase the safety margins of in-vessel melt retention, especially for high power reactors. Meanwhile at the Xi'an Jiatong University in China the COPRA facility has been commissioned and successfully put into operation [START_REF] Bürger | Coolability of particulate beds in severe accidents: Status and remaining uncertainties[END_REF]. The COPRA facility is a 2D 1:1 scaled slice and utilizes the same material to simulate corium melt and same heating system as in the LIVE facility but at a larger scale. The two facilities allow complementary studies of the molten pool behavior under similar conditions for a large range of Ra numbers from 1012 to 1016. A test similar to LIVE is planned also in COPRA in the frame of the ALISA project. Comparison of the results of these two tests will help gaining insight on the influence of geometry (2D/3D), scale (1:1 scale/1:5 scale) and simulant material (molten salt/water) on experimental results, thus improving the extrapolation to prototypic conditions.

DISCO experiment at KIT

The objective of the test will be to analyse the phenomena which occur during an ex-vessel fuel coolant interaction (FCI). The test is focused on the premixing phase of the FCI with no trigger used for explosion phase. The objectives of the test will be to provide data concerning the dispersion of water and melt out of the pit, characterization of the debris and pressurization of the reactor compartments. In previous DISCO tests with water in the reactor pit [START_REF] Repetto | Experimental program on debris reflooding (PEARL) -Results on PRELUDE facility[END_REF] only small water pools were investigated. The planned experiment will be performed similarly to previous ones but with a larger water pool providing insights on the scaling issues of FCI. Moreover, the pit will have a transparent wall to visualize the premixing phase with high-speed video recording. The main objective of the two tests will be study of molten core-concrete interaction (MCCI) in 2D cylindrical crucibles made of concrete typical for Swedish BWRs. To obtain the information on scaling effects, the concrete composition will be close, if not identical, to the composition of SICOPS-BWR experiment at AREVA in Erlangen, Germany, performed at a smaller scale, but with a prototypic corium (section 2.2.16). In MOCKA experiments the corium is simulated by the thermite melt and the volumetric heating of the melt is achieved by addition of thermite and zirconium into the oxidic part of the melt pool. In one of the tests the influence of the steel reinforcement in the concrete (12 wt.%) on the erosion front progression will be studied.

VULCANO experiment at CEA

The test will focus on the influence of crusts on the melt-concrete interface during MCCI. Previous 2D MCCI experiments have shown that silica-rich and limestone-rich concretes exhibit different ablation behaviour. The characteristics of the crust formed at first contact between the melt and the concrete has been considered as a possible explanation of this difference. In the VULCANO experiment the test crucible will be made of a siliceous concrete with a sufficiently thick inner liner made of limestone common sand (LCS) concrete to ensure the global crust failure which is assumed to occur at the beginning of MCCI with LCS concrete. Moreover, the admixture of LCS concrete in the corium melt will additionally decrease the corium solidus temperature that may prevent further formation of crusts on the interface.

2.2.6

VITI experiments at CEA VITI facility will be used to obtain thermophysical properties (density, surface tension and, if feasible, viscosity) of (U, Zr, Fe) metallic alloys representative of reactor compositions (section 2.2.14). For the first time, it will be possible to have a better information on thermophysical properties of prototypic metallic alloys. The measurements will be carried out in inert atmosphere and around the liquidus point.

MISTEE-AL experiments at KTH

In the MISTEE-AL experiments the material effects related to steam explosion were studied. The objectives of the test series are to check the ability of alumina melt to undergo thermal fragmentation, as a mechanism for spontaneous steam explosions observed in the KROTOS tests at CEA with this material, and to study the void produced by the high temperature drops in a water pool. The main conditions of the tests included different water subcooling and melt superheat:

-High subcooling, between 79 K and 84 K; -Medium subcooling, between 53 K and 55 K; -Low subcooling, between 13 K and 26 K; -Low melt superheat, around 67 K; and -High melt superheat, at 210 K.

Triggered steam explosions have been observed in the experiments with high and medium water subcooling of the water (Figure 2) and only one spontaneous steam explosion happened at very high melt superheat and high water subcooling (Figure 3).

First cycle Second cycle Third cycle

Vapor film destabilization Fine Fragmentation

The 8 th European Review Meeting on Severe Accident Research -ERMSAR-2017

Warsaw, Poland, 16-18 May 2017

In-vessel corium and debris coolability, paper 517 The following conclusions are supported by the experimental results:

-The fragmentation characteristics observed for the alumina melt are similar to those observed for materials with a lower melting temperature, such as tin or WO 3 -CaO. Two to three cycles of bubble expansion and collapse appear after a steam explosion which is triggered by a small pressure wave. Due to the higher melt temperature, bigger equivalent bubble diameter and conversion ratio are observed with alumina compared with the other materials previously studied in the MISTEE facility. -The water subcooling and the melt superheat both play an important role in thermal fragmentation as they directly influence the void production and the melt viscosity. Spontaneous steam explosion observed at high subcooling and superheat is sensibly stronger than the triggered explosions in other experiments. -A preliminary steam explosion map of alumina single drop in respect to water subcooling and melt superheat has been developed. However, more data are needed in order to provide a complete picture.

MISTEE-OX experiments at KTH

In the MISTEE-OX experiments the oxidation behaviour of Zirconium during FCI is being studied. The main objective of these experiments is to investigate the ability of pure zirconium melt to undergo thermal fragmentation while falling into water and thereby undergoing oxidation. The measurements include high-speed visualization of the Zirconium melt droplets and water interaction, estimation of hydrogen produced during the interaction and estimation of oxygen content in the debris by performing SEM/EDX analysis. In-vessel corium and debris coolability, paper 517 zirconium melt at a moderate melt superheat (∆T superheat ~ 150 K) under high water subcooling (∆T superheat ~ 85 K) no spontaneous steam explosions have been observed. Here the hydrogen volume produced during the interaction is obtained by quantifying the bubbles departing the surface of the water pool, originally detached from the droplets. Based on the preliminary analysis, ~ 0.14 litres of hydrogen production is estimated. An oxidation ratio of up to 22% is estimated based on the total volume estimation of the detached bubbles (which is assumed to be composed of pure hydrogen). The microstructure of the debris revealed formation of an oxygen rich outer layer to be of almost constant thickness along the surface and the oxidation ratio decreases further towards the core, as it is shown in Figure 5. The objective of this test was to investigate the influence of control rod and instrumentation guide tubes on melt fragmentation in water and debris bed formation. As a main difference to previous experiments performed in the DEFOR test facility, a rod connecting the discharge nozzle and the bottom of the test section was installed to simulate the control rod guide tube. The main test parameters were similar to the DEFOR-A4 test which was characterised by a relatively low melt temperature of 1221 K (melt superheat of 78 K). Several cameras were implemented to visualize the melt jet formation and jet impingement to provide visual imaging of transient meltcoolant mixing and debris formation and fragmentation in water. After tilting the furnace, the melt entered the water pool and the fragmentation started (Figure 6). The particles were collected on the debris catchers and the temperature evolution was measured by the thermocouples installed in the catchers while they were filled by the hot particles and cooled by the water. The objective of the SES test was to measure the energetics of spontaneous steam explosion and investigate the characteristics of the premixing zone in stratified melt under water configuration. 5 litres (39 kg) of molten Bi 2 O 3 -WO 3 eutectic mixture at 132 ºC superheat were delivered through an elongated nozzle with outlet located under water above the impact plate. Such configuration for melt delivery was expected to prevent melt jet fragmentation in water and exclude its possible contribution to the spontaneous steam explosion or triggering. 0.6 sec after the onset of melt release from the nozzle a spontaneous steam explosion occurred. Snapshots of the video recording of melt water interaction are provided in Figure 8. 17.8 tons of dynamic load was measured by the dynamic force sensors and resulted in 421 N•s of explosion impulse. Due to early occurrence of the steam explosion and release of aerosols from the nozzle, the observation of the premixing layer was not possible. The steam explosion was followed by the upward displacement of the test section. The impact of the test section and the nozzle caused the splashing of melt from the funnel. Post-test analysis of the debris demonstrates that about 15.5 kg of melt remained in the funnel, 15.6 kg were found on the containment floor and 2.7 kg remained in the test section in the form of a cake and particles.

The early occurrence of the steam explosion compared to previous SES test without the elongated nozzle suggests that triggering of the steam explosion in stratified configuration cannot be attributed to the existence of the jet. This also corresponds to the findings obtained in the previous experiments in the DEFOR facility, where melt was released into deep water pools and in which steam explosion has never occurred. In-vessel corium and debris coolability, paper 517

In the CERES facility the investigation of the effect of the elevated sump level on the in-vessel melt retention for VVER-440 reactors during the melt retention by flooding of the reactor cavity is planned. One of the main differences to the cooling by the in-vessel water injection is the maximum sump level change during LOCA conditions. Since the varying sump level changes the conditions slightly taking into account the small gap area between the RPV and the cavity wall, it is important to examine its effect on the coolability. The experiment could reveal the cooling conditions with the maximum possible sump level in the containment.

2.2.12

CODEX test at MTA EK

The CODEX test will address the influence of nitrogen on oxidation and degradation of fuel rod claddings in the temperature range of 800-1200 °C. The reference scenario for this test will be a reactor accident with melt through of the vessel lower head and penetration of air-steam mixture from the reactor cavity into the reactor vessel. The experiments will simulate the high temperature interactions of peripheral fuel assemblies in air-steam atmosphere. Slow cool-down will be applied at the end of the test to provide information on bundle state before quench. In-vessel corium and debris coolability, paper 517 reactor fuels and to produce phase diagram data, in particular on liquids and solidus temperatures. A novel "Reflected Light Signal" (RLS) method has been applied to diagnose solid/liquid phase transitions from surface reflectivity effects using suited low-power (mW) probe laser. Experiments with volatile substances were carried out in an autoclave under medium or high pressure (a few bars up to a few thousands bars) of an inert gas in order to suppress as much as possible evaporation but also to study systematically the behaviour of phase transition points at different pressures. FLF facility has been also used to study corium phase diagrams, particularly in the ternary U-Zr-O system. Most compositions studied so far were in the system domains representing PWR corium with a specific U/Zr atomic ratio close to 1.2. All the samples foreseen for this project have been prepared by powder metallurgy within the end of 2016 (Figure 9a)). Details of the spectral emissivity analysis are shown in Figure 9b). The solidus point of a 47.2 % UO 2 , 10.6 % ZrO 2 and 42.2 % Zr sample was determined to be 2400 K ± 25 K. Similar results will be provided for the other compositions studied in this work.

The spectral emissivity at the wavelength of 650 nm of this sample has also been determined (open circles in Figure 9b)), based on the grey body hypothesis. Such hypothesis has been checked to constitute a reasonable approximation for the present compounds. The emissivity at 650 nm changes from a metallic behaviour (emissivity lower than 0. The tests aim at improving the knowledge on the emissivity of the upper metallic layer in oxidizing atmosphere. This parameter influences directly the focusing effect phenomena that is very important for invessel melt retention strategy. The tests should be performed on pure RPV steel and steel+Zr mixtures, allowing comparisons with the experimental data obtained under inert atmosphere, and a first assessment of the impact of an oxidizing atmosphere. The samples will be manufactured for three domains of the U-Zr-Fe alloy composition: Fe-rich, U-rich and Zr-rich. The results from these tests will be used to reduce the discrepancies in the evaluation of the radiative heat transfer currently observed between various severe accident codes.

KUBI experiments at UJV

The objective of the KUBI test was to study a short-term interaction between UO 2 melt and B 4 C pellets with an application to the safety assessment of Sodium-cooled Fast Reactors (SFRs). The experiment has been conducted at UJV in the COMETA facility. The 2 kg of depleted UO 2 were melted in the cold crucible and five B4C pellets (11 g) were added into the melt from the top. Significant gas release has been observed as interaction started. In the post-test analysis a large porosity, attributed to gaseous releases (mainly carbon monoxide according to equilibrium thermodynamic pre-calculations), has been observed.

SICOPS experiments at AREVA

The SICOPS experiments will address the MCCI for prototypic corium and concrete compositions typical for Nordic BWRs. The test objectives are to understand (a) how significant can be the influence of Swedish In-vessel corium and debris coolability, paper 517 concrete and Nordic BWR specific corium composition on MCCI in the context of possible applications of existing models, which are verified against data of experiments with different melt and concrete compositions, (b) if anisotropy of concrete ablation in radial and axial directions can be expected and (c) if improvements of MCCI models for BWR application are needed. The pre-test series have been completed and the main experiment will be carried out in 2017.

Guidelines for selecting simulant materials and scaling approaches

Some of the SAFEST experiments are conducted in scaled-down test facilities, and in the majority of cases with simulant materials. For experiments, a complete similitude between test facility and full scale plant conditions cannot be achieved. Consequently, it is necessary to: (1) give rationales to select simulant materials for the experiments; (2) assure that the important processes of interest are well scaled; and (3) assess the effects of distortions (when present) on processes and/or parameters of interest to a nuclear power plant accident scenario.

The draft of recommendations for selecting simulant materials and scaling approaches was prepared by KIT and contains two major parts: (1) Severe accident scaling methodology (SASM) and (2) Application of the scaling approach to SAFEST experimental facilities. As a guideline to describe the scaling of SAFEST experimental facilities an outline of the scaling methodology is given, which was developed by a Technical Program Group (TPG) that was established by the USNRC in 1989. It consists of 11 steps which should be followed in formulating the methodology. They are divided in 3 elements, which are (1) experimental requirements, (2) evaluation and specification for experiments and testing and (3) data base acquisition and documentation. As such these 3 elements and 11 steps are like a roadmap for the development of the SASM and provide a guide to follow for each of the experimental facilities in the SAFEST Project, in order to derive results which could be applied to the plant scale and plant conditions. The 11 steps are described. They may involve some exploratory experiments and testing before the envisaged experiments are performed. The steps also involve identification of similarity criteria and development of models and closure relations and even separate effect tests to improve understanding of key processes (or phenomena).

The document is currently under development. The description of the scaling methodology for the DISCO facility at KIT provides an example of what needs to be done for other experimental facilities in the SAFEST project and for the other experiments that need to be performed on the various facilities. This document, when completed, will be of great benefit to the EU research programs on corium behaviour in severe accidents.

Conclusions

Direct outcome from the SAFEST project will be progress towards creation of an integrated pan-European laboratory for study of corium behaviour in severe accidents. Indeed, it encompasses a very large spectrum of nuclear reactors severe accident phenomenology dealing with corium (mainly oriented at LWRs, even though several aspects of Gen IV severe accidents can be studied in some of the SAFEST facilities). By strengthening the links between European corium facility operators, preparing a common roadmap for future EU research and improving the capabilities and performance of experimental facilities, this laboratory is a valuable asset for the fulfilment of severe accident R&D programs which are being set up after Fukushima-Daiichi and the subsequent stress tests both at the national level and at the European level.

Due to the links that are established with other European projects or platforms (e.g. CESAM, IVMR, NUGENIA/SARNET, etc.) the SAFEST project offers a unique opportunity for all parties to get involved in the networks and activities supporting safety of existing and advanced reactors and to get access to large-scale experimental facilities in Europe to enhance understanding of reactor core behaviour under severe accident conditions.

The main result of SAFEST activities will be a better understanding of physical background of severe accidents and prototypic corium behaviour. It will benefit the EU utilities and safety organizations, which will be able to validate (either directly through the access to the SAFEST distributed infrastructure or indirectly through R&D) the hypotheses for severe accident scenarios and propose pertinent procedures for accident mitigation taking into account experimental results. The experimental results will be used for the development and validation of models and their implementation in the severe accident codes such as ASTEC, MELCOR, ATHLET-CD. This helps to capitalize the knowledge obtained in the field of severe accident research in the severe accident codes and scientific databases, thus preserving and diffusing this knowledge to a large number of current and future end-users in Europe.

Figure 1 a

 1 Figure 1 a) Section of QUENCH/BWR bundle and b) Test procedure

Figure 2

 2 Figure 2 Typical images of triggered steam explosion (∆Tsuperheat ≈ 167 K, ∆Tsubcool ≈ 82 K)

Figure 3

 3 Figure 3 Spontaneous steam explosion observed for the case W5 (high subcooling ≈ 85 °C and high superheat ≈ 215 °C)

Figure 4 The 8 th

 48 Figure 4 Snapshots of the Zirconium melt and water interaction The molten droplets of pure Zr metal are discharged from the bottom of the furnace, falling and quenched in a deep water pool. The droplets are allowed to settle in a catcher arranged at a depth of 470 mm inside the water pool. Snapshots of the transient interactions are shown in Figure 4. For the tests performed with pure

Figure 5

 5 Figure 5 Micro-structure of the debris particle showing stratification of oxidation in layers 2.2.9 DEFOR experiment at KTH

Figure 6 Figure 7 a

 67 Figure 6 Melt jet fragmentation in water at the beginning, at 0.675 s and at 1.243 s The cumulative particle size distribution of completely fragmented debris collected in the DEFOR/SAFEST-A22 test in catchers 2-4 is shown in

Figure 8

 8 Figure 8 Snapshots of the melt water interaction in SES-S1 test 2.2.13 FLF experiments on U-Zr-O phase diagram at JRC The objective of these tests is receiving experimental data and improving the understanding of the quasibinary section of ternary U-Zr-O diagram in the composition domain of BWR-specific corium composition, i.e. at U/Zr atomic ratio close to 0.9 and Zr oxidation index close to 20 -30%. The method of laser heating combined with fast pyrometry and FLF facility have been intensively used in the JRC Material Research for several decades to study melting and crystallization behaviour of many oxide systems representing different

5 )Figure 9 a

 59 Figure 9 a) Compositions studied in this work plotted in the U-Zr-O ternary diagram, b) Details of the spectral emissivity analysis 2.2.14 FLF experiments on (U, Zr, Fe) emissivity at JRC

  European Review Meeting on Severe Accident Research -ERMSAR-2017 Warsaw, Poland, 16-18 May 2017

  The 8 th European Review Meeting on Severe Accident Research -ERMSAR-2017 Warsaw, Poland, 16-18 May 2017

  test facilities until the end of the project. Up to now four experiments, MISTEE-AL, MISTEE-OX, DEFOR and The 8 th European Review Meeting on Severe Accident Research -ERMSAR-2017 Warsaw, Poland, 16-18 May 2017

  The 8 th European Review Meeting on Severe Accident Research -ERMSAR-2017 Warsaw, Poland, 16-18 May 2017

	2.2.4	MOCKA experiments at KIT

In-vessel corium and debris coolability, paper 517

The 8 th European Review Meeting on Severe Accident Research -ERMSAR-2017 Warsaw, Poland, 16-18 May 2017 In-vessel corium and debris coolability, paper 517