H M Geryville
email: hichem.geryville@univ-lyon2.fr

Y Ouzrout
email: yacine.ouzrout@univ-lyon2.fr

A Bouras

N S Sapidis
email: sapidis@syros.aegean.gr

A collaborative framework to exchange and share product information within a supply chain context

Keywords: Product Lifecycle Management (PLM), Supply Chain Management (SCM), Collaboration, Viewpoint, Product Information Exchange

The new requirement for "collaboration" between multidisciplinary collaborators induces to exchange and share adequate information on the product, processes throughout the products' lifecycle. Thus, effective capture of information, and also its extraction, recording, exchange, sharing, and reuse become increasingly critical. These lead companies to adopt new improved methodologies in managing the exchange and sharing of information. The aim of this paper is to describe a collaborative framework system to exchange and share information, which is based on: (i) The Product/Process/Collaboration/Organization model (PPCO) which defines product and process information, and the various collaboration methods for the organizations involved in the supply chain. (ii) Viewpoint model describes relationships between each actor and the comprehensive Product/Process model, defining each actor's "domain of interest" within the evolving product definition. (iii) A layer which defines the comprehensive organization and collaboration relationships between the actors within the supply chain. (iv) Based on the above relationships, the last layer proposes a typology of exchanged messages. A communication method, based on XML, is developed that supports optimal exchange/sharing of information.

To illustrate the proposed framework system, an example is presented related to collaborative design of a new piston for an automotive engine. The focus is on user-viewpoint integration to ensure that the adequate information is retrieved from the PPCO.

INTRODUCTION

As companies are moving towards providing better and better customer-centric products and services to improve market share and market size with continuously growing revenue, the efficiency and effectiveness of product lifecycle management becomes much more important. Product Lifecycle Management (PLM) is a strategic business approach that applies a consistent set of business solutions to support the collaborative creation, management, dissemination, and use of product definition information across the extended enterprise from concept to end of life -integrating people, processes, and information [START_REF] Brown | The PLM program, an incremental approach to the strategic value of PLM[END_REF]. Moreover, for more efficiency these companies need to integrate their business partners in the collaboration to optimize PLM processes by integrating some Supply Chain Management (SCM) elements.

This collaboration between actors of different specialties depends on exchanging and sharing adequate information on the product, related processes and business throughout the products' lifecycle. Thus, effective capture of information, and also its extraction, recording, exchange, sharing, and reuse become increasingly critical, especially when one considers the collaborators' points of view. All these lead companies to adopt new improved methodologies in managing the exchange and sharing of information, emphasizing closer collaboration between software systems that, up to now, have been operating independently.

This research is focusing on integration of product, process and organization modeling in a collaborative framework. This strategy improves the definition of the product development model, and the quality of the exchanged information by using "multiple viewpoints" connecting collaborators' features, and interests with appropriate parts of the product informationmodel.

In the next section of this paper, an overview of some interesting research on product information exchange topic, within the PLM and SCM, and on viewpoints architectures are presented and discussed. In Section 3, we describe our proposed collaborative framework based on Product/Process/Collaboration/Organization model (PPCO) and multiple viewpoints structure. An illustrated example of this framework is presented in Section 4. The last section summarizes the paper and gives an outlook for the future work.

II. LITERATURE REVIEW

A product is made up of components, which are typically developed and managed by different departments or even outsourced. The components usually have their own definitions, which may not be identical (same interpretation) to the others companies' product definitions. Thus, to make a best collaboration between multidisciplinary actors, the organizations need to capture product development information and knowledge in the whole PLM processes. In the collaborative design case, Szykman et al. [START_REF] Szykman | The NIST Design Repository Project[END_REF] [3] propose a knowledge-based approach for supporting engineering design, so-called "Design Repositories". Design repositories capture not only what is designed, but also how and why the product is designed. Design repositories enable to capture the product evolutionary nature of product knowledge and information throughout the design process. However, the system does not have provisions for modeling the product families and their evolution.

A recent effort for capturing knowledge to support knowledge-intensive design is the development of PLM technologies. Sudarsan et al. [START_REF] Sudarsan | A product information modelling framework for product lifecycle management[END_REF] present a conceptual framework for capturing product knowledge over the life of the product. The authors assert that two limitations are present in current PLM technologies. The first limitation deals with design changes and rationale throughout the product development process. This limitation is not within the scope of this work. However, the second limitation is that most PLM systems and enabling technologies are primarily focused on the form representation of the product. These efforts focus on the overarching scope of knowledge capture and reuse in product development; they offer an excellent basis on which to address the specific problem of knowledge reuse in engineering analysis. Thus, their proposed product information framework integrates only the design and assembly areas including product's family, tolerancy and product's evolution, and does not address collaboration issues which evolve heterogeneous systems.

Currently, Product Data Management (PDM) software approaches the functionality of design repositories and PLM systems most closely. PDM systems enable engineers to capture and share product information and meta-information across extended networks to design team members.

Gzara et al. [START_REF] Gzara | Product information systems engineering: an approach for building product models by reuse of patterns[END_REF] present an approach to build product models by reuse of patterns in product information systems engineering. The product information modeling is intended to represent and regroup data issued from various stages of product lifecycle. This information depends on the actor's activity, and is composed of diverse nature and complex elements (Simulation result, CAD model, bill of material, etc). So, this completes of the standard model of product to be able to treat all the product's abstraction levels: conceptual, generic and physical. All this information constitutes the informational flow elements of the various activities of the product development process.

In the Supply Chain (SC) area, some standards product data [START_REF] Burkett | Product Data Markup Language: A new paradigm for product data exchange and integration[END_REF] [7] and information exchange systems have been proposed to support design practitioners in information management and exchanging data for concurrent engineering. Based on eXtensible Markup Language (XML) and Standard of the Exchange Product Data Model (STEP) [START_REF]Industrial automation systems and integration -Product data representation and exchange -Part 203: Application protocol: Configuration controlled design[END_REF], Burkett [START_REF] Burkett | Product Data Markup Language: A new paradigm for product data exchange and integration[END_REF] proposed a new paradigm for product data exchange -namely the Product Data Mark-up Language (PDML) -to facilitate the integration and interoperability of the product development process. The PDML defines a set of application transaction sets for defining the data requirements to communities. In the same way, Lee et al. [START_REF] Lee | Enhancement of product development through product information mark-up language[END_REF] present a logical model with object technology that can be converted to XML for supporting information exchange between a relational database and a knowledge repository. The authors attempt to propose dynamic data exchange schema based on the integration of a knowledgebased system with object technology and the XML standard.

On the multiple viewpoints and product views, we find Hoffmann [START_REF] Hoffman | Distributed maintenance of multiple product views[END_REF] who proposes a mechanism for maintaining consistent product views in a distributed product information database. In his work, a single repository called a "master model" in which all-relevant product data resides was proposed for the integration of different product information domains, while the other views of the product must be updated to maintain consistency. This architecture builds on different applications distributed over different CAD/CAM systems. Thus Bronsvoort [START_REF] Bronsvoort | Product development with multiple-view feature modeling[END_REF] proposed a multiple viewpoints feature modelling approach to allow a designer to focus on the information that is relevant for a particular product development phase. His system supports conceptual and assembly design, part detail design and part manufacturing planning by providing an own view on a product for each of these applications. Viewpoints as in [START_REF]Information technology -Open Distributed Processing -Reference Model[END_REF] were introduced with the aim to ease the specification of complex software system. The main idea of this approach is to reduce the accessible aspects of the specification such that the developers only have to deal with those aspects of the system, which are important for the current task.

Some research [START_REF] Bidarra | Web-based collaborative feature modeling[END_REF] [14] [START_REF] Li | Feature-based design in a distributed and collaborative environment[END_REF] are focused on the collaborative systems in corporation with feature technology. Collaborative feature-based modelling systems are distributed; these systems provide concurrent working environment, synchronisation of modelling data for distributed users, and user interaction facilities.

The interests of presented works on the viewpoint area are two: 1) to define the integration of a professional point of view (e.g. design process) for all collaborators, and 2) to generate product views interpreted differently following the collaborator objective. The limitation of these studies is that none of them integrate the users' viewpoints about their interests within different product lifecycle phases. A multidisciplinary collaboration on the product lifecycle, including not only the geometric information but also other information (as manufacturing data, business data, etc.) directs us to integrate the multiple viewpoints user on the information itself.

In the next section, the proposed collaborative framework for the supply chain actors including PPCO and the multiple viewpoints approach are presented.

III. PROPOSED EXCHANGING AND SHARING INFORMATION

FRAMEWORK

In intra and inter-organization Multidisciplinary Collaboration (MC), several collaborators exchange and share geometric data and other information on the product (structures, functions, business data, manufacturing data, bill of material, analysis data, marketing, resources, costs, etc.). To extract and exchange the right information following the actors' activities in the collaboration, and their focus on the product, we need to define a generic model on the different information linked to the product and process, and to develop some actor's viewpoints on the product (artifact or sub-artifact).

In Fig. 1 we present different links between the collaborators' activities (ellipse) and the domain (rectangle), based on seven profiles that regroup some of the SC collaborators: Design, Manufacturing, Supplying, Distribution, Maintenance, Client, and Partnering. These links are integrated in the viewpoints approach. (see Sect. In the following subsections, we describe our collaborative framework to exchange and share information among a supply chain context. This system is based on four layers (see Fig. 2):

• The Product/Process/Collaboration/Organization model (PPCO) is the core model of this architecture; PPCO defines product and process information, and the various collaboration methods for the organizations involved in the supply chain.

• Viewpoint model, which describes relationships between each actor and the comprehensive Product/Process model, defining each actor's "domain of interest" within the evolving product definition. This model allows each actor to retrieve automatically the adequate pieces of information required by his/her activity and focus. • A layer defining the comprehensive organization (companies, functions, actors, etc.) and collaboration relationships between the actors within the SC. • Based on the above relationships, the last layer proposes a typology of exchanged messages. A communication method, based on XML, is developed to support optimal exchange/sharing of information. In this paper, the two first layers are described in more details. To illustrate information structure, the information extraction and recording process. In the following subsections, we consider that each collaboration process has one or more collaboration-team with several actors (mono or multi-task) which will intervene jointly within collaboration. (see Fig. 3)

A. The Product/Process/Collaboration/Organization Model

In multidisciplinary collaboration oriented PLM and/or SCM, we need to define a general core model which includes the information on the product (geometry, manufacturing data, etc.), on the process, on the collaboration, and on the structure of the supply-chain organization.

Some research on the product and process information definition, as [START_REF] Szykman | Design Repositories: Next-generation engineering design databases[END_REF], [START_REF] Sudarsan | A product information modelling framework for product lifecycle management[END_REF], [START_REF] Gzara | Product information systems engineering: an approach for building product models by reuse of patterns[END_REF], and [START_REF] Wang | Towards modeling the evolution of product families[END_REF], has motivated our research to regroup and define the core model for our architecture, including a generic model of SC collaboration to describe the different connection (exchange and share) between the collaborators' intra and inter-organizations.

Our first objective of creating the PPCO is to provide a baselevel information model that is open, non-proprietary, generic, extensible, independent of any product development process and a generic collaboration in SC context, capable of capturing the full engineering and business context commonly shared in product development. So, the model is composed of four main parts interconnected directly or indirectly (e.g. using viewpoints) such, product, process, collaboration, and organization. Semantically, Artifact (Fig. 5) represents a distinct entity in a product, whether that entity is the entire product or one of its components. It is defined by three levels:

• Abstraction level which defines (a) Production process (manufacturing, support, and maintenance) relates to a physical artifact (b) Engineering process relates to the model of product according to which exemplars will be manufactured (product-type), and (c) Generic product. • Composition level defines the assembly of the subcomponents to build the final product (Basis, Semifinished, Finished) • Evolutionary level defines the evolution of the product within the time and following customer's requirements, for this level, we include the indices' revision, state and time-constraints. Function represents what the artifact is intended to do. The separate representation of Function renders the PPCO and its extensions capable of supporting functional reasoning in the absence of any information on the artifact's form. Form may be viewed as the proposed design solution to the problem specified by the function and consists of the artifact's Geometry (shape and structure may be synonymous in some contexts) and the Material it is composed of. Behavior represents how the artifact's form implements its function and is evaluated by a causal model [START_REF] Wang | Towards modeling the evolution of product families[END_REF].

Relationship is a relation which links technical object between them; the principal idea is to support a generic exploitation, in particular to seek constituent elements. Constraint gives the possibility to define conditions either on the links of subcomponents or on the application's domain. Requirement applies to some aspect of the function or form of the artifact. There are two specializations of SetRelationship: Undirected_SR groups objects into a set, while Directed_SR groups them into two subsets with different roles Reference links or cross-references entities. Job_View is a regrouping of links intended to facilitate the presentation of various Product information related to activity. For example, a view "Manufacturing" will gather the whole of the nomenclature's link, thus making it possible to an actor to explore the subcomponents.

In the process modeling, we were interested into the processes which contribute directly to the product development throughout its lifecycle: (1) Business process implements a business competence through the activities carried on within the framework of the principal functions related to the product (design, industrialization, manufacturing, maintenance). ( 2) Informational and/or Organizational processes which permit to manage the product information. We define Process as a set of activities (see Fig. 6), where the Activity itself represent the transformation actions of the input/output flows, it is described by (a) an Objective which define the process collaboration focus and the actor focus in the collaboration, and (b) some Conditions which depend on the activity and product context (post-and pre-conditions), and (c) Resources represent all entities which intervene on the flows' transformation (e.g. Actors, tools, machines, etc.). After the definition of the product and the process modeling, we introduce the organization modeling (see Fig. 7), where any SC organization is described as a set of teams, and each team has a specific Objective and Connector with other teams or collaboration units. In this part, the customers define the team member and their respective Role. It would be illusory to modeling the interactions between actors without holding account of different collaborative-organization in which they cooperate, and where will be able to acquire their roles (see Fig. 8). In a collaborative structure, the sharing and exchange information relate always to a goal or an objective. It must be clearly identified by the partners so that own objectives can interact with the common objectives.

As-it was described above, at any level of process' collaboration the actor belongs to a team, and his/her activity is defined into an objective, and the conditions define the level of his competencies to facilitate the information extraction, and the activity's hierarchy in the team permit to optimize the interaction between actors and system. Now, we gather these activities in several families which indicate the principal groupings and hierarchy of interesting information for the actors over the lifecycle (e.g. design analysis, shape design, product structure). Moreover, each family gathers several information batches (e.g. for the family of product structure, it consisted in the following batches: artifact, assembly, constraints, etc.). To facilitate the comprehension of this decomposition, we introduce a "level" notation which determines its importance in the batch and accessibility to the user viewpoint (domain and focus). This level is defined by: (1) important information within a considered domain which includes it and can be used in another domain, (2) useful information in this domain and used by other domains, (3) superficial information within the domain.

After describing the core model (PPCO), we introduce in the next section the multi viewpoints approach to interconnect the PPCO and user needs.

B. Multi-level viewpoints

The viewpoints framework provides an infrastructure for capturing and organizing product information extraction within multidisciplinary collaboration. Our notion of a viewpoint was of an object encapsulating cross-cutting and partial knowledge about activity, process, and domain of discourse, from the perspective of a particular collaborator, or collaboration-team, in the product development process.

Fundamentally, viewpoints organize product/software development knowledge based on separation of concerns. A viewpoint, expresses the concerns of a particular collaborator, such as a development participant or a representative of an area of concern captured by that viewpoint. Thus, a viewpoint may represent an area of concern within a project, a product, or a process, or may simply present a particular perspective expressed in a particular notation. The choice of dimensions of concern along which to create viewpoints may be the result of experience, the nature of the problem at hand, or simply organizational requirements.

The degree of importance and reuse of information changes from one to another collaborator following its objectives and activities sector on the product (see Fig. 1). The use of this information depends on different collaborators viewpoints, competencies, skills, responsibilities and interests on product information and product lifecycle phases. Several collaborators use the product information differently according to the specific requirements of their discipline. Starting from this section, we define the viewpoints as the collaborator's interest on the product, including his/her activity, process, domain, and focuses

1) Multi-level viewpoints description

In a MC context, the human dimension is important and corresponds to the different participants in a product lifecycle, and a knowledge dimension corresponding to the experience, competence and situation of participants. Generally, we can say that a collaborator take a viewpoint according to his/her knowledge, domain of competence and his/her objective. Finch [START_REF] Finch | Viewpoints -Facilitating expert systems for multiple users[END_REF] speaks about a vocational viewpoint for a viewpoint used in a particular work activity.

So, in a MC context we notice that every user has one or more viewpoints following his/her activity in the different phases of product lifecycle process (see Sect. 4). A viewpoint is characterised by four objects (or concept types): User, VP_Domain, VP_Relationship, and VP_Objective (see Fig. 9 and Tab. I).

In Fig. 10, we consider two important parts in a viewpoint. First, the "VP_Objective" which constitutes the focus, second "VP_Domain" and "User" constitute the different angles of view on a same focus.

The concept types (user, domain, objective and relationship) have a different instantiation in the MC context to information restitution, but the information restitution is not always the same. (e.g. if the user has only one viewpoint on the product with any competence level, he does not need the Relationship attribute because he has only one viewpoint. If the user has only End-user viewpoint, he does not need the Domain and Relationship attributes.)

2) Algorithm for filtering criteria

In this section, we present one of the main information filtering algorithms (sub-processes of the main programs are not described in this paper). The filtering action is to find the appropriate information for a particular collaborator, according to his "viewpoints" on the product. However, the collaborators can carry out modifications, according to their rights, on restored information. For every modification, the user will submit his/her update which will be saved temporarily in the database (manually by modifying information one after one, or automatic modification by submitting of XML file), and annotated to all collaborators concerned by this modification. This update will take effect after approval of all concerned collaborators.

VP_Domain

is defined by: • Its Name • Current Activity denotes the unique user's activity domain for each viewpoint (e.g. Electronics, Mechanics…), which is relied to the user's situation.

VP_Relationship

indicates the unique user's viewpoint which has the level competence equal to 3 on the same product.

VP_Objective

is described by: • The Focus denotes the speciality in the user's activity (e.g. Topologic, Material, Thermal, Assemblage…) on a Product.

C. Collaboration relationship

Collaboration tools are one of the most effective technologies in today's competitive business environment, particularly, in the product customization, development, manufacturing, supply and services. According to the nature of the collaboration itself, the collaboration can be classified into five levels, which are communicative, collective, cooperative, coordinated, and concerted. In this level, we try to describe a generic collaboration's relationship within intra-and inter-organization. One part of this level is modeled on the PPCO; we integrate a product collaborative space by connecting different collaboration-teams, and tracing of information evolution from the inputs of collaboration process to its outputs.

D. Typology of exchanged message

Based on the above levels, we propose a typology of exchanged messages to communicate and optimize information exchange and share it between actors. To define the messages' structure, we studied and compared several business frameworks. We noticed that it exist three categories of frameworks: (1) Cross-industry frameworks provide crossindustry vocabularies but are limited to the rough process approach and are not greatly concerned with messaging (e.g. xCBL, OAGIS). ( 2) Specific-industry frameworks give industry-specific vocabularies. However, their main contribution is in business processes, as papiNet (www.papinet.org) and RosettaNet (www.rosettanet.org) which provide a comprehensive description of business processes in a particular industry by applying the detailed process approach.

(3) Process-centric frameworks provide no vocabularies but focus on business processes taking the generic process approach (e.g. ebXML, BPML). In our case, we integrate the OAGIS, papiNet and RosettaNet messages to create a standard XML messages exchange following the business process.

IV. APPLICATION

To illustrate this methodology, we present an example about a Piston of automotive engine (Fig. 11) (Object#: 381009). We present also two viewpoints of same actor/user (Fig. 12).

The user "Georges" (with identifier: 18936) has two viewpoints in the system on the product. To retrieve the appropriate information for its focus on the product, we proceed as follows (see the steps in the last algorithm):

3 . 2 )Figure 1 .

 321 Figure 1. Activities and Domains links

Figure 2 .

 2 Figure 2. Proposal collaborative framework

Figure 3 .

 3 Figure 3. Example of collaboration's process

Fig. 4

 4 illustrates the entities comprising the Product information. All entities are specializations of the abstract class Flow_Entity. Technical_Entity, Control_Entity, Structural_Entity, and Statutory_Entity, Technical_Object, Relationship, and Statutory_Entity are abstract classes. Structural_Entity describes the geometric definition and the interconnection between subcomponents, Satutory_Entity defines the technical object state (e.g. update_is_accepted, rejected, wait_validation). Control_Entity is used to define the framework interactions' exchange and constitutes the communication vectors between actors and the collaboration framework.

Figure 4 .

 4 Figure 4. Technical and Control Product Information

Figure 5 .

 5 Figure 5. Technical Object Information and Relationship

Figure 6 .

 6 Figure 6. Process and Activity modeling

Figure 7 .

 7 Figure 7. Organization modeling

  the product; used to facilitate information extraction and collaboration within a Supply Chain context.

Figure 9 .

 9 Figure 9. Viewpoint definition

Figure 10 .

 10 Figure 10. Example on a description of car-engine assembly

Figure 11 .Figure 12 .

 1112 Figure 11. Piston of car-engine (Object#: 381009)

TABLE I

 I

		.	VIEWPOINTS CONCEPT TYPES
		is described by : • Name of the collaborator or user. • Situation, describes the role of the user through the collaboration, this role is
	User	defined by one of several values of situation-set = {Designer, Engineer, Supplier, Manufacturer, Distributor, Manager, Partner, Client, Other situation}. • Competence, defines the level of competence for each user's activity, and it takes
		a value in {1, 2 or 3}. Every user must have only one activity with a level
		competence equal to 3.

TABLE II.

THE LIST OF ALL VIEWPOINTS OF USER "GEORGES"

Step 3: Filtering of information's batches of each viewpoint Following the level's batch definition, the system regroups the batches with high-level hierarchy, and retrieves the information which is more adequate to the user following its focuses on the product, and its activities on the collaboration.

V. CONCLUSION & DISCUSSION

In this paper, we presented our contribution to improve the exchange and sharing collaborative framework. This framework is based on four layers and instead to capture, exchange, share and reuse information within supply chain context. The integration of collaboration and sc-organization, within product and process information model, will permit to widen its scope of application than PDM systems. The viewpoints approach was integrated to capture the actors' interest on their collaboration over product lifecycle. Of course, this framework is intended to help managing the SC information and has no effects on the collaboration strategies or protocols. The viewpoint mechanism can be undeniable contribution for optimizing the product information exchange. With the integration of multi-viewpoints approach, the system particularly ensures:

• The integration and consolidation of information coming from various sources, and its filtering, transformation and adaptation to various viewpoints needs. • The viewpoints permit to optimize the time of information's restitution and its contents while retrieval only the important information for the user.

• The access to permit information in real-time for collaboration actors (throughout management process). • The information traceability permits to understand the information evolution from one to another state (using index, versions, and authentications of information). • A true remote team work, it will make it possible to exchange "product" information and ideas. Effectiveness of creating an exchange and sharing environment of technical information. As perspectives, we consider to improve definition of the collaboration relationship by integrating some standard scenarios of collaboration. Also, we must to define and integrate other types of viewpoints, especially process' viewpoint on the information and the relationship between user's and process' viewpoints to improve the information update.

REFERENCE


D I Medina

F Chinesta

M R Mackley

Heat Melding of Voided Polyethylene Microstructures

This paper is concerned with the fabrication of voided polyethylene microstructures by heat melding of plastic microcapillary films (MCF) to form microcapillary monoliths (MCM), which are consolidated layers of MCFs forming in two dimensional arrays of microcapillaries. MCMs were manufactured by heat melding together multiple layers of low-voidage MCFs or high-voidage MCFs. The optimal conditions for interface adhesion of the MCFs to create MCMs without compromising capillary integrity and the influence of compatibility between MCFs on melt processing, was investigated.

The MCFs were processed from linear low-density polyethylene (LLDPE) and the melt rheology of the polymer was studied to provide rheological parameters that could be used both to gain an understanding of the character of the polymer and for modeling of the MCM forming process. In particular, the temperature dependent nature of the rheology was investigated. Recognizing the transition from viscous-dominated behavior to elasticdominated behavior was important for the success of the melding process by which MCMs were formed. Modelling of the melding process provided some additional information and confirmed issues in relation to the thermal bonding temperatures and mechanisms.

INTRODUCTION

The voided polyethylene microstructures studied in this paper is referred to as a microcapillary film (MCF), characterized by a parallel array of near uniform capillaries embedded within a thin linear low density polyethylene film as shown in Figure 1.

Hallmark and Mackley [START_REF] Hallmark | The melt processing of polymer microcapillary film (MCF)[END_REF] initially addressed the manufacture of these novel flexible films.

The film has affine properties to standard plastic film [START_REF] Briston | Plastics films[END_REF][START_REF] Han | Rheology in Polymer Processing[END_REF][START_REF] Zatloukal | Application of variational principles in modeling of the film blowing process for high stalk bubbles[END_REF], closed-cell polymer foam [START_REF] Mills | The high strain compression of closed-cell polymer foams[END_REF][START_REF] Zhu | Analysis of the high strain compression of open-cell foams[END_REF] and hollow fibres [START_REF] Dees | Structure Development During Melt Spinning of Linear Polyethylene Fibers[END_REF][START_REF] White | Orientation development and crystallization in melt spinning of fibers[END_REF][START_REF] Syang-Peng | Formation of hollow fibers in the melt-spinning process[END_REF] embracing characteristics of these three. The manufacture of MCFs was attained by entraining air within the polyethylene from injection nozzles during the extrusion process at the point the molten polymer exits. Posterior extruding the molten polyethylene through air-entrained nozzles slit die, the molten film was drawn with a set of chill rollers to produce a solidified sheet, termed low-voidage MCF, which is characterized for having consistent thickness and capillary diameters along the film.

Subsequently different kinds of MCFs have been emerged, such as small diameter lowvoidage MCF, high-voidage MCF and ultra-high voidage MCF [START_REF] Medina | The development of voidage and capillary size within extruded plastic films[END_REF]. Hydraulic capillary diameters on the MCFs range from 3.5 μm to 5000 μm. The MCFs can be classified according to their capillary diameter as small diameter low-voidage (with capillary of hydraulic diameter of order 3.5 µm), low-voidage (with capillary of hydraulic diameter of order 200 µm), high-voidage (with capillary of hydraulic diameter of order 800 µm).

Microcapillary monolith

A micro-capillary monolith (MCM) is a solid polymer block of MCFs, containing a twodimensional array of capillaries. The monolith consists of two or more layers of MCFs permanently bonded together over their full length. This multi-layer structure is created by "hot pressing" at temperatures close the melting point of the polymer. This is a delicate process because the temperature, time and load need to be precisely controlled in order to meld the interfaces and to prevent collapse of the hollow capillaries.

The process of MCM formation relies on 'polymer welding', in which two molten or near molten interfaces are bonded together.

The most common processes for joining plastic components can be classified as: mechanical joining [START_REF] Gao | Mechanism of Mechanical Press Joining[END_REF], adhesive bonding [START_REF] Morris | Adhesive Bonding of Polyethylene[END_REF] and welding [START_REF] Grewell | Welding of plastics: Fundamentals and new developments[END_REF].

LLDPE MCF are heated during the welding process in order to create intimate contact between the interfaces enabling polymer chain diffusion across the interface allowing subsequent entanglements to achieve the join strength [START_REF] Grewell | Welding of plastics: Fundamentals and new developments[END_REF]. The welding process starts when the MCFs are at a temperature close to the melting point of the LLDPE.

At this temperature a reduction in the viscosity and entropy occurs, making the mobilization of polymer chains possible, and since pressure is applied this facilitates the intimate contact of the MCFs. It gives as a result interdiffusion of polymer chains, finishing with interfacial bonding [START_REF] Prager | The Healing-Process at Polymer-Polymer Interfaces[END_REF].

The degree of welding and integrity of capillaries in the MCM formation are mainly the function of three factors, which are: the processing temperature, T, applied compression ratio and melding time.

The welding, or healing, which consists of the diffusion of polymer chains across the interface, is dependent on temperature. The MCM melding process is carried out under isothermal conditions and can be modeled using the theory of reptation. The reptation theory, developed by De Gennes [START_REF] Degennes | Reptation of a Polymer Chain in Presence of Fixed Obstacles[END_REF], which describes the motion of individual polymer molecules in the amorphous bulk is derived from a deduction by Edwards [START_REF] Edwards | The statistical mechanics of polymerized material[END_REF], who established a formula for the free energy of the polymer chains and a model where the chain is enclosed to a tube formed by surrounding chains.

The theory is suitable to define the back or forward movements of each polymer chain which is considered to be closely boxed in by the entanglements of contiguous chains. This model is well known and is illustrated in Figure 2, in relation to the MCF welding process.

During the process it is assumed, that a perfect contact exists at the two MCF interfaces. At time t = 0 all the chains have zero diffusion through the other MCF, at later time (t < t R ), the chains are longer and have crossed the interface. When time is equal to the reptation time (t = t R ), both MCF polymer chains are totally interpenetrated creating entanglements, at this point the interface disappear becoming indistinguishable and the properties at the interface are the same as the ones at any point within the MCF. [START_REF] Kim | A Theory of Healing at a Polymer Polymer Interface[END_REF][START_REF] Wool | Welding of Polymer Interfaces[END_REF].

The degree of healing is defined using the formula [START_REF] Prager | The Healing-Process at Polymer-Polymer Interfaces[END_REF][START_REF] Degennes | Reptation of a Polymer Chain in Presence of Fixed Obstacles[END_REF][START_REF] Yang | Healing of thermoplastic polymers at an interface under nonisothermal conditions[END_REF]

D h (t) = σ / σ ∞ = x/ x ∞ = (l/L) 1/2
Where σ is the bond strength which is related to the interpenetration distance defined as x, which in turn is proportional to the square root of the length l, σ ∞ is the ultimate bond strength at values of x ∞ and L.

In the case where the parts are brought together at temperatures close to or above the melting point, known as hot plate welding [START_REF] Nieh | Hot plate welding of polypropylene. Part I: Crystallization kinetics[END_REF][START_REF] Watson | Recent developments in hot plate welding of thermoplastics[END_REF], the time to achieve maximum bond strength is approximately the same value that it takes to reach intimate contact. As a result, the welding temperature has a profound effect on both the compression ratio and the matrix rheology and therefore on the quality of the fused interface [START_REF] Bastien | A Nonisothermal Healing Model for Strength and Toughness of Fusion Bonded Joints of Amorphous Thermoplastics[END_REF].

EXPERIMENTAL

The linear low density polyethylene (LLDPE) used was a commercially available grade (Dowlex NG5056E, melt index 1.1 g/10 min, density 0.919 g/cm 3 ).

Low-voidage MCFs were fabricated according to the method established by Hallmark and

Mackley [START_REF] Hallmark | The melt processing of polymer microcapillary film (MCF)[END_REF]. The heated extrusion line, shown schematically in Figure 3, used in the production of 19 capillary films consisted of a single-screw extruder connected to a gear pump. Pressure feedback control was present between the inlet of the gear pump and the motor drive to the extruder's screw. The polymer exited the extrusion line through a heated die with a convergent mid-section that contained air entrainment needles.

Upon exiting the extrusion die, the extrudate was taken through the chill rollers whose position relative to the die exit could be easily altered and act as a variable-speed haul-off device. The distance between the die exit and the chill rollers was termed the melt drawing length, L D .

The air entrainment assembly was designed such that the tips of each nozzle were flush with the exit of the die. The die body and 19-injector assembly was attached to the extruder and the extrusion line. The extrusion line was operated at a constant polymer volumetric flow-rate, with the extrudate passing into the rollers and out to the haul-off device. For lowvoidage MCFs the final voidage in the MCF film was close to that of the die injector voidage of 15%.

High-voidage MCF was fabricated using a similar process to the low-voidage-MCF, but with the difference of using two opposing high speed air jets, which where placed at the die exit to quench the film [START_REF] Medina | The development of voidage and capillary size within extruded plastic films[END_REF] The cooling of the molten surface resulted in the internal voidage of the MCF increasing from the die voidage of 10% up to voidage of order 24-70%.

Low-voidage MCM formation process

The processing of the low-voidage MCM consisted of cutting 30 cm length of Microcapillary film, placing them on the top of each other and then heat welding them together to form a MCM. The thickness of the MCM would be a function of the number of bonded microcapillary films. The MCFs were placed in an adjustable custom-designed brass mould. The mould consisted of a brass top and an aluminium bottom plate, each 310 mm x 100 mm. The MCM thickness was controlled with brass spacer strips, which were 0.051 mm, 0.52 mm, 1 mm and 5mm thick. A heated press (Moore E1322) was used in order to obtain a controlled claming load (Figure 4a). The following procedure was used:

The multilayer stack of MCFs was prepared by layering the specific amount of MCFs on top of each other, the MCFs were held together using tape.

The thickness of the untreated stack (t o ) was measured and thickness of the mould (t m ) was also measured. A compression ratio was calculated from the difference of t o minus t m between t m . The brass mould was adjusted to the resulting calculate thickness (t c ) as precisely as possible using the brass strips.

The untreated stack was loaded into the mould at room temperature. After that the mould was introduced into the hot press machine with no applied load, but in contact with the two plates, for six minutes to allow temperature equilibration (Figure 4b). Finally, after a melding time of 5 minutes at a constant temperature, and a load of 4 tonnes (Figure 4c) the pressure was released and the plates taken out of the press and allowed to cool down before opening the mould.

High-voidage MCM formation process

The manufacture of high-voidage MCMs was similar to the low-voidage MCM, with the difference of temperature, load and welding time parameters together with the use of a polymer film interlayer. Optimal parameters in order to avoid collapse or deformation of the capillaries were established.

Rheological characterization

Rheological characterisation experiments were carried out to obtain material parameters that describe the linear, non-linear visco-elastic response and temperature dependence of the base polymer.

The melt processing properties were investigated by performing shear rheometry. An Advanced Rheometric Expansion System rheometer (ARES-LC model 5450DT), was used to carry out these experiments. A stepper motor drives the lower plate in oscillation, while the upper plate is connected to a transducer, which measures torque and normal force (Figure 5a). In dynamic experiments, shear strain, resultant shear stress and the phase angle between these are resolved. As a result the elastic and viscous modulus can be calculated.

The ARES rheometer was configured with 25 mm diameter parallel plates and heated by an air-blast oven. For the solid samples a rectangular/torsion fixture was used as shown in Figure 5b. Rectangular samples (of dimensions x = 1.5 mm, y = 12 mm, z = 30 mm) where mechanical gripped and tested in a similar way to the melt. Differential Scanning Calorimetry (DSC) was carried out on a Pyris 1 Perkin Elmer 300VA calorimeter with heating and cooling rates of 10°C/min over the temperature range 0-200°C. The ramp rate of 10°C/min was chosen to minimise structural reorganisation during heating whilst ensuring that reliable melting temperatures could be obtained [START_REF] Wunderlich | Study of Equilibrium Melting of Polyethylene[END_REF] The sensitivity of the DSC was 0.0001 mg. Samples with mass in the range 7.00 +/-0.50 mg was cut from the low-voidage MCF and HV-MCF samples.

In order to establish the capillary size, shape and interfacial bonding of the MCFs a visual characterization technique was used. An optical microscope Olympus BH-2 allowed effective detailed mapping of the MCFs capillaries size, shape and distribution along the film. A graticule was photographed and used to determine the film thickness and capillary size. These results were confirmed by JEOL 6340F Scanning electron microscopy (SEM) with an accelerating voltage of 5 kV.

RESULTS AND DISCUSSION

The rheology and DSC data are shown in figures 6 and 7 respectively. This data shows that for this polymer a melting transition occurs at around 114 °C and it is in this temperature region that melding experiments were carried out.

Low-voidage MCF melding

High-voidage MCFs

By virtue of its greater voidage, the high voidage MCF is more susceptible to loads than the low-voidage MCF and in addition fundamental differences in interface bonding were discovered. Figure 10 shows a series of high voidage MCM sections for melding at similar conditions to the low-voidage examples. Two things are noticeable; the collapse of the capillaries as shown in Figure 11 and the poor interface bonding. Increasing the temperature or bonding time did not enable bonding to occur without capillary collapse.

It was suspected that the high voidage interface behave in a different way to the lowvoidage interface and X-ray measurements shown in figure 12 indicated that the high voidage MCFs were oriented and the low-voidage were not. The DSC curve in Figure 7 also shows the high voidage MCF has a higher melting point. It appears that orientation reduces the melding ability at these intermediate temperatures and it was not found possible to form high-voidage MCMs in the same way as low-voidage MCMs were achieved.

An effective way of forming high-voidage MCMs was discovered; a plane film of LLDPE was used as an interlayer between adjacent MCFs. This is shown in Figure 13 where conditions were found for good interface bonding and also capillary integrity.

Modelling of MCM formation

A number of aspect for the low-voidage MCM bonding have been modelled including the development of the MCM, thermal profile, capillary distortion due to an uneven interface and reptative polymer diffusion across an interface. The modelling is far from complete but it does help to understanding some of the physical issues involved.

Thermal modelling

The heating temperature kinetics of the MCF stack was calculated and compared with the measure kinetic. A schematic of the geometry is shown in Figure 14 and the heat differential equation (1) given below was numerically solved.

(

) 1
where T is the temperature of the MCM at coordinate x and y at specific time t, ρ is the density, Cp the specific heat capacity and λ the thermal conductivity for the MCF.

The experimentally measured input surface oven plate was introduced as a boundary condition and the temperature rise kinetic of both mould plates and MCF stack established.

The numerical results agree well with the experimental thermocouple temperature profile positioned at the centre of the stack as shown in Figure 15. The modeling showed that most of the thermal resistance came from the heating of the mould and not the MCF itself.

MCF Interface modeling

The surfaces of the MCFs were not perfectly flat and an essential part of the good interface bonding between adjacent MCF surfaces was to have a good contact. A minimum value of compression ratio was necessary to achieve good contact, however if the compression ratio was too high distortion of the hollow capillaries occurred.

In an attempt to gain some insight into this process mechanical numerical modeling was carried out on an elastic MCF with smooth boundary conditions on one side and an irregular boundary on the other. The geometric section of MCF and boundary is shown in Figure 16.

The thermomechanical model was solved numerically assuming the young modulus E = 2.5E5 Pa and poisson ratio ν = 0.45. Figure 17 shows the distortion of the capillaries for a compression ratio deformation of 5.9 %. The results show that if one of the surfaces is irregular, distortion of the capillary holes will occur. In general this was not seen experimentally except in the case of the high voidage MCM where capillary collapse occurred. In reality some plastic distortion almost certainly occurs at an uneven interface when a load is applied and this will need to be included in future modeling.

Interface bonding.

The modeling of the interfacial bonding is difficult unless the two surfaces are considered as molten polymers of unique molecular weight and that the surfaces are in perfect physical contact. The reality is that the surfaces are not necessarily in perfect contact, the polymer contains a distribution of molecular weights, the polymers themselves are not in the fully molten state and that partial crystallinity influences the bonding process. The fact that the oriented high voidage MCF had different bonding characteristics to the unoriented lowvoidage MCF demonstrates that interfacial bonding in the temperature regime considered has considerable complexity.

If a pure melt and perfect interface assumption is assumed, progress can be made in relation to modeling. The reptation concept of De Gennes [START_REF] Degennes | Reptation of a Polymer Chain in Presence of Fixed Obstacles[END_REF], provides a framework for analysis [START_REF] Gao | The Structure and Rheology of Molten Ultra-High-Molecular-Mass Polyethylene[END_REF]. The reptation diffusion, equation [START_REF] Briston | Plastics films[END_REF] (2) can solved, P is the probability density function, which is related to the position s of a chain segment at time t, D is the temperature dependant reptation diffusion constant, the diffusion constant depends of the length of the chain L by an equation (3) [START_REF] Yang | Healing of thermoplastic polymers at an interface under nonisothermal conditions[END_REF] (3) where t R is the reptation time, L is the total length of the chain and D o is the isothermal reptation coefficient at temperature T o . After all, equation (4) shows the relationship between the minor chain length, the total chain length and the time of reptation [START_REF] Degennes | Reptation of a Polymer Chain in Presence of Fixed Obstacles[END_REF][START_REF] Wool | Welding of Polymer Interfaces[END_REF][START_REF] Yang | Healing of thermoplastic polymers at an interface under nonisothermal conditions[END_REF] (4)

Modelling the melding process at temperatures close to the melting point of the polymer is extremely difficult. This model requires knowledge of the reptation time for the polymer at the applied melding temperature. It is possible to obtain relaxation spectrum for the polymer used in this study at temperatures above the melting point. Figure 18 shows the frequency sweep at 140 °C, and using a software program RepTate [START_REF] Ramirez | RepTate -Rheology of Entangled Polymers Toolkit for the Analysis of Theory and Experiments[END_REF], the longest relaxation modes can be identified as showed in Figure 19. This has been carried out for each temperature above the melting point and a plot is shown in Figure 20.

If this data is extrapolated to the melding temperature a τ R of 2632 s is obtained. This almost certainly is an underestimate of the true reptation time at that temperature because the material is still partially crystalline.

The advancement of the diffusion of the chains to the interface, N, can be calculated with the following equation: [START_REF] Zatloukal | Application of variational principles in modeling of the film blowing process for high stalk bubbles[END_REF] This defines the motion of the chain, when it goes out of the tube. A temperature of 114 °C, we get the advancement of the diffusion of the chains to the interface of 11 % when we maintain this temperature for 300 sec. Full reptation is not necessary for complete melding plausible because the long modes correspond to highest molecular weights. Lower molecular weight polymer chains and parts of high molecular weight chains will be able to reptate across the interface with much shorter timescales and evidently give adequate bonding.

Conclusions

This paper has established melding conditions where plastic microcapillary film (MCF) can be bonded together to form a 2D microcapillary monolith (MCM). The problem is a delicate one as if too low temperature is applied the MCFs will not bound, however if too high a temperature is used the polymer melts and the hollow capillaries collapse. A reasonably wide processing window for low-voidage MCF was established in relation to moulding temperature, compression ratio and time.

High-voidage MCFs have intrinsic molecular orientation associated with the quench forming process and because of the orientation it was found difficult to establish a processing window where good interbonding could be achieved. The problem was partially overcome by using an unoriented plane film interlayer.

Rheological data for the LLDPE used to form the MCM has been presented over a temperature range that covers the materials solid and melt behaviour. In particular the region near the melting point brings particular difficulties in measurement, however it is in this region where the melding process occurs.

The formation of MCM was partially modeled by solving the transient heat transfer problem, analyzing the deformation of MCF under load and also examining interfacial reptation diffusion. Overall a picture emerges where a viable processing window can be identified in order that MCMs can be fabricated. This may have future applications for MCFs when used for heat transfer, microreactors or other usage. The transition temperature behaviour of polyethylene presented in the paper has general relevance to polyethylene forming process at and around the melting range of the polymer.

Figure 8

 8 Figure 8 is an example of extreme melding conditions. If melding is carried out at 124 °C as shown in figure 8a there is complete collapse of the capillaries. By contrast if melding is carried out at 100 °C as shown in figure 8b, no interface bonding occurs. Clearly intermediate conditions are required and these are mapped out in Figure 9. The figure shows optical sections of MCM obtained for different compression ratios and melding temperature. All were taken for a 300 s melding time. The figure shows optimum interface formation whilst retaining capillary integrity of order T = 114-120 °C and C R = 0.26 -6.82 %. The diagonal cross hatched zone indicates two weak an interfacial bond and the horizontal hatched zone, partial capillary distortion. The optimum interface formation condition is close to the peak in the DSC trace and also at the cross over to the G', G" trace.

Acknowledgements

Dora I. Medina would like to thank CONACyT for financial PhD support and Malcolm R.

Mackley would like to thank EPSRC for financial support of MCF development.


Huang Xianbei

Liu Zhuqing

Yang Wei

Tang Xuelin ISROMAC Yaojun Li

Comparison of the linear and non-linear SGS models in simulating the internal flow in a centrifugal pump impeller

INTRODUCTION

Large eddy simulation (LES) has been developed for several decades since the pioneer works of Smagorinsky [START_REF] Smagorinsky | General circulation experiments with the primitive equations: I. The basic euqations[END_REF] and Deardorff [START_REF] Deardorff | Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer[END_REF]. The Smagorinsky Model (SM), including the dynamic version (DSM), adopts a linear relationship between the SGS stress tensor and the strain-rate tensor.

According to the results from Tao et al [START_REF] Tao | Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements[END_REF] and Horiuti [START_REF] Horiuti | Roles of non-aligned eigenvectors of strainrate and subgrid-scale stress tensors in turbulence generation[END_REF], the linear relationship adopted by SM is actually not hold. Kosovic [START_REF] Kosovic | Subgrid-scale modelling for the largeeddy simulation of high-Reynoldsnumber boundary layers[END_REF] proposed a polynomial (non-linear) relation of SGS stress which depended on both the strain rate and the vorticity. Wang et al [START_REF] Wang | A dynamic nonlinear subgrid-scale stress model[END_REF] extended the model by applying the dynamic procedure proposed by Germano [START_REF] Germano | Turbulence: the filtering approach[END_REF], named DNM here after. However, the results from linear models are not so satisfying, especially at off-design conditions [START_REF] Pedersen | Flow in a centrifugal pump impeller at design and off-design conditions-Part I: particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) measurements[END_REF]. It

FORMULATIONS

Filtered Navier-Stokes equations

In LES, a low-pass filter (in frequency) is applied to the Navier-Stokes equations to get the following formulations (in Cartesian coordinate):

(1)

  1 i ij ij ij ji i j j i j u uu uu p t x x S x x x x                                (2)
where, the variables with an over bar represent the filtered quantities, u represents the velocity, p ()

0 i i u x    
is the pressure,  is the kinetic viscosity, i S is the source term and ij  is the SGS stress , which is defined as

ij ij ij u u u u   (3)

SGS models 1.2.1 DSM

DSM is a linear eddy-viscosity model. The SGS stress can be expressed as:

2 d ij ij r S    (4)
where ij S is the rate-of-strain tensor, d ij  is the deviatoric part of the SGS stress tensor to be modeled because ij S is zero-trace. r  is the eddy viscosity with

2 rs cS    (5)
where  is the filter width and

1/2 (2 ) ij ij

S S S 

is the characteristic filtered rate of strain. The final form of the Smagorinsky model is obtained as:

2 2 d ij ij s c S S    (6)
In order to dynamically calculate s c , Germano [START_REF] Germano | Turbulence: the filtering approach[END_REF] proposed to apply a second filter called the test filter to the SGS stress:

), ( ij ij ij ij ij ij T u u LT uu    (7)
here, ‗~' denotes test-filtering operation, ij T is the stress at a test filter scale( 2    ).Similarly to equation ( 6)

2 2 d ij ij s T c S S   (8)
where

d ij T is the deviatoric part of ij T .
Combining equations ( 6) and (8):

Using equation ( 9) to provide an approximation to

d ij L : d ij s ij L c M  ( 10
)
Least squares minimization of the error is suggested to be used by Lilly [START_REF] Lily | A proposed modification of the Germano subgrid-scale closure method[END_REF] to calculate the value of

s c : ij ij s kl kl ML c MM  ( 11
)
It is well known that DSM suffers from numerical instability due to the large oscillation of the model coefficient. In this paper, the eddy viscosity is bounded as:

max( , ) rr     ( 12
)
which means that the backscatter can't be larger than the viscous dissipation.

DNM

Kosovic [START_REF] Kosovic | Subgrid-scale modelling for the largeeddy simulation of high-Reynoldsnumber boundary layers[END_REF] proposed a non-linear model which is a simplification of the model investigated by Lund and Novikov [START_REF] Lund | Parametrization of subgrid-scale stress by the velocity gradient tensor[END_REF]. The model can be written as:

22 1 2 2 ( 1 ) ( ) 3 d kj ij ik ij s ik kj ik kj mn nm ij cc c S S S S S S S S             (13)
here ij  is the vorticity, the condition 2    is applied. Wang et al [START_REF] Wang | A dynamic nonlinear subgrid-scale stress model[END_REF] propose to apply Germano's method [START_REF] Germano | Turbulence: the filtering approach[END_REF] to the SGS stress: Use Lily's least squares [START_REF] Lily | A proposed modification of the Germano subgrid-scale closure method[END_REF] to finally determine the three model coefficients:

1 2 d ij ij ij ij ij ij s ij ij d ij ij ij ij ij ij ij ij d ij ij ij ij ij ij ij ij M M M N M P c M L N M N N N P c

RESULTS AND DISCUSSION 2.1 Grid convergence analysis

The impeller under investigated is a shrouded, low specific-speed (dimensionless specific-speed

0.5 s N 
) multistage pump as shown in Figure 1.

Pedersen's results have shown that stalls will appear in every two adjacent channels at quarter-load [START_REF] Pedersen | Flow in a centrifugal pump impeller at design and off-design conditions-Part I: particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) measurements[END_REF]. Therefore, in order to reduce the computational resource, two channels are used for calculation.

In this paper, we use the procedure proposed by Celik et al [START_REF] Celik | Procedure for estimation and reporting of uncertainty due to discretization in CFD applications[END_REF] to examine whether the grid has been in the asymptotic range. To resolve the near-wall characteristics, the y  is set to locate in the viscous sub-layer at all the walls including blade, hub and shroud. Three grids are generated, with the element number equal to As can be seen from Figure 2, the extrapolated velocities are close to these of the fine grid, which is a good indication that convergence been reached. In the following calculations, the mesh with According to Pedersen et al [START_REF] Pedersen | Flow in a centrifugal pump impeller at design and off-design conditions-Part I: particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) measurements[END_REF], this kind of stationary stall is related to the even number of the impeller passages which enables a stable equilibrium between the forces acting on the stall.

In fact, Zhou [START_REF] Zhou | Investigation of stall characteristics in centrifugal pumps[END_REF] studied centrifugal pump impellers with different number of blades and found that only impeller with even blades can maintain stationary stalls at off-design load.

As the flow patterns in the two channels are different, the velocity profiles are inevitably affected. Figure 5

  As a typical turbo-machine, centrifugal pump plays an important role in industry. Due to the superior accuracy, LES attracts more concentrations in the field of centrifugal pump's research and design. In most commercial CFD codes, only linear SGS models are included.

  is necessary to test the performance of the non-linear SGS model. As the implementation of new model into these codes is relatively fussy, the open-source code OpenFOAM [9] is used in this paper. For comparison, the linear model DSM and the non-linear model DNM are used in simulating the flow in a centrifugal pump impeller. The calculation results are compared with the PIV results by Pedersen et al [8].

Figure 1 . 2 b is the outlet width and 2 RFigure 2 .

 1222 Figure 1. Two stages of the investigated centrifugal pump The velocity inlet condition is applied at inlet. At the impeller outlet, a static pressure is applied. The whole domain is calculated in the rotating frame. Rotational periodic conditions are applied to the two sides of the domain. All the walls are fully resolved without near wall treatment.As for the numerical schemes, ‗Gauss linear' scheme (second order) is chosen for the gradient term, and the second order upwind scheme named ‗Gauss linearUpwind' is used for the divergence term. The time scheme is the second order implicit ‗backward' scheme. The time-step size is chosen to ensure an average Courant number smaller than 0.5. The averaging process is turned on when the flow field is statistically stable, and another 5000 time-steps are taken to calculate the time-averaged properties. The radial ( r U ) and ( t U ) tangential relative velocities on the mid-height plane (

2 . 2 2 0.5R and 2 0.Figure 3 .

 22223 Figure 3. Comparison of Radial and tangential velocity profiles at design load(-:DSM, --:DNM, +:PIV results)

Figure 4 .

 4 Time-averaged stall by DSM at pressure side near the outlet in channel A (left)

2 0.5R and 2 0Figure 5 .

 225 Figure 5. Comparison of Radial and tangential velocity profiles at part load(-:DSM, --:DNM, +:PIV results)

ACKNOWLEDGMENTS

The authors would like to acknowledge the financial supports given by the Ministry of Education, Science and Technology Project (Grant No. 113010A), the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130008110047) and the National Natural Science Foundation of China (Grant No. 51209206).


Transposing this to DARIAH (Organisational Question…)

• DARIAH as a federation of national infrastructures

-Reaching out to a wider community at the service of each country -DARIAH as marketplace and hierarchy Transposing this to DARIAH (but also the funding question)

HOWEVER, stability has the advantage of facilitating the provision of trust and branding (the other way round in terms of easy things to achieve)

• Political tool to establish/strengthen national settings -Attractor for the formation of a higher-level identity