Ahmad Shahwan
email: ahmad.shahwan@grenoble-inp.fr

Gilles Foucault
email: gilles.foucault@g-scop.inpg.fr

Jean-Claude Léon
email: jean-claude.leon@grenoble-inp.fr

DERIVING FUNCTIONAL PROPERTIES OF COMPONENTS FROM THE ANALYSIS OF DIGITAL MOCK-UPS

Keywords: Product simulation, design, DMUs, geometric models, assembly, functional designation, mechanics, kinematics, reasoning and knowledge representation

Digital Mock-ups (DMUs) are widespread and stand as reference model for product description. However, DMUs produced by industrial CAD systems essentially contain geometric models and their exploitation often requires user's input data to derive finite element models (FEMs). Here, analysis and reasoning approaches are developed to automatically enrich DMUs with functional and kinematic properties. Indeed, geometric interfaces between components form a key starting point to analyse their behaviours under reference states. This is a first stage in a reasoning process to progressively identify mechanical, kinematic as well as functional properties of the components. Inferred semantics adds up to the pure geometric representation provided by a DMU and produce also geometrically structured components and assemblies. Functional information connected to a structured geometric model of a component significantly improves the preparation of FEMs and increases its robustness because idealizations can take place using components' functions and components' structure helps defining sub-domains of FEMs.

INTRODUCTION

As geometric representations of a product, digital mock-ups (DMUs) provide engineers with assembly and/or sub-assembly models that can be used as input for finite element (FE) analyses during a product development process (PDP). This is the specific context addressed here, even though assembly model processing takes place also at other stages of a PDP.

Virtual and augmented reality techniques, varying from simple visualization to fully-immersive environments, have been used at various stages of a PDP; such as design and modeling, assembly/disassembly (A/D) simulations and planning, to name only few [START_REF] Blümel | Pragmatic Approach to Apply Virtual Reality Technology in Accelerating a Product Life Cycle[END_REF], [START_REF] Raghavan | Interactive Evaluation of Assembly Sequences Using Augmented Reality[END_REF], [START_REF] Schenk | Combining Virtual Reality and Assembly Simulation for Production Planning and Worker Qualification[END_REF]. There also, assembly models are central and their processing addresses issues similar to those addressed in this document.

Anyhow, a finite element model (FEM) derived from an assembly model needs a very large amount of engineers' interactions to be generated from its corresponding DMU. This causes a delay in the availability of such a model up to the point where the simulation becomes no longer useful as its output arrives too late in a PDP. For this reason, reducing the simulation preparation time at the level of assembly models becomes a key issue. Figure 1illustrates this configuration with a complex sub-structure of an aircraft where FEM preparation is too tedious. In fact, assembly processing for FEM generation requires many engineers' interactions to produce interfaces between components that meet the objectives of FE simulation [START_REF] Boussuge | An analysis of DMU transformation requirements for structural assembly simulations[END_REF]. Interfaces are numerous, additionally; simplification processes must take place on some components. Thus, this task is often interactive, despite efforts to automate it [START_REF] Thakur | A survey of CAD model simplification techniques for physics-based simulation applications[END_REF], [START_REF] Léon | A new approach to the preparation of models for F.E. analyses[END_REF]. Its automation requires the identification of similarities among interfaces and components to set up algorithms. Often, engineers refer qualitatively to categories of components and connections between components to structure their FEM preparation, e.g. screws, bearings, bolted assemblies, etc. Indeed, this categorization can be formalized as a need to identify a component or a set of components from its/their function. DMUs conveyed through STEP files or even in native CAD modelers' format are hardly providing the desired information. Indeed, to process the geometric interfaces between components, there must exist some connection between the component designation and its geometric model. This suggests that the functional model of a component refers to a structured geometric model connected to its designation that stands for symbolic information characterizing its function. Hence, it is the purpose of the proposed approach to speed up the simplification processes of assemblies, by providing necessary semantic annotations and structured geometric models to their components through a bottom-up analysis of assembly models.

The rest of the document is presented as follows; we review prior contributions in Section 2. Next, we highlight our contribution in Section 3. Section 4 addresses new concepts related to interfaces and reference states that are central to our approach. In Section 5 we develop the process flow of our approach. Results are briefly shown and explained in Section 6. Section 7 concludes and discusses future works.

RELATED WORKS

The problem of bridging the gap between pure geometric representations and technical features of components has been frequently tackled in the literature. Efforts as early as [START_REF] Joshi | Graph-based heuristics for recognition of machined features from a 3D solid model[END_REF] have been paid in the field of features recognition (FR) in solid models. [START_REF] Zhu | B-Rep model simplification by automatic fillet/round suppressing for efficient automatic feature recognition[END_REF] defines features (also referred to as form features or machining features) to be the representations of shape aspects of a physical product that can be mapped to generic shapes in a given context and are functionally significant.

In [START_REF] Joshi | Graph-based heuristics for recognition of machined features from a 3D solid model[END_REF], a graph representation of the geometric model is generated before graph matching techniques are applied to extract form features, also represented as graphs.

Authors in [START_REF] Thakur | A survey of CAD model simplification techniques for physics-based simulation applications[END_REF] address the problem of functional features extraction out of digital models, and classify existing solutions into human assisted approaches, feature based modeling, and automatic feature recognition and extraction. Their proposed method falls in the last category and suggests a three stage solution that builds a hierarchical structure of part's shape in accordance to the level of details.

In [START_REF] Ames | Production ready feature recognition based automatic group technology part coding[END_REF], the author advocates an expert system approach to recognize application-specific features given the product's solid model as B-Rep.

A survey of recent approaches to feature recognition shows a wide range of techniques that participate to the Computer Aided Process Planning (CAPP) automation [START_REF] Thakur | A survey of CAD model simplification techniques for physics-based simulation applications[END_REF]. In [START_REF] Date | Flexible feature and resolution control of triangular meshes[END_REF] the feature recognition is integrated into the process of simplification as a preliminary step to prepare a tessellated model for FE analysis.

A technique to detect and simplify blending features to enhance the process of functional features detection is presented in [START_REF] Zhu | B-Rep model simplification by automatic fillet/round suppressing for efficient automatic feature recognition[END_REF] where topology is preserved. Another approach, capable of handling more interacting shape features through an iterative method is presented in [START_REF] Venkataraman | Reconstruction of feature volumes and feature suppression[END_REF], where form feature recognition techniques are used to detect features face-sets, and then a feature is removed before passing to the next iteration, where previously interfering features can be detected.

In [START_REF] Sunil | An approach to recognize interacting features from B-Rep CAD models of prismatic machined parts using a hybrid (graph and rule based) technique[END_REF] authors again tackle the problem of features interaction through a hybrid approach for feature recognition that is both graph and rule based.

The abovementioned solutions fall in the category of automatic feature recognition. Although such techniques aim at the extraction of functional information given the pure geometric model, they are still limited to a very small set of simple geometric configurations like holes, pockets, slots, rounds and fillets. Most of prior work fits into a bottom-up approach where features are extracted from low level geometric entities and a detached volume model is processed as an isolated entity. Whenever assemblies are referred they are generally regarded as a collection of components processed with loose or no connections at all between them.

In [START_REF] Albert | Contact and Channel Model for Pairs of Working Surfaces[END_REF] authors do not only emphasize the connection between product's geometry and functional attributes, they also demonstrate with concrete examples the correlation between pairs of interfacing geometrical entities and the expected purpose of a product. It shows through industrial case studies how functionality is tightly coupled with the properties of geometrical interactions between surfaces belonging to different components that provide the desired-or even undesired-behavior.

The strong ties between geometry and semantic properties are again brought forward by [START_REF] Mitra | Illustrating how mechanical assemblies work[END_REF] where authors analyze causal kinematic chains of a product based on its tessellated 3D model. A graph representation of product components and their contact characteristic is used to draw conclusions.

Alongside the reasoning process, reduced user input is solicited interactively.

Efforts are also paid to adapt design models to FEA purposes. Specific operations have been provided to handle contact zones generated by either B-Rep CAD models [START_REF] Clark | Conformal assembly meshing with tolerant imprinting[END_REF], or tessellated geometries [START_REF] Chouadria | Identifying and remeshing contact interfaces in a polyhedral assembly for digital mock-up[END_REF], [START_REF] Lou | Merging enriched finite element triangle meshes for fast prototyping of alternate solutions in the context of industrial maintenance[END_REF]. Those operations however didn't show any connection to the functional attributes of a geometric interaction, leaving an open question of how adequate those adaptations are to the simulation process.

Examining the literature shows that though it is possible to recognize some basic manufacturing features by merely considering local geometric properties of components, the detection of more complicated functional properties requires that the geometric model be regarded from a wider angle, that also covers the interaction between different components.

CONTRIBUTION

Approaches to DMUs' simplification still fail short to efficiently transform their geometrical models in a way that meets FEA requirements. This is because components are lacking functional descriptors and the latter are not connected to the geometric model of the components. Our work comes to fill this gap, enriching the plain geometrical representation with functional annotations and connecting them to structured geometric models as a preliminary step of the FEM preparation process. To this end, we develop algorithms that extract some functional and kinematic features from components as they are in Being committed to simulation objectives; this doesn't only imply functional denomination of groups of geometric objects (i.e. components), but also requires a function annotation at different level of details, starting by elementary functions at the level of geometric interactions. This necessitates a restructuration of the original geometry.

Since functionality is attributed to mutual interactions between components and sub-assemblies in a product, the geometrical study of components as standalone objects is not sufficient to infer any functional knowledge. Components should be studied in their working environment instead. In this work we focus on geometrical interactions between components, rather than their isolated shapes.

A physical dimension is attached to those interactions in a qualitative sense to enable a functional behavioral study. This includes information such as internal forces, moments, and relative velocities. Thus, qualitative interactions between components in an assembly are a basis of a reasoning process that contribute to the characterization of components' functionalities as it is frequently operated with design methodologies [START_REF] Albers | Contact and channel modelling to support early design of technical systems[END_REF], [START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF].

ASSEMBLY MODEL ANALYSIS

In this section we give an overview of our approach and briefly describe its central concepts.

FROM GEOMETRY TO FUNCTIONAL

ANNOTATIONS

The input to our algorithm is a pure geometric representation of a product (see Figure 2). We first extract interesting features out of such input; i.e. the geometric interfaces between adjacent components in the assembly.

Next, we enrich the knowledge about the assembly.

To this end, functional information is incorporated into our reasoning process using the domain knowledge of mechanical engineering.

We start with what geometric interfaces suggest; that is a set of functional interpretations. Then, those interpretations are filtered out to associate a unique function to each interface. This is achieved with the introduction of complementary rules to our knowledge base, such as mechanical equilibrium states that hold truth all across the assembly, considering that its components are rigid bodies. More functional information is inferred qualitatively as more states are considered.

After elementary functional information about components in an assembly is gathered, an ontology describing a hierarchy of FDs is invoked. This is used to classify components of the assembly. The ontology connects to a rule-based matching process to deduce FDs of components, and to provide a knowledge repository enabling querying functions. It is now the purpose of the FEM preparation process to take advantage of this information and of the newly structured components models.

MECHANICAL COMPONENTS AND THEIR

REPRESENTATIONS

Mechanical components are meant to deliver welldefined functionalities through their geometric interfaces with their neighboring components. We can define the 'Real shape' of a component C as the real physical shape of C. A DMU is a set of components with 3D shapes. Here, it is hypothesized that these components are solids, i.e. volumes. They are represented using B-Rep models. Those shapes are located in 3D space, either globally, i.e. according to a global coordinate system, or relatively to other components, using geometric constraints. Geometric interfaces between components are not represented explicitly when using global locations, while they are ambiguously defined when using geometric constraints because the surfaces they involve may not belong to geometric interfaces.

DMUs

represent assembly models whose components are hierarchically structured. This tree structure can reflect subsets called sub-assemblies; however, this structure may be absent. Consequently, this hierarchy is not a robust source of information and, hence, it cannot contribute to functional data. Figure 3 depicts an example of a DMU representing an assembly of a centrifugal pump.

Though solids in a DMU are supposed to reflect the shapes of their corresponding components, observations and design practices show the contrary. In fact, designers try to compromise the real shape of C with the speed of the design process, and the adequacy of solids for other stages in a PDP. This leads to the concept of digital shape. A 'Digital shape' of C is a volume model representing C in a DMU. Here, it is simply designated as a shape. Compared to the real shape of C, its shape derives from a simplification process also called idealization. Though real and digital shapes may be almost identical in one case, they may differ significantly in another (see Figure 3). Conventionally, the threaded part of a real component is simplified or idealized into a cylindrical area; see the difference between Figure 3 (a) and Figure 3 (b). Similarly, teeth of spline links are often removed in their digital shapes leading to interfering cylindrical areas. As a result, threaded areas and spline links produce the same geometric interfaces. Consequently, starting from this geometric interfaces leads to two different functional links. This exemplifies the functional interpretations mentioned in the previous section.

Libraries, such as TraceParts [21], collect 3D models of components as generated by components providers. This means that they are not standardized and may differ from each other even if the components are similar. For example, a threaded hole of a bolt with a given nominal diameter may be found in different 3D models having different thread diameters [START_REF] Foucault | What is the Content of a DMU? Analysis and Proposal of Improvements[END_REF].

Using component shapes as a starting point of a DMU analysis can influence the inference of FDs (Section 4.3) of components. Consequently, there is a strong dependency between shape, interface, and functionality of components as pointed out in design methodologies [START_REF] Albers | Contact and channel modelling to support early design of technical systems[END_REF], [START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF].

FUNCTIONAL DESIGNATION

The functional designation of a component is an unambiguous denomination that functionally distinguishes one class of components from another.

The FD decidedly determines the functional group of its component. One component can only have one FD, though it might have more than one function, indicated by the designation itself. As an example, a 'nut' is a designation relating to the threaded link function, a 'locking nut' contains the addition of its locking function.

In this sense FDs constitute equivalence classes that distinctly sort out all components in a DMU.

FDs do not always match the assigned denomination of components in a bill of materials. Since component names are user-defined, it may not be uniform in a DMU and cannot be exploited in the current analysis process, because it is not reliable [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF]. Even though standards exist [24], [START_REF]ISO Technical Committee TC4, Rolling Bearings[END_REF] that focus on threads, bearings, etc., their content contributes to describe standard functions but they are lacking FDs that are mandatory to generate an unambiguous set of component classes.

FUNCTIONAL TAXONOMIES

Different FDs may share a common generalized function. For example, screws are meant to fasten, and gears are expected to transmit moment, etc. As a result, the functional nomination can fit in a hierarchical structure whose leaves are indeed FDs. We call this hierarchy the taxonomy of FDs. Rooted by a label representing all possible mechanical components, the taxonomy increases details about functional properties as one goes deeper in the hierarchy, until a leaf is reached which indicates an unambiguous definition, i.e. a FD that characterizes a component and its set of functions.

Figure 5 shows a small portion of the FD taxonomy, showing the path to the FD of "cap screw", amongst others.

Representing a FD, each leaf of the taxonomy contains a geometric description of the component interfaces, their relative positioning, and their functional properties. Indeed, the FD taxonomy is a high level one. Other, more generic, taxonomies of a lower level are part of the current approach. They refer to functional interface taxonomy and shape interface taxonomy. The former addresses the interfaces between components and suggests possible functions that can be associated. It also establishes a connection between the shape of an interface, its behavior, and its function using dualities between geometry and interaction forces or relative velocities [START_REF] Albers | Contact and channel modelling to support early design of technical systems[END_REF], [START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF]. The latter is purely geometric and connects with the first one, it classifies the geometric interfaces.

CONVENTIONAL INTERFACES

Interactions between adjacent components reveal essential information that guides the identification of functional properties. We refer to such interactions as conventional interfaces (CI).

A CI is a broad concept that captures all aspects of the relationship between two neighboring components in an assembly; it has geometric, physical, and functional properties. The first step in our analysis is to extract geometric properties as the geometric model is our starting point. Once geometric interactions are defined, the goal shifts to providing some physical parameter to eventually enable the mapping of each CI into a unique functional interpretation. For example, our analysis may lead to the conclusion that a CI geometrically described by a cylindrical interference (see Figure 7) transmits forces and moments in all directions, and allows neither translations nor rotations, as show corresponding physical parameters. This allows us to infer that this CI is a threaded link. We call such interpretation a functional interface (FI) (see Section 4.6).

CIs form a central concept in our approach, around which the work can be divided into three distinguishable phases:

1. The geometric analysis to obtain geometric properties of CIs;

2. Physical interpretations of those geometric properties into FIs;

3. The extraction of FDs of components based on the functional properties of their CIs.

These steps will unfold in the following text.

FUNCTIONAL INTERFACE

Functional interpretations of a CI are materialized in function interfaces. As the name reveals, a function interface describes a zone of interaction between two components that is supposed to deliver certain functionality. This is characterized by mechanical and kinematic properties that allow the expected behavior. Examples are planar support, cylindrical support, pivot link, threaded link, etc. This is much similar to concepts used in design methodologies [START_REF] Albers | Contact and channel modelling to support early design of technical systems[END_REF], [START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF], though our current approach is a bottomup one.

GEOMETRIC INTERACTIONS BETWEEN

COMPONENTS

The geometric interaction between two adjacent components determines the geometric properties of their CIs.

Geometric interactions are described by their interaction types and their interaction zones and are stored in the shape interface taxonomy.

The interaction type may be a contact, interference or clearance.

Contact

A contact between two components C1 and C2 defines one or more shared surfaces or shared curves, without any shared volume (see Figure 6).

The interaction zone of a contact is defined by this set of shared surfaces and curves, leading to potential non-manifold configurations.

A contact representation is usually realistic in the sense that a contact in the geometric model reflects the same configuration in the real product, where C1 and C2 are in touch.

Contacts provide very valuable information to our reasoning, as they usually help defining locations where resulting interaction forces can be transmitted. At the same time they work as motion barriers reducing components' degrees of freedom.

When a clearance between C1 and C2 becomes small enough, it may conventionally reduce to a geometric contact as well. Consequently, a cylindrical contact can be functionally interpreted either as a loose fit or a tight fit, as an example. Qualitative reasoning and reference states aim at selecting the correct interpretation.

In some conventions, however, a contact may represent an idealization of more complex settings, like threaded links or gears and rack-pinion links.

Interference

An interference between C1 and C2 defines a shared volume between them (see Figure 6). Obviously, an interference is a non-realistic representation in the sense that the two digital shapes of C1 and C2 interfering in an assembly don't represent overlapping volumes of C1 and C2 in a product, as this leads to non-physical configurations. Nevertheless, interferences are often the result of local shape simplifications often combined with rather complex settings of components' locations. For instance, threaded links most frequently results in cylindrical interference volumes.

Due to their idealized nature, interferences are harder to interpret than contacts; however, they also provide valuable information to the reasoning process.

Clearance

A clearance occurs when a distance between two surfaces of components C1 and C2 conveys a functional meaning (see Figure 6). Clearances can be organised into two categories. A first one is characterized by non-null distances that exist in the assembly model. The second one appears when clearances become small enough, i.e. an adjusted fitting of C1 and C2. There, the clearance is reduced to a geometric contact, as mentioned previously.

The distance value acting as threshold between the two categories is a matter of user's convention.

Clearances of category one depict an interaction zone between sets of surfaces of C1 and C2, this concept relates to functions. Therefore, it is not possible to address such clearances in a first place starting from the mere geometry of components. It is mandatory to have a FD of C1 and/or C2 to be able to determine the surfaces of C1 and/or C2 locating the clearance, e.g. on Figure 6, the clearance is located once the component is identified as a cap screw and then, its shaft can be located. Indeed, the FD of the cap screw structures the geometric model of this component with its FIs. Therefore, the shaft of the screw can be located, hence the location of the clearance. Section 6 shows how the identification of the FD of a component is connected to its shape structure.

Currently, the focus is placed on functional clearances represented as contacts. Consequently, geometric clearances are not addressed here.

REFERENCE STATES

To evolve from pure geometry toward functions, as pointed at Section 4.5, it is mandatory to connect geometric parameters to other physical ones. FIs follow that path. Now, to connect to functions, the principle is to take advantage of the shape-behaviorfunction relationship often quoted in design methodologies [START_REF] Albert | Contact and Channel Model for Pairs of Working Surfaces[END_REF], [START_REF] Albers | Contact and channel modelling to support early design of technical systems[END_REF], [START_REF] Gero | Design prototypes: a knowledge representation schema for design[END_REF] and functional design approaches [START_REF] Roy | Function-to-form mapping: model, representation and applications in design synthesis[END_REF], [START_REF] Roy | Design with part behaviors: behavior model, representation and applications[END_REF].

Referring to the concept of behavior is performed qualitatively using the concept of state of an assembly model. More details about the qualitative reasoning process can be found in [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF]. A state of an assembly describes its physical and qualitative behavior through equilibrium equations. A behavior law is applied to each of its components where each interface is assigned a possible FI. This behavior law helps characterizing the physical objective of the state and dualities between geometry and mechanics are used to set the parameters of this behavior law from the FIs.

Because geometric interfaces can produce several functional interpretations, i.e. several FIs, the purpose of this qualitative reasoning is twofold:

• Filtering out FIs to reduce them to a single one per geometric interface;

• Identifying components contributing to a function.

It is assumed that assembly models input are consistent. To eliminate non-functional solutions, referential behavioral descriptions of a functional product must be available. Those descriptions are grouped in reference states. We have so far identified three reference states; static equilibrium, loads cycles, and kinematic chains.

Static equilibrium

The mechanical reference state assumes that all components are rigid bodies, and that each component of the assembly in hand is at mechanical static equilibrium; that is:

• The vector sum of all external forces is zero, and

• The sum of moments of all external forces around any axis is zero.

This can be otherwise stated as that the mechanical screws applied to all CIs of a component sum up to zero.

! ! /(!,!,!,!) = 0 0 !∈!"{!} (1)
This is because CIs represent all the possible interactions of a component with its environment; thus, exhaustively incorporate all external forces and their moments. Figure 7 shows a zoomed-in cross section in the centrifugal pump's model at the upper part of the shaft. Here, the planar contact between the nut and the washer can only be interpreted as planar support generating force , an opposite force ′ should be generated by the only other CI of the nut, which is the cylindrical interference defining a threaded link to enable static equilibrium. This reasoning leads to eliminate the spline link connection interpretation of this CI because this FI cannot equilibrate the axial force .

Loads cycles

Based on the previous reference state, certain internal load generators can be recognized (such as springs and threaded links). Those internal loads propagate through force cycles in a functionally-coherent model. Detection of internal force cycles is necessary to group components and interfaces in functional groups, where they all together participate to fulfill certain functionality, such as fastening.

In Figure 7, the internal load generated by the threaded link between the nut and the shaft (blue and grey components respectively) is propagated through the washer then the impeller (brown and red respectively), before it bounces back to the shaft, as shown in Figure 4, forming a cycle.

Load cycles are of particular interest for FE analyses since they identify the component subsets that can be submitted to specific geometric transformations when preparing a FEM, e.g. interfaces between plates tightened together in Figure 6 can be assigned friction behavior. This information can significantly help automate the FE preparation process because it structures the assembly model into functional subsets relevant from a FEA point of view.

Kinematic chains

The kinematic reference states also adopt the rigid body assumption, it is based on closed kinematic chains stating that the relative motion between two bodies A, and B equals to the sum of the relative motion between A and C and the relative motion between C and B, given that A, B, and C are rigid bodies, and that relative motions are expressed as rotational and translational velocities with reference to the same coordinate system.

That can be otherwise stated as that the kinematic screws of all CIs forming a closed cycle in the assembly model with respect to the same coordinate system sum up to zero.

Ω ! ! /(!,!,!,!) = 0 0 !∈{! ! ! ! ! !… ! ! } (1)
This is because the relative motion of a rigid body with respect to itself is zero. By arbitrary choosing one component of our closed cycle, and then repeatedly applying Chasles' equation starting by its first two neighbors, until the cycle is closed, we conclude that the sum of relative motions (represented as kinematic screws) equals to the relative motion between the chosen component and itself, that is zero.

Kinematic classes obtained from this state can connect with FEA hypotheses, e.g. to remove interfaces and merge components, to set contact and friction boundary conditions where relative motions are critical.

Besides assumptions related to each reference state, we also set complementary hypotheses that are valid across states and set the scope of our qualitative reasoning.

Model's consistency

Alongside the qualitative reasoning process, we assume the assembly, hence its geometric model, to be consistent from both functional and conceptual points of view. This means:

• All components of the product are held tight together, which in turn leads to the mechanical reference state;

• A component with two non-coplanar planar contacts that share the same orientation (thus parallel) indicates a design defect (a double contact configuration) because the component is rigid and manufacturing tolerances cannot ensure these multiple contacts;

• Apart from the component mobilities forming the kinematic chains of the assembly, all other mobilities, if any, in this assembly should reduce to rotations only. Unjustified translations signal a design defect because they create undesired dynamic effects.

Time invariance

Each of the reference states described above is subjected to their specific hypotheses. However, these hypotheses address the components and/or their CIs as they appear in the assembly model observed. Indeed, this observation contains another implicit hypothesis shared by all the states previously described: all the CIs of the assembly model studied are time invariant. This means the CIs extracted from the geometric model of an assembly stay unchanged during all the states expressing a set of its behaviors.

Considering different states of an assembly (rest configuration or operational state, action of a single component, among others) enriches the qualitative reasoning process. Unfortunately, an assembly model represents only a configuration at a given time, thus creating ambiguities in locating moving parts. To remove such ambiguities, user's inputs are mandatory though they must be as few as possible.

To identify kinematic chains, user's input can be reduced to a relative movement expressing the start/end of a kinematic chain. Then, the qualitative reasoning process propagates this information throughout the assembly to identify the corresponding chain.

BOTTOM-UP APPROACH

Our reasoning follows a bottom-up approach in that we start from a pure geometric model of an assembly with no explicit functional information. Conventional representations of components produce geometric interfaces that initiate the generation of low level functional information, i.e. functional interfaces.

Then, the qualitative reasoning using static equilibrium can address individual components to start reducing the number of FIs per geometric one, wherever applicable. Increasing the extent of interfaces analyzed, functional information is gained using other reference states such as internal loads cycles and kinematic chains. Also, this leads to further eliminations of FIs if applicable. Then, a matching process using inferences takes place to assign FDs to categories of components, whenever possible, from the functional information gained through a range of behaviors analyzed using reference states (see Figure 2). As an example, cap screws can be identified once the static equilibrium and internal load have been evaluated (see Section 5).

IMPLEMENTATION OVERVIEW

As seen before (Figure 2 and Section 4.5), the generation of functional properties is divided into three major tasks, geometric identification, functional interpretation, and matching. In this section, we address some technical details of each of them.

IDENTIFICATION

This first task performs a pure geometric analysis of an assembly model in order to identify adjacent components and define their interfaces to populate the shape interface taxonomy.

As a result, the interfaces between components are organized in a graph data structure called the conventional interface graph (CIG), whose nodes are the components, and whose arcs are CIs. More precisely, at this stage the CIs only contain the geometric model of interfaces (contacts and interferences).

We adopt the STEP file format [START_REF]STEP Part 204: Application protocol: Mechanical design using boundary representation[END_REF], [START_REF]STEP Part 42: Integrated generic resource: Geometric and topological representation[END_REF] as a standardized representation of our geometric model.

Although ISO 10303 proposes annotations to include functional information in STEP [START_REF] Foucault | What is the Content of a DMU? Analysis and Proposal of Improvements[END_REF], the assembly model is considered to be purely geometric since this information is neither reliable nor accurate because it is user defined [START_REF] Mitra | Illustrating how mechanical assemblies work[END_REF], [START_REF] Ullrich | Generative Object Definition and Semantic Recognition[END_REF], [START_REF] Wessel | Learning the Compositional Structure of Man-Made Objects for 3D Shape Retrieval[END_REF].

The software is developed using Open CASCADE development platform [START_REF]Open CASCADE Technology[END_REF] to set up this geometric analysis.

The current approach identifies interfaces based upon canonical surfaces, i.e. planes, cylinders, cones, tori, and spheres. Those surfaces are most frequently used to define functional surfaces forming the FIs. This originates from manufacturing properties where canonical surfaces are easier to machine. Analyzing the geometry of an assembly is currently subjected to complementary hypotheses based on the analysis of industrial DMUs. Assuming that the tolerance of a geometric modeler describing B-Rep volumes in a CAD software is ε.

= ! ! ∈! ! ! ! ∈! ! ! ! ;
where ! ! designates the distance between two points P 1 and P 2 belonging to adjacent boundaries of patches S 1 and S 2 , respectively. An order of magnitude of ε is 0.001mm for an industrial CAD software. Then, hypotheses can be stated and explained as follows:

-Relative positions of components are accurate.

Indeed, it can be observed that the relative location of components can be far less accurate than the accuracy of a geometric modeler. One category of configurations illustrates this fact through Figure 8. There, the rotational relative position of the components forming the spline link exhibit interfering teeth rather than planar contacts. Generally, there is no strict constraint for the designer to set up a precise relative position between these components. If the kinematic chain does not incorporate any rotational indexing function, any approximate angular position is acceptable, which simplifies the task of the designer when setting up the digital model. Other similar configurations can be identified. Compared to ε, these configurations can produce deviations of several tenths of millimeters in magnitude;

-Digital models of components are accurate. This hypothesis derives from the observation that some surfaces of components may not be modeled as accurately as they are manufactured, i.e. the location of some surfaces significantly

Interferring teeth differs from their theoretical nominal position. These inaccuracies can be observed when these surfaces are not explicitly used to monitor a manufacturing process, e.g. teeth of gears can have their profile directly obtained from specific machine tools. Consequently, the tooth profile and/or the rotational symmetry of teeth can be less accurate than ε (see Figure 9). The loss of accuracy can be an order of magnitude greater than ε;

-Digital models of components are homogeneously accurate and accurate at a level smaller or equal to ε. The lack of homogeneity of component accuracy originates from the collaborative design activity often part of product design.

Consequently, several companies using different conventional representations of components can incorporate digital shapes in the same assembly model, which can greatly influence geometric interfaces and illustrates the inhomogeneous accuracy that can be found in some assembly models. Another type of inhomogeneous accuracy originates from the multiple CAD modelers that can produce different component models belonging to the same assembly when several companies take part to a product design. If ε i is the accuracy of one of these modelers, the geometric analysis of an assembly can be performed with = max ! ε ! , ε . However, if > ε, geometric transformations required to produce an FEM need specific operators to robustly adapt component shapes. This issue is kept for future developments, which reduces the current approach to ≤ ε.

Extending the current hypotheses to process industrial assembly models requires specific operators that are out of scope of the present description.

Maximal B-REP surfaces

STEP describes components' geometric models in a Boundary

Representation (B-Rep) format. Unfortunately, a B-Rep encoding of a geometric object is not unique. That is; two STEP files may represent the same shape differently. This is due to the fact that an edge (then called a wire) can be represented as a set of topologically connected smaller edges laying on the same curve. The same applies to faces, where a face can be divided into smaller ones that share the same surfaces and are topologically connected. This phenomenon originates from the component's modeling process where functional surfaces are often broken down into smaller pieces because of the constructive modeling process inherent to industrial CAD modelers. Additionally, geometric modelers are subjected to topological and parameterization constraints [START_REF] Li | Shape Analysis of B-Rep CAD Models to Extract Partial and Global Symmetries[END_REF]. This prevent the boundary decomposition from matching the real boundaries of a component, e.g. a cylindrical surface can be represented either with two half cylinders or a single cylindrical patch whose boundary contains a generatrix that is meaningless because it is not a boundary of the surface on the real component (see Figure 10).

The representation of real surface boundaries is mandatory to obtain a set of geometric entities that is consistent with the properties used in the qualitative reasoning process.

To obtain this representation of a component boundary, adjacent faces that belong to the same canonical surface are merged into one entity; a maximal face. A maximal face is represented by its underlying oriented, topologically connected faces.

Edges are also grouped into maximal edges using the same criterion. As a result, a cylindrical face can end up with a boundary described by two closed edges without vertices. The corresponding data-structure uses hyper-graphs [START_REF] Foucault | Adaptation of CAD model topology for finite element analysis[END_REF].

Geometric analysis

Bounding boxes are used to allow early filtering of non-adjacent solids. The remaining ones are then checked pairwise for geometric interactions.

For each pair, maximal faces of one solid are compared against those of the other. We adopt a simple, yet extensible approach to extract geometric Interferring teeth Original shape interactions, based on the comparison of the geometric parameters of surfaces.

The purpose is to produce the geometric domain describing each shape interface, e.g. a cylindrical contact, or a cylindrical interference. Other categories include planar contact, linear contact, circular contact, conical contact, etc. as organized in the shape interface taxonomy.

Each shape interface is then encapsulated into a CI connecting two components. The result is then structured in the CIG, as the output of this phase.

INTERPRETATION

Following a simple bottom up approach this second phase associates to each CI all possible functional interpretations it may hold. Interpretations are suggested by its geometric interaction properties (shape interface) and derive from the duality between geometry and internal forces and the functional conventional representations chosen. To this end, a thesaurus has been set up that provides the mapping between shape interfaces and their interpretations as FIs.

Once this association is done at the level of CIG, the qualitative reasoning process begins with the help of reference states. So far, there are three, possibly overlapping, analyses to take place, and they complete each other (see Section 4.8). The static equilibrium and kinematic chain analysis eliminate functional interpretations of CIs that are incompatible with either of them. Load cycles structure the CIG to identify the components contributing to a given function. Throughout this reasoning, physical properties are represented as screws. Those screws, however, do not hold scalar values, but qualitative constraints instead. Such constraints are: positive, strictly positive, negative, strictly negative, not null, arbitrary, and one quantitative value that is null, which is also regarded as a constraint [START_REF] Shahwan | Qualitative behavioral reasoning from components' interfaces to components' functions for DMU adaption to FE analyses[END_REF].

Mechanical analysis

For each component, Eq. 1 must hold truth; that is the screws representing all mechanical interactions exterior to the component being studied at all its CIs must sum up to zero. Considering that one CI may be interpreted as more than one FI, thus it has more than one possible mechanical screw. This analysis ends up with Π !!! ! ! different combinations; where is the number of CIs of the underlying component, and

| ! | is the number of functional interpretations of CI i .
For each of those combinations, the algorithm tests the possibility that all mechanical screws, sum up to zero. This study reveals incoherent combinations that are rejected, leading to the elimination of certain function interpretations of a CI; thus reducing | ! |.

Whenever possible, the goal of this analysis is to end up with only one functional interpretation per CI; that is ! = 1. This may not be achieved from the very first iteration on the components. However, the study of one component may lead to the elimination of some interpretations of an interface shared with a previously studied neighboring component. This adds up information that may in turn help eliminating further interpretations if the neighboring component is put to examination again. For this reason, the reasoning process is iterative. A component is checked once it is studied; however, it can be unchecked whenever an interpretation of one of its interfaces is suppressed, thus reducing the number of leaves in the taxonomy of FIs assigned to it. The iterative process stops whenever all assembly components are checked.

Kinematic analysis

This phase builds upon the kinematic reference state to define what we call kinematic equivalence classes.

A kinematic equivalence class (or kinematic class, for short) is a set of components that share the same relative motion; that means that all members of a kinematic class can be regarded as a single rigid body.

The kinematic reference state is based on rigid body kinematics. It addresses closed loops of connections in the CIG. Eq. 2 is used along with kinematic screws that are properties of the functional interpretation to infer components' relative mobilities.

For this reason, a minimal user intervention may be needed, mainly to describe objects' motion after components are classified in kinematic classes. User's input specifically applies to rotational movements where the surfaces of revolution at t and t+dt cannot bring information about whether a rotation exists or not. The kinematic properties help reducing further the number of leaves in the taxonomy of CIs assigned to each component.

Synthesis of functional designations

After the collection of mechanical and kinematic properties of components, and the generation of FIs, load cycles and kinematic classes; this information is integrated all together to deduce the FD of components.

FIs and load cycles are translated into FDs using a matching process based on inferences. A FD ontology describes the mechanical and kinematic properties of each component category. These properties are based on the type and relative positions of the FIs of each component, independently of its dimensions. For example, a component is classified as a "Cap Screw" when it has a threaded link and a planar support whose normal is parallel to the threaded link axis, with at least another planar support parallel to the first one, between the first one and the threaded link and joining two adjacent components. The candidate component should also belong to the same kinematic class as its two adjacent components.

The taxonomies and ontologies required to define FDs, FIs, etc. are set up using Protégé [35] and inferences are expressed with FACT++ reasoner [START_REF] Tsarkov | FaCT++ description logic reasoner: System description[END_REF].

RESULTS

To validate the proposed approach, we use a model of root-joint from the aircraft industry (see Figure 11). This assembly illustrates the wing-fuselage junction.

We also demonstrate algorithm performances using a centrifugal pump model (Figure 4). Those models contain most of the geometric interactions we are concerned about. Table 1 shows execution times for both assemblies. It is to be noticed that geometry loading time is the time that Open CASCADE takes to load the STEP file. This is out of the scope of our work, and no effort is made to enhance this time.

Ontology load time is managed by FaCT++. Network configurations have an impact here, since we use a client-server paradigm. Though this paradigm reduces performances compared to interfacing with a reasoner through its API, it enables high flexibility when choosing the reasoner (Pellet [START_REF] Sirin | Pellet: A practical OWL-DL reasoned[END_REF] has also been successfully tested). Geometric and qualitative analysis are indeed in the core of our interest in this research. Table 1 shows reasonable times considering the models' sizes.

Semantic reasoning is again performed by FaCT++ for the results shown in the table. However, care was taken to keep rules simple, and to minimize client/server communication, in order to speed up this phase of execution.

Figure 11 shows a snapshot of our application, after running the whole execution cycle on the root-joint example. The legend on the top left corner of the window shows detected FDs in the current model, alongside their respective colors in the geometric viewer part of the window.

A cross section into one of the detected bolted joint is shown in Figure 13. This figure also shows a subgraph of the CIG, depicting how the number of FIs was reduced to one per CI using the qualitative reasoning process. Figure 13 also shows load cycles, colored in magenta. Dotted lines refer to parts of the cycle that leads to the detection of a statically undetermined configuration, characterizing a possible function of a nut, i.e. a counter-nut.

Figure 12 shows how the initial geometry of a component gets structured according to its FIs once its FD is deduced (cap-screw in this case). The load cycles and the geometric model restructuring contribute directly to FEA requirements where load cycles help identifying sets of components related to physical phenomena, e.g. tightening effect of a bolt. FIs define how the geometric zones where specific boundary conditions, e.g. friction, contact, etc. can be applied in a FEM. All this information can significantly speed up the preparation process of a FEM.

CONCLUSIONS AND FUTURE WORK

This work is a step towards a semi-automated identification of components FD in a DMU based on their pure geometric description. Simultaneously with the FD, the geometric model of components gets structured based on their geometric interfaces with neighboring components. We also showed some results of the first phases of our work to validate the efficiency of the proposed approach and demonstrate how multiple interpretations can be reduced to unique ones using the mechanical equilibrium state analysis.

The integration of components neighboring interfaces in the inference process has a strong effect over the structure of a geometric model of a component. Starting with mere geometry, and passing through different other physical, parameters, such as mechanical and kinematic assessment, significant functional properties of component interfaces are derived. Then, the inferences referring to the relative position of the interfaces as necessary condition of a component to belong to a FD effectively subdivides the component with low level functional information. Further work covers the insertion of complementary rules and states to identify a larger range of components; keys, bearings, gears are among the components to be addressed. Interfaces between two components that share similar geometrical properties will be grouped to enlarge the range of interface configurations that can be processed. Identifying punctual contacts and those along lines is another extension of the present work that will help cover a larger range of interface configurations. Higher level functional information will be derived to group components contributing to the same functional behavior. Operators will be developed to widen the hypotheses used to process assembly models for geometric interface detection.

Figure 1 A

 1 Figure 1 A complex assembly of an aircraft sub-structure (courtesy EADS IW).

Figure 2

 2 Figure 2 Overall scheme of processes

Figure 3

 3 Figure 3 Difference between real shape and digital shape. (a) Real cap-screw. (b) Digital model of cap-screw with threaded part smoothed out. (c) Cross section in a real ball bearing. (d) Cross section in a simplified ball bearing.

Figure 4

 4 Figure 4 model of centrifugal pump.

Figure 5 A

 5 Figure 5 A subset of functional designation taxonomy.

Figure 6

 6 Figure 6 illustrates different types of geometrical interactions on the example of two plates assembled together by means of a cap screw.

Figure 6

 6 Figure 6 Geometric interactions of a bolt.

Figure 7

 7 Figure 7 Cross section in pump assembly model.

Figure 8

 8 Figure 8 Approximate relative rotational position of components in a spline link (detailed view on the left, global one on the right) (courtesy ANTECIM).

Figure 9

 9 Figure 9 Effect of rotational symmetry inaccuracies. Not all the teeth are interfering whereas the components are exactly coaxial (courtesy ANTECIM).

Figure 10

 10 Figure 10 Effect of maximal faces and edges generation. Patch boundaries are marked with black edges. Initial boundary decomposition (left), boundary decomposition with maximal faces and edges (right) (courtesy ANTECIM).

Figure 11

 11 Figure 11 Model components colored according to theirFDs.

Figure 13

 13 Figure 13 Sub-graph of CIG alongside its corresponding components in a DMU, showing FI elimination and detection of load cycles.

Figure 12

 12 Figure 12 Restructured geometry of a cap-screw

Table 1

 1 Execution time for root joint and pump models.

					Time (m.s.)
	Example	№ Solids	Load	Load	Geometric	Qualitative	Semantic	Total	№ Cont.	№ Interf.
			Geometry	Ontology	Analysis	Analysis	Reasoning
	Root Joint	148	12234	1060	15733	1406	6320	36755	511	90
	Centrifugal Pump	43	5261	2065	7134	7014	2431	23907	139	11

ACKNOWLEDGMENTS

This work is carried out in the framework of the ANR project ROMMA and the authors thank the ANR for its financial support. This work is also supported by the ERC Expressive.


S Bourgois

J Tensi

J Favier

Experimental Investigations on Fluidic Control Over an Airfoil

This study presents the development of two fluidic actuators -namely, microjets and tangential blowing actuator (TBA), designed for flow separation control. The developed actuators are compact enough to fit inside an ONERA D profiled wing with a chord of 0.35 m. Test bench experiments showed that the microjets (resp. TBA) were able to produce exit velocities up to 330 m/s (resp. 60 m/s). These actuators were placed in the model and were tested in wind tunnels for various blowing rates. The investigations included the use of force balance measurements, on-surface flow visualization with pigmented oil, off-surface flow visualizations with smoke, surface pressure distribution measurements, and Particle Image Velocimetry (PIV). Most of the tests were performed at freestream velocities between 20 m/s (for PIV) and 40 m/s, corresponding to Reynolds numbers in the range 0.47x10 6 -0.93x10 6 . The angle of attack varied from -2 to 20 degrees. Experiments were conducted using the naturally occurring laminar boundary layer as well as for a turbulent boundary layer. In such a case, rough strips were used in the vicinity of the leading-edge. The present tests show the efficiency of these devices to delay separation and improve aerodynamic performances of the wing: for example, a maximum of 30% gain in C L has been reached using the microjets. Both actuators tend to increase the lift coefficient C L after stall and areas of separated flow have been eliminated by applying control, as suggested by flow visualizations and PIV velocity fields.

Introduction

In most aerodynamic applications, whether in internal flows such as engine inlets, diffusers, or external flows, such as flow over wings and other control surfaces, the separation of a boundary layer is highly undesirable due to its adverse effect on performances. Consequently, means of preventing boundary layer separation has received a great deal of attention since the beginning of the twentieth century. Various methods have been employed in the past. Mechanical control techniques were the first to be developed because of their simplicity (slats, flaps, mechanical vortex generator…) [1,2]. Acoustic methods have also been experimented, mainly using loudspeakers. The few fluidbased techniques that were examined in the past mainly relied on boundary layer suctionto remove the low momentum boundary layer fluid, or direct tangential blowingto energize it. However, the high mass flow/power requirement for these methods has, to date, made them impractical for most applications. More recently, the development of Micro Electro Mechanical Systems (MEMS) has driven to an important use of pulsed and synthetic blowing micro systems [3,4], piezoresistive actuators [5] and other devices, which provide an energy input to the flow being manipulated.

In this article, fluidic methods were investigated on the wall of an ONERA D airfoil model by means of discrete injectors in order to delay the separation on the upper side of the wing. Two main blowing techniques were successfully tested: the first one, normally to the chord, using small micro jets [6] regularly drilled along a line parallel to the leading edge; the second one, tangentially applied [7] to the surface through a thin slot. The aerodynamic forces (lift and drag) and the mean wall pressure distribution at mid span were measured.

Other investigations include: wall observations (oil film method), visualizations by laser tomoscopy in the vicinity of the actuators (at low Reynolds numbers), and Particle Image Velocimetry (PIV) measurements in the region of separation.

Wind tunnel facilities

The experiments were conducted in the «Béton» wind tunnel (Figure 1 PIV experiments were performed at the IMFT subsonic wind tunnel "S1". The circular test section (2 m of diameter) is opened allowing large access for optical installations. The velocities tested during the study were from 15 m/s to 25 m/s and the rate of turbulence was 0.5%. The loads measurements were performed using an aerodynamic balance located under the wind tunnel test section.

Experimental PIV set up

Particle Image Velocimetry (PIV) was used to measure instantaneous two-dimensional velocity in the streamwise plane normal to the wall at midspan. The flow field was seeded using particles of DEHS, whose typical size is 1µm. The observation of the flow field was made using a 14 bits PCO 2000 CCD camera which was fixed on a rotary table in order to follow the variation of angle of attack of the airfoil. The camera (2048 x 2048 pixels) was equipped with a 85 mm objective lens at a diaphragm aperture of 8.

The laser used was a double-pulsed Nd-YAG laser Quantel (2 x 200 mJ) and the time interval between two flashes was set to 20 µs or 15 µs depending of the velocity upstream.

The system, both camera and laser, was set to operate at a frequency of 10 Hz. The timing between the two flashes and the synchronisation with the camera was controlled with a PC.

The measurements were carried out at midspan in order to observe the flow field all along the chord. Two areas were investigated, one near the leading edge and the other one further downstream, near the trailing edge. For each configuration (angle of attack and Reynolds number) and each area of measurement, 1000 pairs of images were stored, having a spatial resolution of 2048 x2048 pixels with a dynamic of 16000 grey levels.

After windowing, the digitized frame images (2048 x 1400) are analysed by a crosscorrelation algorithm using the software PIVIS developed at the IMFT (Service Signaux et Images). The algorithm is based on a bi-dimensional FFT cross-correlation function implemented in an iterative scheme with a sub-pixel image deformation, according to Lecordier et al. [8]. Furthermore, the flow field was analysed by cross-correlating 50% overlapping windows to satisfy Nyquist's criterion. The images are subdivided into rectangular interrogation windows of size 16 x 16 pixels. By this way, the smallest window is 2.3 x 2.3 mm in a whole field which size is 30 x 30 cm. Particular efforts were made to reach a sufficiently high resolution to be able to see the effects of the microjets near the leading edge. With all these settings, the correlation peaks are good enough and the need for interpolation is minimal after averaging on the 1000 vector fields.

Airfoil model

The two-dimensional ONERA D airfoil model (Figure 3) has the dimensions of 1 m span (L) and 0.35 m chord (C) and was manufactured with epoxy resin. The leading edge of the model consists of a 0.7 m wide removable hollow insert, making possible the installation of the control devices inside the airfoil. The model was mounted to the balance through the tunnel sidewalls by a spanwise-extended steel tube. A row of 41 streamwise pressure taps is located at midspan. The nominal orifice diameter of the pressure taps is 0.5 mm. Seven 6-port pressure conditioners were connected to the pressure taps then, the signal delivered by the conditioners was transmitted to a 12-bit acquisition board to get the surface static pressure readings. Hot-wire measurements showed a 50 mm thick boundary layer thickness on the tunnel wall at the location where the airfoil was tested. Consequently, two side plates were installed on the model to prevent cross-flow. Experiments were conducted using the naturally occurring laminar boundary layer as well as for a turbulent boundary layer. The boundary layer is made turbulent by tripping it using a very thin carborundum strip (roughness diameter 0.3 mm) deposited along a curvilinear coordinate s/C = 1% from the geometrical leading edge.

Actuators design

The microjets

The first actuator which has been experimented is the «microjets» actuator. It consists of (Figure 4 -right):

-82 cylindrical micro holes regularly drilled every 5 mm. Each hole has a diameter 0.4 mm, -two plenum chambers intended for obtaining uniform spanwise output velocities, -flexible plumbing connecting the plenum chambers to the compressed air supply, outside the test section.

The micro holes were drilled at s/C = 2.8%, perpendicularly to the chord. Because of design reasons, the micro holes cover 40% of the wing total span. There is a distance of taps.

A blowing rate momentum C µ is defined in Eq. ( 1) where U∞ is the incoming flow velocity, ρ∞ is air density, Q the flow rate injected through the holes, V j the exit velocity and S ref a reference surface defined by S ref = L x C = 0.35 m 2 .

2 ref j U S 2 1 QV C ∞ ∞ = ρ µ (1)

The tangential blowing actuator

A thin metal plate is installed on the model in order to deviate a jet coming out from a slot perpendicular to the wall (Figure 4).

Consequently, the actuator involves the presence of a small step and a local deformation which has been softened applying modelling clay. The effects of these small discontinuities have been studied by turning off the actuator and by comparing the aerodynamic behaviour of the profile with the baseline model (without actuator). The tangential slot is located at s/C = 8%. The device (Figure 4 -left) is very similar to the microjets actuator and consists of:

two tangential slots, -two plenum chambers, -flexible plumbing connecting each plenum chamber to the compressed air supply through two distributors.

The slots cover 56% of the wing total span. There is a distance of 48 mm between the two slots at midspan because of the presence of the pressure taps.

A characterization of the jet velocities exiting the slots is made through Pitot tube measurements. Obtained velocity profiles are plotted in Figure 5. The mean velocity is found to be approximately 60 m/s on each slot, yet, the plots highlights a nonuniformity of the jets in the spanwise direction. No further improvement of the velocity profiles could have been achieved.

Results

Baseline configuration

Preliminary experiments mainly consist of surface flow visualizations using pigmented linseed oil, pressure and force measurements performed at various freestream velocities, in the range 30 -60 m/s, which corresponds to Reynolds numbers varying between 0.7x10 6 and 1.4x10 6 . For naturally occurring laminar boundary layer (Figure 6 -left):

• The basic wing has a very docile stall at low Reynolds numbers (Re C ≤ 0.93x10 6 ). This type of stall mechanism, called «leading edge long bubble stall» is characterized by the gradual downstream movement of the separated flow region from the leading edge, as the angle of attack increases;

• At higher Reynolds numbers (Re C ≥ 1.17x10 6 ), the wing is characterized by flow separation taking place rather abruptly over the entire top surface of the airfoil when the bubble bursts, with the origin of this separation occurring close to the leading edge: it is called «leading edge short bubble stall».

For tripped boundary layer (see Figure 7 for details on boundary layer tripping), at every Reynolds numbers investigated, stall is very smooth (Figure 6 -right) and C Lmax is decreased due to the presence of the carborundum strips. The corresponding stall angles are increased. Finding a satisfying roughness size to trip the boundary layer is difficult for two reasons: first, separation occurs nearby the leading edge so there is a short distance between the position of the roughness elements and the separation line (and consequently, the boundary layer thickness we are working with is very low); then, there is a negative/favourable pressure gradient which is very inconvenient to force transition.

Nevertheless, carborundum is used because it allows dissociating the effects of control with the effects of transition.

The results of lift measurements are confirmed by on-surface flow visualizations (Figure 8 & 9). Note that flow is coming from the bottom to the top on these figures. Although, this method highlights a spanwise asymmetry of the flow (it is supposed that this dissymmetry is due to the presence of the wall and to the aspect ratio), oil film visualizations also reveal that separation is smoother using the carborundum strips than with the naturally occurring laminar boundary layer. Surface static pressure distributions (Figure 10) are in good agreement with the previous observations. It can be seen that the magnitude of the suction peak increases as the angle of attack is increased, up to an angle of α = 11°. With reference to these data, characterizing the presence of a localized separation bubble is difficult because there is an insufficient number of pressure ports on the model to reveal any flat pressure distribution. The bubble may be highlighted using the oil film method though. It is interesting to note that with one degree change, the suction peak, for the naturally occurring laminar boundary layer case, has decreased drastically, suggesting a stall which is more violent than for the wing with a tripped boundary layer.

Effects of TBA

Although the principle of this actuator is well-know in aerodynamics, the goal of these experiments is to check the possibility for controlling separation on such a profile. Force measurements for the baseline configuration are made on a wing equipped with a disabled actuator in order to quantify the modifications in aerodynamic forces due to the profile alteration resulting from the presence of the actuator; this is made for both laminar and tripped boundary layer.

For the naturally occurring laminar boundary layer (Figure 11), stall is quite abrupt, indicating that the separation point may be positioned by the geometrical singularity.

Applying a 60 m/s tangential blowing causes an increase in the value of C Lmax . The angle of attack for which stall occurs is increased from 11 degrees for the baseline wing to 13 degrees for the case of TBA actuation. Before stall incidence, the use of TBA does not seem to have any significant effect over the drag coefficient. The decrease in drag at angles of attack between 11 and 15 degrees is due to the suppression of the separated region over the wing. For higher angles of attack (α ≥ 15°), TBA produces a drag increase. Remember that these force measurements are made while control is applied on 56% of the wing span:

balance measurements only provide information of the global effects over the wing of a local actuation.

For the tripped boundary layer (Figure 12), the wing still has a docile stall. Applying TBA actuation generates an increase of the C L value when the stall angle of attack is reached. A drag decrease is observed for the same range of angles of attack as for actuation on a naturally occurring laminar boundary layer. Actuation causes an increase in the value of C L after the stall but the gain is less as compared to Figure 11. Flow visualizations (Figure 13) indicate that a reattachment (red arrows) is induced by actuation in the region where blowing is applied; yet, a separated region is still present near the centreline (blue arrows).

Effects of microjets

Force measurements for the baseline configuration are made on a wing equipped with a disabled actuator in order to quantify the modifications in aerodynamic forces due to the presence of the holes; this is made for both laminar and tripped boundary layer.

For the naturally occurring laminar boundary layer (Figure 14), stall is still quite abrupt.

Applying microjets control does not increase the value of C Lmax . Moreover, the angle of attack for which stall occurs is not increased. Yet, microjets actuation maintains the level of the lift coefficient after the stall angle: the gain in C L is about 30% compared to the baseline configuration. Before stall incidence, the use of microjets does not seem to have any significant effect over the drag coefficient. The decrease in drag at angles of attack between 12 and 16 degrees is due to the suppression of the separated region over the wing, as suggested by the wall flow visualizations (Figure 16). For higher angles of attack (α ≥ 15°), microjets produce a drag increase. Remember that these force measurements are made while control is applied on 40% of the wing span. PIV results are in good agreement with these observations. The longitudinal component of the mean velocity field around the wing at an angle of attack of 16 degrees and a Reynolds number of 4.67x10 5 is represented in Figure 18. The shape of the airfoil is plotted on the graphs and the shadow zone represented in black is a roughly 5 mm non-measured zone near the wall. The velocity fields presented here are obtained by averaging 100 vector fields (because of article deadline reasons). For the case of no actuation, the deep blue area representing the negative velocities in the separated boundary layer indicates that the wake of the wing is very large.

On the other hand, for the actuated case, areas of negative velocities have totally disappeared and even there is still a region of low momentum (green areas) near the wall, the flow seems attached over the leading edge. This result confirms not only the microjets efficiency observed by wall visualization up to angles of attack of 14 degrees but for higher angles (here 16 degrees) at least for a Reynolds number of 4.7x10 5 .

For the tripped boundary layer (Figure 15), the wing still has a docile stall. Applying microjets control generates an increase of the C L value for angles of attack higher than the stall angle. A drag decrease is observed for angles of attack higher than 11 degrees.

Actuation causes a sensible increase in the value of C L after the stall but the gain is less important than previously (Figure 14). The separated region over the wing disappears when control is applied, as suggested by the wall flow visualizations (Figure 17). The comparison between Figure 14 and Figure 15 leads us to the conclusion that the effects of the microjets on the boundary layer transition are not negligible; yet, the device seems to be able to control flow separation since the effects on performances is still visible for the tripped boundary layer.

Conclusions

This study presents the development of two fluidic actuators -namely, microjets and tangential blowing actuator (TBA), and demonstrates their effects in the control of flow separation control on an ONERA D profile. Most of the tests were performed at freestream velocities between 20 m/s (for PIV) and 40 m/s, corresponding to Reynolds numbers in the range 0.47x10 6 -0.93x10 6 . The angle of attack was varied from -2 to 20 degrees.

Experiments were conducted using the naturally occurring laminar boundary layer as well as for a turbulent boundary layer. In such a case, rough strips were used in the vicinity of the leading-edge. Results show that both actuators are more efficient in the case of naturally occurring laminar boundary layer: a maximum of 30% gain in C L has been reached using the microjets. A drag decreases is observed for angles of attack in the range 11 -15 degrees. On-surface visualizations and PIV suggest that the separated region is eliminated by the control. Applying actuation on a tripped boundary layer has to a lesser extent, the same effects: the gain in C L is less important but still observable. Future works will deal with a new model based on a NACA 0015 profile and characterized by trailingedge appearing separation. The goal of this study will be to validate the efficiency of these two actuators and to implement new devices based on instationnary excitation (synthetic and pulsed jets). We are also planning more detailed studies with the goal of examining the important parameters that determine the efficiency of control and understanding some of the fundamental mechanisms behind these control techniques.

  ) located at the Laboratoire d'Etudes Aérodynamiques (LEA). The tunnel is of closed-loop type with a 7:1 contraction ratio. The test section is 2.4 m wide by 2.6 m high by 6 m long. The turbulence-reduction devices upstream of the contraction consist of a honeycomb followed by two filters. An axial fan powered by a 250 kW motor is used to drive the tunnel. Speeds of 60 m/s are reachable in the test section with measured turbulence intensities ∞ component of the velocity) of approximately 0.2%. Plexiglas windows are disposed in the test-section ceiling for wall visualizations. In addition, aerodynamic forces are measured by a force balance installed below the test-section floor.

Figure 1 .

 1 Figure 1. The «Béton» wind-tunnel at LEA

Figure 5 .

 5 Figure 5. Velocity profiles at the exits of the slots.

Figure 7 .

 7 Figure 7. Detailed view of the roughness trip used for forcing boundary layer transition.

Figure 8 .

 8 Figure 8. Surface flow visualizations of the baseline wing at Re C = 0.93x10 6 (naturally

Figure 9 .

 9 Figure 9. Surface flow visualizations of the baseline wing at Re C = 0.93x10 6

Figure 10 .

 10 Figure 10. Surface static pressure distribution of text wing at Re C = 0.93x10 6 : naturally

Figure 14 .

 14 Figure 14. Effect of microjets on aerodynamic performance of the wing at Re C = 0.93x10 6 :

Figure 17 .

 17 Figure 17. Surface flow visualizations of the wing with microjets actuation at Re C = 0.93x10 6 (tripped boundary layer). Angle of attack is set to 12 degrees.

Figure 18 .

 18 Figure 18. Mean velocity field over the wing at Re C = 0.93x10 6 : baseline (left) and

Table 1 .

 1 Results of test bench experiments are gathered in Table1, where the blowing rate momentum is calculated for an incoming velocity U∞ = 40 m/s. Characterization of the microjets actuator performance

	Experiment	Plenum chamber	Flow rate Q	Exit velocity
					C µ
	number	pressure P C (bar)	(L/min)	V j (m/s)
	1	1,29	132,50	205,00	0,198%
	2	1,69	199,79	286,47	0,417%
	3	2,11	251,52	313,16	0,574%
	4	2,54	302,18	313,16	0,690%