Am Élie Beauville Dit Eynaud

Nathalie Klement

Lionel Roucoules

Olivier Gibaru

Laurent Durville

Framework for the design and evaluation of a reconfigurable production system based on movable robot integration

Keywords: Reconfigurable manufacturing system, Reconfigurable assembly system, Reconfigurability, Design methodology, Decision tool, Discrete event simulation

Enterprises now face a global, dynamic, and unpredictable economic environment. In response to quick changes of the demand, the production needs to have the ability to adapt rapidly to meet the production requirements. The Reconfigurable Manufacturing System (RMS) paradigm enables such capabilities. However, defining design and reconfiguration rules is highly challenging, as it requires a broad knowledge encompassing the inclusion of technological, production, and economic metrics, as well as an understanding of a reconfiguration strategy, determining the necessary reconfiguration frequency of the system. For now, no global methodology taking all those aspects into account has been proposed. This article presents an original framework for the design, evaluation, and reconfiguration of the Reconfigurable Production System (RPS). New metrics to measure reconfigurability are defined. The design approach consists in three main steps which are individually developed. The selection of the appropriated production system is based on the comparison of reconfigurability and productivity indicators. Finally, the reconfiguration strategy is presented. The methodology is applied on a case study from the automotive industry.

Introduction

The industry faces today a turbulent market. Product demand is hardly predictable, and the quick variations of customer's needs are complex to anticipate. This implies quick product changes and difficulties to cover the demand with a traditional production installation, unable to adjust to unpredicted changes [START_REF] Esmaelian | The evolution and future of manufacturing: a review[END_REF]. The production variety pulled by the market involves both product variety and production volume changes. Volume changes imply an adaptation in terms of volume capacity, while product variety corresponds to an adaptation in terms of functionality of the production system.

In this context, the target is an ideal production system, able to follow changes of the market regarding product Nathalie Klement nathalie.klement@ensam.eu 1 Arts et Metiers Institute of Technology, LISPEN, HESAM Université, 8 boulevard Louis XIV, 59046 Lille, France 2 Groupe PSA, Route de Gisy, 78943 Vélizy-Villacoublay Cedex, France variety and volume, including during the ramp-up phase [START_REF] Glock | Decision support models for production ramp-up: a systematic literature review[END_REF].

Previous manufacturing systems paradigms, namely the Dedicated Manufacturing Systems (DMS) and the Flexible Manufacturing Systems (FMS), were respectively designed to be highly productive to manufacture a single type of product in the case of the DMS and to produce predefined product variants of the same family (FMS). Flexibility is framed by limits defined at the startup of the production system [START_REF] Möller | Bestimmung der Wirtschaftlichkeit wandlungsfähiger Produktionssysteme[END_REF]. Considering volume adaptation, the DMS is designed for a fixed throughput, and a modification of the takt time requires an interruption of the production for a period of weeks or months. FMS enables some flexibility regarding production volume, but only within pre-defined boundaries. Indeed, FMS is adapted to a relatively predictable economic environment. The Reconfigurable Manufacturing System (RMS), a new production system paradigm introduced by Mehrabi and Ulsoy [START_REF] Mehrabi | State-of-the-art in reconfigurable manufacturing systems: Report 2[END_REF] and Koren et al. [START_REF] Koren | Reconfigurable manufacturing systems[END_REF], aims to cover production demand in a turbulent economic environment [START_REF] Möller | Bestimmung der Wirtschaftlichkeit wandlungsfähiger Produktionssysteme[END_REF]. In a similar way, the Reconfigurable Assembly System (RAS) refers to a modular and quickly changeable assembly system [START_REF] Bi | Current status of reconfigurable assembly systems[END_REF].

A glossary is presented at the end of the paper, to summarise those main definitions. This paper focuses on the term RPS, which covers both RMS and RAS [START_REF] Rösiö | Reconfigurable production system design -theoretical and practical challenges[END_REF].

Industry 4.0 encompasses new modelization methods such as Digital Twins, which is a coupling between measured state variables and a model [START_REF] Jiewu | Digital twin-driven rapid reconfiguration of the automated manufacturing system via an open orchitecture model[END_REF][START_REF] Kousi | Digital twin for designing and reconfiguring human-robot collaborative assembly lines[END_REF]. Morgan et al. [START_REF] Morgan | Industry 4.0 smart reconfigurable manufacturing machines[END_REF] present a literature review on Reconfigurable Manufacturing Systems, including Digital Twins. Our position regarding this state of the art is a contribution to the first research question raised, aiming to give a design recommendation for an RPS capable of rapid changes (agile), with increased throughput and decreased cost. However, our approach based on modelling is not a Digital Twin, as there is no feedback loop to a real system. This paper focuses on reconfigurability indicators and RPS Design methods.

Since the initialization of the RMS paradigm, the research area has been widely documented [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF]. The topic reconfigurable system design has been tackled by means of a participatory design method [START_REF] Andersen | A participatory systems design methodology for changeable manufacturing systems[END_REF], from an architectural point of view [9] or using cladistics [START_REF] Hu | Assembly system design and operations for product variety[END_REF]. Complementary to previous works, this paper aims to propose a global methodological framework aiming to support design, evaluation and reconfiguration of RPS by integrating movable robots.

Companies need support through all steps of the implementation of an RPS: identification of reconfigurability level and needs; choice of the right decision level and associated technological bricks; configuration and layout choice; reconfigurability strategy choice. Companies' awareness regarding flexibility and reconfigurability increased in the last years. Nevertheless, there is still a need in guiding enterprises in order to ensure acceptance of new paradigms and recognition on long-term return on investment [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF]. Furthermore, Glock and Grosse [START_REF] Glock | Decision support models for production ramp-up: a systematic literature review[END_REF] underline the lack of consideration of interlinked problems covering capacity investment and resource assignment and performance measurement.

RPS paradigm is part of Industry 4.0, and belongs to Smart manufacturing systems [START_REF] Qu | Smart manufacturing systems: state of the art and future trends[END_REF], and is enabled through new technologies, such as Cyber Physical Systems, collaborative robotics, Automated Guided Vehicles (AGVs) [START_REF] Dit Eynaud | UML based reconfiguration rate analysis of assembly line depending on robot integration[END_REF][START_REF] Cohen | Assembly systems in industry 4.0 era: a road map to understand assembly 4.0[END_REF], and Mobile Robotic Platforms for manufacturing and assembly [START_REF] Gkournelos | Model based reconfiguration of flexible production systems[END_REF][START_REF] Kousi | Digital twin for designing and reconfiguring human-robot collaborative assembly lines[END_REF]. However, considering the current state of development of these technologies, and the lack of safety regulations to cover human-machine collaboration, it is not possible to implement them today for mass production. This is why the study is based on the hypothesis of technological maturity of aforementioned bricks implying security, safety norms, vision systems, mobile platforms, and a global development implying a decreased price of this new type of equipment.

Figure 1 illustrates the objective of the design approach introduced in this paper. The initial situation is an actual system which is either highly productive, but fixed (robotic cell), or very flexible and reconfigurable but less productive (human worker). The objective is a reconfigurable system which will enable to have a system with both capabilities: productivity and reconfigurability. For now, this figure is qualitative. Indicators presented in this paper will enable to reproduce this figure in a quantitative manner, to prove the contribution of our proposal.

After an analysis of relevant literature in Section 2, new reconfigurability metrics are presented in Section 3. Section 4 describes the original design approach, which is divided into three main steps. The best setting of the production system is selected based on reconfigurability, productivity and cost indicators. Section 5 deals with the application of the methodology on a case study from the automotive industry. This paper ends with a conclusion and a proposal for future research in Section 6.

Literature review

Since introduction of the concept of reconfigurable manufacturing in the 1990s by Sethi [START_REF] Sethi | Flexibility in manufacturing: A survey[END_REF] and Mehrabi and Ulsoy [START_REF] Mehrabi | State-of-the-art in reconfigurable manufacturing systems: Report 2[END_REF], RPS principles have been broadened to different topics: design, control, planning, etc. For the definition of a Fig. 1 Actual situation (left) and reconfigurable system (right) design approach of a reconfigurable system, it is necessary to review the literature on reconfigurability characteristics, design techniques of reconfigurable systems, reconfigurability assessment criteria and reconfiguration strategies.

RPS characteristics

Flexibility is defined as the characteristic of a fixed system having intrinsic changeable abilities (technology or software) to adjust to various planned and predefined product variants. Beyond flexibility, a RPS is composed of standardized sub-entities enabling rapid production change in terms of volume or product type [START_REF] Mehrabi | Reconfigurable manufacturing systems: Key to future manufacturing[END_REF]. It is enabled thanks to production system structure changes. The system can be improved and transformed instead of being replaced [START_REF] Mehrabi | Reconfigurable manufacturing systems: Key to future manufacturing[END_REF]. Finally, the objective is to provide a system able to fulfill desired functionalities or production capacities at the desired moment [START_REF] Benama | Framework definition for the design of a mobile manufacturing system[END_REF].

Koren [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF] identified six characteristics of reconfigurability, namely convertibility, scalability, customization, modularity, integrability, and diagnosability. The first three are critical reconfiguration characteristics, meaning that they were identified as key characteristics enabling transformability properties of the production line, and the last three allow rapid reconfiguration, but do not guarantee changeability as presented in Fig. 2 [START_REF] Koren | Design of reconfigurable manufacturing systems[END_REF]. Convertibility refers to the ability of the system to change easily between functionalities in order to respond to new needs; scalability is the capacity to rearrange the current production system in order to increment or reduce the production volume; customization is the ability to adjust the system in order to meet new requirements within a particular product family; modularity is the fragmentation of functionalities into production system units that can be rearranged during production changes and combined in multiple ways; integrability is the ability to integrate quickly and easily production elements within the system enabled by physical and software interfaces; and diagnosability refers to the capacity to diagnose as soon as possible quality failures and their root causes on the production line, which is a critical point especially during the ramp-up phase [15,[START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF]. An empirical study conducted by Maganha et al. [START_REF] Maganha | Understanding reconfigurability of manufacturing systems: an empirical analysis[END_REF] among more than a hundred of Portuguese companies proved that customization and adaptability characteristics of reconfigurability have a higher level of implementation than modularity, integrability and diagnosability, that are less known or considered yet.

RPS design

Designing production systems able to cope with uncertainty is one of the main challenges, with consideration of requirements needed for transforming the system during early design phases [START_REF] Tolio | The paradigm of pitstop manufacturing[END_REF].

DMS design and RPS design have some common steps: needs specification, functional design, physical design and detailed process design [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF]9]. However, the difference between both lies in the necessity, in a turbulent environment, to take into account the lifespan of the production system on long term, and of the current and future product portfolio.

When designing a production system, two approaches are practicable: design from a blank page or transformation of an existing production system. The first situation enables more freedom concerning resources and layout, while the transformation of a dedicated system into a reconfigurable production line implies limits in terms of compatibility of the new equipment with former installations and control systems.

RMS design has been investigated in the last years. Andersen et al. present in [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF] a systematic design method for the flexible and reconfigurable manufacturing line, further developped in [START_REF] Napoleone | Towards an industry-applicable design methodology for developing reconfigurable manufacturing[END_REF] . The general methodology is divided in five main steps. Before the design, it is important to have a long-term view on the lifespan of the production system and on the planned investments in mind. The first step is strategic planning, which deliverable is the development plan. The procedure for this first step includes financial optimization, analytic hierarchy processing aiming qualitative analysis of the reconfigurable solution in terms of reactivity, costs, etc. After the project plan has been defined, the next stage is the clarification of the design task, with a focus on identifying requirements and drivers for the RMS. This stage delivers requirements specification, which enables the basic design of the production system. During this step, product families are identified, and the degree and type of reconfigurability are defined. Basic design is then followed by advanced design, where production system modules are developed in detail; this encompasses the definition of system interfaces, tools, and the control system. After managing design specifications, the implementation of the system, followed by line startup, can begin. The main focus during this last fifth phase is risk analysis. In addition, during the entire lifespan of the RMS, the system may be reconfigured if changes in functionality or capacity are required. The reconfiguration may be a reiteration of the steps of the design phase.

In an other way, Mesa et al. [START_REF] Mesa | A methodology to define a reconfigurable system architecture for a compact heat exchanger assembly machine[END_REF], Haddou Benderbal et al. [START_REF] Haddou-Benderball | Modularity assessment in reconfigurable manufacturing systems (rms) design: an archived multi-objective simulated annealing-based approach[END_REF], Saliba et al. [START_REF] Saliba | A heuristic approach to module synthesis in the design of reconfigurable manufacturing systems[END_REF], and Gauss et al. [START_REF] Gauss | Module-based machinery design: a method to support the design of modular machine families for reconfigurables manufacturing systems[END_REF] propose each an RMS design methodology based on the evaluation of a modularity criterion.

However, despite the consideration of reconfigurability and modularity in early design phases of the production system, these methods do not take into account the other characteristics of reconfigurability defined by [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF], as well as the implementation of tools needed to apply the proposed models. Those point are a strong limit in the stand-alone application of these methods in the industry.

Reconfigurability evaluation

In order to support RPS design and evaluation, companies are seeking a set of indicators in order to measure the flexibility and reconfigurability level of their facilities and machines [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF][START_REF] Rösiö | Towards an assessment criterion of reconfigurable manufacturing systems within the automotive industry[END_REF].

While Key Performance Indicators (KPIs) of production systems are widely documented, there is no consensus yet on the definition of reconfigurability indicators. Researchers do not agree on a metric to measure reconfigurability.

According to Andersen et al. [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF], there have been some attempts to measure reconfiguration difficulty in terms of cost, time and effort [54]. Huettemann et al. [START_REF] Huettemann | Adaptation of reconfigurable manufacturing systems for industrial assembly ? review of flexibility paradigms, concepts, and outlook[END_REF] define evaluation criteria of the RMS according to the production level (segment, line, workstation) and the field (technical resources, organization, and control). These criteria correspond to resource use rates, production throughput, and therefore could be categorized into performance indicators more than indicators concerning system changeability. Mittal et al. [START_REF] Mittal | Impact of reconfiguration effort on reconfigurable manufacturing system[END_REF] evaluate reconfiguration complexity using a unique indicator, named reconfiguration effort, computed by means of the number of modules needed to add or changed in the production system to realize the transformation. It supports product sequence choice, when the product arrival order has a direct impact on equipment reconfiguration.

Reconfigurability indicators calculation methods can be classified into direct techniques, including the measure of the range of products or volume range covered by a system, and indirect techniques, like the performance measure of the system on different volume scenarios [START_REF] Kapitanov | A study of reconfigurable production system performance[END_REF][START_REF] Wang | Design principles of scalable reconfigurable manufacturing systems[END_REF][START_REF] Weyrich | Simulation of an automotive supplier plant towards designing optimally flexible manufacturing systems. In: 21st International conference on production research ICPR21 innovation in product and production 54[END_REF]. Among direct techniques, Hasan et al. develop a complexity metric, computing the level of part complexity based on sequence and shape features [START_REF] Hasan | Incorporation of part complexity into system scalability for flexible/reconfigurable systems[END_REF]. The authors link the needed scalability of the system with the obtained complexity level. These are quantitative models, but some qualitative models are also discussed. Rösiö et al. propose to evaluate the characteristics of reconfigurability defined by Koren [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF] on a four-values scale ranging from 0 to 1, by inviting experts to qualitatively judge the level of their company on each characteristic [START_REF] Rösiö | Towards an assessment criterion of reconfigurable manufacturing systems within the automotive industry[END_REF].

Based on the characteristics defined by Koren [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF], Wang et al. [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF] propose a mathematical model to assess quantitatively the six characteristics of reconfigurability. The value computed for each characteristic depends on the configuration of the considered production system, the number of modules to add and replace, the time needed for reconfiguration, etc. Compared to the qualitative method proposed by Rösiö et al. [START_REF] Rösiö | Towards an assessment criterion of reconfigurable manufacturing systems within the automotive industry[END_REF], this quantitative assessment of reconfigurability criteria is more precise. This model is therefore very promising. However, it was defined for a manufacturing system composed of Computerized Numerical Control (CNC) machines, so it has to be adapted in order to be used in the case of an assembly system.

In a literature review on RMS, Bortolini et al. [START_REF] Bortolini | Reconfigurable manufacturing systems: Literature review and research trend[END_REF] underline following research directions in the field of RMS: development of an objective-based reconfigurability index able to outperform current subjective evaluation approaches, and a generic method to assess reconfigurability in various industries.

Reconfiguration strategy

After RPS design iteration, the production system is adapted to the current market demand. In order for the system to be optimised in the long run to customer demand in terms of volume and product variability, consecutive reconfigurations will be needed. The ability to notify when a reconfiguration is needed has been underlined [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF]. Indeed, a determined reconfiguration trigger is required which is the starting point for next reconfiguration. Andersen et al. [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF] highlight the necessity to define a method in order to be able to be aware of the need for transformation during the system's lifetime. According to the authors of [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF] and [START_REF] Maganha | The layout design in reconfigurable manufacturing systems: a literature review[END_REF], defining a way to express the need for reconfigurability through a metric should be considered in future works.

Brunoe et al. [START_REF] Brunoe | Reconfigurable manufacturing systems in small and medium enterprises[END_REF] address a notion of reconfiguration frequency, which is supposed to be shorter (on every-day basis) in small-medium enterprises (SMEs) than in large companies (monthly basis). The reason suggested by the authors is that production volumes are higher in large companies than in SMEs. Nevertheless, even if this article is one of the few to address the question of the reconfiguration frequency, it is not sufficient in order to define a strategy.

In an other way, Garbie [START_REF] Garbie | A methodology for the reconfiguration process in manufacturing systems[END_REF] defines not a frequency but a new indicator, named the Needed Reconfiguration Level (NRL), to guide the reconfiguration decision. Above a threshold value of the NRL, the production system should be transformed in order to meet requirements of the market demand. If reconfiguration is necessary, the method described can be followed in order to determine which modifications should be added. This paper is interesting because it brings a first answer regarding a reconfiguration strategy based on a metric. The drawback of the method is the complexity to implement it. Indeed, some metrics let a lot of liberty and flexibility, which raises the question of robustness of the procedure. Furthermore, intermediate calculations are tedious which restrains a regular use of them. The reconfiguration methodology based on the NRL is decomposed into 30 steps. This can be a drawback when deploying the method in an industrial context.

Boucher et al. [START_REF] Boucher | Towards reconfigurable digitalized and servitized manufacturing systems: Conceptual framework[END_REF] identify a four-level tooled methodological framework for reconfigurability management and the successive decision steps for reconfiguration. At each level, aided-decision tools are needed, aiming a life-cycle management of RPS through uncertainty management. Further research needs identified by the authors are the necessity of a tool box for reconfigurability management, covered by this article, and uncertainty modelling and assessment, addressed in [START_REF] Dit Eynaud | Risk and decision analysis for reconfigurable assembly system design under uncertainties[END_REF].

The state of the art on reconfiguration strategy proves that companies lack a reconfiguration method for their production system based on a precise and case-specific metric. However, two strategies can be identified for the production manager to have the information when to reconfigure the production line: either based on a predefined reconfiguration frequency, or based on a metric which triggers a reconfiguration when the threshold value is reached.

Discussion of the literature review

Methods

In the literature dealing with reconfigurable production system design, it has been identified that no global methodology with practically applicable procedure has been proposed yet. Despite the analysis of the literature brought some interesting insights in the field of RPS design rules, no aid decision tool could be identified. A need for a methodology providing an aided decision tool with quantitative metrics associated to a methodology and a reconfiguration strategy, supported by a case application, has been detected. This paper presents in Section 4 a methodology aiming to fulfill this need.

Reconfigurability metrics

What concerns metrics and characteristics, productivity and costs are well-defined in the industry. Regarding criteriabased reconfigurability evaluation, [START_REF] Rösiö | Towards an assessment criterion of reconfigurable manufacturing systems within the automotive industry[END_REF] and [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF] works are very promising. The idea of the first paper to define a value for reconfigurability will be kept and enhanced by quantitative calculations, inspired by the mathematical model proposed by the second paper.

Metrics will support the decision maker regarding the choice for the implementation of a technology and a configuration of the assembly line. To do so, indicators have to be defined. To cover productivity as well as changeability properties, reconfigurability indicators have been defined. Section 3 describes the used performance indicators and investments which will be depicted on the dashboard of the aid decision tool.

Reconfigurability characteristics

In order to guide the decision maker regarding easiness to transform the production system, reconfigurability indicators are required. As described in Section 2.3, indicators provided in the literature were not satisfying regarding both precision and applicability for an assembly line case. Based on the metrics defined by Wang et al. [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF], we propose four new indicators to compute the scalability, the modularity, the integrability, and the customization. The formula to compute convertibility has not been changed, as it is already adapted to calculate the convertibility level of RAS.

Only diagnosability, the sixth reconfigurability characteristic defined by Wang et al. [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF], has not been kept for reconfigurability measurement in this study. Diagnosability is not a critical enabler for reconfiguration and is mainly influenced by the technology exploited for detection and diagnosis and the number of diagnostic equipment on the line [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF][START_REF] Napoleone | Core characteristics of reconfigurability and their influencing elements[END_REF]. In the proposed approach, diagnosis equipment is not considered and not included in models and simulations.

Scalability

Wang and Koren define the scalability as the smallest incremental capacity of the system [START_REF] Wang | Design principles of scalable reconfigurable manufacturing systems[END_REF]. However, this definition does not consider the time and the cost needed for the reconfiguration. As underlined by Cerqueus et al. [START_REF] Cerqueus | Reconfigurable manufacturing systems: From design to implementation, series in advanced manufacturing[END_REF], if a production system is scalable, then reconfigurations are quick, incremental and cost-effective. Thus, our goal was to develop a metric which covers those three aspects. The main challenge is the ratio Time to reconfigure/Takt time, which varies a lot between a fixed system and a reconfigurable system. The same issue occurred for the definition of the customization indicator. The model developed to compute the scalability level S of the assembly system is described by the multiplication of a factor expressing the reconfigurability span and the size of the adjustment gradient in terms of volume changeability of the production system, a time and a cost parameter, and an adjustment parameter representing the number of system modules added. The model is developed for a minimum to maximum evolution in terms of volume through reconfigurations, which explains why only the number of added workstations is considered.

Scalability is decomposed into following parameters: λ T , λ C , and α i , defined by Eqs. 1, 2, and 3, respectively. In following expressions, T cycle is the cycle time after reconfiguration, T reconf is the reconfiguration time needed to perform reconfiguration step Δ, C c is the construction cost of the complete construction instead of reconfiguration, C r is the reconfiguration cost, N r is the number of resources added during reconfiguration and N is the number of resources before reconfiguration. Finally, Eq. 4 computes the scalability value.

λ T = 1 + 0.1 ln T cycle T reconf ( 1
)
λ C = 1 - C r C c (2) α = N r N (3)
Finally,

S = Δ max -Δ min Δ i λ T λ C α i (4)
A higher scalability indicator S indicates a higher capacity incrementation of the assembly system.

Convertibility

Convertibility is defined as the capability to quickly shift to the production of a different product, within a same product family or between product families [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF]. Convertibility is calculated by the computation of convertibility within a product family, that is to say between product variants, and convertibility between product families. Weights ω 1 and ω 2 for the convertibility within a product family and between product families are both set to 0.5.

Wang et al. [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF] defined two separated indicators for convertibility within and between product families. Indeed, the cost of convertibility depends on the difference between products. C 1 , defined by Eq. 5, is the convertibility of the system within a family. N p the number of product types in the product family, 2N p -1 is the number of conversions between products, N t the number of resources that need tool change.

C 1 = 2N p -1 N t ( 5
)
S c , defined by Eq. 6, is the similarity coefficient between product families. C 2 , defined by Eq. 7, is the convertibility coefficient between product families, and N w the number of workstations that need to be added or removed for the conversion between product families.

S c = n ij x i + y i + n ij (6)
N ij : number of workstations used for both products i and j x i : number of workstations for product i only y i : number of workstations for product j only

C 2 = S c N w ( 7
)
The formula for the calculation of convertibility for the whole production system is presented in Eq. 8.

C v = ω 1 2N p -1 N t + ω 2 S c N w (8)
A higher convertibility indicator C v indicates a higher capacity of conversion between products of the assembly system.

Modularity

Modularity evaluates the capacity of the system to be split into modules and to integrate them. Equation 9 presents the calculation of system modularity, where G i is the granularity of the ith workstation, where N ij is the count of interfaces at the j th modular division of the ith workstation, N kl is the count of interfaces at the line level module after conversion k, G k is the granularity of conversion k, and ω 1 and ω 2 are the weightings of the workstation modularity and reconfiguration modularity (in this study arbitrarily set to 0.5).

M = ω 1 G i N ij + ω 2 G k N kl (9)
A higher modularity M denotes a higher modular capacity of the assembly system.

The values for the granularity of the workstation and of the reconfiguration are defined in Tables 1 and2. G i and G k range from 0 to 1. Regarding the workstation granularity value, a deeper level in the factory implies a higher granularity value. Concerning the reconfiguration granularity value, the more we zoom regarding the size of the reconfigured element, the higher G k is.

Integrability

Integrability is the ability to add components to the manufacturing system using adapted interfaces. We define integrability by means of Eqs. 10, 11, and 12, where P is the number of workstations, N i the number of modules in the ith workstation, ω 1 and ω 2 are the weightings of the physical equipment and programming adjustment parameters (set to 0.5), T h j is the equipment installation and set-up time, and T s j is the software installation and set-up time of the j th module of the ith workstation.

α j = -0.1 ln(T h j ) + 1 ( 10
)
β j = -0.08 ln(T s j ) + 1 (11)
I = P i=1 N i j =1
(ω 1 α j + ω 2 β j ) (

A higher integrability I denotes a higher capacity of the production system to integrate system components. I ranges between 0 and 1.

Customization

Customization describes the ability to convert between products thanks to the selection of system components [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF]. The mathematical model to quantitatively measure customization C m is presented in Eq. 13, where P is number of product types in the family, T cycle the cycle time, T reconf the reconfiguration time, N i the number of workstations used for the ith product, and N the overall number of workstations in the system.

C m = 1 + 0.1 ln T cycle T reconf P i=1 1 P N i N (13)
A higher customization C m denotes a higher ability of the production system to convert between product types.

Display of the reconfigurability indicators

Presented formula enable assessment and comparison of various technologies regarding reconfigurability, based on dimensionless criteria. Results can be normalized and presented on a radar diagram. Wang et al. [START_REF] Wang | Reconfiguration schemes evaluation based on preference ranking of key characteristics of reconfigurable manufacturing systems[END_REF] and Beauville et al. [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF] proposed an Analytic Hierarchy Process (AHP)based evaluation of reconfigurability characteristics weight. This enables to weight reconfigurability characteristics according to their relative importance and to present results on a radar diagram. This may help the decision maker for the assessment of the system and comparison between several equipment solutions.

Weighting of reconfigurability characteristics also enables to merge the six indicators into one. This way, we obtain a reconfigurability indicator aggregating the six dimensions of changeability which enables to compute a single value for the reconfigurability.

Conclusion

Reconfigurability indicators have been defined to serve design and setting of a reconfigurable production system. A comparison with indicators from the literature is presented in Table 3. Previous works developed criteria which were qualitative, or quantitative and performance-based or based on the reconfigurability characteristics defined by [START_REF] Koren | Reconfigurable manufacturing and beyond[END_REF], but only suitable for RMS. Proposed quantitative reconfigurability indicators cover a field which has not been handled by the literature before. Driven by the identified need regarding a global methodology for RPS design, and based on already existing methods [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF] presented in Section 2.2, we propose a design procedure which will be detailed in this section. This approach aims to support the industry when designing an assembly line in a long-term investment strategy in a turbulent economic environment. The method supports either design from the blank page or resource addition to an already existing production line.

Based on the analysis of previous literature, our design methodology for the RPS, presented Fig. 3, is divided into 4 steps [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF]: reconfigurability needs identification and design task definition, technological choice and system modelling, configuration assessment through simulation, and at last regular system reconfiguration. Each step is detailed in the following sections.

Changeability needs identification

In order to define needs regarding reconfigurability, the first step of the design method is the identification of company needs. Planning the initial infrastructure for reconfigurability and scalability is crucial, to save space and to have a reconfigurable production system architecture for adding equipment [START_REF] Koren | Value creation through design for scalability of reconfigurable manufacturing systems[END_REF]. Design of the reconfigurable assembly line will be defined by identification of requirements concerning future potential economic market changes [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF]. For this prospective step, Andersen et al. [START_REF] Andersen | A participatory systems design methodology for changeable manufacturing systems[END_REF] apply a questionnaire submitted to experts and decision makers within the investigated companies. Several meetings were required to discuss reasons for reconfigurability motivation within the studied company. Questions were precise and divided into sections, depending if the subject was product, production, facility, or technology. The aim was, through the questionnaire, to specify changeability requirements and to determine the relevant manufacturing system paradigm. In a similar way, Maganha et al. [START_REF] Maganha | Understanding reconfigurability of manufacturing systems: an empirical analysis[END_REF] complete a survey to explore perception of reconfigurability within companies. Results gave information on the level of flexibility and reconfigurability of their production system and on the future actions they plan in this direction.

Based on the two previous works, the questionnaire used in this study partially reuses questions from [START_REF] Andersen | A participatory systems design methodology for changeable manufacturing systems[END_REF] and [START_REF] Maganha | Understanding reconfigurability of manufacturing systems: an empirical analysis[END_REF]. Answers are either evaluated on a Likert scale or are open-ended questions and concern product characteristics, process and facility characteristics [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF]. The aim, through this field study based on a questionnaire, is to open the discussion and raise awareness of the needed changeability capacity of the production system [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF]. This approach enables to collect valuable information about Fig. 3 SADT Diagram of the design approach reconfigurability development chances within the factory. This depends on the similarity between products assembled on the same line, on the sequencing of products before input on the line, precedences between assembly tasks, on the economical context, and on equipment costs.

At this stage, we mainly collect two types of information: what are the requirements for RPS design, and what are the current enablers and limits regarding reconfigurability within the facility. Specification of needs for a RPS and current limitations caused by facility characteristics, architecture and resources are collected.

After changeability needs identification, a first draft of relevant technological solutions, depending on the production system characteristics and architecture in the case of RPS design from an existing production system, is ready. This provides the needs specification for the modelling of the future production line.

System modelling

From the needs identified in the first step, required technological bricks are identified. The choice of the technical solution to implement reconfigurability on the line will then feed a simulation. The production system needs to be modelled in order to build a discrete event simulation model. By running experiments on the model, KPI will be measured. In parallel, the amount of investment and reconfigurability indicators of the assembly line can be computed.

From the analysis of the literature regarding reconfigurable production systems and of the technological maturity of Factory of the future concepts, relevant technological bricks are determined. The adopted principle is to propose for RPS design a limited solution domain. That is to say, we do not have the ambition to create new technical solutions, but to propose to pick a solution among a limited set of technologies. The user selects among a general set the resources to implement and test through the design approach.

Identified technological bricks which will be proposed for RPS design cover three axis: the way of transporting the product through the factory, modularity and standardization of workstations and machines, and mobility of resources. The first corresponds to the study of product flow, which can be serial, parallel, or hybrid [START_REF] Wang | Design principles of scalable reconfigurable manufacturing systems[END_REF]. Modularity of workstations concerns the workstation level, resource level, and tool level. The third axis can be implemented through the use of an AGV, not only to transport the product, but also to relocate a resource. But as the AGV may not be relevant in the cases where reconfiguration do not occur at a high frequency, it may be enough to place the resource on a movable trolley. Either with the aforementioned mobile or movable solution, resource mobility on the production line is enhanced. For each use case, the paradigm for the reconfigurable assembly line must be determined through the field analysis and technological bricks accordingly selected.

The Discrete Event Simulation (DES) model is developed according to the assembly sequence of the future reconfigurable line. Simulation enables to test scenarios at a low cost and deduce implications for the real production system and allows to vary parameters that may not be manageable in real life [START_REF] Fishman | Discrete-event simulation: Modeling, programming, and analysis[END_REF].

DES provides statistical insights on system's performance and gives information on the dynamic behaviour of the system on a determined structural state of the system [START_REF] Albrecht | Planning and optimization of changeable production systems by applying an integrated system dynamic and discrete event simulation approach[END_REF]. This is why several models are needed in order to assess different technologies.

Simulation requires a model of the production line containing all relevant data: workstations, tasks and their durations, precedencies, resources and failure rates, layout. Failure rates of machines are completed from data measured in factories. The objects in the simulation are represented by activities or servers depending on the used software, resources and product data. The model should correctly represent time and processes. The running time is the time period corresponding to the next planning horizon.

In this second step of the design methodology, as the technological bricks and their number are defined, it is possible to compute the amount of investments for the configuration of the RPS.

Manufacturing resources investments reflect the purchased resources. Worker costs are not represented as it is complex to represent on the same scale investments and running costs like workers' salary, energy cost of the production line, etc.

To be able to compare technical solutions on a financial criteria, investments are be depicted as function of time. The goal is to highlight the difference between a very early investment and acquisition of the resources at the right time when it is needed. The cost is required by decision makers to compare a new solution with the existing one regarding return on investment ratio.

Configuration determination

For the third step of the design approach, the DES model is used to assess the system in terms of productivity.

The objective is, through the selected performance criteria, to measure the efficiency of the designed production system.

Selected Key Performance Indicators are the number of assembled products within the simulated time interval, lead time, and machine/resource use rate, which depicts the nonuse time due to forced shutdown, breakdown and waiting time. Manufacturers are familiar with these metrics as these are the same as the ones used in production.

The proposed aid decision tool underlines the articulation between performance criteria, reconfigurability criteria, simulation. Charts are represented on a dashboard which serves the choice based on a compromise between ability to reconfigure, performance of the system and price of the solution. For the simulation model, a scenario corresponds to a product mix ratio and a volume, in the range of sales prediction uncertainty. By comparing provided data, the decision makers is able to choose between different technical solutions.

For the implementation of mobile resources, it is necessary to allocate resources to workstations through an optimization method, minimizing the makespan (total time to finish all jobs). Exact methods are employed to find an exact solution to small size problems, while approached methods, like heuristic algorithms, should be used for non-deterministic polynomial time problems (NPhard problems). To assess a solution provided by the algorithm, setup parameters can be used as input of the simulation model. After a simulation run, performance parameters of the configuration are obtained and can feed as input the optimization model. Hashemi et al. [START_REF] Hashemi Petroodi | Simulation-based optimization approach with scenario-based product sequence in a reconfigurable manufacturing system (rms): a case study[END_REF] deals with the coupling between optimization and simulation mentioned in step A3 of the approach presented Fig. 3.

In conclusion, after the third step, the decision maker obtains an optimised setting solution of the studied production line.

System reconfiguration

The state of the art presented Section 2.4 demonstrates a lack of methods to measure the right reconfiguration period.

We distinguish two main reconfiguration strategies: frequency based strategies and metric-based strategies. In the first situation, independently of the economic context, the production system settings will be verified at a predefined frequency. In the second way, the decline of a metric above a threshold, highlighting the system's incapability to fulfill market's needs, will generate a reconfiguration. The company may tolerate a deviation for a short period of time, and decide to launch a reconfiguration if the critic situation lasts.

We recommend to adopt the metric-based reconfiguration strategy. However, to choose the right threshold value and the allowed time window may be complex. The reconfiguration strategy is case-specific and is to be determined after discussion with experts and decision makers from the studied enterprise.

Case study

The developed methodology has been applied to an industrial case from the French automotive industry. The ability to transform the production system is particularly relevant in this type of industry, where market changes can occur quickly due to political and environmental regulations, seasonality, and are sensitive to the economic health of countries.

The investigated production scenario is presented Fig. 4. We study the ramp-up of an engine assembly line, composed of twenty workstations, for the two first years of production. The ability to react to strong volume changes will be investigated in this scenario. Depending on the targeted volume, the number of resources will have to be updated quickly to avoid non-fulfilment of the market demand. In this case study, chosen assumption is to build the new assembly system from a blank page, instead of adapting the old system.

Design approach

The four steps of design approach presented in Section 3 are applied on the industrial use case.

Changeability needs identification

The first stage corresponds to the changeability needs identification and design task definition. During a field analysis, eight experts coming from various fields of the investigated company have been interviewed individually [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF].

Answers highlighted expectations for an increasing number of product variants and volume uncertainty over the next years, justifying the need to have a more reconfigurable and flexible assembly system. Besides, a lack of expansion capability of the current assembly lines has been reported. Some factories are already fully charged and can not cover the increasing market demand. Interviewed also mentioned a deficiency concerning aging automatons that Fig. 4 Ramp-up scenario of the demand lack in standard architectures, interfaces and programming languages in order to integrate easily and rapidly new equipment. On the other side, the field study reported that the presence of some manual workstations on the assembly line will enable the introduction of light collaborative robots to increase the efficiency of these workstations. The line is already flexible, as different types of product variants within the same product family are assembled and AGVs are used for the transport of product kits, also increasing the flexibility of the plant. After this analysis, it seems that the case company is familiar with the FMS paradigm and now needs to increase the reconfigurability ability of the assembly line. Detailed results of the field study are presented in [START_REF] Dit Eynaud | Identification of reconfigurability enablers and weighting of reconfigurability characteristics based on a case study[END_REF].

Technical features choice and system modelling

Previous section enlightened a need to improve the ability to increment the production capacity and the system's modularity. This statement oriented the choice to a modular solution with quick plug and produce capability. As conclusion of step 1, and based on the bricks identified in Section 4.2, the relevant technological brick to implement is the movable robot. The movable robot is not dynamically mobile during a production shift, but it is placed on a easily movable trolley which position can be changed between workstations. For a first analysis, we will only analyze the relevance of implementing movable robots on the line. To do so, an assembly system with fixed resources will be compared to an assembly system where lightweight collaborative robots can be easily moved between workstations by means of a trolley.

After selection of the technological feature to be implemented, its reconfigurability characteristics are computed and compared to the current production system (Fig. 5). The actual assembly line, a combination of both special machines and fixed robots, is compared to the solution based on movable robots. Reconfigurability characteristics of special machines and fixed robots are very close. The analysis of the reconfigurability based on the five indicators presented in Section 3 highlights that building the same assembly line with movable robots in place of fixed robots or special machines will increase significantly all reconfigurability metrics. Especially, the scalability and the modularity of the system are improved. This result is consistent with the fact that the movable robot consist in a module, easily plug-and-play on the production line. The reconfiguration time is shortened and increases the ability to increment the system in capacity.

Configuration determination

The pilot assembly line is modeled using the DES software Simul8 2019 Version 26.0 Build 3677.

The objective of the third stage of the approach is to measure the performance of the system depending on the evolution of the market demand. The twenty assembly stations of the engine assembly line are simulated. Each workstation is composed of several tasks requiring resources. For example, Fig. 6 presents the precedence diagram of tasks in workstation 2 and Table 4 presents In Simul8 environment, each task is modeled as an Activity, and buffers between workstations as Queues with a maximal filling rate of 1 product. The Mean Time Between Failures (MTBF) follows a normal distribution with a mean of 7450 min and a standard deviation of 200 min, and the Mean Time To Repair (MTTR) follows a normal distribution with mean of 2 min and a standard deviation of 0.5 min. Those values are based on measured breakdowns on the company's assembly lines. Table 5 summarizes experimental factors (inputs) and results (outputs) of the simulation.

Figure 7 plots the resource utilization rate from month 5 (time when the first robot is introduced in the reconfigurable model) to month 12 for the fixed system and the reconfigurable system with movable resources. In average, the resource utilization rate is higher for the RAS than for the fixed system, and the reconfigurable system uses less resources. This is better, because purchased resources should be used at their maximal rate if possible, in order to have the shortest return on investment. In addition, reconfigurability indicators are strongly better when integrating movable robots, which indicates that future reconfigurations will be conducted with less effort, and investments are three times lower. By means of all these indicators, decision makers will prefer the RPS for this use case.

Reconfiguration strategy

The reconfiguration trigger has been defined after discussion with experts of the use case company. The threshold has been fixed to a resource use rate of 95 %. In a rampup phase, when this limit is reached, a resource should be added on the production floor.

Based on this rule, movable resources were added one by one when required. Figure 8 is a schema of the reconfigurable line a the beginning of the ramp-up (a) and after 24 months at the end of the ramp-up scenario (b).

The reconfiguration strategy adopted in a scenario of decrease of the demand also relies on the use rate of resources. The degree of acceptance is a minimum of a 80% load, and a duration of maximum 3 months under 80%. Practically, if a resource is charged less than 80 % of its capacity beyond 3 months during a phase of volume decrease, this resource can be removed from the assembly line.

Discussion

Taking into account changeability requirements at early stages of the design process significantly increases chances to achieve a high level of reconfigurability potential.

Figure 9 displays the amount of investments for the fixed system and the reconfigurable system obtained by application of the proposed design approach. On the graph, the relative costs concerning the fixed system and the RPS are represented, as well as the relative operating costs, which corresponds to the workers' salary (same for both systems). Actual production starts at t = 0. Two aspects are noticeable: for the RPS, investments are lower and are carried out at the latest. The solution proposed by application of the method enables adaptation of the system regarding its volume capacity. On the studied ramp-up scenarios, movable resources are integrated on the assembly line at the right time.

The design approach covers design, evaluation and reconfiguration of reconfigurable assembly systems. Figure 1 depicts qualitatively the target of the approach.

Thanks to the developed indicators and performance measures obtained by simulation, we are able to display this graph with the results of the method. Figure 10 compares, after running the two-years scenario, the actual fixed system and the proposed reconfigurable system for the assembly line of the case study. The abscissa is a measure of the reconfigurability, calculated as the sum of the scalability, convertibility, modularity, integrability and customization. On the ordinate, the capacity utilization is plotted, as ratio of the market demand over the installed capacity. As long as the market demand is fulfilled, the equipment rate will be less than or equal to 1. This metric, relevant in the case of volume reconfigurability, is equal to 1 if the system is able to adapt in terms of volume to the production demand exactly in real-time without excess. In practice, in this case study, the capacity utilization will never reach the value 1. Indeed, the structure of the assembly tasks sequence and tasks allocation between workers and robots imply that resources are not used at 100% of their capacity. However, the revision of the assembly sequence is not in the scope of our study.

Figure 10 enables a simplified rating of the system on only two parameters. The development of the method and associated tool aims at covering the identified need

Conclusion and future works

This article presents a new framework for the design and evaluation of a reconfigurable assembly line, based on previous literature. The methodology was applied successfully on a use case from the automotive industry, consisting in a production line of twenty workstations. To provide comparison between technologies and layouts for companies, new reconfigurability metrics were defined. Solutions are compared on the basis of reconfigurability, productivity and investments. For the presented use case, the method leads to savings, with a higher use rate of resources and a more accurate investment timing. In addition, the overall system has a higher reconfigurability rate, facilitating future changes.

To enhance the comprehensiveness of the score given to a configuration of the production system, an interesting suggestion would be to integrate a maturity indicator of technologies enabling reconfigurability. Indeed, the changeability potential is considerably improved by integration of new agile technological bricks, and the success of the solution in a real production environment strongly depends on the robustness of the solution. As we do not have enough hindsight on technologies involving collaborative robotics, mobile entities and modular production systems, the integration of a maturity indicator could temper the very good results of changing a traditional production system into a reconfigurable one.

After the study of a scenario with volume reconfigurability, the methodology will be applied on a production scenario involving different product types. In parallel, links between modules of the approach (reconfigurability assessment tool, simulation model, dashboard) will be developed, in order to achieve a semi-automatic procedure for the design of a reconfigurable manufacturing system. Simulation-based multi-objectives optimisation could be used to explore the best near-optimal pareto solutions among all scenarios that we could investigate [START_REF] Barrera-Diaz | Simulation-based multi-objective optimization for reconfigrable manufacturing system configurations analysis[END_REF]. In addition, further research would be required to enhance the modelization of the RPS in order to achieve a Digital Twin coupling. Scenarios would be played in the Digital Twin model, and the best solution as a compromise of reconfigurability, productivity and investments could be implemented. The outcome would be a possibility to achieve RPS reconfiguration through an information flow going from the digital model to the production line. The methodology can also be applied on use cases from other industries.

Glossary

DMS :

The Dedicated Manufacturing System is designed to be highly productive to manufacture a specific type of product at a high, fixed throughput by means of automation and fixed manufacturing facilities [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF].

FMS :

The Flexible Manufacturing System is designed to produce a pre-defined range of products variants, using intrinsic hardware or software capabilities [START_REF] Andersen | Towards a generic design method for reconfigurable manufacturing systems[END_REF][START_REF] Möller | Bestimmung der Wirtschaftlichkeit wandlungsfähiger Produktionssysteme[END_REF].

RMS :

The Reconfigurable Manufacturing System aims to cover production demand in a turbulent economic environment, by means of rapid structure changes of the system. The RMS is made of modular sub-entities (hardware and software components), that can be quickly and easily rearranged or replaced [START_REF] Koren | Reconfigurable manufacturing systems[END_REF][START_REF] Mehrabi | State-of-the-art in reconfigurable manufacturing systems: Report 2[END_REF][START_REF] Möller | Bestimmung der Wirtschaftlichkeit wandlungsfähiger Produktionssysteme[END_REF].

RAS :

The Reconfigurable Assembly System refers to a modular and quickly changeable assembly system [START_REF] Bi | Current status of reconfigurable assembly systems[END_REF].

The term is similar to RMS but refers to assembly lines instead of manufacturing centers.

RPS :

The Reconfigurable Production System is a generic term grouping RMS and RAS definitions.

Fig. 2

 2 Fig. 2 Reconfigurability characteristics (critical enablers and enablers for rapid reconfiguration)

Fig. 5 Fig. 6

 56 Fig. 5 Evaluated reconfigurability characteristics

Fig. 7 Fig. 8 Fig. 9 Fig. 10

 78910 Fig.[START_REF] Dit Eynaud | Risk and decision analysis for reconfigurable assembly system design under uncertainties[END_REF] Robots utilization rates for the fixed system (above) and the reconfigurable system (below)

Table 1

 1 Workstation granularity values

	Modular division	Value for G i
	None	0
	Workstation	0.3
	Resource	0.5
	Tool	0.7
	Tool module	0.9

Table 2

 2 Reconfiguration granularity values

	Modular division	Value for G k
	None	0
	Network	0.2
	Product flow	0.4
	Modular line	0.6
	Resource change	0.8
	Tool change	1

Table 3

 3 Reconfigurability indicators comparison

	Reference	Qualitative	Quantitative	Performance-based	Based on reconfigurabil-
					ity characteristics

Table 4

 4

	List of tasks
	(workstation 2)	Station	Task	Relative durations	Precedences
		2	2 . 1	1
		2	2.2	5.6	2.1
		2	2.3	1.9	2.2
		2	2.4	3.8	2.3
		2	2.5	1	2.4
		2	2.6	1.1	2.4
		2	2.7	3.8	2.5 ; 2.6
		2	2.8	1.5	2.7

Table 5

 5 Summary of experimental factors and outputs

	Experimental factor	Output
	Task sequence	Throughput
	Machine breakdowns	Resource use rate
	Product inter-arrival time	Lead time

RMS RAS[54] X X [27] X X X X [40] X X [46] X X X X [51] X X X This paper X X X X

Acknowledgements This document is the result of a research project which took place in the framework of the OpenLab 'Materials and Processes' combining ENSAM network, GeorgiaTech Lorraine and Groupe PSA.

Data availability Data is available on request from the authors.

Code availability

Code is available on request from the authors.

Declarations

Conflict of interest The authors declare no competing interests.

Author contribution Amélie Beauville dit Eynaud carried out the experiment. Amélie Beauville dit Eynaud wrote the manuscript with support from Nathalie Klement and Lionel Roucoules. Olivier Gibaru and Laurent Durville supervised the project.

Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


domain: spi phys

text:
J Reynaud
email: jolan.reynaud@onera.frpierre-elie.weiss@onera.fr

P.-E Weiss

S Deck

ON THE USE OF BI-SPECIES ZDES FOR MULTI-NOZZLES SPACE LAUNCHER CONFIGURATIONS

In order to study the unsteady flows occurring in the wake of space launchers, numerical models have to provide an accurate description of both the turbulent behaviour of base flows and the thermodynamic properties of the multi-species and reactive propulsive jets. As the complexity of models dedicated to each of these objectives can have a significant impact on computational cost, especially for reusable designs including several nozzles, authors have often to establish a compromise between an accurate treatment of turbulence and the taking into account of chemistry effects. To contribute to the improvement of launcher base flow predictions, this paper presents the study of a four-nozzle space launcher configuration with a dedicated numerical workflow focusing on the treatment of turbulence. Indeed, such a case has only been studied with RANS approaches so far, and is treated here with the automatic mode of the Zonal Detached Eddy Simulation (ZDES Mode 2 2020) and hybrid numerical methods, based on Ducros' sensor and allowing to resolve well the turbulent fluctuations of the base flow while capturing the strong normal shock structures inside the jets. The computations are furthermore performed thanks to inert bi-species numerical methods enabling to take into account some thermodynamic properties of the jets with an acceptable computational cost. The bi-species scale resolving numerical workflow is able to reproduce the main features of multi-jets afterbody flows and provides a satisfying agreement with experimental pressure measurements. Compared with RANS calculations, the use of ZDES not only gives access to additional information regarding the unsteadiness of the flow but also provides distinct predictions of the mean aerodynamic field.

Introduction

To support the development of multi-nozzles reusable launcher designs, the accurate prediction of afterbody flows occurring behind the base and around the nozzles during flight is of primary importance to assess the aerodynamic performance and the integrity of the vehicles. Indeed, the reactive multi-gas interactions occurring between the hot propulsive jets and the base flow can induce adverse phenomena such as base drag, due to the low pressure recirculation zone forming behind the base, pressure loads which may damage mechanical structures and base heating linked to the recirculation of hot gases towards the base. As a result of this complexity, the aerodynamic design of new generation launcher afterbody remains a challenge for both experimental and numerical tools.

Focusing on numerical approaches, two main conclusions can be drawn from the literature. First, the need to resolve the large scale turbulent eddies driving the dynamics of base flows in order to perform accurate predictions of the wake flow topology and wall pressure levels has been well documented on generic space launcher configurations (Reynaud et al. 2021a[START_REF] Statnikov | Experimental and numerical investigations of the turbulent wake flow of a generic space launcher at M∞= 3 and M∞= 6[END_REF]). RANS approaches have indeed been shown to have limited capacities to reproduce such massively separated flows whereas RANS/LES approaches, combined with low dissipative numerical schemes, have displayed a good cost/accuracy compromise [START_REF] Pain | Zonal Detached Eddy Simulation of the Flow Around a Simplified Launcher Afterbody[END_REF]. Then, authors such as [START_REF] Gusman | Best Practices for CFD simulations of launch vehicle ascent with plumesoverflow perspective 49th[END_REF]) have shown the need to take into account the thermodynamic properties of the hot reactive propulsive jets to increase the representativeness of space launcher simulations. As the computational cost of both RANS/LES approaches and multispecies reactive flow models is important, authors have often to establish a compromise between an accurate treatment of turbulence and the taking into account of chemistry effects.

Regarding wind tunnel experiments, only few studies have been dedicated to multi-nozzles space launcher configuration with hot propulsive jets [START_REF] Mehta | Base heating sensitivity study for a 4-cluster rocket motor configuration in supersonic freestream[END_REF]). Among them, the case of a four-JP4/LOX-nozzle space launcher configuration studied experimentally in [START_REF] Musial | Base flow characteristics for several four-clustered rocket configurations at mach numbers from 2.0 to 3[END_REF]) is considered as a reference case and has been treated numerically by several authors. These studies (Mehta et al. 2013, Pu and[START_REF] Pu | Assessing Turbulence Models on the Simulation of Launch Vehicle Base Heating[END_REF], which employed advanced thermodynamic models but only used RANS models for turbulence modelling, have provided useful analyses of the flow field but have reported noticeable errors in the evaluation of wall pressure levels.

To contribute to the study of launcher base flow prediction methods, this paper presents a numerical study of the four-nozzle space launcher configuration with a scale resolving framework based on the use of a simple two-species physical model and hybrid numerical methods to allow for an affordable ZDES mode 2 (2020) [START_REF] Deck | Towards an enhanced protection of attached boundary layers in hybrid RANS/LES methods[END_REF] computation. The results will be compared with a two-species RANS computation and with RANS computations including chemistry effects from the literature in order to investigate the benefits of a scale resolving approach for multi-nozzle afterbody computations.

In this article, we first describe the test case and the features of the numerical framework used for the bi-species ZDES and RANS computations. We then characterize the launcher wake flow thanks to instantaneous and mean flow visualizations. In particular, the focus is put on the resulting wall pressure distribution on the base and on the nozzles of the launcher.

Test case and mesh setup

The present study is based on a wind tunnel experiment provided by Musial and Ward, the geometry of the model for this study is shown in Fig. 1. It consists of a four-nozzle subscale rocket model with parameters such as r b = 152.4 mm, L n /D e = 1.53, and D s /D e = 1.67. The four rocket engines operate with a propulsive mixture combining JP-4 as a fuel and LOX as an oxidizer. The selected test flow conditions, corresponding to a flight altitude of 14.9 km, are summarized in Table .1 together with the total pressure P c and total temperature T c inside the combustion chamber. These test conditions correspond to underexpanded jets with an exit Jet Pressure Ratio (JPR=3.4) [START_REF] Mehta | Base heating sensitivity study for a 4-cluster rocket motor configuration in supersonic freestream[END_REF]. The wind tunnel model was instrumented with pressure transducers and temperature probes on its base.

As shown in Fig. 2b a structured mesh has been designed by including one secondary O-H topology for each nozzle in a main O-H topology built around the launcher body. The radial point distribution shown in Fig. 2a is designed in order to ensure Δy + ≈ 1 for every attached boundary layers and to cluster points in the mixing layer forming behind the main body base. With 240 points in the azimuthal direction (Δθ = 1.5 • ) the mesh contains 55.6×10 6 cells overall. 3 Computational set-up

Two-species model

To study the 4 nozzle launcher configuration, an implicit finite volume formulation of the two-species Navier-Stokes equations, presented in [START_REF] Reynaud | Towards Binary Gas Mixture ZDES for Space Launcher Base Flow[END_REF] is used. This approach enables to define the propulsive gas mixture and the surrounding air as two perfect gases. To provide adequate properties for the propulsive mixture, JP-4/LOX equilibrium flow data from [START_REF] Huff | Theoretical performance of JP-4 fuel and liquid oxygen as a rocket propellant II: equilibrium composition NACA Technical report[END_REF]) are used to define constant values for the Sutherland's law constants [μ 0j ,S j ,T 0j ], the specific heat ratio γ j , the volume constant heat ratio c vj and the Prandtl number P r j of the jets gas (see Tab.2). The turbulent Schmidt number is chosen as 0.5 for the mixing between air and the propulsive mixture.

μ0 j (N.s/m 2 ) 1.85.10 -5 T0 j (K) 370 Sj (K) 168 γj 1.224 cv j (J/kg) 1997.5 P rj 0.78
Table 2: Properties of the perfect gas simulating a JP4/LOX mixture

Turbulence modelling and numerical scheme

The RANS computation is performed with the Spalart-Allmaras turbulence model [START_REF] Spalart | A one-equation turbulence model for aerodynamic flows[END_REF]) and an AUSM+ scheme (Liou 1996) for convective fluxes. As this scheme is too dissipative for scale resolving computations, the numerical fluxes for the ZDES computation are evaluated thanks to a hybrid numerical scheme (Reynaud et al. 2021a) built to switch from the AUSM+ scheme in presence of shocks to a low dissipative AUSM+(P) formulation [START_REF] Mary | Large Eddy Simulation of Flow Around an Airfoil Near Stall[END_REF]) in vortical regions. The time step for the ZDES computations is Δt CF D = 2.10 -7 s which enables to ensure that CF L < 6 in the base flow mixing layer. As the vortex shedding period linked to the base diameter was estimated to be T s = 2 * r b 0.2 * U∞ ≈ 1.6 ms, a period of 32 ms= 20 × T s was adopted to clear the flow from transient effect before using a 80 ms ≈ 50 × T s period to compute statistics.

Results

Flow topology

The instantaneous visualisation of the wake flow shown in Fig. 3a enables to observe that the main body boundary layer separates at the base and rolls up into azimuthal vortices to form a mixing layer which bends towards the launcher axis under the effect of an expansion wave. As displayed in the instantaneous pressure field shown in Fig. 3b, a realignment shock forms as the bended flow meets with the propulsive jets boundaries and induces an adverse pressure gradient on the outer side of the jet boundaries. Looking at the underexpanded propulsive jets, we observe that in coherence with results from (Mehta et al. 2013, Pu and 3b that in addition to the azimuthal vortices issuing from the base, the mixing process between the jets engender the formation of a wide variety of turbulent structures in the inter-nozzle area.

The time averaged topology of the base flow results from the combination of the two adverse pressure gradients previously mentioned. We compare in the following the average flow fields obtained with RANS and ZDES computations. First, looking at a longitudinal plane containing two nozzles (Fig. 4a), one can observe the formation of a recirculation zone on the outer side of the nozzles. This recirculation zone interacts with the propulsive jets which entrain the external flow through a mixing layer. This entrainment effect appears stronger in the RANS computation as the recirculation bubble reattaches closer to the nozzle exit than in the ZDES computation. This first flow pattern corresponds to the one usually observed for axisymmetric base flow with a single nozzle (Reynaud et al. 2021a[START_REF] Statnikov | Experimental and numerical investigations of the turbulent wake flow of a generic space launcher at M∞= 3 and M∞= 6[END_REF]). In the present case of 4 propulsive nozzles, additional flow interactions occur. Indeed, due to the impingement between the supersonic propulsive jets, the fluid located between the nozzles is subject to a strong adverse pressure gradient that leads to a reverse flow heading towards the base. We note that the RANS computation provides a higher reverse velocity than the ZDES one. This reverse flow impacts the base and induces the formation of radial wall jets. In a plane containing nozzles, these wall jets will be deflected as they go around a nozzle and part of the reverse flow will regain a positive longitudinal velocity. In a plane located between the nozzles (see Fig. 4b), these wall jets will flow towards the base outer radius and feed the external recirculation zone. In such a plane, the prediction of the recirculation zone topology again differs between the two computations as the S-A model predicts a center position of the recirculation closer from the base than ZDES. Notwithstanding some local differences, the two bi-species computations are able to reproduce the main flow features of a 4-nozzle launcher wake flow [START_REF] Mehta | Base heating sensitivity study for a 4-cluster rocket motor configuration in supersonic freestream[END_REF].

To investigate further the interaction between the propulsive jets and the base flow, the average distribution of the propulsive mixture mass fraction (Y fuel ) in the afterbody area is displayed on Fig. 5. One can note that the RANS computation predicts a much intense mixing between the two gases than the ZDES one. This is shown by the greater predicted growth rate of the jet external mixing layer and by Y fuel levels in the inter-nozzle area nearly twice as high as those found with ZDES. Such discrepancies in the amount of hot propulsive gases flowing back to the base area can be attributed to the strong influence of the turbulent Schmidt number on RANS mixing prediction [START_REF] Reynaud | Towards Binary Gas Mixture ZDES for Space Launcher Base Flow[END_REF] and is expected to induce differences in base temperature predictions. One can indeed observe in Fig. 6 that the RANS computation predicts higher base temperature levels and a wider high temperature zone. Due to the absence of chemistry effects and to the use of adiabatic wall boundary conditions, both computations overestimate the temperature ratio T T c = 0.55 measured experimentally at the center of the base.

Base pressure distribution

To assess the present computations, data from the base pressure experimental probes are used together with RANS results from two studies found in the literature. First, [START_REF] Mehta | Base heating sensitivity study for a 4-cluster rocket motor configuration in supersonic freestream[END_REF]) performed computations with different levels of physical modelling for the propulsive jets; a frozen flow computation (Me1) where the propulsive mixture is considered as a perfect gas with a fixed γ j =1.15 (value corresponding to chamber conditions); a variable γ j computation (Me2) where γ j is a function of temperature and a reactive computation (Me3) where the propulsive gas is modelled as a 10 species mixture and chemical reactions are taken into account. Then, in (Pu and Jiang 2019) several RANS models were tested to perform reactive computations.

Looking at base pressure coefficient distributions displayed in Fig. 7, results from (Metha et al. 2013) showed that, with the Menter BSL RANS model, the use of the simplest physical model (Me1) surprisingly provided the best predictions for base pressure levels as both the variable γ j computation (Me2) and the reactive computation (Me3) lead to a significant underestimation of base pressure levels in comparison with experimental data. The same magnitude of error is found in [START_REF] Pu | Assessing Turbulence Models on the Simulation of Launch Vehicle Base Heating[END_REF] as shown here with the predictions obtained with the RNG turbulence model (Pu RNG), which provided the best results in their study. One can furthermore observe that all of the mentioned RANS computations are unable to reproduce the almost flat pressure profile found experimen-tally as they induce an overestimation of the pressure difference occurring between the center of the base and the outer radius. These discrepancies motivate the use of more advanced turbulence modelling such as the ZDES approach used here. Focusing on base pressure coefficient distributions obtained with the present computations, one can note that the use of an equilibrium flow hypothesis in the nozzles (with γ j =1.224) provides predictions coherent with numerical results from the literature, in between the frozen flow computation and the computations including chemistry effects. The use of ZDES improves predictions in comparison with RANS as it enables to recover a flat pressure profile and higher pressure levels near the outer radius. These disparities can be linked to the previously observed differences in the topology of the recirculation zone.

Nozzle pressure distribution

The evolution of the pressure coefficient (Cp) along generatrix lines located at different angular locations (outer position (OUT), inner position (IN) and side positions (SIDE)) on a nozzle external wall is displayed in Fig. 8 and reveals further deviations between the RANS and the ZDES computations. Indeed, the use of ZDES provides relatively flat Cp profiles (close to Cp = -0.065) on every position around the nozzle whereas the RANS calculation predicts noticeable pressure axial variations for each location around the nozzle and a substantial pressure gap between the inner position and the outer position. Each turbulence modelling approach would thus lead to different estimations of the pressure loads used to study the mechanical behaviour of the nozzles. Based on previous numerical results obtained on launcher configurations with a single nozzle [START_REF] Pain | Zonal Detached Eddy Simulation of the Flow Around a Simplified Launcher Afterbody[END_REF], Reynaud et al.2021b) one can note that the ZDES predictions are used to be more representative than the RANS ones.

To complete the study of side-loads with consideration for the unsteadiness of the flow, the ZDES computation enables to investigate the evolution of the fluctuating pressure coefficient along the nozzles in Fig. 9. The overall increase of fluctuating pressure levels in the direction of the flow observed with the present computation is in coherence with previous RANS/LES results and experimental measurements described in [START_REF] Statnikov | Experimental and numerical investigations of the turbulent wake flow of a generic space launcher at M∞= 3 and M∞= 6[END_REF]) on a launcher with one nozzle placed in an external flow at M ∞ = 3. The computed fluctuations levels are furthermore in the same range as the one displayed in [START_REF] Statnikov | Experimental and numerical investigations of the turbulent wake flow of a generic space launcher at M∞= 3 and M∞= 6[END_REF] with Cp rms ∈ [0.0015, 0.01]. Important differences are however observed depending on the angular position. Indeed, the inner side of the nozzle is subject to pressure fluctuations twice as high as the outer side. These higher fluctuations levels can be related to the large amount of turbulent structures observed earlier in the inter-nozzle area. To investigate the benefits of a scale resolving approach for multi-nozzle afterbody computations, a bispecies numerical workflow based on the combination of the ZDES Mode 2 (2020) and hybrid numerical methods has been applied to a 4-nozzle launcher configuration. The workflow appears as a promising tool able to reproduce the main flow features occur-ring in the wake of a 4 nozzle space launcher and to provide quantitative estimations of the resulting mean and fluctuating loads. In comparison with RANS computations, ZDES provides significant differences in the prediction of base flow topology, gas composition near the base and wall pressure distributions. These encouraging results should motivate further numerical studies combining the resolution of the large eddies forming in the wake of the launcher with more advanced thermodynamic models but also advocates for the realisation of more detailed wind tunnel experiments including hot propulsive jets and unsteady measurements.

Figure 1 :

 1 Figure 1: Schematic view of the 4 nozzle launcher geometry (from (Pu and Jiang 2019))

  (a) Distribution of longitudinal velocity and streamtraces in a plane containing the nozzles. (b) Distribution of longitudinal velocity and streamtraces in a plane between the nozzles

Figure 4 :

 4 Figure 4: Average velocity distribution in the wake of the launcher

Figure 5 :

 5 Figure 5: Distribution of fuel mass fraction in a plane containing the nozzles.

Figure 6 :

 6 Figure 6: Temperature distribution on the base.

Figure 7 :

 7 Figure 7: Base pressure distribution along an internozzle radial line

Table 1 :

 1 Low altitude case initial flow conditions[START_REF] Musial | Base flow characteristics for several four-clustered rocket configurations at mach numbers from 2.0 to 3[END_REF]

	Parameters	Values
	Pc	41.37 bar
	Tc	3469.8 K
	P∞	12209.5 Pa
	T∞	297.7 K
	M∞	2.75

Acknowledgments

The authors wish to thank the Centre National d' Études Spatiales (CNES) for financial support. The Ph.D. work of J. Reynaud is funded by CNES and ON-ERA.