Nagore Alvarez

Marion Real

Iban Lizarralde

Jérémy Legardeur

EKIT'EKO: A SERIOUS GAME TO SUPPORT SUSTAINABLE APTITUDES DURING THE DEVELOPMENT OF ECO-INNOVATIONS

Keywords: Sustainable Innovation, serious game, decision-making

Cooperation between stakeholders is becoming a major challenge for the development of ecoinnovations. Stakeholders are confronted to acquire new competences when they design projects in a triple bottom line prospective (economic, social and environmental considerations). Besides, other skills related to entrepreneurship, product development and collaboration are likewise key skills for eco-innovation. Educational approaches such as instructional simulations can supplement traditional form of educations. In this paper, we suppose that practicing serious games can be useful educational tools to introduce such thematic and reinforce the empowerment and the learning appetence of future designers. A first version of a serious game stemming from a design thinking approach is presented.

1-INTRODUCTION

Ecological risk prevention and challenges of sustainable development involved important social system changes. In industrial system, company and all their stakeholders require to develop ecoinnovative projects which induce to re-think their activities through new offers, new business models or new uses. The training of actual and futures actors is essential to support the development of ecoinnovation. Nowadays, preparing future managers, engineers and designers with real technical knowledge while allowing them to acquire adequate aptitudes and managerial competences, remains a challenge for institutions. Due to the diversity of issues surrounded by eco-innovation, engineering institutes must teach an ever greater number of disciplines to their students. Actually, several types of educational methods (classical amphitheatre theoretical courses, practical work, student projects and internships) co-exist in both virtual and physical learning environment with initial or continuing training students. Teachers need to adapt the form and the content of courses according to the type of skills they want to transmit. Practitioners and academics highly recognize the strong importance of experiencing in context when teaching not only technical but especially behavior and meta-cognitive skills [START_REF] Dupouy | Towards a dialogic management of cognitive competence[END_REF]. Thus, more and more immersive environments are proposed to student to enhance their learning experiences. Internships and student projects are the first answers delivered by the academic institutions to encourage their future engineers to act as actors in real situations. Instructional simulations are other options consisting in a simulation of some type of reality (system or environment) but which also includes instructional elements that help students to explore, navigate or obtain more information about that system or environment that cannot generally be acquired from mere experimentation. Such environment prepares students as if they were practicing in real context. It is accordingly very difficult to reproduce such a training environment when striving for a pedagogical goal with short-term constraints. The gamification of learning defined as "the use of game principles in learning environment" is pervading graduate education adding playfulness to classical courses. This approach is aimed at reinforcing student engagement. It concerns as well board games than video games. Gamification is often considered as a behaviorist approach limited to add competition between students with scoring & rewarding systems. Nickolson [START_REF] Nicholson | A user-centered theoretical framework for meaningful gamification[END_REF] highlight that meaningful gamification focuses on introducing elements of play instead of elements of scoring. Besides, it is necessary to separate result of the game with the way students are evaluated so as to maximize the learning experience and avoid useless conflictual tensions. The potential of combining game elements and instructional simulations into serious games offers some possibilities to encourage the immersion in context, the empowerment and the learning appetence of students. In this paper , we propose a serious game dedicated to be used in educational institutes or companies as a pedagogical tool introducing a training module of eco-innovation. Before presenting the description of the actual version of "Ekit'eko" game, we first explain our serious game design methodology, revisit the different pedagogical objectives supported by eco-innovation training and propose a short state-of-art of existing games in those domains.

2-SERIOUS GAME DESIGN METHODOLOGY

The French institute of education defines 8 principles to consider when designing serious game [3] :

(1) encourage motivation and get students to engage in the situation, (2) identify the knowledge that students will have to handle, (3) give students a freedom governed by rules, (4) introduce instructional elements that allow students to have feedbacks on the strategies they adopt, (5) allow error, don't dramatize the failure, [START_REF] Honig | Entrepreneurship education: Toward a model of contingency-based business planning[END_REF] enhance the interaction between players, (7) take into account the emotional aspects and (8) integrate playfulness phase in the learning situation. A multi skill team was established in order to develop the game. This team includes a psychologist, a product development expert, an eco-innovation expert and a designer. The design process of Etik'eko consists in three stages: the first stage concerns the identification of the pedagogical aims of the game. The second stage can be seen as the classical inspiration and ideation phases of design thinking: an overview of existing games and recent tendencies were elaborated followed by creative sessions aimed at defining the main principles and the environment of the game. The last stage concerns the development and tests of the game in an agile philosophy based on the power of short cycles of improvement. For each iteration, three questions are checked: how the pedagogical objectives of the game are integrated into the game? What about its playfulness? Is there any ergonomic problems?

3-COMPETENCES TO MANAGE ECO-INNOVATION

The eco-innovation training is addressed to future managers and design engineers. Four different modules were elaborated to develop managerial eco-innovation skills to those students: sustainability, entrepreneurship, collaboration and product service system development.

Sustainability

Eco-innovation is looking for designing viable solutions in the triple bottom line perspectives. It implies a capacity to consider economic, social and environmental consequences when assessing situations and creating alternatives. The module introduces several methods which exist to stimulate and evaluate each part of sustainability: eco-ideation, eco-design and life-cycle analysis introduce the complex notions of impact transfer and rebound effect as key reflexes to adopt for analyzing environmental impacts during all life of products. Cost and value analysis are aimed at balancing economic incomes and costs while marketing and more recently CSR-ISO 26 000 approaches are focused on social aspects looking for optimizing the well-being of all stakeholders, particularly the clients.

Collaboration

Two different scopes have been considered related to collaboration. On one hand, the collaboration is dealing with relationships between members of the same company. These members of a new product development team might have to respect constraints related to its function and responsibility scope. Collaboration in this case aims to obtain the global optimum seek for the developing system beyond the local optimums related to each function.

On the other hand, eco-innovation lead to reconsider the question of the collaboration among stakeholders networks with multidisciplinary teams capable of efficient collaboration. The collaboration practices among project stakeholders are an essential catalyst for creative sharing of skills. By its socio-technical characteristic, the collaboration is a relatively complex phenomenon to study and to formalize in the organization. The interaction between the individuals themselves, as well as the interaction with the surrounding systems (offers, context, etc.), creates major concern in the academic and industrial world. The module shows the complexity of collaboration in the industrial context through its numerous "parameters" to consider (personal development, individual and group psychology, enterprise culture, power game, general working habits, etc.).

Entrepreneurship & innovation

Managers of eco-innovative projects require having the entrepreneur streak. The module "entrepreneurship and innovation" is aiming at giving students methods to improve their know-how to be open, creative and opportunist while being objectives and in-law. It is composed of an introduction to creativity, partnership exploration and business plan methods. More formal administrative rules (intellectual property, type of incubation structures) are also presented. Future entrepreneurs need to be aware that their behaviour and each choice they made are influencing the pathway of their projects and how they are perceived by its environment. Recent works on sustainable business model [START_REF] Boons | Sustainable innovation, business models and economic performance: an overview[END_REF] is also introducing new ways of considering triple bottom line perspectives as central values of the project. Entrepreneurs need to promote their projects to their in-construction ecosystem encouraging new dynamic thanks to such values.

Product-Service System development

Whatever the eco-innovation is dealing with product, services or product-service system, students need to be familiar with the different steps of development process of project they are going to manage. The module is presenting several processes according to the domain and the type of systems. Different links between eco-design rules and economy of the functionality and PSS development will be proposed.

The aim of Etik'eko game is to introduce briefly all aspects of the management of eco-innovation so as to improve the empowerment of students and their capacity to understand the coherence between each course.

4-OVERVIEW OF EXISTING GAMES

Different types of games were listed, categorized and analyzed through the prism of three axes: pedagogy, playfulness and ergonomics. (See table 1) From a sustainability point of view, several games are available for different age categories. Some serious games focus on a particular aspect of the environmental category (awareness to the energy problem or to the waste management issues), others aim to find the balance between social, economic and environmental factors in the frame of a new city construction or new business development. Shades of environmental impacts are rarely presented and therefore the impact transfer occurrences are not included in the mechanisms of the analyzed games. From an entrepreneurship point of view, the implication of the educational system on promoting entrepreneurship values has been a mayor center of interest in universities [START_REF] Clarysse | A process study of entrepreneurial team formation: the case of a research-based spin-off[END_REF][6] [START_REF] Kuratko | The emergence of entrepreneurship education: development, trends, and challenges[END_REF]. The development of serious games related to this field has focused mainly on role games bringing the student to follow a new company creation process. Combining with eco-innovation process, such approach demands a triple bottom line focus as the main principle for the serious games that promote entrepreneurship and sustainability. From a new product development point of view, there are several serious games that have been developed focusing on engineering aspects or more production management oriented. We have selected to detail the Delta Design Game [START_REF] Bucciarelli | Delta Design Game[END_REF], which merges the new product development and collaboration aspects.

Virtual

In the Delta Design Game, the team must design a house by assembling equilateral triangles in either red (heating triangle) or blue (cooling triangle) formations. The design team is composed of a project manager, a structural analysis specialist, a heat engineer, and an architect. Each member of the team receives two documents. The first part presents the team composition and target. This directive also specifies the global task to be undertaken by detailing the design requirements of a house. This first part is the same for all participants. The second part of the document, different for each stakeholder, outlines the essential requirements for the correct execution of the role assigned to the player. Therefore, the team task is to design a house that takes into account and integrates all of the stakeholder's rules that are sometimes vague or precise and subjective or formal. The main interest of Delta Design game remains the analysis of the collaboration "highlights". An external viewer or a set of viewer-player can do this analysis for each stakeholder. Analyzing the corpus, the pictures and videos of a session with Delta Design allow us several opportunities for insight and observation of individuals in a collaborative situation. We will not develop the pedagogical interest of this approach as the reader may consult the paper [START_REF] Prudhomme | Toward Reflective Practice in Engineering Design Education[END_REF]. Thereby, through reflective analysis [START_REF] Schön | The Reflexive Practitioner: How Professionals Think In Action[END_REF], he can better understand and analyze his own behavior during a collective action. However, we have identified some limits of the Delta Design game. First of all, the future design product engineers occasionally have a lack of enthusiasm or concern for the experiment. This is related to the fact that the final objective of the experiment is the design of a house assimilated to the formation of architecture and with characteristics not focused on the mechanical product technology. The representation of the object to be designed (under the triangle assembly) seems to be too abstract to solicit more interaction between the players. Moreover, the 2-D format differs from the 3-D formats (CAD) traditionally used in product design. The game format imposes its utilization at the present moment and does not allow for a test in a distributed environment. Taking these limits into consideration, we designed a different game, including more playfulness and focused upon a more familiar system of product/service.

5-PROPOSITION OF THE SERIOUS GAME: EKIT'EKO

Ekit'eko is a simulation-strategic game where participants are asked to develop a new innovative product in the most sustainable way. The chosen product is a sportive sneaker. This market has a high eco-innovative potential and people get easily connected with it.

As in any serious game, the session consists in three parts: the introduction phase, the game session and post-game session.

The introduction phase

It consists in the establishment of groups and the presentation of materials. The game is designed to be played in groups of around three-five people. So participants will be asked to make groups before the game starts. They will be given all the explanations and rules of the usability of each material so that the participants will get connected with the game's process. The game starts with the introduction of the overall context. The mission is introduced to the groups (See Figure 1). Then, participants are proposed to play a role, defined at the presentation of the mission, which is going to determine the way of thinking they will have to defend. Three personas are created: an ecological products design engineer, a business administrator and a marketing director.

Proceeding of a game session

After the introduction of the context, teams will have to make a series of decision concerning the development of their products. The game begins with the choice of a strategic orientation of the company. Each group will have to adopt a strategy that will condition their decisions during the session. Every step to the final result is actually a question that all the groups will have to answer by choosing one of the 3 optional proposed answers. (see Figure 2a) Each of the answers supposes a different impact in the final (and provisional) results, so, all groups will have to study and identify which is, for them, the best option and if it is deemed to be satisfactory in all TBL aspects. These variables are one by one: the economical, the social and the environmental (which is made up of the water pollution, the oil repercussion and the environmental global impact). So that, if a team wants to take care of the environment, they will choose the most ecological option, or on the contrary, if they want to gain a lot of money, they will decide to make a bigger action even if it doesn't care about the environment at all. During the game, the variables will show up the state of each group related to the chosen objectives and the impact they are doing on the different aspects. So, depending on the decisions and answers they will choose, impacts will vary positively or negatively. Every time a decision is made there will be given real time feedbacks that will allow participants to understand the possible consequence of their impacts on the three sustainable variables.(see Figure 2b) Thus, these variables will be key elements to show the progress of each team in real time.

Post-game session

Finally, after answering all the questions, each team will reach to different final results and they will receive a personalized final conclusion of their progress during the game. They could realize if they reach a balanced state between their triple bottom line impacts. At the end of the game, a feedback discussion is initiated with all teams. They compare their results and are asked to talk about the 4 axis of the pedagogical objectives. Finally, teacher introduces the 4 modules. Participants are supposed to have a more important learning appetence and find more coherence in the organization of the course.

Embodiment of the game

The environment of the game is important to facilitate the immersion of participants. The metaphor of a trail was used to design all supports. The progress of the innovation is compared to the pathway of a mountain composed by several steps. The evolution of economic, social and environmental variables is respectively visible through the quantity of liquids available in an energy drink, the number of runners and the number of trashes present in the mountain. (See Figure 3) Both board and video game supports are being developed so as to adapt it according to user preferences. Other ways of interactions are actually considered so as to improve the playfulness of the game: the use of corrective actions to recover points in one of the three variables, the presence of a panel sharing the progress of each team strengthening inter-group competitions and time course.

6-CONCLUSION

The goal of our game is to deal with the socio-technical practices [START_REF] Schön | The Reflexive Practitioner: How Professionals Think In Action[END_REF] underlying the development of eco-innovations. We think that our contribution can be useful in particular in the case of the training of complex skills such as the collaboration faced to sustainable development challenges. It was first developed as an introduction tool for institutional courses on eco-innovation. Etik'Eko could also be used from the early stage of eco-innovation development as a stimulus preparing entrepreneurs and designers to change their classical way of making decision toward sustainability. Several iterations will help us to finalize our rules and supports so as to optimize the three objectives of our serious game (pedagogy, playfulness, ergonomic). We are currently building system dynamic models in order to have personalized feedbacks. Therefore, adapted corrective actions could be proposed for each group. Furthermore, we are planning to organize a test in order to compare how students perceived the four pedagogical modules in both traditional and based on Etik'Eko game sessions.

After first internal tests, we would like to propose an experience between several institutions (engineering schools, universities, companies) in order to test this game in a distributed way (between several teams, at distance (at different locations).

Figure 1 :

 1 Figure 1: Screenshot of the mission presentation interface

Figure 2 :

 2 Figure 2: Screenshot of examples of (a) questions and (b) feedbacks

Figure 3 :

 3 Figure 3: Board of Ekit'Eko in an ongoing game

Table 1 :

 1 Non exhaustive list of educational games reaching one or several of Ekit'eko pedagogical objectivesClimate Defense is a tower-defense game that explores the issue of climate change. The climate is in peril and it's your job to use strategy and tactics to defend it!

	Game	Objectives	Pedagogical	Instructional elements	Playfulness	Ergonomic	Type of
			relation				support
	[8]Climate		Sustainability	Vocabulary of international climate	Realistic scenario	Coherent symbolic and graphics	Virtual
	defense			change organizations	Boardgame with point	Interactive
				Scoring with cost, temperature and	systems Two modes (virtual
				Co2 emissions	or real situations)
	[9] Change	The objective of this game is to grow a business in the	Sustainability and	Customization according student	Boardgame with thimble /	Graphical choices coherent/repetitive	Virtual
	artisans	context of sustainable development. We must therefore make	innovation	profiles / scoring in TBL as a gauge	Bonus-malus cards / Point	music/hard to win
		the right choices to find the balance between social,			systems/Competition
		economic and environmental factors
	[10] EDF Park	Build a park playing on a mix of energy sources to supply the	Sustainability	Disguised in the support / scoring	Time pressure /Scoring	Help menu/clear support	Virtual
		energy needs of its attractions to build.			system/ Construction of
					city/immersive/Competition
	[11] Climcity	Reduce greenhouse gas emissions and develop renewable	Sustainability	Scoring feedbacks and mini-course	Ambitious and visible	Difficult to explore the map	Virtual
		energy in a fairly rural town.		during the game	objectives/ Scoring/Sims	Feedbacks in each action
					inspiration
	[12] Collapsus	The game propels protagonists among a team of 10 people	Sustainability	Documentary parts based on sourcing	Transmedia. Original missions	Interactive experience. Adapted	Virtual
		who seem to be caught in a conspiracy of energy and must		facts.	and esthetic	feedback.
		find new ways to feed the world in clean energy			framework/Cooperation
	[13] Innov'nation As a new manager in the company X, the objective is to	Entreprenership	Wiki / Feedbacks/ scoring on three	Virtual work	Avatar indicates the pathway.	Virtual
		structure the innovative process to find relevant sectors to	and collaboration	variables (resources/Money/Time)	environment/Individual game	Adaptable according to previous
		develop and proposing them to the direction		/collaboration with experts and teams		choices.Not enough freedom
	[14] Delta Design The team must design a house by assembling equilateral	Collaboration and	Simulation	Cooperation intra group and	Well-detailed instructions	Physic
		triangles in either red (heating triangle) or blue (cooling	product	Feedbacks on post-session	competition intergroup	Hard to control
		triangle) formations.	development		Complex solving problem	Support could be improved with
					Lack of enthusiasm	adapted 2D-3D softwares
	[15] Wallbreaker	Several teams must manage the merger of two SSII sizes and	Collaboration	Simulation	Cooperation	Visualization of each group progress	Physic
		very different cultures. Participants determine the actions to		Robust arguments on decisions	Big Board and objectives	Clear &coherent graphical choice
		accompany 10 employees with different profiles		Based on management theory
				Corrective actions
	[16] B to Green	B to green consists in developing eco-innovative strategy in a	Innovation &	Debriefing + adapted pedagogic	Board game with cards	Well-defined and illustrated rules	Physic
		economic context for 5 years. Responsible of concurrent	eco-innovation	sessions	representing competitive	Tutorial video
		companies, participants develop new products and need to			advantages.Three-steps
		have the highest number of marketplaces			process for each year
	[17]Kosmodisea	It is a virtual journey in planning and implementing a	Entrepreneurship Defined agenda with objectives and	Rewarding system with	Graphical choices coherent/	Virtual
		teamwork project and has the objective of promoting		dead-lines/ collaboration with experts	points/competition	Interactive experience/ Clear support
		collaboration and the use of Information and Communication		and teams / scoring/ feedbacks after		(all the information is well
		Technologies.		every delivery		distributed and completed)
	[18] PEGASE	The aim of this platform tool is to help change management	Entrepreneurship	Customized scenarios with indicators/	Construction / Sims	Interactive experience/ Scenario	Virtual
		support during the implementation of a PLM system in an	and Product	Interaction with colleagues and	inspiration/ Interaction with	adapted to the real situation of the
		industrial company	development	training presentations/ informative	other players/ Real product	user
				archives available	data collection
	[19 ]Solidarisk	Each team (for 2 to 4 people) plays the role of members club	Entrepreneurship Collaboration with experts and teams/	Ambitious and visible	Interactive experience. Adapted
		Cigales which will decide whether to support the corporate		feedbacks/ documentary parts	objectives/ rewarding system	feedbacks.
		projects submitted.			with points/ competition

The game will be presented in the form of free tests to the participants of the MOTSP conference.

We would like to acknowledge APESA, the INTERREG project RESOT in the framework of POCTEFA and all IKASI team members which participate to focus groups and experimentations.


Nadine Le Bolay

Alain Lamure

Nora Gallego Leis

Arfan Subhani

Improvement by co-grinding of the use properties of renewable polylactic acid -starch composites

Introduction

For several years, the use of biodegradable polymers is favoured to limit pollution by petrochemical polymers. Among the biodegradable polymers, polyesters such as polylactic acids are used, in particular for packaging. These polymers are often associated to biodegradable fillers such as starch. However, starch is hydrophilic while polylactic acid is hydrophobic. Consequently, a bad adhesion between them, leads to poor and irreproducible blends properties. To improve the interface between the matrix and the filler, several authors propose to use compatibilizers [1,2].

Co-grinding is an alternative to improve the interface without adding a compatibilizer. This process was used to produce composites made of petrochemical polymers filled by a mineral [3] or starch [4], and it was shown that the use properties of composite material could be significantly improved, in comparison to a simple mixing. This paper presents results on the production of starch-filled PLA co-ground composites and on the influence of co-grinding on the properties of the composites.

Experimental procedure

The products were ground in a 5-liter ceramic tumbling ball mill containing ceramic balls (20 vol. %) and the powder (10 vol. %). The chamber speed was 100 rpm. L-polylactic acid (PLA) Galactic was used as the matrix. The granules having an initial diameter of 3 mm were preground in a knife mill, and then sieved. Particles under 400 µm (figure 1-a) were kept. The filler was waxy maize starch (figure 1-b), mainly composed of amylopectin. The particles size varied from 4 to 32 µm (average size close to 13 µm). The PLA -starch mixtures contained 20 wt. % of starch. The materials were ground separately first, and then co-ground for different times.

The size distributions and the mean sizes of the particles were measured by means of a laser diffraction granulometer Malvern Mastersizer 2000. Selected samples were observed with a scanning electron microscope (LEO 435 VP). Surface energies were measured using the sessile drop method (Digidrop GBX). The powders were compacted at 60 °C in a Carver press to form cylindrical pellets on which three

Results and discussion

The two products were first ground separately. PLA mean size increases during the first three hours due to agglomeration phenomena. Then, fragmentation leads to a decrease of the mean size. As for starch, since the particle size is small, no fragmentation is observed. Agglomeration between the particles occurs, leading to a progressive increase of the mean size. Concerning the mixture, the size distributions and the mean sizes are presented in figure 2 for various co-grinding times. The initial size distribution is bimodal (PLA peak at large sizes and starch peak at small sizes).

As co-grinding occurs, the starch peak disappears due to agglomeration of these During grinding, the polar energy of starch decreases, probably due to conformation modifications of starch macromolecules, while PLA energy remains quite constant.

As for the mixture, the initial polar energy is between those of the two products. Cogrinding leads to a drastic decrease of the energy during the 8 first hours. This can be explained by the observations made on size distributions. Indeed, starch sticks first on PLA particles, and then small PLA particles stick on big ones, covering starch.

Consequently, the pellets surface is progressively only constituted of PLA and the mixture energy tends towards the PLA one. For longer times, since the agglomerates are broken, starch may become free and present on the pellets surface. Thus the energy increases to be constant then, when starch is well dispersed in the matrix.

Finally the mechanical properties were studied using the brasilian test. This is a diametral compression test which was performed on pellets, an increasing force being applied on the pellets placed vertically until rupture. The Young modulus, E, and the stress at break, , were determined for PLA and mixture (figure 5). The two parameters do not evolve significantly for PLA. On the contrary, adding starch to PLA and mixing them (without grinding) has a negative effect on both parameters since adhesion of the filler on the matrix is bad. But these parameters increase when co-grinding proceeds. The values after 20 hours co-grinding are 3 to 4 times higher than with a simple mixing and even higher than the values measured for PLA alone. The filler is well dispersed in the matrix and interactions between the materials are enhanced. However, a too long treatment leads to a decrease of the two parameters, probably because of a degradation of the molecular chains. Cogrinding the mixture during an optimum time permits to have better mechanical properties than for the matrix alone, without using a compatibilizer.

Conclusions

With the objective of producing a totally biodegradable composite material, polylactic acid was filled with starch and the mixture was co-ground. Granulometry and morphology analyses have permitted to understand how the filler is dispersed in the matrix. The interactions between the hydrophilic filler and the hydrophobic matrix are favoured by co-grinding, what permits to enhance the composite mechanical properties without using a compatibilizer.

Figure 1 -

 1 Figure 1 -SEM photos of the products

Figure 2

 2 Figure 2 -size distributions and mean sizes of the mixture

Figure 4 -

 4 Figure 4 -Variations of  s p

Figure 5 -

 5 Figure 5 -Young modulus and stress at break of PLA and mixture


Michael Sherry
email: michael.sherry@eng.monash.edu.au

John Sheridan
email: john.sheridan@eng.monash.edu.au

David Lo Jacono
email: david.lojacono@imft.fr

Horizontal axis wind turbine tip and root vortex measurements

The vortical wake of the Tjaereborg wind turbine has been investigated experimentally in a water channel. Both the upwind and downwind configurations were tested. The hydrogen bubble and particle streak techniques were used to visualize the flow prior to obtaining quantitative data using planar particle image velocimetry. Parameters that describe the helical vortex wake, such as the helix pitch, vortex core radius, vortex circulation and vortex meander, were determined for three tip speed ratios, Ȝ=4,7,10. Particular attention was given to the characteristics of the root vortex, which have not previously been measured experimentally. A key finding of the investigation was the rapid diffusion of the coherent root vortex due to the small radius of curvature of the root vortex filament, interaction with the tower section, when in the upwind configuration, and its location near the nacelle boundary layer. The root vortex signal extends further into the wake in the downwind turbine configuration, as there is no tower-vortex interaction, prior to its being diffused in the strong strain field immediately downstream of the nacelle. A coherent tip vortex signal is present over the entire measurement area x/R<2, however the root vortex signal subsides much closer to the rotor plane. The study is part of a more extensive study of the vortex interactions within the wake. The mechanisms affecting wake stability are also briefly commented on.

Introduction

Horizontal axis wind turbines (HAWT's) are now a universally established means of producing renewable energy. Wind turbines have evolved greatly from the early machines implemented in Denmark in the 1980's to become the largest rotating machinery on earth [START_REF] Vermeer | Wind turbine wake aerodynamics[END_REF]. There are two configurations of industrial scale horizontal axis wind turbines, upwind and downwind; in the upwind configuration the supporting tower structure is downstream of the rotor assembly whereas in the downwind configuration the supporting tower is upstream of the rotor assembly. Upwind turbines are by far the most prevalent in currently installed turbines. Installed wind turbines are almost exclusively clustered in wind farms to yield the greatest energy from a given area. Wind turbine wake effects become especially important for turbines sited in wind farms, as turbines will be subjected to coherent vortical structures shed from a single or multiple other turbines within the cluster. The near wake x/D<2, where x is the axial downstream distance and D is the turbine rotor diameter, is dominated by N counter rotating helical vortex pairs, where N represents the numbers of blades. A counter rotating pair is made up of a tip and root vortex shed from each blade. How these coherent structures evolve and interact needs to be understood as their interaction could lead to coherent structure breakdown and eventual wake breakdown.

HAWT wakes have been extensively studied in the past, with notable experimental studies using particle image velocimetry (PIV) by [START_REF] Whale | A study of the near wake structure of a wind turbine comparing measurements from laboratory and full scale measurements[END_REF] and [START_REF] Dobrev | Investigation of the wind turbine vortex structure[END_REF]. Whilst providing valuable phase averaged data of the tip vortex structure, these studies did not document the root vortex, most probably due to the large relative diameter of the hub section compared to the blade radius and hence blockage in the [START_REF] Dobrev | Investigation of the wind turbine vortex structure[END_REF] study. Thus, the vortex interaction mechanisms affecting HAWT wake structure have yet to be determined experimentally. A comprehensive review of the experimental work conducted in the area can be found in [START_REF] Vermeer | Wind turbine wake aerodynamics[END_REF]. Numerical methods have also been applied to HAWT wakes, providing time resolved information on the interaction and evolution of the tip and root vortices [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF][START_REF] Troldborg | Actuator line simulation of wake of wind turbine operating in turbulent inflow[END_REF][START_REF] Walther | A numerical study of the stability of helical vortices using vortex methods[END_REF]. The [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF] and [START_REF] Troldborg | Actuator line simulation of wake of wind turbine operating in turbulent inflow[END_REF] studies are particularly relevant to the results presented here as they also used the Tjaereborg turbine as their model. One drawback to these numerical studies, which use the Actuator Line Method (ACL), is that the simulations simplify the modeled geometry and do not consider HAWT body geometry effects of the tower, hub and nacelle sections [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF][START_REF] Troldborg | Actuator line simulation of wake of wind turbine operating in turbulent inflow[END_REF]. It is for this reason that an experimental study to gain insight into the tip and root vortex structure and interaction within a HAWT wake is being undertaken. Particular focus is applied to the root vortex structure and its evolution, as these areas have not previously been documented experimentally for HAWT. The current results provide a sound database to establish the differences in wake structure between including the turbine tower and nacelle and the simplified geometries used in numerical studies, which don't include these features.

Experimental Set-up

The experiments were conducted in a free surface water channel with dimensions of 4000u600u800 mm. The free stream speed is adjustable in a range of 90mm/s to 460mm/s. A scale model of the Tjaereborg wind turbine which operated in western Denmark between 1988 and 1998 was constructed for the experiments. The original 3 blade upwind HAWT had a rotor diameter of 61 m and blades with both taper and twist (1 R /3m) [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF]. The design tip speed ratio which is ratio between the tip speed and the free stream velocity, as defined in equation 1 was 7.07.

(1) Error!

Error!

where : is the rotational speed of the turbine blades, R is the rotor radius and U f is the freestream velocity. The model turbine has a diameter of 230mm with the swept area of the model producing a channel blockage ratio of 8.6%. The model is powered by an 18V d.c. motor situated above the water channel surface and is connected to the main shaft of the model turbine by a toothed timing belt. The turbine is synchronised with the data acquisition process through an optical encoder which also serves to regulate the rotational speed of the turbine with an accuracy of r1rpm. The uncertainty of the rotational speed is minimal and is incorporated into the measurement uncertainty in the final results. The optical encoder allows measurements to be captured with a minimum angular displacement of 1 R , however here phase averaged measurements (1 image acquisition per rotation) will be presented. Three tip speed ratios, O=4,7,10, were investigated, providing insight into both a lightly loaded rotor and heavily loaded rotor around the design condition. The tip speed ratio range gave a corresponding experimental Reynolds number range of 1 322<Re c <3 223. Where the Reynolds number,

(2) is based on the tip speed ratio, O, free stream velocity, U f and the blade tip chord, c tip . The Reynolds number of a wind turbine in atmospheric conditions is several orders of magnitude different from those in the experimental setting. Therefore, it is expected that viscous forces will be more pronounced in the experiments accelerating the diffusion of the vortical structures. Another phenomenon that is present in the field but less so in the experiments is the higher turbulence seen in the atmospheric boundary layer, which will result in higher levels of turbulent diffusion of the coherent structures. Hydrogen bubble and particle streak flow visualisation techniques were initially used to confirm the areas of interest (tip and root vortex locations) within the flow. Subsequent measurements employed two component planar particle image velocimetry (PIV) to obtain quantitative information about the tip and root vortices. The PIV measurement plane is aligned with the rotational axis of the helical vortex wake such that the axis of rotation of the helical vortex filaments orthogonally intersects the measurement plane. Thus planar PIV can capture the required velocity components needed to characterize rotational motion in the plane of the vortex. From the sectional velocity data, vortical wake properties such as vortex radius, circulation, strength and vortex meander in the axial and radial directions for both the tip and root vortices can be deduced. Measurements are recorded at and then phase averaged when a blade is aligned with the tower structure, and thus within the measurement plane. Only the top half of the wake is measured as depicted in figure 1.

Previously validated [START_REF] Fouras | Target free stereo piv: a novel technique with inherent error estimation and improved accuracy[END_REF] in-house multi-pass cross-correlation PIV software was used to produce the displacement and vorticity fields . A 50% window overlap was used in the final pass of the PIV software. A 25mJ double pulsed Nd-Yag laser with a CCD camera (4008u2672pixels) was employed for the phase averaged measurements. The laser was situated under the channel on a moveable trolley and directed into the channel by a mirror and lens set.

The instantaneous vortex core positions were identified by Gallilean invariant local analysis techniques applied to the velocity gradient tensor, u. Spatial derivatives were evaluated using a second order central differencing scheme. These techniques have been used to elucidate fixed wing tip vortices [START_REF] Carmer | Identification of vortex pairs in aircraft wakes from sectional velocity data[END_REF] and coherent structures (CS) in turbulent boundary layers [START_REF] Chakraborty | On the relationships between local vortex identification schemes[END_REF]. The near field of a wind turbine wake is dominated by strong pressure gradients (i.e. tip and root vortices), however strong velocity gradients (i.e. shear) exist at both the tip and root vortex radial locations. Application of the velocity tensor methods allow us to accurately determine the instantaneous vortex core locations, minimising the effects of user defined inputs and assumptions (such as in circulation based methods whether the integration path is circular). The background level of the invariant is determined and this value is used as a base value to determine the presence of vortical structures.

Planar PIV captures the velocity fields in two axes (here the axial and radial) {x,y} which gives u as,

(3) Error!

If the discriminant, ', of matrix 3 is less than zero, the characteristic equation O 2 + PO + Q= 0, will have a complex conjugate eigenvalue pair, O r rO ci . [START_REF] Zhou | Mechanisms for generating coherent packets of hairpin vortices in channel flow[END_REF] determined that vortices correspond to regions with O ci >0, as particle trajectories about the real eigenvector axis have a finite time period of revolution 2S/O ci . Regions of shear in a fluid field have infinite revolution time periods and correspond to O ci =0. The method is thus able to discern between regions of shear and vortical motions and O ci is a measure of the 'swirling strength' of a vortex [START_REF] Zhou | Mechanisms for generating coherent packets of hairpin vortices in channel flow[END_REF]). An alternate Galillean invariant vortex identification technique is that of [START_REF] Weiss | The dynamics of enstrophy transfer in two-dimensional hydrodynamics[END_REF] which extended the earlier Q criterion work by [START_REF] Hunt | Eddies, stream, and convergence zones in turbulent flows[END_REF] (see [START_REF] Carmer | Identification of vortex pairs in aircraft wakes from sectional velocity data[END_REF]. For two component velocity planar PIV, the Weiss parameter is given by

Q w { Error! (4) = T 2,1 +T 2,2 Z 2,z
where T 2,1 represents normal strain rates, T 2,2 represents shear strain rates and Z 2,z is the squared out of plane vorticity. Vortical structures are identified as regions with a negative Weiss value as the magnitude of vorticity in equation 4, exceeds that of the strain terms. Conversely regions with a positive Weiss value indicate strain dominated regions [START_REF] Carmer | Identification of vortex pairs in aircraft wakes from sectional velocity data[END_REF]. The background level of the Weiss parameter due to experimental noise is determined and used as the minimum threshold level, Q w th . The area of the centroid of the minimum threshold Q w th contour which encapsulates the Q w minimum is taken as the instantaneous vortex core location [START_REF] Vollmers | Detection of vortices and quantitative evaluation of their main parameters from experimental velocity data[END_REF]. The minimum Weiss value is preferable to finding the maximum out of plane vorticity Z z as it distinguishes vortical motions within a shear flow. Also, for instantaneous data describing the dynamic process of the tip vortex roll up, there are often numerous vorticity maxima/minima. For planar PIV data, the swirling strength criteria and the Weiss criteria are directly proportional by Q w =4O 2,ci [START_REF] Carmer | Identification of vortex pairs in aircraft wakes from sectional velocity data[END_REF]. The Gallilean invariant vortex identification methods described above give no indication of the sense of rotation of the vortical structures they identify. The vorticity in the fluid regions where the Weiss parameter locates a vortex is thus checked to determine the orientation of the vortex.

Results

The phase averaged wakes for the design O, are shown in figures 2 and 3 for a downwind and upwind turbine configuration respectively. These figures depict tangential vorticity, Z z within the near wake. The flow is from left to right with the dominant vortical structures clearly evident. In both figure 2 and3, six tip vortices are visible in the shear layer near the unit radius. In addition, several root vortices are also present at small vortex ages (VA), close to the axis of rotation (y/R=0). The vortex age is defined as the angular displacement of the helical vortex filament since creation in degrees (e.g. for the first tip vortex in figures 2 and 3; VA = 120°, for the 2 nd ; VA = 240° etc.).

Figure 2: Phase averaged wake of the Tjaereborg wind turbine operating in an downwind configuration at its design tip speed ratio (O=7) depicting the coherent vortical strucutres within the near wake, contours of tangential vorticity, Z z . Individual blade wakes can also be seen in the region between the root and tip vortices. The blade wakes are the remnants of the bound blade circulation shed into the wake that do not roll up into coherent tip and root vortices; they indicative of a non-uniform radial circulation distribution [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF]. The blade wakes also indirectly reveal the wake radial velocity gradient. It is clear that the alignment differential between the tip and root vortex locations increases with axial distance [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF]. As the tip vortices are in close proximity to the higher velocity freestream fluid they advect faster downstream compared to the root vortices, which are situated adjacent to the low velocity wake core fluid.

The wake structure of an upwind turbine operating at the lower and upper tip speed ratios tested (O 4 and O = 10, respectively), which encapsulate the design tip speed ratio, are shown in figures 4 and 5 respectively. The helical pitch reduces with increasing tip speed ratio, as more vortices are shed into the wake. As the pitch of the helix reduces the helical filaments are likely to become susceptible to the mutual induction instability [START_REF] Widnall | The stability of a helical vortex filament[END_REF]. Thus, the wake for a turbine operating above the design tip speed ratio appears more unstable, with the non uniformity of the spacing of the tip vortices in figure 5 being in both the radial and axial directions. Figure 5: Phase averaged wake of the Tjaereborg wind turbine operating in an upwind configuration above its design tip speed ratio (O=10) depicting the coherent vortical structures within the near wake and the onset on instability, contours of tangential vorticity, Z z .

Phase average smoothing effects

In investigating the characteristics of the vortices the effects the phase averaging of the data has on educed vortex properties needs to be considered. The phase average data allows accurate elucidation of the mean position of the individual vortices, as shown in figure 6. The vortex extraction methods were used on the instantaneous frames and on the phase averaged data; the difference between these in terms of the mean position coordinates was at all times less than 5%. Due to vortex meander, phase averaging leads to undesired spatial smoothing of individual vortex properties. Performing the vortex extraction techniques on the phase averaged data and comparing to results obtained from the instantaneous realisations gives a good indication of the resulting degree of smoothing. Figure 7 indicates the percentage change between the mean value calculated using the instantaneous realisations and the phase averaged data of the minimum Weiss parameter, 'Q w min , with increasing vortex age. It is clearly evident from figure 7 that even at small vortex ages, the phase average is significantly different to the instantaneous realisations and this difference increases with vortex age. Therefore to investigate the characteristics of the tip and root vortices, the vortex identification schemes are used in conjunction with the instantaneous PIV realisations. A slight wake expansion is also seen in figures 3 and 5, with the tip vortices moving radially outward with increasing vortex age. The axial position of the tip vortices follows a linear trend as shown in figure 6 whereas the radial core positions (not shown) vary more with vortex age. The figure also highlights that as the pitch of the helix system decreases with increasing tip speed ratio, the axial advection velocity of the tip vortices increase. There is good agreement between the downwind and upwind axial positions of the tip vortices with the pitch of the upwind results slightly less than that of the downwind results. The difference is minor and within the bounds of uncertainty of the measurements. Looking at individual vortex properties, stronger vortices are shed into the wake with increases in tip speed ratio. The evolution of tip vortex strength with increasing vortex age can be seen in figure 8. It is evident that in the near wake investigated here the rate of vortex diffusion is a function of the initial strength, with the stronger vortices produced by a higher tip speed ratio diffusing faster. From approximately VAt500 R , the rate of diffusion between cases is approximately equal, indicating a possible end to an initially transient decay.

Figure 8: Decay of the tip vortex strength with increasing vortex age, dashed lines and hollow symbols -downwind results, solid lines and symbols -upwind results O=4, O=7, O=10

Vortex meander is a phenomenon that affects both the tip and root vortices. In a multi-vortex system, such as a wind turbine wake, the induced velocity field of a single vortex acts as a perturbation to all other vortices in the field. In addition, it is thought that the wakes of the tower structures will also promote meander of the coherent tip and root vortex structures. Vortex meander is characterised by the standard deviation of the instantaneous vortex cores' position fluctuations in each measurement axis, V x and V y . A probability density function of the instantaneous vortex core position fluctuations was created and a Gaussian profile fitted to the profile [START_REF] Devenport | The structure and development of a wing tip vortex[END_REF]. The standard deviation V i is then extracted as a fitting parameter for each axis and presented in figure 9 versus the vortex age. The trend lines in figure 9 indicate that tip vortices meander increase with vortex age. In a physical sense, increased vortex meander is a possible indication of instabilities that arise within the helix.

The trend lines indicate that a stronger vortex is capable of resisting meander, as a tightly wound vortex will restrict intrusion by turbulent fluid at the outer of the vortex core. The large deviations from the trend, particularly evident in the O=10 case, can be attributed to the wake becoming unstable past x/R>0.7 or VA>360 R . It is thus reasonable to say that at a tip speed ratio greater than the design condition, stronger vortices are created with a reduced helix pitch leading to the wake becoming unstable closer to the rotor plane. This is evident from the qualitative flow visualisations and the quantitative date presented in figure 5.

Root vortex behavior

Coherent root vortices can be seen in figures 2, 3, 4 and 5 at early vortex ages (0°<VA360°) but they diffuse soon thereafter. The numerical study by [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF] indicated that the small radius of curvature of the root vortex helix and the close proximity of adjacent helix turns are the primary reasons for instabilities arising in the root vortex signal. Also, for the early onset of instabilities arising in the root vortex signal, the helical vortex filaments emanating from field turbines will be affected by the tower support structure. The numerical studies of [START_REF] Troldborg | Actuator line simulation of wake of wind turbine operating in turbulent inflow[END_REF] and [START_REF] Ivanell | Analysis of numerically generated wake structures[END_REF], did not model the support structures of the rotor (nacelle, hub and tower sections). Here, these structures are included allowing us to make some further comment on the enhanced rate of diffusion of the root vortices due to the supporting structures.

It is hypothesised that the enhanced diffusion of the root vortices in an upwind turbine wake is primarily due to three phenomena. Firstly, the root vortices are in close proximity to the nacelle boundary layer, secondly, the root vortex must interact with the tower section and lastly the root vortices envelop the low velocity wake core fluid immediately downstream of the nacelle. The root vortices of a downwind turbine will be subjected to the first and third phenomena only. The three effects will now be discussed in terms of an upwind turbine configuration.

The vorticity within the nacelle boundary layer is of the same order of magnitude and opposite sign to the coherent root vortices, which will result in cross annihilation of vorticity as discussed by [START_REF] Ebert | The near wake of a model horizontal-axis wind turbine part 3: properties of the tip and hub vortices[END_REF]. In the model configuration used in the [START_REF] Ebert | The near wake of a model horizontal-axis wind turbine part 3: properties of the tip and hub vortices[END_REF] study the hub vorticity created by the blades is cross annihilated by x/R=0.64.

Due to the small radius of curvature of the root vortex helix, the root vortices are susceptible to adverse effects caused by their interaction with the tower section, here denoted as root vortex-tower interaction (RVTI). A vortex cannot pass through a solid surface (tower section) and this interaction will have detrimental effects on the root vortex structure, possibly leading to instability and early breakdown. The onset of RVTI can be estimated by simulating the theoretical helical pathline (simple helix) of the root vortex core location using parameters obtained from the experimental data, namely the helix pitch and vortex cylinder radius.

For the current model configuration, a turbine operating at its design tip speed ratio, the onset of RVTI occurs at a vortex age (VA) of approximately 270 R . The root vortices in the measurement plane shown in figure 3 will be affected by the RVTI phenomena at an axial distance greater than 0.44R. The root vortex signal diffuses quickly after this point such that it is not evident by VA=480 R . For the turbine model operating at O=4, the onset of RVTI occurs at a vortex age of approximately 225 R . Thus the root vortices in figure 4 will be affected by RVTI phenomena at an axial distance greater than 0.61R. For the turbine model operating at O=10, the onset of RVTI occurs at a vortex age of approximately 315 R . Thus the root vortices in figure 5 will be affected by RVTI phenomena at an axial distance greater than 0.36R.

At axial locations greater than the length of the nacelle the root vortices are subjected to the low velocity fluid immediately downstream of the nacelle section. Flow visualisations have shown this region to be highly turbulent and three dimensional due to the pulsatile inflow created by the rotating blades and the momentum transfer occurring between the outer regions of the wake and the wake core. The three-dimensionality of the fluid in this region promotes instabilities leading to breakdown of the coherent root vortex structures. A combination of the three different phenomena all contribute to the fast breakdown of the root vortex signal.

Conclusion

The wake structure of a model horizontal axis wind turbine based on the Tjaereborg field turbine has been investigated in a water channel facility using planar particle image velocimetry. Three different tip speed ratios were investigated corresponding to a lightly-loaded, design-load and heavily-loaded rotor condition. In addition to characterising the tip vortex structure, particular attention was given to the root vortex. The results indicate a weaker vortex is more susceptible to vortex meander. The meander is a possible indication of instabilities which arise along the helix. With a reduction in helix pitch, at tip speed ratios above the design condition, the wake is susceptible to the mutual induction instability and becomes unstable closer to the rotor plane. The rapid diffusion of the coherent root vortex is hypothesised to be due to three primary factors, namely the root vortex-tower interaction, vorticity within the nacelle boundary layer and the low momentum fluid directly behind the nacelle section. It has been shown that phase-averaged data gives accurate general information on wake structure. However, due to vortex meander, the spatial smoothing which results from phase-averaging can mask a vortex's true properties. Thus it has been shown that instantaneous PIV realisations and suitable vortex identification schemes are required to characterise vortex properties.

Figure 1 :

 1 Figure 1: Experimental setup of the wind turbine in an upwind configuration in the FLAIR water channel

Figure 3 :

 3 Figure 3: Phase averaged wake of the Tjaereborg wind turbine operating in an upwind configuration at its design tip speed ratio (O=7) depicting the coherent vortical structures within the near wake, contours of tangential vorticity, Z z .

Figure 4 :

 4 Figure 4: Phase averaged wake of the Tjaereborg wind turbine operating in an upwind configuration below its design tip speed ratio (O=4) depicting the coherent vortical structures within the near wake, contours of tangential vorticity, Z z .

Figure 6 :Figure 7 :

 67 Figure6: Mean axial position of the tip vortices with increasing vortex age indicating increase in vortex convection speed with tip speed ratio, dashed lines and hollow symbols -downwind results, solid lines and symbols -upwind results O=4, O=7, O=10

Figure 9 :

 9 Figure 9: Axial (left) and radial (right) tip vortex meander increase with vortex age indicating stronger vortices less prone to meander in the near wake, dashed lines and hollow symbols -downwind results, solid lines and symbolsupwind results O=4, O=7, O=10

15th Int Symp on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal, 05-08 July, 2010


Fabrice Ferlin
email: ferlin@math.univ-lyon1.fr

Hugues Chabot
email: hugues.chabot@univ-lyon1.fr

Fabrice Ferlin S2hep

Vortex Theories in the Early Modern Period

Keywords:

Introduction

In the early modern period, various philosophers and scholars have proposed the idea of the vortex, i.e., of a fluid in rotational movement around an axis, in particular Descartes, to explain the movement of the planets around the Sun, in the same direction and in approximately the same plane. Some of Descartes' disciples, the most prominent being Malebranche, generalized this idea by imagining the universe entirely filled with small vortices, of all sizes, in order to explain all physical and chemical phenomena. These theories were gradually abandoned in the first half of the eighteenth century in the face of the growing success of Newtonian mechanics. It was only in the nineteenth century that vortex flows were really understood by physicists.

Kepler and Descartes

In the early modern period, the vortex theory is standardly associated with Descartes, constituting the basis for his explanation of the movement of the planets. The idea of a fluid vortex dragging the stars along their paths and thereby explaining their movements is however an old one, as it was the ancient atomists who first used this concept. Kepler, in turn, used the idea of a vortex driven by the rotation of the Sun around its own axis to explain the movement of the planets in a heliocentric context. Unlike the vortex as conceived by Descartes, Kepler's vortex acts almost immaterially: it is an emanation ("species immaterial") radiating from the Sun and rotating with it, which drives the planets along their orbits. For Kepler, this vortex explains only the general movement of the planets around a circle centered on the Sun, while the variations in distance from the Sun during the orbital path -an ellipse in which the Sun occupies one of the foci -are explained by a magnetic force between the Sun and the planets.

Descartes provided the first description of his vortex theory in a manuscript that remained unpublished during his lifetime, Le monde ou traité de la lumière (Descartes 1664). This text, written in the early 1630s, was contemporary with the condemnation of Galileo's heliocentrism. As Descartes' theory implied the movement of the Earth around the Sun, he preferred to delay its publication and only put partial elements into print: Dioptrique, Météores... (Descartes 1637). It was only in 1644 that Descartes finally published his Principia Philosophiae (Descartes 1644), which gave a complete presentation of his vortex theory.

Descartes' goal, and one he shared with Kepler, was to replace the olds explanations that the scholastics had given for the movement of the planets and so dispense with the crystalline spheres driven by mysterious cosmic forces that carried the planets in their orbits around the Earth. For Descartes, the vortex approach represents a way of "mechanizing" the explanation of celestial movements.

In this system, the matter in the Universe is divided into three types of elements. Most of the space is filled up with the round corpuscles of the second element. The first element, composed of very subtle, small, and mobile corpuscles, makes up the Sun and the stars. The corpuscles of this first element are "scrapings" resulting from the friction between the corpuscles of the second element, and they fill all the gaps between these larger corpuscles, as there is no void in the Cartesian universe. Finally, the Earth and the planets are made up of the much larger and coarser corpuscles of the third element.

Each star, including the Sun, is surrounded by a fluid vortex rotating around it, and this vortex is made up of particles of the second element. All the matter in a vortex tends to move away from the center (occupied by the star or the Sun) due to the centrifugal force generated by the rotation of the vortex. The indefinite expansion of any vortex is prevented by the presence of other vortices, allowing each one to reach a kind of state of equilibrium. This equilibrium is very relative, with some vortices being eroded or even ultimately destroyed by neighboring ones. More importantly, stars that have had their vortices destroyed become planets or comets, the former being captured by a neighboring vortex, while the latter, interstellar travelers, now move from one vortex to another. The matter of the vortices drags the planets along their paths and thus explains the revolution of the planets around the Sun (or the stars) and their orbits. In the case of the solar system, the matter of the vortex rotates more and more slowly as we get further away from the Sun, until the orbit of Saturn, the most distant known planet. Beyond Saturn's orbit lies the outer part of the vortex, by far the largest part. Starting from here, the law of motion is reversed: the further away from the Sun and the closer to the edge of the vortex we get, the faster the fluid rotates around the Sun. For Descartes, this is the domain of comets, which pass with great speed from one vortex to another.

It should be noted that Descartes aims to provide a global description of the Universe and is not, like Kepler, trying to explain the movement of the planets in detail. The matter of the first element, which constitutes the body of the Sun, arrives from the neighboring vortices via the poles of the solar vortex (hence from the north and south), while the same matter is subsequently expelled from the Sun along the plane of the ecliptic, from where it will nourish the neighboring vortices, and thus the neighboring stars, passing once again via the poles of their vortices. There is, therefore, a whole cycle of transport for this material from one star to another. According to Descartes, two neighburing vortices cannot be in contact through their poles. On the other hand, there are neighboring vortices whose poles are in contact with the equator of another vortex, which enables the transport of part of the corpuscles of the first element between the stars. These corpuscles [which are in fact groups of corpuscles forming small columns] have a cross-section in the shape of a curvilinear triangle with concave sides. These concavities form "channels", and these corpuscles are called "channelled" (or channelled parts), a shape that facilitates their movement. As the movement of these small columns of the first element from one pole to the center of the vortex combines with the rotation of the vortex, they describe a spiral trajectory.

Light comes from the action of the stars, according to two processes. First, the very violent agitation of the first element within the body of the Sun and the stars pushes out radially on the surrounding second element, which explains the emission of light in all directions. For Descartes, the propagation of light is instantaneous (infinite speed) and corresponds to the transmission of pressure within the second element. Then there is an additional cause of light emission in a star's plane of rotation, which in the case of the Sun corresponds approximately to the plane of the planetary system, and that is the action of the centrifugal force that pushes the corpuscles of the vortex radially. In the terms of the Cartesian theory, we can say that the first element is the source of light, the second is its vector, and the third reflects light.

Descartes gives an explanation of gravity based on the fact that each planet is also at the center of a vortex of corpuscles of the second element. This vortex, embedded in the great solar vortex, helps to explain the movement of satellites such as the Moon or Jupiter's four main satellites. At the surface of each planet, the vortex has a much higher velocity than the diurnal rotation, so that the centrifugal force of the vortex's corpuscles is greater than that of "ordinary" matter (composed of the third element). The matter of the vortex that circulates beneath any single body separated from the earth's surface rises above this body, and the body descends to occupy the place of the subtle matter. Moreover, according to Descartes, this rapid movement of the second element is not only in the form of a vortex, there are also many different motions of the subtle matter in every direction. The second element, repelled by the hardness of the earthly body, tends to move away from it, and to push the coarse matter toward the center of the Earth (Descartes 1647, Part IV, art. 27) (see [START_REF] Palmerino | Bodies in water like planets in the skies: uses and abuses of analogical reasoning in the study of planetary motion[END_REF], Schuster 2013).

After Descartes

The explanation of the Earth's gravity was the topic of a significant debate at the Royal Academy of Sciences in 1669. This provided Huygens with the opportunity of transforming the qualitative hypothesis of vortices into a physico-mathematical model. After demonstrating with an experiment that a body immersed in a vortex of water is pushed back toward its axis of rotation, he applied theorems of centrifugal force to calculate that the velocity of fluid matter needs to be 17 times higher than that of a point on the equator to produce gravity. However, two facts needed to be explained, namely that heavy bodies are not driven horizontally by the subtle matter and that they are not pushed toward the axis of rotation of the vortex but toward its center. Huygens proposed that subtle matter was moving in circular motions in all directions on spherical surfaces and that under the influence of the very fast and diverse successive impulsions of the subtle matter, heavy bodies do not follow any specific circular motion, while the centrifugal force of the subtle matter produces a gravitational action in all planes of the spherical vortex, i.e., toward its center. In his Discours de la cause de la pesanteur, [START_REF] Huygens | Traité de la lumière, où sont expliquées les causes de ce qui luy arrive dans la réflexion et la réfraction et particulièrement dans l'étrange réfraction du cristal d'Islande. Avec un Discours de la cause de la pesanteur[END_REF] discusses the effect of the Earth's rotation on the period of oscillation of a pendulum. He calculated that the diurnal motion of the Earth reduces the weight by 1/289 at the equator. Another expected consequence was that the Earth should have the shape of an oblate spheroid. Using Newton's model, which consisted in studying the equilibrium of two fictitious channels leading from the center of the Earth to the poles and to the equator, Huygens calculated the ratio of the axes of the terrestrial spheroid, although he arrived at a different result because he assumed that gravity within the Earth was the same as on its surface. Although it was the best developed among all the Cartesian theories of terrestrial gravity, Huygens' approach failed to account for either universal gravitation or the inverse square law.

The influential Cartesians Regius, Rohault, and Régis faithfully adopted Descartes' vortices, making no new contributions to the theory of planetary motion. Like Descartes, they failed to take Kepler's laws into account, although most astronomers knew about them at the time. Rohault's Traité de physique [START_REF] Rohault | Descartes-Agonistes: Physico-mathematics, method and corpuscular-mechanism[END_REF] becomes the reference text for Cartesian physics, especially in Cambridge. The English edition, annotated by Samuel Clarke, was published in 1697 and did not feature any criticism of the vortices and did not even mention Newton's gravitational force of attraction. It was only in the notes added to the book in 1710 that the vortices were presented as fictions for the first time and only in the footnotes of subsequent editions that the editors raised the Newtonian objections to the vortices. In France, Fontenelle popularized the theory of vortices in his Entretiens sur la pluralité des mondes (1686), by associating it with his idea of a plurality of worlds.

The Development of Vortex Theories

Leibniz also proposed a vortex-type theory of planetary motion, partly inspired by Kepler's theory (Leibniz 1689). For Leibniz, a planet's orbit resulted from two different motions: a circular "transradial" motion, centered on the Sun, which was due to the action of the vortex around the Sun, and a radial motion resulting from the action of two forces, namely a centripetal force of gravitation toward the Sun and a centrifugal force due to the planet's motion around the Sun. The gravitational force, he suggested, could be due to rays emanating from the Sun, which would explain why the gravitational force was inversely proportional to the square of the distance of the planet (light intensity also decreases according to an inverse square law). Leibniz was the first author to try to provide a detailed explanation of planetary motion based on a vortex theory, and for a long time, his remained the only such attempt. It was only at the end of the first decade of the eighteenth century that others would try to do this again. This new era was initiated by the clergyman from Lyon; Philippe Villemot who, in 1707, published his Nouveau Système ou Nouvelle Explication du Mouvement des Planètes [START_REF] Villemot | Nouveau système ou nouvelle explication du mouvement des planètes[END_REF]. In this short book, he tried to explain the main laws of planetary motion based on vortex theory, in particular Kepler's third law, which he explained on the basis of an equilibrium between the centrifugal forces of the successive concentric layers of a vortex. This explanation was later adopted by other authors and was elaborated by Privat de Molières from the late 1720s onward. Many theoretical but also experimental (like Nicolas Saulmon's -see Saulmon 1717) works attempted to give an explanation of terrestrial gravity using vortex theories. It should be noted that most of the authors who tried to develop this kind of theory between 1707 and the end of the 1730s lived in France (see [START_REF] Brunet | L'introduction des théories de Newton en France au XVIIIe siècle[END_REF]. This seems to be related to a growing awareness of the threat that Newton's doctrine posed to vortex theories and to Cartesianism in general, in a context where French scholars wanted to defend their fellow countryman. This awareness increased throughout the second decade of the eighteenth century, and was accentuated by the publication of the second edition of Newton's Principia in 1713 (Newton 1713) featuring Cotes' strongly anti-Cartesian preface. This second edition was much more widely disseminated than the first edition of the book. Newton's Principia itself contained virulent attacks on the vortex theories, insisting that such theories were incompatible with Kepler's laws. Another important factor was the controversy between Leibniz and Samuel Clarke, where Leibniz argued that Newton's ideas posed a materialist and antireligious threat to society (see [START_REF] Shank | The Newton wars and the beginning of the French enlightenment[END_REF]. Moreover, Newton's hypotheses concerning the existence of a void and action at a distance were generally not well received, with action at a distance suggesting the resurgence of the "occult ideas" of scholastics that Descartes had succeeded in banishing from natural philosophy.

"Small Vortices"

In his "Eclaircissement XVI" of De la Recherche de la vérité published in 1712 (Malebranche 1712), Malebranche introduced some major reforms in the Cartesian doctrine. Here, he proposed the particularly significant innovation of small vortices of subtle matter to replace Descartes' corpuscles of the second element. There was still no vacuum in this system, as the gaps between the small vortices were filled in by even smaller ones. These small vortices maintained equilibrium thanks to the reciprocal action of their respective centrifugal forces. Malebranche intended these small vortices to play a large role in the explanation of many physical phenomena, such as the hardness and elasticity of bodies, the propagation of light and heat, why heavy bodies fall... Indeed, this concept was adopted by many authors starting in the 1720s.

The theory of small vortices was significantly elaborated by Privat de Molières in his Leçons de Physique (Molières 1733-1739). Molières proposed that Malebranche's small vortices were themselves made up of even smaller vortices, suggesting a chain of small vortices of different orders. The equilibrium and disequilibrium among these small vortices could, it was hoped, be used to explain all physical phenomena, covering not only magnetism and electricity but also chemical reactions. However, the introduction of small vortices did not replace the large Cartesian ones, which continued to be used to explain the motions of the planets and their satellites.

The Twilight Years of Vortex Theories

In general, by the 1730s the supporters of vortex theories had become as virulent as they were dogmatic, although they did try to incorporate some Newtonian results into their conceptual framework. It was during this period that a "Newtonian party" emerged within the Royal Academy of Sciences in Paris around Pierre-Louis de Maupertuis, who with A Discourse on the different forms of the stars (Maupertuis 1732) became the first major French scientist to come out in support of Newtonianism and against the vortex theories. The trend of incorporating Newtonian ideas into vortex theories is clearly visible in the memoirs submitted for the Academy's prizes during this decade by scholars such as Jean and Daniel Bernoulli (see, e.g., Bernoulli 1752) and Pierre Bouguer [START_REF] Bouguer | Entretiens sur la cause de l'inclinaison des orbites des planètes. Jombert[END_REF]. Gamaches also adopted this approach (Gamaches 1740). At the end of the 1730s and beginning of the 1740s, scientists generally abandoned the vortex theories following a generational change in France marked by the disappearance of those who had received their training in a Cartesian setting. Furthermore, expeditions to Lapland and Peru in order to determine the shape of the Earth had a major effect in discrediting the vortex theories at this time. These expeditions provided evidence that the Earth is flattened at the poles as predicted and calculated by Newton and not elongated as predicted by supporters of vortex theories like the astronomer Cassini.

The early 1740s witnessed the triumph of Newtonian theory in France, with landmark publications in favor of the theory by Clairaut (Théorie de la Figure de la Terre, 1743) and D'Alembert (Traité de dynamique, 1743). The 1740 tidal prize stands as a significant indicator of a shift in stance by the Académie Royale des Sciences. For the first time, the judges of this prize accepted "Newtonian" submissions on the subject, although Fontenelle, the perpetual secretary of the Academy from 1697 to 1740, remained an adept of the vortex theory until the end of his life, publishing the last notable text in support of this theory as late as 1752 (Fontenelle 1752). This period also coincides with the production of texts that assessed the many objections that had been made against Cartesian vortices [START_REF] Bouguer | Entretiens sur la cause de l'inclinaison des orbites des planètes. Jombert[END_REF], leading to the marginalization of explanations of gravitation in line with Descartes' mechanical philosophy. Even other mechanical theories that bore no relation to vortex theory, such as Le Sage's corpuscular theory (based on ideas that can already be found in Nicolas Fatio's work), failed to attract any interest because of the absence of any plausible mathematical models.

For more information on vortex theory see the publications by [START_REF] Brunet | L'introduction des théories de Newton en France au XVIIIe siècle[END_REF], [START_REF] Aiton | The vortex theory of planetary motions[END_REF]), Guerlac (1981), [START_REF] Shank | The Newton wars and the beginning of the French enlightenment[END_REF]Borghero (2011); also see the introduction to Crepel and Schmit (2017).

Cross-References


Alien Arias Barreto

Ivonne Rodriguez Donis
email: donis@instec.cu

Arias Barreto

Ivonne Rodríguez Donis

Vincent Gerbaud
email: vincent.gerbaud@ensiacet.fr

OPTIMIZATION OF HETEROGENEOUS BATCH EXTRACTIVE DISTILLATION WITH NON NEGLIGIBLE HEAT EFFECTS

Keywords: batch extractive distillation, heterogeneous entrainer, heat effects, optimization, genetic algorithm

Optimization of batch distillation has been treated extensively in the literature. However, batch heterogeneous distillation has been less considered and even less in extractive mode. The performance of the optimization scheme is illustrated through the separation of chloroform -methanol mixture with water considering non negligible heat effects. The resulting design is compared to the corresponding case in which heat effect is ignored.

The objective function maximizes the overall profit and the optimization variables are the entrainer flowrate, temperature of entrainer feeding, the reflux ratio composed by an optimal proportion of both decanted phases during the chloroform distillation stage and the reflux ratio during the methanol distillation stage. Recovery and purity of chloroform methanol and water are set as constraints during the calculation. The optimization relis upon a genetic algorithm procedure and the simulation of the process is coded in two different modes: considering a short-cut model with constant molar overflow assumption for the negligible heat effect process and taking into account a differential mass balance model computing the molar overflow variation inside the column through the energy balance.

Two different alternatives are compared, taking into account negligible (case I) and not heat effects (case II). Profitability for case II is about 35 % higher compared to case I. The optimal temperature for feeding the heterogeneous entrainer (water) was around 28°C allowing a reduction of 18.4% of entrainer, a lower chloroform-entrainer reflux to the column top (14%) during the chloroform withdrawal and lesser reflux ratio for the recovery of methanol. Besides, better recovery (+3.4%, +1.3%) and purity (+0.2%, +0.5%) of chloroform and methanol were obtained, respectively. This optimal policy allows the feeding of heterogeneous entrainer near to the normal environmental temperature reducing the extra energy spending to heat the entrainer until its boiling temperature.

Introduction

Batch distillation becomes invaluable when it is necessary to take care of small quantities of materials with a great diversity in composition. Azeotropic and extractive distillation processes are the most used processes for separating azeotropic or close boiling mixture always involving the addition of an auxiliary entrainer. Although heterogeneous entrainer has been often used in batch azeotropic distillation, its application has been extended to extractive mode only recently [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF][START_REF] Pommier | Heterogeneous batch distillation processes: Real system optimisation[END_REF]. The main interest of heterogeneous batch extractive distillation (HBED) is that the resulting ternary diagram can exhibit more than one heterogeneous azeotropic mixture. The continuous feeding of the heterogeneous entrainer allows the binary heterogeneous azeotrope being a saddle of the residue curve map to be drawn as top vapor of the distillation column. Unlike to the homogeneous entrainer, the heterogeneous entrainer can be fed at the column top and the process takes place with an extractive section only. The following operating tasks for HBED were considered in this work:

-(T 1 ) Startup of the column at infinite reflux. The unstable node located at the ternary heterogeneous azeotrope reaches the column top. -(T 2 ) Filling the top decanter along with continuous feeding of the entrainer (F E ) using a reflux ratio equals to unity. the saddle binary heterogeneous azeotrope replaces the ternary heterogeneous azeotrope. -(T 3 ) Operation at a given reflux ratio (R') together with (F E ) until molar purity of the partially miscible original component in the distillate drops below 0.99. -(T 4 ) Off cut product distillation using a R offcut =1 in order to diminish the molar composition of immiscible original composition into the boiler less than 0.001. -(T 5 ) Separation between the homogeneous original component and the entrainer at a given reflux ratio (R") without (F E ) feeding.

A stochastic optimization method, genetic algorithm real-coded in MATLAB, is used along with the simulation of the HBED. Simulation is performed considering a differential mass balance inside the column with the typical assumptions: theoretical plates, negligible pressure drop and liquid hold-up on the trays. Top decanter is considered as a total condenser with a significant liquid hold-up. Hence, both decanted phases are refluxed as boiling liquid. Several parametric studies have demonstrated that reflux ratio (R') and the entrainer flowrate are the variables having a key incidence over the overall profit of the HBED. Mujtaba pointed that the optimal overall profit in homogeneous BED is mainly determined by assuring optimal values for F E and R' in the task (T 3 ) because independency between all tasks is not real at all [START_REF] Mujtaba | Optimization of batch extractive distillation processes for separating close boiling and azeotropic mixtures[END_REF]. The effect of the entrainer feeding temperature (T E ) has not been published hitherto. It implicates the inclusion of energy balance in the process modeling. Hence, this work is devoted to optimization of HBED through the solution of an overall profit function taking into account the heat effects and comparing with the corresponding case in which heat effects are ignored. We solve the optimization problem considering the entrainer flowrate (F E ) and its temperature (T E ) and top external reflux ratios (R' and R") as the key operating variables having a direct incidence over the economical profit of the HEBD. Liquid top reflux (R') during the chloroform removal comprises the whole amount of water-rich phase mixed with a portion α of the distillate phase from the top decanter. The decanter water-rich phase amount refluxed to the column top enables to keep constant the decanter light phase level [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF]. Indeed, α is the optimization variable instead of R'. A constant value for optimization variables will be considered because they are the simplest reflux policies commonly used in plant practice.

Optimization problem formulation

Case of study: Separation of chloroform -methanol azeotropic mixture

Optimization problem formulation concerns to the separation of azeotropic mixture chloroform -methanol which is widely used for separating bioactives substances from biological sources. Water was used in practice as an effective heterogeneous entrainer [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF]. Thermodynamic and topological features of the resulting ternary system are shown in Figure 1 including the univolatility curve chloroform -methanol ( 12 ). Thermodynamic calculations were done by using Simulis Thermodynamics®, a thermodynamic property server available in Microsoft Excel [4]. NRTL was chosen as thermodynamic model and the binary coefficients published elsewhere [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF]. Because the univolatility line 12 =1 ends at the edge chloroform -water, the saddle binary heteroazeotrope chloroform -water can be drawn as a vapour overhead at the column if water is fed continuously at the column top, giving rise to two liquid -liquid phases into the decanter after condensation [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF]. The heavy chloroform-rich phase (x II =x D ) can be drawn as distillate product whereas the water -rich phase (x I ) or a mixture composed by both decanted liquid phases can be refluxed toward the column top.

Modeling of HBED with non negligible heat effects

Schematic representation of the heterogeneous extractive distillation process in a rectifying batch column configuration is given in Figure 2. Unlike to the homogeneous extractive distillation, the heterogeneous entrainer is fed at the column top. where -Finite difference of mass and energy balances for the extractive section are:

(3)

Defining and for including in equations ( 3) and (4) become:

B xB (5) (6)
The liquid mole fraction and the reflux can be approximated by a first-order Taylor series expansion:

(7) Taking Δh =1, substituting equations ( 5) in (7) and assuming leads to:

(8)
Vapor phase in equilibrium is determined applying the modified Rachford-Rice procedure for a three-phase mixture as the vapor phase selected as a reference phase. i is the molar amount of each phase, Z i is the molar composition and K ij is the equilibrium coefficient.

(9)

Usually, HBED involves the reflux of the whole water-rich phase L I along with a portion " " of the chloroform rich-phase L II . The proportion of L I and L II inside decanter is determined by the liquid -liquid splitting ratio . Therefore, the liquid external reflux liquid at the top decanter is L R =L I + L II and the reflux ratio can be determines as:

(10) PROBLEM IT IS R' in the text and in the tables For enthalpy calculation , saturated vapor is the reference state, for both phases

(11) ( 12
)
where Tn is the equilibrium temperature and c'est soit lamba majuscule, soit H vap is the vaporization heat for the compound i at the height h. Cp and coefficients were taken from Component Plus® database [4]

Objective function and constraint s

Optimization problem will deal with the maximization of the overall profit of the process and it can be formulated as following:

MAX ) ( " ), ( ), , ( ), , (
) ( * * * * 5 3 3 2 3 2 2 2 1 1 T R T T T T T T F t C S C D C D C OP E E total f S (13)
subject to the constraint s: 99 . 0

D x
, for chloroform in T 3 and methanol in T 5 Recovery yield for all components: Re>90% C 1 (3.012 $/mol), C 2 (0.5085 $/mol) and C S (0.001 $/mol) are the prices of the products chloroform, methanol and the make-up of water, respectively. C f (0.0027 $/min) is the total operating cost of a real bench column. Optimization using some market product prices revealed a non sensitive effect for a given C f . It is assumed that the off-cut product (ternary heteroazeotrope) drawn in step 4 is not a commercial product and it can be recycled to the next batch. Table 1 displays the operating conditions for simulation of the separation of chloroform (1) -methanol (2) with water [START_REF] Mujtaba | Optimization of batch extractive distillation processes for separating close boiling and azeotropic mixtures[END_REF]. Real mixture to be separated contains a little amount of water. Genetic algorithm real-coded in MATLAB is used as optimization method. The initial population was set at 50, the selection rate is 0.8 and the mutation rate is 0.01. The optimization is stopped if not improvement of the objective function is achieved after 10 generations. Optimization by genetic algorithm requires many evaluation of the objective function and thus of calculation of the dynamic model. Use of a differential model as above allows a good approximation of the optimal operation conditions with less computational effort and time. The main results of the simulation are amount and composition in each product tank and the total operating time until the specified average purity of distillate cannot be maintained anymore (stop criterion). If one phenotype of the population doesn't accomplishes any constraint , the associated OP is increased by 10 6 .

The optimization variables are the ratio of (entrainer/vapor) flowrate (F E /V), the temperature of the entrainer feeding (T E ) for task 2 and 3, the reflux of the chloroform-rich phase R'(f( )) for task 3 and the reflux ratio R" for task 5. The aim of the optimization is searching an optimal value for all variables in order to compare the optimization results obtained with and without heat effects. Bounds for the optimization variables are: 1.2 (F E /V) 2 and 0.4 0.9 for chloroform recovery and 4 R" 10 for the separation of methanol -water. In the case of taking into account energy balance 25ºC T E 80ºC was set. The variable range for (F E /V), , T E and R" were taken from previous study according to the purity product constraint s [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF]; in particular the F E /V limit of 1.2 corresponds to the minimal value for the process to bea feasible [START_REF] Van Kaam | Heterogeneous Extractive Batch Distillation of Chloroform -Methanol -Water: Feasibility and Experiments[END_REF].

3-Results and discussion

Optimization of the HBED was performed considering two cases: (I) negligible heat effect and (II) non-negligible heat effect. Table 2 displays the optimal values for (F E /V), and R" for the scenarios I and II and T E for the case II. Value of the objective function OP and total operating time is also shown in Table 2. Case II provides the best optimal results. Profitability for case II is 34.28 % higher than compared to case I. The optimal temperature for feeding water is close to 28 ºC. Cooling the entrainer increases the liquid flowrate inside the column also intensifying the internal reflux ratio. In consequence, recovery and purity of all components are improved. The positive effect of a cooler entrainer feeding is lower (F E /V) ratio and chloroform-rich phase ( value) for the heterogeneous extractive distillation tasks T2 and T3. In the task T5 separation of methanol -water requires a smaller reflux ratio (R"). Overall, the operating time is higher than for case I because of the longer duration of task 5. The simulation results for each optimal operating case are summarized in Table 3. The first operating task concerning to the filling of decanter takes more time for case II because the partial condensation of the top vapor. However, this task has no significant contribution in the total operating time. At the end of the first task, the composition of the chloroform in the organic phase reaches the specified purity. Task T3 separation of chloroform by HBED takes 10 minutes more than case I but provides a higher purity and recovery. However, off-cut task T4 is also necessary for case II because the content of chloroform into the boiler at the end of HBED T3 doesn't match with the specification (less than 0.001). Task T5 final separation of methanol requires a lower reflux ratio but a longer duration (almost one hour more) for case II. However, this optimal operating condition allows a higher recovery and purity for methanol as second distillate product and the water retained inside the boiler at the end of the distillation process.

Conclusions

Multivariable optimization of heterogeneous batch extractive distillation was carried out by using genetic algorithm, an optimiser tool implemented in MATLAB. Total profitability was selected as the objective function taking into account the main variables of each operating tasks involved in HBED. Flowrate of the entrainer feeding, reflux of the chloroform-rich phase, portion of distillate refluxed and the reflux ratio for separating methanol are the typical operating variables for optimizing HBED. Entrainer feeding temperature has been considered as a new optimization variable through the integration of energy and mass balance. Two different alternatives have been developed taking into account negligible (case I) and non negligible heat effects (case II). Profitability for case II is about 35 % higher compared to case I. The optimal temperature for feeding the heterogeneous entrainer (water) was around 28°C allowing a reduction of 18.4% of entrainer, a lower chloroform-entrainer reflux to the column top (14%) during the chloroform withdrawal and lesser reflux ratio for the recovery of methanol. Besides, better recovery (+3.4%, +1.3%) and purity (+0.2%, +0.5%) were obtained, respectively. This optimal policy allows the feeding of heterogeneous entrainer near to the normal environmental temperature reducing the extra energy spending to heat the entrainer until its boiling temperature.

Figure 1 .

 1 Figure 1. Residue curve map of ternary mixture chloroform -methanol -water

Figure 2 .

 2 Figure 2. Column configuration of heterogeneous batch extractive distillation (HBED)

Table 1

 1 Input data for optimisation of HBED

	Parameters	value
	Initial charge (mol)	20
	Initial charge composition *	(0.2704/0.6714/0.0582)
	Decanter holdup (mol)	1
	vapor flow (Kmol/hr)	0.016
	Column pressure (bar)	1.013
	*(chloroform/methanol/water)

Table 2

 2

	Summary of the optimization results
	case F E /V T E (ºC)		R"	Total Time (min)	OP ($)
	I	1.74	100	0.85	8.4	596	25.36
	II	1.30	27.7	0.76	7.3	665	38.59

Table 3

 3 Simulation Results of each operating tasks for optimal operating values

	Operating Parameters	Case I	Case II
	Task 2
	time (min)	8	12
	x D1 in decanter (task 2)*	(0.995/0.005/0.000)	(0.995/0.005/0.000)
	Task 3
	time (min)	145	155
	x D1 in chloroform tank*	(0.992/0.006/0.002)	(0.994/0.005/0.001)
	chloroform recovery (%)	91.49	94.62
	end still composition*	(0.008/0.185/0.806 )	(0.005/0.155/0.839)
	Task 4
	off-cut time (min)	13	5
	Task 5
	time (min)	430	493
	x D2 in methanol tank*	(0.000/0.991/0.009)	(0.000/0.996/0.004)
	methanol recovery (%)	94.27	95.49
	x D3 in water in still*	(0.000/0.099/0.901)	(0.000/0.054/0.946)
	water recovery (%)	91.27	96.38
	*(chloroform/methanol/water)