The Intra-firm Coordination in Highly Innovative SMEs: Evidences from the Brazilian Agri-food Sector

Keywords: Innovation, Interactions, Intra-firm coordination, Knowledge

, reflecting on the governance of knowledge sharing inside organizations, suggests that knowledge may be difficult to transfer because of the boundaries dynamics. Due to this dynamic, innovation centered, it is important to create new ways of analyzing and developing the firm's activities, aiming to enhance its performance and to better understand the solution enablers for the new challenges to come. Therefore, the research question emerges: How can firms manage their intra-firm interactions to enhance the innovative activities? To answer this question, we designed and performed a qualitative study with 4 Highly Innovative Firms (HIF) from the agri-food sector, located in the south of Brazil. We used the dimensions of interactions and brokerage roles adapted from Aalbers (2015), Tsang (2015) and Indarti (2010) to develop a semi-structured instrument for the interviews. We analyzed the interactions that took place during a project of product development in each firm, and the interactions were classified according to: Hierarchy (Horizontal or Vertical); Reach (Unit or Cross-unit); Type (Formal or Informal) and we used Intensity (Frequency) as the base for the analysis. Our results showed two different forms of intra-firm coordination and one specific mechanism for the intra-firm coordination. We hope that this study can provide insights to the innovation studies and the agri-food sector. Defining the interactions was a first step and showcasing the intra-firm coordination, in a product development context, might help the firms to understand the importance that the different types of interactions have to manage the knowledge sharing processes.

INTRODUCTION

Combining a complex web of actions, variables and outcomes has been a big challenging for the researchers trying to understand the phenomenon of innovation. From a firm's perspective, in an ideal and utopic world, the team of workers would be composed by people with equal and complete knowledge about all the operations, methods, processes and techniques enrolled in the firm's activities. However, the reality points to a direction in which individuals hold the different types and amounts of knowledge. This knowledge, according to [START_REF] Indarti | The effect of knowledge stickiness and interaction on absorptive capacity[END_REF] is the key to innovate, and how to access it, share it and make it flow in a continuum inside the firm is the hand that holds this said key.

In the intra-firm perspective, [START_REF] Paruchuri | Intraorganizational networks, interorganizational networks, and the impact of central inventors: A longitudinal study of pharmaceutical firms[END_REF] argues that a firm that can improve the diffusion of knowledge internally will enhance its innovative activity. Yet, [START_REF] References Aalbers | Bridging firm-internal boundaries for innovation: Directed communication orientation and brokering roles[END_REF], reflecting on the governance of knowledge sharing inside organizations, suggests that knowledge may be difficult to transfer because of the boundaries dynamics. These boundaries dynamics are based and built in interactions and due to this dynamic, innovation centred, it is important to create new ways of analysing and developing the firm's activities, aiming to enhance its performance and to better understand solution enablers for the new challenges to come.

Our main goal is the understanding of the innovation process from the intra-firm coordination point of view, using the theory of interactions [START_REF] Becker | A theory of social interactions[END_REF][START_REF] Indarti | The effect of knowledge stickiness and interaction on absorptive capacity[END_REF] to understand the boundaries dynamics inside a firm. Despite wide acceptance that intraorganizational networks are important for organizational and individual outcomes, we know surprisingly little about how intra-organizational relationships evolve over time or how a firm's interaction patterns can be influenced by managerial action (Balkundi and Kilduff 2005).

Knowledge on this matter is particularly scarce when centring on intra-organizational innovation (Tortoriello 2007;[START_REF] Bartunek | Intergroup relationships and quality improvement in healthcare[END_REF]. Further research therefore can produce understanding of what constitutes success or failure of the intra-organizational innovation network by analysing several of its structural characteristics (Smith Doerr et al. 2004;[START_REF] Kijkuit | With a little help from our colleagues: A longitudinal study of social networks for innovation[END_REF].

To analyse the intra-firm coordination dynamic in an innovation centred environment, we performed a qualitative study with what we defined as highly-innovative firms located in the south of Brazil. We followed four firms in their product development process during the year of 2016. This study presents the partial results of a bigger project, involving companies located in South America and Europe. In the next sections we present the intra-firm coordination context, the relevance and motivation to study the Brazilian agri-food sector, the method, results and conclusions.

THE INTRA-FIRM COORDINATION AND THE INTERACTIONS

Digital age, multiple sources of information, non-stop knowledge being built in a borderless world causes the firm's task to realize, manage and coordinate its assets a complex and constantly changing task. We call this context: The intra-firm coordination problem. Firm's that are thirsty for innovation might have or might have not the knowledge needed to innovate, however to discover if the firm possess the knowledge and how to make use of it is basically a puzzle challenge.

In this sense, the role of interactions is highlighted by Foss et al. (2010), the author suggest that knowledge may come to be sticky to transfer because of the dynamics among firm's groups. These in-group-out-group dynamics can create a border to share knowledge with individuals from other groups. While stickiness of knowledge is related to the social embeddedness of those who might partake in knowledge transfer, this intra-firm dynamic of knowledge exactly crosses boundaries that has not been the subject of much scholarly attention. Although, to [START_REF] Salancik | A social information processing approach to job attitudes and task design[END_REF], in order to realize its commercial objectives and expand its innovative activities a firm need to develop its own knowledge or acquire knowledge through the interactions within its own environment. [START_REF] Lundvall | Product innovation and user-producer interaction[END_REF] was one of the first to point-out the advantages of interacting and the interactions as a big construct. The author put interaction defined as a 'mutual or reciprocal action' it refers to a continuous two-way transfer of information between two parties who have a close relationship. The idea of interaction as a two-way effect, opposed to a one-way causal impact, was present in the work of Wagner (1994). In the various sciences, interaction has differently tailored meanings. In a social perspective, [START_REF] Dyer | Specialized supplier networks as a source of competitive advantage: Evidence from the auto industry[END_REF] argues that spatial and cultural proximity plays an important role in the formation of the informal network.

The importance of intra-firm coordination is discussed also at the work of [START_REF] Paruchuri | Intraorganizational networks, interorganizational networks, and the impact of central inventors: A longitudinal study of pharmaceutical firms[END_REF]. The author states that a firm that can improve the diffusion of knowledge internally will benefit from enhanced innovative activity. Even as firms are urged to more readily allow innovative knowledge to cross firm boundaries, innovative knowledge may not easily move to where it can be used in the firm, however [START_REF] Aalbers | Individual connectedness in innovation networks: On the role of individual motivation[END_REF].

In an example of how complex the intra-firm coordination is, [START_REF] Henttonen | Exploring social networks on the team level-A review of the empirical literature[END_REF] argues that, in the multiple networks that constitute a firm, an individual employee may be relatively more internally orientated in one network while being relatively more externally oriented in another. A firm that seeks to benefit from enhanced innovative activity has to manage its intrafirm coordination, in a way that the interactions can provide boundaries that makes the knowledge flow in a proper way within its domain. The success of intra-firm coordination is deeply related on how the firm manages its interactions and provide opportunities to the innovative behaviour rise. Thus, all these dynamics of intra-firm coordination and its interactions relies, essentially, on the rhythm of the knowledge flow inside the firm. With these authors' insights, we believe to be possible to answer the intra-firm coordination problem and to suggest the firms the ways to improve its innovative performance.

THE BRAZILIAN AGRIFOOD SECTOR

In the last decade Brazil has become an agricultural powerhouse, and was the world's fourth leading exporter of agri-food and seafood products in 2015. The country is a dominant force in the sugar, coffee and orange juice markets, and is competing with the United States to be the world's largest soybean exporter (Euromonitor, 2016). The Brazilian agriculture sector employs 15.7% of the workforce and is estimated at 5.9% of GDP (World FactBook, 2016).

According to the CNAE (National Economic Activities Classification) the state we analysed, Rio Grande do Sul, count with 81 activities related to the food sector, which goes from slaughtering activities, rice growing to the production of "ready-to-eat" products. The relevance to study the state relies in the fact that the agriculture is the basis of the state's economy and the state produces a large variety of products such as soybean, rice, wheat, corn, barley, bean, grapes and apples. Considered the second largest grain producer in Brazil, the Rio Grande do Sul State produces 18.6 million of tons, equivalent to the fourth part of the country's entire grain production. Rio Grande do Sul also stands out for its animal production, which includes the cattle, swine and poultry, responding for 20% of national GDP.

The State Government adopts a development strategy that aims at strengthening the existing economic matrix and encouraging the installation of productive sectors considered equally strategic to complement the economic matrix, solve technological problems and generate jobs and income. According to the Brazilian Institute of geography and Statistics (IBGE, 2013), the state is the second largest rural producer; it has the second largest industrial park and the second trade center in Brazil. Responsible for almost 8% of the national production, it also has a GDP of US$ 46.5 billion.

All these characteristics make the food sector of Rio Grande do Sul an important start-point in this work. These aspects, combined with the study of highly-innovative firms, in an innovative context, such as the product development, add to the chances of being successful when explaining the intra-firm perspective of the innovation process.

METHOD

Our choice was to address the intra-firm coordination where the phenomenon is assumed to be more evident, thereby we decided to work with Highly Innovative Firms (HIF) and analyze a single project of product development.

We chosen to work with SMEs from the food segment and we chose four units of analysis. We performed what is called Qualitative non-interactive study with concept analysis, documental analysis and observation of the units.

The research instrument is based on the dimensions proposed by [START_REF] Indarti | The effect of knowledge stickiness and interaction on absorptive capacity[END_REF] and [START_REF] References Aalbers | Bridging firm-internal boundaries for innovation: Directed communication orientation and brokering roles[END_REF] with some specific additions regarding innovation and intra-firm interactions. A semi-structured instrument was used, as well complimentary questionnaires and checklists during the observation period. The interviews were performed in English and Portuguese, the content was recorded, translated to English, validated by the reversal translation method and by specialists. Finally, the interviews were analysed by using the software N-vivo and the content analysis method.

We chose to use content analysis because as a method it has systematic and objective means of describing and quantifying a phenomenon [START_REF] Krippendorff | Reliability[END_REF][START_REF] Downe-Wamboldt | Content analysis: method, applications, and issues[END_REF][START_REF] Sandelowski | Sample size in qualitative research[END_REF]. It is also known as a method of analyzing documents. Content analysis allows the researcher to test theoretical issues to enhance understanding of the data.

As for the units selection, we used the multistage sampling, derived from the cluster sampling method and judgment sampling technique as previously stated. A sample is, according to Field (2005) "a smaller collection of units from a population used to determine truths about that population". In cluster sampling, the cluster, i.e., a group of population elements, constitutes the sampling unit, instead of a single element of the population. The complex form of cluster sampling in which two or more levels of units are embedded one in the other is called multistage sampling.

Multistage sampling refers to sampling plans where the sampling is carried out in stages using smaller and smaller sampling units at each stage. Multistage samples are used primarily for cost or feasibility reasons. Our first clusters are SMEs, second cluster is the food industry, third Brazilian firms from the food industry, fourth Highly innovative firms, which means firms that released at least 1 product new to the market in the last two years. From this point, we mapped out the firms and we intentionally selected four firms to compose our sample.

The four firms we selected had unique products developed, the products were awarded in recognized fairs in Brazil. We focused our interviews in each process of product development, its general context, interactions, main units involved and the responsible for the ideas and to lead the project. Table 1 describes the sector, country, number of units, the presence or not of a R&D department and the size of each firm, as well as the code we use do refer to each firm, from A to D. We followed the suggestions of Tsai ( 2001), Wong & Singh (2004), [START_REF] References Aalbers | Bridging firm-internal boundaries for innovation: Directed communication orientation and brokering roles[END_REF] and Tsang (2015) as taking these dimensions to the development a new product introduced to the market, exploring the whole development.

Firm

• Type of Interaction: The type of interaction is important to verify how the coordination intra-firm is influenced by the hierarchy structure, it might be:

Horizontal -Same hierarchical level or Vertical -Different hierarchical level

• Interaction Reach: According to Tsang (2015) the reach of interactions may define the knowledge flow along the units, it is divided as: Intra-unit -Interactions in the same unit or Cross-Unit -Interactions between different units

• Interaction Mechanism: The Interactions may occur through two mechanisms:

Formal -By schedule and contracts or Informal -With no obligations

• Interactions Intensity:

Frequency -Quantity of Interactions along time

The horizontal and vertical interactions are important to verify how the coordination intra-firm works along the hierarchy structure. As the reach of the interactions, Tsang (2015) argues that cross-unit interactions are important to guarantee the knowledge flow and access to all units, and in times this flow occur in an informal way by a single agent. To verify the existent mechanisms could help us to understand what a firm can make to assure that the knowledge will be available to all units. Finally, the interactions intensity will help us to verify how far the influence of these interactions goes to the innovative process of the agri-food SMEs Regarding the Hierarchy, several authors discuss its influence on what is called Relational/Structural Embeddedness. It is argued that there are several advantages conferred by a structural embeddedness, provided most of the time for organizations with a strong hierarchy established, by manipulating the configuration of an actor's network of contacts. Among these advantages, those that come from having contacts who are more or less connected to each other have received perhaps the most attention. With this type of structure, the instrumental value to managers of having such sparse social networks accrues largely from privileged access to information and greater control over its use. These advantages should also enable mangers to create more value for their firm.

Moreover, a more horizontal and open hierarchy is related to relational embeddedness, one that establishes how much of the firm's potential will be realized. In other words, the quality of social interactions influences which of those resources that are within reach will be accessed, and to what extent. Although an actor may have access to several people who are potentially critical sources of information, personal experience and the quality of past interactions will often influence whom he or she is likely to approach and engage. In this sense, a firm with more soft hierarchy may enhance its interactions disregarding the difference among position levels, making possible that solutions emerge as results of free interactions within the firm.

Regarding the mechanism or nature of the interactions, the relation of formal and informal knowledge sharing might be exemplified, for instance, a strong corporate culture that stresses general sharing behaviour (e.g. in the form of organizational behaviour) may substitute (within certain ranges) for explicit incentive pay (formal incentive, formal interaction) for knowledge sharing. Formal organizational arrangements and informal organizational practices may be complementary to each other with respect to their impact on knowledge sharing.

For example, the effect of explicit incentives on knowledge sharing may be increased by the presence of a culture that accepts substantial pay differences across employees. On the other hand, studies have documented that formal organizational mechanisms (introducing extrinsic rewards in terms of payment) may act against existing informal patterns and practices (intrinsically motivated organizational members) and such a combination may destroy knowledge sharing behaviour and cause irreversible, long-term negative effects on organizational behaviour [START_REF] Osterloh | Motivation, knowledge transfer, and organizational forms[END_REF][START_REF] Robertson | Knowledge creation in professional service firms: Institutional effects[END_REF].

As for the intensity, [START_REF] Indarti | The effect of knowledge stickiness and interaction on absorptive capacity[END_REF] points out that the frequency of interactions might be a good indicative on how much innovative a firm can be. Although it is important to highlight that it is possible that the effectiveness of interaction have a decay level, which means that along the time if repeatedly without any space of a time the knowledge sharing might be compromised and give to meaningless interactions with lack of information exchange.

The same applies at intra-unit interactions, once that the knowledge inside the unit are easily spread, due to closeness it is safe to assume that a balance between cross-unit interactions and intra-unit might be necessary. We can also speculate that the use of instrumental-formal and expressive-informal communication to stimulate interactions can be explored as option to reach this desired balance.

RESULTS

The product development projects are described in table 03: It is important to mention that all the firms in this study export their products and invest at least 2% of their revenue in R&D projects. The table 04 show the most important details of the projects developed by the firms:

Firm A Firm B
• Hierarchy developed for the project.

• Cohesion at the intra-firm coordination. • Product Development was broadly discussed inside the firm. • Formal mechanisms used to share the information. • The structure used for the project remains to new projects.

• Product development was faster than predicts, from 10 months to 6 months. • A single unit was developing the product.

• Informal intra-unit and cross-unit interactions were the core of the coordination. • The centrality was key during the whole development and allowed the firm to make use of informal interactions.

Types of Interactions

With the protocol that was previously established in our methodology, a series of interactions were found in the four companies. According to the interactions pattern we observed in the product development project, by analysing the documents, videos, meetings reports and interview with the managers we found similarities in the type of intra-firm coordination adopted by the firms. To better express the results we found, we named the general orientation of the interactions. In this study we present two types, one oriented to a vertical pattern of interactions, taking the hierarchy as an important part of the innovation process and the second one, that had informal interactions as dominant among the units focusing on the knowledge, with less importance to the hierarchy.

The first form of Intra-firm coordination with our analysis was named the Hierarchy Oriented Coordination, as the name says in this type of coordination the firms focus on the hierarchy to assure the product development project to be performed. In the firm A and B, we found an extremely similar type of intra-firm coordination, the pattern of interactions had the hierarchy as basis to the organizational structure used in the project. The top management had direct contact with the Researchers and the interactions jumped levels to centralized the knowledge at the upper hierarchical levels and the interactions happened mainly as formal interactions. Reports, meetings and emails were broadly used the head of R&D and the Head of the project.

"I controlled our product development from the start and I had to make reports to the board so I usually go direct in the source, ask everything and then I send the reports with copy to everyone, ideas are always welcome"

Firm A

The second type of intra-firm coordination we found was called the Knowledge Flux it is a form of intra-firm coordination in which the firms organize a new structure to the development of the innovation, they settle the employees in the most comfortable position in order for them to interact and make the knowledge flow. It differs from the interactions oriented coordination because there is a change in the structure and in the positions occupied by the employees, rather than just ignoring it.

(...) Ah, we have our whatsapp group for the company and also facebook groups, we know it maybe something that has nothing to do with the project but we use it to share news about technology, new discovers and regular daily stuff, sometimes business opportunities and new ideas come from the group and for sure makes our employees to think more because they love the group. There is the facebook group also, but they use more for each unit and they don't cheap chat, it is just people posting news and asking questions regarding work, our researchers sometimes run some pools to know people opinion"

Firm C

With the analysis highlighted by using the case of firm C we can make a case for the use of specific tools for the intra-firm coordination. New technologies in the field of Information Technology emerge every day and firms that wants to innovate should understand the benefits they can have by using these tools. A proper intra-firm coordination requires established mechanisms and mechanisms requires tools, finally tools require capable individuals to understand how to benefit from it.

CONCLUSION

The intra-firm coordination may vary a lot from firm to firm, managers can use different tools, mechanisms and express their creativity in order to foster innovation. One of the highlights of our study was that it was not found a single unit based only on informal interactions, regardless if cross-unit or intra-unit interactions. This agrees with the management literature, since the work of [START_REF] Rothschild-Whitt | The collectivist organization: An alternative to rational-bureaucratic models[END_REF], authors argued that it is not possible to work without a minimum level of hierarchy sense, in the paradigm we live in. This allowed us to observe the possibility of existence of a limit to both informal and formal interactions, and firms should benefit if able to balance it and increasing both levels together. This should ease the process of innovation and knowledge absorption, making it seems natural for people.

The Brazilian companies highly value the product development, providing the units with more assets after the idea and the concept of the product is already conceived. As stressed during this entire study, the hierarchy plays a central role in the interactions, but due to the characteristics of the firms we studied (Highly innovative, which means, here, more than 2 products launched in the last year) it was not possible to visualize and exploit the results.

The literature points in the direction that hierarchy may interfere negatively in the process, which means it can shrink the frequency and reach of interactions. As for what we seen in the firms from our sample, the formal interactions seem to have a peak, and after this peak it loses its value and does not add knowledge. Informal interactions seem to make it possible to surpass particular obstacles, and may come in hand at special situations. Laukkanen et al. (2015) highlight that the intra-firm coordination can be understood as a catalyst for the innovative activities inside the firm. The main concern is related to how to manage the intra-firm coordination for a better knowledge flow. The interactions shine in this sense, understanding how the dynamics of changing the way that the employees interact may make them more inclined to share their knowledge may be the solution countless firms were looking for.

As for the future research we suggest, first, studies involving a broader sample and diverse methods. Second, we expect firms to incorporate the mechanisms and tools cited in this thesis and be aware that intra-firm coordination can lead to innovation and to the solution of several daily problems. One of the topics that recently gained strength in the field of innovation is the study of the innovation capabilities. In this sense, we suggest that each firm's capability could need a specific type of interaction to be developed, studies in this sense could help firms to understand better the relation interactions x innovation.

  used for the intra-firm coordination.• Multiple mechanisms both to formal and informal interactions. • Low influence of the hierarchy during the project.• Independent centralized management of the interactions.• Low relevance of the hierarchy• Freedom for the Innovation • The product received an award • The development was planned for 6 months and finished in 3 months.

Table 01 : Firms analyzed in the study Source:

 01 The authorsThe dimensions of the dynamics of Intra-firm Interactions are shown in the table 02:

	Dimension	Variation
		Horizontal
	Interaction Type	Vertical
		Unit/Intra-unit
	Interaction Reach	Cross-unit
		Formal
	Interaction Mechanism	Informal
	Interaction Intensity	Frequency

Table 02 : The intra-firm interactions dynamic

 02

Source: Based on

[START_REF] Becker | A theory of social interactions[END_REF]

;

[START_REF] Indarti | The effect of knowledge stickiness and interaction on absorptive capacity[END_REF]

;

[START_REF] References Aalbers | Bridging firm-internal boundaries for innovation: Directed communication orientation and brokering roles[END_REF]

.

Table 03 : Project of Product Development Characteristics Source: The authors

 03

Table 04 : Main facts about of Product Development Project Source: The authors

 04


Calvel Anne

Dubuc David

Caro Alexia
email: alexia.de-caro@ipbs.fr

Grenier Katia
email: grenier@laas.fr

Peytral-Rieu Olivia

Rols Marie-Pierre
email: marie-pierre.rols@ipbs.fr

Performing in vitro biological assays to evaluate the impact of electrochemotherapy treatments

Keywords: electrochemotherapy, permeabilization, viability, clonogenicity

Electrochemotherapy (ECT) treatment is now a routine technique for the treatment of cutaneous and subcutaneous tumors. To better understand the underlying mechanisms and effects of electrochemical stimuli on cells, performing biological experiments is particularly important. We propose to evaluate the impact of ECT treatments on cell permeabilization and cell viability. We present here a comparison between two viability assays -crystal violet staining and clonogenicity assays, on mammalian cells submitted to pulsed electric field used along the ECT protocols.

I. INTRODUCTION

Electroporation (EP) is a non-viral physical method of vectorization consisting in creating pores in the cell membrane by applying electric fields. This highly facilitates the transfer of compounds into cells or the extraction of intra-cellular molecules.

EP can be reversible or irreversible, depending whether the pores reseal, leading to the recovery of the cell functions, or not, leading to the cell death by apoptosis (see Fig 1).

Electrochemotherapy (ECT) is based on reversible EP technique in order to transiently permeabilize the cell membrane, facilitating the intra-cellular penetration of nonpermeant cytotoxic agents [START_REF] Sersa | Electrochemotherapy in treatment of tumours[END_REF]. Standardized in 2006 for the treatment of skin metastases and primary skin cancers, ECT relies more commonly on the use of bleomycin and cisplatin as cytotoxic agents. The electrical treatment generally consists of the application of 8 pulses, of 100 s width, 1.3 kV/cm at a frequency of 1 Hz [START_REF] Marty | Electrochemotherapy -an easy, highly effective and safe treatment of cutaneous and subcutaneous metastases: Results of ESOPE (european standard operating procedures of electrochemotherapy) study[END_REF]. Pulses intensities vary from 1 to 2 kV/cm.

It is of paramount importance to control the applied parameters, such as the electric field intensity and the cytotoxic compounds concentration, during ECT treatments and to evaluate their effects. Especially, it appears crucial to determine cells permeabilization state as well as the impact of such treatments on cells viability.

Cell permeabilization occurs when its membrane reaches a certain potential difference, the latter being the sum of the resting potential difference and the induced potential difference [START_REF] Teissié | An experimental evaluation of the critical potential difference inducing cell membrane electropermeabilization[END_REF]. As described by Schwan's equation, the applied electric field induces a potential difference that depends on the electric field strength:

∆ =
With ∆ the induced potential difference on a cell membrane, F the shape factor of the cell, a function depending on the conductivities of the cell and the pulsing buffer, r the radius of the cell, E the electric field strength and the angle between the direction of the field and the normal to the cell surface.

Determining the intensity of the applied electric field that triggers cell permeabilization, i.e., the permeabilization threshold, Ep, helps to optimize the electrical parameters applied during ECT treatments.

It also appears essential to lead viability assays in order to study whether the treatment induces reversible or irreversible EP. Among viability assays, because of their ease to implement, their low cost and their sensitivity, colorimetric assays are largely employed. Among them, one can encounter MTT, XTT, crystal violet and clonogenicity assays [START_REF] Aslantürk | In vitro cytotoxicity and cell viability assays: Principles, advantages, and disadvantages[END_REF].

Here, we propose a comparison between two colorimetric assays after ECT treatments: (i) crystal violet assay, performed 2, 24 or 48 hours after treatment, and (ii) clonogenicity assay, performed 10 days after treatment.

Crystal violet assays on adherent cell lines, developed in 1989, are based on the use of the crystal violet dye, that enters into the cells and targets DNA and proteins. The intensity of crystal violet staining directly depends on the number of cells present on the Petri dish (i.e., that have adhered to the culture support after ECT treatments).

Clonogenicity tests, developed in the 1950s, assess the ability of single cells to form colonies (i.e., able to divide). These tests are known to be particularly representative and precise [START_REF] Šatkauskas | Different cell viability assays following electroporation in vitro[END_REF].

II. MATERIAL AND METHODS

A. Cell culture and reagents

The studies carried out are based on HCT-116 cells, that are derived from carcinoma colorectal cancer cells. They are grown in Dulbecco's Modified Eagle Medium, supplemented with 20% fetal calf serum and a mixture of antibiotics 100 U/mL penicillin and 100 μg/mL streptomycin. Cells are incubated at 37°C under 5% CO2 for proliferation.

Cells permeabilization sensitization as well as cells viability depend on the medium in which they are pulsed [START_REF] Sherba | The effects of electroporation buffer composition on cell viability and electro-transfection efficiency[END_REF]. Therefore, we select a pulsation buffer with a low conductivity (1.7 mS), consisting of 10 mM K2HPO4/KH2PO4, 1 mM MgCl2, 250 mM of sucrose.

To assess cell permeabilization, we evaluate the entry into the cells of propidium iodide (PI), that is diluted in the cell solution to reach a final concentration of 100 M. PI is a nonpermeant molecule which binds to double-stranded nucleic acids when the cell membrane is damaged.

The ECT treatments consist in administrating bleomycin to the cell solution, to reach a final concentration of 250 nM. By binding to certain portions of DNA, bleomycin leads to the production of free radicals responsible for DNA strand breaks, resulting in cell death during the G2 phase of the cell cycle.

The colorimetric tests conducted in this study are based on the use of crystal violet (0.1% in aqueous solution).

B. Electroporation set up and procedure

Cells culture medium is removed and cells are washed with phosphate buffer saline (PBS). Trypsin is added and the cells are incubated for 5 minutes at 37°C under 5% CO2. A centrifugation (1300 rpm, 3 minutes) is then carried out. The cells are suspended in the pulsation buffer to reach a final concentration of 300,000 cells/mL.

Cells in suspension are then placed between flat and parallel stainless steel electrodes, with an inter-electrode distance of 4 mm. The bottom of the Petri dish serves as an electropulsation chamber.

A generator (Jouan GHT 1287) delivers the electric pulses, whose shape are verified by using an oscilloscope (Tektronix TDS 2012C). Electric pulses, comparable to the ones used during ECT treatments (8 pulses, 100 s width, 1 Hz), are delivered. Different amplitudes are tested, from 0 to 2.5 kV/cm.

C. Biological assays for the evaluation of cells permeabilization and viability i. Permeabilization assay

To assess cell permeabilization, PI is added prior to the application of electric pulses. After the EP treatment, cells suspensions are kept in ice until performing flow cytometry (BD LSRFortessa X-20) analysis over 20,000 cells. The percentage of permeabilized cells is determined. The obtained results are presented in section III (see Fig 3).

ii. Viability assessment

For cells enumeration assays, cells are seeded in 96-well plates at a final density of 15,000 cells/well. For clonogenicity assays, cells are seeded in 6-well plates at a final density of 300 cells/well. Cells are finally incubated at 37°C under 5% CO2.

Cells are removed from the incubator after the received treatment: 2, 24 or 48 hours later for cells enumeration assays (i.e., up to 1 or 2 generations time), and 10 days later for clonogenicity assays.

The culture medium is removed and a rinse with phosphate saline buffer containing calcium and magnesium ions is performed. Crystal violet (0.1% in aqueous solution) is added, a 15-minute agitation is carried out and three successive rinses with phosphate saline buffer containing calcium and magnesium ions are done.

After rinsing, depending on the study, the procedure differs: (i) for clonogenicity assays, a count of the number of clones is realized, whereas (ii) for cells enumeration assays, acetic acid is added to lead to cell lysis. A reading of the optical density is then made with a spectrometer (Varioskan Flash) at a 595 nm wavelength.

III. RESULTS

A. Permeabilization assays

Permeabilization percentage among cells is presented in Fig 3.

The uptake of the fluorescent dye into the cells is the signature of membrane electropermeabilization. We submitted the cells to increasing values of E and determine the permeabilization efficiency (i.e., the percentage of cells which become fluorescent). Permeabilization only appears above a threshold value of pulse intensity Ep. For E < Ep, which as shown in Fig 3 is comprised between 0.6 and 0.8 kV/cm, no permeabilization occurs. Above Ep, increasing E leads to the progressive permeabilization of the whole cell population, that is obtained at 2.5 kV/cm.

B. Short term viability assessments: cells enumeration assays

The next step is the determination of the cell viability in order to assess whether the intensities that lead to cells permeabilization whether induce reversible or irreversible EP.

The 2h, 24h and 48h viability studies show similar viability trends (see Fig 4). As expected, the effect of bleomycin on cells is much more pronounced at 48h, as the drug acts during the G2 phase of the cell cycle.

Bleomycin alone (250 nM) does not induce significant mortality (about 17% of cell death 48 hours after treatment). In agreement with the studies that can be found in the literature, the effect of the treatment is potentiated when an electric field is applied [START_REF] Čemažar | Intrinsic sensitivity of tumor cells to bleomycin as an indicator of tumor response to electrochemotherapy[END_REF]. For example, 48 hours after combining bleomycin to electric pulses at 1 kV/cm, cell death is about 79%.

As the electric field intensity is increased, cell mortality rate increases. For field values higher than 1.5 kV/cm, viability is affected (more than 30% mortality). One can notice that at 2.5 kV/cm, the electric field effect alone is sufficient to induce a high mortality rate (more than 80% mortality).

Once obtained, such a kind of results easily allows to define the best conditions for ECT treatment (high membrane permeabilization with low effect on cell survival). In our present work, the electric field values that can be used range from 0.8 to 1 kV/cm.

C. Long term viability assessments: clonogenicity assay

The results of the clonogenicity tests performed 10 days after ECT treatments confirm the short-term viability assay trend: an increase of cell death is induced when the electric field intensity is increased (see Fig 5). When bleomycin alone induces 70% mortality, electric fields significantly increase the mortality rate (only 5% of cell survival at 1 kV/cm).

IV. CONCLUSIONS

In the present study, we present biological assays to evaluate the effects of ECT treatments on cells permeabilization and viability. Permeabilization assay allows us to define the ranges of electric field intensity that induce permeabilization (E > 0.6 kV/cm). Viability assays allow to highlight the effectiveness of ECT treatments in comparison with the application of electric fields alone or the use of bleomycin alone. We evaluate the impact of these treatments at different temporal scales and evidence their effectiveness as early as 2h post-treatment in the case of crystal violet assays. As a comparison, clonogenicity, which is the gold standard method usually applied due to its high reliability, is much more time-consuming (several days) and requests high quantities of bio-reagents.

Fig 1 -

 1 Fig 1 -Principle of reversible and irreversible EP, inspired of [2].

Fig 2 -

 2 Fig 2 -Test bench for performing EP or ECT treatments on HCT-116 cells in suspension. The test bench includes an electropulsator to which an oscilloscope and electrodes are connected.

Fig 3 -

 3 Fig 3 -Permeabilization assay performed on HCT-116 cells in suspension. 100 M of propidium iodide is added before applying electric pulses, which intensities vary from 0 to 2.5 kV/cm. For each condition, 20,000 cells are analysed by flow cytometry.

Fig 5 -

 5 Fig 5 -Percentage of clones numbers obtained 10 days after EP and ECT treatments on HCT-116 cells in suspension. For all conditions, two batches are studied.

ACKNOWLEDGMENT

The authors acknowledge the support of Université Fédérale Toulouse Midi-Pyrénées and Région Occitanie.


Aliza Abraham
email: aliza.abraham@univ-amu.fr

Thomas Leweke
email: thomas.leweke@cnrs.fr

Experimental investigation of blade tip vortex behavior in the wake of asymmetric rotors

published or not. The documents may come

Experimental investigation of blade tip vortex behavior

in the wake of asymmetric rotors

Introduction

Rotors, such as those found on wind turbines, helicopters, and propellers, shed wakes which are characterized by helical tip vortices. These wakes, and the tip vortices in particular, can have detrimental effects on downstream structures. For example, wind turbine wakes with coherent tip vortices are known to increase the structural loading on downstream turbines within a wind farm, relative to fully turbulent wakes [START_REF] Sørensen | Instability of helical tip vortices in rotor wakes[END_REF]. In addition, tip vortices prevent mixing between the lowerspeed flow within the wake and the freestream flow outside [START_REF] Lignarolo | Tip-vortex instability and turbulent mixing in wind-turbine wakes[END_REF]. When downstream turbines are located within this low-speed wake, substantial power losses up to 40% have been observed [START_REF] Lee | An overview of wind-energy-production prediction bias, losses, and uncertainties[END_REF]. Several methods have been proposed for the mitigation of detrimental wake effects by modifying the whole wake flow through induction control, yaw control, and individual pitch control (see Meyers et al. [4] for an overview of wind farm flow control methods). The current study targets the tip vortices in particular, investigating a passive flow control method for the acceleration of tip vortex breakdown.

Helical vortex systems are subject to instabilities which can cause the vortices to break down. These instabilities fall into two categories: shortwave and long-wave [START_REF] Leweke | Long-and short-wave instabilities in helical vortices[END_REF]. Short-wave instabilities are characterized by perturbations smaller than the vortex core size, and long-wave instabilities, which are the focus of the current investigation, occur when the vortex displacements are large relative to the core size. These long-wave instabilities lead to pairing and leapfrogging, or the swapping of axial positions, between adjacent vortex loops. This pairing instability of helical vortex systems has been studied theoretically for decades, since Widnall [START_REF] Widnall | The stability of a helical vortex filament[END_REF] derived the growth rates of different wavenumber perturbations for a single helical vortex filament. Gupta & Loewy [START_REF] Gupta | Theoretical analysis of the aerodynamic stability of multiple, interdigitated helical vortices[END_REF] and Okulov & Sørensen [START_REF] Okulov | Stability of helical tip vortices in a rotor far wake[END_REF] extended this analysis to systems of multiple interdigitated helical vortices.

Several studies have also investigated the pairing instability in helical vortex systems using numerical methods. Bhagwat & Leishman [START_REF] Bhagwat | Stability analysis of helicopter rotor wakes in axial flight[END_REF] used a free-vortex method to characterize the stability of a helicopter rotor wake, observing several unstable modes including tip vortex pairing. Ivanell et al. [START_REF] Ivanell | Stability analysis of the tip vortices of a wind turbine[END_REF] and Sarmast et al. [START_REF] Sarmast | Mutual inductance instability of the tip vortices behind a wind turbine[END_REF] calculated the growth rates of wind turbine wake perturbations at different frequencies, first by modeling one third of the rotor under the assumption of azimuthal symmetry, then by modeling the whole rotor to highlight the importance of asymmetric modes. To test a practical method of generating unstable perturbations, Huang et al. [START_REF] Huang | Numerical analysis of the effect of flaps on the tip vortex of a wind turbine blade[END_REF] and Marten et al. [START_REF] Marten | Predicting wind turbine wake breakdown using a free vortex wake code[END_REF] modeled wind turbine rotors with flaps, showing that vortex pairing could be induced even with small actuation amplitudes. More recent studies have explored additional practical aspects of tip vortex instabilities in wind turbine wakes, including the excitation of perturbations using existing control actuators such as blade pitch and rotor speed [START_REF] Brown | Accelerated windturbine wake recovery through actuation of the tip-vortex instability[END_REF], the effect of wave-induced oscillations for floating offshore turbines [START_REF] Kleine | The Stability of Wakes of Floating Wind Turbines[END_REF], and the impact of atmospheric shear and thermal stratification on perturbation evolution [START_REF] Hodgkin | Numerical investigation of the influence of shear and thermal stratification on the wind turbine tip-vortex stability[END_REF].

Helical vortex pairing has been observed experimentally since Alfredsson & Dahlberg [START_REF] Alfredsson | A preliminary wind tunnel study of windmill wake dispersion in various flow conditions[END_REF] visualized leapfrogging tip vortices in the wake of a model wind turbine using smoke, though detailed experimental characterizations of the phenomenon are scarce. Felli et al. [START_REF] Felli | Mechanisms of evolution of the propeller wake in the transition and far fields[END_REF] investigated the dependence of the pairing instability evolution in the wake of a propeller on spacing between adjacent vortex loops, finding that leapfrogging occurs earlier when such spacing is reduced. Nemes et al. [START_REF] Nemes | Mutual inductance of two helical vortices[END_REF] confirmed this finding and showed that the measured growth rates of the instability matched the expected theoretical values for the wavenumbers tested. To understand the effect of the pairing instability on wake mixing and recovery, Lignarolo et al. [START_REF] Lignarolo | Tip-vortex instability and turbulent mixing in wind-turbine wakes[END_REF] computed the kinetic energy transport into the wake of a rotor with blades pitched at two slightly different angles. They showed that this kinetic energy transport increases substantially after leapfrogging occurs and the tip vortices break down. Quaranta et al. [START_REF] Quaranta | Long-wave instability of a helical vortex[END_REF] characterized vortex geometry and instability growth rates for a single helix in the wake of a one-bladed rotor, finding good agreement with theoretical modes. Extending this work to a double helix, Quaranta et al. [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF] explored both local and global vortex pairing. Local pairing occurs when the azimuthal wavenumber of the perturbation is nonzero and the distance between adjacent loops varies along the azimuth. Global pairing is characterized by a zero wavenumber perturbation where one of multiple interlaced helices is shifted relative to the other(s), leading to uniform spacing along the azimuth. As demonstrated by Quaranta et al. [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF], global pairing can be triggered by introducing an asymmetry to the rotor generating the helical vortices.

The current study experimentally investigates global pairing in the helical vortex system in the wake of an asymmetric three-bladed rotor. The three-bladed configuration is more relevant to applications such as wind turbines. Furthermore, the addition of a third helix substantially increases the complexity of the vortex interactions. The paper is structured as follows: Section 2 describes the experimental setup, including the design of the three-bladed rotor, the different types of asymmetry tested, and the measurement techniques used in the study. Section 3 presents the results of the comparison between different types of asymmetry and discusses some of the most interesting findings in more detail. Finally, Section 4 delivers the key conclusions of the study. 2 Experimental Methods

Baseline configuration

Experiments were conducted in a recirculating free-surface water channel with a test section of dimensions 150 cm × 38 cm × 50 cm (length × width × height). A three-bladed rotor with a radius of R = 9 cm was mounted on a 1.5cm diameter shaft, driven by a stepper motor at f = 3 Hz (see Figure 3 below). The flow in the channel had a uniform velocity of U 0 = 56cm/s, giving a tip speed ratio of λ = 2πRf /U 0 = 3.0. The airfoil cross-section used for the rotor blades was the NACA2414, which performs reliably at low Reynolds numbers [START_REF] Selig | Summary of Low-Speed Airfoil Data[END_REF] and is sufficiently thick for fabrication using additive manufacturing. This thickness, along with the stiffness of the manufacturing material, Formlabs Rigid 10K resin (flexural modulus of 9 GPa after UV curing [START_REF]Rigid 10K Technical Data Sheet[END_REF]), prevent any significant blade deflections during rotor operation. The blade chord (c) and twist (φ) for the outer 50% of the radius were determined using the Glauert method for wind turbines [START_REF] Glauert | Airplane propellers[END_REF], while the inner 50% was adapted to ensure a smooth connection to the rotor hub, which had a radius of 1.25 mm (Figure 1a). Note that these blades were designed to generate strong tip vortices for the investigation of helical vortex dynamics; the rotor was not optimized for power extraction.

The rotor hub was designed to allow the removal of each blade individually so that rotor asymmetry could be introduced by replacing one or two blades with slightly modified ones. Such modifications are discussed in more detail in 2.2. Each blade was manufactured with a flat base that attached to the hub with screws and a square peg that nests into the corresponding square hole in the hub (Figure 1b). These features ensured each blade was aligned with the hub consistently each time it was replaced. Because the helical vortex system is highly sensitive to perturbations, the baseline case had to be sufficiently symmetric to prevent the instability from appearing until far downstream. The tip positions were measured using a camera synchronized with the rotor rotation that captured images of each blade when it was pointing directly downwards (sample image shown in Figure 1c). The maximum deviations in both the axial and radial directions between the positions of the three blade tips was measured to be around 0.1% of R for the baseline rotor (Figure 1d).

Rotor modifications

In addition to the baseline blade, 11 other slightly modified blades were designed and manufactured. These modified blades were designed to perturb the tip vortex position (r tip , z tip ) in different directions and by different amounts. For example, a blade that was elongated in the radial direction, r, and deflected in the axial direction, z, as shown in Figure 2a, would displace the tip vortex to the new tip position of the modified blade. Seven blades of this type were manufactured, with the tip location of each displaced in the r and z directions by different magnitudes and signs. For each of these cases, radial deformations were implemented by linearly extrapolating (for +r) or truncating (for -r) the chord and twist of the baseline blade. Axial deformations were implemented such that the quarter chord line followed the fourth order polynomial shape predicted by beam theory for a cantilevered beam under a distributed load. Note that the magnitudes of the perturbations are presented as percentages of h, the spacing between adjacent loops of the tip vortex helix, which is measured in the baseline rotor wake (Section 3.1).

The blade shown in Figure 2b displaced the vortex in the azimuthal direction, i.e., in the direction of the rotor rotation. In this case, the quarter chord line of the blade was rotated about the hub axis by 5.7°. Blades featuring added devices, such as a winglet (Figure 2c) and a fin (Figure 2d), were also manufactured. The winglet was designed by linearly extrapolating the chord and twist of the baseline blade, then adding a 45°bend at Fig. 2 Examples of modified blades used to introduce rotor asymmetry, with (a) a perturbation in the positive radial and axial directions (H in Table 1), (b) a perturbation in the azimuthal direction (A in Table 1), (c) a winglet added to the blade tip (W in Table 1), and (d) a fin on the pressure side (F in Table 1). r = R, such that the tip of the winglet was located at (r, z) = (R + 0.13h, 0.11h). The fin was designed based on the findings of Schröder et al. [START_REF] Schröder | Experiments on helical vortex pairs in the wake of a rotor[END_REF], which showed that two vortices are shed in this configuration, one at the tip of the blade and one at the tip of the fin. These vortices merge to form a larger, more diffuse vortex between the position of the fin and tip vortices. The higher the angle of attack of the fin, the more the merged vortex is displaced away from the tip position, so the fin in the current study was designed with an angle of attack of 16°. In addition, the trailing edge of the fin was positioned at the trailing edge of the blade to minimize the distance between the vortices and promote merging, following the results presented by Schröder et al. [START_REF] Schröder | Generation of a wingtip vortex pair using a pressure-side fin[END_REF]. The quarter chord position of the fin was located at (r, z) = (R -0.13h, -0.12h). Finally, one blade was designed with a decrease in angle of attack of 1°relative to the baseline blade to reduce the circulation of the resulting tip vortex. Based on the lift curve for the NACA2414 airfoil, such a decrease in angle of attack was expected to reduce the lift coefficient by 11%, yielding a corresponding decrease in tip vortex circulation of 11%. Table 1 lists all rotor configurations tested experimentally. Note that the listed blade tip locations are measurements obtained from images of the blades, as described for the baseline rotor in Section 2.1. The tip positions of the modified blades deviated slightly from their design conditions by ∼ 0.01h -0.02h due to some tolerance in the blade mounting mechanism. The designed configurations were determined based on the results of the point vortex-based wake model described by Abraham et al. [START_REF] Abraham | Simplified model for helical vortex dynamics in the wake of an asymmetric rotor[END_REF].

Measurement and evaluation techniques

Multiple techniques were used to compare the effects of different rotor asymmetries on the wake.

To visualize the three-dimensional behavior of the tip vortices, a fluorescein dye paste was painted on the tips of the rotor blades outside of the water. The rotor then began spinning and was lowered into the channel. The test section volume was illuminated with two blue LED panels, as depicted in Figure 3, causing the dye entrained in the tip vortices to fluoresce. The tip vortices appear as green interlaced helices in the volumetric visualization LED panels (or laser)

Step images. To track the positions of the vortex centers over time, the LED panels were removed and a laser sheet was used to illuminate a cross-section of the wake in the plane of the shaft. Because the shaft blocked the light from reaching the upper half of the test section, only the bottom part of the cross-section is visible. This occlusion is acceptable because the global tip vortex pairing behavior investigated in the current study is independent of azimuthal position.

The distance from the rotor plane where leapfrogging, or the swapping of axial positions between two adjacent vortex loops, occurs (z s ) is used to compare the effectiveness of different rotor asymmetries at perturbing the vortex system in the wake. A shorter leapfrogging distance indicates a more effective perturbation. This metric is used because it is an indicator of the perturbation evolution speed and it is easily identified from the experimental data. In addition, the point of leapfrogging coincides with the location of minimum distance between two adjacent vortices, corresponding to a greater likelihood of vortex breakdown due to short-wave instabilities [START_REF] Leweke | Cooperative elliptic instability of a vortex pair[END_REF]. In time averages of the volumetric tip vortex visualizations, the leapfrogging position can be identified as the location of maximum radial separation between the inner and outer wake envelopes, as seen in Figure 4a. Cross-section visualization images were used to obtain a more precise leapfrogging location by tracking the positions of the vortex centers over time (Figure 4b). The vortex tracks were obtained using motion-based multiple object tracking in MATLAB. Figures 4c andd show example time series of the axial and radial positions, respectively, of the average positions of the vortices shed from the three rotor blades. Time (t) is normalized by the vortex spacing and circulation, such that t * = tΓ/(2h 2 ), where the tip vortex circulation Γ is measured in the wake of the baseline rotor (Section 3.1). The time when the first vortex is shed from the rotor (i.e., at z = 0) is defined as t * = 0. The distances are normalized by vortex spacing, h, based on Quaranta et al. [START_REF] Quaranta | Long-wave instability of a helical vortex[END_REF]. In the radial direction, the wake mean expansion R w (z), computed as described in Section 3.1, is subtracted from the trajectory. The leapfrogging location is identified as the point where the axial tracks of two vortices cross, as indicated by the black line in Figure 4c. The vortex trajectories shown in Figure 4 correspond to configuration E in Table 1, but they exhibit features observed in all cases tested in the current study, including two vortices moving in opposite radial directions, then crossing in the axial direction at the point of maximum radial separation. This behavior is characteristic of the leapfrogging phenomenon. Particle Image Velocimetry (PIV) was used to obtain wake velocity fields and tip vortex properties. The raw images were obtained by seeding the water channel with 10 µm-diameter silver-coated hollow glass spheres and illuminating the plane of the shaft with a 532 nm-wavelength, doublepulsed Nd:YAG laser. The pulse spacing was 2 ms. The camera and laser were triggered by the rotor and synchronized at 4.5 Hz so that an image was captured every 4/3 rotation. With this timing, the vortices shed from all three blades could be captured in a single acquisition. Each acquisition consisted of 900 image pairs, corresponding to 300 pairs per vortex. For the baseline rotor, this process was repeated 12 times to capture 36 phases of the rotation. These images were processed with an in-house MATLAB PIV code [START_REF] Meunier | Analysis and treatment of errors due to high velocity gradients in particle image velocimetry[END_REF]. First a 64 × 64 pixel correlation window with 50% overlap was used for several passes employing window shifting and deformation, and a final pass was conducted with a 32 × 32 pixel window, also with 50% overlap.

Results

Baseline wake characterization

The flow in the wake of the baseline rotor is first characterized using PIV data. The mean velocity field shows a strong deficit in the wake, as expected for a rotor operating in the turbine regime (Figure 5a). A slight acceleration is also observed outside of the wake due to flow blockage in the channel. Figure 5b presents an example phase-averaged vorticity field corresponding to a rotational phase of 60°. Tip vortices with negative vorticity are clearly visible at r/R ∼ 1. Strong blade root vortices are not observed for two reasons. First, as explained in Section 2.1, the inner 50% of the blade is modified from the original Glauert design, causing positive vorticity to be shed gradually rather than all at once in the form of a root vortex. Second, the boundary layer generated by the rotor shaft contains negative vorticity, which partly neutralizes the positive vorticity at the blade root, as described by Quaranta et al. [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF].

The coordinates of the center of each tip vortex were manually determined from the vorticity phase averages. From these coordinates, the wake radius (R w /R) and vortex spacing (h/R) were determined. Because of the slight residual asymmetry of the baseline rotor, the vortices shed from the three blades follow different trajectories. The geometric wake parameters were determined from the average of these three trajectories. The wake radius shows an initial increase characteristic of wind turbine rotor wake expansion, with a plateau around R w /R = 1.10 ± 0.02, corresponding to R w = (9.9 ± 0.2) cm (Figure 5c). The vortex spacing decreases slightly within the first R downstream of the rotor, then remains at h/R = 0.52 ± 0.01, or h = (4.72 ± 0.09) cm, for the remainder of the wake (Figure 5d). To calculate the circulation of each tip vortex, line integrals of the azimuthal (in the local vortex reference frame) velocity were computed along circles of radius h/3, chosen to encompass as much of the tip vortex vorticity as possible without including trailing vorticity shed from a different blade, as shown in Figure 5b. The axial evolution of the tip vortex circulation for the three blades is presented in Figure 5d. Vortices shed from all three blades exhibit regions of relatively constant circulation at the beginning of the wake until z ∼ 1R, after which the values decrease slowly for the remainder of the imaging region. This decrease may be due to the detrainment of vorticity from the constantradius integration area used for the determination of the circulation, from the interaction with neighboring vortices and/or the inner vorticity layers.

To characterize the circulation of the tip vortices without these effects, the mean of the circulation between 0 < z/R < 1 is used, yielding values of Γ 0 = (168 ± 2) cm 2 /s, Γ 1 = (163 ± 2) cm 2 /s, and Γ 2 = (164 ± 2) cm 2 /s for each of the three blades. The average of the three values (Γ = 165 cm/s) is used for the non-dimensionalisation of time.

Leapfrogging distance comparison

The effect of different rotor asymmetries is now compared for all cases tested. Figure 6 shows the leapfrogging distance for each case, calculated using the tracked tip vortex positions as described in Section 2.3. The cases are labeled according to Table 1. Overall, the leapfrogging distance ranges from z s /R = 4.1 for the baseline case to z s /R = 1.8 for the most perturbed case where one blade is replaced with blade W (winglet) and another is replaced with blade F (fin). The values of z s measured in this study show the substantial impact that even small asymmetries have on the rotor wake, particularly for the baseline case with asymmetries of ∼ 0.1% of R. The subsequent analysis focuses on explaining the key differences and similarities between a few of the other cases tested in this study.

Azimuthal and axial equivalence

Figure 6 shows that the leapfrogging distance resulting from a 5.7°azimuthal tip displacement (blade A, z s /R = 3.2) is nearly equivalent to that resulting from an axial displacement of 0.05h (blade D, z s /R = 3.4). The similarity between these two cases is due to the helical geometry of the tip vortex system. Figure 7a presents the developed plan view of the helical vortex system, with the horizontal axis representing the axial direction and the vertical axis representing the azimuthal direction. This view shows that a displacement of the vortex system along the axial direction (purple arrows) is equivalent to a displacement along the azimuthal direction (orange arrows). Because a full 360°rotation of the rotor causes the vortices to propagate 3h in the axial direction, an axial displacement of h is equivalent to 120°of rotation. Therefore, a blade with an azimuthal perturbation of 6°was designed to be equivalent to an axial perturbation of 0.05h (Figure 7b). Figure 7c shows that when one of the rotor blades is replaced with each of these modified blades, the resulting wake is nearly identical up to the point of leapfrogging. Downstream of z s , the vortex dynamics differ between the two cases. This discrepancy is attributed to the fact that blade D is deformed slightly along the entire length due to the axial deflection, modifying the Fig. 6 Comparison of leapfrogging distance (zs) for all cases tested in the current study, normalized by both rotor radius (R) and vortex spacing (h). The white letters on the bars correspond to the case labels as defined in Table 1.

circulation distribution along the blade and inside the wake. Due to the non-linearity of the vortex system, these small differences are magnified further downstream.

Directional effects

Another key insight gained from Figure 6 is the strong dependence of the leapfrogging distance on the direction of the perturbation. In particular, blades K and H both feature a displacement of the same magnitude, with extensions in the radial direction, but K has a negative axial deflection while H has a positive one. Just changing the sign of the axial deflection puts K and H on almost opposite ends of the range of z s values, with z s /R = 3.8 and z s /R = 2.7, respectively. The cause of this difference is related to the behavior of co-rotating vortex systems, which generate a strain field with elliptic streamlines oriented at 45°relative to the axis connecting the vortices [START_REF] Leweke | Dynamics and Instabilities of Vortex Pairs[END_REF]. When one vortex is perturbed along the direction of positive strain, as is the effect of blade H shown at the top of Figure 8a, the strain field continues to push the vortex away from its initial position. On the other hand, when one vortex is perturbed along the direction of negative strain, as for blade K shown at the bottom of Figure 8a, the strain field pushes the vortex back towards its initial position. Therefore a vortex displacement along the direction of positive strain causes the instability to evolve more quickly than a displacement in the negative strain direction, 1) and (bottom) an azimuthal displacement of 5.7°(A in Table 1). The purple and orange arrows indicating the directions of the perturbations correspond to those in (a). (c) Volumetric visualization images of the wakes of the rotors with one blade replaced with those shown in (b), with the white arrows indicating the leapfrogging distance, zs, for each case.

leading to a shorter leapfrogging distance. The difference in leapfrogging distance between these two cases is clear in the volumetric wake visualizations shown in Figure 8b. In configuration HL, two of the blades induce perturbations along the positive strain direction, further reducing the leapfrogging distance.

(a) (b)

z s z s
Fig. 8 (a) Modified blades used to induce vortex perturbations along (top) the positive strain direction (H in Table 1), indicated by the purple arrow, and (bottom) the negative strain direction (K in Table 1), indicated by the orange arrow, of the co-rotating vortex system. Only the blade tips are shown for clarity. The resulting volumetric visualizations of the wakes of the rotors modified with these blades are shown in (b), highlighting the large difference in leapfrogging distance, zs.

Blade devices

The addition of a winglet to the tip of one of the blades (blade W) strongly displaces the tip vortex. The winglet changes the blade tip location the most of all of the modified blades (Figure 9a), and it displaces the vortex along the positive strain direction, as discussed in Section 3.2.2. Therefore, it causes the strongest perturbation to the vortex system and the shortest leapfrogging distance of all of the configurations with only one blade changed (Figure 9b). Previous studies have shown that, for certain winglet designs, a secondary vortex is formed at the blade bending location at the base of the winglet [START_REF] Gerontakos | Effects of winglet dihedral on a tip vortex[END_REF][START_REF] Ostovan | Experimental investigation of the effects of winglets on the tip vortex behavior of a model horizontal axis wind turbine using particle image velocimetry[END_REF]. Depending on the cant angle of the winglet, this secondary vortex may merge with the vortex formed at the winglet tip, with the final vortex residing somewhere between the positions of the two initial vortices. In the current study, no vortex is observed at the base of the winglet due to the smooth transition between the main blade and the winglet. The vorticity field captured 60°after the winglet blade has crossed the imaging plane, presented in Figure 9c, shows a single vortex downstream of the winglet tip location. On the other hand, the blade with the fin (blade F) is observed to generate two vortices, one at the blade tip and one at the fin tip. This feature can be seen most clearly in the vorticity field shown in Figure 9c, where the vortex most recently shed from the fin blade has two distinct lobes. Note that the resolution of the present PIV data is insufficient for accurate measurements of the vortex core size. However, consistent with the findings of Schröder et al. [START_REF] Schröder | Experiments on helical vortex pairs in the wake of a rotor[END_REF], the two lobes appear to merge, and the merged vortex continues to propagate downstream at a location between the two initial positions. Note that this merged vortex position is also along the positive strain direction. Although the merged vortex does not look significantly different from the vortices shed from the baseline blades in the vorticity field, it appears more diffuse in the volumetric visualization (Figure 9b). The results of Schröder et al. [START_REF] Schröder | Experiments on helical vortex pairs in the wake of a rotor[END_REF] show that the core of the merged vortex is larger than that of the vortices shed from the baseline blade, though this observation cannot be confirmed using the current data, due to the lack of resolution in the vortex core regions. Because of the large vortex displacements caused by both the winglet and the fin, the rotor configuration that uses both of these blades (configuration WF) generates the wake with the shortest leapfrogging distance of all configurations tested.

In addition to vortex displacement, Figure 9d presents the circulation of the vortices shed from all three blades in both configurations. Note that there are fewer data points than in the circulation plot in Figure 5e, as fewer phases of rotation were measured for the asymmetric cases than the symmetric case. The vortex shed from blade W (in the blade 0 position in the left plot of Figure 9d) exhibits significantly higher circulation values than the vortices shed from the other two blades. This circulation increase is related to the length change of the blade. In all the configurations tested, a radial extension causes the tip vortex circulation to increase, while a radial shortening reduces the tip vortex circulation. In general, tip vortex circulation is determined by the chord length, the incident velocity magnitude, and the angle of attack experienced by the blade. A radial extension causes the blade tip to experience a larger incident azimuthal velocity due to rotor rotation, but this effect is cancelled out by the reduction in chord length included in the extrapolated blade design (Section 2.2). Therefore, the main reason for the circulation increase is the change in angle of attack. This change is caused by the fact that the extended part of the blade is at a larger radial position where the rotor induction is lower, so it experiences a larger axial velocity. The increase in axial velocity increases the angle of attack, increasing the circulation of the shed vortex. When a winglet is used to extend the blade, the factors influencing the circulation of the tip vortex become more complex, as the blade tip is no longer perpendicular to the inflow. Still, increased circulation of the tip vortex shed from blade W is observed. The tip vortex shed from blade F also exhibits increased circulation (in the blade 0 position in the right plot of Figure 9d). Consistent with the observations of Schröder et al. [START_REF] Schröder | Experiments on helical vortex pairs in the wake of a rotor[END_REF][START_REF] Schröder | Generation of a wingtip vortex pair using a pressure-side fin[END_REF], this increase is caused by the additional circulation shed from the fin, which merges with the vortex shed from the blade tip. Though asymmetries in both position and circulation of the tip vortices influence the evolution speed of the pairing instability, the findings of Abraham et al. [START_REF] Abraham | Simplified model for helical vortex dynamics in the wake of an asymmetric rotor[END_REF] show that a displacement of 10-15% of h along the positive strain direction reduces the leapfrogging distance more than a circulation increase of 10-15%. Therefore, the vortex displacements induced by the blade devices are primarily responsible for the short leapfrogging distances observed in these two configurations.

Conclusions

The current study experimentally investigates the effects of different types of asymmetries on the development of the helical tip vortex system in the wake of a three-bladed rotor. Rotor asymmetry is introduced by replacing one or two of the blades with slightly modified versions, perturbing the tip vortices and triggering the global pairing instability of the interlaced helical vortex system. The effectiveness of the perturbations is compared using the distance from the rotor plane where adjacent vortex loops swap positions, or the leapfrogging distance. The 14 configurations tested yield leapfrogging distances ranging from 4.1 to 1.8 times the rotor radius, for the baseline (symmetric) case and the most perturbed case, respectively. A few of these 14 configurations are discussed in more detail, highlighting differences and similarities between certain cases. First, the similarity between azimuthal and axial displacements is attributed to their analogous effects on the helical geometry of the system. Next, the effect of displacement direction is investigated. Large discrepancies between equal-magnitude perturbations is shown to relate to the strain field generated by co-rotating vortices. Finally, the impacts of blade devices such as winglets and fins on the tip vortex behavior are explored.

The findings of the current study can be used to develop innovative rotor designs to passively accelerate tip vortex breakdown and mitigate the detrimental effects of the wake. Based on the results of the experiments presented here, even a small rotor asymmetry significantly perturbs the wake. Blades that displace the tip vortex in the direction of positive strain are shown to be especially effective, whether this perturbation is implemented using a full blade modification or through the addition of a device such as a winglet or fin. The magnitude of these perturbations scale with the vortex spacing, which is larger relative to the radius in the current experiments than in the wake of real wind turbine rotors due to the difference in tip speed ratios (typically between 6 and 8, compared to 3 in the current study). Therefore, to achieve the same perturbation magnitudes on a real wind turbine, smaller blade modifications of only 1-2% of rotor radius would be required.

Still, many questions remain to be addressed before this technology can be used on a real rotor. First, additional experiments are underway to investigate the effects of turbulence on tip vortex breakdown. In the water channel used in the current study, the turbulence intensity is very low (< 1%). This lack of turbulence could be responsible for the absence of vortex breakdown in the current experiments. In addition, the current study characterizes the wake, but does not quantify the impacts of the modified wake on structures in the downstream flow. The experimental setup does not allow for additional rotors to be mounted in the wake of the rotor, but high-fidelity simulations are underway to quantify the effects of an asymmetric rotor wake on the structural loading and power generation of a downstream wind turbine [START_REF] Ramos-García | Multi-fidelity vortex simulations of rotor flows: validation against detailed wake measurements[END_REF]. Finally, asymmetry is expected to generate fluctuating loads on the support structure and the asymmetric rotor itself. The possibility of compensating for these additional forces, e.g., with a counterweight, should be explored to enable the practical implementation of asymmetric rotors.

Fig. 1

 1 Fig. 1 (a) Chord (c) and twist angle (φ) of the baseline rotor blades. (b) Exploded view of the rotor showing how the blades attach to the hub. The white screw in the center connects the rotor to the shaft. (c) Sample image of one rotor blade used to identify the blade tip position. The red box around the blade tip indicates the region shown in (d), where the colored outlines representing the edges of the tips of the three blades from the images are compared. The black square marks the position of the inset in (d), which shows a closer view of the deviation between the blade tip center locations (r tip , z tip ), indicated by the circles with error bars.

Fig. 3

 3 Fig. 3 Schematic of the water channel test section, including the components powering and supporting the rotor, the positioning of the light source for vortex visualization, and a sample volumetric visualization image of the tip vortices in the rotor wake.

Fig. 4 (

 4 Fig.4(a) Time-average of volumetric visualization images, with one image brighter and in green. (b) Timeaverage of cross-section visualization images, with one image brighter and in green. In both, the leapfrogging distance, zs, is indicated by the white arrow. Vortex trajectories in the (c) axial and (d) radial directions obtained from tracking the vortex cross-sections over time. The dimensionless time (t * s ) and location (zs/h) where leapfrogging occurs are indicated by the dashed lines. All panels show results for configuration E in Table1.

Fig. 5 (

 5 Fig. 5 (a) Mean velocity field in the wake of the baseline rotor, averaged over 36 rotation phases. The color represents the normalized streamwise velocity and the arrows indicate the direction. The displayed vector spacing is 1/10 of the actual resolution for readability. (b) Phase-averaged vorticity field in the wake of the baseline rotor corresponding to a rotation phase of 60°. The black circles around the tip vortices represent the lines used to calculate their circulation. (c)Axial evolution of the wake radius normalized by rotor radius. The gray points represent the position of each vortex, the open black circles are the mean at each axial location, and the solid black line is the fit of the mean points to a trend line that asymptotically approaches a constant value (dashed line). (d) Axial evolution of tip vortex spacing normalized by rotor radius. The gray points represent the spacing between adjacent vortices, the open black circles are the mean at each axial location, and the solid black line is the trend line. (e) Axial evolution of tip vortex circulation for the vortices shed from each of the three blades. The points represent the circulation values of each vortex, with the color indicating the blade from which it was shed. The dashed lines show the mean values of Γ i (i = 0,1,2) between 0 < z/R < 1 for each blade.

Fig. 7

 7 Fig. 7 (a) Developed plan view of the helical vortex system. The original vortices are in green and the displaced vortex is in blue. Purple arrows represent an axial displacement and orange arrows show the equivalent azimuthal displacement. (b) Modified blades used to induce (top) an axial displacement of 0.05h (D in Table1) and (bottom) an azimuthal displacement of 5.7°(A in Table1). The purple and orange arrows indicating the directions of the perturbations correspond to those in (a). (c) Volumetric visualization images of the wakes of the rotors with one blade replaced with those shown in (b), with the white arrows indicating the leapfrogging distance, zs, for each case.

Fig. 9

 9 Fig. 9 (a) Modified blades with (top) an added winglet (W in Table1) and (bottom) an added fin (F in Table 1). Only blade tips are shown for clarity. The corresponding visualizations are shown in (b) with leapfrogging distance (zs) indicated, and the vorticity fields from the PIV data are shown in (c). The insets show zoomed-in views of the most recently shed vortices from the modified blades. White contour lines at ωR/U 0 = -25 highlight the vortex shape differences between the two cases. (d) Tip vortex circulation for the winglet (left) and fin (right) cases, where blade 0 is the modified blade.

Table 1

 1

Acknowledgments. The authors gratefully acknowledge the contributions of Eric Bertrand to the design and manufacture of the rotor.

Availability of data and materials. Data and codes are available on request from the authors.

Declarations

Ethical approval. Not applicable.

Competing interests. The authors have no competing interests to declare.

Authors' contributions. A.A. analyzed the experimental data and wrote the manuscript. T.L. edited the manuscript and acquired the funding. Both A.A. and T.L. conducted the experiments.

Funding. This work was supported by the technology transfer company SATT Sud-Est (Marseille).