Alex A Alblas
email: a.a.alblas@rug.nl

Kristian Peters
email: k.peters@rug.nl

Hans Wortmann
email: j.c.wortmann@rug.nl

Process Alignment for Sustainable Product Development: The Essential Role of Supplier and Customer Involvement Processes

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

During the past decade, sustainability has become increasingly popular in new product development (NPD). Various pressures and incentives to improve sustainability are mentioned in academic literature, such as laws and regulations, customer demands, cost reduction, improvement of quality, mitigation of risks, and improvement of image [START_REF] Porter | Toward a New Conception of the Environment-Competitiveness Relationship[END_REF][START_REF] Bansal | Why Companies Go Green: A Model of Ecological Responsiveness[END_REF][START_REF] Seuring | From a literature review to a conceptual framework for sustainable supply chain management[END_REF][START_REF] Horbach | Determinants of environmental innovation-New evidence from German panel data sources[END_REF][START_REF] Forsman | Environmental Innovations as a Source of Competitive Advantage or Vice Versa?[END_REF]. While its importance is more and more acknowledged in corporate mission and strategies of firms, sustainability oftentimes remains a lip service of motivated individuals working in operational levels of firms [START_REF] Alblas | Fuzzy sustainability incentives in new product development: Empirical explorations of sustainability challenges in manufacturing companies[END_REF]. Many firms face difficulties in the management of sustainable product development (SPD) due to its farreaching impacts on the organization, and the firms' business model, supply chain and operations [START_REF] Driessen | Green New Product Development: The Pivotal Roleof Product Greenness[END_REF][START_REF] Sroufe | The new product design process and design for environment: Crossing the chasm[END_REF][START_REF] Seuring | Core Issues in Sustainable Supply Chain Management: a Delphi Study[END_REF][START_REF] Dangelico | Mainstreaming green product innovation: why and how companies integrate environmental sustainability[END_REF][START_REF] Pinske | Challenges and Trade-Offs in Corporate Innovation for Climate Change[END_REF]. Besides these practical complexities, the meaning of sustainability and its implications remain ambiguous in both literature and practice. Preliminary work reveals two conceptual complexities that can impede firms to manage SPD effectively. First, firms can regard sustainability as a homogeneous objective with a 'one size fits all' set of organizational practices. Instead, sustainability covers multiple objectives, and a wide array of sub-themes that consequently require tailored practices and aligned business models [START_REF] Peters | Selection of Big Themes in Sustainable Product Development: a framework of actions and measures in business as found in CSR reports and case companies[END_REF]. Secondly, firms can approach SPD as traditional NPD complemented with several design for environment (DfE) approaches (e.g., [START_REF] Kobayashi | Strategic evolution of eco-products: a product life cycle planning methodology[END_REF], [START_REF] Choi | A Framework for the Integration of Environmental and Business Aspects Toward Sustainable Product Development[END_REF]). SPD however shows increased complexity compared to traditional NPD, and therefore requires specific managerial approaches [6 -9].

Given its importance and its problems, we seek to provide a more nuanced understanding of the relations between various types of sustainability, the organizations' business model (e.g., value proposition, infrastructure), and organizational processes (i.e., in this paper, supplier and customer integration). To accomplish this research aim, we conducted a multiple case study in which we investigate the type of sustainability that is currently pursued by the SPD function in a firm in relation to the type of supplier and customer integration in the early stages of SPD.

Research questions and background

The research focusses on three perspectives: (1) the types of sustainability innovation, depending on the firm's business model and sustainability focus; (2) the type of SPD organization with the specific focus supplier and customer involvement; and the ultimate aim, (3) SPD performance. These perspectives are reflected in three research questions:

-Can SPD innovations be categorized based on their type of sustainability focus and business model? -What types of SPD organizational processes1 are required for what type of SPD innovations? -How does the interaction between SPD innovations and SPD organizational processes 1 contribute to SPD performance?

In the first part of this section we will explain how sustainability can be characterized in different themes and business models. Then, we will explain the process management perspective that is used to characterize different types of SPD organizations.

Finally, we will elaborate on some prior literature related to supplier and customer involvement in product development.

Sustainability focus: Sustainability themes

Sustainability has various meanings in business settings, and can be achieved or improved in product development in various ways. This section provides an overview of types of sustainability innovations in discrete manufacturing. The overview is the result of analyzing sustainability themes associated with products as reported in CSR reports of discrete manufacturing firms, and is subsequently supplemented with Design for Environment strategies. The details of the theoretical underpinnings and methodology can be found in [START_REF] Peters | Addressing the gap between manufacturers' sustainability intentions and effective sustainable product development: The Big Themes Framework[END_REF].

Peters et al. [START_REF] Peters | Addressing the gap between manufacturers' sustainability intentions and effective sustainable product development: The Big Themes Framework[END_REF] identify three levels to describe types of sustainability innovations in discrete manufacturing, namely 1) object level, 2) life cycle stage(s) and resource or release level, and 3) solution or measure level. In this paper, the object is a product, whereas other object foci can be e.g., packaging or production plant. For a product, sustainability themes and solutions concern one or more (or all) product life cycle stages, and one or more resource and release categories: 1) materials/parts, 2) energy and CO 2 emissions, 3) (other) greenhouse gasses (GHG) emissions, and 4) hazardous and toxic substances. The combination of object + life cycle stage + resource or release, can be improved by various types of measures or solutions that product developers can implement through one or more Design for Environment (DfE) strategies, as described next. Table 1 presents an overview of sustainability themes with the related DfE strategies. DfE strategies are design principles and procedures to develop environmentally conscious products [START_REF] Srivastava | Green supply-chain management: A state-of-the-art literature review[END_REF], [START_REF] Boks | Essential perspectives for design for environment: Experiences from the electronics industry[END_REF]. The measures, solutions and DfE strategies can subsequently be divided in two categories, namely dematerialization strategies and substitution strategies [START_REF] Robèrt | Strategic sustainable development -selection, design, and synergies of applied tools[END_REF], [START_REF] Waage | Fitting together the building blocks for sustainability: A revised model for integrating ecological, social, and financial factors into business decision-making[END_REF]. Dematerialization concerns increased resource productivity and/or less waste, e.g., design for durability or design for energy efficiency. In addition, we discern where the system boundaries of the solutions or measures are drawn. Dematerialization can be achieved by solely looking at the product (e.g., using less materials, or consume less energy), but it can also be achieved by influencing the system design in which the product ultimately is used (e.g., redesign of both system and pump for energy efficiency, or use waste produced by product in different function in system, or make sure product parts are re-used after end-of-life). Substitutive measures imply a change to a substitute resource or release leading to a more sustain-able product, e.g., design for renewable material and design for non-toxic and nonhazardous substances.

Sustainable business model

A business model is affected by the firms' strategy towards sustainability. Its effectiveness is influenced by the way customer perceive the sustainable value proposition, and its efficiency is influenced by the firm organizational processes to best encounter those desires. "The essence of a business model is in defining the manner by which the enterprise delivers value to customers, entices customers to pay for value, and converts those payments to profit" [START_REF] Teece | Business Models, business strategy and innovation[END_REF].

Literature is diverse in terms of the attributes that constitute a business model. Table 2 presents an overview of various attributes mentioned in the literature. In this study we will analyze the companies on (1) Market segment, (2) Value proposition, (3) Elements of value chain (distribution channel, customer relationships), (4) Positioned in value network (network partners), ( 5) Competitive strategy.

Type of SPD organizational processes

The introduction of sustainability in NPD introduces complexity e.g., [START_REF] Matos | Integrating Sustainable Development in the Supply Chain: The Case of Life Cycle Assessment in Oil and Gas and Agricultural Biotechnology[END_REF]. Complexity can be reduced by the employment of process management techniques by the reduction of variance and the improvement of stability and repeatability [START_REF] Winter | Organizing for continuous improvement: Evolutionary theory meets the quality revolution[END_REF][START_REF] Benner | Process Management and Technological Innovation: A Longitudinal Study of the Photography and Paint Industries[END_REF][START_REF] Benner | Exploitation, Exploration, and Process Management: The Productivity Dilemma Revisited[END_REF][START_REF] Adler | Perspectives on the productivity dilemma[END_REF]. Process management is based on a view of an organization as a system of interlinked processes. It involves concerted efforts to map, improve, and adhere to organizational processes [START_REF] Benner | Exploitation, Exploration, and Process Management: The Productivity Dilemma Revisited[END_REF]. The principle postulation of this study is that the type of sustainability innovation needs to be aligned with specific SPD processes. To illustrate this point this paper specifically investigates the role of suppliers and customers processes in relation to different types of sustainability innovations. We expect that firms need address and (re)organize supplier and customer integration processes for many types of sustainability innovations.

For example, to implement remanufacturing, a company needs to efficiently organize reverse logistics cf. [START_REF] Sarkis | An organizational theoretic review of green supply chain management literature[END_REF]. For reverse logistics, customers have to be able and willing to return end of life products. The product design directly influences the effectiveness of this process, because it influences the ease of contribution in terms of size, ease of disassembly, traceability, etc. Furthermore, in order to influence the user phase in the product life cycle, a product has to be aligned not only with the customer requirements in terms of functionality, but also with the acceptance of specific sustainability functionality and the existing infrastructure at customers' sites. Therefore, alignment is required between the product design and the suppliers' and customers' infrastructures.

Previous literature has shown that early supplier involvement is an important process in supply chain design, product design and process design e.g., [START_REF] Petersen | Supplier integration into new product development: coordinating product, process and supply chain design[END_REF]. Petersen et al. [START_REF] Petersen | Supplier integration into new product development: coordinating product, process and supply chain design[END_REF] distinguish between three types of supplier integration: (1) White box -design and specification decisions are the responsibility of the company, but discussions are held with suppliers about this with suppliers; (2) Grey box -formal or informal involvement of suppliers in development, which may include information and technology sharing and joint decision making regarding design specifications; (3) Black box -almost complete supplier responsibility for the purchased item with only review on the purchased item's specifications by the buying company.

Concerning the customer perspective various authors mention the importance of customer empowerment in product development in terms of their engagement to create ideas for new product designs; and their permission to select the product designs to be produced e.g., [START_REF] Fuchs | Customer empowerment in new product development[END_REF]. Moreover, the type of customer involvement affects the type of engineering work that is conducted and impacts the overall product delivery strategy of a firm [START_REF] Veldman | Managing design variety, process variety and engineering change: a case study of two capital good firms[END_REF]. Customer involvement can vary from very limited involvement, to very intensively involvement, i.e., having lots of influence on the design decisions of a company. Thus, firms could operate according to open product delivery strategies that allow customers to specify engineering work completely (fully engineer-toorder), whereas on the other side of the spectrum, firms operate according to a closed product delivery strategies towards customers (e.g., make to order, assembly to order, make to stock). The above-mentioned types of supplier and customer integration will be used to categorize the cases in their intensity of supplier and customer integration in SPD.

Methodology

Present research is an exploratory multiple case study [START_REF] Yin | Case study research: Design and methods[END_REF]. The cases used for this study were selected by combining two sampling strategies: homogenous sampling and (maximum) variation sampling. With regard to the homogeneity of the sample, we concentrate on companies that aim to improve the sustainability of their products in product development, and who operate in discrete manufacturing industries. With regard to variation, we selected either companies for whom the improvement concerns the first step into managing sustainability in product development, or companies for whom it concerns further developing and expanding SPD. The selection process resulted in six discrete technology manufacturers (i.e., company A, B, C, D, E, F).

Data collection and analysis comprised the following steps. Firstly initial interviews were conducted to investigate the roles of suppliers and customers in SPD. Then, literature was analyzed and a framework was constructed. Based on the operationalization, we collected generic data on the roles of suppliers and customer in SPD. Subsequent data will be collected about the roles, the processes and decisions of suppliers and customers in cooperation with the companies in the different stages of the FFE. The data was reduced and condensed by using tables and data displays following the framework.

The results of the data analyses are summarized in in two figures (Figure 1 (a), (b)). Figure 1a represents the positions of the cases on supplier and customer integration, and Figure 1b positions the sustainability themes on the required supplier and customer integration. The position of the cases and sustainability themes on supplier and customer integration are assessed based on the dimensions presented in Section 2.

Results

In this section we describe the case study results. For each case we will give a brief overview of their business model and sustainability theme, followed by an analysis of how the case company organized supplier and customer integration. Figure 1(a) and Figure 1(b) illustrate together the link between the (a) position of the cases and (b) the various sustainability themes a firm can focus on given the position on supplier and customer integration. Figure 1(b) illustrates that the various sustainability themes differ in the required supplier and customer integration. For example, Materials Dematerialization: materials use optimization (linear system)' requires limited downstream integration, because the organization of a return flow is not required and the impact the customer specification is limited (see Figure 1). The 'Materials Dematerialization: materials and component reuse' theme requires more downstream integration, because the organization of the return flow and a specific consideration of remanufacturing in the product design are required.

The majority of case companies (i.e., Companies A, C, E and F) make products that have multiple sustainability characteristics, e.g., durability, safety, reliability, maintenance-free, and energy efficiency, as a result of their past en present business models. Today, these companies intend to incorporate new sustainability characteristics in their products, or bring existing qualities to a higher level. It is however questionable whether the business models of companies C, E and F enable new sustainability innovations. In order to illustrate this point, we discuss the business models of these three case companies, starting with company's C, in relation to the type of sustainability innovation each company intends to realize within SPD. Additionally, we contrast the 'problematic' cases with other cases that have been more successful in SPD, or that have an enabling business model in place. Company C is a traditional supplier of centrifugal pumps: based on customer requirements (i.e., usually a certain pump capacity) the most economic pump is selected and sold to the customer. The newer and more energy efficient pumps lead to a higher initial list price for the pump, but should improve the Total Cost of Ownership. But Company C's sales force are confronted with customers that do not perceive energy efficient pumps as an attractive advantage, and therefore still prioritize a lower initial cost price over energy efficiency savings or environmental advantages. This problem especially applies to Company C customers who are not end-user of the product yet, for instance original equipment manufacturers (OEM's). Another reason is the lack of information, tools and skills of the sales personnel regarding the implementation and possibilities of the pump in an energy efficient system for the customer. Thus, Company C's current business model is not yet compatible with the new sustainability focus of Company C.

Company A, also a manufacturer of pumps, employs a different business model. Instead of waiting on customers telling them what kind of pumps they want based on a few parameters as in Company C, Company A aims to be involved as early as possible in the design of the system in which their pumps will operate. In this way, Company A can ensure their customers buy pumps that function optimal in their systems from both economical as well as environmental points of view. Moreover, Company A can advise their customer to adjust certain aspects of their system, for instance piping diameters or hydraulic head, so that pumps will even function more efficient. Company A's level of integration in the value chain can be an example for Company C.

Company E supplies electric switching gear to utility companies and industries. In utility companies, CO 2 footprint and climate change are the most important sustainability themes. Company E has therefore adopted CO 2 reduction as a major theme for sustainability innovations. Moreover, unlike most switching gear equipment produced by competitors, Company E's equipment does not contain sulfur hexafluoride (SF 6 ), which is the most potent greenhouse gas in the world (23,900 times higher global warming potential than CO 2 ). Despite this unique characteristic, and Company E's other SPD efforts to contribute to the CO 2 theme of their customers, sustainable product successes are mixed. According to Company E's R&D manager: "the share of our equipment in the total customer's CO 2 footprint is marginal". Consequently, customers have better alternatives to invest in than Company E's CO 2 -friendly switching gear. Innovations aimed at CO 2 reduction do not fit within the current business model of Company E. Company E is now reconsidering its type of sustainability innovations (e.g., material efficiency), and explores how this may affect their current business model (e.g., offering leasing construction).

Lastly, Company F has traditionally concentrated on offering high efficient gasbased solutions to generate hot water and heating. It has recently developed new techniques, most notable combined cogeneration technology. Yet this technology is still too expensive given current market conditions, and moreover, requires changes in the energy market (e.g., the household as a supplier of energy) that have not been implemented. Company F therefore wants to explore other sustainability opportunities, such as material efficiency. Because Company F intends to stick to its current business model, the possibilities for material efficiency improvements are very limited. In this respect, Companies B and D have shown that significant material efficiency gains can only be achieved when the business model is aligned.

The data presented in Figure 1 show that the case companies vary in their process management capability with respect to customer and supplier integration and thus their ability to implement sustainability themes. It is for example illustrated that Company C has challenges in supplier and customer integration. They produce centrifugal pumps, which have substantial impact on energy consumption in the use phase and the overall sustainability performance of the customers water management system. These customers, however, are required to be convinced, and cooperation is needed in the design of the overall water management system in order to be able to improve the 'Energy Dematerialization: energy efficiency of the system and use phase' theme (see Figure 1).

Based on the interviews, generic patterns on supplier and customer integration are found. Figure 1(a) illustrates that Companies C, A, E, and F have limited supplier and customer integration whereas Companies B and D have more integration. All in all, we found that early supplier involvement is perceived as very important for SPD with very innovative business models and/or transitions towards new business models and very ambitious sustainability initiatives. One of the key findings is that, because of the lack of supplier and customer integration, several cases have limited influence on the supply chain, which leads to challenges to implement new sustainability business models. In order to be able to reach their sustainability goals, these firms are required to align their supplier and customer integration with their sustainability focus and their sustainability business model.

Discussion and conclusion

The first research question of the study is: "Can SPD innovations be categorized based on their type of sustainability focus and business model?". Present study has shown that SPD innovations can change substantially due to their differences in focus, scope, impact and type of business model. We use the sustainability themes framework developed in previous studies as a starting point [START_REF] Peters | Selection of Big Themes in Sustainable Product Development: a framework of actions and measures in business as found in CSR reports and case companies[END_REF], [START_REF] Peters | Addressing the gap between manufacturers' sustainability intentions and effective sustainable product development: The Big Themes Framework[END_REF]. Further research could aim at the development of a more detailed SPD innovation typology.

The second research question is: "What types of SPD organizational processes are required for what type of SPD innovations?". In this study the focus was on the specific processes related to supplier and customer integration. The results show contribution, however this depends on the type of SPD innovation a firm focusses on. Some sustainability foci and business models require more integration then others. The authors intent to investigate in future research other types of SPD organizational processes in different SPD stages that contribute to SPD performance.

The third research question is: "How does the interaction between SPD innovations and SPD organizational processes contribute to SPD performance?". Based on the study, several generic patterns are distilled. Figure 2 illustrates the proposed relation between SPD alignment between SPD organization and SPD innovation, and SPD performance. 'SPD alignment' refers to ensuring that the 'SPD organization' characteristics are consistent with the 'SPD innovation' characteristics.

One of the most important observations is that when firms persist in the assumption that traditional NPD and engineering methods (such as traditional DfEs) deliver enough support to create sustainable products, the eventual proportion of sustainable products in the total portfolio of these companies will be limited. Instead, it is expected that solutions towards SPD performance are related to the ability of a firm to align the type of SPD innovation (e.g., type of business model, type of sustainability focus) with the SPD organization (e.g., type of SPD process, SPD stage) (See Figure 2).

The case examples demonstrate that many of the present organizational routines within NPD often do not facilitate organizational or external level activity aimed at sustainability. The unaligned cases call for process management of various processes of SPD that enable the exploration for new sustainability opportunities and business models. Future research could focus on investigating important process areas and related practices in SPD that facilitate different forms of SPD innovation. It is furthermore assumed that companies show diversity in their maturity in SPD: some of them focus on relative simple sustainability business models, while others have more advanced ambitions with the required advanced SPD organization. The area of process maturity in relation to SPD is thus promising a direction for further research.

Fig. 1 .

 1 Fig. 1. Position of the cases and sustainability themes Due to new EU law and regulation regarding the energy consumption of centrifugal pumps, Company C concentrates on energy efficiency innovations. Although Company C already studied the possibilities to increase energy efficiency, because they expected the recently implemented EU law and regulations for energy consumption, not much has changed. According to Company C's R&D manager: "the organization, and especially the sales force, do not fully embrace energy efficiency".Company C is a traditional supplier of centrifugal pumps: based on customer requirements (i.e., usually a certain pump capacity) the most economic pump is selected and sold to the customer. The newer and more energy efficient pumps lead to a higher initial list price for the pump, but should improve the Total Cost of Ownership. But Company C's sales force are confronted with customers that do not perceive energy efficient pumps as an attractive advantage, and therefore still prioritize a lower initial cost price over energy efficiency savings or environmental advantages. This problem especially applies to Company C customers who are not end-user of the product yet, for instance original equipment manufacturers (OEM's). Another reason is the lack of information, tools and skills of the sales personnel regarding the implementation and possibilities of the pump in an energy efficient system for the customer. Thus, Company C's current business model is not yet compatible with the new sustainability focus of Company C.Company A, also a manufacturer of pumps, employs a different business model. Instead of waiting on customers telling them what kind of pumps they want based on a few parameters as in Company C, Company A aims to be involved as early as possible in the design of the system in which their pumps will operate. In this way, Company A can ensure their customers buy pumps that function optimal in their systems from both economical as well as environmental points of view. Moreover, Company

Fig. 2 .

 2 Fig. 2. Proposed Framework: SPD alignment

Table 1 -

 1 Sustainability Themes with DfE strategies (see also Peters et al.,[START_REF] Waage | Fitting together the building blocks for sustainability: A revised model for integrating ecological, social, and financial factors into business decision-making[END_REF])

	Resource /		Sustainability themes with DFE strategies
	release	Measure category	DfE Strategy
	Materials	Dematerialization Material use optimisation (linear system)
			(Design for resource conservation; Avoidance of waste;
			Reduction of material use; Design for durability)
			Material and component reuse (circular system)
			(Use recycled and recyclable materials; Design for
			recycling; Design for disassembly; Design for re-use;
			Design for remanufacturing)
		Substitution	Sustainable material use
			(Use renewable material; Use bio degradable materials)
	Energy &	Dematerialization Energy efficiency (product/function)
	co 2		(Use of lower energy content material; Design for
			energy efficiency; Reduce weight of the product
			(transport)/design for efficient distribution)
			Energy efficiency (system)
			(Design for energy efficient system; Design for use
			CO 2 in other functions in system)
		Substitution	Sustainable energy
			(Design for cleaner use; Design for renewable energy
			sources)
	Ghg/	Dematerialization Cleaner use
	Hazardous		(Minimize GHG and toxic or hazardous substances;
	Substances		Design for re-use)
		Substitution	Clean substances and emissions
			(Avoid GHG, and toxic or hazardous substances; De-
			sign for use GHG in other functions in system

Table 2 -

 2 Different business model attributes

	Verhulst and Boks	Chesbrough	and	Osterwalder	(2010)	Crawford	and
	(2012) [24]		Rosenbloom	(2002)	[26]		DiBenedetto (2011)
			[25]				[27]
	Sustainable	design	Xerox spin off business	Business model building	New products man-
	strategies		models (not SPD)		for planet, people and	agement
					profit
	• Value proposition	• Market		• Customer segment	• Market focus
	• Customer interface	• Value proposition	• Value proposition	• End-user bene-
	• Infrastructure		• Value chain		• Customer relation-	fit/insight
	• Financial viability	• Value network		ships		• Technological focus
			• Cost and profit		• Distribution channels
			• Competitive strategy	• Partner network
					• Key resources
					• Key activities
					• Revenue stream
					• Cost structure

In this paper the focus in on the investigation of the supplier and customer integration processes.

Acknowledgements

The authors gratefully acknowledge the support of the Innovation-Oriented Research Programme 'Integral Product Creation and Realization (IOP IPCR)' of the Netherlands Ministry of Economic Affairs.


Hervé Belloc
email: herve.belloc@isae.fr

Vincent Chapin
email: vincent.chapin@isae.fr

Francesco Manara
email: francesco.manara90@gmail.com

Francesco Sgarbossa
email: sfrancesco90@gmail.com

Alexander Meyer Forsting

Alexander Meyer

Influence of the air inlet configuration on the performances of a paraglider open airfoil

Keywords: air inlet, air inlet configuration, paragliders, paragliders airfoils, open airfoils, ram air parafoils, ram air parachutes, separation bubble, pressure coefficients, internal pressure, aerodynamic coefficients

A finite volume flow solver was used to solve the Reynolds averaged Navier-Stokes equations for the 2D flow field on a paraglider open airfoil. The canopy was assumed to be smooth, rigid and impermeable. The parametric study performed concerns the position and the width of the air inlet at the leading edge. The range of values used covers the air inlet geometries from classical ram-air parafoil to sport paraglider airfoil, including transition toward the full closed baseline airfoil. Results are focused both on lift and drag coefficients for performance analysis and on the internal pressure coefficient which can be critical for a real flexible wing regarding the risk of collapse. Depending on the appearance of a separation bubble over the upper edge, two well separated behaviours can be observed. The first behaviour is more typical of ram-air parachutes and the second one corresponds to the design of performance paragliders. For paraglider configurations, it is shown that the aerodynamic coefficients of the open airfoil can be easily deduced from the pressure coefficients of the baseline airfoil without solving the internal flow.

Introduction

Paraglider wings differ from rigid wings in several ways. To give the wing its structural integrity, a leading edge opening, which acts as a ram-air intake, is needed to maintain the canopy inflated. This opening is also called air inlet, or simply inlet, even though most of the time no flow enters when a steady state solution is considered. In fact it acts more as a pressure inlet. In that way a paraglider airfoil is similar to a ram-air parafoil for gliding parachutes.

However, for performance purposes and without constrains like airdrop or parachute inflation, paraglider airfoils have the air inlet underneath the leading edge and further downstream. The inflated wing geometry remains stable only if the internal pressure remains greater than that of the external flow everywhere along the airfoil. A structural support can have a stabilizing effect in one way or another (e.g. arch strengthener or rigid ribs). As this form of support cannot easily be applied to the entire wing surface, this pressure condition remains a limitation for using such an airfoil at low angles of attack, which allow for higher flight velocities, and also for robustness in atmospheric turbulence.

Experimental investigations [START_REF] Burk | Static Aerodynamic Characteristics of Three Ram-Air Inflated Low Aspect Ratio Wings[END_REF][START_REF] Nicolaides | A Review of Para-foil Applications[END_REF][START_REF] Ware | Wind Tunnel Investigations of Ram-Air Inflated All-Flexible Wings of Aspect ratio 1.0 to 3.0[END_REF][START_REF] Tribot | Large Gliding Parachute Experimental and Theoretical Approaches[END_REF], have established that the leading edge air inlet has a significant impact on the flow characteristics and thus the performance of a parafoil. These findings have been reproduced numerically by two-and three-dimensional potential flow computations performed by [START_REF] Ross | Computational Aerodynamics in the Design and Analysis of Ram-Air-Inflated Wings[END_REF]. He already pointed out that the limiting factor for the performance would be the structural integrity of the wing. To extend Ross's approach to viscous flow phenomena, twodimensional Reynolds-averaged Navier-Stokes (RANS) analyses were carried out by [START_REF] Mittal | Computation of Two-Dimensional Flows Past Ram-Air Parachutes[END_REF] and [START_REF] Balaji | Effect of Leading Edge Cut on the Aerodynamics of Ram-Air Parachutes[END_REF]. They mainly focused on the developing instabilities due to the leading edge air inlet but also hinted at a smaller inlet improving the glide ratio. More recently Mohammadi and Johari (2010) investigated the flow features which develop around the air inlet to explain these performance differences by using a refined structured mesh around the leading edge and a Spalart-Allmaras turbulence model replacing the Baldwin-Lomax model used previously. On a parafoil derived from the Clark-Y airfoil, he found a little reduction in the lift curve slope and a major effect on drag. He also suggests ΔCd = 0.5 h/c as a first estimate for the additional drag coefficient due to the air inlet, where c is the airfoil chord and h is the height of the cut. Mashud and Umemura (2006) undertook wind tunnel experiments on an inflatable 3-D cell model. All preceding studies were concentrated on airfoils with cut off nose cones, creating a blunt body more characteristic for ram-air parachutes. Their study differs in such a way that it exhibits the transition from open to closed airfoil, once they started closing the air inlet by increasing the length of the upper lip. As they used flexible materials, the results included the effects of skin deformation. They noticed that the internal pressure varies with the squared sine of the angle between the air inlet and the free stream. They also showed that the internal pressure applied into the open airfoil modifies drag and lift at the air inlet region.

The airfoil studied in the present paper refers to an existing paraglider, with a chord length of 2.4 meters and which fly at a speed about 11 m/s. As a consequence, the free stream Reynolds Number in standard conditions is 1.8x10 6 . Consequently, airfoil geometry and Reynolds number are fixed but still realistic. The angle of attack varies from medium to relatively low values, representative of normal to accelerated flight, respectively. The main objectives are to quantify the influence of the position and the width of the air inlet on the aerodynamic performances and relate them to physical phenomena such as the appearance of separation bubbles. This is achieved by the analysis of the streamlines and pressure coefficient distributions. Results are focused on lift and drag coefficients as well as internal pressure. The position value extends from forward air inlet, as it is for ram-air parachute airfoils, to an underneath and rear position as it is for paraglider airfoils. The width values extend from the closed baseline airfoil to one that is representative of sport paragliders. Thus, the transition from a parachute design to a paraglider design is covered, as well as the transition from the baseline closed airfoil to the paraglider open airfoil.

Numerical methodology

The 2-D simulation of the cross section of the airflow around a paraglider airfoil was obtained by solving the steady-state Reynolds Averaged Navier-Stokes equations (RANS) over a rectangular flow domain. The flow was considered incompressible with constant properties. For the free stream Reynolds Number of 1.8x10 6 , the turbulent Reynolds stresses were taken into account by choosing the turbulence model proposed by [START_REF] Spalart | A One-Equation Turbulence Model for Aerodynamic Flows[END_REF]. Due to practical constraints, the interior of the paraglider was solved using the same turbulence model, regardless of the low Reynolds number in this area for which this model may not be well adapted.

The baseline closed airfoil and paraglider airfoil geometries were imported into the mesh generator software Gambit, which can build both structured, unstructured or hybrid meshes.

Over the airfoils, a rectangular uniform structured mesh was used to analyse the boundary layer in the proximity of the canopy to its full extent. For the interior of the paraglider airfoil and the outer domain, an unstructured triangular mesh was used.

The mesh files were handled by the widespread finite volume flow solver FLUENT, which solves the RANS equations and manages the numerical simulations. The paraglider fabric was presumed rigid and impermeable. The boundary conditions on the computational domain included uniform velocity at the inflow, upper and lower boundaries to allow for the freestream velocity V  to enter at the specified angle of attack α (Figure 1). For the upper and lower boundaries, when the value chosen for the angle of attack results in an effective outflow, the solver automatically changes the condition to pressure outlet. The outflow condition was specified as pressure outlet. The no-slip boundary condition was applied to the interior and exterior surfaces of the airfoils. The numerical calculation was executed on a Linux workstation with one processor and two cores. The convergence of all numerical solutions presented is obtained with a second order numerical scheme.

In order to automate the mesh generation and the numerical simulation, the numerical framework VLab (V. [START_REF] Chapin | Analysis design and optimization of navier-stokes flows around interacting sails[END_REF], was used to define a specific parametrical script and run Gambit and FLUENT as a unique process. The main post-processing, which included the creation of streamlines, vorticity, internal and external pressure plots and other features, was also accomplished autonomously by this VLab script.

Mesh and domain sensitivity

There were no airfoil data sets available for the paraglider airfoil and its baseline closed airfoil. Nevertheless, a numerical simulation with the well-established software Xfoil [START_REF] Drela | XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils[END_REF]) was carried out for the baseline airfoil with a forced transition at 5% of the chord length.

As there was no experimental reference, and this study being closely related to the general approach of Mohammadi (2010), the same domain of 16x10 of the chord length was assumed to be valid. These dimensions refer to the domain extent in the chord direction and in the transverse direction respectively. The airfoil was placed halfway between the top and bottom boundaries, and five chord lengths from the inflow as shown in Figure 1.

The airfoil surface was covered by a boundary layer-type mesh and an unstructured triangular mesh elsewhere (Figure 2). In order to obtain a theoretical value of y+ of less than 2.5, necessary to ensure the existence of a grid point inside the viscous sublayer [START_REF] Kalitzin | Near-wall behaviour of RANS turbulence models and implications for wall functions[END_REF], a first cell transverse dimension of 0.0055% of the chord length was employed. The Spalart-Allmaras model is one of the most sensitive to the location of the first cell center, therefore the condition for a maximal y+ value was analysed to ensure that the majority be below 5. For the baseline airfoil at α = 14°, it was found to be 5.60, nevertheless its value for α = 6° was more significant to the optimization and only 4.41. The leading edge inlet did not have a significant impact (max. 4.43), except in the very localized recirculation bubbles. There it reached up to 14 in the worst cases, but this was accepted as it was limited to very few cells.

In order to evaluate the mesh resolution effects, the rectangular-cell dimension on the airfoil surface and the height of the first rectangular cell above the surface were systematically modified. Moreover, the number of lines constituting the structured rectangular mesh refinement for the boundary layer and the growth rate of the unstructured triangular mesh were varied.

Following each change in the mesh parameters, the resulting lift and drag coefficients were used as convergence criteria in regard to mesh sensitivity. Finally, the meshes around the baseline airfoil were composed of 78k cells and 69k nodes and the meshes around the paraglider airfoil were composed of 112k cells and 84k nodes.

The resulting lift (Figure 3) and drag (Figure 4) curves were then compared to the results obtained using Xfoil for mesh validation. The computed lift coefficients did not exhibit significant differences in their linear part. However, the drag coefficients predicted by FLUENT were generally greater than the ones calculated by Xfoil. This behaviour can be explained by the intrinsic tendency of FLUENT to overestimate the drag coefficient [START_REF] Silva | Numerical Study of the Airflow around the Airfoil Selig 1223[END_REF] and by the model's assumption of a fully turbulent flow simulation.

In order to execute the automated computation, a mesh validation was performed using VLab with the same specifications (first row size etc.) for mesh generation. The mesh sensitivity analysis resulted in the following characteristics: 65 lines for the boundary layer refinement mesh (resulting in 0.098c for the total size of the structured rectangular mesh), 0.2c for the size of the wake zone and 15 mesh points on the edge of each boundary of the structured zone of the flow domain. A further refinement was implemented on the leading edge with a rectangular-cell dimension on the airfoil surface of 0.00125c chord length.

For the paraglider airfoil, an unstructured triangular mesh covered the interior computational domain. The interior mesh characteristics were adapted to the number of nodes of the leading edge refinement.

Results

To respect the freestream Reynolds Number 1.8x10 6 with a unitary chord at sea level, a freestream velocity of 26.4 m/s was selected. Three angles of attack, 2°, 4° and 6°, were investigated for each inlet configuration. For the most significant cases, the range was extended to -4°  α  14° to exhibit the airfoil characteristics in more depth. For the paraglider airfoil, the air inlet parameters consisted of its width and of its position, with respect to its midpoint. The spline length of the width Sw, and the spline length between the leading edge and the midpoint of the inlet Sc, were normalized with the total spline length of the lower surface which is 1.027c (Figure 5), regardless of whether the air inlet extended over the upper surface which was sometimes the case. The following dimensions were analysed: Sw = [1% -4%] in 1% intervals and Sc = [0%, 0.5%, 1%, 1.5%, 2%, 2.5%, 3%, 4%]. The parameters were chosen in this particular way as this corresponds to the common limits used in paragliding and parachute production. The excessive position Sc = 5.3% was added. For each case, the lift and drag coefficients, as well as the vorticity contours, the streamlines and the pressure coefficient on all airfoil surfaces, were given as an output.

Baseline airfoil

The baseline airfoil had a thickness ratio of 18.5%. The lift coefficient Cl (Figure 3) displayed a linear dependence on the angle of attack α, for -4°  α  8°, with a slope of 6.10 rad -1 . This is slightly below the 6.28 rad -1 predicted by linear theory. The drag coefficient increases slightly from its minimal value 0.013, at α 0 , to 0.019 for α = 8°, and subsequently rises clearly. The zerolift angle of attack was found to be α 0 = -1.3°, and the maximum glide ratio to be 51.2 at α = 10°.

Nevertheless, the analysis focused on α = 6°, as this is a more suitable angle of attack for a real 3D wing which receives additional induced and parasitic drag, due to the lines and the pilot. For α = 6°, the minimum pressure coefficient on the airfoil was Cp = -2.16, occurring on the upper surface between 0.09c and 0.095c (Figure 6). After this peak, the flow slows down, so that the pressure coefficient on the upper surface progressively recovers, and becomes slightly positive at the trailing edge. The stagnation point, Cp = 1, is situated on the lower side, right after the leading edge at 0.005c. Further downstream, the pressure on the lower surface decreases and stays close to zero, from 0.3c to the trailing edge. Since the pressure on the lower surface is always greater than the pressure on the upper surface, lift is generated all along the airfoil. At this angle of attack there is no flow separation, and the vorticity contours (Figure 7) display a fully attached boundary layer, which thickens along the two surfaces toward the trailing edge.

The boundary layer on the suction side nearly doubles compared to the boundary layer on the pressure side.

Flow analysis around the leading edge

This section presents a physical description of various flow patterns obtained in the region of the leading edge. Before this, a more general remark must be made on the internal flow. At the interior of the paraglider airfoil, some vortices of considerable dimensions are displayed. Their number and extent either depends on the configuration of the air inlet or the angle of attack. For instance, Figure 8 shows, for the case α = 8° with Sc = 2%, Sw = 1%, which is detailed later, the values of the turbulent viscosity ratio inside and around the airfoil. The internal value reaches 60 in the core of these vortices. On the external side, the value is about 170 in the boundary layer and 350 in the wake. However, the turbulence model adopted is not optimal for these low Reynolds number phenomena, and no wind tunnel experiments are available to observe and validate this output. In addition, the interior velocity is almost zero everywhere, so the streamlines showing these vortices are somewhat misleading in this practically stagnation area.

As a matter of fact, the internal pressure has a constant value, except for a restricted area near the air inlet.

Referring to the main stream direction, the stagnation point can precede, coincide with, or follow the air inlet, depending on the position of the inlet and on the angle of attack. When the stagnation point is located after the air inlet on the lower surface (Figure 9a), the flow along this surface is nearly unperturbed by the presence of the air inlet itself. This situation happens with an air inlet oriented ahead and/or an increased angle of attack. To the contrary, the flow along the upper surface is disturbed and the boundary layer is thicker than that of the baseline airfoil. This effect is more obvious when the air inlet width is increases. Moreover, especially if the width rises, a larger amount of air can penetrate the airfoil. Subsequently, it has to circumvent the solid canopy to exit, thus resulting in an additional stagnation point at the interior of the leading edge.

A strong separation bubble appears on the external surface, at the front end. Circulation and boundary layer are altered, decreasing the lift coefficient and increasing the drag coefficient.

When the stagnation point is just before the air inlet in the leading edge area (Figure 9c), the physical behaviour is a mirror image of the one illustrated above. A second stagnation point appears at the opposite inlet end, or at the interior of this end, toward the lower surface. A separation bubble can form on the external surface of the inlet end. In this case, the lift coefficient is not decreased but a negative effect on the drag coefficient is still present. As for the previously analysed case, when a separation bubble occurs the boundary layer is thicker than for the baseline airfoil. Here the phenomenon is less significant. When the beginning of the air inlet is further downstream, its distance to the stagnation point increases. As a consequence, when the flow reaches the air inlet, it has had a larger distance to accelerate and has become tangent to the canopy (Figure 10). Hence, the deflection of the fluid, which penetrates the canopy, is reduced.

However, the internal pressure decreases, this will be examined in more depth in the following section.

When the stagnation point coincides with the air inlet as in Figure 9b, it is located inside the airfoil and stays behind the upper or the lower leading edges. For increasing values of the air inlet width, external separation bubbles can form on one or both of the air inlet ends. On the other hand, when the stagnation point is within the air inlet, in conjunction with a small width (Figure 11), no separation bubbles form and the flow slows down in front of the air inlet. Thus it leads to the highest pressure coefficient at the interior of the canopy and to an almost unperturbed external flow. In this case the air inlet acts like a total pressure tap.

External and internal pressure

A systematic study shows that the external pressure coefficient curve around the open airfoil is, in every case, mostly equal to that of the baseline airfoil, a difference appears only if a separation bubble occurs near the opening (Figure 12). If it is on the lower edge as in Figure 9c, the curve modification remains in the region of the bubble and is characterized by a local additional depression. If the bubble is on the upper edge as in Figure 9a, there is also a local effect and a global one in addition. This is obvious from a loss at the main depression peak further on the upper side.

A 3-D mapping of the internal pressure coefficient, with respect to position and width of the air inlet, was performed for an angle of attack of 2° (Figure 13). This angle was evaluated as optimal to describe this phenomenon because it represents, among our studied cases, the most critical for deflation risk due to internal pressure loss. Examining the plot, the influence of the position of the air inlet is essential, while its width represents only a minor contribution to the internal pressure value. The systematic study of pressure coefficient curves correlated with the flow patterns brings a more precise explanation for the way the internal pressure varies. When the stagnation point is located in the air inlet like in Figure 9b, the internal pressure coefficient is maximal with a value of 1. When the stagnation point moves out of the air inlet, the internal pressure is, in all our cases, exactly equal to the external value existing on the edge at the inlet end which is the same side as the external stagnation point (Figure 14). This result is very interesting, as we established previously that the external pressure curve for an open airfoil is nearly the same as that for baseline airfoil. It shows that the internal pressure can be well estimated with only the closed baseline results and the air inlet location.

At present, an absolute quantitative 3D method to evaluate the structural stability of a paraglider regarding the differential pressure between the inner and outer canopy surfaces has not been established. Indeed, even if the structure can help to maintain the geometry under a local inward pressure balance, the higher the internal pressure, the better the resistance to deflation. So, in our study, Sc1% tends to present an elevated robustness to deflation for every air inlet dimension considered. Internal pressure coefficients decayed rapidly by setting back the air inlet. Increasing the air inlet size partially compensates this loss by enlarging the opening towards the stagnation area. This result confirms that parafoils are more robust to deflation than paragliders because they maintain a high internal pressure at low angles of attack. This behaviour can be explained by examining the position of the stagnation point for every case. In fact, air inlet positions tailored for gliding parachutes had stagnation points situated either on the location of the air inlet (Figure 9b) or just after on the lower surface (Figure 9a). For this second case, considering that the internal pressure was nearly the same as the one on the edge end between the internal and external fields, the internal pressure coefficient is close to that of the stagnation point. Therefore the internal pressure for parachutes is always equal to, or approaching, Cp = 1. On the other hand, paraglider airfoils can have the stagnation point situated before the air inlet, in the leading edge area, especially if the inlet is located further on the lower surface and the angle of attack is low (Figure 10). This means higher velocities appear on the edge end at the air inlet, therefore causing a decrease in the internal pressure.

In order to focus on a critical case, internal and external surface pressure coefficients plotted versus the relative position to airfoil chord x/c are highlighted for Sc = 3% at the smallest width Sw = 1% and α = 2° (Figure 15). The internal pressure is greater than the external one, except for a small portion close to the leading edge. This condition suggests that the canopy can potentially begin to reverse its curvature locally due to pressure inversion. If this failure extends, the airfoil can be distorted to such an extent, that the frontal collapse limit is reached. Nevertheless, in modern paragliding industry a solution to delay the problem, such as reinforcing the leading edge with a semi-rigid structure, is often considered. Depending on the type of structure used, some critical configurations become stable. Thus the limit at low angles of attack is extended.

Influence of the air inlet configuration on lift and drag

Figure 16 shows the lift slope coefficient curves between 2° and 6° for all cases. For small air inlet widths Sw, there is no difference in the slope between the baseline airfoil and the paraglider airfoils. Only when the air inlet is centered at the leading edge can a little gap be noticed. As the width is increased, the difference progressively grows. A more important alteration of the slope clearly appears for some configurations, suggesting two distinct behaviours. At Sw = 2% it concerns Sc0.5%, at Sw = 3% it involves Sc1.0% and at Sw = 4% it concerns Sc1.5%. All these configurations are characterized by an air inlet extending over the beginning of the upper side, just like parafoils. So this first group was named "parachute-like" on the Figure 16. The second group concerns all the other air inlet configurations. They are entirely located on the lower surface of the airfoil and are much "paraglider-like". In the scope of tested parameters values, the degradation of the slope for "parachute-like" is well correlated with the size of the upper separation bubbles growing with the angle of attack as shown in Figure 17. It can be related to the associate loss found at the main depression peak on the upper side suggesting a global effect on the circulation around the airfoil. Inversely, when there is no visible bubble with increasing angle of attack like for Sw = 1% at Sc = 0% (Figure 18), the value of the lifting slope stays similar to that of the baseline. Other local contributions to the lift change, with respect to the baseline airfoil, can be found in the pressure field balance. They derive from the cut part of the airfoil and the depression caused by the separation bubble.

The width effects on polar curves are presented for three air inlet positions, namely Sc = 0% (Figure 19), 2% (Figure 20) and 5.3% (Figure 21). They clearly show different tendencies. At Sc = 0%, thus for a symmetric air inlet, an increase in the width tends to increase the drag a lot and reduce the lift slightly. This effect becomes more pronounced as the angle of attack increases. Sc = 2% stands in contrast, the curves now converge with increasing angles of attack and the lift coefficient Cl rises slightly with the width, especially for low angles of attack. The final position Sc = 5.3%, relatively far downstream, differs from the previous positions with very similar polar curves. There is just, depending on the extent of the width extent, a little additional drag for the closed airfoil case.

For an open airfoil, the aerodynamic force is obtained by the integration of pressure and skin friction on the both sides of the upper and the lower surfaces. Mashud and Umemura (2006) detailed this calculation for the pressure part. Assuming that the internal pressure was uniform, they showed that the result is equal to the integral of the external pressure applied to the upper and lower surfaces, plus the internal pressure applied at the external side of the straight line joining the two inlet extremities.

In order to express this calculation with only the closed baseline airfoil results, another way of decomposition is possible for a paraglider airfoil in its performance range. Applied to the Figure 5 geometry, the pressure integration of the open airfoil is expressed in equation (1). For this kind of performant airfoils, within the range of parameters investigated, there is not a strong separation bubble. Our results show that the external pressure coefficient curve matches very well the baseline airfoil and also that the internal pressure is almost constant. Thus P ext = P extb can be used to write equation (2). Adding and subtracting the pressure integration on the both sides of the curve segment corresponding to the air inlet area gives equation (3). As P int is constant, its integration around the closed airfoil equals zero and gives equation ( 4). In the first term, the integration of the external pressure around the baseline airfoil gives its aerodynamic force. In the second term, the integration of the constant pressure P int on a curve segment is equal to this pressure applied on the straight line joining its extremities. Finally, the aerodynamic force on the open airfoil is obtained with equation ( 5). As shown previously, the internal pressure can be deduced from the external pressure field on the baseline airfoil, therefore the force can be evaluated only with baseline airfoil results. This greatly facilitates a quantitative estimation by using published data for closed airfoils or classical airfoil software.

𝐹 ⃗ 𝐴 = ∫ (𝑃 𝑖𝑛𝑡 -𝑃 𝑒𝑥𝑡 ). 𝑛 ⃗⃗. 𝑑𝑠 Where 𝐹 ⃗ 𝐴 is the total aerodynamic force, 𝑛 ⃗⃗ is a unit outward normal vector, s is the curvilinear abscissa, A is the lower extremity of the air inlet, B is the upper extremity of the air inlet, T is the trailing edge point and b is a subscript for the baseline airfoil.

That decomposition is also an interesting approach to explain the way that the air inlet influences drag and lift. Thus, the additional force on the paraglider airfoil based on the baseline airfoil, is reduced to the localized pressure integration at the air inlet location on the closed baseline airfoil. On the internal side, externals results from the baseline are applied, whereas on the external side the internal pressure from the open paraglider airfoil is used.

When the external pressure field around the air inlet location is almost uniform, it follows from the above that the internal pressure in the paraglider airfoil is also equal to that uniform pressure. So, the integrated pressure is almost the same on the both sides. As a consequence the influence of the air inlet on the pressure force is small and the performance is weakly altered. This situation can arise in two ways: when the air inlet is reduced in size close to the stagnation point or when the air inlet is located downstream on the lower surface. This second case corresponds well to Figure 18. The internal pressure is high in the first case and low in the second, but, in both cases, the influence of the air inlet on the total aerodynamic force is small.

When the stagnation point is just beside the air inlet, an accelerated flow is observed at the inlet location. For this case, it has already been shown that the internal pressure is equal to the external pressure at the extremity A or B of the air inlet which is on the stagnation point side. This internal value is greater than that for the external accelerated flow. So, when evaluating the added force by applying this pressure field on the both sides of the inlet part removed from the baseline airfoil, an extra force appears, directed from the air inlet into the open airfoil. Two subcases must be distinguished. The first one is when the stagnation point is located just after the air inlet on the lower surface, like for gliding parachute airfoil at increasing angle of attack. In front of the air inlet the flow accelerates substantially towards the upper side. Therefore the additional force is significant and oriented mostly backward. This is in correlation with the tendency observed in Figure 19, even though it must be kept in mind that there are also the effects of the separation bubble and the influence of the skin friction. The second subcase arises when the stagnation point is located just before the air inlet in the leading edge area, like for realistic paraglider configurations at low angles of attack, e.g. Sc = 2% and Sw2% at α = 2°.

Here the flow accelerates moderately in front of the air inlet, towards the lower surface. The additional force is moderate and oriented upwards (lift) and backwards (drag). This corresponds well with the remarks made about Figure 20.

Best configuration

Results are summed up in three 3-D plots where each performance parameter is compared with the result found for the baseline airfoil for α = 6°, representative of a cruise gliding flight.

In Figure 22 the influence of the air inlet configuration on the additional lift coefficient is displayed. When the midpoint of the air inlet is further downstream, a lift coefficient equal or even slightly greater than the value obtained for the baseline airfoil is achieved. On the other hand, as the air inlet midpoint moves upstream, the lift coefficient decreases if the width increases. This is the main effect of the parachute-like behaviour previously noticed.

The influence on drag coefficient (Figure 23) reveals a minimum when Sc = 2%, regardless of its width. Width Sw = 1% and position Sc = 1.5% leads to nearly the same value. When position Sc move below 1.5%, and width Sw is simultaneously increased above 1%, the drag coefficient clearly increases. This is the second aspect denoting a parachute-like behaviour. Its origin is in the previously viewed effect of adding the air inlet contribution in the pressure integration of the baseline airfoil.

The influence on the glide ratio is shown in Figure 24. The observations made for the drag coefficient can be made again here. The efficiency degrades when the position moves towards the leading edge and when the air inlet dimension is increased. As a matter of fact, Sw = 1% and Sc = 2% (Figure 25) was found to be the configuration with the best performance. For the same width, but with Sc = 1.5%, practically the same performance was obtained. These two positions have in common the total absence of separation bubbles around the air inlet, whatever the angle of attack. In the section 4.3 it was shown that these two configurations fully inflate.

Therefore, the Sw = 1%, Sc = 2% case, was investigated for a wider range of angles of attack, i.e. -4°  α  14°, and compared to the baseline airfoil. The drag coefficient for the paraglider airfoil was marginally higher at α0°, slightly lower at α10° and nearly identical elsewhere. The computed lift coefficient was slightly greater than the value calculated for the baseline airfoil at negative angles of attack, practically identical between 0° and 10°, and slightly lower for α greater than 10°. This resulted in two nearly superimposed lift to drag ratio curves.

Conclusions

Even if the baseline airfoil used is highly realistic, and representative of a performance paraglider, the results of this study are limited to this shape, at a single Reynolds number, and in the scope of the investigated parameters variations. Under this restriction, it can be concluded that:

The flow pattern reveals one stagnation point when the flow separates in front of the air inlet and two stagnation points when it separates to one side or another. One of these points is always located on the internal side or just at the extremity of one of the air inlet ends. The second stagnation point, when it occurs, is located on the external side of the other air inlet end. When it is located on the internal side, a stagnation point can be associated with a more or less important separation bubble on the external side of the same border. A larger air inlet promotes the development of this separation bubble.

The internal pressure in the airfoil is constant everywhere except near the air inlet. It is equal to the stagnation pressure when the flow separates in front of the air inlet. It decreases when the flow separates to one side of the air inlet, at an external stagnation point. The value of the internal pressure is equal to the external pressure at the inlet end which is on the same side as the stagnation point.

If there is no separation bubble, the external pressure curve on the open airfoil is the same as for the closed baseline airfoil. For this case, lift and drag of the open paraglider airfoil can be calculated only by knowing the closed baseline airfoil pressure curve, the air inlet location and the value of the internal pressure. From the above conclusion, the internal pressure can also be deduced from the baseline airfoil results. A good approximation is also possible in the same way, for small bubble on the lower surface. These results are important because, generalized to similar airfoils, they give paraglider designers a simple way to obtain a good estimate of the performances and internal pressure with only classical closed airfoil software.

A larger air inlet causes deterioration of the aerodynamic characteristics. A rise in drag is mainly due to a loss of frontal suction in the pressure integration at the air inlet. It is even more important when the air inlet is positioned forward and thus oriented more ahead in an accelerated flow. For a lower amount, the drag increase is also due to the thicker boundary layer obtained when separation bubbles occur.

The association of a large air inlet (>2%) and a forward position (<2%) results in a specific behaviour. It is characterized by a lower lifting curve slope, which originates from the growth of a separation bubble over the leading edge when the angle of attack increases. This affects the whole external pressure curve over the airfoil. Combined with the drag increase, it results in a degraded lift to drag ratio. A position of the air inlet located further downstream leads to less performance alterations, even for large dimensions. Thus, the internal pressure clearly decreases for lower angles of attack. Hence, two clearly separate behaviours for open airfoils are found.

The first one is "parachute-like", with the air inlet acting rather like as a total pressure tap, resulting in good deflation robustness but performance losses. The second one is "paragliderlike", at low angles of attack, the air inlet tends to act as a static pressure tap, resulting in less altered performances but lower deflation robustness.

For a paraglider, at a typical cruise angle of attack of α = 6°, the configuration with an air inlet midpoint at 2% and a width of 1% shows the best performances, almost equal to those of the baseline airfoil.

  = ∮(𝑃 𝑖𝑛𝑡 -𝑃 𝑒𝑥𝑡 𝑏 ). 𝑛 ⃗⃗. 𝑑𝑠 -∫ (𝑃 𝑖𝑛𝑡 -𝑃 𝑒𝑥𝑡 𝑏 ). 𝑛 ⃗⃗. 𝑑𝑠 𝐴 𝐵 (3) 𝐹 ⃗ 𝐴 = -∮ 𝑃 𝑒𝑥𝑡 𝑏 . 𝑛 ⃗⃗. 𝑑𝑠 -∫ 𝑃 𝑖𝑛𝑡 . 𝑛 ⃗⃗. = 𝐹 ⃗ 𝐴 𝑏 -𝑃 𝑖𝑛𝑡 . ‖𝐴𝐵 ⃗⃗⃗⃗⃗⃗ ‖. 𝑛 ⃗⃗ + ∫ 𝑃 𝑒𝑥𝑡 𝑏 . 𝑛 ⃗⃗.

Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25

 23456789101112131516171819202122232425 Figure 2 Mesh produced for Sw = 2% and Sc = 2% a) around the whole airfoil, b) focused on the air inlet region

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