domain: phys chim

text:
H Caillet

A Bastide

G Chuppa

T Petit

L Adelard

ANAEROBIC DIGESTION OF VINASSE AND CFD MODELLING APPROACH

Keywords: anaerobic digestion, computational fluid dynamics (CFD), Newtonian, non-Newtonian, large-eddy simulation, mechanical mixing

The study's ultimate goal consists of modelling and optimising the co-digestion of particulate substrates like sewage sludge, biowaste and vinasse from sugar cane. Given these substrates, the medium is highly heterogeneous and has particular physical characteristics and behaviour. Moreover, anaerobic digestion could be lead in wet-mode or in dry-mode, thus we want to develop a model valid for both configurations. In this context, the fluid flow modelling is of interest. Indeed, the contact between substrates and microorganisms has a significant influence on the anaerobic digestion process. It is directly correlated to the flow inside the digester. The research question is therefore the following: Is it possible to predict the spread of microorganisms inside the digester for both liquid and solid digestion? In this paper, we present the context of the work and the mathematical model based on Navier-Stokes equations with the Boussinesq approximation. Large-eddy simulation (LES) is used for the turbulence modelling. The sliding mesh method is used to characterise the impeller rotation. In further work, we will present the simulation results validated with the literature data. The differential equations will be solved on OpenFOAM software using the finite volume method. The flow will be simulated for both Newtonian (vinasse) and non-Newtonian fluids (manure) and at different total solid (TS) rates for non-Newtonian fluids. The obtained results will be the velocity and temperature profiles within the digester. It will hence be possible to optimise the process through both the medium physical properties (TS rate and viscosity) and the digester configuration. We will also consider the multiphase flow. Alongside numerical simulations, experiments are carried out on the substrates studied in order to estimate the methane production. In this article, we present the results of experiments on the vinasse and the development of the CFD model.

1-INTRODUCTION

The development of renewable energies is generally growing in relation to the current context, particularly, due to the depletion of fossil fuels and the need to limit the negative effects on the environment. Anaerobic digestion is a widely used process in waste treatment (agro-industrial waste, biowaste, manure, sewage sludge, vinasse...). The interest of anaerobic digestion is twofold, it allows organic waste to be treated with energy recovery. Thus, this process meets the particular needs of Reunion Island, which by its insular character, must call for sustainable solutions in terms of waste treatment. In fact, the household waste produced in Reunion Island is currently buried while the landfills are reaching their saturation point. It is therefore urgent to find durable solutions for waste management. It is in this perspective that studies are funded by the Region to examine the methanogenic potential of waste produced in Reunion Island (biowaste, sewage sludge, and vinasse) as well as to optimise the process on an industrial scale. In addition, local renewable energy production is a real asset for insular territories. In methanisation industrial plants, the main process parameters are the temperature, the hydraulic retention time, the biomass and the mixing conditions. These parameters are directly correlated to the efficiency of the process. The mixing conditions are of utmost importance because mixing allows the temperature homogenisation and fosters the contact between the substrate and the microorganisms. The substrate is naturally crucial in the methane yield because the yield will depend on the nature of the substrate. In addition, mono-digestion and co-digestion are two means of carrying out anaerobic digestion. Co-digestion is subject to many studies, in a review published in 2014, the authors stated that anaerobic co-digestion is a feasible option to overcome the drawbacks of mono-digestion and to improve the economic feasibility of industrial plants [START_REF] Mata-Alvarez | A critical review on anaerobic co-digestion achievements between 2010 and 2013[END_REF].

1-CONTEXT OF THE STUDYWORK CARRIED OUT 1-1-INHIBITION AND FAILURE RISKS IN ANAEROBIC DIGESTION

Various phenomena can destabilise the process of anaerobic digestion lowering it to complete failure of the biogas production. Anaerobic digestion is subjected to inhibition or failure risks due to the following reasons: 1. While the hydrolysis phase is largely considered as the rate-limiting phase for complex organic, intermediate product concentrations like free ammonia, volatile fatty acids and sulphide/sulphate can lead to inhibitions. Methanogenesis can also be considered like a rate-limiting phase [START_REF] Yuan | Progress in inhibition mechanisms and process control of intermediates and by-products in sewage sludge anaerobic digestion[END_REF] for easily biodegradable substrates such as wastewater sludge. Total nitrogen concentration measured on the vinasse is approximately 2000 mg.L -1 , which is relatively high for anaerobic digestion. Although this concentration is relatively high, anaerobic digestion is possible if the micro-organisms are acclimatised to the substrate [START_REF] Rozzi | Methods of assessing microbial activity and inhibition under anaerobic conditions: a literature review[END_REF]. 2. For liquid anaerobic digestion (TS < 15%), inhibitions can occur because of an uneven distribution of biomass and substrates, the intensity and duration of the mixing as well as the retention time, must therefore be precisely studied to optimise the hydrodynamic behaviour of the process. Unsuitable mixing conditions can break the flocs of micro-organisms, disturbing the synergetic effects. Proper mixing conditions also have to be established to control the volume of dead zones and turbulence. 3. For solid anaerobic digestion, where dry processes are concerned, i.e. if the dry solid content reaches 15% or for cases of codigestion, high viscosity leads to limited mass and heat transfer among enzymes, bacteria and substrates in the digester. Mechanical mixing is in this case, considered to be the most efficient way to optimise the diffusion processes [START_REF] Karim | Anaerobic digestion of animal waste: Waste strength versus impact of mixing[END_REF]. However, few studies have been carried out on the hydrodynamics of media.

4. Anaerobic co-digestion is often recommended to optimise biogas yield. However, co-digestion can lead to solid digestion and inhibitions due to the accumulation of volatile fatty acids. In that case, the development of biofilms among the substrate can disrupt the liquid flows [START_REF] André | Solid anaerobic digestion: State-of-art, scientific and technological hurdles[END_REF].

1-2-ANAEROBIC DIGESTER MODELLING

We have seen a rise in numerical models, especially CFD models in recent years. Regarding the process modelling, the biochemical and physicochemical processes are taken into account in the ADM1 model [START_REF] Batstone | The IWA anaerobic digestion model no 1 (ADM1)[END_REF]. To meet the needs related to the industrialisation of the methanisation, the development of models taking the flows into account in a precise way, is necessary. There is experimental evidence that mixing schemes and intensities have an impact on biogas production [START_REF] Kaparaju | Effects of mixing on methane production during thermophilic anaerobic digestion of manure: Lab-scale and pilot-scale studies[END_REF]. Indeed, all the chemical reactions leading to the complete digestion of the substrates can only occur when they are in contact with the microorganisms involved in each reaction. To do this, the digestion medium must be stirred. The agitation mode and type thus influences the quality of the digestion of the substrates. In fact, vigorous mixing suppresses growth and the propagation of methanogenic centres if methanogenesis is the rate-limiting step, but also may enhance methane production and degradation if hydrolysis is the rate-limiting step [START_REF] Vavilin | Anaerobic degradation of solid material: Importance of initiation centers for methanogenesis, mixing intensity, and 2D distributed model[END_REF]. In addition, anaerobic digestion can also be carried out by the dry route (TS > 15%). In this case, the medium agitation is even more significant than in the wet digestion, since the homogenisation of the medium becomes more difficult. Moreover, the waste treated by this process also has particular rheological properties which influence the flow and therefore have a role in the optimisation of the mechanical agitation. Indeed, these fluids can be viscous, Newtonian or non-Newtonian. The rheology of waste including sewage sludge, manure and biowaste, has been studied in order to model the flow of these fluids which have a Newtonian or non-Newtonian behaviour according to the rate of total solid [START_REF] Terashima | CFD simulation of mixing in anaerobic digesters[END_REF]- [START_REF] Landry | Physical and rheological properties of manure products[END_REF]. It has been shown that the fluid dynamics in the digester can be affected by the TS [START_REF] Yu | Numerical simulation of mechanical mixing in high solid anaerobic digester[END_REF]. CFD provides accurate results on the flow and is therefore of great interest for anaerobic digestion modelling and optimisation. The major interest of the CFD is to characterise the flows within the digester in order to study configurations (digester, impeller) that allow optimal contact between the substrates and the microorganisms. Ultimately, in our study, we wish to model the displacement of microorganisms within the digester for both Newtonian and non-Newtonian fluids, in order to propose stirring optimisation. Indeed, to ensure that all substrates will be digested, it is necessary to ensure the spread of micro-organisms at any point in the digester. With this in mind, we conducted a literature review of CFD models applied to anaerobic digesters to identify studies that have already been carried out using this technique. These models are implemented to optimise the industrial process. The following table outlines the literature review of the aims of CFD in digesters.

Objectives Phase model Fluid property [START_REF] Vesvikar | Flow pattern visualization in a mimic anaerobic digester using CFD[END_REF] Study the impact of the design of the digester (diameter of the draft tube) on the flows by studying the position and the volume of the dead zones.

Liquidgas N [START_REF] Alcamo | Large-eddy simulation of turbulent flow in an unbaffled stirred tank driven by a Rushton turbine[END_REF], [START_REF] Jian | Large eddy simulations of mixing time in a stirred tank[END_REF] Compute the flow with LES techniques. Liquid N [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF] Optimise the power supply and reduce the volume of dead zones or weakly stirred area.

Liquid N-N [START_REF] Terashima | CFD simulation of mixing in anaerobic digesters[END_REF], [START_REF] Jahoda | CFD Modelling of Liquid Homogenization in Stirred Tanks with One and Two Impellers Using Large Eddy Simulation[END_REF], [START_REF] Wu | CFD prediction of mixing time in anaerobic digesters[END_REF] Study the liquid homogenisation in stirred tanks and the required time for homogenisation (RANS and LES).

Liquid N ; N-N [START_REF] Karim | Gas-lift digester configuration effects on mixing effectiveness[END_REF] Reduce the percentage of poorly mixing zones in gas-lift digesters by testing configurations of the bottom of the digesters.

Liquid N-N [START_REF] Meroney | CFD simulation of mechanical draft tube mixing in anaerobic digester tanks[END_REF] Simulate the characteristics of digesters: the rates of mixing and the slug injection of tracers from the digester volume turnover time, the mixture diffusion time, and the hydraulic retention time.

Liquid N [START_REF] Wu | CFD analysis of mechanical mixing in anaerobic digesters[END_REF] Study different mechanical stirring configurations. Liquid N ; N-N [START_REF] Zadghaffari | A mixing study in a double-Rushton stirred tank[END_REF] Investigate the flow fields, power and mixing time in a fully baffled stirred vessel with mechanical agitation (LES).

Liquid N [START_REF] Wu | Computational Fluid Dynamics Investigation of Turbulence Models for Non-Newtonian Fluid Flow in Anaerobic Digesters[END_REF], [START_REF] Wu | CFD investigation of turbulence models for mechanical agitation of non-Newtonian fluids in anaerobic digesters[END_REF] Investigate turbulence models. Liquid N-N [START_REF] Yu | Numerical simulation of mechanical mixing in high solid anaerobic digester[END_REF] Simulate mechanical agitation in high solid anaerobic digester. Liquid N-N [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF] Model the flows with mechanical agitation. Liquid N-N [START_REF] Yu | Multiphase modeling of settling and suspension in anaerobic digester[END_REF] Describe the settling and suspension in anaerobic digester and evaluate the biomass retention physical process.

Three phases N [START_REF] Craig | CFD simulation of anaerobic digester with variable sewage sludge rheology[END_REF] Model the flows for fluids with variable rheology to study the impact on the performance of the digester.

Liquid N-N [START_REF] Wu | CFD simulation of gas mixing in anaerobic digesters[END_REF] Study the stirring performance of gas recirculation agitation configurations, and the impact of agitation intensity on biological processes.

Liquidgas N [10]

Study the hydraulic performance of an existing digester (percentage of dead zones, recirculation volume).

Liquid N [START_REF] Zhang | Effect of impeller on sinking and floating behavior of suspending particle materials in stirred tank: A computational fluid dynamics and factorial design study[END_REF] Study the impact of the agitator on suspended particles in order to optimise the digester.

Liquidsolid N [START_REF] Rasool | EFFECT OF[END_REF] Study the effect of impeller rotational speed and velocity field in the mixing tank.

Liquid N [START_REF] Dapelo | Euler-Lagrange Computational Fluid Dynamics simulation of a fullscale unconfined anaerobic digester for wastewater sludge treatment[END_REF] Study the influence of the behaviour of the sludge on the flow and the consequences on the quality of the agitation.

Liquidgas

N-N N = Newtonian, N-N = non-Newtonian.

Table 1: Objectives of CFD models.

1-3-TURBULENCE MODELLING

A point of attention is the modelling of turbulence phenomena. The interest comes from the fact that the mass transfer during the process is dependent on the turbulence phenomena in digesters [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], and the contact between micro-organisms and substrate is correlated to turbulence [START_REF] Koerich | Numerical evaluation of the low Reynolds turbulent flow behaviour in a bioreactor[END_REF]. Moreover, studies show that flow predictions are particularly sensitive to the turbulence model implemented [START_REF] Coughtrie | Effects of turbulence modelling on prediction of flow characteristics in a bench-scale anaerobic gas-lift digester[END_REF]. Thereby, the choice of the turbulence model is important in the simulations. Mainly Reynoldsaverage Navier-Stokes (RANS) simulations were conducted on digesters [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF], [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF], [START_REF] Wu | CFD simulation of mixing in egg-shaped anaerobic digesters[END_REF], [START_REF] Yu | Numerical simulation of mechanical mixing in high solid anaerobic digester[END_REF], [START_REF] Vesvikar | Flow pattern visualization in a mimic anaerobic digester using CFD[END_REF], [START_REF] Wu | CFD analysis of mechanical mixing in anaerobic digesters[END_REF], [START_REF] Wu | Computational Fluid Dynamics Investigation of Turbulence Models for Non-Newtonian Fluid Flow in Anaerobic Digesters[END_REF], [START_REF] Yu | Multiphase modeling of settling and suspension in anaerobic digester[END_REF]- [START_REF] Wu | CFD simulation of gas mixing in anaerobic digesters[END_REF], [START_REF] Coughtrie | Effects of turbulence modelling on prediction of flow characteristics in a bench-scale anaerobic gas-lift digester[END_REF]- [START_REF] Wu | CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters[END_REF]. The SST k-omega model [START_REF] Craig | CFD simulation of anaerobic digester with variable sewage sludge rheology[END_REF], [START_REF] Wu | CFD simulation of gas mixing in anaerobic digesters[END_REF], [START_REF] Coughtrie | Effects of turbulence modelling on prediction of flow characteristics in a bench-scale anaerobic gas-lift digester[END_REF]- [START_REF] Wu | CFD simulation of gas and non-Newtonian fluid two-phase flow in anaerobic digesters[END_REF], the standard k-epsilon model [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF], [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF], [START_REF] Yu | Numerical simulation of mechanical mixing in high solid anaerobic digester[END_REF], [START_REF] Meroney | CFD simulation of mechanical draft tube mixing in anaerobic digester tanks[END_REF], [START_REF] Wu | CFD investigation of turbulence models for mechanical agitation of non-Newtonian fluids in anaerobic digesters[END_REF], [START_REF] Bakker | Numerical modelling of non-Newtonian slurry in a mechanical flotation cell[END_REF] and the realisable k-epsilon model [START_REF] Wu | CFD simulation of mixing in egg-shaped anaerobic digesters[END_REF], [START_REF] Wu | CFD prediction of mixing time in anaerobic digesters[END_REF], [START_REF] Wu | CFD analysis of mechanical mixing in anaerobic digesters[END_REF], [START_REF] Wu | CFD investigation of turbulence models for mechanical agitation of non-Newtonian fluids in anaerobic digesters[END_REF], [START_REF] Yu | Multiphase modeling of settling and suspension in anaerobic digester[END_REF] are recommended by many authors among the RANS models. Furthermore, other authors claim that the Reynold stress model (RSM) is the most suitable model to predict the behaviour of this bioreactor [START_REF] Koerich | Numerical evaluation of the low Reynolds turbulent flow behaviour in a bioreactor[END_REF], [START_REF] Coughtrie | Effects of turbulence modelling on prediction of flow characteristics in a bench-scale anaerobic gas-lift digester[END_REF]. However other studies have been conducted using the large-eddy simulations (LES) to model turbulence phenomena in anaerobic digesters and stirred tanks [START_REF] Alcamo | Large-eddy simulation of turbulent flow in an unbaffled stirred tank driven by a Rushton turbine[END_REF], [START_REF] Alcamo | Large-eddy simulation of turbulent flow in an unbaffled stirred tank driven by a Rushton turbine[END_REF]- [START_REF] Jahoda | CFD Modelling of Liquid Homogenization in Stirred Tanks with One and Two Impellers Using Large Eddy Simulation[END_REF], [START_REF] Zadghaffari | A mixing study in a double-Rushton stirred tank[END_REF], [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], [START_REF] Hartmann | Assessment of large eddy and RANS stirred tank simulations by means of LDA[END_REF]. In these studies, the outcomes show that LES provide a better flow description than RANS simulations [START_REF] Alcamo | Large-eddy simulation of turbulent flow in an unbaffled stirred tank driven by a Rushton turbine[END_REF], [START_REF] Alcamo | Large-eddy simulation of turbulent flow in an unbaffled stirred tank driven by a Rushton turbine[END_REF]- [START_REF] Jahoda | CFD Modelling of Liquid Homogenization in Stirred Tanks with One and Two Impellers Using Large Eddy Simulation[END_REF], [START_REF] Zadghaffari | A mixing study in a double-Rushton stirred tank[END_REF], [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], [START_REF] Hartmann | Assessment of large eddy and RANS stirred tank simulations by means of LDA[END_REF]. In the study conducted by Wu in 2012, the free subgrid scale (SGS) models investigated are the Smagorinsky-Lilly (LES-SL) model, the wall-adapting local eddy-viscosity (LES-WALE) model and the kinetic energy transport (KET) model [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF]. The three models give very similar results for flow fields [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF]. The comparison between simulated and measured axial velocities shows that the LES shapes are in general agreement with the experimental data but they differ clearly in velocity magnitudes [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF]. Concerning the impeller power and flow numbers, the SGS models give excellent predictions and the KET model provides the best results [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF]. The author also compares the results with Reynolds-averaged Navier-Stokes turbulence models (realisable k-e model, standard komega model, Reynolds stress model) [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF]. The disadvantage of the LES approach is the computing cost, but a hybrid simulation approach can overcome this problem on industrial applications [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF]. Given the ultimate goal, which is to predict the displacement of microorganisms within the digester, the modelling of these flows requires precision, thus we chose the LES turbulence model which offers the most accurate results. In this work, we use the dynamic Lagrangian SGS model of turbulence developed by [START_REF] Meneveau | A Lagrangian dynamic subgrid-scale model of turbulence[END_REF] [START_REF] Meneveau | A Lagrangian dynamic subgrid-scale model of turbulence[END_REF]. This approach allows us to optimise the SGS model coefficients [START_REF] Meneveau | A Lagrangian dynamic subgrid-scale model of turbulence[END_REF]. The Lagrangian model is derived by minimising the error incurred by inserting the Smagorinsky model into the Germano identity along fluid-particle trajectories [START_REF] Meneveau | A Lagrangian dynamic subgrid-scale model of turbulence[END_REF]. This method is applicable to complex-geometry and unsteady flows [START_REF] Meneveau | A Lagrangian dynamic subgrid-scale model of turbulence[END_REF].

2-MATERIALS AND METHODS

2-1-THE CHARACTERISATION OF SUBSTRATES

The study examines the biochemical potential (BMP) of the vinasse. The vinasse and the sewage sludge for the BMP tests come from the active mesophilic biogas plant of the sugar-cane distillery Rivière du Mât (Saint-Benoit, Reunion Island). The inoculum was sieved through a 900-1000 μm mesh screen in order to remove coarser materials. No pre-treatment was done on the substrates. The inoculum is stored at ambient temperature and then incubated at 37°C which is the test temperature before the BMP tests. The vinasse is stored at 4°C for few days until the tests.

The substrates are characterised with TS, volatile solids (VS) and pH triplicate measurements. The TS content is obtained after drying 20g of the samples for 24h at 105°C and the VS content after burning the dried samples for 4h at 550°C. The pH value is determined with a pH metre. The measured characteristics are the TS, the VS, the pH, the chemical oxygen demand (COD), the total organic carbon (TOC), the ammonium, the alkalinity and the Kjeldahl azote. The vinasse is autoclaved for sterilisation. The samples were then homogenised with the Ultra turrax IKA T25 digital at 12,000 rpm for 10 min.

2-2-THE BIOCHEMICAL POTENTIAL TESTS AND THE PILOT TEST

The BMP tests are done using the Automatic Methane Potential Test System II (AMPTS II -Bioprocess Control). The BMP tests were performed according to the latest recommendations [START_REF] Holliger | Towards a standardization of biomethane potential tests[END_REF]. The system includes 15 digesters of 500mL. The substrate quantity is calculated with the ratio of VS from the inoculum to VS from the substrate (I/S ratio). The recommended ratio is between two and four [START_REF] Holliger | Towards a standardization of biomethane potential tests[END_REF]. In these BMP tests, the ratio used is two. All the tests are carried out in triplicate. Two controls must also be made, the blank assay and the positive control. The blank assay allows us to estimate the endogenous methane production. The positive assay enables the inoculum activity to be validated [START_REF] Holliger | Towards a standardization of biomethane potential tests[END_REF]. The digesters are supplemented with distilled water to obtain identical test volumes. The BMP tests were carried out under mesophilic conditions at 37°C. The pilot (10L) test is also carried out with the vinasse in mesophilic conditions for 41 days. The working volume is 7L and 1.6L are added during the period test because of analysis. The initial pH of the digestion medium is 7.29. The produced biogas is analysed daily in order to measure the percentage of methane.

3-CFD MODELLING 3-1-MODEL ASSUMPTIONS

At the beginning, we consider the following hypotheses for the development of the mathematical 3D single-phase model: digestion is carried out in a mesophilic regime (37°C); vinasse is a Newtonian fluid; sewage sludge is a non-Newtonian fluid; the digestion medium is isothermal and incompressible; the digester is heated at its walls; the impeller initial rotation speed N is 500 rpm.

3-2-CONSERVATION EQUATIONS

The conservation of mass and momentum equations with the Boussinesq approximation are used. The momentum equation and the heat transfer equation are coupled by the Boussinesq term. The spacefiltered equations of an incompressible Newtonian fluid can be written as:

0 i i u x    (1)       i j ij ij i z j i j j uu u P ge t x x x x                    ( 2
)
Where t is the time,  is the fluid density, i u is the filtered velocity component in the xi direction, is the kinematic viscosity, P is the filtered pressure,  is the filtered temperature, g is the gravity force,  is the thermal expansion coefficient and ij  is the subgrid scale (SGS) stress tensor.

The filtered heat transfer equation in convection-diffusion is:

2 .0 T i i j j D u t x x x            (3)
Where

P T D C   is the thermal diffusion coefficient, p C
is the specific heat and  thermal conductivity .

The stress tensor for Newtonian incompressible fluid is:

j i ij ji u u xx          (4)
The SGS stress tensor for incompressible flow is expressed as:

2 ij t ij S   (5) 1 2 j i ij ji u u S xx         (6) 2 ij ij ij S S S  (7)
Where

2 SGS tS LS   is the SGS turbulent viscosity, ij S is the rate of strain,   min , sS L d C
  is the mixing length, is the Von Karman constant, d is the distance to the closest wall, S C is the Smagorinsky constant, and

3 V 
in whichV is the volume of the computational cell. We use the dynamic Lagrangian model. In this model, the fluid particle trajectory for earlier time t' < t is [START_REF] Meneveau | A Lagrangian dynamic subgrid-scale model of turbulence[END_REF]:

   , t t z t x u z t t dt          (8)

3-3-RHEOLOGICAL EXPRESSIONS

The non-Newtonian viscosity for power-law fluids is expressed as:

1 n k    ( 9
)
Where k is the consistency coefficient,  is the shear rate and n is the power-law index. The consistency coefficient and the power-law index for liquid manure are defined as [START_REF] Achkari-Begdouri | Rheological properties of Moroccan dairy cattle manure[END_REF]:

  4830 0.58319 10
8.722 10

T TS ke      (10)
  0.6894 0.0046831 273 0.042813 n T TS       (11)
Where T is the temperature. The density  , the specific heat p C and thermal conductivity  are expressed [12], [43], [44]:

4187.5 28.9

p C TS    (12
        (14)

3-4-DIMENSIONLESS NUMBERS

The two dimensionless numbers typically used in a stirred vessel are the power and flow expressed as [START_REF] Paul | The handbook of industrial mixing[END_REF]:

P P N Nd   (15) 3 Q Q N Nd  ( 16
)
Where P is the power input, N is the impeller rotation speed, d is the impeller diameter and Q is the flow rate through the moving zone. The power and flow numbers are two good indicators for model validation. We will compare their values, as Wu [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], to measured values in literature data [START_REF] Spicer | The effect of impeller type on floc size and structure during shear-induced flocculation[END_REF]: NP=0.3 and NQ=0.56.

3-5-THE PHYSICAL DESCRIPTION OF SUBSTRATES

Our study is about mesophilic anaerobic digestion whose optimum temperature is 37°C. This is an important parameter because the physical parameters depend on it. Rheological experimental measurements at different temperatures (10°C, 25°C, 40°C and 60°C) showed that the viscosity and the yield stress decrease as the temperature increases [START_REF] Baudez | The impact of temperature on the rheological behaviour of anaerobic digested sludge[END_REF]. Moreover, this study showed that the rheological behaviour is irreversibly altered by the thermal history [START_REF] Baudez | The impact of temperature on the rheological behaviour of anaerobic digested sludge[END_REF]. Firstly, we consider the vinasse. The vinasse has a pseudoplastic behaviour for temperatures between 10 and 20°C [START_REF] Chacua | Mathematical models for prediction of rheological parameters in vinasses derived from sugar cane[END_REF]. Indeed, when the temperature is superior to 30°C, the power-law index is close to 1, indicating an approach to the Newtonian model [START_REF] Chacua | Mathematical models for prediction of rheological parameters in vinasses derived from sugar cane[END_REF]. In another study, the vinasse is considered as Newtonian fluid [START_REF] Koerich | Optimization of bioreactor operating conditions using computational fluid dynamics techniques[END_REF]. The sludge treated in a Wastewater treatment plant anaerobic digester is also considered as Newtonian fluids [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF]. The total dissolved solids (TDS) contents sludge of this plant were 2.5, 5.4 and 9.1% [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF]. We will thus perform simulations on the flow of vinasse and sludge, which are Newtonian. The corresponding physical parameters are given in Table 3. [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF], [START_REF] Koerich | Optimization of bioreactor operating conditions using computational fluid dynamics techniques[END_REF].

Secondly, we study the flow of sewage sludge which is a non-Newtonian fluid. We can use the liquid manure rheological properties to characterise sewage sludge [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF]. In order to compare our results, we use the same properties as Wu [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF], [START_REF] Wu | CFD simulation of mixing in egg-shaped anaerobic digesters[END_REF], [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF] (Table 2). The manure slurry exhibits pseudo-plastic fluid behaviour when TS is superior to 2.5% [START_REF] Wu | CFD simulation of mixing in egg-shaped anaerobic digesters[END_REF]. The manure is modelled with a pseudoplastic model in studies [START_REF] López-Jiménez | Application of CFD methods to an anaerobic digester: The case of Ontinyent WWTP, Valencia, Spain[END_REF], [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF], [START_REF] Wu | CFD simulation of mixing in egg-shaped anaerobic digesters[END_REF], [START_REF] Yu | Numerical simulation of mechanical mixing in high solid anaerobic digester[END_REF], [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], [START_REF] Achkari-Begdouri | Rheological properties of Moroccan dairy cattle manure[END_REF], [START_REF] Wu | Advances in the use of CFD to characterize, design and optimize bioenergy systems[END_REF]. Moreover, viscosity and shear stress increase exponentially as TS increases [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF]. The lower and upper limits of viscosities are calculated from the equation ( 11) [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF]. The physical properties for different values of TS are given in Table 4. [START_REF] Wu | CFD simulation of non-Newtonian fluid flow in anaerobic digesters[END_REF], [START_REF] Landry | Physical and rheological properties of manure products[END_REF], [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], [START_REF] Achkari-Begdouri | Rheological properties of Moroccan dairy cattle manure[END_REF].

TS

3-6-GEOMETRY AND MESHING

In order to compare our results with simulations conducted by Wu [START_REF] Wu | Large eddy simulation of mechanical mixing in anaerobic digesters[END_REF], we used the same geometry. This consists of a cylindrical tank with 0.152m diameter (with a 25° slope on the hopper bottom) and 0.26m liquid height. The agitation is performed by a Lightnin A313 impeller (0.062m diameter). The digester geometry is given in Figure 1.

Concerning the meshing approach, two main strategies are used for modelling stirred tanks: the reference frame (RF) (known as the "frozen rotor approach") and the sliding mesh (SM) [START_REF] Cortada-Garcia | Experimental and CFD studies of power consumption in the agitation of highly viscous shear thinning fluids[END_REF]. The RF convergences fast, but it is suitable only for steady-state flows [START_REF] Cortada-Garcia | Experimental and CFD studies of power consumption in the agitation of highly viscous shear thinning fluids[END_REF]. In contrast, SM is suitable also for unsteady flows, for which it provides a time-dependent solution, but at the expense of significant computational effort and time [START_REF] Cortada-Garcia | Experimental and CFD studies of power consumption in the agitation of highly viscous shear thinning fluids[END_REF]. A comparison between the multiple reference frame (MRF) and SM techniques showed that the SM technique is more accurate, but it is also much more timeconsuming than the MRF [START_REF] Jahoda | CFD Modelling of Liquid Homogenization in Stirred Tanks with One and Two Impellers Using Large Eddy Simulation[END_REF]. In recent studies, the MRF is widely used for its simplicity and the quality of the results [START_REF] Zhang | Effect of impeller on sinking and floating behavior of suspending particle materials in stirred tank: A computational fluid dynamics and factorial design study[END_REF], [START_REF] Rasool | EFFECT OF[END_REF], [50]- [START_REF] Wang | Influence of fluid dynamics on anaerobic digestion of food waste for biogas production[END_REF]. However, transient simulations require the SM method, some authors used MRF method for a first approximation and then SM method [START_REF] Zadghaffari | A mixing study in a double-Rushton stirred tank[END_REF], [START_REF] Zadghaffari | Large-eddy simulation of turbulent flow in a stirred tank driven by a Rushton turbine[END_REF]; whereas others used SM method directly [START_REF] Jian | Large eddy simulations of mixing time in a stirred tank[END_REF], [START_REF] Hartmann | Assessment of large eddy and RANS stirred tank simulations by means of LDA[END_REF].

In our study, our choice will be based on the SM method to characterise the impeller rotation. The cylindrical moving zone contains the impeller with 0.98m diameter, and the rest of the digester is the stationary zone. The cylindrical moving zone is 0.234m height and 0.152m diameter. The two zones are schematised in Figure 1. The mesh will be then refined at the digester edges, at the interface between the stationary zone and the moving zone, and at the agitator edges.

4-RESULTS AND DISCUSSION

The cumulated BMP curves (Figure 2) shows that vinasse is a complex substrate which can be difficult to treat in anaerobic digestion. The maximum production of methane is not reached beyond 45 days. The maximum methane production is 284.29 LCH4.kgCOD in the BMP test and 114.64 LCH4 in the pilot test. The biogas production of the pilot is 270.22 L. The vinasse is composed of complex molecules like proteins. The COD is also quite difficult to treat, and these curves show why in most digesters using sugar cane vinasse, only half of the COD is treated by anaerobic digestion. The results from CFD simulations of Newtonian and non-Newtonian fluids flow will be presented in further studies. The simulations will allow us to choose the frequency and the intensity of mechanical stirring of the pilot digester. Furthermore, the fluid movement allows contact between the microorganisms and the substrate. Thus, the flow is linked to the substrate composition and the digestion rate, which are part of ADM1 parameters. The fluid rheological properties depend on the substrate composition, but also on the digestion rate. In other words, some ADM1 results, the digestion rate and the composition, are useful in CFD simulations, and CFD simulations bring results, the velocities profiles, which are not considered in ADM1 model.

5-CONCLUSION

This article presents the reasons justifying the importance of setting up a CFD model of industrial digesters. The main purposes being the strong link between the flows and the biogas yield as well as the physical characteristics of the substrates treated in anaerobic digestion. In conclusion, the CFD model is naturally based on the Navier-Stokes equations. This model is also coupled with the heat transfer equation given the impact of temperature on the process. In addition, we use the LES approach to model turbulence with the Lagrangian dynamic model, to predict turbulent flow accurately. The modelling of the digester will be carried out for Newtonian fluids and non-Newtonian fluids, and for different dry matter rates (both wet and dry digestion). Currently, we develop a single-phase model. Then, we will realise the multiphase model (liquid, gas, solid), the liquid phase will be the digestion medium, the gaseous phase will be the biogas and the solid phase will be the microorganisms. It will thus be possible to study the propagation of microorganisms within the digester. Subsequently, we want to couple the CFD model with the ADM1 model in order to study the impact of flows (influenced by mechanical agitation) on the biogas production and on the inhibition phenomena. The CFD model is an additional tool for digester configuration choices. The emphasised inhibition phenomenon will be the detachment of the biofilm, which is a recurring problem in mechanically stirred anaerobic digesters.

Fluid

Figure 1 :

 1 Figure 1: Digester geometry (mm).

Figure 2 :

 2 Figure 2: Cumulative methane production average as a function of time of vinasse in BMP (left) and pilot (right) tests.

Table 2 :

 2 The chemical tests were conducted on the Hach Lange DR5000 Spectrophotometer, using the Hach Lange tests LCK 914 (COD), LCK 381 (TOC), LCK 303 (Ammonium), LCK 362 (Alkalinity) and LCK 338 (Kjeldahl nitrogen). The values are reported in Table2. According to the results, the C/N ratio of the vinasse is 15.23.

	Substrates	TS %	VS %	pH	COD gO2.L -1	TOC mg.L -1	Ammonium mg.L -1	Alkalinity mg.LCaCO3 -1	Kjeldahl nitrogen mg.L -1
	Sewage sludge 2.2480 0.9700 4.84	9.93	-	517.67	-	-
	Vinasse	6.6391 4.0378 7.57 79.67 27646.11	239.00	3651.25 1815.00

Physico-chemical characteristics of vinasse and sewage sludge.

Table 3 :

 3 Physical parameter values of vinasse at 35°C (Newtonian model)

Table 4 :

 4 Physical parameter values of manure (power law model)


Torbjørn Cunis
email: torbjoern.cunis@recherche.enac.fr

Murat Bronz
email: murat.bronz@enac.fr.

Jean-Philippe Condomines
email: jean-philippe.condomines@enac.fr.

Analysis of the Aerodynamic Coefficients for the Evolvable Demonstrator for Upset Recovery Approaches with Evaluation in the Wind-tunnel

While in-flight loss of control has remained a severe threat to aviation, few of the upset recovery approaches designed by aeronautical research has been demonstrated in flight tests. Enabled by the on-going success of micro air vehicles, we discuss the concept of an aerial experimental platform for upset recovery, EDURA (Evolvable Demonstrator for Upset Recovery Approaches), allowing cheap and flexible flight demonstrations. The aerodynamic coefficients of the vehicle presented here are numerically computed and extended to a full-envelope aerodynamic model using piece-wise polynomials in pre-and post-stall. Eventually, the aerodynamics are verified with wind-tunnel force measurements for a 3Dprinted mock-up.

I. Introduction

I n-flight loss of control (LOC-I) imposes the highest risk to aviation safety 1 and has remained the foremost cause of fatal accidents for the last decades. Generally defined as any deviation from the desired flight-path by FAA, 2 LOC-I especially includes upset situations such as stall, high and inverted bank angle, as well as post-stall spirals and rotations. [START_REF] Chambers | Aerodynamic Characteristics of Airplanes at High Angles of Attack[END_REF] Nowadays, current autopilots are not capable to drive the aircraft in such situation. In normal cases, pilots are able to pull back the aircraft by reducing the angle of attack. But if the stall occurs suddenly due to vertical gusts for example, the pilots don't have enough time to react. This can lead to catastrophic consequences. Especially for drone pilots who lack of awareness of the flight situation, it is a harder task to save the drone in case of stall. The case will be worse if the drone has to fly into clouds where vertical gusts often happen and where the visual inspection of the flight condition is not possible. Therefore, an autopilot that can deal with the stall is of high necessity. With their unstable and highly non-linear characterizations, these situations require extensive control effort and adequate approaches to recover the upset aircraft and return into the flight envelope. To handle this problem, non-linear behaviour of aircrafts in the post-stall flight regime has been investigated analytically [START_REF] Caroll | Bifurcation Analysis of Nonlinear Aircraft Dynamics[END_REF][START_REF] Jahnke | Application of Dynamical Systems Theory to Nonlinear Aircraft Dynamics[END_REF][START_REF] Goman | Application of bifurcation methods to nonlinear flight dynamics problems[END_REF][START_REF] Kwatny | Nonlinear Analysis of Aircraft Loss of Control[END_REF][START_REF] Engelbrecht | A Multi-mode Upset Recovery Flight Control System for Large Transport Aircraft[END_REF] and in wind-tunnel studies. [START_REF] Foster | Dynamics Modeling and Simulation of Large Transport Airplanes in Upset Conditions[END_REF][START_REF] Frink | Computational Aerodynamic Modeling Tools for Aircraft Loss of Control[END_REF] As a result, researchers developed control laws for upset recovery. [START_REF] Burcham | Development and Flight Test of an Emergency Flight Control System Using Only Engine Thrust on an MD-11 Transport Airplane[END_REF][START_REF] Burcham | Manual Throttles-Only Control Effectiveness for Emergency Flight Control of Transport Aircraft[END_REF][START_REF] Urnes Sr | Flight Control for Multi-engine UAV Aircraft using Propulsion Control[END_REF][START_REF] Chang | Aircraft Trim Recovery from Highly Nonlinear Upset Conditions[END_REF][START_REF] Xargay | L 1 adaptive controller for multi-input multi-output systems in the presence of nonlinear unmatched uncertainties[END_REF][START_REF] Stepanyan | Stall Recovery Guidance Algorithms Based on Constrained Control Approaches[END_REF][START_REF] Engelbrecht | Automatic Flight Envelope Recovery for Large Transport Aircraft[END_REF][START_REF] Crespo | Analysis of Control Strategies for Aircraft Flight Upset Recovery[END_REF][START_REF] Richards | Vehicle Upset Detection and Recovery for Onboard Guidance and Control[END_REF][START_REF] Gregory | Flight Test of L 1 Adaptive Control Law: Offset Landings and Large Flight Envelope Modeling Work[END_REF] For the recovery approaches found in literature as well as proposed by the authors in 21 are model-based, there is a need for reliable flight dynamics data. However, though the NASA generic transport model (GTM) offers a scaled unmanned aerial platform, well-investigated in wind-tunnel studies, to test control systems, [START_REF] Jordan | AirSTAR: A UAV Platform for Flight Dynamics and Control System Testing[END_REF] only Gregory et al. [START_REF] Gregory | Flight Test of L 1 Adaptive Control Law: Offset Landings and Large Flight Envelope Modeling Work[END_REF] report flight tests of the designed upset recovery approach. In the past decade, the market for Micro Air Vehicles (MAVs) has grown considerably. Widely available now, MAVs both offer cheap and repeatable experiments while being easy to replace and maintain in case of unsuccessful tests. On the other hand, indoor flight tests provide several benefits such as availability of accurate position tracking systems and reduction of disturbances in the test area, while requiring a smallscale vehicle other than the GTM. Combining the mentioned points-accurate aerodynamic data, indoor tests, and usage of established MAV supply chains-, in this paper we present a first version of a small-scale, fixed-wing experimental platform resembling an easy-to-model flying plate; based on a commercial-off-theshell aircraft and the open-source autopilot software Paparazzi UAV. A catapult launcher allows repeatable and configurable test conditions including upset situtations like insufficient air speed, high angle of attack, or inverted bank angle. Based on a CAD model of the aircraft, we conclude with deriving its aerodynamic coefficients both in the pre-and post-stall part of the flight-envelope. The modelled aerodynamics are to be evaluated in wind-tunnel force measurements with a mock-up which is based on the CAD model. This paper is organized as follows: in §II, we review upset recovery approaches in recent literature for the context of the paper. The concept of the Evolvable Demonstrator for Upset Recovery Approaches (EDURA) and its first prototype with the catapult launcher are presented in §III and §IV. We discuss the aerodynamic coefficients of the aircraft in §V and provide an evaluation by wind-tunnel tests in §VI.

II. Upset Recovery Approaches

Control approaches for upset recovery which have been presented in literature include state-based switching multi-mode control, 8 throttle-only control in case of hydraulic of the control surfaces, [START_REF] Burcham | Development and Flight Test of an Emergency Flight Control System Using Only Engine Thrust on an MD-11 Transport Airplane[END_REF][START_REF] Burcham | Manual Throttles-Only Control Effectiveness for Emergency Flight Control of Transport Aircraft[END_REF][START_REF] Urnes Sr | Flight Control for Multi-engine UAV Aircraft using Propulsion Control[END_REF] linear-optimal control, 14 L 1 -adaptive control, [START_REF] Xargay | L 1 adaptive controller for multi-input multi-output systems in the presence of nonlinear unmatched uncertainties[END_REF] non-inear dynamic inversion, [START_REF] Stepanyan | Stall Recovery Guidance Algorithms Based on Constrained Control Approaches[END_REF] and Lyapunov-based control. [START_REF] Engelbrecht | Automatic Flight Envelope Recovery for Large Transport Aircraft[END_REF] We will review some of those approaches here:

II.A. Multi-mode flight control

As part of his later PhD thesis, [START_REF] Engelbrecht | Automatic Flight Envelope Recovery for Large Transport Aircraft[END_REF] Engelbrecht et al. presented a multi-mode flight control system aiming to stabilize the upset aircraft sequentially, that is damping angular rates first, afterwards restoring angle of attack and side-slip, air speed (in this order), and finally compensating for height loss. 8

II.B. LQR feedback control

Based on a linear-quadratic regulator (LQR), an upset recovery system was designed and tested in simulation for a model of an F/A-18 fighter jet. 14

II.C. L 1 -adaptive control

To the authors knowledge, this has been the only approach presented in literature which was tested in a real flight-test. 20

III. EDURA Concept

Indoor flight arenas, as existing at several research sites today, provide an ideal test environment for unmanned air vehicles. Wind and gust disturbances are reduced due to their closed walls and optical tracking systems provide position, attitude, and velocity information at both high accuracy and frequency. However, they are limited in space and hence unsuitable for larger vehicles. While clearly benefiting from indoor flight conditions, a suitable fixed-wing MAV is mainly required to be small. Depron is a light-weight material which allows effortless processing. Wings cut of a single layer of depron show a rectangular surface and thus can be modelled as flying plate to obtain the aerodynamics coefficients. An aircraft made of depron offers design, making, and aerodynamic modelling of an aerial experimental platform in short iterations, evolving the flight dynamics as suitable. Furthermore, it accounts for the smallscale design necessary for indoor flight tests. Today's miniature microcontrollers, sensors and actuators, and auxiliary boards complete the setup albeit deliver full flight control and navigation on-board. Eliminating the necessity of propulsion, a catapult launcher initially accelerates the aircraft to the desired air speed. In addition, it provides a configurable initial angle of attack and flight-path angle. The configuration of all three air speed, angle of attack, and flight-path angle after launch is repeatable over multiple executions of a single test case. Fig. 1 shows the general setup of the EDURA aircraft and catapult launcher within the ENAC flight hall. A grid of high accuracy infrared cameras on the ceiling of the flight hall provides tracking of the aircrafts position and attitude during flight test for post-flight evaluation.

IV. EDURA-0 Aircraft

The first aircraft is based on an E-flite UMX Yak 54 3D commercial off-the-shelf radio-controlled aircraft, a as shown in Fig. 2a. This 35 g vehicle with a wing span of 42.4 cm and length of 46.3 cm is made of 35 mm thick depron and resembles a flying plate with trapeze-shaped wings (Fig. 2b). The control surfaces, elevator, rudder, and left and right ailerons are driven by four linear servos. The E-flite aircraft has been originally shipped with a Spectrum radio receiver, which was replaced by a Lisa-MXs autopilot board b and an ESP8266-9 wifi module for UDP-based communication (Fig. 3). The autopilot runs the open-source software Paparazzi UAV. c For unpropelled flight, the propellor and its motor will be removed and replaced by a respective weight for balance. The catapult launcher (Fig. 4) is designed of three components, the rail, a cart moving lateral along the rail, and a cage to carry the aircraft. The cart is accelerated by an elastic band fixed to the front of the rail, while the same band attached to the end, too, a http://www.e-fliterc.com/Products/?ProdID=EFLU3550 b Not publicly available yet. c http://paparazziuav.org slows down the cart after ejecting the aircraft. The initial air-speed, i.e. the speed of the cart with respect to the rail can be configured by pulling the cart backwards thus stretching the elastic to a certain length with respect to its resting point. The desired angle of attack and flight-path angle at launch is defined by the orientation of the cage and the rail, respectively.

V. Aerodynamic Coefficients

For the design and demonstration of upset recovery approaches, a full-envelope model of the aerodynamic coefficients is crucial. Based on a CAD model of the aircraft, the linear part of the coefficients can be computed and a comparison can be made between the expected and measured flight trajectories. According to the comparison, it will be possible to verify the linear coefficients and identify the non-linear part in order to extend and improve the numerical estimation of the coefficients using the AERODAS polynomial equations [START_REF] Spera | Models of Lift and Drag Coefficients of Stalled and Unstalled Airfoils in Wind Turbines and Wind Tunnels[END_REF] for the pre-and post-stall aerodynamic coefficients.

V.A. Linear aerodynamic coefficients

Fuselage, wings, and control surfaces of the UMX Yak 54 3D aircraft were measured and modelled in CAD (Fig. 5). Aerodynamic coefficients are obtained numerically by using a program based on vortex-lattice method, called AVL d . As a modification to the existing program, the two-dimensional airfoil characteristics obtained from XFOIL is integrated as a database. This added database supplies the corresponding drag coefficient for each sectional lift coefficients that are calculated at local Reynolds number. Integration of the additional drag over the whole span gives the viscous drag of the wing. As a result, a set of linearized stability derivatives around the selected operating point is given in Table 1. (For the moment the table is representative, and will be corrected for the final paper.). Using a linear model, AVL can not determine the stall angle of the examined vehicle. In order to overcome this, the modifications made by Bronz 24 has been used. Basically, the modification adds a subroutine that checks the lift coefficient of each wing strip and compares it with corresponding airfoil's C Lmax maximum lift coefficient at the defined Reynolds number. If the required strip lift coefficient is higher than the airfoil's C Lmax , then an error message is written into an external log file without disturbing any AVL calculation. With the help of the log file, the user or the external program that calls AVL can see if the aircraft can sustain the equilibrium with the selected airfoil without stall or not.

V.B. Pre-and post-stall model

Spera proposed a set of piece-wise defined, polynomial equations for the pre-and post-stall region of the aerodynamic equations, 23 making use of the linear part as well as the stall angle of attack given by AVL. While the AERODAS model is initially designed for infinite-length airfoils, adjustments have been made for finite-aspect wings. The AERODAS model of Spera is displayed in Fig. 6, fitting the lift and drag coefficient piece-wise in the pre-and post-stall regimes. The inputs to AERODAS are the angle of attack A0 at zero lift (C L (A0) = 0) as well as the corresponding drag CD0 = C D (A0), the maximal lift CL1max as well as the corresponding angle of attack ACL1 and drag CD1max, and the derivative S1 of the lift coefficient at A0; these can be determined using the AVL output of §V.A. The lift and drag coefficients in pre-stall are then given by

C pre L (α) = S1 (α -A0) -RCL1 α -A0 ACL1 -A0 N1 (1) C pre D (α) = CD0 + (CD1max -CD0) α -A0 ACD1 -A0 M (

VI. Wind-tunnel measurements

Static force measurements of lift and drag in the wind-tunnel are state of the art in aeronautical research to determine the aerodynamic coefficients of an aircraft. Rather than initially measuring the aerodynamic coefficients, we are going to verify the data obtained in §V in the wind-tunnel afterwards. However, the Depron material is likely no to withstand the wind forces acting on the structure; we will survey a mock-up model instead. As we have already obtained a full model in CAD of the UMX Yak 54 3D (Fig. 5), we can directly 3D-print a mock-up in any suitable scale. This will lead us to a simplistic as well as, to the authors' knowledge, unprecedented method to investigate the aerodynamics of an aircraft in a wind-tunnel.

VII. Conclusion

In this paper, we have argued the need of an experimental platform for flight tests of upset recovery approaches. We have therefore discussed the benefits of indoor flights of suitable MAVs and proposed the EDURA concept of an evolvable small-scale, fixed-wing MAV as demonstrator. An additional catapult launcher allows repetition of the initial flight conditions. The first prototype based on a commercial-off-theshelf aircraft has as well been presented as the design of the catapult launcher.

The system illustrated will be evaluated in launch tests with indoor position tracking in order to proof repeatability of the initial conditions. Overall, we have introduced an aerial experimental platform to test and demonstrate upset recovery approaches based on the aerodynamic model of the aircraft, where the modus operandi is going to allow the evolution of the vehicle's parameters and test conditions.

We derived the aerodynamic coefficients of the aircraft in the linear part by AVL. Together with the aspect ratio of the wings and the estimated stall angle of attack, we could extend those to a full-envelope aerodynamic model. The results of the modelling will be evaluated with wind-tunnel force measurements using a mock-up of the aircraft.

  (a) Experimental setup. Commissioned illustration by Sarah Gluschitz, licensed under CC BY-ND. (b) ENAC flight hall under construction, to be finished by November 2017.

Figure 1 :

 1 Figure 1: Setup of the EDURA aircraft and catapult launcher (a) within the ENAC flight hall (b).

  (a) Side view. (b) Top view.

Figure 2 :

 2 Figure 2: Side view (a) of the EDURA-0 vehicle based on an E-flite UMX Yak 54 3D commercial-off-the-shell aircraft; and CAD drawing (b) from the top with measures: wing span, root chord, tip chord, and length (Quantities in millimetres).

Figure 3 :

 3 Figure 3: Autopilot configuration (from left to right): ESP8266-9 wifi module, Lisa-MXs board, and the linear servo for the elevator.

Figure 4 :

 4 Figure 4: The EDURA catapult launcher with aircraft (a) and the main components in CAD.

Figure 5 :

 5 Figure 5: CAD model of the EDURA-0 aircraft and its control surfaces(a) and AVL Mesh(b).

  2) with RCL1 = S1 (ACL1 -A0) -CL1max and N1 = 1 + CL1max / RCL1. The post-stall coefficients are now functions of the geometry of the wings and the empirical maxima of C L and C D in post-stall.

Figure 6 :

 6 Figure 6: Fitting of lift and drag coefficients by the AERODAS model of Spera 2008, 23 Fig. 2.

Table 1 :

 1

(This table will be updated for the final paper) Stability derivatives extracted from AVL program for the aircraft at 4 m/s equilibrium cruise speed. All derivatives are in 1/rad or s/rad except the control derivatives δ which are in 1/°.

d http://raphael.mit.edu/avl

Acknowledgements

The authors wish to thank the TU Delft Micro Air Vehicle Laboratory for providing the Lisa-MXs hardware and support. CAD models of aircraft and aircraft launcher were created in the free-to-use cloud platform Onshape. e