H Helbling
email: hugo.helbling@univ-lille.fr

A Benabou

A Van Gorp

M El

A Tounzi

W Boughanmi

D Laloy

Effect on magnetic properties of inhomogeneous compressive stress in thickness direction of an electrical steel stack

Keywords: magnetic properties, iron losses, manufacturing process, compressive stress

The manufacturing processes of electrical machines may lead to significant degradation of magnetic core properties and therefore of the machine performance.

Laminations are usually stacked and pressed which affects the magnetic properties and the iron losses. However, the influence of this step must be still investigated when large generators are considered. Indeed, in that case, the stator and rotor stacking process consists in assembling several stacks of electrical steel sheets separated by airvents. The surface of the airvent spacers represents about ten percent of the lamination surface of the magnetic circuit, implying, during the compaction process, an inhomogeneous stress distribution with significant local stresses. The present work deals with the experimental characterization of a lamination stack, including airvents, under compressive stress in the thickness direction. A mock-up has been designed and built-up to study magnetic properties of lamination stacks under pressing conditions corresponding to the industrial process.

Introduction

In order to increase the energy efficiency of high power electric machines, the reduction of losses is a key point. However, there still exist differences between the expected losses obtained from material models used in the design of the machines and those measured on the manufactured ones. One reason for these differences not considered in the material model is the impact of the manufacturing process on the magnetic core properties. To address this issue, the most commonly studied processes in the literature are the cutting, welding, pressing or shrink-fitting [START_REF] Bali | Modeling the Effect of Cutting on the Magnetic Properties of Electrical Steel Sheets[END_REF]- [START_REF] Miyagi | Effect of Compressive Stress in Thickness Direction on Iron Losses of Nonoriented Electrical Steel Sheet[END_REF] . The effect of degradation due to cutting is mainly located at the cutting edges, whereas the welding may induce higher eddy current losses. When the stator is placed inside a housing, the shrink-fitting is relevant as it induces a mechanical stress gradient that impacts the magnetic properties.

The present work deals with the case of large generators for which the magnetic circuit is constituted of several stacks separated by airvents that are pressed together in the thickness direction of the laminations. To maintain the applied pressure, the whole magnetic circuit is then placed inside a steel cage that is usually welded on the outer diameter of the stator and/or clamped through end rings by axial screws. The impact of this step on magnetic properties of laminations has been investigated in some articles without considering the compressive stress distribution or by assuming that the stress distribution was homogeneous [START_REF] Miyagi | Effect of Compressive Stress in Thickness Direction on Iron Losses of Nonoriented Electrical Steel Sheet[END_REF]- [START_REF] Maeda | Development of the apparatus for measuring magnetic properties of electrical steel sheets in arbitrary directions under compressive stress normal to their surface[END_REF]. Other works, such as [START_REF] Alatawneh | Design and analysis of a toroidal tester for the measurement of core losses under axial compressive stress[END_REF], computed the stress distribution within a toroidal sample by mechanical Finite Element (FE) study, in order to have the most homogeneous possible distribution of stress. All these works show that the compressive stress has an impact on the magnetic properties.

However, in the case of large generators, the compressive stress distribution in the magnetic core may be inhomogeneous because of the airvents spacers, implying significant inhomogeneous and localized stresses. In the literature, no work has addressed this problematic. The aim of this paper is to investigate the effect on magnetic properties of inhomogeneous compressive stress in thickness direction of a toroidal sample. An experimental mock-up has been developed to study the compressive stress distribution on magnetic properties of a M400-65A electrical steel stack, because this steel grade is usually used for large generators. The experimental device was developed with the aid of mechanical FE study in order to analyze the stress distribution in the magnetic core.

This work presents several highlights. First, the developed mock-up enables to study the effect on magnetic properties of inhomogeneous compressive stress in thickness direction of an electrical steel stack which represents a practical industrial case in the presence of airvents that has not yet been studied in the literature. Second, inhomogeneous and homogeneous stress distributions obtained with and without airvents are precisely known by mechanical FE simulations. Third, the mock-up has been built-up to study magnetic properties of lamination stacks under parameters corresponding to industrial conditions. Fourth, the toroidal electrical steels were cut by the Wire Electrical Discharge Machining (WEDM) technique to reduce the impact of cutting on magnetic properties [START_REF] Manescu Paltanea | Energy Loss Analysis and Magnetic Properties of Non-Oriented Electrical Steel Cut through Different Technologies[END_REF]. Moreover, it allows to have only the impact of pressing in order to avoid results like those in [START_REF] Alatawneh | Design and analysis of a toroidal tester for the measurement of core losses under axial compressive stress[END_REF] where measured electrical steel losses are well above those given by the lamination grade, even without any compressive stress. Fifth, the obtained results were compared and validated with a reference measurement, including the repeatability analysis. Furthermore, measurements were made up to 4 MPa for homogeneous stress distribution and up to 80 MPa local stress for inhomogeneous stress distribution, with various sinusoidal magnetic field density waveform of frequencies from 5 Hz to 400 Hz. The impact of compressive stress is not observed only on the total iron losses but also on hysteresis losses.

The paper is organized as follows. Part 2 describes the methodology of this work: the design of the mock-up with the mechanical FE study, the development of the mock-up and the experimental protocol that was followed. The air flux compensation method is introduced in Part 3. In Part 4, results and discussions about tests with homogenous and inhomogeneous stress distributions are given. Finally, in Part 5, the main conclusions of the study and future work are presented.

Methodology and experimental mock-up

Methodology

The methodology of this work is as follows. First, mechanical FE simulations are performed to design and develop an experimental mock-up that allows having homogeneous and inhomogeneous stress in the magnetic core. Then, the magnetic properties (constitutive law, iron losses) are measured under different levels of homogeneous and inhomogeneous compressions in the thickness direction. Finally, the impact of the compressive stress distribution on the magnetic properties is compared for different configurations.

Geometry of the mock-up

The mock-up is composed of a magnetic circuit, a primary and secondary windings and an axial compression system. As the compressive stress must be applied on the whole magnetic circuit area, two winding frames (Figure 1-d) are place on both sides of the magnetic circuit. A clamping screw is used in order to apply and maintain the stress on the magnetic core (Figure 1-a). Finally, two PVC plate (Figure 1-c) are added to improve the homogenization of the compressive stress and a force sensor (Figure 1-b) is inserted between one of the PVC plates and the head of the clamping screw to measure the force and better distribute the effort. Airvents (Figure 1-e) are added for the study of inhomogeneous stress distribution. In the homogeneous case, airvents plates (Figure 1-e) are removed. The whole geometry is presented in Figure 1 and a cross section view is presented in Figure 2.

Design and specification of the mock-up

To design the mock-up, mechanical FE simulations were firstly performed. Materials for the force sensor, the plates and the magnetic core previously described in Figure 1 are respectively: anodized aluminum, PVC and M400-65A. The material used for the winding frames is nonmagnetic and electrically non-conductive. It must allow transmitting accordingly the homogeneous and inhomogeneous stress distributions on the magnetic circuit, have sufficient compressive stress resistance and be easily machined. The FE mechanical simulations are performed on SimScale software [10]. The contacts between the different parts are modeled by Coulomb friction. For each contact, we have chosen a Coulomb coefficient of 0.5. It is an arbitrary choice which voluntarily oversees the coefficient in order to be in the most unfavorable case, in particular for the contact between winding frames and the magnetic circuit. Moreover, to model the compressive stress application, a perpendicular force to the surface of the force sensor is applied. To build the mechanical model we consider one fourth of the device, according to the revolution axis, with symmetry planes as boundary conditions. Also, along the height of the device, a zero displacement boundary condition is set in the middle plane. Material parameters (Young's modulus, Poisson's ratio, density) are defined according to Table 1.

Material

Young Simulation results are presented in Figure 3. For more convenience, the stress level scale is set to 4 MPa maximum to facilitate the reading but in practice, local stress reaches about 20 MPa. To be representative of industrial conditions, height of studied magnetic core is the same as that of the stacks separated by airvents in stators of large generators (about 42 mm). Similarly, the stress levels are representatives of those employed in the manufacturing process for these large generators. The electrical steel stack is composed of 65 toroidal electrical steel sheets of M400-65A, cut by WEDM with outer diameter of 100 mm and inner diameter of 86 mm. The laminations were not annealed. Because of the winding frame design, the winding was realized by hand with 120 turns at the primary and 60 turns at the secondary.

Validation of the mock-up

The objective is to study the impact of compressive stress on the magnetic properties. It is necessary to have reference measurements on the magnetic properties of the core without stress and to validate that the mock-up gives reliable results in these conditions. Therefore, two reference magnetic circuits composed of the same sheets were made, Figure 3. Magnetic measurements are made on MPG200D Brockhaus ring core tester. Measurements of magnetic field and induction are done in accordance with IEC 60404-4 and IEEE standard 393-1991 [START_REF]IEEE standard for test procedures for magnetic cores[END_REF]. Moreover, intrinsically the repeatability of the ring core tester equipment is less than 0.1 %. However, in practice, accounting for the accuracy of the force sensor and the error introduced by the viscolesactic behavior of the winding frames, the observed repeatability for several levels of stress is less than 0.5%. As this will be emphasized in the experimental results section, the effect of the normal stress is significantly higher than the repeatability error.Figure 4 shows the iron loss and the B-H normal curves, built from the B max (H max ) of centered hysteresis loops, for both magnetic circuits. Magnetic properties are similar for both magnetic circuits. For instance, the iron losses under sinusoidal magnetic flux density of 1.5 T (peak) and 50 Hz are 3.75 W/kg, which means that studied M400-65A electrical steel sheets respect their grade (and that the sample cutting did not affect significantly the material properties).

The different measurements conducted on the two reference circuits confirm that there is a negligible dispersion in the magnetic properties of the toroidal electrical steel sheets. The next step deals with the comparison between these references and the mock-up circuit. First, magnetic circuits used for the mock-up and for the references have the same outer and inner diameter. Also, they were cut at the same time, with the same technique (WEDM) and come from the same lamination coil. Only the height and the windings are different. For the reference ring cores, a height of 15mm has been chosen. The cross section is well above the one recommended by the standard. Concerning the windings, the mock-up circuitrequires the compensation of the air flux due to the use of winding frames. The best way to do this is to implement a compensation coil but, due to the complexity of the winding and of the mock-up shape, an approximated mathematical factor was implemented to compensate the air flux. First, as iron losses are related to the mass of the magnetic core which has been considered by the ring core tester, the air flux has no impact on it and results shown in Figure 5 validate our experimental mock-up concerning iron losses. Furthermore, Figure 6 (a) shows the comparison between B-H curves of the reference magnetic cores and of the mock-up, with and without air flux compensation. The compensation method gives very satisfactory results when comparing the B-H curve with air flux compensation to the reference measurement. Moreover, effect of the compressive stress on the B-H curve, Figure 6 (b), is higher than the remaining discrepancy after air flux compensation. We can therefore conclude on the reliability of the experimental mock-up.

Measurements, results and discussion

Measurements

This part describes the measurement protocol, with an emphasizing on its key points. As previously mentioned, mechanical FE simulations were carried out to validate the stress distribution for both considered stress configurations (homogeneous and inhomogeneous) and the mechanical resistance.

The nonmagnetic material for the winding frames was chosen so that it can support high local stress, i.e. with a typical compressive resistance of about 110 MPa. However, for studied stresses, this material has viscoelastic behavior [START_REF] Ferry | Viscoelastic Properties of Polymers[END_REF] that should be considered. Indeed, when the mock-up is compressed, stress level will sligthly decrease due to the viscoelasticity of the material. To reach the desired stress level, it requires to tighten the clamping screw a few times until the stress level is stable. Also, for magnetic field densities higher than 1.4 T, the winding frames will heat up due to the current in the coils which will induce a greater stress on the mock-up magnetic core. Measurements were done with a fan cooling system to limit this effect. On the contrary, measurements on the reference magnetic circuits were carried out without the fan cooling system because these have no viscoelastic problem. Moreover, temperature of the reference magnetic circuit was less than 40°C during measurements.

In the homogeneous case, measurements were carried out for stress levels up to 4 MPa. In the inhomogeneous stress distribution (with airvent spacers) measurements were made with the same compressive forces as for the homogeneous case, which means that, even if the global pressure on the magnetic circuit is the same, the local stress in the vicinity of the airvent spacers reaches levels up to 80 MPa in our case. This local stress is calculated analytically from the applied force divided by the area of the airvent spacers. Same results are obtained by FE simulations. Measuremeents have been observed to be repeatable in the elastic domain. Concerning the topology of the airvents spacers in the inhomogeneous stress distribution, the paper deals with the case presented in Figure 7.

Measurements were carried out from 0.05 T to 1.6 T for frequencies of 5 Hz, 25 Hz, 50 Hz, 100Hz, 150 Hz, 200 Hz and 250 Hz. Moreover, measurements were carried out from 0.05 to 1 T at 400 Hz. For the homogeneous stress distribution, tests are made at 0 MPa, 1 MPa, 2 MPa, 3 MPa and 4 MPa.

It must also be noted that the results shown in the following are considered for the representative lamination stack (42mm) whatever the stress configuration case. In particular, for the inhomogeneous case, the global stress is obviously transmitted along the whole stack but locally there is a gradient between the extremities of the stack where the airvent spacers are placed. For more convenience, the presented results should then be seen as the global stack magnetic behavior.

Results and discussion

First, the effect of different normal stress levels on the major hysteresis loops is given in Figure 9 at 50Hz and 250Hz, showing modifications mainly in the knee regions. In Figure 10 -(A) and Figure 10, the impact of the compressive stress on B-H curve is shown. We observe that the inhomogeneous case is, as expected, the most impacting one. This is mainly observable in the knee region of the curves. To further analyze this impact, Figure 11 -(A) and Figure 11 -(B) show the required magnetic field depending on the magnetic induction, at 50 Hz. For the other frequencies, the relative impact of the compressive stress on the B-H curve is globally the same as for 50Hz each one of them. It is clear that the presence of the airvent spacers significantly increases the magnetic field necessary to reach induction levels higher than 0.6 T. Below 0.5 T, the impact of the compression is less significant and can, according to the stress distribution and the value of the global stress, increase or decrease the magnetic field. Rather than looking at the required magnetic field for a given induction, one can look at the reached magnetic induction for a given magnetic field. This corresponds to the same phenomena but it is interesting to note that the maximum relative decrease is up to 10% at 4 MPa for the inhomogeneous case, which represents approximately 0.1 T. First, two magnetization regions can be considered with these results: average magnetization (below ~0.5T) and high magnetization (above ~0.5T). For the high magnetization region, which in accordance with the literature, the compressive stress leads to the iron losses increasing in the magnetic core. Moreover, the more compressive stress is significant, the more iron losses increase. Similarly, a significant increase of iron losses is observed at 250 Hz and 400 Hz. However, for all studied frequencies, results show inhomogeneous compressive stress distribution with the airvent spacers increases more significantly the losses than in the homogeneous case. In fact, its impact is up to five times higher for the inhomogeneous case, Figure 12 -(B). When reaching saturation, the relative difference tends to decrease.

For the low and average magnetization regions, iron losses show a decrease in the homogeneous case at 1MPa/50Hz (Figure 11 -(B)) and this observation is even more pronounced at 5Hz whatever the configurations (Figure 11 -(A)).

Previous figures reveal that the inhomogeneous compressive stress distribution induces a higher degradation on magnetic properties of the M400-65A magnetic core than a homogenous compressive stress distribution, due to significant local stress.

To further analyze these results, the evolution of the hysteresis losses is shown on Figure 13. We consider the classical losses as constant because at the studied pressure levels the electrical conductivity of the lamination is not modified. Also, there is no significant deformation of the magnetic circuit. However, the hysteresis losses are impacted significantly as illustrated in Figure 13. Considering that the relative difference on the hysteresis losses should not be modified with increasing frequency, we observe that the relative difference on the total losses still increases with the frequency (see for example Fig. 12-B and-C). This observation can be interpreted as the increase of the excess losses with the compressive stress. This is especially observed for average magnetic flux densities.

Figure 13 -Impact of the compressive stress on hysteresis losses and on excess losses One hypothesis based on our simulation and experimental results but also on physical considerations, is that the compressive stress in the thickness direction will induce stress in the laminations plane, the inhomogeneous case. Indeed, Figure 14 and Table 2 give average Cauchy stress (σ) along ⃗ , ⃗ and ⃗ in different area of the magnetic circuit. 2. Cauchy stress in the magnetic circuit along ⃗ and ⃗ for homogeneous and inhomogeneous case First, concerning the homogeneous case, the impact on magnetic properties seems to be only due to the compressive stress in thickness direction. These modifications of magnetic properties may be related to magnetostriction effect [START_REF] Shirkoohi | Effects of stress on magnetostrictive properties of low silicon non-oriented electrical steel[END_REF], which could explain the fact that we observed decrease on hysteresis losses for low inductions, Figure 13. However, furthers studies need to be conducted in order to improve the understanding of magnetostriction effect along the height of the laminations. Second, our hypothesis concerning the observed differences on magnetic properties between homogeneous and inhomogeneous case is that, because of the airvent spacers, the compressive stress along ⃗ induces few stresses along ⃗ and more stresses along ⃗ . This one is in compression (A1 and A4) and in traction (A2 and A3). It is known, in the literature, that tensile stress, in the flux direction and in elastic domain, could degrades or improves the magnetic properties and that the compressive stress degrades them [START_REF] Shirkoohi | Effects of stress on magnetostrictive properties of low silicon non-oriented electrical steel[END_REF], [START_REF] Miyagi | Influence of Compressive Stress on Magnetic Properties of Laminated Electrical Steel Sheets[END_REF]. According to Table 2., compressive stress level is higher than the tensile one. The increase on iron losses and the degradation on normal B-H curves compared to the homogeneous case can be related to the induced compressive stress on ⃗ (A1). Nevertheless, as for the homogeneous case, further studies need to be conducted in order to improve the understanding of these phenomena.

Conclusions

The presented study deals with the effect on the magnetic properties of a compressive stress in the thickness direction of a lamination stack. Two stress configurations have been considered, homogeneous and inhomogeneous (due to airvent spacers). Experimental results show that in the second case, the impact on the magnetic properties is more significant due to higher local stresses. The magnetic behavior law is mainly degraded at average levels of magnetic flux density (in the knee region of the B-H curve). Moreover, the analyze of the iron loss by extracting the hysteresis loss contribution, showed that this latter is mostly impacted by the compressive stress at low and average magnetic flux density levels. Also, the observation of the impact on the global losses is not only explained by the impact on the hysteresis losses. This means that, under the assumption that classical losses are not modified by the stress level, the excess losses are also impacted by the compressive stress.

These results allow considering the design of large generators by including the effect of the lamination stack assembly with airvent spacers. This requires considering compressive stress in the material models. Additional experimental tests must be also carried out by varying the number of airvent spacers but also their shapes. Indeed, airvent spacers are located on the stator tooth and stator yoke as with an orientation either perpendicular or parallel to the path of the magnetic flux density. Finally, this paper demonstrates the interest of studying the impact on magnetic properties of compression in the thickness direction of lamination stacks separated by airvents.

Figure 1 .Figure 2 .

 12 Figure 1. Experimental mock-up -(a) = Clamping screw, (b) = Force sensor, (c) = PVC plate, (d) = Winding frame, (e) = Airvents, (f) = Laminated circuit (washer samples, outer diameter = 100 mm, inner diametre = 86 mm, height = 42 mm)

Figure 2 .

 2 Figure 2. Von Mises Stress on the mock-up cross section (top) and on the magnetic circuit (bottom) for the inhomogeneous case (left) and the homogeneous case (right) (1): Force sensor, (2): PVC plate, (3): Winding frame, (4): Airvents, (5): Magnetic circuit

Figure 3 .

 3 Figure 3. References magnetic circuits

Figure 5 .

 5 Figure 5. Iron losses comparison between reference and mock-up magnetic cores

Figure 7 -

 7 Figure 7-Layout of the airvent spacers

Figure 9 -Figure 10 -Figure 11 -

 91011 Figure 9 -Impact of compressive stress distribution on hysteresis cycles at 50 Hz and 250 Hz -Inhomogeneous distribution

Figure 12 -

 12 Figure 12 -Impact of compressive distribution on iron losses at 5 Hz, 50 Hz, 250 Hz and 400 Hz

Figure 14 -

 14 Figure 14 -Cylindrical coordinates and definition of areas

Table 1 .

 1 Material parameters for the FE mechanical simulations

		's modulus	Poisson's	Density
		(GPa)	ratio	(kg/m 3 )
	Force sensor	70	0,34	2700
	PVC	3	0,4	1500
	Winding frame	3,5	0,36	1250
	Magnetic circuit	211	0,29	7874


Meryeme Jamil

Abdelkader Benabou
email: abdelkader.benabou@univ-lille.fr

Stéphane Clénet

Sylvain Shihab

Laure Le

Bellu Arbenz

Jean-Claude Mipo

Meryeme Toto Jamil

Laure Le Bellu Arbenz

Magneto-thermal characterization of bulk forged magnetic steel used in claw pole machine

Keywords: Temperature dependence, magnetic properties, magneto-thermal characterization, electrical conductivity. 1

Introduction

Magnetic materials are at the heart of the energy conversion in electrical machines.

Their electric and magnetic properties are strongly related to the machine performances and energy efficiency. In order to study and to simulate the electrical machine under its operating conditions, the material electromagnetic behavior should be well known and well characterized not only at room temperature but also at the machine operating temperatures. In fact, during the machine operation, in some hot spots, the magnetic core temperature may reach up to 180°C [START_REF] Brisset | Thermal modelling of a car alternator with claw poles using 2D finite element software[END_REF]. As a consequence, the magnetic core properties may considerably change as the electrical conductivity to which eddy current losses are directly linked [START_REF] Yafei | Temperature and carbon content dependence of electrical resistivity of carbon steel[END_REF]- [START_REF] Nakaoka | Examination of Temperature Characteristics of Magnetic Properties Using a Single Sheet Tester[END_REF].

Thus, when a massive magnetic core is involved, especially the claw pole rotor, the temperature effects must be carefully considered in the energy conversion process. Therefore, to predict accurately the machine performances, it is necessary to perform both thermal and electromagnetic analyses, starting by characterizing the temperature dependence of the core electromagnetic properties.

In the standard experimental approaches for magnetic measurements, the characterization techniques are rarely adapted to temperatures up to 200°C. Different authors designed specific magneto-thermal characterization devices based on specific needs. Some of them employed the ring core method [START_REF] Takahashi | Examination of Magnetic Properties of Magnetic Materials at High Temperature Using a Ring Specimen[END_REF], [START_REF] Takahashi | Comparison of Magnetic Properties of Magnetic Materials at High Temperature[END_REF], [START_REF] Bui | Caractérisation et modélisation du comportement des matériaux magnétiques doux sous contrainte thermique[END_REF] while few others used adapted Single Sheet Tester (SST) [START_REF] Nakaoka | Examination of Temperature Characteristics of Magnetic Properties Using a Single Sheet Tester[END_REF], [START_REF] Chen | Measurement research on magnetic properties of electrical sheet steel under different temperature, harmonic and dc bias[END_REF] or even rarely Epstein frame [START_REF] Chen | Temperature Dependence of Magnetic Properties of Silicon-Iron[END_REF]. However, these techniques are limited to steel sheets. Likewise, they are not adapted to forged heterogeneous bulk core as it is the case for the claw pole (CP) of automotive alternator.

Unlike other magnetic cores made of steel sheets, the CP is a special case that requires a specific methodology. This magnetic core is a massive forged piece with a complex shape through which the magnetic flux has three dimensional trajectories. Also, because of the manufacturing process the CP magnetic properties turn out to be strongly heterogeneous [START_REF] Borsenberger | Contribution to the identification of the interaction between process parameters and functional properties of work pieces: Application to forging and to electromagnetic properties of alternator claw poles[END_REF].

They vary not only in a given CP but also from one to another. For these reasons, a specific testing device was developed in order to characterize bulk parallelepiped samples extracted from different regions of the CP [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF]. However, this characterization device was limited to ambient temperature measurements.

In this paper, a specific methodology and an experimental set-up are proposed to characterize the electromagnetic properties of the CP as a function of the temperature up to 200°C. The temperature dependence of the electromagnetic properties, especially the B-H curve, iron losses and electrical conductivity, are studied. First, the experimental setup is described. Then, the experimental results of the temperature effect on the electrical conductivity and magnetic properties are presented and discussed. Finally, the link between the conductivity and the dynamic losses dependence with temperature is considered.

Experimental setup

The illustration of the device is given in ) up to 260°C. As presented in [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF], the setup is composed of one yoke, the primary coil to create magnetic field, a secondary coil to measure the polarization J and two Hall sensors to measure the magnetic field. These latter include temperature compensation up to 200°C, with very small linearity error (typically 0.1 % up to 1.5 T). The measurement device has been validated by numerical 2D / 3D simulations as detailed in [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF]. Furthermore, the mini-SST measurements were compared, at room temperature, with those made on a standardized SST, and a very good agreement was observed between measurements made on both devices. The gap between the magnetic fields to reach 1.5T is equal to 1.15%. Likewise, for the same level of magnetic flux density, the gap is equal to 2.3% for the specific losses. The electrical conductivity is measured at different temperatures using the four probes methods and applying a geometry correction factor as explained in [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF], [START_REF] Arbenz | Characterization of the local Electrical Properties of Electrical Machine Parts with non-Trivial Geometry[END_REF].

For both the electrical and magnetic devices, the used cables and copper wires can support temperatures above 200°C. In order to control the temperature of the environment, the device is placed in a drying and heating chamber (Binder, model M53) with a heating capability ranging from 5°C above the room temperature to 300°C. The temperature chamber is also equipped with forced convection and adjustable fan speed functions that allow to have a homogeneous temperature with less than 2°C of variation within the heated volume.

Moreover, in addition to the temperature sensor in the heating chamber, a thermocouple is placed on the sample to check its temperature and ensure the thermal equilibrium in the heat chamber.

The experiments were carried out on two bulk parallelepipedic samples with dimensions 35 mm x 10 mm x 1 mm. The samples were extracted by wire Electrical Discharge Machining (EDM) in two different locations of a CP made from SAE1006 steel.

The EDM process has been chosen because of its low impact on the electromagnetic properties.

Figure 1 Magneto-thermal characterization device

Measurement results and discussion

Electrical conductivity

The experimental protocol for the measurement of the electrical conductivity consists in placing the sample in the heating chamber and heating by increasing steps of 25°C starting from the room temperature (25°C) and up to 200°C. After each step, once the thermal steady state is reached, the electrical measurement is performed. As mentioned in the previous section, the electrical conductivity is deduced from the following equation: where is the electrical conductivity, current, the distance between the voltage probes, the measured voltage, the section of the sample and is a correction factor that accounts for the geometry of the sample [START_REF] Jamil | Development and validation of an electrical and magnetic characterization device for massive parallelepiped specimen[END_REF].

The results of the electrical measurement of both considered samples "S1 and S2"are reported in Figure 2. As expected, a linear relationship is observed between the electrical conductivity and the temperature, which can be written:

( ) ( ) (Eq 2)
where ( ) is the electrical conductivity at the temperature T (°C) and σ 0 is the electrical conductivity at room temperature T 0 (25°C). Thus, for the temperature between 25°C and 200°C, the electrical conductivity decreases with a rate of 0.23% /°C. This decrease in the conductivity was expected. In fact, due to thermal agitation, the mobility of the charge carrier decreases and, as a result, the ability of the material to conduct electrical current is reduced [START_REF] Yafei | Temperature and carbon content dependence of electrical resistivity of carbon steel[END_REF]. However, an accurate determination of the rate can only be done experimentally.

Magnetic properties

In the same way, as for the electrical conductivity, the experimental protocol consists in placing the whole device (supporting frame + sample) inside the temperature chamber and performing the measurement once the thermal steady state is reached. The considered temperatures for the magnetic measurements are the room temperature (25°C) and by 50°C steps starting from 50°C and up to 200°C. The measurements were systematically carried out on both the samples to ensure the reproducibility of the observations. And, as expected, both the samples showed similar behaviors. Thereafter, only the results of the measurement made on sample S1 are presented.

In Figure 3, hysteresis loops are illustrated for the considered temperatures and for 1.5

T peak magnetic induction at 50Hz frequency. the sample, with increasing temperature [START_REF] Chen | Temperature Dependence of Magnetic Properties of Silicon-Iron[END_REF]. Besides, as the temperature increases, thermal energy tends more and more to break the spontaneous alignment of atoms. As a result, the magnetization and the susceptibility decrease [START_REF] Bozorth | Ferromagnetism[END_REF]. This behavior was barely noticeable, on the saturation zone in Figure 3, as the saturation induction is reduced by 3%. The same temperature dependence was observed on FeSi sheets in [START_REF] Takahashi | Examination of Magnetic Properties of Magnetic Materials at High Temperature Using a Ring Specimen[END_REF], [START_REF] Chen | Temperature Dependence of Magnetic Properties of Silicon-Iron[END_REF].

The normal magnetization curve, obtained from the tips B p -H p of increasing induction level of minor hysteresis loops, is presented in

(a) (b)
Figure 4 for different temperatures. It is found that, as temperature increases, the magnetic flux density increases for low magnetic fields but decreases slightly at higher magnetic fields above the knee region. This result may be explained by the combination of two effects. The first is the temperature dependence of the saturation magnetization which decays with the temperature, and is more pronounced at high magnetic field. The second is related to the dynamic effects which are more visible at low magnetic field. In fact, the total magnetic field H is the sum of the static field (frequency-independent) and the dynamic field due to eddy-currents. When the temperature increases, the eddy currents decrease due to the decrease of the electrical conductivity as shown in the previous section.

Consequently, the dynamic field decreases as well with the temperature. Therefore, at low magnetic field, to reach a given magnetic flux density level, the total required magnetic field is less important when the temperature increases. This effect is more noticeable at high frequency measurement ( when the dynamic effects are more pronounced. However, compared to the variation due to the frequency, the temperature effect on the magnetization curves is less significant. The same behavior was observed in [START_REF] Chen | Influence of temperature on magnetic properties of silicon steel lamination[END_REF]. The previous observations can be emphasized by plotting the relative permeability calculated by (Eq 3)

(Eq 3)
where µ 0 is vacuum magnetic permeability and (H p , B p ) are the tips of minor loops. The effect of temperature on the relative permeability is reported in Figure 5. It is observed that, when the temperature increases, the permeability increases at low magnetic flux density whereas it decreases at high magnetic flux density. This is associated to the temperature dependence of the material susceptibility and eddy current effects as noted, previously, on the magnetization curves.

It should be noted that the increase of the magnetic permeability with temperature at low flux density may also be explained by the Hopkinson effect as shown in [START_REF] Takahashi | Examination of Magnetic Properties of Magnetic Materials at High Temperature Using a Ring Specimen[END_REF]. This effect is noticeable at high temperature when approaching the Curie temperature. Nevertheless, regarding the considered temperature range in the present study (below 200°C) and the SAE 1006 material (T Curie = 770 °C) this effect is barely pronounced. (Eq 4)

To determine the hysteresis loss component, energy losses ( ) measurements at five different frequencies, respectively 5Hz, 20Hz, 50Hz, 100Hz and 200Hz, were used. The hysteresis losses were calculated by extrapolating these measurements to zero frequency. The dynamic losses were then obtained after subtracting hysteresis losses from the total losses for each frequency. Note that the dynamic loss contribution includes the classical losses and the excess losses as defined in the Bertotti's loss decomposition approach. Indeed a measurement at 1Hz was carried out, but at higher magnetic flux density the quality of measurement remains limited because of the degradation of the signal to noise ratio. The losses separation was performed with and without considering the 1 Hz measurements. Except for high flux density (>1.6T), the results were very close showing that the measurement at 1Hz is not required. So, to stay consistent, we decide to remove the measurement at 1Hz keeping only the measurement at 5 Hz.

The evolution of the dynamic losses as a function of frequency, at 1.5 T is presented, for different temperatures, in Figure 7. It is observed that this evolution is proportional to the square of the frequency, as it is the case of classic losses due to macroscopic eddy currents [START_REF] Bertotti | General properties of power losses in soft ferromagnetic materials[END_REF]. It confirms that, in the following, the dynamic losses could be assimilated to the classic losses. In addition, to describe and to quantify the relative variation with temperature of each of the hysteresis and dynamic losses, the losses were normalized respectively to

( ) and ( ) : ( ) ( ) ( ) ( )
(Eq 5)

Figure 8 illustrates the temperature dependence of these loss components at 0.5T, 1T and 1.5T peak induction levels. It is noted that the hysteresis losses decrease slightly with temperature (0.07% /°C) while the dynamic losses decrease more significantly. The noted behavior is the same for different peak induction levels. This modification of the dynamic losses is obviously explained by the variation of the eddy current losses which are directly linked to the electrical conductivity. Theory predicts that the dynamic losses are a linear function of the electrical conductivity [START_REF] Bertotti | General properties of power losses in soft ferromagnetic materials[END_REF] and we have shown experimentally that the electrical conductivity is a linear function of the temperature. Consequently, we can expect the dynamic losses to exhibit a linear behavior in function of the temperature with a coefficient of variation close to the one of the electrical conductivity. The experimental results presented in Figure 7 confirm that the dynamic losses are a linear function of the temperature and that the coefficient equal to 0.21%/°C is close to the one of the electrical conductivity which is equal to 0.23%/°C.

Conclusions

In this paper a methodology for the characterization of the electromagnetic properties of bulk materials under different temperatures up to 200°C was proposed. The characterization results showed a clear temperature dependence of the electromagnetic properties. The coercive field, the saturation magnetization and the material permeability decrease when the temperature increases. Also, for the considered material, the electrical conductivity decreases in a linear way with temperature. Consequently, the eddy currents are reduced and thus the total losses decrease. The temperature affects also the magnetization curve which was found to be more influenced by the frequency and varies slightly with the temperature. Finally, from the separation of the losses, it has been concluded that the variation of the dynamic losses as a function of temperature is close to the one of the electrical conductivity. Yet, this result can further be used in the development of a loss prediction model using temperature dependent electrical conductivity measurements and iron loss measurement at room temperature only. In the context of electrical machine applications, the electromagnetic properties dependence of the machine operating temperature will be then accounted in a further easier way to obtain a realistic simulation of the machine performance.

Figure 1 .

 1 Figure 1. It consists in a miniaturized SST able to work from room temperature and up to 200°C. The supporting frame is made from Polyether ether ketone (PEEK) which exhibits a low coefficient of thermal expansion (10 -5 .K -1 ) up to 260°C. As presented in [11], the setup

Figure 2 .

 2 Figure 2. The electrical conductivity ratio as a function of the temperature (with the electrical conductivity measured at 25°C)

Figure 3 .

 3 Figure 3. Hysteresis loop of the claw pole sample characterized at 1.5T/50 Hz at different temperatures

Figure 4 .

 4 Figure 4.(b)) when the dynamic effects are more pronounced. However, compared to

Figure 4 .

 4 Figure 4. B-H curves (log-scale for H-field) of the sample characterized at different temperatures, (a) at 50 Hz and (b) at 200 Hz.

Figure 5 .Figure 6 .

 56 Figure 5. Relative permeability of the claw pole sample characterized at 50 Hz at different temperatures

Figure 7 :

 7 Figure 7 : Dynamic power losses as a function of frequency at 1.5T for different temperatures.

Figure 8 :

 8 Figure 8: Normalized hysteresis and dynamic losses as a function of temperature measured at 0.5T, 1T and 1.5T.


Dr Basma Abdi
email: basma.abdi@aphp.fr

Thuy Nguyen

Sophie Brouillet

Nathalie Desire

Sophie Sayon

Marc Wirden

Aude Jary

Guillaume Achaz

Lambert Assoumou

Romain Palich

Anne Simon

Roland Tubiana

Marc-Antoine Valantin

Christine Katlama

Vincent Calvez

Anne-Geneviève Marcelin

Cathia Soulie

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

No HIV-1 molecular evolution on long-term antiretroviral therapy initiated during primary HIV-1 infection

Introduction

Primary-HIV1 (PHI) infection is the initial phase of infection. It represents the time when the virus is first disseminating throughout the body and induces host immune responses [START_REF] Kassutto | Primary HIV Type 1 Infection[END_REF][START_REF] Volberding | Antiretroviral Therapy in Acute and Recent HIV Infection: A Prospective Multicenter Stratified Trial of Intentionally Interrupted Treatment[END_REF][START_REF] Fiebig | Dynamics of HIV viremia and antibody seroconversion in plasma donors: implications for diagnosis and staging of primary HIV infection[END_REF] The HIV reservoir is established very rapidly during this stage, due to the provirus integrated into the genome of cells that enables the persistence and the establishment of a latent reservoir which remains the major obstacle to eliminate the virus [START_REF] Bacchus | A Single HIV-1 Cluster and a Skewed Immune Homeostasis Drive the Early Spread of HIV among Resting CD4+ Cell Subsets within One Month Post-Infection[END_REF].

Several studies have demonstrated that early antiretroviral therapy (ART) initiation can be particularly effective for long term control of HIV-1 replication and it is associated with a faster decay of the latent reservoir, a restriction of its size and an optimal immune restoration [5-7].

Whilst, large clinical trials demonstrated that the benefits of earlier treatment mentioned above were limited at these specific criteria because treatment interruption is usually followed by rapid viral rebound, CD4+ T-cells loss and increased risk of morbidity and mortality [8][9][10][START_REF] Fidler | Virological Blips and Predictors of Post Treatment Viral Control After Stopping ART Started in Primary HIV Infection[END_REF].

In case of clinical effective ART, residual viremia has been evidenced and could be caused by ongoing low-level virus replication or by release of viral particles and/or viral genome from infected cells [START_REF] Chaillon | Size, Composition, and Evolution of HIV DNA Populations during Early Antiretroviral Therapy and Intensification with Maraviroc[END_REF]. Effectively, it has been suggested that persistent virus replication at low levels may be an important contributor to the maintenance of the reservoir particularly in lymphoid tissue sanctuary sites [START_REF] Lorenzo-Redondo | Persistent HIV-1 replication maintains the tissue reservoir during therapy[END_REF]. However, other studies suggest that there is no evidence of HIV replication on ART and the lack of genetic structure of HIV populations during ART argues against ongoing residual replication [START_REF] Lorenzo-Redondo | Persistent HIV-1 replication maintains the tissue reservoir during therapy[END_REF][START_REF] Van Zyl | HIV evolution and diversity in ART-treated patients[END_REF][START_REF] Kearney | Lack of Detectable HIV-1 Molecular Evolution during Suppressive Antiretroviral Therapy[END_REF].

A better understanding of changes in HIV-1 population genetics with ART is necessary to conclude between these two hypotheses and then for designing and optimizing new eradication strategies. PHI is a particular situation where the low diversity of the transmitted viruses has been described and thus investigating patients who started ART during the earliest stages of their HIV infection provides an opportunity to detect evidence of viral evolution.

We aim to study HIV-1 diversity in patients diagnosed with a primary HIV-1 infection, treated at the time of acute infection and with strict effective long term suppressive ART.

Materials and methods

We analyzed HIV-1 genetic variation and divergence of viral populations over time in plasma samples (RNA) before ART initiation and in blood cell samples (DNA) during 5 years of viral suppression on ART.

Patients

We retrospectively studied 20 patients diagnosed during PHI in the Departments of Infectious Diseases and Internal Medicine at Pitié-Salpêtrière Hospital (Paris, France). PHI was defined as detectable plasma HIV-RNA and an incomplete HIV-1 Western blot, irrespective of the ELISA result (positive or negative) and p24 antigenaemia (positive or negative).

Patients received antiretroviral therapy very early after infection and were identified with a strict viral suppression (HIV plasma RNA < 20 copies/mL without any blips) for at least 5 years afterward under ART. Analyses were performed retrospectively on frozen samples of whole blood taken during 5 years of standard follow-up.

Ethical considerations

This retrospective study was conducted in accordance with Good Clinical Practices and the ethical principles of the Helsinki declaration, and following ANRS standard practices for clinical research. Patients had written consent that the remnant of their samples could be used for research purpose.

Total HIV-DNA quantification

Cell-associated HIV-1 DNA was quantified by ultrasensitive real-time PCR (Generic HIV-DNA assay, Biocentric, Bandol, France) as previously described [START_REF] Avettand-Fènoël | LTR real-time PCR for HIV-1 DNA quantitation in blood cells for early diagnosis in infants born to seropositive mothers treated in HAART area (ANRS CO 01)[END_REF].

HIV-RNA quantification and Ultra-Sensitive Viral Load

Plasma Viral Load (pVL) was quantified using the Cobas AmpliPrep/CobasTaqMan HIV-1 assay (Roche Diagnostics; lower detection limit of 20 copies/mL

HIV drug resistance testing by UDS

To identify Drug Resistance Associated Mutations (DRAMs), the sequence reads were analyzed with IDNS ® © SmartGene 2019 (Advanced sequencing platform) and resistance (Cutoff detection of minority resistant variant of UDS sequences =2%) was interpreted using the latest ANRS resistance algorithm (http://www.hivfrenchresistance.org). Variants present in more than 20% of the quasispecies were considered to be majority resistant variants and variants present at a proportion between 2% and 20% were considered to be minority variants.

Phylogenetic analysis

We used Geneious research software (version 11) for phylogenetic analysis [START_REF] Kearse | Geneious Basic: An integrated and extendable desktop software platform for the organization and analysis of sequence data[END_REF]. The pairedend reads are merged and quality-filtered to remove noise. Alignment is performed using a target-specific profile and a consensus is produced based on a user-selected ambiguity threshold. We used PhyML for maximum-likelihood (ML) phylogenetic reconstruction (Generalized time-reversible model (GTR)). The best subtree pruning and regrafting (SPR) and the nearest neighbor interchange (NNI) heuristic options were selected. The reliability of tree topologies was assessed by bootstrapping using 1000 replications (values ≥ 70% were considered significant). ML trees were rooted on an outgroup: HIV subtype B consensus (HxB2: K03455; www.hiv.lanl.gov)). Tree figures were viewed and modified with FigTree software (http://tree.bio.ed.ac.uk/software/figtree/).

Diversity analysis

To look for evidence of ongoing viral replication during ART, HIV populations in samples taken at baseline were compared with the populations present during and after long-term ART in RT and gp120 genes. Phylogenetic trees were constructed for each patient with sequences obtained from plasma at baseline prior ART initiation and HIV DNA associated with peripheral blood cells under effective ART (first point of pVL < 20 copies/mL and 5 years follow-up period). Population genetic diversity was calculated as average pairwise difference (APD) using MEGAX ( http://www.megasoftware.net ) [START_REF] Tamura | Estimation of the number of nucleotide substitutions in the control region of mitochondrial DNA in humans and chimpanzees[END_REF].

Viral evolution was established when temporal structure on ML maximum-likelihood phylogenetic trees and significant change over time of HIV-1 genetic diversity (APD) were observed.

HIV-1 Tropism

HIV-1 co-receptor usage was predicted by a genotypic method that used the Geno2phenoreceptor rule (https://coreceptor.geno2pheno.org/) and according to ANRS rules (http://www.hivfrenchresistance.org/hiv-tropism.html).

Statistical analysis

All reported values are medians with interquartile range (IQR) for continuous variables and frequencies and percentages for categorical variables. Changes in cell associated HIV-DNA and CD4 cell count were compared between baseline and month 60 using paired

Evolution of immulogical and virological parameters

Evolution of immunological and virological parameters is presented in figure 1. A median of 10 longitudinal plasma HIV-1 RNA was evaluated per patient (197 samples in total). The median HIV-RNA viral load (VL) at time of PHI was 5.7 log10 copies/mL (IQR: 4.94-6.26) and decreased quickly with all patients reaching VL < 20 copies/mL in a median of 95 days (IQR: 40 -119) of ART initiation. Ultrasensitive VL (presence of detectable signal between 1-20 copies/mL) was found at least once during the 5 years follow-up in 13/20 patients (65%).

The total cell-associated HIV-1 DNA level was assayed for a median of 8 longitudinal blood samples per participant (158 samples in total). The median HIV-1 DNA load at PHI and over 5 years of follow up was 3.24 log10 copies/10 6 cells (IQR: 2.72 to 3.49) and 1.60 log10 copies/10 6 cells (IQR:1.60), respectively. The analysis revealed a global and significant decrease in total HIV-1 DNA during follow up period (p= 0.02). The total cell-associated HIV-1 DNA load was not detectable (<40 copies/10 6 cells) for 14 (70%) patients at the end of follow up.

Resistance analysis and tropism

At baseline, DRAMs were detected in RT gene in 3 (15%) patients with 2 majority resistant variants: 2 K103N (98%) and 1 minority resistant variant Y188H (2% Fifteen patients (75%) harbored a CCR5-tropic virus. The genotypic prediction of C2V3 coreceptor tropism did not vary over time in all patients.

Search of potential HIV genetic evolution -Phylogenetic studies

Phylogenetic analyses were processed in the 20 individuals, in RT and gp120 gene. Analysis showed that in all patients, sequences were intermingled: in each patient, sequences obtained from three different time points were highly homogenous. Tree topologies showed an absence of segregation between sequences in HIV-1 RNA at baseline prior to ART and in cell-associated HIV-DNA during 5 years of ART (figure 2).

The average nucleotide pairwise distance (APD) was estimated between the reads obtained from each time point. In the first sample (in HIV-RNA at baseline prior to ART), the median of APD was 1% (IQR: 1-1), 1% (IQR: 1-1) and 2% (IQR: 1-2) in RT1 fragment, RT2 fragment and gp120 gene respectively. In the second sample (in cell associated HIV-DNA; first time point of plasma VL < 20 copies/mL) the median of APD was 1% (IQR: 1-2), 1% (IQR: 1-1) and 2% (IQR: 1-3.75) respectively in RT1 fragment, RT2 fragment and gp120. In the third sample (in cell associated HIV-DNA after 5 years of follow up), the median of APD was 1%

(IQR: 1-2), 1% (IQR: 1-1) and 2% (IQR: 1-2) in RT1 fragment, RT2 fragment and gp120 gene respectively. This comparison of the APD in sequences obtained from samples taken at different times showed the absence of arguments of significant viral diversity evolution between primary infection and during the following 5 years.

Discussion

To our knowledge, it is the first study to report quantitative and qualitative analysis by UDS of HIV-1 reservoir in twenty patients diagnosed in the acute phase of infection, treated very early and had strict effective long term suppressive ART (during at least 5 years of follow up). There was a significant decay of HIV-RNA and cell-associated HIV DNA in our study in participants who started ART during the first month of their infection. Phylogenetic analysis showed the absence of genetic divergence and diversity in the RT and gp120 genes over time. However, despite sustained virological control under ART, some minor variations (emergence or disappearance) of DRAMS were evidenced associated or not with the current antiretroviral treatment.

Our results are in line with a number of studies showing the faster decrease of HIV DNA in patients starting ART during acute HIV-1 [START_REF] Chéret | Combined ART started during acute HIV infection protects central memory CD4+ T cells and can induce remission[END_REF][START_REF] Chéret | Impact of early cART on HIV blood and semen compartments at the time of primary infection[END_REF][START_REF] Leite | Reduction of HIV-1 Reservoir Size and Diversity After 1 Year of cART Among Brazilian Individuals Starting Treatment During Early Stages of Acute Infection[END_REF] infection . However, some clinical trials evidenced a viral rebound after prolonged virologic suppression with no difference in virological and immunological parameters between immediate and delayed treatment in the vast majority of cases [8][9][10][START_REF] Fidler | Virological Blips and Predictors of Post Treatment Viral Control After Stopping ART Started in Primary HIV Infection[END_REF][START_REF] Pantazis | The effect of antiretroviral treatment of different durations in primary HIV infection[END_REF].

In this study, 15% of NNRTI DRAMs (2 K103N and 1 Y188H) were revealed at the time of primary HIV infection. This prevalence is similar to the latest data (2014-2016) from the French cohort of primary infections showing that 18.6% of patients had DRAMS at baseline with the highest level of resistance to the NNRTI class (13.4%) [START_REF] Visseaux | Surveillance of HIV-1 primary infections in France from 2014 to 2016: toward stable resistance, but higher diversity, clustering and virulence?[END_REF].

Concerning longitudinal dynamics of minority variants, new DRAMs, not detected at baseline, appeared during follow-up in some patients treated early during the acute phase of HIV-1 infection despite a fully controlled vireamia < 20 cp/mL and absence of detected residual viremia in 45% (4/9) of cases. This finding is consistent with the assessments carried out by Gantner et al; they used the UDS technique to assess the longitudinal dynamics of viral resistant quasispecies archived in blood and demonstrated that, despite virological control, the diversity of the quasispecies continued to evolve [START_REF] Gantner | Drug resistance and tropism as markers of the dynamics of HIV-1 DNA quasispecies in blood cells of heavily pretreated patients who achieved sustained virological suppression[END_REF]. This could be the result of persistence of a residual viremia below the limit of standard quantification in some patients. Other researchers suggested that the new variants have most probably been selected directly in the blood compartment or other reservoirs because of insufficient drug penetration [START_REF] Gantner | Drug resistance and tropism as markers of the dynamics of HIV-1 DNA quasispecies in blood cells of heavily pretreated patients who achieved sustained virological suppression[END_REF][START_REF] Palmer | Low-level viremia persists for at least 7 years in patients on suppressive antiretroviral therapy[END_REF][START_REF] Doyle | Plasma HIV-1 RNA detection below 50 copies/ml and risk of virologic rebound in patients receiving highly active antiretroviral therapy[END_REF]. In addition, some of these new DRAMs in blood cells were G-to-A mutations implicating APOBEC3 editing, a cellular enzyme action and not viral replication [START_REF] Fourati | Differential impact of APOBEC3-driven mutagenesis on HIV evolution in diverse anatomical compartments[END_REF].

The results of phylogenetic analysis, as well phylogenetic tree and average pairwise distance, suggested the absence of genetic changes in archived HIV-1 DNA in our patients treated during the acute phase of infection with effective ART. Our findings support the majority of the studies reporting the lack of viral evolution during suppressive ART in chronically HIV infected adults, as well as in children treated shortly after birth when viral diversity is low [START_REF] Van Zyl | HIV evolution and diversity in ART-treated patients[END_REF][START_REF] Kearney | Lack of Detectable HIV-1 Molecular Evolution during Suppressive Antiretroviral Therapy[END_REF][START_REF] Van Zyl | No evidence of HIV replication in children on antiretroviral therapy[END_REF]. This absence of sequence divergence is indicative of long-lived cells infected and argues against viral replication being the major source of persistent viremia [START_REF] Van Zyl | HIV evolution and diversity in ART-treated patients[END_REF][START_REF] Kearney | Lack of Detectable HIV-1 Molecular Evolution during Suppressive Antiretroviral Therapy[END_REF][START_REF] Van Zyl | No evidence of HIV replication in children on antiretroviral therapy[END_REF][START_REF] Kearney | Ongoing HIV Replication During ART Reconsidered[END_REF][START_REF] Kearney | Origin of Rebound Plasma HIV Includes Cells with Identical Proviruses That Are Transcriptionally Active before Stopping of Antiretroviral Therapy[END_REF]. On another side, Lorenzo et al. reported that anatomical sanctuary sites such as the lymph nodes can allow residual viral replication on ART, contributing to the maintenance of the HIV reservoir [START_REF] Lorenzo-Redondo | Persistent HIV-1 replication maintains the tissue reservoir during therapy[END_REF].

These findings were strongly criticized by Kearney et al. who re-analyzed data and reported limits of data according to the low number of samples, the short time of the survey and absence of evidence of viral evolution using more complex analyses [START_REF] Kearney | Ongoing HIV Replication During ART Reconsidered[END_REF]. There are several reasons to explain controversy results such as differences in study populations (children treated shortly after birth, adults with chronic infection, patients diagnosed in acute phase of infection), in sampling (plasma, cell associated HIV-DNA, lymph nodes), in sequencing (Sanger sequencing, Single Genome Sequencing, UDS: 454 Roche and Illumina technology) and in analysis (phylogenetic analysis, measure of the APD, test of panmixia and others mathematics methods...) [START_REF] Lorenzo-Redondo | Persistent HIV-1 replication maintains the tissue reservoir during therapy[END_REF][START_REF] Van Zyl | HIV evolution and diversity in ART-treated patients[END_REF][START_REF] Kearney | Lack of Detectable HIV-1 Molecular Evolution during Suppressive Antiretroviral Therapy[END_REF][START_REF] Van Zyl | No evidence of HIV replication in children on antiretroviral therapy[END_REF][START_REF] Kearney | Ongoing HIV Replication During ART Reconsidered[END_REF][START_REF] Kearney | Origin of Rebound Plasma HIV Includes Cells with Identical Proviruses That Are Transcriptionally Active before Stopping of Antiretroviral Therapy[END_REF][START_REF] Achaz | These genes were amplified using two rounds of PCR amplification. Details of primers used for amplification are listed in table 1. PCR1 Forward (for) and PCR1 Reverse (rev) for PCR round one, and PCR 2 for and PCR2 rev for PCR round 2 (nested PCR). To amplify RT1 and RT2 fragments, the following thermocycler parameters were used for PCR1: 50 °C for 30 minutes (mn), 94 °C for 7 mn, 94 °C for 10 seconds (s), 55 °C for 30s, 68 °C for 1 mn, 35 cycles of steps 3-5 and 68 °C for 7 mn. We used a[END_REF].

Phylogenetic analysis allowed the comparison of the integrality of sequences which is more informative about viral diversity than the study of few resistance positions in the RT sequence.

Then, the impact of rare resistant variants could be diluted and doesn't impact phylogenetic analysis and could explain the apparent discrepancy between the DRAMs variation and the stability in phylogenetic analysis in our study.

Conclusion

In conclusion, this study is the first to use the UDS technique to assess the longitudinal dynamics of viral populations in plasma prior to ART and in archived blood cells in sustained ART in patients diagnosed with a primary HIV-1 infection and treated very early. Despite a slight variation of minority resistance-associated mutation variants, there was no clear evidence of viral evolution during a prolonged period of time. Our results underlined that ART initiation during PHI is fundamental to positively impact quantitative and qualitative biological parameters related to the HIV-1 reservoir in order to reduce its size and to control the viral diversity in the perspective to design of HIV-1 cure strategies.

(

  RNA) at baseline and cell-associated HIV-1 DNA (DNA) under effective antiretroviral Therapy: results in % (mutation frequency among all reads); ; NRTI=nucleoside reverse transcriptase inhibitor; NNRTI= non-nucleoside reverse transcriptase inhibitor; 3TC: lamivudine; ABC: abacavir; TDF: tenofovir disoproxil fumarate; FTC: emtricitabine; RPV: rilpivirine; EFV: efavirenz; DRV/RTV: darunavir/ritonavir; RAL: raltegravir; DTG: dolutegravir, EVG: elvitégravir;; MVC, maraviroc; COB:cobicistat DNA*: first point of plasma viral load < 20 copies/mL, DNA**: 5 years of follow-up period Underlined: mutations associated with prescribed treatment; Italic: mutations not related with prescribed treatment; Bold: G-to-A mutations; Bold and Underlined: patients with at least 1 residual vireamia during follow up.

Figure 1 :

 1 Figure 1: Median of longitudinal plasma HIV-1 RNA, cell associated HIV-1 DNA levels

Figure 1 :

 1 Figure 1 : Example of phylogenetic tree for patient 18 constructed from HIV-RNA at baseline prior

Ultra-Deep-Sequencing RNA and DNA extraction, amplification and ultra-deep sequencing

	HIV RNA was extracted from 1 ml of plasma using easyMAG® (bioMérieux Clinical
	Diagnostics, France) and HIV DNA was extracted from 400 mL of PBMC using the MagnaPure
	LC DNA Isolation Kit from Roche according to the manufacturer's instructions.
	UDS was performed using Illumina Miseq technology (Illumina, San Diego, CA, USA). We
	deep sequenced 2 fragments RT1 and RT2 of reverse transcriptase (RT) gene (413pb: 2618-
	3031 and 446pb: 2877-3323 relative to HXB2 genome, respectively) and C2V3 region of gp
	120 gene (367pb: 7011-7378 relative to HXB2 genome). Details of primers and PCR
	procedures used for UDS are described in Supplemental Data.
	Three samples were sequenced per patient: one RNA-HIV: plasma at baseline prior ART
	initiation, two HIV DNA associated with peripheral blood cells under effective ART: first point
	of pVL < 20 copies/mL and 5 years follow-up period. Library construction from purified PCR
	products (RT1, RT2 and C2V3 amplicons) and 2x300 bp Illumina Miseq paired-end sequencing
	were performed at the Genotyping and Sequencing Platform, ICM Brain and Spine Institute
	(Paris, France). Sequences were demultiplexed automatically on the MiSeq platform as part of
	the data processing steps and two paired fastq files were generated for each sample representing
	the two paired-end reads.

). Ultra-sensitive viral load (USVL) in the range of 1-20 copies/mL was indicated qualitatively (presence or absence of detectable signal).

  , baseline HIV cell-associated DNA, HIV-1 subtype, CD4 cell count and HIV cellassociated DNA during follow up.All reported P values are two-tailed, with significance set at 0.05. Analyses were performed with SPSS statistics version 23.0 for Windows.

	Wilcoxon test
	and the Mann-Whitney test was for comparison between participants with DRAMs dynamics
	and those with not. Univariable model was used to identify factors associated with DRAMs:
	age, sex, transmission group, duration of ART, baseline CD4 and CD8 cell counts, CD4/CD8
	ratio, nadir CD4 cell count, time since HIV diagnosis, duration of suppressed viraemia, time to

ART initiation, time to undetectable viral load under ART, duration of infection, pre-ART pVL, peak of pVL

Results

Patients' characteristics at time of PHI

Twenty patients with strict viral suppression (HIV viral load <20 copies/mL without any blips)

were included in the study with a median age of 47 years (IQR 34-53). Eighteen (90%) were male. Nine of the patients (45%) and 11/20 (55%) were diagnosed at Fiebig stages III and IV, respectively. Fifteen patients (75%) were symptomatic at time of PHI. Time to ART initiation, time to undetectable viral load under ART and duration of infection was in median 5 days (IQR 1-12), 95 days (IQR 40-119) and 6 years (IQR 6-7), respectively. Of the 20 patients, 12 (60%) were infected with the clade B virus. Main characteristics of patients are summarized in table 1.

5

  Strain MC, Little SJ, Daar ES, Havlir DV, Gunthard HF, Lam RY, et al.

Effect of treatment, during primary infection, on establishment and clearance of cellular

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HIV Viral Rebound following Protocol-Indicated Cessation of ART Commenced in Primary and Chronic HIV Infection.

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	doi:10.1371/journal.pone.0043754
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No Treatment versus 24 or 60 Weeks of Antiretroviral Treatment during Primary HIV Infection: The Randomized Primo-SHM Trial.

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	Characteristics	Total= 20
	Age (years), median (IQR)	47 (34 -53)
	Sex-n (%)
	-Male	18 (90 %)
	-Female	2 (10%)
	Origin-n (%)
	-Caucasian	19 (95%)
	-Others	1 (5%)
	Transmission group-n (%)
	-Men who have Sex with Men	15 (75%)
	-Heterosexual	5 (25%)
	Symptomatic PHI-n (%)	15 (75%)
	HLA B57*01-n (%)
	Negative	10 (50%)
	ND	10 (50%)
	Fiebig stage
	III	9 (45%)
	IV	11 (55%)
	HIV-1 RNA Zenith (log10 copies/mL), median (IQR)	5.82 (4.94-6.26)
	HIV-1 RNA (log10 copies/mL), median (IQR)	5.7 (4.94-6.26)
	HIV DNA (log10 copies/10 6 cells), median (IQR)	3.24 (2.72-3.49)
	CD4 nadir cell count (cells/mm 3 ), median (IQR)	417 (325-522)
	CD4 cell count (cells/ mm 3 ), median (IQR)	483 (325-566)
	Duration of infection (years), median (IQR)	6 (6-7)
	Time from diagnosis to ART initiation (days), median (IQR)	5 (1-12)
	Time to undetectable viral load (days), median (IQR)	95 (40 -119)
	ART regimen n (%)
	-2 NRTI+2 PI	8 (40%)
	-2 NRTI + 1 INI	8 (40%)
	-2 NRTI + 1 NNRTI	2 (10%)
	-2 NRTI+2 PI+MVC	1 (5%)
	-2 NRTI + MVC	1 (5%)
	doi:10.1371/journal.pmed.1001196
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	impact of transient combination antiretroviral treatment in early HIV infection on
	viral suppression and immunologic response in later treatment. AIDS 2016; 30:879-
	888.

Table 1 : Patients' characteristics at the time of primary infection

 1

	PHI=primary HIV-1 infection; ND: Not Determined; NRTI=nucleoside reverse transcriptase
	inhibitor; NNRTI= non-nucleoside reverse transcriptase inhibitor; PI= protease inhibitor;
	MVC=maraviroc;

Table 1 : UDS evolution of archived Drug Resistance Associated Mutations in plasma

 1

ACKNOWLEDGEMENTS

The Genotyping and Sequencing Platform, ICM Brain and Spine Institute (Paris, France). TRANSPARENCY DECLARATION Acknowledgements B.A., C.S., A.G.M., V.C. designed the study; R.P., A.S., R.T., M.A.V., C.K provided medical care to the participants and collected clinical data; B.A., T.N., S.S collected biological data and performed experiments; B.A., T.N., N.D., S.B., G.A., L.A., analyzed results; B.A., C.S. wrote the paper; All authors reviewed and accepted the final version of the manuscript.

No HIV-1 Molecular Evolution On Long Term Antiretroviral Therapy Initiated During

Primary HIV-1 Infection.

Running head: Viral Diversity In Primary HIV infection


Martin Bourhis

Michael Pereira
email: michael.pereira@ensam.eu

Florent Ravelet

Ivan Dobrev

Numerical assesment of a small

Keywords: Small scale wind turbine, Low tip-speed ratio, Rotating wake

come

INTRODUCTION

Wind energy is one of the most growing source of renewable energy. This energy resource is worldwide distributed and has attracted in the past two decades a lot of research. The technology of largescale horizontal-axis wind turbines, that is to say with rotor diameters of the order of 10 m is nowadays a mature technology with very high levels of performance. The best performances are obtained with three-blades horizontal-axis wind turbines, operating at tip-speed ratios Λ of the order of 6 to 7 and that are designed with the help of the "Blade Element / Momentum theory " [START_REF] Sharpe | A general momentum theory applied to an energy-extracting actuator disc[END_REF][START_REF] Hansen | Aerodynamics of Wind Turbines[END_REF]. This kind of wind turbines can reach up to 85% of the maximum power that could be extracted from a stream tube of cross section equal to the are that is swept by the rotor -the Betz limit.

The downsizing of wind turbines towards diameters of the order of 100 to 500 mm may be of interest to use them in urban environment, to take advantage of natural air circulation in buildings and to power autonomous connected sensors in the field of IOT [START_REF] Hirahara | Testing basic performance of a very small wind turbine designed for multi-purposes[END_REF][START_REF] Kishore | Efficient Direct-Drive Small-Scale Low-Speed Wind Turbine[END_REF][START_REF] Zakaria | Experimental investigation and performance modeling of centimeterscale micro-wind turbine energy harvesters[END_REF][START_REF] Pozo | Mini Wind Harvester and a Low Power Three-Phase AC/DC Converter to Power IoT Devices: Analysis, Simulation, Test and Design[END_REF]. This downsizing is not straightforward. Foremost, theses machines operate at lower Reynolds numbers, close to the boundary layers transition and the aerodynamic profiles have to be adapted to this [START_REF] Mctavish | Evaluating Reynolds number effects in small-scale wind turbine experiments[END_REF][START_REF] Lee | Experiments and numerical simulations of the rotor-blade performance for a small-scale horizontal axis wind turbine[END_REF][START_REF] Nishi | Study on the rotor design method for a small propeller-type wind turbine[END_REF][START_REF] Natarajan | The insight investigation on the performance affecting parameters of Micro wind turbines[END_REF][START_REF] Abdelsalam | Experimental study on small scale horizontal axis wind turbine of analytically-optimized blade with linearized chord twist angle profile[END_REF]. Then, when lowering the mechanical power while keeping a relatively high angular velocity ω, the mechanical torque generated by the wind turbine T may eventually become far too small to cope with mechanical friction in the bearings. One way of facing this problem is to lower the angular velocity, that is to design wind turbines with much smaller tip-speed ratios Λ.

Let us recall some basic concepts about horizontal-axis wind turbines. For an incoming wind of air with density ρ flowing at velocity V ∞ and for a rotor of tip radius R t , the available power is

P a = 1 2 ρV 3 ∞ πR 2 t .
The maximum amount of mechanical power that could be extracted from this stream tube is given by the Betz limit P B = 16 27 P a [START_REF] Hansen | Aerodynamics of Wind Turbines[END_REF]. The power coefficient C p is defined as the ratio of the actual mechanical power P = T ω to the available power is P a : C p = P Pa and thus the Betz limit corresponds to C p 16 27 0.59. The tip-speed ratio is the ratio of the tip-velocity to the incoming wind velocity: Λ = Rtω V∞ . Formally, the Betz limit which is obtained with the axial momentum balance equation corresponds to rotors of infinite Λ and both axial and angular momentum balances have to be taken into account. Among various models, the optimal model of "Glauert" gives for instance a maximum C p 0.54 for Λ = 3 and C p 0.42 for Λ = 1 [START_REF] Sørensen | General Momentum Theory for Horizontal Axis Wind Turbines[END_REF].

Most of the horizontal axis wind turbines with tip radius in the range 250 R t 500 mm are designed to operate at a tip-speed ratio around Λ = 3 [START_REF] Hirahara | Testing basic performance of a very small wind turbine designed for multi-purposes[END_REF][START_REF] Lee | Experiments and numerical simulations of the rotor-blade performance for a small-scale horizontal axis wind turbine[END_REF][START_REF] Natarajan | The insight investigation on the performance affecting parameters of Micro wind turbines[END_REF][START_REF] Abdelsalam | Experimental study on small scale horizontal axis wind turbine of analytically-optimized blade with linearized chord twist angle profile[END_REF] and have been designed with the Blade Element / Momentum Theory, using 3 or 4 blades that are considered to work as independent lifting profiles. In the present study, a rotor of tip radius R t = 150 mm is considered. The tip-speed ratio is chosen to be Λ = 1. For such a low value, the blade cascade solidity σ, which is defined as the ratio of the chord length to the azimuthal pitch, would become large and the turbine may have more blades [START_REF] Duquette | Solidity and Blade Number Effects on a Fixed Pitch, 50 W Horizontal Axis Wind Turbine[END_REF]; and as stated by Sharpe [START_REF] Sharpe | A general momentum theory applied to an energy-extracting actuator disc[END_REF]: "Such turbines would have to be of very high solidity, with a large number of blades. To complete the design, the blade element theory would need to be employed, but the only available blade element data are for isolated, twodimensional aerofoils. The mutual interactions between the closely spaced, probably overlapping, blades would be large and so the available aerofoil data would be useless for the purpose of designing high-solidity turbines".

We thus propose a different design method for a rotor with R t = 150 mm, Λ = 1 and 8 blades, that is based on the Euler's turbomachinery theorem. The aim of this paper is to numerically assess the performance of this wind turbine, and to give insight into the wake velocity and pressure fields, with the underlying idea of getting strong rotating component in the wake that could be used to rotate a second rotor in a counter-rotating arrangment for a future work [START_REF] Habash | Performance of a Contrarotating Small Wind Energy Converter[END_REF][START_REF] Wang | An experimental study on the aerodynamic performances and wake characteristics of an innovative dual-rotor wind turbine[END_REF][START_REF] Faisal | Aerodynamic Performance and Flow Structure Investigation of Contrarotating Wind Turbines by CFD and Experimental Methods[END_REF][START_REF] Zhao | The aerodynamic coupling design and wind tunnel test of contra-rotating wind turbines[END_REF].

DESIGN OF THE TURBINE

The design is based on the Euler's turbomachinery theorem, i.e. on the angular momentum balance, and on the classical axial momentum balance accross an actuator disk. The problem will be considered as axisymmetric. If one considers an annular streamtube between radii r and r + dr through which a mass flow-rate d ṁ circulates, and if index 1 refers to upstream of the rotor and 2 downstream of it, the angular momentum balance reads:

d ṁ (rC θ,2 -rC θ,1 ) = dT
where dT is the elementary torque that is applied on the fluid, and C θ is the tangential velocity in a Galilean reference frame. Multiplying this equation with the angular velocity of the rotor ω would give the elementary mechanical power that is transfered to the shaft. In the classical axial momentum theory, with uniform axial velocities and equal and uniform far upstream and downstream pressures, one introduces the axial induction factor a which accounts for the velocity defect in the wake of the active disk in such a way that the velocity accross the disk is (1a)V ∞ . Then the total power that is extracted from the fluid reads in dimensionless form

C p,w = 4a (1 -a) 2
The maximum, i.e. the Betz limit, is obtained for a = 1/3. If, we make the asumption that the process is isentropic, that the discharging flow is uniform and that C θ,1 = 0, then, one should have, with R h the hub radius and H = R h Rt the hub ratio: . The rotation plane is horizontal. Index 1 refers to upstream, 2 to downstream of the blade cascade. U is the solid body peripheral velocity, W the relative velocity in the rotor's reference frame and C = U + W the absolute velocity. At this peculiar radius, the blade cascade solidity is σ = 0.99 If one assumes a uniform outlet tangential velocity C θ,2 = cte, it should be such that:

Rt R h d ṁω (rC θ,2 ) = 4a (1 -a) 2 1 2 ρV 3 ∞ πR 2 t Rt R h r 2 C θ,2 dr = a (1 -a) V 2 ∞ R 2 t 1 ω C1 U W1 C2 Cz2 Cθ2 U W2
C θ,2 V ∞ = 3a (1 -a) Λ (1 -H 3 )
The main idea is to force the fluid to follow this kinematics by constraining it in a blade cascade arrangment. At each radius, a blade cascade consisting of circular lines which are tangent to the relative velocity W 1 at leading edge and W 2 at trailing edge is drawn (see Fig. 1). The lines are then thickened with NACA0010 profiles. The chord length of this line c is determined by a choice of the local blade cascade solidity σ. With Z blades, the local solidity is defined by:

σ = Zc 2πr
According to usual axial turbines, the solidity should be of the order of 1 to ensure the required flow deviation with acceptable losses [START_REF] Dixon | Chapter 3 -Two-Dimensional Cascades[END_REF]. The final design of the turbine has been done with R t = 150 mm, R h = 45 mm, V ∞ = 10 m.s -1 , Λ = 1 -i.e. ω = 66.7 rad.s -1 -a = 1/3, Z = 8 blades and a linear variation of the local solidity from hub to tip between σ h = 1.65 and σ t = 0.70. With these parameters, the expected values of the discharging and tangential velocities in the near wake of the wind turbine are expected to be, respectively, C z,2 = 0.67V ∞ and C θ,2 = 0.68V ∞ . The resulting turbine is displayed in Fig. 2.

NUMERICAL SETUP

The commercial Computational Fluid Dynamics code StarCCM+ 15.02 has been used to study the flow around the wind turbine. One eight of the wind turbine is simulated with periodic side boundary conditions. The simulations are steady, with a fluid of constant density and the SIMPLE pressure-velocity coupling algorithm is used. The flow is solved in a rotating reference frame. The turbulence is modeled with the kω-SST RANS model. The mesh is polyhedral with prismatic layers close to the surface. The mesh parameters are discussed in the following, and are such that, on the one hand the dimensionless wall distance y + are close to 3 and on the other hand the mesh is fine enough to capture the tip vortices in the wake. The quantity that is monitored is the power coefficient of the wind turbine. It is compared to experimental results obtained in the LIFSE wind tunel where the torque and angular velocity on a 3D printed wind turbine have been measured with a rotating torquemeter. In the experiment, the wind turbine is coupled to a Maxon DC motor used as a generator and loaded with a rheostat in order to explore the whole C p vs. Λ characteristic curve. The torquemeter and the motor are hidden in a cylindrical pipe of diameter 42 mm and lenght 600 mm which has been modeled in the simulations as a no-slip wall, which is steady in the laboratory reference frame. In this paragraph, all the simulations are performed at Λ = 1 for which the experimental power coefficient is C p,exp (1) 0.31.

For such an external flow, the definition of the domain surrounding the wind turbine and of adequate boundary conditions is quite arbitrary. Very large domains are often used in the available litterature [START_REF] Song | CFD Simulation of the NREL Phase VI Rotor[END_REF][START_REF] Lee | Experiments and numerical simulations of the rotor-blade performance for a small-scale horizontal axis wind turbine[END_REF][START_REF] Nishi | Study on the rotor design method for a small propeller-type wind turbine[END_REF]. We thus first present a parametric study on the influence of the domain size and boundary conditions (see Fig. 3).

The inlet boundary condition consists of a uniform velocity field. The outlet boundary condition to a uniform pressure field. The upper boundary is a cylinder of radius R p and is a wall boundary condition. For this boundary, a comparison between slip and no-slip condition has been done and the slip conditions has been chosen as it is found to improve the estimation of the power coefficient by about 2%. The length of the domain downstream of the turbine L d has been varied in the range 4 to 8R t , the radius R p in the range 3 to 8R t and the upstream lenght of the domain L u from 2 to 9R t .

The results are plotted in Fig; 4. All the numerical results overestimate the experimental C p . The effect of L d is not reported as it has very lttle influence on the results in the explored range. A size of L d = 8R t has been chosen. Surprisingly enough, the size of the upstream domain has a great influence. The convergence seems to be reached for L u 5R t . Concerning the surrounding pipe radius R p , a value of R p 6R t seems sufficient. Thus, the final configuration is L d = 8R t , L u = 7R t and R p = 8R t .

A grid convergence test has been performed with this geometrical parameters. The base size 4: Effects of the domain dimensions on the power coefficient. Up: variation of R p at constant L u = 3R t and L d = 8R t , bottom: variation of L u at constant R p = 6R t and L d = 8R t . Black squares ( ) stand for the numerical resultswith constant meshing parameters, the blue dot (•) is the final configuration with a refined mesh, the solid blue line is C p,exp (1) and the red cross (×) corresponds to the common configuration between the two plots of the mesh has been varied between 40 mm and 25 mm and the mesh has been locally refined in a cylinder domain of radius 2R t with a size ranging from 6 mm to 1.25 mm. A prismatic layer with 8 geometrically spaced layers representing 10% of the local base size has been added around the wind turbine. The results are plotted in Fig. 5. The mesh that is considered in the following section contains 5.8 millions cells and corresponds to a base size of 30 mm, refined to 2.25 mm within r 2R t and 8 geometrically spaced layers covering 3 mm. The power coefficient C p for 8 values of Λ in the range 0.25 Λ 2 have been measured in the simulation and are reported in Fig; 6. They are compared to experimental results. The numerical results are in fairly good agreement with the experiment on the whole range of Λ. The maximum efficiency is obtained at Λ = 1 which supports a first validation of the design method. The numerical result at Λ = 1 is C p,num 0.324 and overestimates the experimental one by 4%.

RESULTS AND DISCUSSIONS

The pressure field obtained numerically at Λ = 1 in the plane θ = 0 that contains the leading edge of the blade is displayed in Fig. 7; the absolute tangential and axial velocity fields are displayed respectively in Fig. 8 and Fig. 9. The dynamic pressure in the incoming flow is 600 Pa. The lowest pressure that is observed on the blades is of the order of -60 Pa. One can first notice a high pressure field upstream of the wind turbine in the shape of a bubble that extends up to 5R t for p 4 Pa, which may explain why an upstream 7R t is necessary to reach convergence (see lower part of Fig. 4). Then, one can notice the presence of a vortex street in the wake, with a distance between the vortices of the order of 0.58R t ip. The position of these vortices reveals The most noticeable feature in this wake is the presence of high tangential velocities, as expected. It is of the order of 0.6V ∞ and the axial velocity in the wake is of the same order of magnitude. The swirl number is thus of the order of the unity and, contrary to the numerical results presented in the chapter 6 of Ref. [START_REF] Sørensen | General Momentum Theory for Horizontal Axis Wind Turbines[END_REF] for a Joukowsky rotor of similar size at Λ = 1, there is no noticeable large recirculation bubble nor vortex breakdown in our case, which is consistent with preliminary flow visualizations in the wind tunnel. Profiles of azimuthally-averaged velocity fields have been extracted and are plotted in Fig. 10, at an axial position corresponding to 2R t /3 downstream of the blades' leading edges. The axial velocity in the wake is not uniform as stated in the design method though it is of the expected order of magnitude and corresponds to an average axial induction factor of 0.34. The tangential velocity profile is not uniform; it decreases almost linearly from hub to tip. It is of the expected order of magnitude and large enough to get used to entrain a second rotor.

CONCLUSION

A wind-turbine of small-scale and operating at a small tip-speed ratio Λ = 1 has been designed with an innovative design method. It has been tested experimentally in a wind tunnel and presents good performances. A numerical study has been made and shows that a stable and highly rotating wake is obtained, which could be used to entrain a second counter-rotating rotor that will be adapted to this flow field and that will be designed in a future work.

Figure 1 :

 1 Figure 1: Blade cascade and velocity triangle at mean radius r = R h +Rt 2

Figure 2 :

 2 Figure 2: CAD of the horizontal axis wind turbine, based on blade cascade design

Figure 3 :

 3 Figure 3: Typical mesh, geometric parameters and boundary conditions. R t is the tip radius of the turbine, R p the radius of the surrounding pipe, L u the upstream length, L d the downstream length

Figure 5 :

 5 Figure 5: Grid convergence test on final domain configuration with L d = 8R t , L u = 7R t and R p = 8R t

Figure 6 :

 6 Figure 6: Power coefficient C p as a function of tipspeed ratio Λ. The black crosses (×) represent the experimental data and the blue dots (•) the results obtained with the CFD

Figure 7 :

 7 Figure 7: Static pressure field for Λ = 1, with ρ = 1.2 kg.m -3 and V ∞ = 10 m.s -1 . Mesh of 5.8 millions cells with L d = 8R t , L u = 7R t and R p = 8R t . The black lines are iso-contours of static pressure at -2, 0 and +2 Pa

Figure 8 :

 8 Figure 8: Absolute tangential velocity field C θ for Λ = 1, with ρ = 1.2 kg.m -3 and V ∞ = 10 m.s -1 . Mesh of 5.8 millions cells with L d = 8R t , L u = 7R t and R p = 8R t . The black line is an iso-contour of C θ = 0

Figure 9 :Figure 10 :

 910 Figure 9: Absolute axial velocity field C z for Λ = 1, with ρ = 1.2 kg.m -3 and V ∞ = 10 m.s -1 . Mesh of 5.8 millions cells with L d = 8R t , L u = 7R t and R p = 8R t . The black line is an iso-contour of C z = 0