Lopez Quesada
email: glopezqu@insa-toulouse.fr

Optimizing the internal design of a miniaturized fluidic oscillator for active flow control over a scaled NACA-4412

Optimizing the internal design of a miniaturized fluidic oscillator for active flow control over a scaled NACA-4412

Guillermo Lopez Quesada, Ahmad Batikh, Stéphane Orieux, Nicolas

Mazellier, Lucien Baldas

To cite this version:

Guillermo Lopez Quesada, Ahmad Batikh, Stéphane Orieux, Nicolas Mazellier, Lucien Baldas. Optimizing the internal design of a miniaturized fluidic oscillator for active flow control over a scaled NACA-4412. 3AF-AERO2022, Mar 2022, Toulouse, France. hal-03627608

INTRODUCTION

In order to control the separation of the boundary layer with active flow control techniques, a variety of actuators can be found in the literature [START_REF] Cattafesta | Actuators for active flow control[END_REF]. Among these, fluidic oscillators have been in a rising trend in the recent years because their oscillations are completely self-induced and self-sustained and only depend on the internal fluid dynamics, without any moving part, which is positive in terms of reliability and robustness.

In the ongoing Cleansky PERSEUS project, the goal is to design, fabricate and implement different assemblies of fluidic oscillators that will permit an active control of the turbulent flow separation over a scaled NACA-4412 airfoil (length of wingspan 110 cm, chord 30 cm). In the present work, the focus is on the internal design of the fluidic oscillators taking into account the fabrication constraints of the actuators, the physical constraints linked to the scaled airfoil and the targeted performances for the future tests in the wind tunnel.

An experimental characterization of the scaled NACA-4412 airfoil has already been conducted in the wind tunnel of the PRISME laboratory (Orléans, France); along with numerical simulations and a sensitivity analysis to determine the most sensible location and injection angle of the PJAs to apply for the active flow control [START_REF] Passagia | Wind-tunnel experiments and separation control of a NACA4412 with 25º sweep at high Reynolds numbers[END_REF]. The characterization was provided for a free stream velocity of the wind tunnel U ∞ =30-50 m/s. The sensitivity analysis shows that in order to improve the aerodynamic performances (i.e. lift-to-drag ratio), the PJAs should be located close to the leading edge and the momentum should be injected tangentially to the boundary layer.

Therefore, the plan is to design and manufacture different PJAs covering 55% of the wingspan length (60 cm length of the PJAs body), with the outlets at different positions from the leading edge (i.e. 5% -15% of the chord length), and having the direction of the outlets as tangentially as possible to the airfoil surface. As a result, the PJAs will 3D printed in one piece and integrated into the airfoil as shown in Fig. 1-a and Fig. 1-b. The objective being to allow flow control along the span of the wing, a large assembly of oscillators is required. If the oscillators were left independent from each other, their oscillatory frequencies could vary or not be in phase due to manufacturing imperfections or variations in the operating conditions. However, the proposed design allows for a self-induced synchronization of the assembly by interconnecting the feedback loops of the different oscillators (Fig. 1-c). A total of 6 oscillators will be included in the 60 cm length along the span of the wing allocated for the PJAs, providing 12 outlets with a separation of 44 mm between the pulsated jets outlets.

For the purpose of evaluating and comparing the efficiency of a jet injection for the separation control, three dimensionless numbers are typically use: the injection momentum coefficient C µ (Eq. 1), the velocity ratio V R (Eq. 2) and the injection frequency F + (Eq. 3)

out m out 2 1 UL 2 V C     (1) R V max U V   (2)
F U fL    (3)
Where m out is the injected mass flow rate by the PJAs, V out is the velocity at the outlets of the PJAs, ρ is the density of the injected fluid, L is the flow characteristic length (typically the chord), ω is the span width of the controlled flow, V max the maximum velocity at the outlets, f the oscillation frequency and U ∞ the free stream velocity around the airfoil.

Several works have studied the optimal values of these parameters on ramp or hump flows [START_REF] Seifert | Active Flow Separation Control on Wall-Mounted Hump at High Reynolds Numbers[END_REF][START_REF] Luedke | Characterization of Steady Blowing for Flow Control in a Hump Diffuser[END_REF][START_REF] Greenblatt | Experimental Investigation of Separation Control Part 2: Zero Mass-Flux Oscillatory Blowing[END_REF][START_REF] Cerretelli | Boundary Layer Separation Control With Fluidic Oscillators[END_REF][START_REF] Joseph | Flow control on a 3D backward facing ramp by pulsed jets[END_REF]. For C µ , large discrepancies have been found by different groups which could be explained by the large difference between the studied configurations. However, in most cases, the optimal values found for V R are between 2 and 3, and the optimal F + is between 1 and 3. Consequently, the targeted performance of the PJAs to be design should be close to these values of V R and F + , which for the particular case on the scaled NACA-4412 airfoil considered (length 1 m, chord 0.3 m and free stream velocity of the wind tunnel U ∞ =30-50 m/s) result in maximum outlet velocities V max =60-150 m/s and oscillatory frequency in the range f =100-500 Hz.

The present paper shows first the working principle of the fluidic oscillator, its basic design and the methodology followed for the numerical simulations.

Next, an initial design is proposed and evaluated, highlighting an unexpected behaviour of the oscillator differing from the anticipated performance. Then, a modified design is proposed with significant changes in the geometry correcting the deviation from the expected operation found on the initial design. In addition, a prototype fabricated following this modified design is characterized with hot wire anemometry to compare with the numerical investigation. Finally a conclusion is proposed and future steps are discussed.

WORKING PRINCIPLE

The Pulsed Jet Actuators introduced in this work are based on bi-stable relaxation fluidic oscillators [START_REF] Wang | On the modelling of the switching mechanisms of a Coanda fluidic oscillator[END_REF] with some modifications in order to make them suitable for their integration in the NACA4412 airfoil. These new PJAs (Fig. 2) consist of one inlet nozzle connected to a switching zone that is divided by a splitter in two branches (S1 and S2), each of them leading towards a feedback loop (F1 and F2). These feedback loops reconnect to the switching zone through their respective control ports (C1 and C2). At the beginning of each feedback loop an elbow connects with a reservoir and the outlet channels (O1 and O2).

The oscillatory behavior of the actuator is provided by the feedback loop geometry and the control ports connected to the switching zone. Considering for example an initial flow from the inlet nozzle attached, thanks to the Coanda effect, to the branch S1, part of the flow would exit from the actuator through the outlet O1 while the rest of the flow would run along the feedback loop F1 and its corresponding control port C1, increasing the pressure in this loop with a compression wave propagating roughly at the speed of sound. When this pressure wave reaches C1, it is reflected back and generates a pressure increase at the connection between F1 and S1. The same phenomena occur but with expansion waves on the other side of the oscillator. Thus, the pressure imbalance between S1 and S2 together with pressure imbalance between C1 (control port with flow, higher pressure) and C2 (control port without flow, lower pressure), results in the switching of the flow stream from S1 towards S2. Then this process is repeated in the same way for the opposite feedback loop F2 and control port C2, providing the oscillatory change of the flow stream from S1 to S2 and effectively generating pulsating jets at the outlets O1 and O2.

Following this, the main control parameter for the frequency f of oscillation is typically the length L fb of the feedback loop as shown in Eq. 4 [START_REF] Wang | On the modelling of the switching mechanisms of a Coanda fluidic oscillator[END_REF], where C 0 is the speed of the pressure wave propagation, typically the speed of sound, which travels back and forth each of the two feedback loops during one period.

C 0 4 L fb f   (4)
Considering the targeted frequency of the PJAs should be f =100-500 Hz (corresponding to F + =1-3), the range of the feedback loop length is L fb =170-850 mm. However, given the spatial constraints due to the limited separation between oscillators of only 44 mm, the classic simple feedback loop design must be changed and increased in complexity.

METHODOLOGY

The numerical investigation has been performed with ANSYS Fluent using the coupled solver, the realizable k-ε turbulent model and a second order upwind spatial discretization scheme. A preliminary validation of the methodology was done on a first simple model to check the numerical dependence on the mesh quality and time step size of the unsteady simulation. The 3D model of 2 synchronized oscillators shown in Fig. 3-a In Table 1, the oscillation frequency obtained for the 9 different configurations in terms of mesh density and time step size are shown. The relative difference between each of the simulations compared to the most detailed case (7•10 6 elements and 10 -7 s) is also displayed. The results in terms of mesh density, for 1.5•10 6 and 3•10 6 elements show a relative difference between 1.09% and 3.29%, with the error increasing with the time step size. On the other hand, the coarser mesh (6.5•10 5 elements) provide a much bigger difference, with the oscillation frequency being 6.72% to 12.82% larger than the reference case when the time step size is increased from 10 -7 s to 10 -5 s. Following this sensitivity analysis in terms of the mesh density and the time step size, the configuration with 1.5•10 6 elements and a time step size of 10 -5 s provides a good compromise between computing time and accuracy of results. With this configuration the deviation from the reference case is only 3.29% while the computing time is greatly reduce. With this particular mesh density, the 1 st inflation layer next to the wall is smaller than 4•10 -5 m resulting in a maximum value of y + around 37 to resolve the turbulent flow with the standard wall function treatment. Therefore, the numerical investigation provided in the following sections will be using similar mesh characteristics and a time step size of 10 -5 s. Also, at least 2 oscillators will be simulated in order to check a proper synchronization between the jets at the outlets.

INITIAL DESIGN

The initial design is shown in Fig. 4-a where the geometry of the switching zone is identical to the one in Fig. 3-b, but the simple feedback loop geometry is replaced by a longer feedback loop with several serpentines in order to accommodate a large feedback loop length within the 44mm of separation between oscillators. The total feedback loop length is L fb =190 mm, with a width of 1mm. The depth of the oscillators is 2 mm while the outlets section is 1x2 mm 2 .

The numerical results for the average velocity profiles at the outlet are shown in Fig. 4-b, with the oscillating jet displaying velocities of between 70 m/s and 180 m/s and a frequency of oscillation f =743 Hz. The maximum velocity around 180 m/s is slightly over the targeted V max of 60-150 m/s, but this is not a big concern since the outlet section can be increased to reduce the overall velocity at the outlets. It should be noted that the after an initial transitory state for the first oscillation, a stable regime is reached with a proper synchronization between the 2 oscillators However, the frequency of oscillation f =743 Hz is significantly larger than the expected one (Eq.4) of 450 Hz. Therefore the internal flow of the fluidic oscillators is analyzed in Fig. 4-c by observing the velocity contours in the middle plane of the switching zone at four different times during one oscillation period (i.e. each quarter of the period). It is evident then, that the fluidic oscillators were not working as intended since the flow was flapping around the splitter walls instead of switching completely from one branch to the other.

In a first attempt to address this issue, the inlet total pressure was increased up to 5 bar but the oscillatory frequency still remained around 750 Hz. It seems that due to the increased complexity in the feedback loop combined with its small size (1x1 mm 2 cross section) generates a rather high resistance to the flow. This causes the flow to be mostly directed towards the outlet reservoirs instead of filling the feedback loops, failing to generate the required pressure waves for a complete switch of the jet from one branch to the other.

Therefore, for the following iteration of the numerical study of the PJAs, the width and depth of the feedback loop was increased and the complexity of the feedback loop was reduced. This however, limits the length of the feedback loop, making it difficult to reach the targeted oscillatory frequency. Additionally, in order to facilitate the Coanda effect and help attaching the jet to the walls opposite to the splitter, the walls in the switching zone were made slightly rounded.

MODIFIED DESIGN

The modified design is shown in Fig. 5-a with a detailed view of the adjusted switching zone in Fig. 5-b. The feedback loop length is set to 100 mm. This should provide a slightly larger oscillatory frequency than initially targeted (expected frequency of 850 Hz), but with the given constraints in terms of size, the focus is now to have a fluidic oscillator with a proper switching. The inlet total pressure is set to 3 bar while the outlets are kept at atmospheric pressure.

The average velocity at the outlets is shown in Fig. 5-c, with an oscillatory frequency of 817Hz and values going from around 45 m/s to 125 m/s. It can also be observed that the after an initial transitory state for the first oscillation, a stable regime is reached with a proper synchronization between the 2 oscillators. The flow in the switching zone is shown in Fig. 6 at different times revealing that the switching is indeed complete in this case from one branch to the other. Additionally, it can be observed how a recirculation bubble is generated between the jet and the splitter when the jet is completely attached to the branch walls. This could be a potential phenomenon to exploit in order to delay the switching of the jet and decrease the oscillatory frequency of the PJAs even while keeping the same feedback loop geometry.

EXPERIMENTAL CHARACTERIZATION

An assembly of PJAs corresponding to the modified design shown in Fig. 5-a has been fabricated for comparison with the numerical results and future tests on the wind tunnel with the airfoil. The schematic of Fig. 7-a shows the structure of the mounted device consisting of the 3D printed fluidic oscillators, a reservoir to provide the supply pressurized air, a plate separating the fluidic oscillators from the reservoir and a rubber joint. The interface plate separating the reservoir from the oscillators is glued to the 3D printed piece to later screw them to the reservoir with the rubber joint in between the separating plate and the reservoir. Also, the separating plate between the oscillators and the reservoir is pierced in order to let the pressurized air flow from the gas feed reservoir into the fluidic oscillators. Fig. 7-b shows the 3D printed piece and the reservoir before being mounted.

The jet at the outlets has been characterized with hot wire anemometry. A DANTEC probe type 55 hot wire has been used with a frequency of acquisition of 60 kHz. In Fig. 7-c the velocity measured at the outlet of the PJAs is shown, with a range of the velocity measured at the outlet of V out =28.4-93.9 m/s. Compared to the velocity range obtained in the simulation, the measured values are 25% to 36% lower. This can be explained by the fact that the hot wire is not positioned exactly at the outlet, but at a certain distance (less than 5 millimeters) from the outlet section. Regarding the oscillatory frequency, in Fig. 7-c the Welch method is applied to the signal acquired by the hot wire to extract the frequency of oscillation at the outlet. The frequency extracted from the measurement is f =820 Hz, which is almost identical to the frequency obtained in the simulations of 817 Hz, but slightly lower than the theoretical frequency of 850 Hz.

CONCLUSIONS

A numerical investigation has been performed in order to design a series of synchronized PJAs to control the flow over a scaled NACA-4412 airfoil. Realistic constraints related to the implementation of the PJAs in the airfoil as well as the fabrication and a targeted performance based on the optimal operation extracted from previous works have been considered. An initial design based on previous works was investigated, however, due to the modifications included to adjust the oscillators to the constraints; the switching of the internal jet between branches was not accomplished. This is mainly due to the high resistance to the flow in the feedback loop derived from the small cross section and high complexity. Therefore, a modified design is proposed in which the cross section of the feedback loop is increased and the resistance to the flow due to the feedback loop complexity is reduced. Additionally, the switching zone is modified in order to induce more easily the Coanda effect and attach the internal jet to the branch walls. A prototype has been fabricated with the geometry of the modified design and characterized with hot wire anemometry. The comparison between the numerical investigation and the experimental measurements shows a good agreement in terms of the oscillatory frequency, while the velocity measured is lower than the simulated one. This is due to the hot wire not being exactly positioned at the outlet, but at a few millimeters from the outlet.

Following the work presented, the next steps are the implementation of the prototype in the NACA-4412 airfoil to characterize the performance of the active flow

Figure 1 :

 1 Figure 1: (a) interior and (b) exterior view of PJAs implemented in an airfoil and (c) internal design of the interconnected fluidic oscillators.

Figure 2 :

 2 Figure 2: geometry of a single fluidic oscillator.

  was meshed with 3 different mesh sizes resulting in approximately 6.5•10 5 , 1.5•10 6 and 7•10 6 elements. Three time step sizes were used 10 -5 s, 10 -6 s and 10 -7 s. A detail of the switching zone is shown in Fig.3-b. The feedback loop length is L fb =30mm and the outlet sections are 1x5 mm 2 . The inlet total pressure is 3 bar while the outlets are considered as pressure outlets kept at 1 bar. With the given geometry, the frequency of oscillation calculated from Eq.4 should be around 2833 Hz.

Figure 3 :

 3 Figure 3: (a) 3D model of 2 synchronized oscillators and (b) detailed view of the switching zone.

Figure 4 :

 4 Figure 4: (a) 3D model of 2 synchronized oscillators of the initial design, (b) average velocity at each of the four outlets and (c) velocity contours in the switching zone at four different times during one period of the oscillation.

Figure 5 :

 5 Figure 5: (a) 3D model of 2 synchronized oscillators of the modified design, (b) detailed view of the switching zone geometry and (c) average velocity at each of the four outlets.

Figure 6 :

 6 Figure 6: velocity contours in the switching zone at four different times during one period of the oscillation.

Figure 7 :

 7 Figure 7: (a) schematic of the PJAs assembly, (b) pictures of the mounting of the actuator, (c) velocity measured with the hot wire anemometry and (d) frequency of the signal acquired using the Welch method.

Table 1 :

 1

Comparison of the frequency calculated for different mesh densities and time step sizes.

ACKNOWLEDGEMENTS

This project has received funding from the Clean Sky 2 Joint Undertaking (JU) under grant agreement No 887010. The JU receives support from the European Union's Horizon 2020 research and innovation programme and the CleanSky 2 JU members other than the Union.


Dr Lizeth Bodero

Dr Karine Guitot

Dr Nathalie Lensen

Olivier Lequin

Thierry Brigaud

Sandrine Ongeri
email: sandrine.ongeri@universite-paris-saclay.fr

Dr Grégory Chaume
email: gregory.chaume@cyu.fr

Prof Thierry Brigaud

Prof Sandrine Ongeri

Prof Olivier Lequin

Introducing the Chiral Constrained α-Trifluoromethylalanine in Aib Foldamers

Keywords: foldamers, helical structures, fluorinated peptides, circular dichroism, conformational analysis

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Introduction

Replicating protein folding through synthetic molecules is a main approach in chemical biology. These synthetic analogs called foldamers can be defined as oligomers with a strong tendency to fold into well-defined secondary structures such as helices, sheets or turns, able to mimic the structural properties of proteins. [1,2] In particular, the field of peptide-based foldamers has gained considerable interest in medicinal chemistry to circumvent some of the issues of short peptides by increasing their conformational stability and their stability towards proteolysis. [3,4] This feature makes peptidomimetic foldamer chemistry an important resource for the design of cell penetrating peptides (CPP), [5][6][7][8][9] antimicrobial peptides (AMP) [10][11][12] and inhibitors of protein-protein interactions (PPI). [13,14] Among the different types of foldamers, those constituted by several units of α-aminoisobutyric acid (Aib) have been widely investigated for their ability to form stable 310-helices [15,16] and their similitude with peptaibols, a natural type of AMP. [17,[START_REF] Toniolo | Peptaibiotics: Fungal Peptides Containing α-Dialkyl α-Amino Acids[END_REF] Because of the achiral nature of Aib, these hydrophobic foldamers do not exhibit axial chirality and present equal population of lefthanded (M) and right-handed (P) helical screw-senses. Nevertheless, it is possible to alter this equilibrium between the two forms and to induce a screw-sense preference by introducing chiral units, called controllers, at the C-or the N-terminus. Clayden et al. have shown that the control of the screw-sense preference could be achieved more readily from the N-than from the C-terminus. [START_REF] Solà | [END_REF] They also demonstrated that the left-or righthanded sense of helical induction arises from the nature of the βturn at the N-terminus: tertiary amino acids (e.g. L-Val) induce lefthanded helicity through a type II β-turn while quaternary amino acids (e.g. L-α-methylvaline) favor right-handed helicity via a type III β-turn. [20,21] The screw-sense preference can be quantified using different 1 H, [START_REF] Solà | [END_REF] F and 13 C NMR spectroscopic probes along with CD, IR spectroscopy and X-ray crystallography. [22,23] The use of fluorine-containing amino acids is becoming a very promising tool for the design of new bioactive molecules. [24,25] However, their use for the design of fluorinated peptide-based foldamers remains in its infancy with only a few examples reported so far. [26][27][28][29][30][31] We aim to give some inputs in the vast but unknown field of exploring the rational incorporation of fluorine atoms into peptidomimetic foldamers to lead to novel molecular architectures, and to improve or modulate their physicochemical properties, and their biological profile. As α-trifluoromethyl-α-amino acids (Tfm-AAs) are interesting to promote the helical secondary structures of peptides, [31][32][33] we propose here to investigate the ability of (R)and (S)-α-trifluoromethylalanine (TfmAla) to stabilize the 310 helical conformation and to induce a screw-sense preference when incorporated at the N-terminus of short Aib oligomers. Because of the stereo-electronic effects of the trifluoromethyl group (CF3), additional advantages are also expected for the fluorinated oligomers compared to their non-fluorinated analogs, including hydrophobicity, thermal resistance, conformational constraint, polarization effects on neighboring groups as well as H-bonding and dipole induction. [34][35][36][37][38][39][40][41] The CF3 group can also be used as a highly sensitive probe for 19 F NMR spectroscopy. [32,33,42] In contrast with achiral [START_REF] Solà | [END_REF] F NMR reporters based on β,β'-difluoroAib inserted at the C-terminus, [43] TfmAla has been investigated here as a multiple tool: first, as a chiral controller to induce a screw-sense preference, and second, as an NMR reporter to both quantify and assign it. It could also contribute to provide other valuable information about the fluorinated foldamers (orientation in membrane, conformation, dynamics, interactions with partners, kinetics of degradation, …). [42]

Results and Discussion

Two series of fluorinated Aib foldamers have been designed (Figure 1). The first series is based on the incorporation of a single fluorinated chiral residue, namely (S)-or (R)-Cbz-TfmAla, at the N-terminal position of Aib pentamers, constituting a sufficient length to ensure the stabilization of the 310 helical conformation. [20,21,[44][45][46] The introduction of C-terminal ester groups can locally disturb the regular helical structure of peptide derivatives, and this effect is known as C-terminal destabilising Schellman motif. Since the size of the C-terminal ester group and the resulting Schellman motif can play a significant role in determining the overall secondary structure of short Aib sequences in solution, [47] we prepared two sets of compounds bearing respectively a methyl (OMe) (1) and a tert-butyl (OtBu) (2) ester. In the second series, a glycinamide residue was added at the C-terminal position to quantify the induced screw-sense preference of the helix. Indeed, compared to other NMR reporters, [20] the glycinamide at the C-terminus has been reported to be more suitable, not only because of its availability and its easy incorporation into peptides, but above all because the signals of its pair of diastereotopic protons stand clear of the other resonances in the 1 H NMR spectrum, allowing the ready observation of their anisochronicity (chemical shift separation). Two different protecting groups, namely Cbz (compounds 3) and acetyl (Ac) (compounds 4), were introduced at the N-terminus to assess their effect on the level of control of the chiral controller even if it has been reported that, in general, the control by quaternary amino acid is maximized by a carbamate protecting group. [START_REF] Solà | [END_REF] Reference compounds 5 and 6, containing the L-αmethylvaline residue (L-α-MeVal) as chiral controller and previously reported by Clayden's group, [20,21,44] were also prepared to study the conformations obtained with fluorinated oligomers compared to non-fluorinated ones. The helical conformation and screw-sense preference of the synthesized oligomers were studied using CD spectroscopy, X-ray crystallography, and different NMR probes, including the measurement of anisochronicity between the C-terminal diastereotopic "reporter" protons and 19 F NMR spectroscopy. Oligomers 1-6 were synthesized as indicated in Scheme 1.Aib tetramers precursors 10 and 11 bearing respectively a methyl or a tert-butyl ester at the C-terminus were prepared following the reported procedure via iterative coupling of N3-Aib-Cl 7 and reduction of the N-terminal azide functional group. [45][46][47] The pentamer 12 [44] containing a C-terminal glycinamide residue was obtained upon removal of the tert-butyl group of 11, activation with acetic anhydride and reaction with glycinamide hydrochloride. The incorporation of the Cbz-protected quaternary amino acids (S)-and (R)-TfmAla [48,49] and L-α-MeVal at the N-terminal position was carried out after the azide reduction of 10, 11 and 12 under typical EDC/HOBt coupling conditions in solution to afford the final compounds 1-3 and 5. [21] The Cbz group of 3 and 5 was also substituted by an acetyl by catalytic hydrogenolysis and further treatment with acetic anhydride to provide the peptides 4 and 6. [21] The screw-sense preference of the fluorinated foldamers 1-4 was determined and compared with the non-fluorinated ones 5 and 6, by acquiring their CD spectra in methanol. This solvent is trickier for preserving intramolecular hydrogen bonding and folding in comparison with aprotic organic solvents but it was chosen for comparison with data reported in the literature for Aib oligomers and as the closest solvent to water. In Figure 2 are shown the CD spectra of the compounds 3-6 of the series 2 (see Supporting Information Figures S1 andS2 for the CD spectra of 1 and 2 respectively). The fluorinated compounds 1-4, regardless of the identity of the N-terminal protecting group, exhibited a major band near 205 nm, which plays a central role in the assignment of 310 helix handedness, as proven by experimental and DFT-calculated CD spectra. [44] A weaker band near 220 nm has previously been observed as a shoulder of the main band. This is apparent in the spectra of 3 but not compound 4. These features are similar to the spectra of the reference compounds 5-6 and consistent with a 310-helix structure. [50] Moreover, the CD spectra of the R enantiomers of the fluorinated foldamers 1-4 resulted in the mirror image of the corresponding S peptides, indicating the opposite screw-sense orientation of the 310-helices. In agreement with the literature, the negative band at 205 nm indicated that the N-terminal quaternary L-α-MeVal of the reference compounds 5 and 6 induces a righthanded helicity (P). [44,50] Surprisingly, the Cbz-protected compound 3-(S) and its N-acetylated analogue 4-(S) exhibited similar CD signature to the ones of the reference compounds 5 and 6, respectively. This result was unexpected as the van der Waals volume of the CF3 group is reported to be only slightly larger than that of the isopropyl group (i-Pr), [51] which would make peptides 3-(R) and 4-(R) the isosteric analogues of the reference compounds 5 and 6, respectively. Therefore, the reversal of the screw-sense orientation observed for the fluorinated foldamers may be rather attributed to the electronic effects conferred by the CF3 group. Recrystallization of peptide 4-(S) from MeOH/H2O gave crystals suitable for solid state structure analysis by X-ray crystallography (CCDC reference numbers: 2107837 (4-(S))). However, this could not be used to confirm the preferential helical screw-sense observed in solution by CD. Indeed, the crystallographic structure of 4-(S) showed two independent conformers 4-(S)M and 4-(S)P with opposite screw-sense, aligned in an antiparallel arrangement in the asymmetric cell unit and held together through (C-terminal acetamido) N-H•••C=O (Aib 4 residue) intermolecular hydrogen bonds (1.99 Å and 2.06 Å) (see Supporting Information Figure S3). This result suggests that the crystallization favors the selection of the two screw-sense helices in the cell unit. Similar observations have been reported on related Aib compounds showing structures in the crystal state different to the conformational preference observed in solution. [21,52,53] The structures of each conformer of 4-(S) in the solid state indicate the presence of five consecutive i + 3 → i N-H•••C=O bonds, consistent with the 310 helical conformation (Table 1 and Figure S4 in Supporting Information). Inspection of the ϕ, ψ backbone torsion angles in Table 1 reveals that the two conformers (4-(S)M and 4-(S)P) form mainly 310-helical structures along their Aib4 peptide chain. These angles exhibit similar values but opposite signs, indicating reversed screwsenses in the two structures. For the conformer 4-(S)M, the ϕ, ψ torsion angle values of Aib residues range from 54.3° to 57.4° and 26.4° to 32.6°, respectively, close to those typical for left-handed (M) 310-helix (57°, 30°) while for 4-(S)P, the ϕ, ψ values range from -53.8° to -59.5° and -27.4° to -33.0°, respectively, close to those typical for right-handed (P) 310-helix (-57°, -30°). [53] Due to the presence of the Gly-NH2 residue, the 310 helix conformation of 4-(S)M and 4-(S)P is slightly distorted at the C-terminus with the presence of a type I/I' β-turn (ϕ = -90°, ψ = 0° and ϕ = 90°, ψ = 0°, respectively). The helical screw-sense of the two structures seems to be driven by the ϕ, ψ backbone torsion angles of the chiral TfmAla residue at the N-terminal position. Because quaternary L-α-MeVal residue is reported to favor right-handed helicity via a type III β-turn, [20] it was anticipated that the (S)-TfmAla, a fluorinated analogue of the D-α-MeVal, would also promote left-handed helicity. However, this was opposite to the experimental CD results, that showed a major right-handed helix conformation. In the 4-(S)M conformer, the TfmAla 1 displays positive torsion angles (ϕ = 47.3°, ψ = 42.3°) corresponding to a slightly distorted type III' β-turn (ϕ = 60°, ψ = 30°), but allowing a left-handed helicity (Figure 3A). The CF3 group of the TfmAla, corresponding to the bulkiest group, is almost perpendicular to the C=O group (the torsion angle of F3C-C-C=O is 103.3°) (Figure 3B). In contrast, the TfmAla 1 of the 4-(S)P conformer displays negative torsion angles (ϕ = -32.1°, ψ = -57.9°) which significantly deviate from those expected for a type III β-turn, but still allowing the right-handed 310-helical structure (Figure 3C). Interestingly, these unusual ϕ, ψ backbone torsion angles place the CF3 group eclipsed to the C=O group (the torsion angle of F3C-C-C=O is 6.5°) leading to an alignment of their dipole (Figure 3D). This particular electronic effect of the CF3 group could thus induce the major right-handed helix conformation of 4-(S)P observed in solution, as indicated by CD experiments. The fluorinated oligomers 1-4 were then fully characterized by NMR in methanol-d3, using 2D experiments (e.g., HSQC, HMBC, ROESY) to assign the chemical shifts of 1 H and 13 C NMR resonances. No concentration-dependence was observed in methanol indicating the absence of aggregation. The NMR data of the non-fluorinated oligomers 5 and 6 were in full agreement with those reported in the literature. [20,44] In order to gain insight into the intramolecular H-bond arrangement, the temperature coefficients (Δδ/ΔT) of NH chemical shifts of fluorinated oligomers 1-4 were calculated. In all the compounds, the Δδ/ΔT values obtained for NH protons of the Aib residues 3, 4 and 5 were superior to -4 ppb/K, indicating the existence of intramolecular H-bonds (Figure 4), while the two Nterminal NH protons exhibit significantly larger temperature coefficients (Tables S6 andS7 in Supporting Information). [54] For compounds 3 and 4, two additional H-bonds were identified involving the NH of the Gly residue and one of the C-terminal amide protons (Figure 4). These results are consistent with the i ← i + 3 hydrogen bonding pattern of 310 helix structure. [20] Conversely to the reported observations on tetrameric Aib oligomers, the presence of the Schellman motif at the C-terminus of oligomers 1 and 2 did not perturb the intramolecular hydrogenbonding contacts, even when using the more sterically demanding tert-butyl ester. [47] We were also pleased to observe that the incorporation of the TfmAla residue at the N-terminus of Aib oligomers did not hamper the H-bonding pattern of the 310 helix despite the stronger H-bond donating effect of its vicinal N-H amide due to the electron withdrawing effects of the CF3 group. Information from the ROESY spectra of 1-4 in methanol-d3 supports the existence of stable helical conformations. Sequential NH(i)/NH(i+1) ROE correlations, characteristic of α and 310 helices, [47,55,56] were detected in the amide region for all the fluorinated foldamers with no difference within each pair of enantiomers (see Supporting Information Figures S5-S11). Due to signal overlapping, we could not identify any CH3  (i)/NH(i+2) cross-peaks in the ROESY spectra. However, the absence of NH(i)/NH(i+2) cross-peaks supports the 310 helix conformation. [55] As a representative example, the ROESY spectrum of compound 4-(S) is shown in Figure 5. Further evidence of the helicity of the fluorinated foldamers was given by the anisochronicity of Aib gem-dimethyl groups signals in 13 C NMR (see Supporting Information Table S9). This anisochronicity, also known as chemical nonequivalence (CNE), can exceed 2 ppm in the presence of a stable helical conformation. [20,57] The CNE values of Aib methyl groups of peptides 1 and 2 were above 2 ppm, with exception of the last Aib residue. This suggests a loss of helicity at C-termini possibly due to the presence of the ester group that has been reported by Clayden et al. as destabilizing Schellman motif. [47] In the case of peptides 3-6, containing an additional Gly unit at C-terminus, the CNE values were around 2 ppm for all Aib residues. The slight decrease of the CNE values observed in the N-acetyl compounds 4 and 6 compared to their Cbz-analogues 3 and 5 confirms the superior effect of the carbamate protecting group over the acetyl one in stabilizing helical conformation in Aib oligomers. [START_REF] Solà | [END_REF] Interestingly, a more defined separation pattern was observed for fluorinated peptides 3 and 4 compared to reference compounds 5 and 6, respectively. The interproton distances NH(i)/NH(i+1) of 4-(S) have been estimated from the integration of their cross-peaks observed on the ROESY spectra (See Supporting Information Table S8) [20] and compared to the values determined from the X-ray crystal structures 4-(S)M and 4-(S)P (Table 2). There is a good correlation between the three sets of distances and the values, ranging from 2.55 to 3.07 Å, are consistent with the presence of a regular helical conformation both in solution and solid state. The quantification of the magnitude of the screw-sense preference in solution for compounds 3-6 was then enabled by their NMR spectroscopic probes. First, the helical excess (h.e.) was calculated by measuring the ratio of anisochronicity of the Gly diastereotopic protons at fast and slow exchange regime in methanol (h.e. = Δδfast/Δδslow) (Table 3). [21,22] The sign of the helical excess indicated in Table 3 was assigned on the basis of the CD signature (negative in a left-handed helix and positive in a right-handed helix). [20,21] The h.e. values for the reference compounds 5 and 6 were first assessed. Compared to those (ppb) [a] Δδslow 193K (ppb) [b] 1 H NMR reporter h.e.obs [c] , h.e.0 [d] (%)

H N O N H O N H O H N O O H N NH 2 O PGHN R 1 R 2 H N O N H O N H O H N O OR 3 O CbzHN R 1 R
F NMR reporter h.e.obs [e] (%)

3-(S)

261 417 +62, +81 +80 reported in the literature, [21] peptides 5 and 6 displayed much higher h.e. values (ca. 18% increase). This trend can be ascribed to the fact that the h.e. values from the literature have been calculated from the hypothesized Δδslow value of the GlyNH2 reporter of ca. 530 ppb. [21] In the course of our study, this value was determined experimentally by NMR at very low temperature (-80°C) to ensure the slow exchange regime. The maximum peak separation of the GlyNH2 reporter measured for peptides 5 and 6 was found to be significantly smaller (ca. 380 ppb), explaining the higher values of their helical excess. The fluorinated peptides 3 and 4 displayed slightly higher Δδslow value (ca. 417 ppb) compared to their non-fluorinated analogues. Their helical excess was similar for each pair of enantiomers and slightly inferior (ca. 10% less) to the reference compounds 5 and 6, respectively. Moreover, the screw-sense preference of the fluorinated Aib oligomers was more pronounced (ca. 15% higher) in the case of Cbz-protected compounds compared to their N-acetylated analogues, as observed in the non-fluorinated series. Because the CF3 group can also be used as highly sensitive probe for [START_REF] Solà | [END_REF] F NMR spectroscopy, we next investigated the opportunity to use the CF3 group of the chiral (S)-and (R)-TfmAla residue and [START_REF] Solà | [END_REF] F NMR spectroscopy to quantify the magnitude of the screwsense preference. The presence of this second NMR reporter at the N-terminus should allow assessing the degree of control exerted by the chiral TfmAla controller itself and the variation of conformational preference along the peptide chain. [START_REF] Solà | [END_REF] F NMR of peptides 3 and 4 at room temperature revealed a single average peak, indicating a fast regime exchange and preventing the quantification of the screw-sense preference (Figure 6 and Figure S13 in Supporting Information). Upon cooling to -60°C, the slow regime exchange was reached and two distinct peaks corresponding to the CF3 resonances of the (M)-and (P)-helices were observed. The helical excess of peptides 3 and 4, obtained by integrating the isolated resonances, were found to be ca. 80% and 67%, respectively (Figure 6 and Figure S13 in Supporting Information). Compared to the helical excess (h.e.obs) measured at the C-terminus using the Gly-NH2 1 H NMR reporter (Table 3), the values observed at the N-terminus of peptides 3 and 4 were much higher. This result was anticipated due to the decay of the helical excess along the peptide chain. [21] However, it is possible to estimate the control exerted by the chiral controller at the N-terminus by extrapolating the measured helical excess (h.e.obs) at the C-terminus using the 1 H NMR reporter (see Supporting Information). The corresponding inferred helical excess values (h.e.0) exerted by peptides 3 and 4 are very similar to those obtained using the [START_REF] Solà | [END_REF] F NMR reporter (Table 3). We next explored the possibility to assign the sign of the screwsense preference by observing whether the predominant CF3 signal appears upfield or downfield to that of the minor one. Indeed, the CF3 group of the chiral TfmAla residue has not the same chiral environment along a right-or a left-handed 310 helix. [59][60][61] Thanks to the CD spectra of peptide 4 (Figure 2), we were able to assign the right-handed (P) helix to the downfield major [START_REF] Solà | [END_REF] F NMR signal of peptides 4-(S) (Figure 6B) and the lefthanded (M) helix to the downfield major [START_REF] Solà | [END_REF] F NMR signal of peptides 4-(R) (Figure 6D). The same observation was done with peptide 3 (see Supporting Information Figure S13). A deep examination of the crystal structure of 4-(S) gives an explanation for the position of the predominant CF3 signal relative to the minor signal observed in [START_REF] Solà | [END_REF] F NMR spectra. In the structure of 4-(S)M, corresponding to a left-handed 310 helix (M), the CF3 group is staggered with respect to the TfmAla carbonyl group (Figure 3B and 6A) while it is eclipsed with respect to the TfmAla carbonyl group in the right-handed 310 helix (P) of the structure of 4-(S)P (Figure 3D and6A). Therefore, the eclipsed CF3 group with respect to the TfmAla carbonyl group undergoes a downfield shift in [START_REF] Solà | [END_REF] F NMR spectra. This trend is important to note because, in the case of non-fluorinated residues, the more eclipsed alkyl group with respect to the carbonyl was reported as resonating at higher fields (upfield shift) in 13 C NMR spectra. [44,45,[61][62][63][64] The different behavior between the two nuclei with respect to the carbonyl group can be explained by an electric field effect. Indeed, in non-fluorinated series, it has been proposed that the high electron density of the carbonyl oxygen polarizes the C-H bond of the eclipsed methyl group. [65] As a result, the carbon atom gains some electron density, causing an upfield shift, while the hydrogen atom undergoes reduced electron density, causing its downfield shift. A similar behavior could be envisioned for the C-F bond of the eclipsed CF3 group. Thus, this [START_REF] Solà | [END_REF] F-NMR parameter can successfully be exploited to assess the helical screw-sense preference of fluorinated Aib-foldamers, provided that the absolute configuration of the Tfm-Ala residue is known. For Aib oligomers with (S)-Tfm-Ala residue at the N-terminus, the CF3 group of the right-handed (P) helix falls downfield with respect to the CF3 group of the left-handed (M) helix (Aib oligomers with (R)-Tfm-Ala residue display opposite behavior). The helical excess (h.e.) of the peptides 3 and 4 can be also estimated by using the relationship: h.e.(%) = (δobs -δmean) / (Δδslow / 2), where δobs is the chemical shift of the coalesced [START_REF] Solà | [END_REF] 6B). The helical excess (h.e.) value of peptide 4-(S) was found to be +70%, in good agreement with the helical excess assessed using low temperature [START_REF] Solà | [END_REF] F NMR (Table 3). The peptide 4-(R) exhibits similar helical excess with opposite sign (-70%). The peptides 3-(S) and 3-(R) show helical excess values of +90% and -94%, respectively, slightly higher than those obtained using low temperature [START_REF] Solà | [END_REF] F NMR (ca. 12% increase). The chemical shift values of the two CF3 resonances at slow regime exchange, and consequently the Δδslow and the δmean values, were found to be similar within the Cbz-and Ac-protected series, respectively. Therefore, the quantification and the assignment of the screw-sense preference of related fluorinated Aib oligomers of peptides 3 and 4 could be easily deduced by extrapolating directly from the chemical shift value of the coalesced [START_REF] Solà | [END_REF] F NMR signal observed at room temperature (δobs). Finally, we estimated the energy barrier of the 310-helix interconversion of the fluorinated Aib oligomers by dynamic NMR study. The coalescence temperatures (Tc) of peptides 3 and 4 were found to be similar (Tc ≈ 243 K) corresponding to an energy barrier of G ‡ ≈ 11.1 kcal.mol -1 (See Supporting Information Table S10). This value is in good agreement with the one reported for Aib foldamer (G ‡ ≈ 11 kcal.mol -1 at 265 K). [59,60]

Conclusion

We have reported the synthesis of Aib-based short fluorinated foldamers containing α-Tfm-Ala as a chiral controller of the helical screw-sense at the N-terminal position. NMR studies and X-ray crystallography confirmed the presence of 310 helix type and CD spectroscopy indicated a right-handed screw-sense preference for the (S)-TfmAla enantiomers and left-handed screw-sense preference for the (R)-TfmAla form. The selectivity of the screwsense is reversed compared to that induced by the nonfluorinated L-α-MeVal chiral inducer due to the electronic properties of the CF3 group. This 19 F NMR probe allows the easy determination of both the magnitude of the screw-sense preference and the assignment of its sign. Moreover, the energy barrier of the 310 helix interconversion has been determined using [START_REF] Solà | [END_REF] F NMR. This work demonstrates that [START_REF] Solà | [END_REF] F NMR is an easy to handle tool to provide valuable insights into the structuration and the kinetic and thermodynamic parameters of fluorinated foldamers. As this technique avoids the problem of overlapping NMR signals inherent to 1 H NMR, we may now consider using this probe to further study the behavior of fluorinated foldamers in interaction with various biological partners such as proteins and membrane models.

Experimental Section

Deposition Numbers 2107837 (for 4-(S)) contain the supplementary crystallographic data for this paper. These data are provided free of charge by the joint Cambridge Crystallographic Data Centre and Fachinformationszentrum Karlsruhe Access Structures service.

2 2 6 : 5 :Figure 1 . 5 - 6 (

 265156 Figure 1. Chemical structure of the target fluorinated foldamers 1-4 and nonfluorinated analogues 5-6 (Ref 44-46).

5 : 6 :Scheme 1 .

 561 Scheme 1. Synthesis of foldamers 1-6: a) N3-Aib-Cl 7, Et3N, DCM, 0 °C to rt, overnight; b) H2 (1 bar), Pd/C (10% w/w), MeOH, rt, overnight; c) Cbz-(S)-Tfm-Ala or Cbz-(R)-Tfm-Ala, EDC.HCl, HOBt, iPr2NEt, DMF, 0 °C to rt, overnight; d) TFA/DCM 1:1, rt, overnight; e) Ac2O, HCl.GlyNH2, iPr2NEt, reflux 72 h; f) Cbz-(S)-Tfm-Ala, Cbz-(R)-Tfm-Ala or Cbz-L-α-MeVal, EDC.HCl, HOBt, iPr2NEt, DMF, 0°C to rt, overnight; g) Ac2O, iPr2NEt, DCM, rt, overnight.

Figure 2 .

 2 Figure 2. CD spectra of peptides 3-6 (0.3 mM in MeOH, 20°C)

Figure 3 .

 3 Figure 3. First turn conformation as observed in the X-ray crystal structure of peptide 4-(S) (the rest of the molecule is omitted for clarity). A: side view of conformer 4-(S)M; B: top view of conformer 4-(S)M; C: side view of conformer 4-(S)P; D: top view of conformer 4-(S)P. Conformers 4-(S)M and 4-(S)P display lefthanded (M) and right-handed (P) 310 helical conformation, respectively. Intramolecular H-bonds are indicated as dashed.

Figure 4 .

 4 Figure 4. H-bond patterns for foldamers 1-4 consistent with 310 helix structures

Figure 5 .

 5 Figure 5. Amide region of the ROESY spectrum of compound 4-(S) (400 MHz, m = 280 ms, 2.5 mM in MeOH-d3; 298 K).

Table 2 .

 2 Distances (Å) obtained by 2D-NMR and X-ray crystallography for 4-

  Chemical shift separation between the anisochronous peaks arising from the diastereotopic protons of the Gly 6 residue in the 1 H NMR spectrum in CD3OD at 293 K. [b] Chemical shift separation between the anisochronous peaks arising from the diastereotopic protons of the Gly 6 residue in the 1 H NMR spectrum in CD3OD at 193 K. [c] Observed helical excess (h.e.obs) is calculated using h.e. = Δδfast/Δδslow, as defined in ref 58. [d] Inferred helical excess (h.e.0) corresponds to the helical excess induced by the controller at the N-terminus of the oligomer; see the text for discussion and ref 21. [e] Observed helical excess (h.e.obs) is calculated by integrating the isolated CF3 resonances in the 19 F NMR spectrum in CD3OD at 213 K. [f] In parentheses, h.e. values reported in ref 21. Helical excess (h.e.) is negative in a left-handed helix and positive in a right-handed helix.

Figure 6 .

 6 Figure 6. A: Newman projections of the N-terminal turn of 4-(S) in left-handed and right-handed helices; B: 19 F NMR spectra of 4-(S) in CD3OD at three different temperatures; C: Newman projections of the N-terminal turn of 4-(R) in left-handed and right-handed helices; D: 19 F NMR spectra of 4-(R) in CD3OD at three different temperatures. 19 F NMR spectra were calibrated by setting the C6F6 peak to -165.37 ppm. The dash line indicates the mean of the chemical shifts at slow regime exchange (δmean). TFA: trifluoroacetic acid.

  F NMR signal observed at room temperature (fast exchange regime), δmean corresponds to the mean of the chemical shift values of the two CF3 resonances at slow regime exchange, and Δδslow the chemical shift difference between the two CF3 resonances at slow regime exchange. In the case of an equal population of the two helices (i.e, h.e. = 0%), the δobs value corresponds to the δmean value. It is therefore possible to estimate the sign of the screw-sense by determining the relative position of the δobs value with respects to the δmean chemical shift. For instance, the fluorinated peptide 4-(S) displays at room temperature (293 K) a single CF3 resonance at δobs = -75.7 ppm and, two CF3 resonances (-75.3 ppm and -78.0 ppm) at slow exchange regime, from which Δδslow = 2.7 ppm and δmean = -76.65 ppm have been deduced (Figure

Table 1 .

 1 Structural parameters for conformers 4

-(S)M and 4-(S)P observed

  in the X-ray structure of 4

-(S) 4-(S)M 4

	(S)-TfmAla 1	47.3	42.3	2.11	-32.1	-57.9	2.03
	Aib 2	55.8	32.6	2.27	-59.5	-31.4	2.28
	Aib 3	57.4	26.8	2.13	-57.0	-27.4	2.15
	Aib 4	54.9	26.4	2.06	-54.4	-28.6	2.05
	Aib 5	54.3	31.4	2.17	-53.8	-33.0	2.10
	Gly 6	81.8	10.2		-80.8	-9.6

-(S)P Residue ϕ (deg) ψ (deg) i -1 (C=0) to i + 2 (H-N) H-bonding distance (Å) ϕ (deg) ψ (deg) i -1 (C=0) to i + 2 (H-N) H-bonding distance (Å)

Table 3 .

 3 Anisochronicity in the CH2 protons of Gly residue

		Δδfast
	Compound	293K

Acknowledgements

The CY Initiative of Excellence (grant "Investissements d'Avenir" INEX 2019 FluoSPep) is thanked for financial support of Lizeth Bodero. Authors thank Dr. Pascal Retailleau (Departement of Xray crystallography at Institut de Chimie des Substances Naturelles -UPS, CNRS-UPR2301 -Gif sur Yvette) for help with the crystal structure solution.

Entry for the Table of Contents

The chiral α-trifluoromethylalanine is shown to induce and control the screw-sense preference of short Aib oligomers. Due to the electronic properties of the CF3 group, the screw-sense is inversed compared to that induced by its non-fluorinated isosteric L-α-MeVal analogue. It also plays the role of [START_REF] Solà | [END_REF] F NMR reporter allowing the easy determination of both the magnitude of the screw-sense preference and the assignment of its sign.

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