domain: spi phys phys.meca.acou

text:
Paul Zehner
email: paul.zehner@alumni.enseeiht.fr.

Fabrice Falissard
email: fabrice.falissard@onera.fr

Xavier Gloerfelt
email: xavier.gloerfelt@ensam.eu.

Vortex Model and Blade Span Infuence on Orthogonal Blade/Vortex Interaction Noise

The influence of vortex impingement location, on the aerodynamic and acoustic response of a rotating blade during an orthogonal interaction, is studied by means of computational fluid dynamics. The objective is to identify and quantify precisely the noise reduction achieved by reducing the blade span. The Batchelor vortex model is primarily considered as it accounts for the axial velocity deficit observed in the core of realistic tip vortices. Separated simulations were also carried out for a Lamb-Oseen vortex and a purely axial velocity deficit to highlight and quantify the influence of the vortex velocity components on the interaction as well as to balance design optimizations performed relying on methods not able to model viscous effects. Analysis of the blade aerodynamic and acoustic responses show that the magnitude of the thrust fluctuation and radiated noise are always higher for a Batchelor vortex than for a Lamb-Oseen vortex when the vortex core impinges below the blade tip. For both vortex models, the thrust fluctuation and radiated noise reach their peak for an interaction close to the blade tip. They decrease slowly as the vortex impingement moves inward the blade and decrease strongly as the vortex passes above the tip. Finally, the noise directivity pattern is dipolar for interaction close to or above the blade tip and becomes more and more quadrupolar as the radius of interaction moves toward the blade root.

I. Introduction

Orthogonal blade/vortex interactions (OBVI) occur on single propellers in pusher configuration or on aft rotors of contra-rotating open-rotors (CROR) that operate in the wake of a fixed or rotating lifting surface. This wake, consisting of a velocity deficit and of vortices generated at the tip or root, gives rise to impulsive thrust and torque fluctuations on the propeller, increasing significantly vibrations and noise radiation. These phenomena can be partially mitigated by placing adequately the side-edges of the control surfaces upstream to a single propeller or by reducing the radius of the aft rotor on CRORs [START_REF] Woodward | Noise of a Model Counterrotation Propeller With Reduced Aft Rotor Diameter at Simulated Takeoff/Approach Conditions (F7/A3)[END_REF]. This is usually done in the early stages of the design process using preliminary design methods unable to handle the complexity of OBVI.

In the past, OBVI has been studied thoroughly within the helicopter field with a focus on main rotor/tail rotor interactions [START_REF] Coton | Helicopter tail rotor orthogonal blade vortex interaction[END_REF]. Analyses were carried out by means of dedicated experiments [START_REF] Pegg | Exploratory Wind Tunnel Investigations of the Effect of Main Rotor Wake on Tail Rotor[END_REF][START_REF] Schlinker | Rotor-Vortex Interaction Noise[END_REF][START_REF] Cary | An Experimental Investigation of the Chopping of Helicopter Main Rotor Tip Vortices by the Tail Rotor, Part II: High Speed Photographic Study[END_REF][START_REF] Marshall | On the instantaneous cutting of a columnar vortex with non-zero axial flow[END_REF][START_REF] Krishnamoorthy | Three-dimensional blade-vortex interaction in the strong vortex regime[END_REF][START_REF] Doolan | Three-dimensional vortex interactions with a stationary blade[END_REF][START_REF] Doolan | Surface Pressure Measurements of the Orthogonal Vortex Interaction[END_REF][START_REF] Doolan | The Effect of a Preceding Blade on the Orthogonal Vortex Interaction[END_REF], analytical modeling [START_REF] Howe | On unsteady surface forces, and sound produced by the normal chopping of a rectilinear vortex[END_REF][START_REF] Marshall | Vortex Cutting by a Blade, Part 1: General Theory and a Simple Solution[END_REF] and numerical computations [START_REF] Krishnamoorthy | Three-dimensional blade-vortex interaction in the strong vortex regime[END_REF][START_REF] Marshall | Vortex Cutting by a Blade, Part II: Computation of Vortex Response[END_REF][START_REF] Marshall | Penetration of a blade into a vortex core: vorticity response and unsteady blade forces[END_REF][START_REF] Yin | Helicopter Main-Rotor/Tail-Rotor Interaction[END_REF][START_REF] Liu | Blade penetration into a vortex core with and without axial core flow[END_REF][START_REF] Filippone | Orthogonal blade-vortex interaction on a helicopter tail rotor[END_REF][START_REF] Saunders | Vorticity reconnection during vortex cutting by a blade[END_REF][START_REF] Saunders | Transient lift force on a blade during cutting of a vortex with non-zero axial flow[END_REF]. These studies came to the conclusion that OBVI is complex and exhibit various regimes depending on several non-dimensional parameters such as: the ratio of the vortex advection speed and vortex maximum tangential velocity, the ratio of the blade thickness and vortex core radius, the ratio of the vortex axial velocity deficit or excess and vortex maximum tangential velocity. Yet, most of the computations performed in the studies cited above were carried out considering untwisted rectilinear blades with translation motion, which is quite different to the blade/vortex interaction occurring on propellers and open rotors. In fact, the blade rotation, the rotor advance ratio, and the location of the interaction on the blade influence strongly the blade aeroacoustic response to the interaction. These parameters have started to be accounted for in recent studies launched to better understand and characterize OBVI [START_REF] Falissard | Investigation of Counter Rotating Open Rotor Orthogonal Blade/Vortex Interaction Noise[END_REF][START_REF] Delattre | Influence of Torque Ratio on Counter-Rotating Open-Rotor Interaction Noise[END_REF][START_REF] Delattre | Open rotor interaction noise reduction through front rotor wake modification[END_REF][START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF][START_REF] Yang | Propeller and inflow vortex interaction: vortex response and impact on the propeller performance[END_REF][START_REF] Yang | Aerodynamic impact of a streamwise vortex on a propeller[END_REF] in the context of open rotors and to improve the reliability of fast prediction methods [START_REF] Roger | On vortex-airfoil interaction noise including span-end effects, with application to open-rotor aeroacoustics[END_REF][START_REF] Quaglia | A 3D analytical model for orthogonal blade-vortex interaction noise[END_REF][START_REF] Moreau | Advanced noise modeling for future propulsion systems[END_REF].

Roger et al. [START_REF] Roger | On vortex-airfoil interaction noise including span-end effects, with application to open-rotor aeroacoustics[END_REF] showed by analytical means that for a Lamb-Oseen vortex interacting with a finite blade, the radiated noise is maximum when the vortex impinges exactly at the blade tip. The noise decreases as the impingement occurs closer to the blade root, and decreases even sharper as it occurs above the blade tip. Yang et al. [START_REF] Yang | Propeller and inflow vortex interaction: vortex response and impact on the propeller performance[END_REF][START_REF] Yang | Aerodynamic impact of a streamwise vortex on a propeller[END_REF] simulated the interaction of a propeller with a Batchelor vortex. They found that blade torque fluctuation increases as the interaction occurs closer to the blade tip and deduced that maximum torque fluctuation is obtained for an impingement at the blade tip. Zehner et al. [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF] focused on the relative influence of vortex axial and tangential velocities on the aerodynamic and acoustic response of the blade during the interaction. They showed that the vortex tangential velocity is responsible for the low-frequency content of the thrust fluctuation and noise radiation, whereas the axial velocity deficit in the vortex core accounts for the high-frequency content, with some constructive interference mechanism in between.

The present paper investigates the influence of the vortex impingement location on the blade aerodynamic and acoustic response to the interaction. It extends previous results and analyses [START_REF] Zehner | Influence of Blade Thickness and Blade Span on Orthogonal Blade/Vortex Interaction Noise[END_REF], with the objective to identify and quantify precisely the noise reduction achieved by reducing the blade span in order to avoid the vortex core during the interaction. The dimensionless parameters characterizing the vortex response [START_REF] Coton | Helicopter tail rotor orthogonal blade vortex interaction[END_REF] are the same as in Ref. [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF], resulting in a subcritical interaction in the weak-vortex regime where the cutting of the vortex by the blade does not alter significantly the vortex structure. For this type of interaction, Liu and Marshall [START_REF] Liu | Blade penetration into a vortex core with and without axial core flow[END_REF] have demonstrated that the physical mechanisms governing the cutting process are mostly inviscid, and that the flow physics is not particularly sensitive to Reynolds number. The governing equations solved for the current study are thus the unsteady Euler equations in the compressible regime, that have proven to capture the main physical phenomena of blade/vortex interaction with respect to blade aerodynamic and aeroacoustic responses [START_REF] Falissard | Computation of Airfoil Vortex Interaction Using a Vorticity-Preserving Scheme[END_REF].

To be as representative as possible, this study considers a Batchelor vortex model to account for the axial velocity deficit observed in the core of realistic tip vortices. However, aerodynamic preliminary design studies and optimizations are often carried out relying on fast prediction methods, for instance lifting line or panel methods, that cannot account for viscous features and results in tip vortices consisting only in tangential velocity fields. Simulations are thus also performed considering separately a Lamb-Oseen vortex and a purely axial velocity deficit to highlight and quantify the influence of the vortex velocity components on the interaction as well as to balance the results of design optimization performed relying on such methods.

The paper is organized as follows. Section II presents the blade geometries, vortex characteristics and numerical setup of the OBVI simulations carried out for this study. The results are presented and analyzed in section III, first from an aerodynamic viewpoint, and then from an aeroacoustic perspective.

II. Setup of the numerical experiment

The numerical setup is derived from the one used in a previous study to analyze the aeroacoustic response of a rotating blade interacting with a Batchelor vortex for an impingement located at 90% of the blade span [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF]. It consists in a single blade of external radius R 0 = 1 m, of inner radius R root = 0.2 m, with NACA 0002 airfoil section of chord C = 0.2 m, rotating with a tip Mach number M 0 = 0.65 within a coaxial flow of upstream Mach number M ∞ = 0.25, as sketched in Fig. 1. The vortex model considered in this study is a Batchelor vortex [START_REF] Batchelor | Axial flow in trailing line vortices[END_REF], with core radius r c = 2.5 × 10 -2 R 0 . The tangential velocity magnitude is set to one quarter of the blade tip helical velocity, v max θ = v Hel Tip /4 with v Hel Tip = (M 2 ∞ + M 2 0 ) 1/2 /c 0 , and c 0 the sound speed. The magnitude of the Gaussian axial velocity deficit in the core v max a is taken equal to v max θ . The infinite upstream flow in the reference frame attached to the vortex center is thus given by:

v θ = v max θ (1 -e -α 2 r 2 )/( r (1 -e -α 2 )) (1)
v x = v ∞ -v max a e -α 2 r 2 (2)
with α 1.121 so that the maximum tangential velocity is reached for r = 1. Density and pressure fields are calculated by integrating the radial equilibrium equation with an homentropic hypothesis. In order to better quantify the contribution to the interaction of the vortex tangential and axial velocity components, simulations have also been carried out considering separately a Lamb-Oseen vortex [START_REF] Oseen | Über Wirbelbewegung in einer reibenden Flüssigkeit[END_REF][START_REF] Lamb | Hydrodynamics, Sixth edition, chap. XI[END_REF], with tangential flow field given by eqn (1), and with a purely Gaussian axial velocity deficit of eqn [START_REF] Coton | Helicopter tail rotor orthogonal blade vortex interaction[END_REF].

The three dimensional unsteady compressible Euler simulations are computed using a near-body/off-body meshing strategy [START_REF] Péron | Automatic off-body overset adaptive Cartesian mesh method based on an octree approach[END_REF][START_REF] Benoit | Cassiopee: a CFD pre-and post-processing tool[END_REF], with a curvilinear blade mesh rotating within an octree of Cartesian meshes. Contrarily to viscosity, compressibility cannot be neglected a priori due to the relative high helical Mach number of the blade section interacting with the vortex core. Actually, depending on the vortex strength and blade thickness, flow acceleration at the blade leading edge could lead to the formation of supersonic pockets possibly resulting in the creation of vorticity or vortices due to the loss of colinearity of the density and pressure gradient (baroclinic term of the vorticity equation) through curved shocks [START_REF] Falissard | Computation of Airfoil Vortex Interaction Using a Vorticity-Preserving Scheme[END_REF].

The spatial discretization schemes are respectively third-order and fifth-order accurate [START_REF] Saunier | Third-order Cartesian overset mesh adaptation method for solving steady compressible flows[END_REF][START_REF] Saunier | High-order accurate Cartesian partitioning methods. Application to rotor flows[END_REF] on the near-body curvilinear meshes and background Cartesian meshes. The time integration is implicit and second-order accurate. The computational fluid dynamics (CFD) is coupled with an aeroacoustic integral method to compute the noise generated by the interaction. The Ffowcs-Williams and Hawkings equation [START_REF] Williams | Sound Generation by Turbulence and Surfaces in Arbitrary Motion[END_REF] is solved in its rotating solid surface formulation [START_REF] Prieur | Aeroacoustic integral methods, formulation and efficient numerical implementation[END_REF] to compute the noise radiated on a sphere of radius 20R 0 . The Fourier analysis of the time acoustic signal is performed for 100 harmonics of the Blade Passing Frequency (BPF ≈ 35.17 Hz). More details about the computational setup and its accuracy can be found in Ref. [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF].

In order to change the interaction location, only the blade span has been modified, all other parameters have been kept constant. For all cases the radius at which the vortex impinges on the blade is thus R Int = 0.9R 0 . The simulations have been run for seven blades with relative tip radii, defined as R * Tip = R Tip /R 0 , ranging from 0.818 to 1.125. These values have been chosen so that the relative interaction radius, defined as R * Int = R Int /R Tip , varies linearly between 0.8 and 1.1, see Tab. 1. The vortex core impinges at the blade tip for R * Int = 1, above for R * Int > 1, and below for R * Int < 1. The different blade geometries and surfaces affected by the blade/vortex interaction are represented in Fig. 2. For each blade geometry, three simulations were performed, one with a Batchelor vortex (tangential vortex with axial flow), one with a Lamb-Oseen vortex, and one with a Gaussian axial velocity deficit. Note that an extra computation for the smaller blade was done without vortex to quantify the numerical noise of the setup.

III. Results and discussions A. Blade aerodynamic response to the interaction

For an OBVI between a blade in translation motion and a vortex without axial velocity, the flow exhibits a symmetry between the upper and lower sides of the blade and no lift is created during the interaction. This is not the case anymore when a rotation motion is added to the blade. In this configuration, any flow disturbance will create an unsteady thrust component, positive or negative, depending on the modification of the velocity triangle at each radial station. The velocity triangles accounting for the Batchelor and Lamb-Oseen vortices, and axial velocity deficit are compared to the velocity triangles without perturbation in Fig. 3 for blade radial stations corresponding to the vortex center, and the vortex center plus or minus the vortex radius.

In case of an interaction with a Lamb-Oseen vortex exhibiting the same direction of rotation as the blade, the summation of the mean flow and vortex velocity components increases the relative velocity seen by the blade at R = R Intr c , and generates a positive incidence. At this radial station, the Lamb-Oseen vortex interaction results in a local upwash and a positive thrust fluctuation. At R = R Int + r c , we observe a decrease of the relative velocity as well as a negative incidence, resulting in a local downwash and a negative thrust fluctuation at this radial station during the interaction. Note that since the velocity is zero in the vortex core, the Lamb-Oseen vortex does not alter the relative velocity at R = R Int .

In case of an interaction with a purely axial velocity deficit, we observe in Fig. 3 a decrease of the norm of the relative velocity seen by the blade and a positive incidence for the three radial stations. The interaction with an axial velocity deficit leads to an upwash around the radial station R = R Int , and thus a positive thrust fluctuation. The maximum incidence is obtained at R = R Int .

Finally, for an interaction with a Bachelor vortex, whose velocity field is the summation of the Lamb-Oseen vortex and the axial velocity deficit, we observe an increase of the velocity norm and a strong positive incidence at radial station R = R Intr c , and a decrease of the velocity norm and a lesser negative incidence at radial station R = R Int + r c . The behavior at R = R Int is similar to the one observed for the axial velocity deficit. The Batchelor vortex generates an upwash, respectively a downwash, on the blade span below, respectively above, the interaction radius. Consequently, when the vortex core is chopped by the blade, the latter experiences a positive thrust fluctuation from the root and approximately up to the interaction radius and a negative thrust fluctuation on the upper part and up to the blade tip. This phenomenon can also be observed on the unsteady component of the pressure coefficient at the blade leading edge, plotted in Fig. 4, where the areas colored in red highlight the displacement of the stagnation point along the blade span during the interaction. Let us introduce the relative upwash velocity experienced Fig. 5 Relative upwash velocity induced by the vortex in the frame attached to the blade section at the azimuth of interaction.

(a) R = R Int -r c (b) R = R Int (c) R = R Int + r c
by the blade at the azimuth of interaction, defined by v * upwash = v upwash /v Hel , where v upwash is the projection of the instantaneous velocity on the direction normal to the blade chord, and v Hel is the kinematic helical velocity, i.e. the colored arrows in Fig. 3. The formula giving v * upwash was derived in Ref. [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF] from the vortex tangential and axial velocities, blade kinematics, and blade geometry. It is plotted in Fig. 5 as a function of the non-dimensional interaction radius R * Int . For a Batchelor vortex having tangential and axial velocity components of same magnitude, this upwash changes of sign slightly above the vortex center, resulting in a downwash on the external part of the blade. For a Lamb-Oseen vortex, this sign change occurs exactly at the vortex center while it is always positive for a purely axial velocity deficit. For the different blade spans considered in this study, it is thus expected that the maximum thrust fluctuation due to the OBVI will be reached for a vortex impingement radius corresponding to the sign change of the upwash.

The unsteady component of the blade thrust coefficient [START_REF] Nelson | Airplane propeller principles[END_REF], based on the reference blade radius and defined as C R 0 T = T/(16ρ ∞ n 2 R 4 0 ) with T the thrust, ρ the density, and n the blade angular frequency, is plotted in Fig. 6 for azimuth angles around the interaction. Only four cases are displayed to enhance readability. The interaction is clearly visible close to 360°and the thrust fluctuation has a larger magnitude and a steeper shape at its maximum for the Batchelor vortex than for the Lamb-Oseen vortex. This is due to the contribution of the axial velocity deficit in the vortex core that results in an impulsive and localized thrust fluctuation that adds itself to the thrust fluctuation due to the tangential velocity component. The highest thrust fluctuations are observed for interaction radii close to the blade tip, with a significant decrease when the vortex core impinges lower on the blade or passes above the blade tip. The maximal value of the thrust coefficient is plotted in Fig. 7 for all relative interaction radii of Tab. 1. For interactions with a Lamb-Oseen vortex, the magnitude of thrust fluctuation increases progressively with the interaction radius, reaching a maximum exactly at the blade tip. The peak of the thrust fluctuation is always greater for the Batchelor vortex with a similar rise as the blade tip is approached and a rapid fall when the vortex core passes above the blade tip. The magnitude is then almost equal for the two vortex models. The maximum value for the Batchelor vortex is reached for an interaction radius slightly before the tip, for R * Int between 0.95 and 1.

For each vortex model, the highest thrust fluctuation is reached when the whole blade experiences a positive velocity upwash during the interaction. For the Lamb-Oseen vortex, this happens when the vortex core impinges at the blade tip. For the Batchelor vortex, the flow incidence variation β depending on the blade section, derived in Ref. [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF], yields:

β = arctan v ∞ -v a (r -R Int ) -rΩ + v θ (r -R Int ) + arctan v ∞ rΩ (3)
where v ∞ is the upstream flow velocity, and Ω is the angular speed. Looking back at Fig. 3, the incidence variation β is the angle between the relative velocities seen by a blade section with and without flow pertubation. Its value is plotted for both vortex models and the purely axial velocity deficit in Fig. 8. The curve corresponding to the Batchelor vortex with tangential and axial velocities of same magnitude becomes negative for a radius slightly higher than the vortex center.

For our interaction parameters, equation ( 3) shows that β is positive for r ≤ 0.921 and negative for r ≥ 0.921, meaning that the blade aerodynamic response is maximum when the vortex core impacts just below the blade tip, for R * Tip = 0.921, i.e. R * Int = 0.977. This value is slightly below the one extrapolated by Yang et al. [START_REF] Yang | Aerodynamic impact of a streamwise vortex on a propeller[END_REF].

The pressure coefficient C p on the blade suction side at azimuth 360°is displayed in Fig. 9 for four relative interaction radii. The aerodynamic response of the blade to the OBVI is mostly located around the blade leading edge, extending from the blade root to the blade tip. This large extension is due to the low decay of the potential velocity field of the vortex and means that OBVI cannot be fully avoided by cropping a blade. The change of sign of the pressure coefficient on the suction side is located very close to R Int for the Lamb-Oseen vortex and is slightly shifted toward the blade tip for the Batchelor vortex in accordance with the variation of flow incidence displayed in Fig. 5. Finally it is noteworthy that the C p distribution on all blades is very close to the one that would be obtained by truncating the blade with the largest span.

B. Blade acoustic response to the interaction

The noise radiated in the far-field by the OBVI has been computed on a sphere of radius 20R 0 . The acoustic signatures have been Fourier-transformed and integrated to compute the over all sound power level (OASWL), plotted in Fig. 10. The trend observed on the OASWL is very similar to the one already observed on the thrust fluctuation displayed in Fig. 7. For interactions with a Lamb-Oseen vortex, the OASWL increases progressively as the vortex core moves toward the blade tip and decreases with a stronger rate as the vortex core passes the blade tip. This behavior is coherent with the results obtained by Roger et al. [START_REF] Roger | On vortex-airfoil interaction noise including span-end effects, with application to open-rotor aeroacoustics[END_REF] for this vortex model. For interactions with a Batchelor vortex, the OASWL increases also progressively as the vortex core moves toward the blade tip but the maximum is reached for R * Int between 0.95 and 1. Once the maximum is reached, the slope of the OASWL decreases drastically and for R * Int ≥ 1.05, the levels become the same for the two vortex models since the axial velocity deficit within the vortex core does not impinge on the blade anymore. The contribution of the axial velocity deficit results in an increase of 4 dB for R * Int ≤ 0.95 on the OASWL for the Batchelor vortex, and of 2 dB when the impact occurs at the blade tip. and its harmonics are plotted in Fig. 11 for a selection of blades, for the two vortex models and the axial velocity deficit. For the two blade-vortex interactions, the maxima are obtained for BPF = 2 and follow the trend observed for the OASWL, with highest levels for interactions near the blade tip. Consistently, SWLs are always higher for the interaction with the Batchelor vortex, with a significant contribution at high frequencies which is due to the axial component, as demonstrated in [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF].

Since this supplementary contribution vanishes as the vortex passes above the tip, the curves are identical for both vortex models for R * Int ≥ 1.05. For interactions with a Lamb-Oseen vortex, the SWLs decrease strongly and linearly up to a certain frequency after which the slope becomes less steep. This transition frequency varies with the radius of interaction on the blade. For interactions with a Batchelor vortex, the gentler slope of the spectra is due to the mid-and high-frequency contributions of the Gaussian velocity deficit in the vortex core [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF] also plotted in Fig. 11. Consequently, the gap between the Batchelor and Lamb-Oseen interactions increases with the frequency, and its amplitude is directly linked to the magnitude of the velocity deficit. For interactions with the Lamb-Oseen vortex, the frequency at which the change of slope occurs in the spectra cannot be linked to a specific component of the velocity field and appears to depend on the blade length. To investigate this point, acoustic directivities of tones below and above the transition frequency, around 10 BPF, have been plotted in Fig. 12 for the interaction at R * Int = 0.8. The directivity patterns are dipolar for frequencies lower than the transition frequency and quadrupolar for frequencies higher than the transition frequency. This means that the relative interaction radius act as a filter on the tangential velocity decomposition in the Fourier space. A simple analysis can be carried out based on the sketch drawn in Fig. 13. Fourier components of the vortex velocity whose wavelength are lower than twice the distance between the interaction radius and the blade tip are supported by the blade and will behave acoustically as two dipoles of opposite phase, thus leading to a quadrupolar directivity. On the contrary, Fourier components of the vortex velocity with larger wavelengths are not supported by the blade and will result only in an acoustic dipole on the blade span lower than the interaction radius. This reasoning on the transition frequency, noted f dq , between dipolar and quadrupolar directivities leads to the very simple formula:

f dq BPF = πR * Int 1 -R * Int ( 4
) (a) f = BPF (b) f = 11BPF (c) f = 21BPF
Fig. 12 Far-field acoustic directivity of selected tones for a Lamb-Oseen vortex interaction at R * Int = 0.8. According to this formula, the transition frequency exists for any relative interaction radius in the interval [0, 1]. This strengthens the results of Roger et al. [START_REF] Roger | On vortex-airfoil interaction noise including span-end effects, with application to open-rotor aeroacoustics[END_REF] who observed a transition from quadrupolar to dipolar directivity patterns when accounting for blade span-end effect. The predicted frequency, plotted in Fig. 14, is compared to the transition frequency measured for Lamb-Oseen vortex interactions at different blade radii. Predicted values are very accurate for R * Int ≤ 0.9 but precision diminishes as the interaction moves to the blade tip, notably due to the difficulty to identify clearly f dq in the spectra.

Finally, the over all sound pressure level (OASPL) directivities are displayed in Fig. 15. For OBVI close to or above the blade tip (R * Int ≥ 0.9), OASPL directivities exhibit a dipolar pattern for the two vortex models. For R * Int = 0.8, the directivity pattern of the OASPL radiated by the interaction with a Lamb-Oseen is mainly quadrupolar and this quadrupolar pattern seems partly present in the OASPL directivity of the interaction with the Batchelor vortex. Shifting the interaction radius toward the inner section of the blade would thus reduce the radiated OASWL and change the directivity into a quadrupolar pattern rather than a dipolar one.

IV. Conclusion

The influence of vortex model and blade span on orthogonal blade/vortex interaction has been studied by means of numerical simulation relying on a validated methodology detailed in Ref. [START_REF] Zehner | Aeroacoustic study of the interaction of a rotating blade with a Batchelor vortex[END_REF]. The vortex model primarily considered in this study is the Batchelor vortex, which exhibits a velocity field with tangential and axial components as do realistic tip vortices. To gain insight and deepen the analysis, simulations have also been carried out using a Lamb-Oseen vortex (azimuthal velocity only), and a purely Gaussian axial velocity deficit. Changing the vortex impingement radius on the blade is achieved by increasing or reducing the blade span and seven relative interaction radii, ranging from 0.8 to 1.1, were studied.

The main results based on the analysis of the blade aerodynamic and acoustic responses are the following: when the vortex core impinges below the blade tip, the magnitude of the thrust fluctuation and radiated noise are always higher for a Batchelor vortex than for a Lamb-Oseen vortex. For both vortex models, the thrust fluctuation and radiated noise reach their peak for an interaction close to the blade tip, exactly at the tip for a Lamb-Oseen vortex and just below (R * Int = 0.98) for the Batchelor vortex. The aerodynamic and acoustic responses decrease slowly as the vortex impingement moves inward the blade and decrease strongly as the vortex passes above the tip. Finally, the noise directivity pattern is dipolar for interaction close to or above the blade tip and becomes more and more quadrupolar as the radius of interaction moves toward the blade root. As a consequence, design optimization aiming at propeller/vortex interaction noise should not focus on sound power level only but account also for the directivity of the interaction noise.

Fig. 1

 1 Fig. 1 Scheme of the blade/vortex interaction.

Fig. 2

 2 Fig. 2 Area of blade/vortex interaction depending on the blade span.

Fig. 3

 3 Fig. 3 Velocity triangle modifications at blade azimuth zero and at different blade radii depending on the velocity perturbations added to the meanflow. No perturbation ( ), Batchelor vortex ( ), Lamb-Oseen vortex ( ), axial velocity deficit ( ).

Fig. 4

 4 Fig. 4 Pressure coefficient fluctuation and streamlines on the blade leading edge at azimuth 0 deg for the interaction at R * Tip = 1 (i.e. R * Int = 0.9) with different flow perturbations. Blade thickness enlarged for visualisation.

  (a) Batchelor vortex. (b) Lamb-Oseen vortex. (c) Axial deficit.

Fig. 6

 6 Fig. 6 Evolution of thrust coefficient during orthogonal blade/vortex interaction for different values of R * Int .

Fig. 7

 7 Fig. 7 Maximum value of thrust coefficient as a function of R * Int .

Fig. 8

 8 Fig. 8 Variation of flow incidence induced by the vortex in the frame attached to the blade section.

Fig. 9

 9 Fig. 9 Pressure coefficient C p on the blade suction side for different blade spans. Blade at azimuth 360°.

  (a) Batchelor vortex. (b) Lamb-Oseen vortex. (c) Axial deficit.

Fig. 11

 11 Fig. 11 Radiated sound power levels depending on R * Int

Fig. 13 Filtering

 13 Fig. 13 Filtering of the velocity upwash by the blade.

Fig. 14

 14 Fig. 14 Predicted and measured transition frequency between dipolar and quadrupolar directiviy patterns.

  (a) Batchelor vortex. (b) Lamb-Oseen vortex.(c) Axial velocity deficit.

Fig. 15 OASPL

 15 Fig. 15 OASPL acoustic directivity in far-field.

Table 1

 1 Relative blade tip and blade/vortex interaction radii.

	R * Tip	0.818 0.857 0.9 0.947 1	1.059 1.125
	R * Int	1.1	1.05	1	0.95	0.9 0.85	0.8

Acknowledgments

The authors thank Yves Delrieux and Stéphanie Péron for their advises and technical support during this study.


Nathalie Beaujean
email: nathalie.beaujean@jouy.inra.fr

Epigenetics, embryo quality and developmental potential

Keywords: chromatin, development, reprogramming, environment, histone post-translational modifications, DNA methylation Running head: Epigenetics and embryo quality

It is very important for embryologists to understand how parental inherited genomes are reprogrammed after fertilization in order get good quality embryos that will sustain further development. In mammals, it is now well established that important epigenetic modifications occur after fertilization. While gametes carry special epigenetic signatures, they should attain embryo-specific ones, some of which are crucial to produce healthy embryos. Indeed, it appears that proper establishment of the different epigenetic modifications and subsequent scaffolding of the chromatin are crucial steps during the first cleavages. This "reprogramming" is promoted by the intimate contact between the parental inherited genomes and the oocyte cytoplasm after fusion of the gametes. This review aims at introducing two main epigenetic players: histone post-translational modifications and DNA methylation as well as the importance of their role during early embryonic development.

Introduction: epigenetics and chromatin compaction

Epigenetics is currently defined heritable changes of genomic activities that occur without change in the DNA sequence [START_REF] Goldberg | Epigenetics: a landscape takes shape[END_REF]. These epigenetic changes orchestrate chromatin remodelling and dictate heritable patterns of gene expression. Epigenetic control is mainly achieved by chemical modifications, which can be propagated through mitosis, and in some cases through meiosis [START_REF] Bonasio | Molecular signals of epigenetic states[END_REF]. These changes include DNA methylation/hydroxymethylation and post-translational modifications of histone tails (e.g. acetylation, phosphorylation, methylation.....) as well as chromatin structure and nuclear architecture [START_REF] Bernstein | The mammalian epigenome[END_REF][START_REF] Schneider | Dynamics and interplay of nuclear architecture, genome organization, and gene expression[END_REF].

DNA methylation in mammalian cells is mostly found on Cytosines from CpG dinucleotides. DNA methyl-transferases (DNMT) are the enzymes responsible for this modification, and are divided in two groups: the maintenance DNMT1, which insures that DNA methylation patterns are copied on newly-synthesized DNA during replication; and the de novo DNMT 3A and 3B, which establish methylation on new regions [START_REF] Jin | DNA methylation: superior or subordinate in the epigenetic hierarchy?[END_REF]. The opposite reaction, demethylation, can occur in two ways: 1) passive demethylation results from the absence of DNMT 1, leading to a progressive loss of methylation through cellular divisions; 2) an active mechanism that has long remained elusive as no DNA demethylase could be identified. However, the discovery of 5hydroxymethylcytosine (5-hmeC), which is obtained through 5-meC oxidation, in embryonic stem cells (ESC) has provided new insights in the field [START_REF] Tahiliani | Conversion of 5-methylcytosine to 5-hydroxymethylcytosine in mammalian DNA by MLL partner TET1[END_REF][START_REF] Ito | Role of Tet proteins in 5mC to 5hmC conversion , ES-cell self-renewal and inner cell mass specification[END_REF]. This reaction is catalyzed by enzymes of the Ten Eleven Translocation (TET) family, that can further oxidize 5-hmeC into 5-formylcytosine (5-fC) and 5-carboxylcytosine (5-caC) [START_REF] He | Tet-mediated formation of 5-carboxylcytosine and its excision by TDG in mammalian DNA[END_REF][START_REF] Ito | Tet proteins can convert 5-methylcytosine to 5-formylcytosine and 5-carboxylcytosine[END_REF]. 5-fC and 5-caC can then be removed by Thymidine-DNA Glycosylase (TDG) mediated excision [START_REF] He | Tet-mediated formation of 5-carboxylcytosine and its excision by TDG in mammalian DNA[END_REF][START_REF] Maiti | Thymine DNA glycosylase can rapidly excise 5-formylcytosine and 5carboxylcytosine: potential implications for active demethylation of CpG sites[END_REF][START_REF] Zhang | The Involvement of 5-Hydroxymethylcytosine in Active DNA Demethylation in Mice[END_REF].

On the other hand, N-terminal histone tail, which emanates out of the nucleosome, the fundamental unit of the chromatin, can be targeted by enzymes that allow post-translational modifications on various residues: lysine residues can for example be either acetylated, methylated or coupled to ubiquitin [START_REF] Peterson | Histones and histone modifications[END_REF][START_REF] Kouzarides | Chromatin modifications and their function[END_REF]. Moreover, some residues can be modified several times (eg. di-or tri-methylated). There are several "chromatin-modifying" enzymes such as histone acetylases (HATs) and deacetylases (HDACs) that coordinate acetylation/deacetylation; the histone kinase family and phosphatases acting on phosphorylation/dephosphorylation or the histone methyltransferases (HMTs) and lysine demethylases (KDMs) able to add/remove methyl groups [START_REF] Peterson | Histones and histone modifications[END_REF][START_REF] Tsukada | Histone demethylation by a family of JmjC domain-containing proteins[END_REF][START_REF] Black | Histone lysine methylation dynamics: establishment, regulation, and biological impact[END_REF]. Among histone post-translational modifications, acetylation has the highest potential to "open" chromatin, since it neutralizes the basic charge of lysine residues, decreasing their binding to DNA [START_REF] Hasan | Histone acetyl transferases: a role in DNA repair and DNA replication[END_REF]. Acetylation is therefore often associated to gene expression, whereas histones in condensed chromatin areas are relatively hypoacetylated but marked by the presence of methylation such as histone H3 lysine 9 trimethylation (H3K9me3) [START_REF] Schneider | Dynamics and interplay of nuclear architecture, genome organization, and gene expression[END_REF]. This epigenetic information is not uniform, but is applied regionally, and it signals or preserves local activity status, such as gene transcription or silencing. Epigenetic modifications are indeed found at functionally distinct regions of the genome (coding regions, promoters and enhancers) where they function as "on/off" switches which can modulate chromatin structure and drive gene expression. Whereas genes provide the framework for the manufacture of RNAs and proteins, chromatin structure and nuclear architecture control the accessibility of proteins to the DNA, especially transcription factors and RNA polymerase, and thereby gene expression [START_REF] Schneider | Dynamics and interplay of nuclear architecture, genome organization, and gene expression[END_REF]. Moreover, as epigenetic modifications can modulate the contacts between the nucleosomes and the chromatin, they can lead to either compaction or relaxation of the DNA fiber. They can therefore not only "open/close" regions for transcription but also play essential roles in DNA repair, DNA replication and chromosome condensation during mitosis [START_REF] Peterson | Histones and histone modifications[END_REF][START_REF] Kouzarides | Chromatin modifications and their function[END_REF]; [START_REF] Schneider | Dynamics and interplay of nuclear architecture, genome organization, and gene expression[END_REF]. Finally, epigenetic modifications also participate in the distinction of the two main types of chromatin domains: euchromatin, which is gene-rich, lightly packed, and heterochromatin, known as being gene-poor, which is tightly packed. Euchromatin is more accessible to the transcriptional machinery thanks to its "open state" configuration; whereas heterochromatin, has a more "repressive" chromatin structure and contains mainly silent transcriptional genes [START_REF] Grewal | Heterochromatin and epigenetic control of gene expression[END_REF][START_REF] Grewal | Heterochromatin revisited[END_REF][START_REF] Jost | Heterochromatin and gene positioning: inside, outside, any side?[END_REF]. In mammals, the degree of heterochromatin clustering varies with cell type, cell cycle phase and differentiation stage [START_REF] Alcobia | Spatial associations of centromeres in the nuclei of hematopoietic cells: evidence for cell-type-specific organizational patterns[END_REF][START_REF] Bartova | Nuclear architecture in the light of gene expression and cell differentiation studies[END_REF]. Within the nucleus of interphase somatic cells for example, heterochromatin located at the centromeric and pericentromeric regions from different chromosomes gather into foci which form very compact clusters, intensely stained by DNA dyes [START_REF] Alcobia | Spatial associations of centromeres in the nuclei of hematopoietic cells: evidence for cell-type-specific organizational patterns[END_REF][START_REF] Guenatri | Mouse centric and pericentric satellite repeats form distinct functional heterochromatin[END_REF]. It should be noted that epigenetic modifications often recruit non-histone proteins such as the CBX (ChromoBoX) or MBD (Methyl-CpG-binding domain) proteins, which mediate downstream chromatin compaction and accessibility [START_REF] Kutateladze | SnapShot: Histone Readers[END_REF]. In somatic cells, pericentric heterochromatin is for example characterized by trimethylation of the histone H3 at Lysine 9 which recruits ChromoBox protein homolog 1 (CBX1 or Heterochromatin Protein 1) [START_REF] Festenstein | Modulation of heterochromatin protein 1 dynamics in primary mammalian cells[END_REF][START_REF] Hiragami | Heterochromatin protein 1: a pervasive controlling influence[END_REF].

The whole epigenetic information is termed the epigenome. Unlike the genome, the epigenome is highly variable between cells of each individual and fluctuates in time according to environmental conditions even within a single cell. There are at least as many epigenomes as there are cell types. It is therefore widely thought that epigenetics play key role in cellular identity [START_REF] Bernstein | The mammalian epigenome[END_REF][START_REF] Keenen | Chromatin Remodeling in Embryonic Stem Cells : Regulating the Balance Between Pluripotency and Differentiation[END_REF][START_REF] Roper | Defining pathways that enforce cell lineage specification in early development and stem cells[END_REF].

Epigenetics in preimplantation embryos

Research in recent years has shown that epigenetic changes play a key role in embryonic development. Indeed, in mammals, the first stages of development are the siege of important genome rearrangements and epigenetic modifications, which are thought to play a very important part in Embryonic Genome Activation (EGA). After fertilization, the genome of the newly formed embryo is transcriptionally silent and its development is sustained by maternally inherited RNA and proteins. The embryonic genome will then take over progressively: in most species a first "minor" activation will take place very early, by the end of the 1-cell stage [START_REF] Christians | Sequential acquisition of transcriptional control during early embryonic development in the rabbit[END_REF][START_REF] Bouniol | Endogenous transcription occurs at the 1-cell stage in the mouse embryo[END_REF][START_REF] Memili | Control of gene expression at the onset of bovine embryonic development[END_REF]. Rapid increase in the synthesis of transcripts known as "major activation" then follows and the embryonic contribution becomes more important than the maternal one. The timing of this major activation varies between mammalian species: mouse appears an exception, as it occurs very early (at 2-cell stage) [START_REF] Flach | The transition from maternal to embryonic control in the 2-cell mouse embryo[END_REF][START_REF] Nothias | Regulation of gene expression at the beginning of mammalian development[END_REF], while in most other mammals major EGA starts later: at 4-cell stage in human [START_REF] Braude | Human gene expression first occurs between the four-and eight-cell stages of preimplantation development[END_REF], 8-cell stage in bovine and rabbit [START_REF] Camous | Cleavage beyond the block stage and survival after transfer of early bovine embryos cultured with trophoblastic vesicles[END_REF][START_REF] Pacheco-Trigon | Molecular characterization of genomic activities at the onset of zygotic transcription in mammals[END_REF], and 16-cell stage in sheep embryos [START_REF] Crosby | Control of protein synthesis during early cleavage of sheep embryos[END_REF]. Importantly, failure to activate properly the embryonic genome leads to developmental arrest [START_REF] Flach | The transition from maternal to embryonic control in the 2-cell mouse embryo[END_REF][START_REF] Bolton | The relationship between cleavage, DNA replication, and gene expression in the mouse 2-cell embryo[END_REF].

DNA methylation

During these early stages of development, DNA methylation changes drastically: while most of the paternal genome is rapidly and actively demethylated, methylation of the maternal genome is lost progressively [START_REF] Mayer | Demethylation of the zygotic paternal genome[END_REF][START_REF] Oswald | Active demethylation of the paternal genome in the mouse zygote[END_REF][START_REF] Santos | Dynamic reprogramming of DNA methylation in the early mouse embryo[END_REF], [START_REF] Rougier | Chromosome methylation patterns during mammalian preimplantation development[END_REF]. Upon fertilization, the genomes of maternal and paternal origin form two distinct haploid pronuclei (PN) that remain physically separated up to the first mitotis [START_REF] Adenot | Differential H4 acetylation of paternal and maternal chromatin precedes DNA replication and differential transcriptional activity in pronuclei of 1-cell mouse embryos[END_REF]. During the first cell cycle in the mouse, the paternal PN undergoes active DNA demethylation but the maternal PN resists demethylation [START_REF] Santos | Dynamic reprogramming of DNA methylation in the early mouse embryo[END_REF].This striking asymmetry between the two parental genomes is lost as the maternal genome later undergoes passive demethylation, in the absence of the maintenance methyltransferase DNMT1 during the replication phases of the subsequent cell cycles [START_REF] Cardoso | DNA methyltransferase is actively retained in the cytoplasm during early development[END_REF]. This discrepancy between the two parental genomes has clearly been demonstrated in mouse but is less evidenced in other species [START_REF] Abdalla | Active demethylation of paternal genome in mammalian zygotes[END_REF]. Studies have indeed been led in many mammalian species, giving more contrasted results suggesting that DNA methylation dynamics were not fully conserved. We, for example, showed that paternal genome rapid demethylation does do not take place in sheep or rabbit one-cell embryos (Beaujean et al., 2004a;[START_REF] Young | DNA methylation in the preimplantation embryo: the differing stories of the mouse and sheep[END_REF][START_REF] Reis Silva | Dynamics of DNA methylation levels in maternal and paternal rabbit genomes after fertilization[END_REF] and that sheep, rabbit and monkey embryos are not fully demethylated during preimplantation development (Beaujean et al., 2004b;[START_REF] Yang | Epigenetic marks in cloned rhesus monkey embryos: comparison with counterparts produced in vitro[END_REF][START_REF] Reis E Silva | Alteration of DNA demethylation dynamics by in vitro culture conditions in rabbit pre-implantation embryos[END_REF]. Our work emphasizes the importance of proper staging of the embryos to establish a real kinetics and the importance of image acquisition/quantification (Beaujean et al., 2004b;[START_REF] Reis Silva | Dynamics of DNA methylation levels in maternal and paternal rabbit genomes after fertilization[END_REF][START_REF] Salvaing | 5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote[END_REF]. It corroborates the work from Park and colleagues on bovine and rabbit embryos [START_REF] Park | Dynamic DNA Methylation Reprogramming : Active Demethylation and Immediate Remethylation in the Male Pronucleus of Bovine Zygotes[END_REF]. In fact, in both species, an initial decrease in 5-meC staining is observed but is followed by an increase in the paternal PN at the end of the 1-cell stage [START_REF] Park | Dynamic DNA Methylation Reprogramming : Active Demethylation and Immediate Remethylation in the Male Pronucleus of Bovine Zygotes[END_REF]; Reis e [START_REF] Reis Silva | Dynamics of DNA methylation levels in maternal and paternal rabbit genomes after fertilization[END_REF]. Similarly, while very few studies are available on human embryos, they agree that there is limited demethylation of the paternal PN at the 1-cell stage (Beaujean et al., 2004a;[START_REF] Fulka | DNA methylation pattern in human zygotes and developing embryos[END_REF], and limited demethylation over the next cleavages [START_REF] Fulka | DNA methylation pattern in human zygotes and developing embryos[END_REF][START_REF] Santos | Evaluation of epigenetic marks in human embryos derived from IVF and ICSI[END_REF]. Finally, we and others also pointed out recently that DNA demethylation of the paternal pronucleus of mouse embryos is not as complete as the initial studies suggested [START_REF] Li | Persistence of cytosine methylation of DNA following fertilisation in the mouse[END_REF][START_REF] Salvaing | 5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote[END_REF]: in particular, it remains particularly strong on heterochromatin regions located at the periphery of the nucleoli.

The mechanism of this active demethylation has long remained elusive, but recent breakthroughs have been made with the finding that TET proteins can convert 5-meC to 5-hmeC. In mouse embryos, the first studies emphasized the complementarity observed between 5-hmeC and 5-meC stainings during the first cell cycle [START_REF] Gu | The role of Tet3 DNA dioxygenase in epigenetic reprogramming by oocytes[END_REF][START_REF] Iqbal | Reprogramming of the paternal genome upon fertilization involves genome-wide oxidation of 5-methylcytosine[END_REF][START_REF] Ruzov | Lineage-specific distribution of high levels of genomic 5-hydroxymethylcytosine in mammalian development[END_REF][START_REF] Wossidlo | 5-Hydroxymethylcytosine in the mammalian zygote is linked with epigenetic reprogramming[END_REF]. Indeed, following active demethylation of the paternal genome, 5-hmeC seems to replace 5-meC and increases. 5-hmeC is then present during all mouse preimplantation development [START_REF] Iqbal | Reprogramming of the paternal genome upon fertilization involves genome-wide oxidation of 5-methylcytosine[END_REF][START_REF] Ruzov | Lineage-specific distribution of high levels of genomic 5-hydroxymethylcytosine in mammalian development[END_REF]. It has been suggested to be lost passively (Inoue and Zhang, 2011) or by further oxidation in 5-fC and 5-caC which are detected at least until the 4-cell stage (Inoue et al., 2011). However, we demonstrated that in 1-cell mouse embryos, 5-meC/5-hmeC stainings are not 100% complementary and that 5-hmeC is not a simple intermediate in an active demethylation process; it could play a role on its own during early development [START_REF] Salvaing | 5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote[END_REF]. Indeed, several lines of evidence indicate that the role of DNA methylation derivatives cannot be reduced to intermediates in the demethylation process. In particular, in ES cells, 5-hmeC plays a role in the regulation of transcriptional activity and seems mainly associated with "open" chromatin structures [START_REF] Ficz | Dynamic regulation of 5-hydroxymethylcytosine in mouse ES cells and during differentiation[END_REF][START_REF] Pastor | Genome-wide mapping of 5-hydroxymethylcytosine in embryonic stem cells[END_REF][START_REF] Song | Selective chemical labeling reveals the genome-wide distribution of 5-hydroxymethylcytosine[END_REF][START_REF] Williams | TET1 and hydroxymethylcytosine in transcription and DNA methylation fidelity[END_REF][START_REF] Wu | Dual functions of Tet1 in transcriptional regulation in mouse embryonic stem cells[END_REF]Xu et al., 2011;[START_REF] Kubiura | Chromosome-wide regulation of euchromatin-specific 5mC to 5hmC conversion in mouse ES cells and female human somatic cells[END_REF]. Remarkably, we have shown the existence of a peak of 5-hmeC in both PN coinciding with the minor EGA in mouse [START_REF] Salvaing | 5-Methylcytosine and 5-Hydroxymethylcytosine Spatiotemporal Profiles in the Mouse Zygote[END_REF] although activation of LINE-1 (long interspersed nucleotide element 1) and ERVL (endogenous retroviruses class III) transposable elements, that occurs in both paternal and maternal genomes in 1-cell mouse embryos, does not seem to be mediated by 5-meC oxidation [START_REF] Inoue | Transcriptional activation of transposable elements in mouse zygotes is independent of Tet3-mediated 5-methylcytosine oxidation[END_REF].

Finally, at the blastocyst stage, the first lineage specifications appear between inner cell mass (ICM) and trophectoderm cells that will give rise to the fetus and to (parts of) the extra embryonic tissues, respectively [START_REF] Wang | Roadmap to embryo implantation: clues from mouse models[END_REF]. At that stage, DNA methylation is asymmetrically distributed between these two types of cells in most species showing high levels of 5-meC within the ICM [START_REF] Fulka | DNA methylation pattern in human zygotes and developing embryos[END_REF][START_REF] Santos | Evaluation of epigenetic marks in human embryos derived from IVF and ICSI[END_REF][START_REF] Deshmukh | DNA methylation in porcine preimplantation embryos developed in vivo and produced by in vitro fertilization, parthenogenetic activation and somatic cell nuclear transfer[END_REF][START_REF] Ruzov | Lineage-specific distribution of high levels of genomic 5-hydroxymethylcytosine in mammalian development[END_REF][START_REF] Reis E Silva | Alteration of DNA demethylation dynamics by in vitro culture conditions in rabbit pre-implantation embryos[END_REF]. Furthermore, DNA methylation changes appear to be necessary for the establishment of pluripotency [START_REF] Farthing | Global mapping of DNA methylation in mouse promoters reveals epigenetic reprogramming of pluripotency genes[END_REF] and are essential to sustain full term development [START_REF] Li | Targeted mutation of the DNA methyltransferase gene results in embryonic lethality[END_REF][START_REF] Tate | The methyl-CpG binding protein MeCP2 is essential for embryonic development in the mouse[END_REF]. On the other hand, knockdown of Tet1 in mouse pre-implantation embryos results in a bias towards trophectoderm differentiation, suggesting a role of TET1 protein in ICM specification [START_REF] Ito | Role of Tet proteins in 5mC to 5hmC conversion , ES-cell self-renewal and inner cell mass specification[END_REF]. It was also recently shown in pig that TET 1 and TET3 enzymes are both playing an important role during early embryogenesis, especially regarding the expression of NANOG at the blastocyst stage [START_REF] Lee | Dynamics of TET family expression in porcine preimplantation embryos is related to zygotic genome activation and required for the maintenance of NANOG[END_REF].

Histone post-translational modifications

Histone post-translational modifications reinforce epigenetic asymmetry between the paternal and maternal genomes after fertilization. After fertilization, protamines inherited from the sperm are actively exchanged with oocyte inherited histones resulting in a rapid decondensation of the paternal genome [START_REF] Adenot | Dynamics of paternal chromatin changes in live one-cell mouse embryo after natural fertilization[END_REF][START_REF] Van Der Heijden | Sperm-derived histones contribute to zygotic chromatin in humans[END_REF]. In mouse, this decondensation is clearly associated with a more rapid increase of histone acetylation in the paternal pronucleus [START_REF] Adenot | Differential H4 acetylation of paternal and maternal chromatin precedes DNA replication and differential transcriptional activity in pronuclei of 1-cell mouse embryos[END_REF][START_REF] Van Der Heijden | Transmission of modified nucleosomes from the mouse male germline to the zygote and subsequent remodeling of paternal chromatin[END_REF][START_REF] Santenard | Heterochromatin formation in the mouse embryo requires critical residues of the histone variant H3.3[END_REF]. Conversely, the maternal genome is more methylated as compared to the paternal one: H3K4, H3K9 and H3K27 methylation are higher in the maternal PN, although histones of the paternal PN become progressively methylated during the first cell cycle [START_REF] Lepikhov | Differential dynamics of histone H3 methylation at positions K4 and K9 in the mouse zygote[END_REF][START_REF] Santos | Dynamic chromatin modifications characterise the first cell cycle in mouse embryos[END_REF][START_REF] Yeo | Methylation changes of lysine 9 of histone H3 during preimplantation mouse development[END_REF]. Similarly, in bovine, we observed that both H3K9me3 and H3K27me3 are asymmetrically distributed between the two inherited parental genomes, with specific targeting of the maternal genome as in mouse [START_REF] Breton | Nuclear Profiles of H3 Histones Trimethylated on Lys27 in Bovine (Bos taurus) Embryos Obtained after In Vitro Fertilization or Somatic Cell Nuclear Transfer[END_REF][START_REF] Pichugin | Dynamics of constitutive heterochromatin: two contrasted kinetics of genome restructuring in early cloned bovine embryos[END_REF]. Asymmetric staining of H3K27me3 has also been observed pig [START_REF] Bogliotti | Mechanisms of histone H3 lysine 27 trimethylation remodeling during early mammalian development[END_REF]. On the other hand, we recently showed that H3K36me3 displays mostly undetectable and heterogeneous localization pattern throughout bovine pre-implantation development in contrast to mouse [START_REF] Bošković | Analysis of active chromatin modifications in early mammalian embryos reveals uncoupling of H2A.Z acetylation and H3K36 trimethylation from embryonic genome activation[END_REF], indicating again that the dynamics of some epigenetic marks is not conserved between all mammalian species. Thereafter, histone modifications levels can be maintained up to the blastocyst stage, completely disappear or disappear and reappear later, usually after EGA [START_REF] Beaujean | Histone post-translational modifications in preimplantation mouse embryos and their role in nuclear architecture[END_REF].

From a functional point of view, it is hypothesized that this asymmetry may be required for proper embryonic development, especially during the onset of the minor phase of EGA. The reprogramming of the paternal genome that becomes hyperacetylated and hypomethylated may indeed increase chromatin flexibility and allow the minor EGA at the end of the 1-cell stage [START_REF] Aoki | Regulation of transcriptional activity during the first and second cell cycles in the preimplantation mouse embryo[END_REF][START_REF] Bouniol-Baly | Dynamic organization of DNA replication in onecell mouse embryos: relationship to transcriptional activation[END_REF]. Remarkably, the major satellites repeated sequences located in the pericentromeric regionsare among the first sequences transcribed at that stage, especially the paternal ones, and are clearly required for further development [START_REF] Probst | A Strand-Specific Burst in Transcription of Pericentric Satellites Is Required for Chromocenter Formation and Early Mouse Development[END_REF]. Reprogramming of histone modifications is also involved in the major EGA [START_REF] Beaujean | Histone post-translational modifications in preimplantation mouse embryos and their role in nuclear architecture[END_REF]. Increasing histone acetylation with a histone deacetylase inhibitor (HDACi), can for example stimulate global transcription by 60% in mouse embryos at major EGA [START_REF] Aoki | Regulation of transcriptional activity during the first and second cell cycles in the preimplantation mouse embryo[END_REF]. Reversely, inhibition of H3K4 demethylation induces aberrant expression of Oct4 and inhibits the cleavage to 4-cell [START_REF] Shao | Role of histone methylation in zygotic genome activation in the preimplantation mouse embryo[END_REF]. Similarly, we showed that components of the PRC1 complex that binds H3K27me3, serve transcriptional functions during oogenesis that are essential for proper EGA and further development [START_REF] Posfai | Polycomb function during oogenesis is required for mouse embryonic development[END_REF]. Altogether it appears that histone modifications are closely related with the formation of an "open" chromatin state allowing transcription and that they participate in the regulation of gene expression during preimplantation development.

Conversely, the enzymes "writing" and "erasing" these histone modifications from the genome are of prime importance: inactivation of KMT5A catalyzing methylation of H4K20, for example, induces early embryonic lethality prior to the 8-cell stage [START_REF] Oda | Monomethylation of histone H4-lysine 20 is involved in chromosome structure and stability and is essential for mouse development[END_REF]. Similarly, after deletion of JMJD2C, the H3K9me3 demethylase, embryos stop developing before the blastocyst stage [START_REF] Wang | The histone demethylase JMJD2C is stage-specifically expressed in preimplantation mouse embryos and is required for embryonic development[END_REF]. Similarly, in bovine, the activity of JMJD3, an enzyme with lysine-specific histone demethylase activity, is necessary for the reprogramming of H3K27me3 and for normal embryonic development [START_REF] Canovas | Jumonji domain-containing protein 3 regulates histone 3 lysine 27 methylation during bovine preimplantation development[END_REF].

At the blastocyst stage, some histone modifications have been found to differ between the ICM and the trophectoderm (TE) [START_REF] Beaujean | Histone post-translational modifications in preimplantation mouse embryos and their role in nuclear architecture[END_REF]. In mouse, this is the case for histone H4/H2A serine 1 phosphorylation (H4/H2AS1P) which is more intense in the TE [START_REF] Sarmento | Dynamic alterations of specific histone modifications during early murine development[END_REF]. Reversely, methylation of H3K27 presents a strong overall staining of the ICM while TE cells show a particularly intense staining concentrated on the inactive X chromosome [START_REF] Erhardt | Consequences of the depletion of zygotic and embryonic enhancer of zeste 2 during preimplantation mouse development[END_REF]. However, species differences are again observed: the onset of X chromosome inactivation for example differs completely between mouse and human or rabbit embryos [START_REF] Okamoto | Eutherian mammals use diverse strategies to initiate X-chromosome inactivation during development[END_REF]. Remarkably, the presence of histone modifications differences between the ICM and TE is in line with the results from gene analysis by use of carrier ChIP (CChIP) in mouse embryos [START_REF] Vermilyea | Transcription-independent heritability of induced histone modifications in the mouse preimplantation embryo[END_REF]. In the ICM, where Nanog and Oct4 are highly expressed, the promoters of both genes are enriched in H4K8ac and H3K4me3 whereas in the TE, where Nanog and Oct4 are silent, their promoters are enriched in H3K9me2. The opposite epigenetic patterns are observed for Cdx2 which is silent in the ICM and highly expressed in the TE. This relationship between histone modifications and gene expression has also been underlined by experiments targeting the corresponding regulatory enzymes. In the mouse blastocysts, upregulation of H3R26 methyltransferase CARM1 for example has been shown to induce the upregulation of the ICM pluripotency markers NANOG and SOX2 [START_REF] Torres-Padilla | Histone arginine methylation regulates cell fate and pluripotency in the early mouse embryo[END_REF], whereas depletion of H3K27 lysine-specific demethylase KDM6B abrogates CDX2 and GATA3 expression in the nascent TE-lineage and leads to implantation failures [START_REF] Saha | EED and KDM6B Coordinate First Mammalian Cell Lineage Commitment to Ensure Embryo Implantation[END_REF].

Nuclear Transfer as a model

The relevance of chromatin epigenetic modifications during preimplantation development has been sustained by studies on cloned embryos derived from nuclear transfer (NT).

Since Dolly the sheep, NT has been achieved in a variety of mammalian species [START_REF] Rodriguez-Osorio | Reprogramming mammalian somatic cells[END_REF]. NT has potential applications for human health (eg. the derivation of patient-specific stem cells; [START_REF] Tachibana | Human embryonic stem cells derived by somatic cell nuclear transfer[END_REF] and for agronomical purposes (eg. to reproducing superior livestock or conserve exotic and endangered species; [START_REF] Campbell | Somatic cell nuclear transfer: Past, present and future perspectives[END_REF]. It has also caught the interest of many groups for basic biological research. Despite the great achievement in cloning mammals using NT, the overall efficiency of cloning is quite low. It is believed that incomplete reprogramming of the donor nucleus, especially the incomplete re-establishment of the embryonic epigenetic patterns may be among the causes leading to developmental arrest before or soon after implantation [START_REF] Ogura | Recent advancements in cloning by somatic cell nuclear transfer[END_REF][START_REF] Long | Reshaping the transcriptional frontier: epigenetics and somatic cell nuclear transfer[END_REF].

After NT, the donor cell has to setback its differentiated state to a totipotent one by reprogramming its epigenetic memory. If the epigenetic reprogramming of the donor genome is not complete the appropriate embryonic genes will not be activated at the appropriate time and in the appropriate lineage. Reversely, proper inactivation of somatically expressed genes is also required [START_REF] Bui | Retrotransposon expression as a defining event of genome reprogramming in fertilized and cloned bovine embryos[END_REF]. In line with these hypotheses, NT inefficiency seems correlated with the differentiation state of the donor cell [START_REF] Heyman | Frequency and occurrence of late-gestation losses from cattle cloned embryos[END_REF][START_REF] Ogura | Recent advancements in cloning by somatic cell nuclear transfer[END_REF]. Neural stem cells for example can be more efficiently cloned than terminally differentiated neuronal cells [START_REF] Blelloch | Reprogramming efficiency following somatic cell nuclear transfer is influenced by the differentiation and methylation state of the donor nucleus[END_REF]. We also observed that the induction of plutipotency in the donor cell (iPS induction) prior to their transfer in recipient oocytes allows a better reprogramming and gave much higher rates of live-born cloned mice [START_REF] Liu | Induced pluripotent stem-induced cells show better constitutive heterochromatin remodeling and developmental potential after nuclear transfer than their parental cells[END_REF]. NT therefore represents a unique opportunity to understand how the epigenome has to be reprogrammed to get good quality embryos that will further develop.

In the past 15 years, many studies pointed out abnormal epigenetic reprogramming in NT embryos. DNA methylation for instance remains much in cloned embryos than in normal fertilized embryos in many species [START_REF] Kang | Aberrant methylation of donor genome in cloned bovine embryos[END_REF][START_REF] Dean | Epigenetic reprogramming in early mammalian development and following somatic nuclear transfer[END_REF]Beaujean et al., 2004b;[START_REF] Yang | Epigenetic marks in cloned rhesus monkey embryos: comparison with counterparts produced in vitro[END_REF][START_REF] Lan | Methylation patterns in 5' terminal regions of pluripotency-related genes in bovine in vitro fertilized and cloned embryos[END_REF]Yamanaka et al., 2011a;[START_REF] Couldrey | DNA methylation at a bovine alpha satellite I repeat CpG site during development following fertilization and somatic cell nuclear transfer[END_REF]); Livecell imaging studies on cloned mouse embryos showed that pericentromeric heterochromatin domains are particularly hypermethylated [START_REF] Yamagata | Centromeric DNA hypomethylation as an epigenetic signature discriminates between germ and somatic cell lineages[END_REF]. Moreover, the related enzyme, the methyltransferase DNMT1, was detected in cloned mouse embryos one stage earlier than in fertilized ones [START_REF] Chung | Abnormal regulation of DNA methyltransferase expression in cloned mouse embryos[END_REF]. Remarkably, in bovine, knockdown of DNMT1 by small interfering RNA (siRNA) in NT embryos successfully induced DNA demethylation of the satellite I region and improved the developmental rate of these embryos to blastocysts (Yamanaka et al., 2011b).

As epigenetic modifications are in close relation to chromatin flexibility, several groups, including ours, also investigated the consequences of these abnormal levels of various epigenetic marks on global nuclear organization. It was shown that heterochromatin can be remodeled into an embryonic-like pattern after NT in mouse, bovine and rabbit [START_REF] Martin | Genome restructuring in mouse embryos during reprogramming and early development[END_REF][START_REF] Merico | Epigenomic differentiation in mouse preimplantation nuclei of biparental, parthenote and cloned embryos[END_REF][START_REF] Pichugin | Dynamics of constitutive heterochromatin: two contrasted kinetics of genome restructuring in early cloned bovine embryos[END_REF][START_REF] Yang | Heterochromatin reprogramming in rabbit embryos after fertilization, intra-, and inter-species SCNT correlates with preimplantation development[END_REF]. However, a great number of cloned embryos presents abnormal heterochromatin redistribution. Interestingly, the percentage of such abnormalities will depend on the differentiation status of the nucleus transferred: ES cell nuclei undergo better remodeling after NT than cumulus cell nuclei [START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF]. Moreover, it seems that only the cloned embryos with a good nuclear reorganization manage to develop up to the blastocyst stage [START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF]. In mouse, we observed that H3S10P and H3K9me3S10P, two epigenetic modifications related to chromatin compaction, are the ones found on the part of the pericentromeric heterochromatin that is remodeled correctly, resembling exactly the embryonic heterochromatin configuration of naturally fertilized embryos. Conversely, H3K9me3 and its associated protein HP1 were detected in the perinuclear clumps of heterochromatin, making obvious the maintenance of the somatic epigenetic signature within these nuclear regions [START_REF] Ribeiro-Mason | Nuclear dynamics of histone H3 trimethylated on lysine 9 and/or phosphorylated on serine 10 in mouse cloned embryos as new markers of reprogramming?[END_REF]. Similarly, in bovine NT embryos derived from fibroblast cells, 42% of the NT embryos displayed premature compaction of pericentromeric heterochromatin with accumulation of H3K9me3 and HP1 at the 4-cell stage, one stage earlier than in fertilized embryos [START_REF] Pichugin | Dynamics of constitutive heterochromatin: two contrasted kinetics of genome restructuring in early cloned bovine embryos[END_REF]. These results demonstrate that some specific epigenetic marks can be good candidates to evaluate chromatin reorganization following NT.

Another epigenetic marker also attracted researchers' attention: H3K9 acetylation. Indeed, cloned embryos are hypoacetylated when compared to their in vivo counterparts [START_REF] Wang | Dynamic reprogramming of histone acetylation and methylation in the first cell cycle of cloned mouse embryos[END_REF]. As hyperacetylation of the paternal genome has been linked to chromatin remodeling after fertilization and to the onset of EGA (see above), this observation gave rise to a new method to improve the SCNT technique: the use of histone deacetylases inhibitors (HDACi). The use of HDACi, such as trichostatin A (TSA), has shown significant improvements in cloning efficiency for many species [START_REF] Kretsovali | Histone Deacetylase Inhibitors in Cell Pluripotency, Differentiation, and Reprogramming[END_REF][START_REF] Tachibana | Human embryonic stem cells derived by somatic cell nuclear transfer[END_REF]. As expected, HDACi causes hyperacetylation, therefore enhancing the acetylation state of the cloned embryos that nearly reach the acetylation levels of fertilized ones [START_REF] Wang | Dynamic reprogramming of histone acetylation and methylation in the first cell cycle of cloned mouse embryos[END_REF][START_REF] Iager | Trichostatin A improves histone acetylation in bovine somatic cell nuclear transfer early embryos[END_REF][START_REF] Shi | Trichostatin A (TSA) improves the development of rabbit-rabbit intraspecies cloned embryos, but not rabbithuman interspecies cloned embryos[END_REF][START_REF] Cervera | Trichostatin A affects histone acetylation and gene expression in porcine somatic cell nucleus transfer embryos[END_REF][START_REF] Yamanaka | Acetylation level of histone H3 in early embryonic stages affects subsequent development of miniature pig somatic cell nuclear transfer embryos[END_REF]. It also favors global chromatin reprogramming and nuclear reorganization. It was indeed shown to increase the levels of H3K4me2 (a marker of transcriptionally active chromatin) and reduce H3K9me3 (a marker of inactive chromatin) [START_REF] Bui | Effect of trichostatin A on chromatin remodeling, histone modifications, DNA replication, and transcriptional activity in cloned mouse embryos[END_REF]. We also observed that TSA improves the structural remodeling of pericentromeric heterochromatin in mouse cloned embryos and that it dramatically increases the rate of full term development (10 times increase) [START_REF] Maalouf | Trichostatin A treatment of cloned mouse embryos improves constitutive heterochromatin remodeling as well as developmental potential to term[END_REF].

These results evidence a link between the developmental inefficiency of NT embryos and aberrant chromatin reprogramming. Remarkably, epigenetic modifiers such as HDACi are able to improve epigenetic reprogramming after NT and thereby improve the quality of the embryos obtained which are then able to reach development to term.

Conclusions and perspectives

It is now clear that epigenetic changes play a key role in embryonic preimplantation development but that it also contributes to the birth of healthy offspring. Determining what components are affected and to what extend alterations in the environment can cause disease and disturb normal development is a major challenge for future studies.

Environmental changes can indeed appose epigenetic marks on genes which are passed from one generation to the next [START_REF] Feil | Epigenetics and the environment: emerging patterns and implications[END_REF][START_REF] Dupont | Maternal environment and the reproductive function of the offspring[END_REF]. Looking at the epigenetic modifications that may be caused by assisted reproductive technologies is therefore attracting much attention nowadays, not only in human but also in mouse (as a model) and in domestic animals [START_REF] Urrego | Epigenetic disorders and altered in gene expression after use of Assisted Reproductive Technologies in domestic cattle[END_REF]. DNA methylation, especially with regards to imprinted genes, is a large matter of debate in human assisted reproductive technologies (ART) [START_REF] Van Montfoort | Assisted reproduction treatment and epigenetic inheritance[END_REF][START_REF] El Hajj | Epigenetic disturbances in in vitro cultured gametes and embryos: implications for human assisted reproduction[END_REF]. In contrast to embryos fertilized in vivo, in vitro fertilized (IVF) embryos are indeed exposed to in vitro culture medium. In mouse for example, 5-meC staining of 2-cell embryos revealed that suboptimal culture media can lead to developmental arrest [START_REF] Shi | Aberrant methylation patterns at the two-cell stage as an indicator of early developmental failure[END_REF]. It was also shown that the H3K4me3 level is significantly lower in the IVF embryos [START_REF] Huang | Comparison of histone modifications in in vivo and in vitro fertilization mouse embryos[END_REF][START_REF] Wu | Differences in H3K4 trimethylation in in vivo and in vitro fertilization mouse preimplantation embryos[END_REF], inducing gene expression changes in the corresponding embryos [START_REF] Fernandez-Gonzalez | Histone modifications at the blastocyst Axin1(Fu) locus mark the heritability of in vitro culture-induced epigenetic alterations in mice[END_REF]. In ART, many groups also focus on oocyte vitrification or cryopreservation. After vitrification, acetylation abnormalities have been observed in the mouse: embryos derived from vitrified oocytes had abnormal acH4K12 patterns upon IVF [START_REF] Suo | Effect of cryopreservation on acetylation patterns of lysine 12 of histone H4 (acH4K12) in mouse oocytes and zygotes[END_REF]. Moreover, HDAC1 expression in these embryos was significantly lower than in the controls and this correlated with lower developmental rates [START_REF] Li | Histone deacetyltransferase1 expression in mouse oocyte and their in vitro-fertilized embryo: effect of oocyte vitrification[END_REF]. Again, epigenetics, embryo quality and developmental potential appear to be linked.

It should also be mentioned that in this review we introduced two main epigenetic players: histone post-translational modifications and DNA methylation. However, epigenetics also include small non coding RNAs: microRNAs (miRNA), small interfering RNAs (siRNA) and Piwi-interacting RNA [START_REF] Bourc'his | A small-RNA perspective on gametogenesis, fertilization, and early zygotic development[END_REF]. In somatic cells, it has been shown that complementary pericentromeric transcripts which are processed to small RNAs, guide heterochromatin formation and establishment of a transcriptionally silent state [START_REF] Muchardt | Coordinated methyl and RNA binding is required for heterochromatin localization of mammalian HP1alpha[END_REF][START_REF] Lu | Proliferation-dependent and cell cycle regulated transcription of mouse pericentric heterochromatin[END_REF]. Pericentromeric heterochromatin can be easily disrupted by RNAse treatments [START_REF] Maison | Higher-order structure in pericentric heterochromatin involves a distinct pattern of histone modification and an RNA component[END_REF] and abnormal accumulation of centromeric transcripts leads to impaired centromeric architecture and function in human cells [START_REF] Bouzinba-Segard | Accumulation of small murine minor satellite transcripts leads to impaired centromeric architecture and function[END_REF]. In mouse embryos, it has recently been suggested that transcripts generated by pericentromeric genomic repeats are also involved in heterochromatin clustering at EGA and that interference with this phenomenon results in developmental arrest [START_REF] Probst | A Strand-Specific Burst in Transcription of Pericentric Satellites Is Required for Chromocenter Formation and Early Mouse Development[END_REF][START_REF] Santenard | Heterochromatin formation in the mouse embryo requires critical residues of the histone variant H3.3[END_REF]. The expression and potential roles of all the small non coding RNAs in reproduction will therefore probably required much investigations in the coming years [START_REF] Hale | Small RNA regulation of reproductive function[END_REF].

Acknowledgements

I would also like to thank my fellow lab members, past and present, for their assistance and support over the years. Funding is currently provided by the Laboratoire d'Excellence Revive (Investissement d'Avenir, ANR-10-LABX-73).