Rémi Vallée
email: remi.vallee@univ-nantes.fr

Antoine Coutrot
email: antoine.coutrot@ls2n.fr

Nicolas Normand
email: nicolas.normand@univ-nantes.fr

Harold Mouchère
email: harold.mouchere@univ-nantes.fr

Accurate small bowel lesions detection in wireless capsule endoscopy images using deep recurrent attention neural network

Keywords: Deep learning, recurrent attention model, Crohn's disease, medical images classification

Wireless capsule endoscopy (WCE) allows medical doctors to examine the interior of the small intestine with a noninvasive procedure. This methodology is particularly important for Crohn's disease (CD), where an early diagnosis improves treatment outcomes. However, the viewing and evaluation of WCE videos is a time-consuming process for the medical experts. In this work, we present a recurrent attention neural network for the detection in WCE images of CD lesions in the small bowel. Our classifier reaches 90.85% accuracy on our own dataset annotated by experts from the Hospital of Nantes. The model has also been tested on a public endoscopic dataset, the CAD-CAP database used for the GIANA competition, and achieves high performance on detection task with an accuracy of 99,67%. This automatic lesion classifier will greatly reduce the amount of time spent by gastroenterologists in reviewing WCE videos, which will likely foster the development of this technique and speed-up the diagnosis of CD.

I. INTRODUCTION

Since the mid-1990s, the development of wireless capsule endoscopy (WCE) improves the diagnosis of the Crohn's disease (CD) and its early treatment [START_REF] Eliakim | The impact of panenteric capsule endoscopy on the management of Crohn's disease[END_REF]. This minimally invasive technology offers significant diagnostic performance due to its ability to fully explore the 3 to 4 metres of the small bowel. It is now well accepted by the entire scientific community [START_REF] Luján-Sanchis | Current role of capsule endoscopy in Crohn's disease[END_REF]. As angiodysplasia, its establishment is largely based on the detection of intestinal lesions that can be more easily detected with WCE aid. The diagnosis of CD is based on two scores: the Capsule Endoscopy Crohn's Disease Activity Index (CECDAI) [START_REF] Gal | Assessment and Validation of the New Capsule Endoscopy Crohn's Disease Activity Index (CECDAI)[END_REF] and Lewis' score [START_REF] Gralnek | Development of a capsule endoscopy scoring index for small bowel mucosal inflammatory change[END_REF]. These indicators depend on the number of lesions, their types and locations in the small bowel. As these scores are related to the number and precise identification of the lesions, it is necessary for gastroenterologists to view all 50,000 images generated by the WCE for each patient, which can be very time-consuming (30-60 minutes per read in most studies [START_REF] Mcalindon | Capsule endoscopy of the small bowel[END_REF]). Various systems have been developed to limit the time required for gastroenterologists to analyze data. Many efforts have been made to detect intestinal lesions from images obtained by WCE. These works can be classified into two main categories: algorithms based on ad hoc techniques presented in section II-A and algorithms based on convolutional neural networks (CNN), presented in section II-B. These networks allow the automatic extraction of features that make them more resilient and accurate, but also more complex to train because of the large amount of labeled ground truth required to learn their parameters. To gather enough data to train neural networks, we set up a collaboration between the Hospital of Nantes and the Digital laboratory of Nantes. 3128 labeled WCE images have been collected and will continue to be totted. The choice was therefore made to create a recurrent neural network with attention in the manner of Mnih et al. [START_REF] Mnih | Recurrent Models of Visual Attention[END_REF]. This network, rather than taking the entire image as an input, chooses several patches successively extracted from the original image through unsupervised learning that will allow a classification decision to be made after multiple views of the same image. We hypothesize this framework to be particularly efficient with WCE images.

II. RELATED WORKS A. Ad hoc methods

The first category of algorithms, not based on deep learning, focuses on the extraction of features from WCE images. A classifier is trained to make the link between the characteristics and image classes. Yu et al. [START_REF] Yu | Ulcer detection in wireless capsule endoscopy images[END_REF] use the Local Binary Pattern (LBP) descriptor and the Scale Invariant Feature Transform (SIFT) descriptor before classification using an SVM to detect images containing ulcers. Other algorithms, such as the one developed by Li et al. [START_REF] Li | Computer-based detection of bleeding and ulcer in wireless capsule endoscopy images by chromaticity moments[END_REF], are based on extracting the colors of the images based on the observation that the color of the ulcers is predominantly white/yellow, then using a network of multilayer perceptrons to perform the classification. There are also techniques based on texture extraction as in Chen et al. [START_REF] Chen | Ulcer detection in wireless capsule endoscopy video[END_REF]. The problem with theses approaches is that they are not very robust to variations in lighting, angle of view and often specific to a type of lesion, making it more difficult to apply in real situations.

B. Deep learning methods

Over the past 4 years, new algorithms based on deep neural networks have been developed to segment and detect lesions from WCE images. These networks stand out for their different architectures and the data used to train them. Aoki et al. propose a network based on an architecture called Single Shot multibox Detector [START_REF] Liu | SSD: single shot multibox detector[END_REF]. This network learns to generate delimitation boxes around areas considered pathological. Fan et al. propose a detection algorithm using the AlexNet network [START_REF] Krizhevsky | ImageNet Classification with Deep Convolutional Neural Networks[END_REF] driven on their own database containing 8000 WCE images. There is also a deep neural network in the literature called TernausNetV2 [START_REF] Iglovikov | Ter-nausNetV2: Fully Convolutional Network for Instance Segmentation[END_REF], a network for image segmentation. This algorithm was applied to the segmentation of images from WCE [START_REF] Shvets | Angiodysplasia detection and localization using deep convolutional neural networks[END_REF] and was awarded first place in the GIANA competition. Since these different algorithms are tested on different databases, it is difficult to compare their performance.

III. NETWORK ARCHITECTURE

In this article, attention is considered as a sequential decision-making process of an agent interacting with a visual environment. The network is based on the one presented by Mnih et al. 2014 [START_REF] Mnih | Recurrent Models of Visual Attention[END_REF] and on the REINFORCE algorithm of Williams 1992 [START_REF] Williams | Simple statistical gradient-following algorithms for connectionist reinforcement learning[END_REF]. From this base network, the local features extraction of the What? Network has been improved thanks to a pre-trained VGG16. The memory process has also been upgraded by the addition of a Gated Recurrent Unit (GRU). The ability to control the patch size has been given to the network and is learn by reinforcement learning (RL).

A. Recurrent attention neural network

The global architecture of the network is described in Fig. 1. An endoscopic image X is provided as input to the network. The Glimpse Sensor will then extract a patch ρ(X) from the original image according to l t = (x, y, z) where the coordinates x and y are normalized in the interval [-1; 1], i.e. (0, 0) is the center of the image, and z is a zoom coefficient between ]0; 1]. With s x × s y the resolution of the original image, we get a resolution patch (s x × z) × (s y × z). This patch is then resized to keep a fixed size at the network input. The subnetwork What? Network, based on VGG16 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] with batch normalization, pre-trained on ImageNet [START_REF] Deng | ImageNet: A Large-Scale Hierarchical Image Database[END_REF], allows to extract the characteristics of the patch ρ(X). Only the 12 first layers of VGG16 and the first fully-connected layer have been preserved. In parallel, information about extracting the patch l t crosses the Where? Network composed of 2 fully-connected layers, thus allowing the extraction of the characteristics relative to the extraction position of the patch ρ(X). The two characteristic vectors produced by this network are of identical size and multiplied before being subjected to ReLu non-linearity. The new characteristic vector g t at the output of the non-linearity then contains the "Where?" and "What?" information extracted by the Glimpse Network at time t. A Gated Recurrent Unit [START_REF] Cho | On the properties of neural machine translation: Encoder-decoder approaches[END_REF] (GRU) allows to merge the characteristics extracted at time t by the network with those extracted at the previous time contained in the previous internal state h t-1 of the GRU. This internal state of the GRU Fig. 1. Architecture of the RANN : At each time t, we provide the Glimpse sensor with an endoscopic image X and the location l t-1 of the patch to extract from the original image. Two independent neural networks, the What? Network and the Where? Network, will then extract information related to the content and location of the patch. A Gated Recurrent Unit (GRU) will then merge the characteristics previously extracted by the network to produce the current system state ht. From this state, three subnets will independently produce lt, the position of the next patch to extract, at, a vector containing a score associated with each class and bt, the baseline from which is calculated the reward for RL.

will be reused at the next time step. From the new internal state produced by the GRU, the Action network will produce a vector associating a score to each class. The Baseline Network will allow it to calculate the reward associated with a prediction so that it can train the Location Network by reinforcement. Learning by reinforcement is unsupervised and associates to each action of the network a reward that should be maximized by the network. Thus the network will increase the probability of locations maximizing the reward function. If the network classifies the image correctly, the reward is worth the number of views placed on the image minus the sum of baselines calculated by the network.

B. Loss function

The network cost function is a sum of three cost subfunctions L a , L b and L r . First, the cross entropy function L a computes the network classification error at the last glance at the image with the network prediction Ŷi and the ground truth Y i :

L a = - 1 n n i=1 Y i log( Ŷi ) . (1)
Then, function L b calculates the mean square error between the R i t reward and the b t baseline established by the network (2). The reward is equal to the number of glances placed on the image if the latter has been correctly classified, 0 otherwise. This baseline, depending on the present and past contexts, allows the reward to be adjusted in order to push the network to improve on its previous results.

L b = 1 n n i=1 T t=1 (b t -R i t ) 2 (2)
Function L r allows to set up the unsupervised RL (3). The principle is as follows: a strategy π(τ j ; θ), depending on the network parameters θ associates a probability to the path τ j . A path is a succession of actions u t , in our case the change of the location of the patch extraction. Each action results in a new state s t , in our case a new patch at the system input. This new state then influences the system that will produce a new action that will lead to a new state. The objective of the reinforcement algorithm is to maximize the probability of trajectories that maximize the reward (R tb t ) and a contrario to decrease the probability of trajectories leading to a low reward. We use Monte Carlo methods to estimate the expected return from a state by averaging the return from M multiple rollouts of a policy.

L r = - 1 n 1 M n i=1 M j=1 T t=1 logπ(u j t |s j i:t ; θ)(R j t -b t ) (3)

IV. EXPERIMENTAL RESULTS AND DISCUSSIONS

The different medical image segmentation and detection algorithms mentioned in above were each tested on different databases, not all containing the same types of lesions. Currently, results of the different methods presented during the Giana competition on the CAP-CAD database [START_REF] Dray | CAD-CAP: une base de données franc ¸aise à vocation internationale, pour le développement et la validation d'outils de diagnostic assisté par ordinateur en vidéocapsule endoscopique du grêle[END_REF] are not available but will be published shortly.

A. Results on GIANA

The training dataset contains 1800 images obtained by WCE divided into 3 classes: 600 images with vascular lesions, 600 with inflammatory lesions and 600 containing no pathology. The images of the training base undergo random transformations (rotations, y-mirroring and elastic distortion) during training in order to increase the diversity of examples, thus making it easier for the network to generalize its knowledge. 80% of the images in the database are used to train the network and 20% for validation. The confusion matrix presented in table III-A show results obtained on the test dataset of the GIANA competition that contains 900 images.

An accuracy of 93.78% is obtained for the three-class classification task (inflammatory lesion, vascular and normal). Since our problem deals with the detection of lesions, the classes vascular-lesions and inflammatory-lesions have been grouped into a "pathological" class. The maximum accuracy on the two-class classification task (pathological, non-pathological) is 99.67%, i.e., about one error for 300 images. Table III-A summarizes different metrics evaluations.

B. Results on CROHN-IPI

The CROHN-IPI (CI) database includes 3218 images divided into 7 different classes, 6 corresponding to different types of pathological lesions (aphtoid ulceration, ulceration from 3 to 10 mm, ulceration greater than 10 mm, edema, stenosis, erythema) and a class containing images of nonpathological intestines. These data have been annotated by two gastroenterologists and come from 39 different patients. The dataset contains 1590 pathological images and 1628 nonpathological ones. 70% of the images in the database are used to train the network, 10% for validation and 20% for evaluation. The results obtained are grouped in table III-A. An average accuracy of 89.26% is obtained after 10 crossvalidations, for an architecture using 4 views of resolution 80 × 80 on the images from WCE and 7 rollouts network from Monte-Carlo sampling.

C. Discussion

The results obtained are inferior on the CI database than on the GIANA database (one error every 10 images on CI versus one error every 300 images on GIANA). There are several reasons for this discrepancy. First, vascular lesions in angiodysplasia are significantly easier to recognize by their bright red color than lesions in Crohn's disease. Secondly, the GIANA dataset includes 600 images of each of the lesions and 600 non-pathological images, allowing the network to train on 300 examples before being tested. For CI, some classes of lesions such as stenosis or erythema are under-represented (less than 70 examples). Then, it can also be explained by the way GIANA's images were chosen compared to those of CI. GIANA images seem much cleaner, containing less image noise (blurred, low light) and intestinal activity noise (fewer bubbles on the images).

As we can see in Fig. 2, the network looks at relevant parts of the image to make the classification decision. These artificial saliency maps are generated by plotting the 4 glimpses for the 7 rollouts networks from Monte-Carlo sampling.

V. CONCLUSION

This article presents the implementation of a recurrent attention neural network architecture. It was trained and tested on two different datasets: GIANA and CI obtaining an accuracy of 99.78% and 90.85% respectively. The prediction on CI, the dataset built in partnership with the Hospital of Nantes, are less accurate due to the number of complex and more realistic images it contains. The addition of new examples to this database, selected thanks to the understanding of where the network focuses, should allow the network to integrate new cases and thus improve results.

Fig. 2 .

 2 Fig. 2. Examples of artificial saliency maps according to the detection result (with P for the pathological class and NP for the non-pathological one).

TABLE I CONFUSION

 I MATRIX ON CAP-CAD TEST DATASET PROVIDED BY GIANA ORGANIZERS.

			Non-pathological	Pathological
			Normal	Inflammatory-lesions	Vascular-lesions
	Normal		289		0	3
	Inflammatory-lesions	0		297	25
	Vascular-lesions	0		28	258
				TABLE II
	NEURAL NETWORK PERFORMANCE EVALUATION ON GIANA AND CROHN-IPI DATASETS.
		3 classes			2 classes
	Dataset	Accuracy	Accuracy	Specificity	Sensitivity	F1	F2
	GIANA	93.78%	99.67%	100.00%	98.97%	99.24%	99.51%
	CROHN-IPI	-	90.85%	91.47%	90.22%	90.44%	90.67%


Yanfeng Yang
email: yanfeng.yang@ensam.eu

Cyrille Baudouin

Tudor Balan

Effect of the plasticity model on the yield surface evolution after abrupt strain-path changes

Abrupt strain path changes without elastic unloading have been used in the literature to investigate the yield surface of sheet metals, both experimentally and theoretically. Such pioneering studies emphasized an apparent non-normality of the plastic strain rate tensor with respect to the trace of the yield surface in stress space, following such a strain-path change. They inspired numerous subsequent developments of plasticity models including nonassociated flow rules. In this paper, this type of abrupt strain-path changes is investigated using state-of-the-art plasticity models. The aim is to emphasize the respective contributions of elasticity, isotropic-kinematic hardening, and rate sensitivity, to the apparent violation of the normality condition. The results show that these classical ingredients of plasticity models significantly contribute to the apparent vertex and loss of normality. These effects are quantified for typical sheet metals subject to biaxial-to-shear orthogonal strain path change.

Introduction

An abrupt strain-path change without elastic unloading has been used to determine the shape of the subsequent yield surface after an initial loading. Plasticity theoretical calculations as well as experimental validations have shown an apparent non-normality of plastic flow, with a vertex formed on the yield surface [1,2]. Based on these pioneering studies, numerous phenomenological and physical plasticity models including non-associated flow rules were developed in last two decades, e.g., in [3][4][5][6].

According to these research results, some reasons have been pointed out to explain the presence of a vertex and of the loss of normality, like the role of elasticity and rate sensitivity. However, the respective contributions to non-normality of these ingredients were not investigated in detail, and need to be further clarified. In particular, a majority of the former studies consider only isotropic hardening, thus the influence of kinematic hardening, if any, was not studied yet.

This paper analyzes and compares the effects on the apparent non-normality on subsequent yield surface from two factors of constitutive modeling: isotropic-kinematic hardening and rate sensitivity after abrupt strain-path change. These effects are quantified for typical sheet steel subject to biaxial-toshear strain path change. The aim of the investigation is to clarify which fraction of the observed results needs to be described by specifically-added non-normality effects, which otherwise may be overestimated. The apparent non-normality is simply quantified by the angle between the actual strain rate tensor and the trace of the subsequent loading path, which is supposed to stay close to the yield surface, as illustrated by angle  in Figure 1. The material model used for the investigation is described in Section 2, while Section 3 describes the numerical simulations and the results, leading to the final conclusions. following the experimental results reported in [2].

Elaso-visco-plastic model

In sheet metal forming processes, the material usually undergoes large deformation and its mechanical behavior is described by rate constitutive equations. In this paper, the total strain rate tensor 𝛆 is additively decomposed in elastic strain rate 𝛆 𝑒 and visco-plastic strain rate 𝛆 𝑣𝑝 . A hypo-elastic law linearly relating the Cauchy stress rate is expressed as

𝛔 = 𝐂 ∶ (𝛆 -𝛆 𝑣𝑝 ) (1)
where 𝐂 is the fourth-order elasticity tensor.

The plastic flow rule defines the direction of the visco-plastic strain rate as a function of the stress tensor components. The equivalent stress 𝜎 𝑒𝑞 employed here is von Mises for simplicity

𝜎 𝑒𝑞 = √ 3 2 (𝛔 ′ -𝐗) ∶ (𝛔 ′ -𝐗) (2)
where 𝛔 ′ denotes the deviatoric part of the Cauchy stress tensor and 𝐗 is a second-order tensor which describes kinematic hardening. The plastic flow rule can be written as

𝛆 𝑣𝑝 = ε 𝑒𝑞 𝑣𝑝 𝐕 , 𝐕 = 𝜕σ 𝑒𝑞 𝜕𝛔 = 3 2 (𝛔 ′ -𝐗) σ 𝑒𝑞 (3)
where ε 𝑒𝑞 𝑣𝑝 is the equivalent visco-plastic strain rate which is defined by the following relationship

ε 𝑒𝑞 𝑣𝑝 = ε * 𝑠𝑖𝑛ℎ( σ * 𝑘 * ) (4
) where 𝑘 * and ε * are material parameters. The scalar "overstress" σ * denotes the increase of stress intensity due to visco-plastic strain rate so that σ 𝑒𝑞 -σ 0 -𝑅 -σ * ≤ 0

(5) In this equation, σ 0 is a material parameter designating the initial yield stress, and 𝑅 is the isotropic hardening of the material.

In the framework of the developed constitutive model, isotropic hardening law is implemented in the generic form 𝑅 = ℎ 𝑅 ε 𝑒𝑞 𝑣𝑝 (6) which can describe various hardening models like Voce, Swift, or their combinations. In this paper, the kinematic hardening described by the backstress tensor 𝐗 is governed by 𝐗 = 𝐶 𝑥 (𝑋 𝑠𝑎𝑡 𝐍 -𝐗)ε 𝑒𝑞 𝑣𝑝 (7) where 𝐶 𝑥 and 𝑋 𝑠𝑎𝑡 are material parameters and 𝐍 is the unit tensor parallel to the visco-plastic flow direction.

Numerical model and simulation results

According to the experimental study with metal sheets in [2], abrupt strain path change simulations were performed by a specifically developed program. Among possible two-step loading processes, the first step of loading considered in the simulations was a biaxial loading prescribed by 𝜀 11 =𝜀 22 >0. When the nominal strains reach the values 𝜀 11 =𝜀 22 =0.01, the applied total strain rate is abruptly converted to 𝜀 22 =-𝜀 11 with 𝜀 11 >0. In order to investigate the respective non-normality contributions of isotropic-kinematic hardening and rate sensitivity, three simulation groups which include its corresponding material parameters, C 𝑥 , X 𝑠𝑎𝑡 and 𝑘 * , were simulated and analyzed. It is noteworthy that the isotropic hardening model was readjusted for each simulation in order to make sure that the stress-strain response during the first loading path is identical for all the simulations in the investigation.

Apparent loss of normality caused by rate sensitivity

The stress path for abrupt strain path change following equibiaxial pre-strain loading and the plastic flow directions are shown in Figure 2 for different values of the strain rate sensitivity parameter 𝑘 * . Only isotropic hardening is considered in these simulations. It is obvious that rate sensitivity plays a significant role in the shape of the subsequent yield surface with a severe blunt "corner" effect. This effect also implies an apparent non-normality, with angle  significantly larger than 90° during the transient phase after strain-path change. Both effects increase when the rate sensitivity parameter increases (or, alternatively, when the strain rate increases). After the transient zone following the strain-path change, the direction of plastic strain rate tends to become perpendicular to the stress path. following equibiaxial pre-strain loading, and directions of plastic strain rate (for 𝒌 * =200).

Apparent loss of normality due to kinematic hardening

Figure 3 shows the stress path for abrupt strain path change following equibiaxial pre-strain loading and corresponding plastic flow directions, when kinematic hardening is added along with isotropic hardening. In these simulations, 𝑋 𝑠𝑎𝑡 =50MPa. It appears that kinematic hardening has an influence on the apparent non-normality of plastic strain-rate direction with respect to the stress path. This effect appears with a delay after the strain-path change; this delay decreases when 𝐶 𝑥 increases. This effect does not seem to have been investigated deeply in the literature. Parameter 𝑋 𝑠𝑎𝑡 has a similar influence, as displayed in Figure 4, with larger effects corresponding to larger values of 𝑋 𝑠𝑎𝑡 .

Conclusion

An elasto-visco-plastic model including isotropic-kinematic hardening and rate sensitivity was used to simulate a typical abrupt strain-path change as described in [1,2]. The apparent non-normality observed in this configuration was shown to depend, at least partly, on the constitutive response of the material according to classical plasticity modeling. The material's strain rate sensitivity had a strong influence during the early transition zone after strain-path change, while kinematic hardening contributed to this apparent non-normality at a later stage. These findings will be further explored in order to assess the part of this apparent non-normality phenomenon that would correspond to a specific non-normality behavior of the material.

Figure 1 .

 1 Figure 1. Schematic illustration of apparent non-normality situation after abrupt strain-path change,following the experimental results reported in[2].

Figure 2 .

 2 Figure 2. Influence of the rate sensitivity parameter 𝒌 * . Stress path for abrupt strain path changefollowing equibiaxial pre-strain loading, and directions of plastic strain rate (for 𝒌 * =200).

Figure 3 .

 3 Figure 3. Influence of the kinematic hardening parameter 𝑪 𝒙 . Stress path for abrupt strain path change following equibiaxial pre-strain loading. The direction of plastic flow is also indicated, at specified values of subsequent plastic strain.

Figure 4 .

 4 Figure 4. Influence of kinematic hardening parameter 𝑿 𝒔𝒂𝒕 . Stress path for abrupt strain path change following equibiaxial pre-strain loading, and plastic strain rate directions.


domain: spi phys

text:
Célestin Ott

Quentin Gallas

Jérôme Delva

Marc Lippert

Laurent Keirsbulck

High frequency characterization of a sweeping jet actuator

Keywords: Flow control, Sweeping Jet, Sychronized Hot-Wire, Conditional Approach, Dynamic Characterization

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

Active flow control is the ability to manipulate a flow field in order to improve the efficiency or performance of a fluidic system [START_REF] Cattafesta | Actuators for Active Flow Control[END_REF]. Flow control is of great technological interest and constitutes a leading area of research for scientists and engineers in fluid mechanics. Active flow control generally uses actuators to inject energy in the flowb(to amplify instabilities or to increase the boundary layer robustness for instance). Conventionally, these actuators can be turned on and off during an experiment, and some settings can be adjusted (frequency, amplitude ...). It is currently a growing field, thanks to the recent improvements of the fluid mechanics' scientific community's understanding. Active flow control can be divided into two main strategies. The first one aims to affect the flow behavior using high amplitude "brute-force" control. The second flow control strategy is based on the injection of small-amplitude perturbations into the flow to amplify the flow instabilities. The latter approach provides the advantage of reducing the power, size, and mass of the actuators ( [START_REF] Cattafesta | Actuators for Active Flow Control[END_REF], [START_REF] Ternoy | Overview of ONERA Actuators for Active Flow Control[END_REF], [START_REF] Chovet | Dynamic characterization of piezoelectric microblowers for separation flow control[END_REF], [START_REF] Naik | Microfluidics for generation and characterization of liquid and gaseous micro and nanojets[END_REF], [START_REF] Housera | Microfabrication of dielectric barrier discharge plasma actuators for flow control[END_REF]). Resulting in lower power consumption, faster response, more reliability, and lower cost [START_REF] Kral | Active Flow Control Technology[END_REF], which are desired characteristics for flow control actuators. [START_REF] Duda | Unsteady Flow Simulation of a Sweeping Jet Actuator[END_REF] Among the various existing control devices, sweeping jets are an emerging type of actuators with the particularity of working without energetic inputs and being very robust. They started to be developed in the late 1970s at Harry Diamond Research Laboratories where they were initially considered to be used in analog computers and as a fluidic amplifier ( [START_REF] Warren | Some Paremeters Affecting the Design of Bistable Fluid Amplifiers, Fluid Jet Control Devices[END_REF], [8]). For years they have been mostly used with water as working fluid (as oscillating windshield washers on cars, showerheads and irrigation systems). These actuators have recently gained interest as controllers thanks to their simple and robust design, as well as their wide range of use concerning flow conditions ( [START_REF] Vollmer | Bistable fluidic elements in LIGA technique for flow control in fluidic microactuators[END_REF], [START_REF] Theofilis | Role of instability theory in flow control[END_REF], [START_REF] Sattarzadeh | Experimental investigation on the steady and unsteady disturbances in a flat plate boundary layer[END_REF] [START_REF] Gallas | Characterization of Fluidic Micro-Actuators[END_REF], [START_REF] Ternoy | Overview of ONERA Fluidic Actuators in Aerodynamics[END_REF], [START_REF] Poisson-Quinton | Recherches théoriques et expérimentales sur le contrôle des couches limites[END_REF], [START_REF] Poisson-Quinton | Survey of French Reasearch on the Control of Boundary Layer and Circulation, s.l. Boundary Layer and Flow Control[END_REF], [START_REF] Horne | Acoustic Study of a Sweeping Jet Actuator for Active Flow Control Applications[END_REF], [START_REF] Koklu | Sweeping Jet Actuator in a Quiescent Environment[END_REF], [START_REF] Koklu | Effect of a Coanda Extension on the Performance of a Sweeping-Jet Actuator[END_REF]). To design an efficient control strategy, the knowledge of the actuator dynamic response is critical and requires appropriate characterization to understand the jet topology, to quantify the homogeneity and the amplitude responses (concerning velocity, frequency, rms ...). The range of sweeping frequency of the actuators is quite wide (from 10 Hz to 25 kHz [START_REF] Raman | Cavity Resonance Suppression Using Miniature Fluidic Oscillators[END_REF]). Fig. 1 shows the frequency and velocity ranges of some sweeping jet actuators studied in the state of art.

f (Hz) U (m/s) 1000 - 2000 - 3000 - 4000 - 100 - 200 - 300 - 400 - • • • • • • • • • Koklu M. [17]
• Woszidlo R. [START_REF] Woszidlo | Parametric Study of Sweeping Jet Actuators for Separation Control[END_REF] • Raman G. [START_REF] Raman | Cavity Resonance Suppression Using Miniature Fluidic Oscillators[END_REF] • Ott C. The literature gives numerous characterization methods such as local time-resolved at high sweeping frequency ( [8], [START_REF] Raman | Cavity Resonance Suppression Using Miniature Fluidic Oscillators[END_REF], [START_REF] Woszidlo | Parametric Study of Sweeping Jet Actuators for Separation Control[END_REF], [START_REF] Peters | Femtosecond Laser Tagging Characterization of a Sweeping Jet Actuator Operating in the Compressible Regime[END_REF]), spatially-resolved snapshots ( [START_REF] Ostermann | Sweeping Jet from a Fluidic Oscillator in Crossflow[END_REF]), spacetime resolved at low sweeping frequency ( [START_REF] Hirsch | An Experimental and theoretical study of active flow control[END_REF], [START_REF] Ostermann | Sweeping Jet from a Fluidic Oscillator in Crossflow[END_REF], [START_REF] Ostermann | Phase-Averaging Methods for the Natural Flowfield of a Fluidic Oscillator[END_REF]), numerical analysis and simulations ( [START_REF] Sieber | Lagrangian Coherent Structure in the Flow Field of a Fluidic Oscillator[END_REF], [START_REF] Arnault | Numerical study of an isolated sweeping jet, rapport de stage ONERA[END_REF], [START_REF] Duda | Unsteady Flow Simulation of a Sweeping Jet Actuator[END_REF], [START_REF] Kara | Numerical Study of Internal Flow Structures in a Sweeping Jet Actuator[END_REF]). Since the flow control actuation by sweeping jet is relatively recent [START_REF] Seele | Performance Enhancement of a Vertical Tail Model with Sweeping Jet Actuators[END_REF], the state of art shows a lack of characterization process in order to correctly define the high frequency dynamic response. For this reason, a conditional approach based on a synchronization methodology is presented and tested on a particular operating point of a sweeping jet actuator. This requires first a full characterization of the sweeping jet actuator. The present paper is arranged as follows: first, the design and principle of the in-house sweeping jet are described in section 2. Then the synchronization methodology used to obtain a space-resolved and time-resolved characterization and the experimental setups used to characterize this actuator at the Onera Lille are presented in section 3. These measurements, involving shadowgraph visualizations and single-wire hot-wire measurements, are used to obtain a baseline flow field characterization, which is reported in section 4. It leads to the particular operating point of interest (639 Hz) and an apropriate setup (sensors locations) to test the synchronization methodology. This characterization is achieved by using two single-hot-wire sensors, including one that is scanning the interest zone. The method is used to describe characterize the flow at the exit nozzle of the actuator at high sweeping frequencies. The results of this dynamical response of the in-house actuator are introduced in section 5. In the present paper the superscript * denotes the dimensionless parameters by h, the sweeping jet length, T , the sweeping period and U max the maximum velocity.

Device Principle and Design

This section presents the sweeping jet actuator principle and the specific configuration that is developed in this paper. Sweeping jet actuators are attractive because they do not need an energetic controller to work and do not contain any moving parts. This type of actuator generates an oscillating jet when continuously supplied with pressurized air. From a flow control point of view, the working process of this actuator can be assimilated to the steady blowing, although it uses less air ( [START_REF] Dandois | Active flow control for Low and High-Speed Flows[END_REF], [START_REF] Tewes | On The Use of Sweeping Jets to Augment the Lift of a λ-Wing[END_REF]). The actuator blows a continuous jet that oscillates from one side of the outlet nozzle to the other. Fig. 2(a) shows the conventional design of a sweeping jet actuator, made of: an air input A, where the inlet pressure and mass flow is controlled, a main channel B, two feedback channels C that are propagating an over-pressure or a pressure drop from the outlet to the inlet, and an outlet nozzle D. The principle of the sweeping jet is the following : after switching on the steady air supply, the air flows through the actuator main cavity and attaches to either side of the cavity due to Coanda effect (Fig. 2(b)). A backflow develops in the feedback channel and forces the jet flow separation from that surface and the reattachment to the opposite surface (Fig. 2(c)). Then backflow also develops in the other feedback channel (Fig. 2(d)) which forces the jet to switch back to its initial state (Fig. 2(e)). The process then repeats, thus producing a self-sustaining oscillation process. The sweeping frequency and velocity of the jet depends on the inlet pressure and the flow rate passing through the inlet nozzle. The only way to modify the actuator behavior is to modify its geometry (for instance the feedback channel size to modify the frequency or the inlet and outlet nozzle for the velocity). The design of the in-house sweeping jet actuator studied is based on the work of I. Wygnanski et al.( [START_REF] Seele | Improving Rudder Effectiveness with Sweeping Jet Actuators[END_REF], [START_REF] Graff | Sweeping Jet Actuators: A New Design Tool for High Lift Generation, Innovative Control Effectors for Military Vehicles[END_REF]). The actuator was validated for inflight flow control uses during a flight test campain to increas the side force on an aircraft vertical tail [START_REF] Seele | Performance Enhancement of a Vertical Tail Model with Sweeping Jet Actuators[END_REF]. The actuator geometrical proportions are conserved ( [START_REF] Woszidlo | Parametric Study of Sweeping Jet Actuators for Separation Control[END_REF]). However, the actuator is scaled up to provide an exit nozzle of 25 mm × 2.5 mm and feedback channels of about 12 mm long. As shown further in this article, this geometry allows to have a wide range of outlet velocities (from 40 m.s -1 to 140 m.s -1 ) and sweeping frequency (300 Hz to 1 kHz) for a narrow inlet pressure range (from 0.5 bar to 4.5 bar). For further experiments (sweeping jet in crossflow), the actuator is integrated into an enclosure with a 45 • inclined jet. This angle is chosen with the expectation of an efficient flow control actuator in the flat plate boundary layer configuration (intended in further experimentation). Fig. 3 shows a schematic of the main geometric characteristics of the fluidic device used in the present work. This actuator is manufactured using resin stereolithography (which is a cost effective, robust and accurate manufacturing process in this case and at this scale). Lengths are in mm on the diagram.

Experimental Setup

The sweeping jet actuators presented in the previous section is characterized using different techniques. The shadowgraph technique provides qualitative results in order to assess the main structure of the jet. The time-resolved velocity flow field is also measured with a single hot wire probe. This section presents these techniques and the post-processing methodology developed to convert local time-resolved signal into spatially-resolved snapshots.

Shadowgraph Technique

The shadowgraph bench at Onera Lille uses a mirror system to visualize the second derivative of the density field. 24 high-resolution cameras are deployed to acquire the shadowgraph visualizations. The bench (Fig. 4) is made of two parabolic mirrors with a focal

Hot-Wire Measurements

The hot-wire characterization is performed on the actuators test bench at Onera Lille ( [START_REF] Gallas | Characterization of Fluidic Micro-Actuators[END_REF]). The bench is equipped with a 6 bar air supply, a Sentronics proportional valve that regulates the pressure with a precision of 0.01 bar measured and regulated approximately 40 cm upwind the actuator inlet nozzle, inside the supply pipe, and a motorized arm with stepping motors to move the hot-wire with an accuracy of 0.1 mm in all directions. Dantec Dynamics single-hot-wire probe type 55P15 and 55R01 (operating at constant temperature) connected to a Dantec Dynamics conditioner (featuring a Wheatstone bridge and a low pass filter with a cutting frequency of 10kHz) are employed to survey the velocity response of the actuator at its outlet nozzle. The velocity measurements are sampled at 20kHz and the test duration is chosen to be equal to 4s (corresponding to more than 3000 sweeping jet periods). Since the velocity measured is under 100 m/s, the compressibility effect on hotwire measurement are considered as insubstantial. The sensor is calibrated between 0 m/s and 150 m/s. The uncertainty is obtained from the calibration unit and can be evaluated to be less than 0.5 m/s for the present measured velocity range.

Hot-Wire Synchronization Methodology

In order to perform a conditional analysis, a stationary hot-wire sensor is used as a reference for the time synchronization of the two hot-wire sensors. This reference hotwire, placed at the left-hand edge of the exit nozzle, used to identify the velocity peaks corresponding to the sweeping periods. The position of this sensor is critical: on one hand, the sensor has to be close enough to the jet in order to capture every period. On the other hand, it has to be placed at the edge of the jet to capture only one peak per period and to minimize the impact of the sensor on the jet development. In fact, the reference hot-wire being upstream the traveling hot-wire, the intrusiveness of the sensor is a substantial factor. The optimal position of the probe is found with an iterative process based on a trial and error approach. The final position is at 1 mm downwind the exit nozzle, and at 2 mm from the exit nozzle in the span direction. The peaks measured with the reference sensor are used to synchronize the time references between the two sensors with a conditional approach: the peaks are used as triggers. The second hot-wire sensor is mounted on a traverse system which scans the exit nozzle of the actuator. The velocity is measured at a frequency of 20 kHz in order to provide time-resolved measurements. The moving mechanism go through a fine mesh with 1 mm × 1 mm spatial discretization, in a parallel plan to the exit nozzle. For each point, the velocity and the reference measurements are done simultaneously on the same time base. To synchronize all the measurements, a conditional approach is employed using the reference sensor trigger in order to have a new time origin. Thanks to the local data synchronization, the 2D velocity field is reconstructed for each time step in a typical period of the sweeping jet actuator. These instantaneous space-solved velocity fields can be animated in time to finally have a spatially-resolved and time-resolved velocity field.

To have an efficient characterization in space and time, a nominal point has to be chosen. The amplitude of the velocity peaks has to be strong, and the sweeping frequency steady. Since an inlet pressure of 1 bar gives great results in terms of frequency steadiness, this pressure will be retained for the present analysis. This inlet pressure corresponds to a [START_REF] Duda | Unsteady Flow Simulation of a Sweeping Jet Actuator[END_REF] sweeping frequency of 639 Hz. Fig. 6 shows the flowchart of the conditional synchronization procedure. This procedure leads to a 2D space-time resolved velocity field, which allows following the sweeping motion of the jet in time and space.

Baseline Flow Field Characterization

This section presents the baseline flow field obtained with the characterization methods stated in section 3, applied to the in-house sweeping jet actuator. These preliminary results are used to improve the understanding of the unsteady flow behavior, while optimizing the experimental setup that will be used for the dynamic analysis of the unsteady flow field (in terms of sensors positioning, sweeping frequency ...).

Jet Characteristics

The shadowgraph method allows visualizing a refractive index variation created by a density variation. However, the jet velocity has to be high enough to have a refractive index variation that can be captured. The flow visualization is done for various inlet pressure ranging from 0.5 bars to 6 bars. The main structure of the jet can be quantitatively observed from instantaneous snapshots.

Mean Flow Characterization

Single-hot-wire measurements are performed in order to characterize the velocity field at the exit nozzle of the actuator. An average flow field is captured (average velocity on 1000 sweeping periods) to visualize the velocity peaks distribution at the exit nozzle. Fig. 8 shows the single-hot-wire 2D mapping done for a 25 mm × 5 mm area. In order to avoid perturbations from the interactions between the flow and the sensor, the measurement plan was located at Z = 1 mm from the nozzle. U * is defined by the ratio between the average velocity on each point U and the maximum velocity on the whole field U max . X * and Y * are the dimensionless spatial coordinates using the length of the exit nozzle h. The jet center is determined by the condition U (x, y) ≥ 95% × U max this configuration the flow crosses the measurement plan with a 45°angle in the YZ plan. The single-wire hot-wire sensor is parallel to the X axe. The streamline velocity measured is then a combination of the Y and Z components of the velocity. This configuration was chosen considering that the X velocity of the jet center is weaker than the jet mean velocity (respectively 30 m/s against 81 m/s at 1 bar inlet pressure). The results show that the maximum average velocity is delivered in a crossflow surface of about 40% of the total nozzle surface and is localized at its center. The average jet center is 0.5h wide and 0.1h thick. The unsteady nature of the jet can be quantified by the rms (root mean square) profile. Two symetrical peaks are clearly visible and highlight the large fluctuations due to the switching behavior of the jet leading to strong shear layer unsteadiness around X * = 0.15 and X * = 0.82. The rms velocity data obtained from the hot-wire measurements are nondimensionalized with the local maximum velocity at each position on Fig. 9.

March 15, 2019

Similar behaviors with two rms peaks were also observed by Koklu and al. [START_REF] Koklu | Sweeping Jet Actuator in a Quiescent Environment[END_REF]). The present results show a maximum turbulent intensity of 104 % for the left peak (at X * = 0.15) and 112 % for the right peak (at X * = 0.82). To focus on the dynamic response of the actuator, measurements are performed with a fixed hot-wire. It is placed in the middle of the exit nozzle, between the two rms peaks. Fig. 10 shows the shape of the raw signal that can be captured in 2 periods of time (here with an inlet-nozzle pressure of 0.5 bar).

At the center of the exit nozzle, the hot-wire captures the double frequency (two jet peaks per period). The jet peaks have silimar shapes and velocities magnitudes independently of the sweeping motion (from right to left or left to right as shown on Fig. 10). This method allows to measure the maximum velocity and the frequency response for several inlet pressure (Fig. 11 Left). This characterization shows that the actuator has a repeatable behavior up to 4.5 bar. For higher inlet pressures (4.5 bar to 6 bar not shown here), the frequency responses are not steady. This restriction was observed by Gosen and al. [START_REF] Gosen | Experimental Investigation of Compressibility Effects in a Fluidic Oscillator[END_REF]. In this range of pressure the actuator is blowing from 40 m.s -1 to 140 m.s -1 and is sweeping from 300 Hz to 1 kHz. These ranges are in agreement with previous the researches: among others, Kokul and al. [START_REF] Koklu | Sweeping Jet Actuator in a Quiescent Environment[END_REF] presented a sweeping jet actuator sweeping at 150 Hz and blowing at March 15, 2019 100 m.s -1 . Woszidlo and al. [START_REF] Woszidlo | Parametric Study of Sweeping Jet Actuators for Separation Control[END_REF] introduced a sweeping jet actuator that can sweep from 500 Hz to 4.5 kHz with a velocity from 10 m.s -1 to 450 m.s -1 . Raman and al. [START_REF] Raman | Cavity Resonance Suppression Using Miniature Fluidic Oscillators[END_REF] used a miniature fluidic oscillator that reached nearly 3 kHz for an inlet pressure of 3 bar (with a 1.693 mm × 0.954 mm square-wave nozzle). Taking into account the high-pressure loss coefficient induced by the strong geometric variations especially at the output of the device, the range of exit velocity is correlated with isentropic calculations.The Fig. 11 Right shows the impact of both a crosswind velocity and the inlet pressure on the sweeping angle. It shows that at a low sweeping frequency and a low actuator velocity, the impact of the crosswind is high (20 m/s crosswind decreases the sweeping angle of 20%). For inlet pressure higher than 1 bar, the crosswind velocity has a lower impact on the sweeping angle (20 m/s crosswind decreases the sweeping angle of only 1%). The inlet pressure decreases the sweeping angle as well (13% losses in sweeping angle for 2.5 bar of inlet pressure increment). To characterize the time dependence of the sweeping jet frequency, two operating points are chosen: one at low sweeping frequency (640 Hz for 1 bar inlet pressure) and one at high sweeping frequency (967 Hz for 4 bar inlet pressure). A Ricker wavelet study is proceeded at these sweeping frequencies. The wavelet is able to analyse the hot-wire signals in time and scale [35] [36]. This process is similar to a sliding Fast Fourier Transform on a time window. However, the Fourier transformation is not adapted to non-stationary processes. As the time-frequency decomposition method allows to keep the temporal dimension of the spectrum, this method is usually more suitable to describe the time-frequency interaction of such unsteady flows. Continuous wavelet transformation (CWT) is used in the present paper and can be defined as:

c(s, t) = ∞ 0 u(t) Ψs,t (t) dt.
The complex conjugaison is denotes by ˜, the subscript s and τ denote the scale and the time shaft, and Ψ is the mother wavelet used:

Ψ s,τ (t) = 1 √ s t -τ s , with Ψ(t) = 1 -t 2 e -t 2 2 .
The scalar product of the wavelet coefficient c is used in order to give information about the unsteady flows. The wavelets shown on Fig. 12 indicate that the sweeping frequency is more steady for low velocity and low sweeping frequencies than for high velocity and sweeping frequencies. Indeed, for a 1 bar inlet pressure, the sweeping frequency trace has higher amplitudes and is quasi-periodic: the sweeping frequency is almost steady. For a 4 bar inlet pressure, the sweeping frequency trace is broader and less intense. The periodicity does not appears as blatantly as for lower inlet pressure: the sweeping frequency becomes gradually unsteady for high inlet pressure.

Based on this global characterization of the sweeping jet actuator response and its jet topology, the experimental setup of the two single-hot-wire can be adjusted and implemented to investigate the dynamic motion of the sweeping jet. The synchronization process described in sub-section 3.3 is now applied to the in-house sweeping jet actuator to characterize its dynamic response using spatially-resolved snapshots. The setup determined in section 4 is used: the inlet pressure is set at 1 bar, which corresponds to a sweeping frequency of 639 Hz. The flying single-hot-wire sensor scans a 25 mm × 5 mm xy plan at Z = 1 mm over the exit nozzle. This sensor is traveling with Z = 1 mm increments. It stays 3 s per location (1 s waiting for the flow to be established and 2 s of measurements). The synchronization wire is motionless and is located at the left edge of the jet, where it can capture only one velocity peak per sweeping period. The position of this sensor is roughly chosen using the shadowgraph visualizations, and then refined by trial-error. The synchronization trigger is determined on this raw signal with a maximum localization process. To isolate a sweeping period, phase locked averaging method does not give satisfying results: variations in the internal flow conditions contribute to the variations in the instantaneous oscillation frequency which changes randomly. Koklu and al.([17]) quantified this frequency deviation from 10% to 20% around the dominant frequency. This «jittering» makes it difficult to implement a phase averaging post-treatment process. For this reason, the time-resolved mapping is performed on raw data for three sweeping periods on Fig. 13. By animating these 2D snapshots in time, the motion of the jet peak at the exit nozzle can be followed. It allows to measure the amplitude and the spreading angle of the jet. This video can be found at the following link: https://vimeo.com/286171518, but Fig. 14 shows a set of snapshots extracted from this video. The jet center is noticed easily on the snapshots, and the wake of its horizontal motions enables to determine whether it comes from the right or from the left. The jet velocity magnitude is higher when the jet is at the center of the exit nozzle than when it is on both edges. Also, the size of the jet center is bigger. Peaks on both edges of the exit nozzle are quasi-symmetrical. By using all snapshots, the jet center can be followed in time. Fig. 15 shows the position reports of the jet center during one period. Position reports of jet center shows sawtooth periodic signal. In terms of sweeping velocity, this observation shows that the jet center switches position (bi-stable attachment) with a quasi-constant velocity. This horizontal velocity averages 0.3 × U max with maxima at about 0.7 × U max . The sweeping process is instantaneous: the jet does not stay on one side or the other. As soon as it reaches one of the extremum positions, the pressure balance in the feedback channels reverses and the jet motion the amplitude of the sweeping motion, the jet center runs through 0.92 × h along the exit nozzle.

Dynamic Analysis of the Unsteady Flow Field

Conclusions

This paper presents an experimental methodology to characterize at high frequency a sweeping jet actuator in space and time. In the first part of the paper, the in-house sweeping jet actuator is described. Its design is based on the literature, however, the global size is extended to be compatible with a prospective experiment. The actuator is manufactured at Onera Lille. The second part of this paper presents the metrology equipment used to characterize the sweeping jet flow, and the double single-hot-wire procedure for the conditional synchronization approach is introduced. This novel approach gives a space-time resolved characterization at high sweeping frequency using two synchronized hot-wire sensors: one used as a reference signal and the other used as a flying sensor. In the third part of the paper, the base flow of the sweeping jet is characterized at the exit nozzle by shadowgraph visualizations. Thanks to these visualizations, the jet topology can be defined. Consequently, the position of the sensors can be adjusted for the measurements. Single-hot-wire measurements are then performed to define the dynamic response of the actuator and be able to link the inlet pressure with the velocity response of the sweeping frequency. This simple hot-wire characterization shows a sweeping jet actuator that is in accordance with the literature in terms of frequency range and behavior. Thanks to these measurements a nominal inlet pressure is chosen for the conditional approach characterization. In the fourth and last part of the paper, the conditional synchronization approach is used to characterize the dynamic response of the sweeping jet actuator at the nominal point chosen, which corresponds to a sweeping frequency of 639 Hz. The flying hot-wire sensor covers a 125 mm 2 2D mapping at the exit nozzle plan with a time resolution of 20 kHz and a spacial resolution of 1 mm. This characterization is well suited for sweeping jets because there is no electronic input or output signal (unlike pulsed or synthetic jet, for which there is an input signal that can be used as a trigger). Further investigations will be done with this actuator to study the interaction between the sweeping jet and a crossflow (turbulent boundary layer). The same characterization process will be applied with hot-wire scanning in a volumetric mesh. For this application the present method has some limitations. The synchronization hot wire is quite intrusive and disturbs the flow downwind. Moreover, the sweep angle being a function of the cross-flow strength, the synchronization sensor will not necessarily be in the correct location and thus will not capture the jet peak for each period. Therefore, the reference hot-wire sensor will be replaced by a pressure sensor in one of the feedback channels for future research.

Acknowledgements

The present work has been supported by Campus International pour la Sécurité et l'Intermodalité des Transports, la Région Hauts-de-France, l'Union Européenne, la Direction de la Recherche, Enseignement Supérieur, Santé et Technologies de l'Information et de la Communication and le Centre National de la Recherche Scientifique. The authors gratefully acknowledge the support of these institutions. [START_REF] Duda | Unsteady Flow Simulation of a Sweeping Jet Actuator[END_REF]

Figure 1 -

 1 Figure 1 -Sweeping Jet Actuator Response in the State of Art.

Figure 2 -

 2 Figure 2 -Sweeping Jet: principle Cross symbol denotes the high pressure region.

Figure 3 -

 3 Figure 3 -In-house sweeping jet actuator design. Lengths are in mm on the diagram.

Figure 4 -

 4 Figure 4 -Shadowgraph Setup

Figure 5 -

 5 Figure 5 -Spatial System Coordinates

Figure 6 -

 6 Figure 6 -Hot-wire procedure for the conditional synchronization approach

  Fig.7 is extracted from visualizations with an inlet pressure of 5 bars. The shadowgraph in the yz plan (Fig.7 Left) clearly shows the 45 • angle of the jet as expected from the design of the actuator. These indications are used to center the jet in the mesh of the hot-wire scanning. The visualization also highlighted the expansion length of the jet. For this inlet pressure (5 bars) the jet is able to reach a distance of 0.8h in the 45 • plan. The sweeping nature of the jet is demonstrated with the xz plan shadowgraph measurement (Fig.7 Right). It can be noticed that the jet can potentially interact with the crossflow up to a distance of 0.2h. Based on these flow observations, the hot-wire sensors positions are adjusted in order to capture the induced flow dynamics.

Figure 7 -

 7 Figure 7 -Instantaneous shadowgraph snapshots

Figure 8 -

 8 Figure 8 -Single-Wire Hot-Wire 2D Scanning (Time-Averaged) U * is defined by the ratio between the average velocity on each point U and the maximum velocity on the whole field U max . X * and Y * are the dimensionless spatial coordinates using the length of the exit nozzle h. The jet center is determined by the condition U (x, y) ≥ 95% × U max

Figure 9 -

 9 Figure 9 -1D Single-Hot-Wire Scanning (rms profils) U rms + is defined by the ratio between the rms velocity U rms and the local time-average velocity U moy . The spatial coordinates are nondimensionalized with the exit nozzle length h.

Figure 10 -

 10 Figure 10 -Single-hot-wire scanning (time-resolved signal -raw experimental data) With U * = U/U max the velocity nondimensionalized by the maximum velocity in time, and t * the dimensionless time defined by t * = t/T with T the sweeping period.

Figure 11 -

 11 Figure 11 -LEFT: Actuator Dynamic Response without crossflow The red curve denotes the frequency response, and the green curve the maximum velocity of the actuator for an inlet pressure varying from 0.5 bar to 4.5 bar. Umax is the maximum velocity measured on the total acquisition time (4 seconds at 20 kHz). RIGHT: Parametric Characterization of the Sweeping Angle with crossflow By defining the jet span as the region where U RM S > 30, the sweeping angle can be calculated and the dimensionless sweeping angle is defined by Sweeping Angle * = SweepingAngle/M aximumSweepingAngle. These measurements are done for inlet pressure from 0.5 bar to 3 bar and for three crosswind conditions (0 m/s, 10 m/s, and 20 m/s).

Figure 12 -

 12 Figure 12 -Frequency steadiness investigation using wavelets Dimensionless wavelet energy scalogram c(s, τ ) 2 obtained from raw hot-wire data with 4 bar inlet presure. The horizontal axis are the time nondimensionalized with the sweeping jet period, and the vertical axis are the frequencies in Hz.

Figure 13 -

 13 Figure 13 -Space-time resolved mapping: example at 639 Hz For each point, the trigger is localized and the local time-base is replaced by the universal time-base (the new origin corresponding to the trigger peak). The local time-respoved files are then dispatched into 2D space-resolved snapshots for each time step.

Figure 14 -

 14 Figure 14 -Instantaneous snapshots dataThis set presents some of the instantaneous snapshots. Only ten times instants are chosen, representing the extremum positions of the jet during 2 periods. The time instants t * are defined by t * = t/T with T the sweeping period. The velocity magnitude is noted U * defined by the ratio between the local velocity and the maximum velocity on the whole field U max . The cross symbol denotes the jet center, the red curve is the center trajectory.

+Figure 15 -

 15 Figure 15 -Jet center position report for each time instant, the position of the subscript c denotes the position of the jet center. The position is nondimensionalized by the exit nozzle length h, and the time by the period t * = t/T .

[START_REF] Duda | Unsteady Flow Simulation of a Sweeping Jet Actuator[END_REF]


A Resano-Garcia

S Champmartin

Y Battie

A Koch

A En Naciri

A Ambari

N Chaoui

Highly-repeatable generation of very small nanoparticles by Pulsed-Laser Ablation in Liquids of a high-speed rotating target

Keywords: Laser ablation, Nanoparticles, Colloids, Optical properties, Catalysis

By irradiating a cylindrical silver target rotated at high-speed within the range 300 -2400 rpm (lateral speed 0.16 -1.25 m.s -1 ) in pure water, we prepare ligand-free Ag nanoparticles (NPs) with size of 4±2 nm which are likely to be primary particles. Usually, the generation of NPs showing such a small size requires either a laser post-treatment and/or chemical additives. As the rotation rate of the target is increased, calculated 3D flow patterns revealed different hydrodynamic regimes which clearly influence the ablation rate and repeatability of the process as well as the colloids properties. In addition to revealing the importance of fluid dynamics in Pulsed-Laser Ablations in Liquids, this study provides a way for producing in one step pure NPs with size below 5 nm which are suitable for applications in catalysis.

Introduction

In its principle, Pulsed-Laser Ablation in Liquids 1,2,3,4 (PLAL) appears as simple and versatile method to produce ligand-free nanoparticles 2,3,4 which found applications in areas such as biomedicine 5,6 , bio-sensing 7,8 and catalysis 9,10 . However, due to the numerous processing parameters and their complex interdependence, this method has the main disadvantages of i) presenting a lack of particle size control ii) having a relatively weak productivity 2,3,4 iii) being hardly reproducible 2 . The complexity of PLAL is well-illustrated by the progressive attenuation of the laser beam by the colloids during the ablation. When performed in a steady solution, the mechanisms responsible for the particles transport are mainly diffusion (Brownian motion) and free convection due to changes in liquid density 11 . Because these processes are slow, particles accumulate in front of the target due to the multi-pulses ablation explaining this attenuation of the laser beam. This attenuation of the laser beam has consequences on the nanoparticles size /shape distributions and the ablation rate.

Tsuji et al 12 studied the effect of wavelength on the ns-laser ablation rate of a silver target in water on the resulting particle size. They observed a decrease of the mean particle diameter from 29 to 12 nm and of the ablation rate with decreasing laser wavelength. They explained these results by the wavelength dependence of the absorption of the laser beam by the colloids. During ns-pulsed irradiation of silver at 1064 nm in water, Prochazka et al. 13 observed a decrease of the mean diameter of nanoparticles down to 12 nm as the number of pulses was increased. Further decrease of the size of Ag NPs, below 10 nm, using ns-laser pulses requires the use of ligands as shown by Mafuné et al. 14 . Recently, we also showed the impact of this attenuation of the laser beam on the shape distribution of the nanoparticles 15 .

Regarding ablation rate and relative productivity, it is still difficult to find clear information about silver colloids. In conventional batch system, the ablated amount of silver is usually evaluated from the extinction value at 250 nm in the interband region of the spectra which not affected by the size and shape of the NPs 12,14,14,16,17 . Using ns-laser pulses at 1064 nm for preparing silver colloid by PLAL, Mafuné et al. 14 estimate an ablation rate of the order of 2.10 -4 mg/pulse which corresponds, in their experimental conditions, to a relative productivity (mass/processing time/laser power) of about 1 mg/Wh. The effect of forced convection during ns-laser ablation in liquid has been examined by several authors who found that the ablation rate of the experiment were significantly improved Erreur ! Signet non défini., 17,17 showing again the importance of the particles transport in the PLAL process. The productivity is further improved by using liquid flow-based systems. By performing ps-laser pulse ablation of silver at 1064 nm in a closed-loop liquid flow cell, Barcikowski et al 18 achieved a maximum relative productivity of 5.6 mg/Wh. R. Streubel et al. 19 demonstrated the possibility to generate Ag colloids with absolute productivity of 1.8 g/h (measured after one hour ablation) in a liquid flow cell. They used ultra-high repetition rate laser (1030 nm, 3 ps, 10.1 MHz) that was scanned on the target surface at high speed (500 m.s -1 ). In addition to renew the surface under the laser flux to avoid excessive digging, scanning the target at high-speed aims to bypass the cavitation bubble which is the major issue encountered at high repetition rate. 19,19 In this system, the particle transport is performed by the liquid flowing along the target surface using a circulating pump with limited flow velocity in order to ensure sufficiently concentrated colloids.

In this work, we adopt an alternative and complementary strategy in which the laser beam is stationary and the target surface is set in motion at high-speed. We propose a novel design of PLAL setup, based on the irradiation of cylindrical target rotated at high-speed in analogy with the principle of the rotating cylinder electrode 20 . There is a fundamental difference between scanning a target surface using a galvanometer and setting in motion the target surface. In addition to renewing the surface exposed to the laser flux, the rotation of the target drives fluid flow and a shear stress in the vicinity of the surface. This should promote efficient nanoparticles transport from the surface of the bulk and reduce the screening effect of the generated particles as the laser proceeds. We investigate the effect of the rotation rate of the target on the fluid dynamics and nanoparticles mass transport and their impacts on the properties (size and shape) of the produced colloids, the ablation rate and the repeatability of the process.

Experimental section

The PLAL experiments (Fig. 1) were carried out using the fundamental wavelength (1064 nm) of a Nd-YAG laser (Continuum Surelite I-10) with a pulse duration of 6 ns and operated in all experiments at a repetition rate of 10 Hz. A λ/2 plate in combination with a thin polarizer was used as an extracavity attenuator in order to allow a precise adjustment of the laser energy and to ensure, at the same time, a good pulse-to-pulse stability (< 2%).

A 10 mm-long and 1 mm-thick silver tube (Aldrich, 99.99 % purity) with external diameter of 10 mm was used as a target. It was press fitted on a rod with 8 mm diameter that was attached to a DC brushless motor (BLDC 58, McLennan). The target was immersed in a 40 mm-light path borosilicate cell filled with 20 ml of ultra-pure water (18 MΩ.cm). The rotation rate of the target was varied within the range 300 -2400 rpm. Table 1 presents the lateral speed, the Reynolds number and the lateral interpulse distance at 10 Hz for several values of rotation rate. The lateral speed of the target reaches 1.25 m.s -1 which is comparable to the scan velocities of galvanometer scanners 21 . The laser beam was focused on the target surface (spot diameter: 600 µm) through the entrance face of the cell by means of a plano-convex borosilicate lens of 30 mm focal length.

In all experiments, the target was exposed to the laser beam during 300s at a laser fluence of 10 J/cm 2 (30 mJ/pulse).

In order to avoid excessive laser flux on the focusing lens and the entrance face of the cell, a beam expander (x2) has been placed before the focusing lens. The distance covered by the laser beam in the water was 12 mm.

Before each experiment, the silver target was polished with a 4000 micromesh sand paper to achieve a smooth surface. The target was then successively cleaned in ultrasonic baths with acetone, isopropanol and deionized water (10 min. each). We use ANSYS Fluent (CFD) software to obtain the numerical solutions of the flow patterns.

It is based on the finite-volume discretization method to evaluate the governing equations in the form of algebraic equations. In our simulations, the physical properties of water are taken constant ( = 10

. and = 10 / ). According to Gabe and Walsh 20 , the flow around a rotating cylinder is fully turbulent for = /2 > 100. Using the target diameter = 10 and its angular speed = 2 , the Reynolds number in our simulations is within the range 1571-12570 (table 1) and we use the standardturbulence model. Likewise in these regimes, the flows are possibly unsteady and the time step is taken as Δ = 1/(100 ) in order to accurately capture the time-dependent phenomena. For each frequency , we perform a grid convergence study on a structured HOH mesh topology. A special care is taken for the grid close to the target where the velocity gradients are the largest and the centrifugal hydrodynamic instabilities are likely to occur. To accelerate the computation, the deformation of the free surface close to the spinning target is neglected and a zero shear stress boundary condition is imposed on this horizontal free surface. We have recently shown Erreur ! Signet non défini. that the width of laser-machined groove on the target reflects the attenuation of the laser energy by the generated particles which accumulate in front of the target (in the hydrodynamic boundary layer) during the process. Therefore, they were systematically examined after each experiment set. Fig. 2 present a photograph of the 6 grooves left by the laser on the target rotated at 300 rpm (Fig. 2 (c)) and 2400 rpm (Fig. 2 (d)).

Results

At low rotation rate, the grooves present sharp edges and their widths are highly repeatable whereas at high rotation rate, except for the two firsts, they are irregular, narrower and a close inspection of the image (inlet in Fig. 2(d)) shows that some of them present wavy edges.

These results also reveal a clear correlation between the repeatability of the groove width and the repeatability of the colloids properties as appreciated from the extinction spectra. The TEM micrographs (Fig. 3(a),(b)) of the particles agree well with the general aspect of the extinction spectra. For low and high rotation rate, the number-weighted size distribution of the nanoparticles is well-described by a monomodal lognormal law. At low rotation rate very small and spherical particles with mean size of 3.3 nm can be obtained in pure water while at high rotation rate the mean size of the particles is twice larger. Furthermore, in this latter case, nanoparticles with Feret diameter larger than 15 nm are more frequent as seen from the representative TEM images (Fig. 3(b)) and the number-weighted distribution (Fig. 3(d)).

While number-weighted size distribution shows a monomodal distribution, the volumeweighted size distributions (Fig. 3 (e), (f)) clearly shows a bimodal distribution. The first mode is centred around 8-10 nm while the second one is in the range 15-30 nm. Note that the second mode is more intense for the particles generated at high rotation rate (Fig. 3(f)). This difference between number-and volume-weighted distributions has been previously reported by Marzun et al. 22 for palladium colloids prepared by PLAL with ps-laser pulses. The main characteristics of the extinction spectra are considerably affected by the concentration, size, shape and aggregation level of the NPs. Therefore, UV-visible spectroscopy can also provide information on the particles population 14,16 . The extinction at 250 nm which is related to the amount of ablated material 14,16 and the plasmon band intensity are presented in Fig. 4 Since all the parameters were kept constant except for the rotation rate, the different regimes described in Fig. 4 are likely to be related to changes in the liquid flow as the rotation rate is tuned. Figure 5 shows the results of the numerical simulations of the 3D flows calculated at 300 (regime A), 1200 (regime B) and 2400 rpm (regime C) in front of the target. As the rotation rate is increased, the flow patterns in the bulk solution and in the vicinity of the target exhibit significant modifications. As our system is akin to a Taylor-Couette device, we can suspect that the flows in our simulations are prone to the same centrifugal instability, leading to the various flow patterns numerically obtained. The positions of the laser-machined grooves on the target have been indicated as grey rectangles as guide for the eyes.

At 300 rpm (Fig. 5(a)), the part of the solution nearer the target surface tends to rotate with the target with a quite smooth and simple profile. In the bulk, due to the centrifugal forces, the flow is mainly composed of two large superposed and steady counter-rotating toroidal vortices that meet in the horizontal mid-plane of the target, generating a high velocity zone in this plane. Between the base of the target and the bottom of the cell, two smaller vortices appear which are related to a von Kármán layer [START_REF] Couette | Études sur le frottement des liquides[END_REF][START_REF] Von Kármán | [END_REF] (flow induced by a rotating disk). Similar flow patterns were obtained for the calculation performed at 600 rpm (not presented here).

As the rotation rate is increased, the flow patterns become more and more complex. At 1200 rpm (Fig. 5(b)), in the bulk solution, the large vortex in the lower part of the cell grows and the upper one shifts upward and shrinks. The flow field close to the target becomes less uniform and new flow patterns start to develop. The significant changing in the flow field is the typical feature of a hydrodynamic bifurcation. As the rotation rate is further increased (2400 rpm, Fig. 5(c)), the flow becomes space and time-dependent and four small unsteady vortices appear close to the target (Fig. 5(c)).

These modifications in flow regime have direct consequences on the torque exerted by the fluid on the rotating target. Its evolution as a function of time is presented for different values of the rotation rates (Fig. 6). At low rotation rates, the torque quickly reaches a steady value.

For increasing values of the rotation rate, the appearance of the unsteady flow seen in Fig. 5(b) coincides with the onset of a time dependence of the torque. This is clearly apparent at 2400 rpm where the torque fluctuates randomly with time. In Fig. 7 we have plotted the velocity module along two particular lines. In Fig. 7 (a), the curves are plotted along the x-direction at a constant altitude z=1.3 cm above the bottom of the cell (radial distribution of the velocity module). The curves at 300 rpm and 1200 rpm are

Discussion

The flow patterns (Fig. 5) and the three different regimes described in Fig. 4 appear to be closely related. In regime A, the hydrodynamic boundary layer is quite simple and can clearly be correlated to the repeatability of the process as well as that of the laser-machined groove characteristics on the target (Fig. 2(c)). The flows are mainly azimuthal (except in the midplane) and steady along the target explaining the high repeatability of the process. The particles are efficiently taken away from the target and mixed in the bulk solution. In regime C, the flow patterns were found to be markedly different. In the vicinity of the target, the flow is characterized by four small toroidal vortices which are space and time-dependent. The lack of repeatability of the process and the lower production yield at this flow regime is consistent with the onset of such instabilities. The regime B corresponds to a transitional regime (bifurcation) where the large cells are unstable and start to deform.

The transient nature in regime C of these flow patterns might also rationalize the characteristics of the grooves which are in some cases narrow and wavy at their edges. This suggests that the four small unsteady vortices are responsible for the enhancement and the transient character of the attenuation of the laser beam reaching the target surface. This can be explained by particles trapping in the vortex cores where the pressure is lesser so that they stay a longer time near the target surface. This scenario is consistent with the increase in the average sizes of the particles observed in regime C. Likewise, another explanation for the role of the small unsteady vortices in the laser beam attenuation could be the trapping of bubbles in the vortices cores. Microbubbles are formed during the ablation process18 and migrate in the solution under the combined effect of buoyancy forces and fluid flow. There are several theoretical and experimental evidences 25,26 that these bubbles can also accumulate in low pressure zones corresponding to the vortices cores.

A further interesting result was the size distribution of the produced particles and the fact the particles are mainly spherical with no evidence of fusion and aggregation. Usually such small particles can only be generated by PLAL using surfactants 14 . The main characteristics of the produced NPs (size, shape, purity) are very suitable for catalysis and other applications involving charge transfer and/or surface functionalization. 27,28 The generation of so small Ag nanoparticles in pure water by PLAL has rarely been reported. Pyatenko et al. 29 obtained a similar size distribution to that presented in Fig. 3 (c) using, as in this work, a tightly focused beam and a repetition rate of 10 Hz but with much higher energy (320 mJ/pulse) and different wavelength (532 nm) . As assumed by these authors in their study, it is also likely that our generated particles are primary particles. The latter correspond to particles formed at the earlier stage of the process via coalescence mechanisms in the laser induced cavitation bubble. Their size distribution is log-normal with a large tail to the right in good agreement with coalescence 30 as expected for their formation mechanism in the cavitation bubble 31,32,33,34 . Furthermore, these as-formed particles are quickly carried in the bulk solution by the flow preventing i) local accumulation of the particles in front of the target and their aggregation/coalescence 3 and ii) their interaction with subsequent laser pulses and fragmentation 16 . Even at the lowest rotation rate, the flow velocity of the liquid near the target is about 10 -1 m.s -1 (Fig. 7(a)) which means that during the pulses (0.1 s) the particles carried by the flow almost travel 1 cm. It should also be noted that we used a focusing lens with low f/# (f/4). In such focusing conditions, the laser fluence decreases rapidly as the distance from the target increases because of its inverse dependence on the diameter squared. The particles fragmentation may occur in the region of the beam where the fluence is sufficiently high to provoke their vaporisation otherwise they can only be, in the best case, reshaped via melting 15 . Additionally, to have a significant impact on the size distribution, the interaction volume with fluence above the vaporization threshold must be not too small compared to the total volume of the solution otherwise longer experiment duration is required 35 . The fluence threshold for the vaporisation/fragmentation of particles with size in the range of tens nm is estimated from Ref. 15 to be 2 J/cm 2 . Due to the convergence of the laser beam, the irradiated volume above this fluence threshold is of the order of 2×10 -3 cm 3 which is four order magnitudes lower than the total volume of the solution (20 cm 3 ). Furthermore, the volume-weighted size distribution (Fig. 3(e,f)) revealed that the observed average size of the primary particles is similar to that estimated from in situ study using small angle X-ray scattering 31,32,33 (SAXS) carried out with laser parameters close to ours. This is explained by the fact that SAXS is more sensitive to volume (or mass) rather than particle number 31,32,33 .

For all these reasons, it is much more likely that the generated particles are primary particles rather than fragmentation products.

Using theoretical calculations based on shape distributed effective medium theory (SDEMT) Erreur ! Signet non défini. , the volume fraction of the obtained particles was estimated to be about 10 -4 % (with an relative uncertainty of about 10 %) which corresponds to an ablation rate of about 1.2 mg/h which corresponds to a relative productivity of about 3.6 mg/Wh. The production yield can be further improved by increasing the repetition rate of the laser 19,36 . To this end, the fact that the repeatability of the process is conserved in regime B (up to about 1500 rpm, Fig. 3(a)) should enable the conduction of the process with much higher repetition rate. Commercially available Nd-YAG laser sources can display repetition rates of several hundreds of Hz offering the possibility to increase the production yield by one order of magnitude. Further increasing by another order of magnitude the repetition rate (in the kHz range) would raise the issue of the interaction of the laser beam with the cavitation bubbles 18 .

In laser conditions close to those of this work, the cavitation bubble generated, after a laser pulse, can reach a radius of about 1 mm in 150-200 µs 34 . At high repetition rate, the interaction of the laser pulse with the bubble generated by the previous laser pulse can scatter, absorb or reflect this laser beam reducing the ablation rate. Therefore, the distance between two consecutive laser impacts on the target must exceed the maximum bubble diameter. At 1500 rpm, the maximum repetition rate of the laser that fulfills this condition has been calculated to be about 4 kHz which would in theory increases by a factor 400 the productivity.

Conclusions

In summary, PLAL with a high-speed rotation target enables the generation of very small particles in pure water that are very likely to be primary particles. When tuning the rotation rate of the target, the calculated flow patterns reveal different hydrodynamic regimes which are correlated to the repeatability and the ablation rate of the process. The use of this system at higher laser repetition rate (kHz range) would in principle enables the repeatable production of high-purity nanoparticles showing average size of 3.3 nm. However, another problem raised by the increase of the repetition rate is the accumulation of the generated particles in front of the target. At 4 kHz, it is not clear whether the particles transport in the bulk solution would be sufficiently rapid to prevent this problem. This last point requires further investigations on the combined effects of repetition rate of the laser and rotation rate of the target and experiment with longer ablation time.

Figure 1 :

 1 Figure 1: Schematic diagram of the experimental setup used to produce the Ag colloids.

Figure 2

 2 Figure 2 compares a set of six extinction spectra of colloidal solutions prepared at low (300

Figure 2 :

 2 Figure 2: Set of 6 extinction spectra of silver colloidal solutions prepared at a rotation rate of

Figure 3 :

 3 Figure 3: Representative TEM micrographs (a, b), number-weighted size distribution with

Figure 4 :

 4 Figure 4: (a) Extinction at 250 nm and plasmon band intensity and (b) Full-width at half

  (a). Both curves drop abruptly around 750 rpm and otherwise remain almost unchanged as the rotation speed of the target increases. The amount of ablated silver and the plasmon band intensity were on average reduced by about 20 %. Above approximately 1500 rpm, the repeatability of the process markedly decreases as seen from the increase uncertainty bars in Fig.4(a). These trends reveal three different rotation rate regimes which we have called regimes A, B and C. In regime A (low rotation rate), the particles are produced with the highest production yield and a high repeatability while in regime B, the production yield decreases by 20 % without consequences on the repeatability which remains unchanged. In regime C, both repeatability and production yield appear clearly degraded. By contrast, the FWHM and the position of the plasmon band (Fig.4(b)) do not show significant dependence on the rotation rate. This is consistent with the fact that the particles size and shape are poorly affected by the rotation rate of the target.

Figure 5 :

 5 Figure 5: Velocity fields calculated for a rotation rate of (a) 300 rpm (regime A), (b) 1200

Figure 6 :

 6 Figure 6: Time evolution of the torque exerted by the fluid on the target for several rotation

  shape (evidently at 1200 rpm greater velocities are found) but the flow disturbance due to the fluid motion in the radial direction extends little and rapidly decays.The curve at 2400 rpm is markedly different. The flow field disturbance extends further radially evidencing a change in the hydrodynamic regime and the manifestation of the toroidal vortices stacked one on top of the other along the target. In order to better highlight this phenomenon, we have also plotted the velocity module in another direction (Fig.7(b)). The curves are plotted along the z-direction at a constant x position x=-0.1 cm to the left of the target (axial distribution of the velocity module). At 300 rpm, the profile is almost symmetrical with respect to the midplane z=1 cm with no vortices. At 2400 rpm, the vortices are now clearly visible. At the intermediate rotation rate 1200 rpm the hydrodynamic instability is not fully developed yet (transitional regime).

Figure 7 :

 7 Figure 7: (a) Horizontal profile at constant altitude z=1.3 cm (z=0 at the bottom of the cell) of

Table 1 :

 1 Lateral speed, Reynolds number and lateral interpulse distance for several rotation rates of the target (in rpm and Hz)

	Rotation rate	Rotation rate	Lateral speed	Reynolds	Lateral interpulses
	(rpm)	(Hz)	(m.s -1 )	number	distance at 10 Hz (cm)
	300	5	0.16	1571	1.6

Acknowledgements

N.C. wishes to thank Pr. Stephan Barcikowski for helpful discussions.