Candy Guiguet-Auclair

Baptiste Boyer

Keltoume Djabour

Mehdi Ninert

Estelle Verneret- Bord

Françoise Vendittelli

Anne Debost-Legrand

Validation of the French Women Abuse Screening Tool (WAST) to routinely identify intimate partner violence

Keywords: screening, intimate partner violence, WAST, accuracy

Background: Health care professionals strongly underestimate prevalence of intimate partner violence (IPV), and a few of them think that they screen and refer victims appropriately for assistance. The aim of this study was to cross-culturally validate a French version of the Woman Abuse Screening Tool (WAST).

Methods: A multicenter case-control study was performed in the forensic medicine unit of the University Hospital and two offices of the women's rights association in France. Abused and non-abused women self-completed the WAST and a questionnaire assessing their level of comfort in responding to the WAST during the study and during a hypothetical consultation with a physician in primary care. We analyzed the psychometric properties and screening performance of the WAST.

Results:

Respondent acceptability was very good, with response rates exceeding 95%. The WAST had a good internal consistency (Cronbach α coefficient = 0.95). Its screening performance with a cut-off score of 5 was excellent: area under the ROC curve was 0.99, sensitivity 97.7%, specificity 97.1%, positive predictive value 97.2% and negative predictive value 97.7%. The levels of comfort were significantly lower among abused compared with nonabused women. Both groups of women were more comfortable answering the WAST during the study than in a hypothetical consultation.

Conclusion:

The French version of the WAST was found to be a well-accepted and valid screening tool for routine use in IPV. It may help health care professionals to detect women experiencing abuse early and to refer them more quickly to specific assistance.

INTRODUCTION

Intimate partner violence (IPV) is well recognized as a major public health problem. [START_REF] García-Moreno | Global and regional estimates of violence against women: prevalence and health effects of intimate partner violence and nonpartner sexual violence[END_REF] IPV prevalence in Europe is estimated to exceed 20% in women aged 15 years and older. [START_REF]Violence against women: an EU-wide survey Main results[END_REF] In France, every year, almost 220 000 women aged 18 years and older are victims of physical and/or sexual violence by their current or former partner: one woman is killed every three days. [START_REF]Etude Nationale sur les morts violentes au sein du couple[END_REF] It accordingly appears important to identify abused women as early as possible, but this is not always done in primary health care settings, even though it has been reported that this screening is generally well accepted by women, who even appear to favor generalized screening. [START_REF] Taft | Screening women for intimate partner violence in healthcare settings[END_REF][START_REF] Usta | Involving the health care system in domestic violence: what women want[END_REF] Several studies have attempted to identify the obstacles to screening by various health professionals. [START_REF] Waalen | Screening for intimate partner violence by health care providers. Barriers and interventions[END_REF] The first barrier was their lack of experience and any specific training: [START_REF] Taft | Screening women for intimate partner violence in healthcare settings[END_REF][START_REF] Gutmanis | Factors influencing identification of and response to intimate partner violence: a survey of physicians and nurses[END_REF] they sometimes lack knowledge and have prejudices about IPV. Health care professionals strongly underestimate the prevalence of IPV, and a few of them think that they screen and refer victims appropriately for assistance. [START_REF] Cann | Domestic violence: a comparative survey of levels of detection, knowledge, and attitudes in healthcare workers[END_REF][START_REF] Ramsay | Domestic violence: knowledge, attitudes, and clinical practice of selected UK primary healthcare clinicians[END_REF] Other studies indicate that they do not screen for it because they lack the tools and referral procedures necessary for them to provide effective care for these patients. [START_REF] Waalen | Screening for intimate partner violence by health care providers. Barriers and interventions[END_REF][START_REF] Beynon | Why physicians and nurses ask (or don't) about partner violence: a qualitative analysis[END_REF] National guidelines about IPV screening have also been discordant. [START_REF] Thombs | Consistency and sources of divergence in recommendations on screening with questionnaires for presently experienced health problems or symptoms: a comparison of recommendations from the Canadian Task Force on Preventive Health Care, UK National Screening Committee, and US Preventive Services Task Force[END_REF] Several questionnaires have been developed to screen for IPV. [START_REF] Feltner | Screening for Intimate Partner Violence, Elder Abuse, and Abuse of Vulnerable Adults: An Evidence Review for the U.S. Preventive Services Task Force[END_REF] To our knowledge, however, no screening tool is currently validated in French for use by health care professionals in standard medical consultations to refer victims as early as possible to local resources appropriate for their situation. For routine use in primary care settings, an effective tool must be easy to use, have a simple scoring procedure and cut-off scores, screen for all areas of abuse and have good psychometric properties. Long screening tools are too detailed to be suitable in clinical situations.

Among the brief tools suitable for clinical use, the Woman Abuse Screening Tool (WAST), an English-language questionnaire, asks about physical, psychological and sexual abuse.

Developed for the family practitioners -to be practical for them, understandable and acceptable to women, [START_REF] Brown | Development of the Woman Abuse Screening Tool for use in family practice[END_REF] it has been used in several studies. [START_REF] Feltner | Screening for Intimate Partner Violence, Elder Abuse, and Abuse of Vulnerable Adults: An Evidence Review for the U.S. Preventive Services Task Force[END_REF] Wathen et al. [START_REF] Wathen | Who is Identified by Screening for Intimate Partner Violence?[END_REF] reported sensitivity and specificity of almost 90% with a cut-off score of 4. [START_REF] Feltner | Screening for Intimate Partner Violence, Elder Abuse, and Abuse of Vulnerable Adults: An Evidence Review for the U.S. Preventive Services Task Force[END_REF][START_REF] Wathen | Who is Identified by Screening for Intimate Partner Violence?[END_REF] Its internal consistency is good, with a Cronbach's α coefficient of 0.75. [START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] Acceptability is also good with more than 90% of the women stating they would be (hypothetically) or were comfortable when asked these questions by their family physician. [START_REF] Brown | Development of the Woman Abuse Screening Tool for use in family practice[END_REF][START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] Family physicians also report that they are comfortable administering the WAST and perceive this tool to be very helpful in screening for IPV. [START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] Our main objective was to cross-culturally validate a French version of the WAST and evaluate its psychometric properties and its performance in screening for IPV. A secondary objective was to assess women's comfort in completing the WAST during the study and a hypothetical consultation with a primary care physician.

METHODS

Study design

This multicenter case-control study took place from July 2016 through April 2019 in France.

The case women had been abused, while the control women had not. All women in both groups were asked to participate voluntarily and assured their information would remain anonymous.

Participants and settings

Participants were aged 18 years or older, able to understand, speak and read French and involved in an intimate relationship with one partner for at least 12 months. Professionals identified and approached the abused women at three different sites: the forensic medicine unit of the Clermont-Ferrand University Hospital and two offices of the women's rights association in Auvergne (Centre d'informations des droits des Femmes et des Familles, CIDFF). The control women were selected among the investigators' professional and private contacts, students in postsecondary paramedical and public health faculties. Women were asked not to participate if they believed they had a history of IPV.

All participants provided informed consent. The French regional ethics committee (Comité d'Ethique des Centres d'Investigation Clinique de l'Inter-région Rhône-Alpes-Auvergne, CECIC, Grenoble, IRB 5921) approved the project.

Data collection

All women completed self-administered questionnaires, in a private room, the cases during an appointment with investigators, the controls during an information session about the survey.

The women were left alone while they completed the questionnaire. Information leaflets pertaining to IPV and to locally available resources for women exposed to violence were distributed to the controls.

Measures

The self-completed questionnaires included:

-The WAST instrument which comprises eight items. The first two items assess difficulties in relationship between the woman and her partner. The next six items assess the woman's experience of physical, emotional and sexual violence. Each item is rated on a 3-point Likert-like scale from 0 to 2. The total score is calculated by summing the scores of the eight items (only for women who answered all items) and ranged from 0 to 16. The higher the total score, the greater the abuse.

-A questionnaire assessing women's level of comfort in responding to the WAST and each of its items during the study, and what they thought their level of comfort would be if they had to answer these questions during a consultation with a physician in primary care. Ratings were based on a 5-point Likert-like scale, from 1 (not at all comfortable) to 5 (very comfortable).

-Demographic data: for women: age, employment and marital status, relationship duration, current living situation, birth country, education level, parity and pregnancy at the moment of the interview; for their partner: age, education level and employment.

Translation and cultural adaptation of the WAST

We followed established guidelines to cross-culturally adapt this instrument from English into French. Forward translations from English to French were independently performed by three French native-speaking bilingual translators fluent in English, two of them experts in IPV and one unfamiliar with this topic. Next, two English mother tongue translators fluent in French and blinded to the original English version performed backward translations. A multidisciplinary expert committee (composed of two methodologists, a language professional and two IPV experts) reviewed the process, compared the source and target versions and resolved discrepancies. The consensus French version was pretested on a sample of 20 women: 11 abused and 9 not. Their responses and comments were reviewed to check the understandability and content validity of the WAST items. The committee adopted this last version as the prefinal one (Supplementary material 1).

Statistical Analysis

All statistical analysis were performed with SAS v9.4 software (SAS Institute). Two-sided Pvalues < 0.05 were considered statistically significant. Continuous data are presented as means (standard deviations). Categorical data are presented as numbers (%).

We calculated the sample size based on a WAST sensitivity of 88% with a standard error of 0.01. [START_REF] Wathen | Who is Identified by Screening for Intimate Partner Violence?[END_REF] We aimed to obtain an 86% sensitivity for the French version, corresponding to the lower endpoint of the 95% confidence interval, with a precision of 5%. Given that our casecontrol study had one case for each control, we calculated that 185 subjects would be required in each group.

Characteristics of abused and non-abused women were compared with Chi-square, Fisher exact or nonparametric Mann-Whitney tests.

For the psychometric evaluation of the WAST:

1. Data completeness (to measure respondent acceptability) was determined by looking at response rates for the complete questionnaire (all eight items together) and for each item individually.

2. Descriptive statistics and score distribution were assessed: percentages were used for the distribution of each item score; the mean, standard deviation, range, median and interquartile range were used for the distribution of the WAST total score. We estimated the percentages of women with the minimum and maximum scores: a floor or ceiling effects were defined if these percentages were more than 15%. [START_REF] Terwee | Quality criteria were proposed for measurement properties of health status questionnaires[END_REF] Chi-square (or Fisher's exact) tests were used to compare the two groups for each item rating and nonparametric Mann-Whitney tests for the total score. 3. Internal consistency was tested with Cronbach's α coefficient. Item-total consistency was analyzed to evaluate the extent of the linear relation between each item and the total score, corrected for overlap. A minimum correlation coefficient of 0.40 was considered indicative of good item-total consistency. [START_REF] Ware | Conceptualisation and Measurement of Health for Adults in the Health Insurance Study[END_REF] 4. The performance of WAST as a screening test for IPV was evaluated by a receiving operating characteristic (ROC) curve and the area under it (AUC). [START_REF] Zhou | [END_REF] The ROC curve represents the WAST's ability to discriminate between women who have and have not experienced abuse.

The AUC ranges from 0.5 to 1 with higher values indicating better accuracy.

Finally, we compared the groups for their level of comfort with the WAST with nonparametric Mann-Whitney tests.

RESULTS

Participants' characteristics

In the study, 361 women participated: 181 who had and 180 who had not been abused. Among the abused women, 39.8% had been recruited at the hospital's forensic medicine department, and 60.2% at the CIDFF.

Table 1 shows the characteristics of both groups. They differed significantly for all characteristics assessed except age (of women and their partners) and pregnancy. Abused women were more frequently separated or divorced, and their relationships with their current partners were of shorter duration (P = 0.03). Abused women more often did not live with their partner (P < 0.0001), were more likely to have been born in a foreign country (P = 0.0002) and to have children (P = 0.008). Moreover, 31.4% of the abused women lived in single-parent households compared with 4.1% of those not abused (P < 0.0001).

Data completeness and WAST score distributions

The response rate to all eight WAST items was 97.5% (97.8% of the abused women and 97.2% of those not abused). For each item, response rates ranged from 97.8% to 99.4% among abused women and from 98.9 to 100% among the others. No ceiling effect was found, but a floor effect for the total score was observed among the non-abused women: 61.7% scored the minimum zero points.

Table 2 shows the distribution of each WAST item and the total score. Significant differences were found between women who had and had not experienced abuse for each item (P < 0.0001). Of the non-abused women, 97.8%, 93.3% and 99.4% reported that they had never been abused physically, emotionally or sexually, respectively; compared with 12.4%, 5.6% and 70.2% in the abused group. The mean total score was significantly higher in the abused group (P < 0.0001).

Internal consistency of the WAST

The French version showed good internal consistency, with a Cronbach's α coefficient of 0.95 (0.81 in the abused group and 0.79 in the non-abused group) (Table 3). Corrected item-total correlations ranged from 0.50 to 0.88 and were all significant.

Screening performance of the WAST

The area under the ROC curve was 0.99 (95% CI, 0.98-1.00), showing excellent discrimination by the total score. A cut-off point of five yielded optimal results with a sensitivity of 97.7%, a specificity of 97.1%, a positive predictive value of 97.2% and a negative predictive value of 97.7%. With the use of this cut-off, true victims of violence would be 34.2 times more likely to be classified as abused than true non-victims and true non-victims only 0.02 times more likely to be classified as abused than a true victim.

Patient comfort with the WAST

Table 4 presents the women's ratings of comfort in answering the WAST questionnaire and each of its items during the study and during a hypothetical consultation with a physician in primary care. Comfort was significantly lower among abused compared with non-abused women. Both groups of women were more comfortable answering these questions during the study than in a hypothetical consultation.

DISCUSSION

The French cross-cultural validation of the WAST demonstrated good validity and screening performance for IPV with excellent discrimination between the women with and without experience of IPV.

Respondent acceptability was very good, with response rates exceeding 95% in both groups for every item. Earlier research has indicated that women are fairly favorable to studies of IPV. [START_REF] Macmillan | Approaches to screening for intimate partner violence in health care settings: a randomized trial[END_REF][START_REF] Macmillan | Screening for intimate partner violence in health care settings: a randomized trial[END_REF] These high response rates confirm that women are more reassured by approaches providing confidentiality and privacy, for example, allowing them to complete questionnaires alone in private settings. [START_REF] Macmillan | Screening for intimate partner violence in health care settings: a randomized trial[END_REF][START_REF] Hussain | A comparison of the types of screening tool administration methods used for the detection of intimate partner violence: a systematic review and meta-analysis[END_REF] The Cronbach α coefficient of 0.95 confirmed the WAST's good internal consistency and was higher than those obtained in the original study [START_REF] Brown | Development of the Woman Abuse Screening Tool for use in family practice[END_REF][START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] or in the Spanish or Indonesian validation studies. [START_REF] Fogarty | Screening for abuse in Spanish-speaking women[END_REF][START_REF] Iskandar | Testing the woman abuse screening tool to identify intimate partner violence in Indonesia[END_REF] The corrected item-total correlations of the WAST exceeded 0.40; to our knowledge, they have not previously been studied.

The ROC analysis yielded a cut-off score of five to discriminate between women with and without experience of abuse. Both sensitivity and specificity exceeded 95%.The prevalence of IPV in France is estimated at 26% in the general population, 2 so that the positive and negative predictive values of the WAST are nearly 90%. The largest study using the WAST with a cutoff score of four reported a sensitivity of 87% and a specificity of 89% in a population of women from various clinical settings. [START_REF] Wathen | Who is Identified by Screening for Intimate Partner Violence?[END_REF][START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] Another study in Indonesia reported a sensitivity of 41.9% and a specificity of 96.8% with a cut-off score of four. [START_REF] Iskandar | Testing the woman abuse screening tool to identify intimate partner violence in Indonesia[END_REF] In our study, the women in the abused group were single mothers much more often than the general population of French women (31.4% versus 13.1%), and they had a more vulnerable occupational status, with a higher unemployment rate (31.1% versus 7.8%). 24 Their education level was nonetheless similar to that of women of this age group in France. They may therefore belong to a particular category of IPV victims; the data about the association between socioeconomic status and IPV are contradictory. [START_REF]Violence against women: an EU-wide survey Main results[END_REF][START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF][START_REF] Dias | Social support and the intimate partner violence victimization among adults from six European countries[END_REF][START_REF] Costa | Male and female physical intimate partner violence and socio-economic position: a cross-sectional international multicentre study in Europe[END_REF] The abused women in our study were older than those in other studies. Nonetheless, the older women in this study reported less IPV than younger women, as in the literature. [START_REF]Violence against women: an EU-wide survey Main results[END_REF][START_REF] Coker | Frequency and correlates of intimate partner violence by type: physical, sexual, and psychological battering[END_REF] These points, as well as the more frequent socioeconomic difficulties among the abused women, may be related to the recruitment procedure: two-thirds of the abused women were recruited from the CIDFF (women's rights association). Its principal mission is to support women seeking access to jobs and occupational training. However, Costa et al. [START_REF] Costa | Male and female physical intimate partner violence and socio-economic position: a cross-sectional international multicentre study in Europe[END_REF] also found that a low level of education and disadvantaged socio-economic status were associated with IPV. Brown et al. [START_REF] Brown | Development of the Woman Abuse Screening Tool for use in family practice[END_REF] and Wathen et al. [START_REF] Wathen | Who is Identified by Screening for Intimate Partner Violence?[END_REF] found differences between abused and non-abused women according to marital status and socioeconomic status, as in our study.

Our study showed that abused women were less comfortable than their non-abused counterparts in answering the WAST questionnaire. Their level of discomfort was still higher for a hypothetical face-to-face consultation with a physician in primary care, as previously reported. [START_REF] Brown | Development of the Woman Abuse Screening Tool for use in family practice[END_REF][START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF][START_REF] Fogarty | Screening for abuse in Spanish-speaking women[END_REF][START_REF] Brown | Screening for violence against women. Validation and feasibility studies of a French screening tool[END_REF] The levels of comfort for hypothetical consultations in our study were lower than those reported by Brown et al. [START_REF] Brown | Development of the Woman Abuse Screening Tool for use in family practice[END_REF][START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] but higher than in Fogarty et al.. [START_REF] Fogarty | Screening for abuse in Spanish-speaking women[END_REF] This result underlines the disadvantage of screening by health care professionals, especially by those in private practice. [START_REF] Feder | Women exposed to intimate partner violence: expectations and experiences when they encounter health care professionals: a metaanalysis of qualitative studies[END_REF] Physicians must establish a climate of confidence and respect to be able to approach this issue; women look to physicians for help more often than to other professionals. [START_REF] Feder | Women exposed to intimate partner violence: expectations and experiences when they encounter health care professionals: a metaanalysis of qualitative studies[END_REF][START_REF] Feder | Identification and Referral to Improve Safety (IRIS) of women experiencing domestic violence with a primary care training and support programme: a cluster randomised controlled trial[END_REF][START_REF] Mørk | Barriers among Danish women and general practitioners to raising the issue of intimate partner violence in general practice: a qualitative study[END_REF] The training of health care professionals combined with their use of effective tools appears to be a lever that enables useful management of victims. [START_REF] Feder | Identification and Referral to Improve Safety (IRIS) of women experiencing domestic violence with a primary care training and support programme: a cluster randomised controlled trial[END_REF] Our study has some limitations. First, we do not know the women's response rates: how many women were approached for eligibility, how many were eligible, how many refused to participate and why. So, we could not compare the characteristics of respondents and nonrespondents. However, our recruitment was based on the sample-size achievement. We did not reach the planned sample size of 185 women per group. Nonetheless, post-hoc analysis showed that sensitivity was estimated with a precision of 2% compared with the 5% hypothesized in our sample size calculation.

We did not study the level of comfort of the health care professionals using the WAST, as Brown et al. [START_REF] Brown | Application of the Woman Abuse Screening Tool (WAST) and WAST-short in the family practice setting[END_REF] did. The usefulness of WAST as perceived by professionals remains to be evaluated.

Our study included only women with a clear history of abuse in the abused group, and we discouraged women with such a history from participating in the control group. Accordingly, the performance of the WAST may be overestimated in our sample compared with the general population. Moreover, some women among controls were recruited from the investigators' professional and private contacts. A declaration bias due to social desirability could exist as contacts could hide abuse. However, less than ten close contacts were finally recruited in the control group so that misclassification bias may hardly occur.

Future research is needed. Our results must be confirmed in a community sample. Moreover, screening is only a first stage and cannot be effective until it is accompanied by measures appropriate for these women such as helping the women develop a safety plan and referring them to appropriate service providers. [START_REF] Taft | Screening women for intimate partner violence in healthcare settings[END_REF][START_REF]Responding to Intimate Partner Violence and Sexual Violence Against Women: WHO Clinical and Policy Guidelines[END_REF] Health care professionals' knowledge about IPV and their ability to aid victims must be assessed if appropriate training is to be developed. This training must aim to meet two objectives: first, to learn to use screening tools such as the WAST to identify victims as early as possible; and second, to master the best procedures for referring these women to appropriate assistance to remove or reduce their exposure to violence and improve their QoL. [START_REF] Taft | Screening women for intimate partner violence in healthcare settings[END_REF] In summary, the French version of the WAST was found to be a well-accepted and valid screening tool for use in IPV. Its screening performance with a cut-off score of 5 was excellent.

WAST may help health care professionals to detect women experiencing abuse early and to refer them more quickly to specific assistance.

Table 1 : Characteristics of abused and non-abused women Abused women Non-abused women

 1

	(n = 181)	(n = 180)	P Value

Table 2 : WAST item responses and total score Abused women Non-abused women

 2

	(n = 181)	(n = 180)	P Value

Table 3 : Internal consistency and corrected item-total correlations of the WAST

 3

	Abused	Non-abused	Total
	women	women	(n = 361)
	(n = 181)	(n = 180)

Table 4 : Women levels of comfort completing the WAST during this research and during a hypothetical consultation with a physician in primary care (range 1 -not all comfortable to 5 -very comfortable) Research context Hypothetical consultation in primary care context

 4

	Abused	Non-abused		Abused	Non-abused
	women	women		women	women
	(n = 181)	(n = 180)	P Value	(n = 181)	(n = 180)	P Value

Acknowledgments

The authors thank the CIDFF and the forensic medical department for participating in this study.

Funding

This work was supported by the Conseil Régional d'Auvergne.

Conflict of Interest

None declared.

Key points

• The French version of the woman abuse screening tool (WAST) is validated

• The WAST cut-off score was established at 5 in the French version

• Screening performance of the WAST is excellent with a sensitivity over 95%.

• Women feel uncomfortable reporting abuse in primary consultation

Supplementary material 1 : French version of the WAST

Questionnaire WAST

Ces questions portent sur les 12 derniers mois.


S Meynet
email: serge.meynet@coria.fr

V Moureau

G Lartigue

A Hadjadj

AUTOMATIC SURFACE AND VOLUME MESH GENERATION FOR ROUGHNESS-RESOLVED LES OF ADDITIVE-MANUFACTURING HEAT EXCHANGERS

In order to quantify the impact on the heat exchanger performances of the wall roughness introduced by additive manufacturing, roughness-resolved Large-Eddy Simulation (RRLES) is a valuable tool. However, representative rough surfaces and highquality body-fitted grids of these surfaces are difficult to generate automatically, which prevents from building parametric RRLES databases that can be used for model development. In this work, a rough surface generator with a fine control on the height distribution in the three space directions is proposed. This tool creates triangulated surfaces that are the input of a parallel body-fitted tetrahedral mesh generator. In this latter, the cell size and its gradient and the element skewness are well controlled enabling their use for high-fidelity LES.

Introduction

In the aeronautical and aerospace engineering, additive manufacturing paves the way for new designs of critical components and especially heat exchangers [START_REF] Carozza | Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls[END_REF]. Recent progresses in additive manufacturing are a great opportunity for innovation aiming at Compact Heat Exchangers (CHX). Pressure loss and heat transfer performances are the two main characteristics to be optimized for heat exchanger efficiency. However, the important roughness introduced by additive manufacturing strongly impacts these performances [START_REF] Arie | Performance Characterization of an Additively Manufactured Titanium (Ti64) Heat Exchanger for an Air-Water Cooling Application[END_REF]. There is a lack of fundamental knowledge on how these untypical roughness structures modify the heat transfer and pressure loss introducing a strong uncertainty between computer design and industrially printed parts. Reducing this uncertainty and better controlling the performance of 3D printed heat exchanger could be achieved with better rough-wall models and roughness-resolved Large-Eddy Simulation databases could help in this task. This paper focuses on how defining representative rough surfaces and how to generate 3D roughnessresolved unstructured and body-fitted meshes with a fine control on the cell size distribution.

2 Rough-surface generator (RSG) Surface roughness parameters that characterize the height moments of a surface are categorized into three groups: amplitude, spacing and hybrid. Predominant roughness parameters commonly used in the literature are the arithmetic average height denoted S a , the rootmean-square height S q , skewness Sk, kurtosis Ku and the roughness density (Λ) or the effective slope ES [START_REF] Gadelmawla | Roughness parameters[END_REF]ISO 25178-2). The arithmetic average height is the most known among the parameters and is usually used to control the roughness of manufactured parts. This is defined as the average absolute deviation of the roughness irregularities compared to the mean roughness height z m , which is assumed to be zero throughout the paper. The rootmean-square height S q is also another important parameter which is more difficult to measure. While skewness quantifies the asymmetry of the PDF, kurtosis describes its sharpness. Surface with high peaks or deep valleys correspond to respective positive or negative skewness. If Ku < 3, the distribution curve is said to be platykurtoic and has relatively few sharp peaks. In contrary if R ku > 3, the distribution is said to be leptokurtoic and many sharp peaks are located on the surface. The case Ku = 3 belongs to a Gaussian PDF. Additional information is needed about the spatial properties of the surface in the other wall-tangential space directions. Studies [START_REF] Napoli | The effect of the slope of irregularly distributed roughness elements on turbulent wall-bounded flow[END_REF][START_REF] Carozza | Numerical observations of turbulence structure modification in channel flow over 2D and 3D rough walls[END_REF] have underlined the predominance of the effective slope in predicting roughness effects, defined as the average of the slope of the roughness along the streamwise direction:

ES = 1 L x L y Lx Ly | ∂z(x, y) ∂x | dxdy (1)

Roughness in additive manufacturing

In additive manufacturing, several factors have an impact on the surface topography like the thickness of printed layers, the angle of the surface compared to the horizontal build bed, powder's particle size distribution for power bed methods or the laser power and scan speed for Selective Laser Melting (SLM), the material used and many more. For the targeted applications in this present work, surface finishing is not considered as such procedure can not be applied for CHX.

Nevertheless, one key point is that surfaces produced with AM are likely non-Gaussian and anisotropic. Due to the layer-by-layer nature of AM process, patterns of peaks or valleys called welding tracks can be distinguished in general. Slags also appear on surface due to powder particles or material which are not correctly melted (Cabanettes et al., 2018).

Numerical method

The chosen method to generate numerically rough surfaces relies mainly on the algorithm described by [START_REF] Hu | Simulation of 3-D random rough surface by 2-D digital filterand Fourier analysis[END_REF] and with improvements from [START_REF] Bakolas | Numerical generation of arbitrarily oriented non-Gaussian three-dimensional rough surfaces[END_REF]. They have developed a random surface generation approach based on Fourier analysis, filtering, and Johnson translator system (Johnson, 1947). These key points are described here.

Heightmap and areal autocorrelation function.

Due to the fact that rough surfaces can be assimilated to a random process, two statistical functions are sufficient to obtain a given surface: the elevation distribution PDF and the areal autocorrelation function (AACF). The latter represents the dependence between height values at one specific location on such values at another position. It is defined as:

AACF (τ x , τ y ) = E[z(x, y)z(x + τ x , y + τ y )] (2)
with E the expected value of the product between height elevation at two different locations. This definition introduces two correlation lengths τ x and τ y respectively along the x-axis and the y-axis. They characterize the length at which the AACF drops to 10% of its nominal value in the given direction. For isotropic surfaces, these lengths are equal but their values differ for anisotropic ones.

Considering the patterns observed in additive manufacturing, only anisotropic surfaces are considered in this work. The AACF incorporated in the RSG and imposed as input is the following:

AACF (x, y) = S 2 q exp   - x τ x 2 + y τ y 2 1 2   (3)
Filtering and Fourier analysis. The considered procedure is based on 2D digital filtering technique exposed by [START_REF] Hu | Simulation of 3-D random rough surface by 2-D digital filterand Fourier analysis[END_REF]. Such filter is a system transforming an initial

(N +n) x (M +m) matrix [η i,j ] into an output N x M matrix [z i,j ].
With finite impulse response (FIR) filters particularly, and given a 2D random sequence [η(i, j)], the transformation is written as:

z(i, j) = n k=1 m l=1 h(k, l)η(i + k, j + l) (4)
where coefficients h(k, l) are to be determined for producing the expected AACF. As suggested by [START_REF] Hu | Simulation of 3-D random rough surface by 2-D digital filterand Fourier analysis[END_REF], a windowing function w(k, l) is applied onto the filter coefficients to reduce the Gibbs phenomenon. The chosen w(k, l) is a Gaussian window function:

h w (k, l) = h(k, l)w(k, l) (5)
The Fourier transformation of the equation ( 4) yields:

Z(w x , w y ) = H(w x , w y )A(w x , w y ) (6)
Fourier transform of z and η are respectively Z and A. The transfer function H can be calculated with the relation between power spectral densities (PSD) of η (S η ) and z (S z ):

S z (w x , w y ) = | H(w x , w y ) | 2 S η (w x , w y ) (7)
As [η(i, j)] is considered being a Gaussian sequence, the PSD S η is equal to a constant value. S z corresponds to the Fourier transformation of the expected AACF. An inverse Fourier transformation applied on H(w x , w y ) gives the filter coefficients h(k, l).

For anisotropic non-Gaussian surfaces, another transformation step applied to the sequence η is required to give a non-Gaussian sequence η . This is done through a so-called Johnson translator system (Johnson, 1947). The root-mean-square S q is conserved but new skewness Sk η and kurtosis Ku η factors have to be modified for η . A convolution between filter coefficients and this new sequence yields desired S q , Sk, Ku and AACF for the output surface z(i, j).

The Johnson curves are integrated in the outer-loop algorithm given by [START_REF] Hill | Algorithm AS 99: Fitting Johnson Curves by Moments[END_REF] and modified by [START_REF] Tuenter | An algorithm to determine the parameters of SU-curves in the johnson system of probabillity distributions by moment matching[END_REF] to determine the parameters S U of the Johnson curves.

Implementation of periodic boundaries

Useful for some cases, a procedure for ensuring periodic boundaries with continuous slope has to be integrated into the RSG as exposed in Fig. 1. First, the desired planar surface is repeated in xand y-directions. Then a 2D Savitzky-Golay filter is applied on the global surface. This kind of filter is widely known for signal processing. Finally, we extract the half of the surface in each direction which ensures the periodicity.

Generated surfaces and geometries

The RSG has been applied successfully to periodic and non-periodic planar surfaces, parallel planes, square and cylindrical channels. Furthermore, unmelted particles and slags are present on the surface topography in AM. Thus, a union of spheres procedure has been incorporated as an option to enable this characteristic of AM surfaces. Examples of these geometries are shown in Fig. 2.

Performances and limitations

In the surface generation process, many Gaussian series have to be generated until the transformed data set matches the required statistical parameters. Then, as a high precision is required on the generated surface properties, a lot of series are necessary. This is why we have introduced a threshold on desired values for skewness and kurtosis. This threshold corresponds to +/-5% of the target value. For the testing of the RSG, several planar surfaces were generated with different roughness parameters and correlation lengths values. The spacing along x-axis and y-axis is 2 µm and the AACF used is written in equation 3. In addition, some results on performances are presented in the table 1. The chosen correlation lengths for these tests are τ x = 50 µm, τ y = 20 µm. Once the STL surface is generated, meshing is a critical step for predictive roughness-resolved LES. The challenge lies in the strict control of both the mesh size and quality. The size is important as it gives the cut-off between the resolved and modeled scales. The cell-size gradient is also important as it may lead to space commutation errors in LES or to local mesh quality issues. Finally, the mesh quality, often measured through the cell skewness, has to be good enough to avoid introducing numerical errors in the finite-volume schemes. This is why a fullyautomatic and well-controlled procedure for generating roughness-resolved meshes is required. The idea is that both the fluid and solid domains have to be discretized with body-fitted tetrahedral-based meshes with a controlled resolution at the wall. The RRMG, whose principle is exposed in Fig. 3, is a volume-based mesh generator. It is not strictly a mesh generator as it requires a coarse input mesh that will be modified and cut to obtain the final mesh. The RRMG is based on many features available in the YALES2 code. YALES2 is an unstructured low-Mach number code developed at CORIA for the Direct Numerical Simulations and Large-Eddy Simulations in complex geometries [START_REF] Moureau | Design of a massively parallel CFD code for complex geometries[END_REF]. It heavily relies on the parallel volume and surface mesh adaptation developed jointly with INRIA, LEGI and SAFRAN TECH. This adaptation provides a fine control on the cell size and its gradient over the volume and at the roughness surface. However, the mesh adaptation requires to know where to adapt the mesh in the coarse initial mesh, i.e. where the resolved-roughness boundary is located. To this aim, many other features of YALES2 are used: handling of partitioned triangle sets similar to STLs, level set creation and displacement, computation of geometric distance to a level set or to triangles in parallel on unstructured grids, ... All these features participate to the process which is exposed hereafter. Given one or several STL files, one has to prescribe a desired cell size per STL and the name of the new boundary condition which will be created. One or several interior points have to be prescribed in order to distinguish between the interior and the exterior of the surface (fluid or solid).

Principle

Numerical procedure of the RRMG

Step 1: Reading of the STL surface and distribution on processors.

The first step of the process is the reading of the STL files and a first isotropic adaptation step in order to get enough triangles to perform the distribution onto the processors. The isotropic STL file adaptation is performed in the code with calls to the MMGS adaptation library. Then, the STL is colored with the METIS library and distributed. Each group of triangles is represented as a master sub-surface on one processor and several slave or ghost surfaces on the other processors which also have a bounding box which crosses the one of the sub-surface. From the initial surface generated with the RSG illustrated in Fig. 4, the refinement and the distribution are represented in Fig. 5. This distribution mechanism is essential to get good performances on a large number of processors. Step 2: Generation of Lagrangian markers from the surface. Once the STL file is read, refined and distributed on the processors, lagrangian particles are created at the triangle barycenter and at the nodes of the master surfaces as shown in Fig. 6. These lagrangian particles carry some data as the original triangle node coordinates and the desired cell size but, they are easier to handle than triangles. These particles are relocated on the grid to find to each cell they belong and they can then be used to compute approximate distance, i.e. the minimum distance of a node of the mesh to the particles, or an exact distance based on the projection on the triangles carried by the lagrangian particles.

Step 3: Computation of approximate distance to surface.

After the particles are relocated on the volume mesh, the approximate distance of each node of the volume mesh to the surface is computed. This distance is used to build the desired cell size in the volume.

Step 4: Volume adaptation of the Eulerian mesh.

With the approximate distance, the cells in the vicinity of the surface can be refined by defining a specific metric field. This metric field is smaller at the surface location and has to respect a maximum cell size gradient condition. In order to keep a good quality of the volume mesh, several successive steps are performed. At the final step, the metric at the surface is equal to the desired cell size. The number of steps can be adjusted depending on the ratio between the cell size of the initial mesh and the final desired cell size at the surface. For the moment, the interior and the exterior of the final flow domain are not distinguishable and the cells close to the surface do not coincide with it.

Step 5: Calculation of a levelset function from interior points and markers.

In order to ultimately get a body-fitted mesh, the surface has to be materialized in the unstructured mesh. To this aim, an implicit representation of the surface is created thanks to a distance-based level set method. In this method, a signed distance function has to be generated. The surface is then the zero isocontour of this level set. Building a distance function, which is positive on both sides of the surface is trivial. However, building a signed-distance function is more challenging. The chosen algorithm here is based on a level set displacement. The algorithm is the following:

• a geometric distance to the lagrangian particles is computed in a narrow band around the surface. This parallel algorithm is based on a fastmarching method [START_REF] Janodet | An unstructured conservative level-set algorithm coupled with dynamic mesh adaptation for the computation of liquid-gas flows, 29th European Conference on Liquid Atomization and Spray Systems Johnson, N.L[END_REF]. The idea is to build at each node the list of the closest lagrangian particles to the surface. The distance is then obtained by projecting the node position onto the triangles represented by the lagrangian particles.

• the desired cell size is substracted from the geometric distance creating a small negative distance region around the surface. This step creates two zero iso-contours of the level set around the surface.

• from the interior points and based on the volume mesh connectivity, the interior domain up to the first level set is flagged and kept. The remaining domain is given a negative distance. At the end of this step, only one level set remains.

• The remaining level set is displaced back by adding the desired cell size.

While this methodology gives an approximate description of the surface on the volume mesh, the errors have been assessed and they are small and of the order of a fraction of the desired cell size. The great benefit of using a level set is that it automatically corrects some topology issues of the STL files. Since the algorithm is distance-based, no topological properties is needed for the STL files.

Step 6: Cutting of the Eulerian mesh.

Once the signed-distance level set function is built, the Eulerian mesh is cut, i.e. that all the edges, faces and cells which are crossed by the level set function are tessellated in order to transform the implicit surface into an explicitly meshed surface. In a tetrahedron, the cutting algorithm has to consider the number of edges that are crossed by the level set (3 or 4 edges). Then, to have a fully parallel algorithm, a global index of the nodes has to be considered in order to have compatible faces between two cut elements that share a parallel interface.

Step 7: Removal of the outer cells. After the cut, the outer cells that are already flagged can be removed from the volume mesh. This step requires to rebuild some connectivity in parallel and to distribute the grid again onto the processors to keep good performances.

Step 8: Volume/surface adaptation of the interior Eulerian grid.

The mesh that undergoes the preceding steps is of good quality inside the volume but of very poor quality at the surface as the mesh cut generates very small edges and potentially highly skewed elements. Then, parallel volume and surface adaptation is performed with the MMG library to recover a correct mesh. The final mesh is represented in Fig. 7. The final mesh obtained at the end of the full generation process and illustrated in Fig. 7 is assessed in this section. To this aim, the skewness distribution and the cell-size distribution based on the cell volume are given in Fig. 8 and9. To minimize the truncation errors of the finite-volume schemes of YALES2, it is necessary that a mesh contains cells which the maximum skewness is below 0.8. The obtained skewness distribution shows that the number of cells with high skewness is very limited and the distribution is centered around 0.25. The cell-size distribution is also representative of what is prescribed. A large number of cells have the prescribed cell size at the interface and the cell size grows fast to the size in the original grid. The mesh properties are summarized in Table 3. The flow is assumed incompressible, the fluid kinematic viscosity is set to ν = 1.517 10 -5 m 2 /s and the maximal CFL number used is equal to 0.8. The turbulence model is the WALE sub-grid scale model [START_REF] Nicoud | Subgrid-scale stress modelling based on the square of the velocity gradient tensor[END_REF]. A recycling boundary condition enables to make the flow periodic in the streamwise direction while slip walls are used on the side walls and no-slip walls are imposed on the rough surface. The shear Reynolds number is defined as Re τ = uτ h ν with h the half channel height, and u τ the friction velocity based on the streamwise pressure gradient. The chosen value for the present case is Re τ = 970. With these parameters, the maximum non-dimensional wall distance of the first point in the flow y + is less than 5. Figure 10 shows Q-criterion iso-contours to illustrate the vortical structures at the wall vicinity. This case is part of a larger database that is being built.

Assessment of final mesh

Conclusions

The surface and mesh generators have been presented in detail as well as their capabilities in this paper. They are required to create automatically bodyfitted meshes of resolved roughness with imposed parameters. The rough surface generator (RSG), based on some roughness parameters, is able to accurately yield different types of roughness and different geometries in the STL format. An option for periodic boundaries with continuous slope was also introduced. Concerning the resolved-roughness mesh generator (RRMG), the procedure is fully-automatic and enable a control on the cell size at the wall. Both fluid and solid domains are discretized. Thus body-fitted tetrahedral-based meshes with a good quality are obtained with the RRMG and resolved-roughness Large-Eddy simulations can be therefore performed.

Figure 1 :

 1 Figure 1: Procedure for obtaining periodic boundaries

Figure 2 :

 2 Figure 2: Examples of geometries generated with the RSG

Figure 3 :

 3 Figure 3: General principle of the RRMG

Figure 4 :

 4 Figure 4: Original STL file

Figure 6 :

 6 Figure 6: Lagrangian particles for the calculation of approximate and exact distance

Figure 7 :

 7 Figure 7: Final mesh after surface/volume adaptation.

Figure 8 :

 8 Figure 8: Skewness distribution

Figure 10 :

 10 Figure 10: Q-criterion iso-contours in the RRLES

Table 2 .

 2

	ES Cells CPUs	CPU hours	RAM /CPU
	Case 1 0.24 82M	560	930h 1205Mb
	Case 2 0.72 67M	280	812h 1690Mb

Table 2 :

 2 Meshing performances To demonstrate the properties of the surface/mesh generation process, the RRLES of the channel with two rough parallel planes and with the effective slope ES = 0.24 (cf table 2) is conducted.

	Resolved-Roughness	Large-Eddy	Simulation
	(RRLES)

Table 3 :

 3 Parameters of the RRLES

Acknowledgments

The STREAM project has received funding from the Clean Sky 2 Joint Undertaking (JU) under grant agreement No 865378. The JU receives support from the European Union's Horizon 2020 research and innovation program and the Clean Sky 2 JU members other than the Union. This abstract reflects only the authors' view, the Joint Undertaking is not responsible for any use that may be made of the information it contains.