Yann Cressault

Linlin Zhong

Xiaohua Wang

Mingzhe Rong

Effects of copper vapour on thermophysical properties of CO2-N2 plasma

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

CO 2 ,N 2 and their mixtures have been dedicated many efforts to for a few decades because of their wide applications both in astrophysics and industries. For example, as main components of many planetary atmospheres (e.g. Martian and Venusian atmospheres), the high-temperature CO 2 -N 2 mixtures have been studied for their thermodynamic and transport properties since 1960s [START_REF] Lee | Transport Properties at High Temperatures of CO2-N2-O2-Ar Gas Mixtures For Planetary Entry Applications[END_REF][START_REF] Freeman | [END_REF]. Even recently, the research on CO 2 -N 2 plasma can be found for thermophysics and hydrodynamics [3][4][5][6][7][8]. In industries, due to the high global warming potential (GWP) of SF 6 (24 000 times higher than that of CO 2 [9]), CO 2 and N 2 are also applied to replace SF 6 and reduce GWP, for example, as insulating medium in gas-insulated switchgears (GIS) [10] and as arc quenching medium in gas circuit breakers (GCB) [11]. Besides, CO 2 and N 2 are used as shielding gases in metal-inert-gas (MIG) welding and gas metal arc welding (GMAW) [12,13].

However, few attention was paid to effects of impurities (e.g. metallic vapour) on CO 2 -N 2 plasma. Actually, the presence of such impurities could modify significantly characteristics of plasmas. For example, in a number of arc devices, such as circuit breakers, arc heaters, torches, and arc welding apparatus, the metallic vapour (e.g. copa e-mail: xhw@mail.xjtu.edu.cn b e-mail: cressault@laplace.univ-tlse.fr per vapour) resulting from electrode surfaces can mix with a working gas and thus exert influence on arc characteristics [14]. Chervy et al. [15], Paul et al. [16], and Wang et al. [17] all found that electrical conductivity of SF 6 -Cu mixtures is strongly dependent on copper concentration. Zhong's et al. [18], Cressault and Gleizes [19], Cressault's et al. [20] works on combined diffusion coefficients also revealed the significant effect of metallic vapour on SF 6 and Air plasmas. In arc welding, the presence of metal vapour was proved to have a major influence on the properties of arc and the size and shape of weld pool [21]. In extinction process of circuit breakers, copper contamination due to electrode erosion was also proved to have a cooling effect at the arc center and broaden the arc column [22,23]. Therefore, the thermophysical properties of CO 2 -N 2 plasma are expected to be affected by metal vapour (e.g. copper in the present investigation) when used as arc quenching gas in GCB or shielding gas in MIG and GMAW. To our knowledge, no corresponding works have been reported. What's more, the combined diffusion coefficients which were proposed by Murphy [24][25][26][27] and greatly simplify the treatment of diffusion, are indispensable input data in developing model of metal vapour transfer both in arc welding [28] and circuit breakers [29]. Another aim of the present work is therefore to provide these four kinds of combined diffusion coefficients due to composition gradients, applied electric fields, temperature gradients, and pressure gradients respectively [18], which have not been reported either.

In this paper, the influences of copper vapour on thermophysical properties of CO 2 -N 2 plasmas are investigated at temperatures of 2000-30 000 K. The collision integrals were calculated using the newly developed potential and cross sections. The properties include equilibrium compositions and thermodynamic properties (mass density, specific enthalpy, and specific heat), transport coefficients (electrical conductivity, viscosity, and thermal conductivity), and four kinds of combined diffusion coefficients (combined ordinary diffusion coefficient, combined electric field diffusion coefficient, combined temperature diffusion coefficient, and combined pressure diffusion coefficient), which are presented and discussed in Sections 2-4, respectively. It is notable that copper and/or copper oxide are likely to condense at low temperatures and hence the plasma is not established in CO 2 -N 2 -Cu mixtures but in CO 2 -N 2 mixtures. Therefore, the lower limit of temperature is set to be 2000 K in this work, following the recommendation of Cressault et al. [20,30].

Effects of copper on compositions and thermodynamic properties

The particles in CO 2 -N 2 -Cu mixtures (e.g. CO 2 -N 2 plasma contaminated by copper vapour) is assumed to be gaseous and in local thermodynamic equilibrium (LTE). The minimization of the Gibbs free energy is then used to obtain the equilibrium compositions, as described in our previous work [14,[31][32][33]. Totally 76 species, namely

C, C 2 ,C 3 ,C 4 ,C 5 ,C O ,C O 2 ,C 2 O, C 3 O 2 ,C N ,C N 2 , C 2 N, C 2 N 2 ,C 4 N 2 ,N ,N 2 ,N 3 ,N O ,N O 2 ,N O 3 ,N 2 O, N 2 O 3 ,N 2 O 4 ,N C O ,O ,O 2 ,O 3 ,C u ,C u 2 ,C u O ,C + ,C 2+ , C 3+ ,C 4+ ,C -,C + 2 ,C - 2 ,C - 3 ,C - 4 ,C - 5 ,C O + ,C O -,C O + 2 , CO - 2 ,C N + ,C N -,N + ,N 2+ ,N 3+ ,N 4+ ,N + 2 ,N - 2 ,N + 3 , N - 3 ,N O + ,N O -,N O + 2 ,N O - 2 ,N 2 O+, N 2 O -,O + ,O 2+ , O 3+ ,O 4+ ,O -,O + 2 ,O - 2 ,O + 3 ,O - 3 ,C u + ,C u 2+ ,C u 3+ , Cu 4+ ,C u 5+ ,C u -
as well as electrons, are taken into account. The corresponding basic data were compiled from NASA Glenn thermodynamic database [START_REF] Mcbride | NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species[END_REF], NIST-JANAF thermo-chemical tables [START_REF] Chase | NIST-JANAF Thermochemical Tables[END_REF], and Third Millennium thermo-chemical database [START_REF] Burat | Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables[END_REF]. All mixing ratios of mixtures in the whole paper are given in molar proportion.

As an example, Figure 1 shows the compositions of CO 2 -N 2 (mixing ratio 7:3) mixtures at ambient pressure, compared with the compositions contaminated by 10% Cu as shown in Figure 2. At temperatures below 5000 K, copper mainly exists in the form of Cu, Cu 2 ,a n dC u O , showing little influence on the fractions of oxygen and oxides (e.g. O, O 2 ,C O ,C O 2 , and NO), because the concentration of CuO is very low (<0.3%). However, at temperatures above 5000 K, due to its lower ionization energy (Cu 7.73 eV < C1 1 .26 eV < O1 3 .62 eV < N1 4 .53 eV [START_REF] Sansonetti | [END_REF]), copper causes the mixtures to ionize at a lower temperature. What's more, as illustrated in Figure 3, the number density of electrons increases with copper proportion going up.

After obtaining the compositions, the thermodynamic properties (including mass density, specific enthalpy, and specific heat at constant pressure) can be determined directly according to their definitions. The corresponding formulas were given in our previous publication [14].

The effect of copper concentration on mass density and specific heat of CO 2 -N 2 (mixing ratio 7:3) mixtures at ambient pressure is described in Figures 4 and5, respectively. Obviously, with the increase of copper content, the values of mass density go up in the whole temperature range, whereas specific enthalpy drops down except at temperatures below 4500 K. This is because copper has larger molar mass (63.5 g mol -1 )t h a nC O 2 (44.0 g mol -1 )a n d N 2 (28.0 g mol -1 ). In addition to the difference of molar mass, more atoms (e.g. Cu) and less molecules (e.g. CO 2 and N 2 ) result in smaller volume because of the contribution of dissociation products of molecules, also reducing mass density. For specific enthalpy, considering that the molar enthalpies of the species composed of Cu are different from those composed of C, N, and O, the balance between molar enthalpy and mass density leads to the contrary observation below and above 4500 K. The influence of copper on specific heat was also investigated for CO 2 -N 2 (mixing ratio 7:3) mixtures at 1 bar in Figure 6. As can been, the CO 2 -N 2 mixtures with a low or medium copper concentration ( 50%) have three peaks in specific heat at around 3300 K, 7200 K, and 15 000 K, which correspond to the decompositions of O 2 and CO and ionization of N respectively. When more copper is mixed, these threes peaks will disappear gradually, and instead, two new peaks at round 9800 K and 20 000 K will be observed, which correspond to the first and second ionizations of copper. In general, copper reduces specific heat in the whole temperature range because of the increase of mass density (as shown above) as well as its smaller heat capacity than that of CO 2 and N 2 .

Effects of copper on transport coefficients

The transport coefficients (including electrical conductivity, viscosity, and thermal conductivity) of a gas plasma are always useful when determining whether it can be applied in a certain industrial application. For example, in high-voltage circuit breakers (HVCB), a successful interruption requires that the arc quenching gas must have high thermal conductivity to remove energy quickly from itself [START_REF] Christophorou | Gases for Electrical Insulation and Arc Interruption: Possible Present and Future Alternatives to Pure SF[END_REF]. The calculation of transport coefficients was based on the Chapman-Enskog method and was detailed in our previous work [17,33]. Among all the steps, the collision integrals which describe the interactions between each particles in mixtures, are the key pre-calculation [START_REF] Hirschfelder | Molecular Theory of Gases and Liquids[END_REF]. They are also essential to determining combined diffusion coefficients in Section 4.

Collision integrals

In order to determine collision integrals, four kinds of interactions, namely neutral-neutral, neutral-ion, neutralelectron, and charged-charged interactions, should be considered. For charged-charged interactions, the Coulomb potential was adopted [START_REF] André | [END_REF]. Following our previous work [14,17], the Debye length is calculated without consideration of ions. For neutral-electron interactions, the transport cross sections of C [33], C 2 [33], C 3 [33], CO [33], CO 2 [33], O [33], O 2 [33], N [20], N 2 [20], NO [20], and Cu [17] interacting with electrons were integrated to obtain collision integrals [15]. For the collisions e-Cu 2 ,e -CuO, e-CN, and e-NO 2 , following the work of Cressault et al. [20], the polarizability potential was used to calculate collision integrals. The other neutral species were neglected because of their low concentration when existing with electrons. For neutral-neutral and neutral-ion interactions, the Lennard-Jones like phenomenological model potential [4,41] was preferred rather than the classical potential, for the reason presented in our previous work [17].

Figures 7 and8 present collision integrals Ω(1, 1) and Ω(2, 2) for C-C, N-N, O-O, and Cu-Cu interactions, showing the much larger values of Cu-Cu than the others, which predictably can affect the transport coefficients. In Section 3.2, these collision integrals will help to explain the behaviours of transport coefficients.

Electrical conductivity, viscosity, and thermal conductivity

Using the above collision integrals, the transport coefficients of CO 2 -N 2 -Cu mixtures were calculated based on the work of Deveto [42] and Bulter et al. [43], which was validated in our previous publication [17]: electrical conductivity was calculated to a third-order approximation, neglecting the contribution of ions; viscosity was calculated to a first-order approximation without contribution of electrons; thermal conductivity was calculated as the sum of three components, namely the translational thermal conductivity, internal thermal conductivity, and reaction thermal conductivity. The results are illustrated in Figures 9-11 for electrical conductivity, viscosity, and thermal conductivity respectively. The copper propor- tion ranges from 1% to 99% and system pressure is constantly 1 bar.

As seen in Figure 9, the temperature range can be fragmented into three parts for electrical conductivity: 2000-4500 K, 4500-15 800 K, and 15 800-30 000 K. Below 4500 K, due to the very weak ionization as shown in Figure 3 for electron number density, electrical conductivity of mixtures is almost zero and therefore independent of copper content. From 4500 to 15 800 K, with the increase of copper and gradual enhancement of ionization, electrical conductivity is raised because copper is easier to ionize than the other species in mixtures. However, at temperatures above 15 800 K, electrical conductivity drops dramatically despite the increase of copper. This can be explained by charged-charged interactions in this temperature range. According to the work of Deveto [42], electrical conductivity is inversely proportional to collision integrals in a first approximation. Although copper results in more electrons, more ions are generated simultaneously. As a result, the large collision integrals between charged particles cause electrical conductivity to decrease with copper proportion [17].

Compared with electrical conductivity, the effect of copper on viscosity is more clear. As observed in Figure 10, increasing copper diminishes dramatically the viscosity of CO 2 -N 2 -Cu mixtures, especially from 7000 to 16 000 K. At the beginning of this temperature range (before viscosity peaks the value), atoms instead of molecules play an import role in mixtures. Considering that viscosity is in inverse proportion to collision integral [15], the large collision integrals of Cu-Cu interaction (as shown in Figs. 7 and8) are responsible for such significant decrease of viscosity. After viscosity reaches the maximum, charged particles start to dominate the mixture and the large collision integrals due to ion-ion interactions reduces the viscosity. More copper leads to more ions and therefore lower viscosity. Besides, as discussed before, copper has larger molar mass than CO 2 and N 2 , which also contributes to the decrease of viscosity.

Influence of copper on thermal conductivity of CO 2 -N 2 mixtures was also investigated. It is found that copper reduces thermal conductivity significantly both in the low and high temperature ranges. At low temperatures, the reaction component dominates the total thermal conductivity. The increase of copper and thus decrease of CO 2 and N 2 lead to the drop of reaction thermal conductivity because of the decomposition of molecules. At high temperatures, the translation of electrons plays the leading role in the total thermal conductivity. However, although more electrons are generated through ionization with more copper, the stronger interactions and thus larger collision integrals between charged particles result in the decrease of thermal conductivity. What's more, similar to specific heat as shown in Figure 6, the three peaks can be observed at 3300 K, 7200 K, and 15 000 K respectively in Figure 11 for thermal conductivity of CO 2 -N 2 mixtures with small fraction of copper. These three peaks can also be attributed to the dissociation of O 2 and CO and ionization of N respectively. When increasing copper proportion, due to the gradual reduction of O 2 ,C O,an dN ,t h epeaks of thermal conductivity will gradually diminish and vanish eventually.

Effects of copper on four kinds of combined diffusion coefficients

Diffusion coefficients are the essential data in describing the diffusion phenomena in thermal plasmas. To completely model the diffusion in a mixture composed of q species, a total of q(q -1)/2 ordinary diffusion coefficients D ij , q -1 thermal diffusion coefficients D T i ,a n d q mass conservation equationsh a v et ob ec a l c u l a t e da n d solved [18]. To simplify this treatment, Murphy [24][25][26][27] proposed the combined diffusion coefficients, namely the combined ordinary diffusion coefficient D x AB , combined electric field diffusion coefficient D E AB , combined temperature diffusion coefficient D T AB , and combined pressure diffusion coefficient D P AB , which describe the diffusion due to composition gradients, applied electric fields, temperature gradients, and pressure gradients respectively. The calculation of combined diffusion coefficients are based on the collision integrals presented in Section 3.1, and was detailed comprehensively in our previous publication [18]. Murphy's combined diffusion theory requires that the gases do not react with each other [44], which cannot be satisfied strictly in this work. Therefore, following the previous work [18], we choose gas A to consist of the species derived from CO 2 and N 2 , and gas B the species derived from Cu as well as CuO. The results for these four kinds of diffusion coefficients of CO 2 -N 2 (mixing ratio 7:3) mixtures are presented in Figures 12131415. The effects of copper on the coefficients are discussed here. At low temperatures, the mean free path of neutral particles play a major role in D x AB [19,20,24]. The contamination of copper changes the mean free path so weakly that D x AB is almost independent of copper concentration, as observed in Figure 12. However, at high temperatures, copper raises D x AB dramatically. The turning points are found to be at the round of the peaks of D x AB ,a n df u rthermore, the temperatures corresponding to the peaks are shifted to higher values when more copper is mixed. As discussed in the previous work [18], D x AB is mainly affected by the Coulomb interactions between charged particles at high temperatures. According to standard chemical equilibrium considerations, copper with higher concentration ionizes at higher temperature, which means that the Coulomb interaction becomes important at higher temperature, causing the shift of the peak in D x AB . Similar to the discussion of electrical conductivity in Section 3.2, the temperatures in Figure 13 for D E AB can also be divided into three ranges: 2000-4000 K, 4000-16 500 K, and 16 500-30 000 K. Below 4000 K, due to the negligible effect of ionization, D E AB is approximately zero, whatever the proportion of copper. Above 4000 K, because of the electric field acting on the ionized mixtures, the sign of D E AB reverses at nearby 16 500 K. In these two temperature ranges, the influence of copper is not monotonous but changes with copper concentration. This can be explained by the balance of dependences of D E AB on the mass and the ionization degree of mixtures, because D E AB decreases with mass but increases with ionization degree [18].

As for D T AB and D P AB , copper also exerts strong influence on them: generally, if the proportion is not extremely high (<90%), copper raises both the values of D T AB and D P AB because of the impact of its large mass. However, as illustrated in Figures 14 and15, the further increase of copper (>90%) starts to reduce the values of D T AB and D P AB . This is because copper leads to the increase of mass density, as shown in Figure 4, considering that D T AB and

D P

AB are approximately in inverse to mass density of mixtures [18].

Conclusions

In the present work, the equilibrium compositions, thermodynamic properties (including mass density, specific enthalpy, and specific heat), transport coefficients (including electrical conductivity, viscosity, and thermal conductivity), and four kinds of combined diffusion coefficients due to composition gradients, applied electric fields, temperature gradients, and pressure gradients respectively, were calculated for CO 2 -N 2 (mixing ratio 7:3) plasma contaminated by copper vapour at ambient pressure. The effects of copper on such properties are discussed. The following conclusions can be drawn:

(1) Copper causes the mixtures to ionize at a lower temperature and leads the number density of electrons to increase. (2) With the increase of copper, mass density and specific heat of the mixtures increase and decrease respectively in the whole temperature range, whereas specific enthalpy goes up and down below and above 4500 K respectively. (3) With the increase of copper, viscosity and thermal conductivity are both reduced while the effect of copper on electrical conductivity varies in three different temperature ranges. (4) With the increase of copper, D x AB is raised sharply after it reaches the peak value; D E AB shows the similar observation as electrical conductivity and should be considered in three temperature ranges; D T AB and D P AB are also raised when proportion of copper is below 90% in general and reduced otherwise. (5) Copper also changes the number and position of peaks both in specific heat and thermal conductivity. (6) The better ionization ability and larger molar mass of copper and larger collision integrals related to copper, are always responsible for its significant influences on the thermophysical properties of CO 2 -N 2 -Cu mixtures.

Fig. 1 .

 1 Fig. 1. Equilibrium compositions of CO2-N2 (mixing ratio 7:3) mixtures at 1 bar.

Fig. 2 .

 2 Fig. 2. Equilibrium compositions of CO2-N2 (mixing ratio 7:3) mixtures contaminated by 10% Cu (molar proportion) at 1 bar.

Fig. 3 .

 3 Fig. 3. Electron number density of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 4 .

 4 Fig. 4. Mass density of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proport i o n )a t1b a r .

Fig. 5 .

 5 Fig. 5. Specific enthalpy of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 6 .

 6 Fig. 6. Specific heat of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 7 .

 7 Fig. 7. Collision integrals Ω(1, 1) for C-C, N-N, O-O, and Cu-Cu interactions using the Lennard-Jones like phenomenological potential.

Fig. 8 .

 8 Fig. 8. Collision integrals Ω(2, 2) for C-C, N-N, O-O, and Cu-Cu interactions using the Lennard-Jones like phenomenological potential.

Fig. 9 .

 9 Fig. 9. Electrical conductivity of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 10 .

 10 Fig. 10. Viscosity of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 11 .

 11 Fig. 11. Thermal conductivity of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 12 .

 12 Fig. 12. Combined ordinary diffusion coefficient D x AB of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 13 .

 13 Fig. 13. Combined electric field diffusion coefficient D E AB of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu at 1 bar.

Fig. 14 .

 14 Fig. 14. Combined temperature diffusion coefficient D T AB of 70%CO2-30%N2 mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

Fig. 15 .

 15 Fig. 15. Combined pressure diffusion coefficient D P AB of CO2-N2 (mixing ratio 7:3) mixtures contaminated by different proportions of Cu (molar proportion) at 1 bar.

This work was supported by National Key Basic Research Program ("973" Program) of China (No. 2015CB251001), National Natural Science Foundation of China (Nos. 51407136 and 51521065), Fok Ying Tong Education Foundation (No. 141058). This work was also supported by the program of China Scholarship Council (CSC) for joint-Ph.D. students (No. 201506280131).

Author contribution statement

All the authors were involved in this work and contributed equally to the paper.


Erwan Pansard

Mathieu Thaunat

Marie Vigan

Michael Wettstein

Xavier Flecher

Impact of bone deformities and labral and cartilage lesions on early functional results of arthroscopic treatment of femoroacetabular impingement

Introduction. -Femoroacetabular conflit (FAC) is a common cause of inguinal pain. Its treatment has a failure rate between 2.9% and 13.2%. The objective of our study was to investigate the influence of preoperative bony deformities (DO), labrum lesions (LL), and cartilage lesions (LC) on the clinical outcomes of patients who benefited from arthroscopic treatment of CFA. Material and Method. -A prospective operative study included patients undergoing hip arthroscopy for DWI. Patients had a complete radiographic workup preoperatively and at 1 year and an NAHS score for clinical evaluation. Hips > Tönnis 1, coxa profunda (ECV > 35), and borderline dysplasia (ECV < 25) were excluded. Czerny's classification was used for the labrum and Beck's for the cartilage. The objective of our study was to investigate the influence of preoperative OD, LL, and LC on the clinical outcomes of patients who had benefited from arthroscopic treatment of CFA. Our primary hypothesis was that lesion type did not influenc¸ early functional outcome at 1 year regardless of the technique used for the labrum. Results. -One hundred ninety-seven patients were included. The mean preoperative NAHS score was 59.1 ± 17.5.145 patients benefited from labral suture (73.6%), 42 from labral resection (21.3%), and 10 from conservative treatment (5.1%). At 1-year follow-up, the mean NAHS was 88.1 ± 15.3. The improvement was significative (p < 2.2,10-16). It was also significative in the subgroups debridement, conservative, and suture. Bone lesions (LO) were significative in the population (postoperative alpha angle at 48.2• vs. 66.7•, sign of crossing present postoperatively in 14.5% vs. 62.9%). No statistically significative difference was found between patients' functional scores based on the extent or type of labral lesion or type of chondral lesion. At follow-up 3 patients (1.5% of the population) required repeat hip arthroscopy. Conclusion. -Our study showed that the early functional outcome of arthroscopic treatment of DWI was not influenced by the extent of the bony deformity (alpha angle and VCE), the extension or type of labral lesion, and the type or extension of this chondral lesion. In our study, regardless of OD, LL, and LC, the clinical outcome at one year was satisfactory if all bone abnormalities were considered during arthroscopic treatment. Level of evidence. -IV; non-comparative prospective study

Introduction

Femoro-acetabular conflit (FAC) is recognized as a cause of hip or inguinal pain in the young active subject [START_REF] Frank | Evaluation of hip pain in young adults[END_REF]. There are 3 types of CFA: conflit by CAME effect, by pinch effect or mixed. It is most often accompanied by chondro-labral lesions. Hip arthroscopy can be used to treat bony deformities, labrum lesions, and some car-tilaginous lesions [START_REF] Sogbein | Predictors of outcomes after hip arthrosco-pic surgery for femoroacetabular impingement: a systematic review[END_REF]. It is also said to accelerate recovery and reduce the rate of complications, pain and postoperative morbidity compared to open techniques [START_REF] Sogbein | Predictors of outcomes after hip arthrosco-pic surgery for femoroacetabular impingement: a systematic review[END_REF].

However, the failure rate of this procedure varies from 2.9% to 13.2% [START_REF] Cvetanovich | Hip arthroscopic surgery for femoroacetabular impingement with capsular management: Factors associated with achieving clinically significant outcomes[END_REF][START_REF] Harris | Complications and reoperations during and after hip arthroscopy: a systematic review of 92 studies and more than 6,000 patients[END_REF]. This can be defined by the persistence of pain, stiffness despite rehabilitation, or an inability to return to activities of choice [START_REF] Ayeni | Surgical management of labral tears during femoroacetabular impingement surgery: a systematic review[END_REF]. The most common cause of failure is persistence of the causative bone lesions (LO), but it may also be due to past inaperc¸ ous acetabular dysplasia, soft tissue laxity with microinstability [START_REF] Dangin | Microinstability of the hip: a review[END_REF], or incipient coxar-throsis [START_REF] Bogunovic | Why do hip arthroscopy procedures fail?[END_REF]. Options then include repeat hip arthroscopy, open surgery (peri-acetabular osteotomy) or sometimes total hip replacement (THR) [START_REF] Bogunovic | Why do hip arthroscopy procedures fail?[END_REF].

Clinical and demographic criteria predictive of good outcomes of hip arthroscopy for DWI are clearly definis [START_REF] Sogbein | Predictors of outcomes after hip arthrosco-pic surgery for femoroacetabular impingement: a systematic review[END_REF]. The radiographic data predictive of postoperative outcome of hip arthroscopy are in the vast majority of cases radiographic OA scores. The predictive OL of poor results found in the literature are of 2 types: hip dysplasia and CFA by morbid effect [START_REF] Sogbein | Predictors of outcomes after hip arthrosco-pic surgery for femoroacetabular impingement: a systematic review[END_REF][START_REF] Cvetanovich | Hip arthroscopic surgery for femoroacetabular impingement with capsular management: Factors associated with achieving clinically significant outcomes[END_REF][START_REF] Harris | Complications and reoperations during and after hip arthroscopy: a systematic review of 92 studies and more than 6,000 patients[END_REF][START_REF] Ayeni | Surgical management of labral tears during femoroacetabular impingement surgery: a systematic review[END_REF][START_REF] Dangin | Microinstability of the hip: a review[END_REF][START_REF] Bogunovic | Why do hip arthroscopy procedures fail?[END_REF][START_REF] Haefeli | What are the risk factors for revi-sion surgery after hip arthroscopy for femoroacetabular impingement at 7-year followup?[END_REF][START_REF] Degen | Radiographic predictors of femoroacetabular impingement treatment outcomes[END_REF][START_REF] Hatakeyama | Predictors of poor clinical outcome after arthroscopic labral preservation, capsular plication, and cam osteoplasty in the setting of borderline hip dysplasia[END_REF][START_REF] Giordano | Acetabular morphologic characteristics predict early conversion to arthroplasty after isolated hip arthroscopy for femoroacetabular impingement[END_REF]. Our study excludes patients with an ECV> 35• or < 25•. Therefore, it is only interested in non-dys-plasmic hips. Infin, patients with a hip with a Tönnis stage > 1 were also excluded, the influence of OL was more specifically sought.

A current challenge is therefore to identifier the good and poor prognostic factors accessible during arthro-scopic management of causative or induced joint injuries [START_REF] Ayeni | Surgical management of labral tears during femoroacetabular impingement surgery: a systematic review[END_REF]. The influence of the type of causal bone deformity (OD) on early functional outcomes has been mostly studied in patients with hip dysplasia [START_REF] Bogunovic | Why do hip arthroscopy procedures fail?[END_REF][START_REF] Haefeli | What are the risk factors for revi-sion surgery after hip arthroscopy for femoroacetabular impingement at 7-year followup?[END_REF][START_REF] Giordano | Acetabular morphologic characteristics predict early conversion to arthroplasty after isolated hip arthroscopy for femoroacetabular impingement[END_REF][START_REF] Beck | Hip morphology influences the pattern of damage to the acetabular cartilage: Femoroacetabular impingement as a cause of early osteoarthritis of the hip[END_REF][START_REF] Nakashima | Clinical and radiographic predictors for unsalvageable labral tear at the time of initial hip arthro-scopic management for femoroacetabular impingement[END_REF] but little on the outcome of CFA surgery [START_REF] Anwander | Labral reattachment in femoroacetabular impingement surgery results in increased 10-year survivorship compared with resection[END_REF]. Regarding induced lesions, debridement of a labrum lesion (LL) is reported to have a poor prognosis [START_REF] Ayeni | Surgical management of labral tears during femoroacetabular impingement surgery: a systematic review[END_REF] and the current preference is for labrum retention [START_REF] Philippon | Arthroscopic hip labral repair[END_REF][START_REF] Larson | Arthroscopic debridement versus refixation of the acetabular labrum associated with femoroacetabular impingement: mean 3.5-year follow-up[END_REF]. Cartilage lesions (CL), especially at the labro-cartilage junction, also play a major role in the clinical outcome of hip arthroscopy [START_REF] Nepple | The reliability of arthroscopic classification of acetabular rim labrochondral disease[END_REF]. The objective of our study was to investigate the influence of the type of preoperative OD, preoperative LL and LC on the cli-nical outcome of patients who benefited from arthroscopic treatment of CFA. Our primary hypothesis was that the type of bony (cam, pincer, or mixed), labral, or limited cartilage lesion (Beck 0, 1, or 2) [START_REF] Beck | Hip morphology influences the pattern of damage to the acetabular cartilage: Femoroacetabular impingement as a cause of early osteoarthritis of the hip[END_REF] does not influence early functional outcome at 1 year.

Matériel et méthode

A prospective study was carried out in 8 centers, 5 private clinics and 3 university hospitals (CHU).

Selection criteria

The study included patients from 9 senior surgeons, operated between July 2017 and July 2018 for hip arthroscopy for DWI. Patients had to be older than 18 years, with no previous surgical history of the hip under consideration. They had to have preoperative imaging that included: an en face pelvis radiograph, an en face hip radiograph, a DUNN profil, and imaging with contrast injection (arthro-scanner or arthro-MRI). An identical radiographic workup was performed at 1 year after surgery. The quality of each X-ray was monitored [START_REF] Tannast | Femoroacetabular impingement: radiographic diagnosis-what the radiologist should know[END_REF][START_REF] Meyer | Comparison of six radiographic projections to assess femoral head/neck asphericity[END_REF].

Exclusion criteria

Patients with a Tönnis grade > 1 [START_REF] Tonnis | Normal values of the hip joint for the evaluation of x-rays in children and adults[END_REF], a Wiberg VCE angle < 25• or > 35• [START_REF] Wiberg | epiphysiolysis of the hip joint[END_REF] or a recoil <1 year on the preoperative radiographic workup were excluded.

Endpoints.

The primary endpoint was the NAHS score [START_REF] Christensen | The nonarthritic hip score: reliable and validated[END_REF] at 1 year. Secondary endpoints were the occurrence of further conservative surgery (hip arthroscopy or open surgery) or the placement of a THP. Patients were classified into 3 subgroups according to the procedure performed on the labrum: debridement/resection, conservative or suture.

Radiographic evaluation

Each included patient benefited from a coxometry preoperatively and at one year. These were performed manually by the operator. Acetabulum coverage was assessed by Wiberg's VCE angle [START_REF] Wiberg | epiphysiolysis of the hip joint[END_REF], Hilgenreiner's HTE angle [START_REF] Merckaert | Residual hip dysplasia in children: osseous and cartilaginous acetabular angles to guide further treatment-a pilot study[END_REF]. Nötzli's alpha angle was measured by the DUNN profil [START_REF] Notzli | The contour of the femoral head-neck junction as a predictor for the risk of anterior impingement[END_REF]. A crossing sign, acetabular protrusion of the femoral head, and coxa profunda were looked for [START_REF] Tannast | Femoroacetabular impingement: radiographic diagnosis-what the radiologist should know[END_REF].

Intraoperative assessment

An accurate arthroscopic assessment of the LL and LC was performed. The location and extension of the LL was definished according to Woyski et al. [START_REF] Woyski | Surgical treatment of labral tears: debridement, repair, reconstruction[END_REF] (lesion < 3H or > or = 3H). LLs were classified according to Czerny et al [START_REF] Czerny | Lesions of the acetabular labrum: accuracy of mr imaging and mr arthrography in detection and staging[END_REF] (lesion without inferior extension Czerny type 1a + 1b vs lesion with inferior extension Czerny type 2a, lesion without degenerative aspect Czerny type 2a and 3a vs lesion with degenerative component Czerny type 2b and 3b). The chondro-labral junction and the LCs were classified according to Beck et al [START_REF] Beck | Hip morphology influences the pattern of damage to the acetabular cartilage: Femoroacetabular impingement as a cause of early osteoarthritis of the hip[END_REF] (Beck 0 and 1 vs Beck 2).

Functional assessment

Le Non Arthritic Hip Score (NAHS) a été utilisé [START_REF] Christensen | The nonarthritic hip score: reliable and validated[END_REF] avec des données recueillies en préopératoire et à un an. Ce score évalue la douleur, la gêne fonctionnelle, les difficultés dans la vie quotidienne and in sports activities.

Assessment of postoperative complications

There was one repeat surgery for either iterative revision surgery or THR.

Statistical analysis

Preoperative group comparability was analyzed by a Kruskal-Wallis test, the evolution of the preoperative and postoperative clinical score by the Wilcoxon and Fisher tests. The influence of LL and LC was analyzed by an ANOVA test. A p value of less than 0.05 was considered statistically significative.

Results

The prospective series included 197 patients. There were no lost to follow-up or incomplete records. There were 123 men and 74 women with a mean age of 33. [START_REF] Cvetanovich | Hip arthroscopic surgery for femoroacetabular impingement with capsular management: Factors associated with achieving clinically significant outcomes[END_REF] 1.

Preoperative radiographic data figured in Table 2.

There was a significative difference between the groups for the alpha and HTE angles. The mean alpha angle was 66.7• ± 12.0 with a lower angle in the suture group having a mean at 65.2• ±11.6. The mean VCE angle for the entire population was 30.7• ± 5.6. It was higher in the conservative group (with a mean of 33.7• 6.4). The donnographic data at 1 year figured in Table 3. The mean alpha angle was 48.2• 6.6. It was corrected signifi-catively in the total population as well as in the 3 subgroups (Table 4). In the total population the other values were also corrected significatively. Regarding the subgroups, only the sign of the crossover and the HTE angle were not corrected significatively in the conservative treatment subgroup. The distribution of LL and LC figure in Table 5. No statistically significative difference could be demonstrated between the patients' functional scores according to the extent or type of LL or the type of chondral lesion (Table 6). At follow-up, 3 patients (1.5% of the population) required repeat hip arthroscopy for persistent CFA.

No patient had a THP.

Discussion

Our study mainly showed that the early functional outcome of arthroscopic treatment of DWI was not influenced by the extent of bony deformity (alpha angle and VCE), extension, or type of labral lesion.

In our series, all LOs studied (alpha angle, VCE, HTE, and crossing signs) were significatively corrected and the postoperative NAHS score was significantly improved. Thus, OL cannot be a bias in the analysis of our results. In the subgroups (labral resection, conservation of the labrum and labrum suture) only the HTE and the sign of the crossing were not significantly corrected. This may be explained by the low The number of patients in the conservative treatment group (10 patients) and therefore the statistical power lacks. was not significative for the HTE angle in the suture group. This can probably be explained by poorer visualization of the acetabulum roof if the labrum is not completely detached. The improvement in NAHS was significative in all 3 subgroups regardless of the technique used at the labrum, which is in contrast to recent work [START_REF] Larson | Arthroscopic debridement versus refixation of the acetabular labrum associated with femoroacetabular impingement: mean 3.5-year follow-up[END_REF][START_REF] Nepple | The reliability of arthroscopic classification of acetabular rim labrochondral disease[END_REF][START_REF] Tannast | Femoroacetabular impingement: radiographic diagnosis-what the radiologist should know[END_REF][START_REF] Meyer | Comparison of six radiographic projections to assess femoral head/neck asphericity[END_REF][START_REF] Tonnis | Normal values of the hip joint for the evaluation of x-rays in children and adults[END_REF][START_REF] Wiberg | epiphysiolysis of the hip joint[END_REF][START_REF] Christensen | The nonarthritic hip score: reliable and validated[END_REF][START_REF] Merckaert | Residual hip dysplasia in children: osseous and cartilaginous acetabular angles to guide further treatment-a pilot study[END_REF][START_REF] Notzli | The contour of the femoral head-neck junction as a predictor for the risk of anterior impingement[END_REF][START_REF] Woyski | Surgical treatment of labral tears: debridement, repair, reconstruction[END_REF][START_REF] Czerny | Lesions of the acetabular labrum: accuracy of mr imaging and mr arthrography in detection and staging[END_REF][START_REF] Krych | Arthroscopic labral repair versus selective labral debridement in female patients with femoroacetabular impingement: a prospective randomized study[END_REF][START_REF] May | Francophone Arthroscopy Society (SFA). Does labral repair have a clinical benefit during arthroscopic treatment of femoro-acetabular impingement? Prospective multicentre study with 2-year follow-up[END_REF]. Thus, labrum preservation would not be a prognostic factor for good clinical outcomes in our series. For Sogbein et al [START_REF] Sogbein | Predictors of outcomes after hip arthrosco-pic surgery for femoroacetabular impingement: a systematic review[END_REF], labrum resection is a prognostic factor of poor outcome. However, other studies do not find this result. For Menge et al [START_REF] Menge | Femoroacetabular impingement in professional football players: return to play and predictors of career length after hip arthroscopy[END_REF], there is no difference between debridement and repair. At the extreme, in their review of the literature, Sogbein et al [START_REF] Sogbein | Predictors of outcomes after hip arthrosco-pic surgery for femoroacetabular impingement: a systematic review[END_REF] found six studies in which labral repair was an operative criterion of poor prognosis, however none of them found significative results.

We did not find any significative difference in clinical outcomes according to the type of LL according to Czerny's classifica-tion [START_REF] Czerny | Lesions of the acetabular labrum: accuracy of mr imaging and mr arthrography in detection and staging[END_REF] whether according to its extension to the labrocartilaginous junction (type 1 or 2) or its acute or degenerative nature (subgroup A or B). For Mose et al [START_REF] Mose | High frequency of labral pathology in symptomatic borderline dysplasia: a prospective magnetic reso-nance arthrography study of 99 patients[END_REF], there is no association between the type of labral lesion and pain, either pre-or postoperatively. However, for Chahla et al [START_REF] Chahla | Influence of acetabular labral tear length on outcomes after hip arthroscopy for femoroacetabular impingement syndrome with capsular plication[END_REF], the length of the LL is an independent predictor of a good outcome of hip arthroscopy for DWI if the length of the LL is < 2.5 cm. Moderate LCs (Beck 1 and 2) did not appear in our study to have an influence on 1-year outcomes. from a cartilaginous detachment [START_REF] Nepple | The reliability of arthroscopic classification of acetabular rim labrochondral disease[END_REF]. This study had several limitations. It has a low statistical power notably by the small sample of several subgroups (conservative treatment and debridement). Concerning the OD, we did not study the femoral neck-shaft angle and femoral rotation, which may be prognostic factors [START_REF] Degen | Radiographic predictors of femoroacetabular impingement treatment outcomes[END_REF]. Femoral retroversion [START_REF] Fabricant | The effect of femoral and acetabular version on clinical outcomes after arthroscopic femoroacetabular impingement surgery[END_REF] is thus recognized as a radiographic pejorative factor. Our patients did not pre-sent LC Beck 4 probably because patients with Tönnis stage > 1 were excluded which limited the study of the influence of cartilage lesions but allowed for more specific study of the influence of LOs. This study is multi-centric and multi-operator which can be problematic for operator-dependent intraoperative classifications (Beck, Czerny in particular) and the labrum reinsertion techniques used which can introduce bias. The use of MRI classification (Czerny) preoperatively to classify LLs is also debatable. The cut-off of 3 cm for LLs may not have been relevant, with Chahla et al [START_REF] Chahla | Influence of acetabular labral tear length on outcomes after hip arthroscopy for femoroacetabular impingement syndrome with capsular plication[END_REF] choosing 2.5 cm. Enfin the 1-year follow-up is short.

Conclusion

Our study showed that the early functional outcome of arthroscopic treatment of DWI by cam or mixed effect excluding deep hips and borderline dysplasias as well as severe chondral lesions (Tönnis > 1, Beck 3), is not influenced by the extent of preoperative bone deformity (alpha angle and VCE), the extension or type of labral lesion, and the type or extension of chondral injury. In our series, whatever the LO, LL and LC, the clinical evolution at one year is satisfactory if all the bone abnormalities are taken into account during the arthroscopic treatment.

  Score NAHS préopératoire et à 12 mois en fonction de l'étendue de la lésion labrale, de l'étendue et du type de lésion chondrale.

	Tableau 4
	p comparant les données radiographiques préopératoires et à un an.
			Toute la	Traitement	Traite	Traitement
			population	débridement/rés	ment	suture
					ection		conser
							vateur
	Angle alpha VCE HTE		<0,0001 <0,0001 0,005	<0,0001 <0,0001 0,02	0,03 0,03 1	<0,0001 <0,0001 0,06
	Cross over	<0,0001	<0,0001	0,4	0,0004
	Tableau 5
	Score NAHS préopératoire et à 12 mois en fonction de la classification de Czerny.
	NAHS M12 82,9± 2,3	80,1± 2,2	p = 0,5969 78,7± 1,9	85,8± 1,9	p =
	0,180
	Tableau 6
		Lésion		Lésion	Lésion		Lésion	Lésion	Lésion
		labrale	labrale	chondr	chondr	chondr	chondr
		localisé	étendu	ale		ale	ale	ale
		e à 1H	e à 3H	localisé	étendu	Beck 0	Beck 2
		ou 2H	ou	e à 1 h		e à 3H	et 1 (n =	(n = 65)
		(n = 77)	plus (n	ou 2 h		ou plus	122)
				= 111)	(n = 72)	(n = 75)
	NAHSpreop 0,352 54,9± 1,3 56± 1,3 59,1± 2,3 57,7± 2,2 p = 0,458 NAHS M12 81,5± 1,9 84,3± 1,8		p = 0,589 62,1± 1,8 p = 0,453 83,9± 2,2	59,3± 1,9 p = 85,1± 2,1 p =
	0,772	83,3± 2,4 89,5± 2,2 p = 0,279
				Correction of OD

Funding

None.

Declaration of interest

The authors declare that they have no ties of interest.

Authors' contributions

All authors contributed to the study.

Références