Mark R Marshall
email: markrogermarshall@icloud.com

Keywords: PD peritonitis, peritoneal dialysis, ANZDA-TA, RDPLF, NZ PD Registry

Peritoneal Dialysis Associated Peritonitis Rate -Validation of a Simplified Formula

(Taux de péritonite en dialyse péritonéale : validation d'une fomule de calcul simplifiée) Mark R Marshall 1,2 , Gerald P Waters 3,4 , Christian Verger

Résumé

La péritonite est la complication la plus importante de la dialyse péritonéale (DP). Malheureusement, de nombreux centres de DP dans le monde n'enregistrent pas précisément le taux de péritonite, principalement parce qu'ils ne peuvent pas déterminer la durée de soumission au risque en raison de difficultés pour obtenir le nombre de jours-patients à partir des dates individuelles de début et fin de traitement. Nous proposons une méthode de calcul simplifiée de cette durée à partir du nombre de patients en début et fin d'année. Nous avons comparé les mesures de référence des taux annuels de péritonite avec des mesures simplifiées dans les registres australien et néo-zélandais de dialyse et de transplantation (ANZDATA) / registre néo-zélandais (NZ) et le Registre de Dialyse Péritonéale de Langue Française et hémodialyse à domicile (RDPLF). 268 centres de 9 pays avec 4311 années-centres et 110 185 années-patients de suivi ont été modélisés.

La concordance globale est excellente, avec un coefficient de corrélation de concordance de 0,978 (intervalle de confiance à 95 % 0,975-0,980) et un biais moyen (limites de concordance à 95 % tel que défini par Bland et Altman) de 0,002 (-0,138-0,142) dans le registre ANZDATA / NZ. Les statistiques correspondantes sont 0,978 (0,977-0,980) et 0,004 (-0,111-0,119) dans le RDPLF. La concordance est statistiquement plus faible pour les petits centres, bien que la formule simplifiée offre toujours une bonne précision. Il doit cependant être utilisé avec prudence dans les très petits centres (< 5 patients). La méthode simplifiée de calcul du taux de péritonite en PD est précise et permettra à davantage de centres de mesurer, communiquer leur taux de péritonite et de travailler sur leur réduction.

Bulletin de la Dialyse à Domicile

Summary

Peritonitis is the most important therapy-related complication of peritoneal dialysis (PD). Unfortunately, many PD centers around the world do not measure peritonitis rate, mainly because they cannot ascertain PD patient time-at-risk from "patient flow" -that is, calculating PD patient-days from the date at which patients start and finish PD. We propose a simplified method for calculating PD peritonitis rate from "patient stock" -that is, calculating PD patient-days from the number of prevalent PD patients at a given center at the beginning and end of a year. We compared gold-standard measurements of annual PD peritonitis rates with simplified ones in the Australia and New Zealand Dialysis and Transplant Registry (ANZDA-TA) / New Zealand (NZ) PD Registry, and Le Registre de Dialyse Péritonéale de Langue Française et hémodialyse à domicile (the RDPLF). A total of 268 centers from 9 countries with 4311 center-years and 110,185 patient-years of follow-up were modelled. Overall agreement is excellent, with a concordance correlation coefficient of 0.978 (95% confidence interval 0.975-0.980) and average bias (95% limits of agreement as defined by Bland and Altman) of 0.002 (-0.138-0.142) in ANZDATA / NZ PD Registry. Corresponding statistics are 0.978 (0.977-0.980) and 0.004 (-0.111-0.119) in the RDPLF. Agreement is statistically poorer for smaller centers, although the simplified formula still provides good accuracy. It should, however, be used with caution in very small (<5 patients) centers. The simplified method of calculating PD peritonitis rate is accurate, and will allow more centers to measure, report, and work on reducing PD peritonitis rates.

INTRODUCTION

Peritonitis is the most urgent and important therapy-related complication to affect peritoneal dialysis (PD). Over the last two decades, improvements in technique and service delivery have reduced the probability of PD peritonitis to an all-time low [START_REF] Marshall | A systematic review of peritoneal dialysis-related peritonitis rates over time from national or regional population-based registries and databases[END_REF]. Despite this excellent progress, PD peritonitis still accounts for up to 5% of all deaths on PD (2). It is the leading priority for improving patient centered outcomes [START_REF] Manera | Establishing a Core Outcome Set for Peritoneal Dialysis: Report of the SONG-PD (Standardized Outcomes in Nephrology-Peritoneal Dialysis) Consensus Workshop[END_REF][START_REF] Manera | An international Delphi survey helped journal officiel du Registre de Dialyse Péritonéale de Langue Française RDPLF www[END_REF]. For this reason, PD peritonitis rate is arguably the leading metric for assessment of quality assurance of PD care around the world [START_REF] Li | ISPD Peritonitis Recommendations: 2016 Update on Prevention and Treatment[END_REF].

Despite the importance of PD peritonitis rate, only a minority of health jurisdictions measure and report PD rates [START_REF] Marshall | A systematic review of peritoneal dialysis-related peritonitis rates over time from national or regional population-based registries and databases[END_REF]. This is largely because of the difficulties that individual PD centers face when calculating PD peritonitis rate. Sometimes, it is that the actual formula that is not well understood. In most cases, however, the difficulties arise from lack of requisite data. PD peritonitis rate is computed as the number of episodes as a function of cumulative time-at-risk. For a given year and cohort, and expressed in episodes per patient-year, the gold-standard computation uses the following formula (6):

In most PD centers, recording and recalling number of PD episodes over a given period of observation is not difficult. However, many PD centers around the world do not have systems that accurately record "patient flow" -that is, the date when patients start and finish PD. Even when they do have access to such data, many do not have the resources to manually retrieve it and calculate cumulative time-at-risk for their cohort.

We propose a simplified calculation that is easier to compute in a practical sense. This simplification replaces the time-at-risk denominator in the gold-standard formula above. The simplified time-at-risk denominator is calculated from "patient stock" -that is, the number of patients in a center at any point in time, a more easily accessible statistic for most PD centers [START_REF] Gliklich | Registries for Evaluating Patient Registries: A User's Guide: AHRQ[END_REF]:

The equivalence between the gold-standard and simplified formulae relies on a key assumption: namely, that patients start and finish PD at a uniform rate throughout the year (that is, at random).

In this paper, we explore the accuracy of the simplified formula in two databases. The first is Australia and New Zealand Dialysis and Transplant Registry (ANZDATA) / New Zealand (NZ) PD Registry. The second is Registre de Dialyse Péritonéale de Langue Française et hémodialyse à domicile (RDPLF).

METHODS

Study Design

We performed an observational cohort study to measure agreement between gold-standard annual PD peritonitis rates and those estimated using the simplified formula. The National (NZ) Health and Disability Ethics Committee (IORG0000895) approved the study protocol, and waived the need for patient consent under the provisions for observational research.

Patient Participants and Data Source

The ANZDATA Registry collects data on all kidney failure (KF) patients from every dialysis centre in Australia and New Zealand. KF patients are defined as those with a diagnosis of chronic kidney disease, in whom renal replacement therapy is intended as an indefinite treatment. Data on PD peritonitis in Australia and New Zealand has been collected since 2004 (in NZ, directly by ANZDATA until June 2021, but through data linkage with the NZ PD Registry thereafter). The RDPLF collects data on corresponding patients from every dialysis centre in France, as well as larger PD centres in Algeria, Francophone Belgium, the Kingdom of Morocco and Southern Provinces, Luxembourg, Francophone Switzerland, and Tunisia. PD peritonitis has been collected since the registry's inception in 1986. Details of the structure and methods of all the registries are reported elsewhere (www.anzdata.org.au, www.pdregsitry.org.nz, https://rdplf.org/ [START_REF] Mcdonald | ESRD in Australia and New Zealand at the end of the millennium: a report from the ANZDATA registry[END_REF][START_REF] Hayat | Study of early complications associated with peritoneal dialysis catheters: an analysis of the New Zealand Peritoneal Dialysis Registry data[END_REF][START_REF] Hayat | Predictors of technique failure and mortality on peritoneal dialysis: An analysis of New Zealand peritoneal dialysis registry data[END_REF][START_REF] Verger | Synthetic 2018 data report of the French Language Peritoneal Dialysis and Home Hemodialysis Registry (RDPLF)[END_REF]).

We created a study cohort of KF patients treated with PD. In ANZDATA / NZ PD Registry, this cohort comprised children and adults over a period of observation starting on 1-Jan-2004. Prevalent PD patients at the start of this period of observation were included, and these and any incident PD patients were followed through until 31-December-2019. In the RDPLF, the study cohort comprised corresponding adult patients between the dates of 1-Jan-2000 and 31-December-2020.

Primary Exposure and Outcome Variables

The primary exposure in this study is PD peritonitis, as recorded in the respective registries based upon the opinion of the treating physician / PD team. Gold-standard annual PD peritonitis rates were calculated using Equation 1 above, and estimated annual PD peritonitis rates from Equation 2.

For ANZDATA, the attributed center of PD treatment for each patient-episode was the one at PD inception, since only a very small proportion of PD patients change centers in Australia and New Zealand. For the RDPLF, episodes are split by center at source, and the attributed center of PD treatment for each patient-episode is therefore time-varying.

Statistical Methods

Agreement between gold-standard and estimated annual PD peritonitis rates were assessed using concordance statistics. The relationship-scale framework underpins Lin's implementation of the concordance correlation coefficient (CCC), which combines measures of both precision (Pearson correlation coefficient) and accuracy (the bias-correction factor) to determine how far the observed data deviate from the line of perfect concordance (that is, the line at 45 degrees on a square scatterplot). Lin's CCC increases in value as a function of the tightness of the data about its reduced major axis (the precision of the estimation) and the nearness of the data's reduced major axis to the line of perfect concordance (the accuracy of the estimation) [START_REF] Lin | A concordance correlation coefficient to evaluate reproducibility[END_REF][START_REF] Lin | Assay Validation Using the Concordance Correlation Coefficient[END_REF][START_REF] Lin | A note on the concordance correlation coefficient[END_REF][START_REF] Krippendorff | Bivariate Agreement Coefficients for Reliability of Data[END_REF]. The data-scale framework underpins Bland and Altman's limits-of-agreement (LoA) procedure, which is complementary to the relationship-scale approach [START_REF] Bland | Statistical methods for assessing agreement between two methods of clinical measurement[END_REF].

We tested for effect modification of by comparing concordance statistics between subgroups of centers. For each year in which annual peritonitis rates were calculated, subgroups of centers were created based on their patient case mix. For example, in Australia and New Zealand centers during 2004, 2 subgroups of centers were created according proportion of their patients who live either regionally or remotely (>median for all centers in 2004 versus < median). We then checked for significant differences in Lin's CCC between each subgroup. In ANZDATA, we assessed for effect modification by the following factors: country (Australia versus New Zealand), pediatric [< 18 years] versus adult [>= 18 years]), size of PD population, proportion of patients on APD, proportion of males, proportion with indigenous or Pacific ethnicity, proportion with high-risk primary kidney disease (ischemic or diabetic nephropathy), late referral for nephrology pre-dialysis care, and rurality. In RDPLF, the corresponding assessments involved: country (France, Algeria, Francophone Belgium, the Kingdom of Morocco and Southern Provinces, Luxembourg, Francophone Switzerland, and Tunisia), size of PD population, mean age of patients at PD inception, proportion of patients on APD, proportion of males, proportion of patients with diabetes mellitus, and presence and extent of medical co-morbidity (> median CCS versus < median CCS).

Comparisons of CCC between subgroups were made using a z-test with a null hypothesis that the difference between CCC was of zero. For subgroups of more than two, comparisons were made by ANOVA [START_REF] Altman | Interaction revisited: the difference between two estimates[END_REF].

In all analyses, and error trap was utilized to exclude those centers with an annual PD peritonitis rate > 3 episodes per patient-year.

RESULTS

Descriptive Data

The ANZDATA dataset comprised 80 PD centers from 2 countries with a total of 1085 center-years and 48,256 patient-years of follow-up. There were 19,669 episodes of peritonitis over this period. Summary statistics of center characteristics (or more accurately, summary statistics of each center-year characteristics) are shown in Table I. The RDPLF dataset comprised 188 centers from 7 countries (Table II) with a total of 3226 center-years and 61,929 patient-years of follow-up. There were 22,482 episodes of peritonitis over this period.

Three center-years from ANZDATA were excluded through the error trap, with annual PD peritonitis rates of 3.2, 3.4 and 11 episodes per patient-year at respective centers. During those years, the centers had patients stock and flow of only between 0-2 PD patients. Four center-years from the RDPLF were excluded through the error trap, with annual PD peritonitis rates of 3, 4, 10, and 12 episodes per patient-year at respective centers. During those years, the centers had stock and flow of only between 0-1 PD patients.

Main results

Overall, the average agreement between gold-standard and estimated annual PD peritonitis rates were high, as assessed using concordance statistics and Bland and Altman analysis. For ANZDA-TA / NZ PD, the CCC was 0.978 (95% confidence interval [CI] 0.975-0.980) and average bias (95% LoA) 0.002 (-0.138-0.142). For the RDPLF, the corresponding statistics were 0.978 (0.977-0.980) and 0.004 (-0.111=0.119), respectively.

. Graphical description of agreement between gold-standard and estimated PD annual peritonitis rates for every center in ANZDATA 2004-2019

Annual peritonitis rate for every center in ANZDATA 2004 to 2019 (episodes per patient-year)Lin's concordance correlation coefficient 0.978 (95% Cis 0.975, 0960)

Annual peritonitis rate for every center in ANZDATA 2004 to 2019 (episodes per patient-year)y=0 is line of perfect average agreement Graphical descriptions of relationship-scale and data-scale agreement for ANZDATA are shown in Figure 1 for the entire period of observation and in Figure 2 for the last year (2019) of available data. Table III shows the results of testing within subgroups of centers defined by their patient case mix. The strongest effect modifier was found in center size, with poorer agreement between gold-standard and estimated rates in smaller centers. There was statistically poorer agreement in centers that were pediatric, located in Australia, with lower proportions of patients of Indigenous or Pacific ethnicity, and higher proportions of people on APD. However, these characteristics also correlated with center size: pediatric versus adult (mean PD stock per center of 7 versus 50 patients), Australia versus New Zealand (40 versus 70), lower proportion Indigenous / Pacific ethnicity versus not (37 versus 58), higher proportion of APD versus not (31 versus 59). Statistical differences in agreement between these subgroups were not present when assessed within the same strata of center size. Notwithstanding, these are still center characteristics indicative of situations associated with poorer concordance between gold-standard and estimated rates of PD peritonitis rates. III. Effect modification of concordance statistics in ANZDATA centers according to their casemix lack of agreement is greatest for centers with less than 5 patients, and does not depend on submodality of PD treatment, rurality, or patient age or co-morbidity. In centers with less than 5 patients, the directional relationship between gold-standard and estimated PD peritonitis rate is not predictable: in ANZDATA, estimated rates were consistently higher than gold-standard ones, and in RDPLF, the opposite.

DISCUSSION

In this paper, we show that annual PD peritonitis rate can be estimated fairly accurately using the number of episodes of PD peritonitis for a given center over a given observation period, as well as their "patient stock" (i.e., patients on PD) at the at the start and end of the period). This avoids the need for cumbersome collection and computations based on their "patient flow" (i.e., number of prevalent patients-days during the year). We show that this estimation is good enough for almost every type of PD center, although it is most accurate in larger ones. The greatest lack of agreement is seen with very small centers with 5 or less patients. Notwithstanding, concordance was still very good in most smaller centers in both ANZDATA (Lin's CCC of 0.972 in centers averaging 12 PD patients at year-end) and the RDPLF (Lin's CCC of 0.973 in centers averaging 8 PD patients at year end). The very small centers in both ANZDATA and the RDPLF generally had 3-4 fold more PD peritonitis than average, and it can be argued that under-or overestimation of gold-standard PD peritonitis rate by 10-20% either way is not going to jeopardize wise decision-making in a meaningful way.

Difficulties in monitoring PD peritonitis rate are unhelpful for centers that want to identify or address issues with the quality of their PD care, and an impediment to increased uptake of PD. Improvements in PD technology, exchange procedures and patients training protocols have all been helpful in reducing PD peritonitis rates, but this complication is still an important one and responsible for almost all therapy-related deaths. The ability to monitor, compare and report PD peritonitis rates between centers is a fundamental requirement to reduce PD peritonitis rates further.

In a recent systematic review, it was determined that only a minority of health jurisdictions capture PD peritonitis rates in a systematic way [START_REF] Marshall | A systematic review of peritoneal dialysis-related peritonitis rates over time from national or regional population-based registries and databases[END_REF]. This was mainly found to be a problem in emerging economies and not so common in developed countries or those with mature PD programs. This limitation appears to arise in 2 main settings. First, it can be due to lack of information systems for storage and recall. Second, it can be due to workload or staffing changes that leave centers under-resourced for both clinical care and also clinical quality. Naturally, the former is prioritized at the cost of compromise to the latter. In both cases, the retrieval and processing of information become untenable, especially when it involves tracking detailed metrics like timeat-risk on PD.

CONCLUSION

We recommend that the gold-standard formula is used under certain circumstances. First, if there is a strong and unbalanced pattern to starting and discontinuation of PD at a center (e.g. when a center is rapidly losing patients or gaining them over the year in a non-linear manner). Secondly, any PD peritonitis rate that is close to clinical threshold of 0.5 PD peritonitis episodes per patient- year with the estimated formula ought to be checked with the gold-standard one -the simplified formula should be used with a view to increasing the access of patients to appropriate care, not to limit it. Thirdly, in centers with less than 5 patients the gold-standard formula should be used, In all of these three settings, if there are exceptionally high PD peritonitis rates then the use of the simplified formula will probably be sufficient to guide good clinical decision-making. Outside of these limitations, the simplified formula is an adequate substitute for the gold standard one.

Finally, there is some further work to be done to test the formula over shorter time period (e.g. monthly PD peritonitis rates), and also in centers with wide variations in PD peritonitis rate.

In the meantime, we hope that this formula allows for wider monitoring and clinical quality assurance to prevent and address high rates of this complication.

5 1.

 5 Faculty of Medical and Health Sciences, University of Auckland, Auckland, New Zealand, 2.Department of Renal Medicine, Counties Manukau Health, Auckland, New Zealand , 3. Regional Renal Service, Waikato District health Board, Hamilton, New Zealand, 4. New Zealand Peritoneal Dialysis Registry, Hamilton, New Zealand 5. Le Registre de Dialyse Péritonéale de Langue Française et hémodialyse à domicile (RDPLF), Pontoise, France

Registre de Dialyse Péritonéale de Langue Française RDPLF www

	journal officiel du
	Mots clés : péritonite, dialyse péritonéale, ANZDATA,
	RDPLF, NZ PD Registry

.rdplf.org

  We also used patient characteristics in our models, to identify any effect modification on concordance statistics arising from variation in patient case mix between centers. The clinical and demographic characteristics used in ANZDATA / NZ PD Registry models were: country, age at PD inception, PD sub-modality (automated PD [APD], continuous ambulatory PD [CAPD]), gender, ethnicity (Caucasian / other, Aboriginal or Torres Strait Islander, Asian, NZ Maori, Pacific peoples), primary kidney disease (diabetic nephropathy, ischemic / hypertensive nephropathy, glomerulonephritis, other), late referral for nephrology pre-dialysis care (<3 months before dialysis inception), and rurality (living in a major city, living in a regional town or remotely). Corresponding characteristics in RDPLF models were: country, age at PD inception, PD sub-modality (APD, CAPD), gender, diabetes mellitus (none, type 1 or type 2), and medical co-morbidity (Charlson co-morbidity index [CCS](12)).

	www.bdd.rdplf.org Volume 4, n° 4, december 2021
	https://doi.org/10.25796/bdd.v4i4.63443
	ISSN 2607-9917
	www.rdplf.org
	Langue Française RDPLF
	Dialyse Péritonéale de
	Registre de
	journal officiel du
	Data Measurement and Quantitative Variables

Table II :

 II Summary characteristics of centers in the RDPLF 2000-2020Figure1

			www.bdd.rdplf.org Volume 4, n° 4, december 2021
				https://doi.org/10.25796/bdd.v4i4.63443
					ISSN 2607-9917
		N	Median	P25	P75
	PD centers	Total	188
		Algeria	1
		Belgium	17
		France	155
		Luxembourg	1
		Morocco and	5
		Southern Provinces
		Switzerland	3
		Tunisia	6
	Total center-years		3226
	Patient	Stock (N @ end of year) during year) Flow (total N	16 24	8 13	26 38	www.rdplf.org
	Age (years) Gender* Diabetes mellitus Charlson Modality*	@ PD start Male Female APD CAPD	66.25 0.59 0.41 0.3 5.78 0.35 0.65	61.02 0.5 0.33 0.2 4.85 0.21 0.48	70.52 0.67 0.5 0.4 6.5 0.52 0.79	Dialyse Péritonéale de Langue Française RDPLF
						Registre de
						journal officiel du
	Simplified Calculation of PD Peritonitis Rate

  Annual peritonitis rate for every center in ANZDATA in 2019 (episodes per patient-year)y=0 is line of perfect average agreement Figure 2. Graphical description of agreement between gold-standard and estimated PD annual peritonitis rates for every center in ANZDATA during the latest year available (2019)

			www.bdd.rdplf.org Volume 4, n° 4, december 2021
			https://doi.org/10.25796/bdd.v4i4.63443
				ISSN 2607-9917
	Annual peritonitis rate for every center in ANZDATA in 2019 (episodes
	per patient-year)Lin's concordance correlation coefficient 0.972 (95%
	Cis 0.956, 0982)
					www.rdplf.org
					Langue Française RDPLF
	Characteristics Center size Table	> median number of patients	Lin's CCC (95% Cis) 0.996 (0.995-0.997)	P-value of two-way interaction <0.0001	Dialyse Péritonéale de
	Age Country peoples Indigenous / Pacific	< median number of patients Adult Pediatric Australia New Zealand proportion > median	0.972 (0.966-0.976) 0.980 (0.978-0.983) 0.967 (0.954-0.976) 0.976 (0.972-0.979) 0.994 (0.992-0.995) 0.982 (0.979-0.985)	0.03 <0.0001 0.0003	Registre de journal officiel du
		< median	0.972 (0.967-0.976)
		proportion
	Major city residents	>=50% of patients	0.975 (0.970-0.978)	0.77
		<50% of patients	0.976 (0.970-0.981)
	High-risk primary	> median	0.975 (0.970-0.979)	0.07
	kidney disease	proportion
	(diabetic / ischemic)
		< median	0.980 (0.977-0.983)
		proportion
	APD versus CAPD	> median	0.986 (0.983-0.988)	<0.0001
		proportion on APD
		< median	0.973 (0.968-0.977
		proportion on APD
	Simplified Calculation of PD Peritonitis Rate

journal officiel du Registre de Dialyse Péritonéale de Langue Française RDPLF www

  .rdplf.org www.bdd.rdplf.org Volume 4, n° 4, december 2021 https://doi.org/10.25796/bdd.v4i4.63443 ISSN 2607-9917

Acknowledgements

Contributions: research idea and study design: MM, CV; data acquisition: MM, CV, GP; data analysis/interpretation: MM, GP, GP; statistical analysis: MM. Each author contributed important intellectual content during manuscript drafting or revision and accepts accountability for the overall work by ensuring that questions pertaining to the accuracy or integrity of any portion of the work are appropriately investigated and resolved. MM takes responsibility that this study has been reported honestly, accurately, and transparently; that no important aspects of the study have been omitted, and that any discrepancies from the study as planned have been explained.

MM wishes to thank CC Szeto for his helpful comments in the early stages of this thought experiment.

The ANZDATA, RDPLF, and NZ PD Registries exists because of the tireless work of the nephrology community throughout Australasia and the Francophone world in collecting the information.

Table IV: Effect modification of concordance statistics in the RDPLF centers according to their casemix

Graphical descriptions of relationship-scale and data-scale agreement for the RDPLF are shown in Figure 3 for the entire period of observation and in Figure 4 for the last year of available data (2020). Table IV shows the results of testing within subgroups of centers defined by their patient case mix. Like ANZDATA, the strongest effect modifier in the RDPLF was found in center size, with again poorer agreement between gold-standard and estimated rates in smaller centers. There was statistically poorer agreement in centers with a number of other characteristics, although like ANZDATA some of these characteristics also tended to correlate with center size: older versus younger (mean PD stock per center of 17 versus 21 patients), higher proportion of APD versus not (20 versus 18). The top three countries with the highest concordance statistics were also those with the largest mean PD patient stock per center (Tunisia 39, France 19, Belgium 16).


domain: spi phys

text:
N Fdida

T Le Pichon

A Vincent-Randonnier

N Dorval

C Brossard

Characterization of a kerosene liquid jet injected in a high temperature Mach 2 supersonic crossflow

Fuel jets injected into a transverse supersonic air flow are submitted to successive physical phenomena before combustion and their interactions with shocks are complex. Penetration of a single kerosene jet injected in a high temperature Mach 2 crossflow was studied experimentally in the LAPCAT-II Dual Mode Ramjet Combustor of ONERA. Several operating points were studied with momentum flux ratio between liquid and gas from 3.1 to 8.6. The penetration height of the liquid jet is measured with high-speed imaging and compared with the literature. Moreover, laser-induced fluorescence imaging is used to study the vaporization and the mixing of kerosene/air.

Introduction

The air-breathing supersonic combustion ramjet (scramjet) is the most promising mode of propulsion for long-range hypersonic cruise vehicles due to its high specific impulse for flight Mach number ranging from 3 to 10, which means burning fuel with the atmospheric air instead of carrying both fuel and oxidizer (gain in volume and mass). Using scramjet engines is probably the most promising way to achieve this goal but many difficulties have to be addressed when designing these engines, such as improving ignition, stabilising the combustion in the supersonic internal flow or withstanding the high stagnation enthalpies with appropriate thermal protection systems. The way the fuel is injected in the combustor and its properties are part of the solutions for those two problems. Depending on the Mach of flight, supersonic combustion is controlled by the kinetics of combustion reactions, the mixing of the fuel with air in the combustor and the flame propagation. Up to Mach 7-8, liquid hydrocarbon fuels are considered as good candidates thanks to their high densities and their cooling capacities, especially if they undergo endothermic chemical reactions.

After a brief description of the LAPCAT-II Dual Mode Ramjet Combustor and its operating conditions, the optical setup used to achieve high-speed schlieren and Planar Laser Induced Fluorescence (PLIF) will be described. The paper will then focus on the experimental results obtained in the stationary phase of the supersonic. Based on schlieren images, the penetration depth of the fuel is measured for three conditions of momentum flux ratio between liquid and gas. PLIF diagnostics are used to study the vaporization and the mixing of kerosene/air. The competition between the different fluorescence signals is discussed * Corresponding author: nicolas.fdida@onera.fr Proceedings of the European Combustion Meeting 2023 to explain the vaporization of the liquid jet in the supersonic flow.

Experimental setup The ONERA LAERTE Facility and the LAPCAT-II Dual Mode Ramjet Combustor

Experiments are performed with the LAPCAT-II dual-mode ramjet combustor, at the ONERA-LAERTE facility, presented in Vincent-Randonnier et al. [START_REF] Vincent-Randonnier | Combustion of Hydrogen in Hot Air Flows within LAPCAT-II Dual Mode Ramjet Combustor at Onera-LAERTE Facility -Experimental and Numerical Investigation[END_REF]. In order to work as a dual-mode ramjet, the kerosene fuelled combustion chamber has two parts and two injection stages. The first part is slightly diverging and is mainly dedicated to supersonic combustion at a high flight Mach number, whereas the second one allows subsonic combustion at a lower flight Mach number, with a thermal throat located near the chamber end [START_REF] Scherrer | Research on Supersonic Combustion and Scramjet Combustors at ONERA[END_REF]. In the ramjet mode, the supersonic air flow enters the intake and slows down to subsonic through a series of shocks before entering the combustion chamber. In the scramjet mode, the flow remains supersonic through the combustor. The dual-mode scramjet bridges the gap between the ramjet and scramjet, using the same combustor for both combustion modes but operating with a thermal throat in the ramjet mode. This may theoretically enable a vehicle to be operated from flight Ma ≈ 3 to Ma ≈8 with only minor engine modifications. Previous studies with experimental and computational comparisons of the LAPCAT-II supersonic combustor fuelled with hydrogen, provided a better knowledge to describe the mechanism underlying this reacting flow [START_REF] Vincent-Randonnier | A Combined Experimental and Computational Study of the LAPCAT II Supersonic Combustor[END_REF]. The present study is the first one to be performed with the LAPCAT-II combustor with injection of a liquid fuel (Jet-A1). Note that no means to ignite the combustion is employed. Only autoignition may occur.

The LAERTE facility with the LAPCAT-II combustor is presented in Fig. 1, as a schematic view of the facility (a), a picture of the combustor (b) and a schematic of its longitudinal cross-section with the locations of the side windows (c). The facility is operated in the blow-down mode with the combustor acting as a heat-sink. The combustor is fed with air, thanks to a 2-tons and 25 MPa storage. The air flow is preheated by the two-stage hydrogen burner. Therefore, the flow at the inlet of the combustor is vitiated with water vapor, the molar fraction of O2 being kept at 0.21 by an upstream replenishment of oxygen (Fig. 1a). As indicated in Fig. 1c, the reference position, x= 0 mm, corresponds to the throat of the Mach 2.0 de Laval nozzle, used for this study. The combustor width is 40 mm and the inlet height is 35.4 mm. The combustor is 1257 mm long and contains four successive sections: the first has a constant cross-sectional area, whereas the following sections have 1°, 3° and 1° of diverging halfangles respectively to prevent thermal choking.

Windows are placed at different locations, allowing optical accesses for either single-point measurements or imaging techniques. The flow in the combustor is over-expanded and the flow transition from supersonic to subsonic occurs in the far downstream part of the combustor, more specifically in the third combustor section, around x≈750 mm to 800 mm, located in the second window.

Each run consists of a test sequence of ≈60 s providing 5 to 10 s of stationary injection conditions at the required stagnation temperature T0. During this test campaign, around hundreds of runs have been performed with experimental conditions tested for different T0, vitiated air and fuel mass flows.

The operating conditions were chosen in order to study separately the influence of the liquid mass flow rate on the jet penetration. The operating conditions considered in this study focus on a supersonic combustion at a fixed total pressure of P0≈0.40 MPa, Ma=1.955 and a total temperature T0 of 1500 K. Kerosene Jet-A1 is injected at room temperature, at x=200 mm in the first visualisation section of the test rig as shown in Fig. 1d. Three different fuel flowrates are injected m ̊j: 6.7 g/s (LQ), 8.9 g/s (MQ) and 11.1 g/s (HQ) through a single 0.6 mm in diameter injection hole. More information concerning experimental conditions and data collected are presented in detail in Fdida et al. [START_REF] Fdida | Penetration of a kerosene liquid jet injected in a high temperature Mach 2 supersonic crossflow[END_REF]. An important non dimensional parameter used to describe the jet penetration is the jet-to-crossflow momentum flux ratio q defined as q=ρjuj²/ρair*uair*², where u is the flow velocity and ρ the fluid density. The behaviour of the flow and combustion is characterized with 124 pressure measurements implemented along the combustor walls whereas the stagnation temperature T0 is estimated based on 3 thermocouple located at x=220 mm. A typical instantaneous image of the kerosene jet injected in the test supersonic flow is illustrated on Fig. 1d. Images are recorded from a trigger sent by the test sequence, at t0+20 s, at the opening of the kerosene valve. Measurement results presented here were obtained during the stationary phase of the flow.

High-speed schlieren

The schlieren imaging method, as described by Desse and Deron [START_REF] Desse | Shadow, Schlieren and Color Interferometry[END_REF], involves intercepting, with a knife, some of the light rays which are deflected in the test section. Schlieren is used as an imaging technique to visualize the density gradient in a flow resulting from deviations through the optical path of the light rays crossing the supersonic flow. In this experiment, schlieren allows to visualize the shock structures as white lines, the fuel vapor and turbulent mixing area in grey level gradients and the spray in black.

The imaging setup has a spatial resolution of 6.1 pix/mm. Presented images are recorded at 5 or 10 kHz with an image size of 800 × 256 pix² to visualize the whole penetration of the liquid jet. On the typical schlieren images presented in Figure 2, the main physical processes of the liquid injection in a supersonic crossflow can be observed: the shocks and their reflections on the walls can be seen as white lines and the liquid jet as dark pixel values. The bow shock is located approximately at 0.3 mm upstream from the base of the liquid jet. Moreover, the position of the leading edge shock can be seen as a diagonal line upstream from the bow shock. When a supersonic flow meets an obstacle, a shock is generated upstream from this obstacle. In the case of a jet injection, a so-called bow shock appears a few millimeters upstream, following the base of the liquid column. This shock turns to an oblique shock once the liquid jet has penetrated deeper in the chamber. The bow shock originating at the base of the injection point appears to follow the liquid column in the first millimeters and the penetration line, illustrated by a white arc in dashed line. On the left-hand side of the liquid column, namely the windward region, surface instabilities can be seen as small waves travelling along the interface between the fuel jet and the crossflow (i.e. on the left-hand side of the liquid column). To the right of the injection point, namely the leeward region, the spray is too dense optically to see the interface and the breakup of the liquid column. Following the bended liquid column, once past a breaking point, which cannot be seen in this image, ligaments and drops are created in the jet plume. At the right end of the image, an area with strong fluctuations of grey levels indicates density gradients due to turbulence and kerosene vapor and liquid mixing with the supersonic flow.

Planar Laser Induced Fluorescence setup

A single laser system is used for both OH-PLIF and kerosene-PLIF experiments. The second harmonic of a pulsed Nd:YAG laser (Quantel YG980) at 532 nm is used to pump a tunable narrow-linewidth dye laser (Quantel TDL+)). The dye laser beam is frequency doubled in a second harmonic generation crystal. The laser wavelength is tuned to 282.75 nm for excitation of OH radicals through the Q1(5) line in the A²Σ -X²Π (1-0) band. This excitation wavelength also enables to induce kerosene fluorescence emission which arises from the excitation of mono-and di-aromatics naturally present in this multi-component fuel. The output energy is 13 mJ/pulse, the pulse duration is ~10 ns and the repetition rate is 30 Hz. The laser beam is focused into a laser sheet by using a set of spherical and cylindrical lenses (length of 47 mm and thickness of approximately 400 µm). The laser is introduced into the vertical median plane of the combustor. The same detection system is used for OH and kerosene fluorescence light detection. PLIF images are recorded perpendicularly to the laser excitation plane. Fluorescence signals are amplified by an intensifier (IRO, LaVision) and imaged by a sCMOS camera (LaVision). The intensifier is equipped with a 100 mmfocal length, f/2.8, UV lens (Cerco). A combination of a high-pass filter (ZUL 300, Asahi) for laser scattering rejection and a band pass filter centered at 310 nm (FWHM = 10 nm, ZBP 310, Asahi) for fluorescence selection is used. The intensifier gate width is set to 100 ns. Images are recorded at 30 Hz repetition rate. Laser sheet optics and mirrors, as well as the detection system, were mounted on a motorized horizontal translation stage in order to investigate different axial locations from the injection point (x = 200 mm). The laser sheet energy profile was characterized by recording fluorescence images of gaseous acetone inside a cell, positioned in place of the test section for various axial measurement positions (from the injection point to 300 mm downstream of the injection point). Even though challenging in terms of optical alignment, the homogeneity of the laser sheet could be kept mostly unchanged over this large displacement range.

Results

Penetration depth of the liquid jet

The penetration of the liquid jet into the supersonic flow may be an important feature when designing a liquid-fueled scramjet combustor. A deep penetration may be desired to increase the mixing and thus lower the ignition distance. One may also wish to avoid spray impingement onto the combustor walls. Since 1970, many experimental studies can be found in the literature with various injection configurations for subsonic [START_REF] Broumand | Liquid jet in a subsonic gaseous crossflow: Recent progress and remaining challenges[END_REF], but also supersonic flows [START_REF] Ren | Supersonic spray combustion subject to scramjets: Progress and challenges[END_REF]. In such a situation, the momentum flux ratio q is the main parameter that drives the penetration length. The penetration height Y is defined as the liquid maximum penetration perpendicularly to the crossflow, from the injection point. The penetration measurements presented here are obtained in single jet injected in a supersonic flow with 3.1<q<8.6 and compared to other studies with a similar injection setup.

Time-averaged schlieren images are presented in Figure 3, and are sorted by increasing q from top to bottom. The liquid column penetrates farther from the injection point as q increases. Indeed, as m ̊j increases, the amount of kerosene becomes more important, consequently, the liquid is present farther away from the wall before it is vaporized. LQ: T0 =1500 ± 5 K, m ̊j = 6.7 ± 0.2 g/s MQ: T0 =1500 ± 5 K, m ̊j = 8.9 ± 0.3 g/s HQ: T0 =1500 ± 5 K, m ̊j = 11.2 ± 0.5 g/s An image processing algorithm has been developed to measure the spray penetration height y/dj from images of Figure 3. It is based on the binarization of the time-averaged image for each operating condition. A set of instantaneous normalized images recorded during the stationary phase of the flow is averaged. The resulting time-averaged image is then binarized to separate the denser part of the liquid phase of the gaseous and dispersed phase. For that purpose, an automatic threshold method is used to binarize these images, characterized by a bimodal grey level histogram. A relative threshold is then defined from the grey level histogram thanks to the "Minimum method" originally proposed by Prewitt and Mendelsohn [START_REF] Prewitt | The analysis of cell images[END_REF] and implemented in Image J [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF]. In this method, the histogram is iteratively smoothed using a running average of size 3, until there are only two local maxima. Once the binarized image is obtained, the maximum position of the black pixels, perpendicularly from the upper wall is extracted to calculate the penetration height, relatively to the injector position. The penetration heights presented in the next paragraph are then calculated from 5000 schlieren images (0.5 or 1 s).

In Figure 4, dimensionless penetration heights y/dj versus the longitudinal distance from the injection point x/dj are presented for the three cases. Axial and vertical distances are normalized by the injector orifice diameter dj. Experimental uncertainties involved in the measurement of Y are due to the image pixel resolution and have been highlighted in the plots of Figure 4 with vertical error lines. The calculated uncertainty Δy/dj linked to the pixel resolution leads to an absolute uncertainty 0.3 for schlieren images. As the test bench is operated at constant P0 and Mach number, an increase of temperature results in a decrease of ρair* and m ̊air* and an increase of uair*. Consequently, the momentum flux ratio q that drives the penetration is similar for those two conditions, leading to close penetration curves. In Figure 4, the studied high temperature conditions are compared to correlations from literature obtained with either shadowgraphy [START_REF] Lin | Penetration height of liquid jets in high-speed crossflows[END_REF] or PDPA [START_REF] Lin | Structures of water jets in a Mach 1.94 supersonic crossflow[END_REF]. The correlation proposed by Lin et al. [START_REF] Lin | Penetration height of liquid jets in high-speed crossflows[END_REF] was calculated for different liquids (water, alcohol or a mix of water and alcohol), injected in a Mach 1.94 supersonic flow at ambient temperature 293 K. In Lin et al. [START_REF] Lin | Structures of water jets in a Mach 1.94 supersonic crossflow[END_REF], pure water is injected through a single injector in a supersonic flow (Mach 1.94), at a total temperature of 477 K and 533 K. These measurements were performed in the range 25<x/dj<200 and 2<q<15, except for the injected liquid (water instead of kerosene) and the temperature of the supersonic flow.

In Figure 4, the penetration height predicted by the correlation obtained with PDPA (dash line) is higher than the experimental presented cases (solid curves) and that predicted by correlation derived from their previous work from shadowgraph images [START_REF] Lin | Penetration height of liquid jets in high-speed crossflows[END_REF]. According to Lin et al. [START_REF] Lin | Structures of water jets in a Mach 1.94 supersonic crossflow[END_REF], the correlation obtained with PDPA overestimates the penetrations obtained with shadowgraph by 40%, because shadowgraph images show primarily droplet number density and may not show the upper portion of the spray plume, which contains large droplets at low number density. The penetration trajectories obtained in the present study are about 20% lower than their work, at x/d=10, which cannot be explained only by the different measurement methods bringing to this correlation. Time averaged images can differ from one to another test case due to slight differences in the optical setup, such as pollution on the windows or inhomogeneities in the background that cannot be completely eliminated by the normalization. Consequently, the threshold value that is found automatically with the minimum method can double from a test to another. Doubling the threshold value induces an increase of the penetration of 10%. Another explanation could be the difference in the fluid injected. Indeed, the dynamic viscosity of kerosene is 1.9 times higher than the water viscosity at ambient temperature. Amongst the authors who studied the influence of the viscosity on the penetration of various fluids injected in a subsonic crossflow in different conditions, Stenzler et al. [START_REF] Stenzler | Penetration of liquid jets in a cross-flow[END_REF] reported a dependency of the penetration with the viscosity ratio to water such as (µj/µwater) a where 0.027<a< 0.108. It means that in our case, the penetration length could be reduced of about 5% due to the fuel viscosity. The influence of the momentum flux ratio q can be seen on Figure 4 by comparing LQ, MQ and HQ, with increasing q, for a given total temperature of about 1500 K. Solid lines refer to the present experiment, with the solid line color getting darker as q increases.

Fluorescence results

The first experimental configuration without any kerosene fuel injection is the fluorescence imaging of the OH radicals present in the combustor vitiated air flow downstream from the two-stage hydrogen preburner. OH-PLIF allows us to visualize the topology of this preheated supersonic flow inside the test section, in particular in the injector region. An instantaneous OH-PLIF image in the preheated supersonic flow is presented in Figure 5 in false colors for visualization purposes. The flow is going from left to the right. The limits of the upper and lower walls of the test section are the black to blue horizontal frontiers. The fuel injection point is located at the left border of the laser sheet and indicated by a vertical white arrow in Figure 5. For the axial position corresponding to Figure 5, the homogeneity of the laser sheet was ensured to be ±15% of the averaged central value, defined by two vertical dashed lines. At the horizontal blue to green frontiers of the instantaneous image, Kelvin-Helmholtz-like structures can be observed on the upper and lower parts of the test section. Our current assumption is that these structures are generated between the walls boundary layers and the supersonic main flow. The fluorescence signal drop in the boundary layer region could be resulting from a nonuniform flow at the preburner exit, featuring a colder outer flow with less OH radicals than in the main flow. These interpretations are currently investigated. The time-averaged image was calculated over 225 images recorded at 30 Hz during the stationary phase of the flow.

The second experimental configuration with fuel injection is dedicated to the detection of kerosene fluorescence signal alone. The excitation wavelength is detuned away from the OH absorption line. A typical instantaneous kerosene-PLIF image is presented in Figure 6. The images are composed of mixed LIF signals from aromatics in both liquid and gaseous phase. Indeed, the highest signal intensity region (yellow, red and white regions, white means detector saturation) corresponds to the kerosene fuel injection at the position indicated by a vertical white arrow. This liquid region location agrees well with the instantaneous Schlieren image (Fig. 2). The lower fluorescence signals (green/blue) could be attributed to the aromatics in gas phase but the exact frontier between the liquid and gaseous aromatics regions is not clearly defined. The time-averaged image (225 images sample) presented in Figure 6 shows a plume shape similar to the shape of the jet as observed in the image at the bottom in Figure 3, penetrating vertically 5 to 10 mm from the injection point located on the upper wall. This shape also agrees well with the penetration curve presented in Figure 4. The third experimental configuration consists of OH-PLIF diagnostics in presence of kerosene (see Figure 7). In order to better discriminate the OH fluorescence from the kerosene fluorescence, a narrower bandpass filter (FWHM = 5.6 nm) at 310 nm was added. The laser wavelength was tuned to OH absorption line at 282.75 nm. We can notice the presence of OH radicals upstream from before the injection point, which are produced by the two-stage preburner, recognizable by its lower level signal (blue/black) frontier with Kelvin-Helmholtz-like structures. In the center of the images, there is a black horizontal wavy line corresponding to a deposit on the window. From the injection point (x=200 mm, Figure 7) to x=500 mm (not shown), there is no OH radical produced by combustion of the kerosene vapors with the supersonic air. Indeed, due to the mixing, vaporization and self-ignition delays, kerosene combustion does not occur inside the combustor test section, but farther downstream. Analysis of fluorescence images obtained in this configuration is difficult because OH and aromatics LIF signals are mixed (liquid and gaseous phases). By stopping a part of the laser sheet introduced in the test section, a vertical region with no signal in the PLIF image can be seen (Figure 7). This region is indicated by two vertical dashed lines in Figure 7 (left). We can see that there is no LIF signal between the two vertical lines in the lower half part of the image where there is only OH in the gas flow, whereas in the plume of the liquid jet, some signal is detected. This signal is attributed to the fluorescence of kerosene droplets present in this zone, which is excited by multiple laser light scattering. We checked that this spurious signal is not due to elastic scattering by kerosene liquid particles thanks to the high rejection power of the couple of 310 nm-bandpass filter (ZBP310) and high-pass filter. Outside the scope of these experiments, a simple test consisting of introducing some water droplets in the test section did not show any signal. This out-of-field fluorescence induced by laser light scattering by droplets could be therefore an indicator of the presence of liquid kerosene. It seems that multiple light scattering still exists at 100 mm from the injection point but could become negligible at 200 mm from the injector (work still in progress).

Conclusions

The deep penetration of atomized liquid fuel into the supersonic airflow is a key physical process to maintain the combustion. There is a lack of experimental studies in conditions close to engines operation (i.e. with real fuel and hot air flow). Atomization and penetration of a kerosene jet injected in a Mach 2 crossflow were studied experimentally in the LAPCAT-II Dual Mode Ramjet Combustor at Onera, using high speed schlieren. This experimental study presents measurements in high temperature conditions, with kerosene as liquid fuel. The fuel spray was injected through a single orifice, perpendicularly to a Mach 2 supersonic air flow, at temperatures at 1500 K and jetto-crossflow momentum flux ratio from 3.1 to 8.6. Three different test cases were investigated to characterize the effect of the momentum flux ratio q on the atomization process. Penetrations of the kerosene jet were measured for these three test cases and compared to other studies of the literature, in the lower temperature cases. OH-PLIF and kerosene-PLIF experiments were also conducted in these three configurations. OH-PLIF was performed to visualize the hot supersonic vitiated air flow in the test section, with and without the kerosene jet. The PLIF images allow to visualize in a vertical laser sheet, i.e. with spatial resolution and depth-of-field effect, the kerosene spray and vaporization along the flow. Perspectives of this study are to further process PLIF images in order to investigate the area where multiple light scattering occurred, with the use of a stop on the laser sheet, and to determine if the vaporization is complete far from the injection point and within the optically accessible region of the combustor. The analysis of the sheet images obtained with acetone could be used to take into account the horizontal intensity profile in PLIF images. Moreover, schlieren images and PLIF images on aromatics could be compared more precisely in order to estimate the position of the penetration line in the PLIF images and to eventually define a threshold level range to identify regions with kerosene vapor in the images.

Figure 1 :

 1 Figure 1: Schematic plan of the LAERTE facility, (b) photo of the LAPCAT-II combustor, (c) geometry of the LAPCAT-II combustor (d) Instantaneous schlieren image, case HQ.

Figure 2 :

 2 Figure 2: Instantaneous Schlieren images, m ̊j =11.1 g/s, HQ

Figure 3 :

 3 Figure 3: Time-averaged schlieren images showing the effect of fuel mass flow rate on the jet penetration and related shocks. Scale: 5mm.

Figure 4 :

 4 Figure 4: Penetration height as a function of axial distance from the injection point, obtained with schlieren images.

Figure 5 :

 5 Figure 5: Instantaneous (left) and time-averaged (right) OH-PLIF images of the preheated supersonic flow, HQ flowrate, 1500K total temperature.

Figure 6 :

 6 Figure 6: Instantaneous (left) and time-averaged (right) kerosene-PLIF images of the preheated supersonic flow, HQ flowrate, 1500K total temperature.

Figure 7 :

 7 Figure 7: Instantaneous (left) and time-averaged (right) OH-PLIF images of the heated supersonic flow, HQ flowrate, 1500K total temperature.

Acknowledgments

The authors thank Mr Carru, Cherubini, Roux, Taieb and Ms Lecointe for their assistance in conducting the experiments and optical diagnostics.