domain: sdv sde

text:
M Bidon

A J P Philip

A Braun

A Herman

J Roy

Z Pedrero-Zayas

S Fontagné- Dicharry

Affiliations

Stéphanie Fontagné-Dicharry
email: stephanie.fontagne-dicharry@inrae.fr

Interaction between dietary selenium and methylmercury on growth performance, deposition and health parameters in rainbow trout fed selenium-rich tuna-based diets or selenium-poor plant-based diets

Keywords: Methylmercury, sodium selenite, selenomethionine, tuna by-products, inflammation, rainbow trout

Highlights

 Se addition in plant diets prevented growth reduction induced by MeHg at 21 days  SeMet in tuna diets hampered MeHg-induced pro-inflammatory response at 21 days  Se(IV) in tuna diets reduced Hg body level in fish fed MeHg at 21 days  MeHg addition in tuna diets limited growth reduction by Se(IV) at 168 days  MeHg addition in plant and tuna diets increased body Se content at 168 days 3

Introduction

Global concerns of public opinion rise on aquaculture production and its impact on the environment, due to the use of fishmeal (FM) and fish oil (FO) produced from wild fish catch (FAO, 2022). Plant and other alternative ingredients are increasingly used in aquafeed formulation to replace FM and FO (FAO, 2022). Another strategy is to increase the part of fish by-products: in 2020, 27% of the global production of FM and 48% of the total production of FO came from by-products [START_REF] Iffo | By-product[END_REF]. Tunas represent one of the most high-value fish group with their high catch volume and important economic value. In 2020, catches of tuna and tunalike species represented 7.8 million tonnes (FAO, 2022). Tuna cannery industry generates high amount of by-products made of viscera, head, bones, skin and fins, representing up to 70% of processed fish (FAO, 2022). Reports are available concerning the use of tuna by-products as aquafeed ingredient for FM replacement. A substitution up to 30% of FM by tuna by-products during 7 weeks in olive flounder juveniles [START_REF] Kim | Substitution effects of fishmeal with tuna byproduct meal in the diet on growth, body composition, plasma chemistry and amino acid profiles of juvenile olive flounder (Paralichthys olivaceus)[END_REF] and a substitution up to 75% during 12 weeks in Korean rockfish juveniles [START_REF] Kim | Tuna by-product meal as a dietary protein source replacing fishmeal in juvenile Korean rockfish Sebastes schlegeli[END_REF] had no adverse effect on growth compared to fish receiving a non FM-substituted commercial diet. On the other hand, a FM replacement by 55% of tuna by-products decreased final body weight and increased feed conversion ratio of rainbow trout, compared to fish fed a commercial diet with anchovy meal as FM after 12 weeks of feeding [START_REF] Tekinay | Effects of dietary tuna by-products on feed intake and utilization of rainbow trout Oncorhynchus mykiss[END_REF]. Tunas accumulate contaminants like mercury (Hg), lead and arsenic [START_REF] Ormaza-González | Low mercury, cadmium and lead concentrations in tuna products from the eastern Pacific[END_REF] and Hg levels in tunas vary widely depending on factors such as species and tissues [START_REF] Ruelas-Inzunza | Bioaccumulation of As, Hg, and Se in tunas Thunnus albacares and Katsuwonus pelamis from the eastern Pacific: tissue distribution and As speciation[END_REF].

Therefore, contrary to plant feedstuffs that present other nutritional limitations [START_REF] Gatlin | Expanding the utilization of sustainable plant products in aquafeeds: a review[END_REF], the presence of Hg in tuna by-products raises some concern with regards to fish welfare and consumer safety as World Health Organization has classified Hg in the top ten chemicals of major concern for public health. Hg toxicity depends, among others on chemical Hg form [START_REF] Jang | A comparative study of effects of dietary mercuric chloride and methylmercury chloride on growth performance, tissue accumulation, stress and immune responses, and plasma measurements in Korean rockfish, Sebastes schlegeli[END_REF]. Methylmercury (MeHg) is the predominant chemical form found in the environment and threatens human health to a higher extent than Hg inorganic forms [START_REF] Honda | Recent advances in evaluation of health effects on mercury with special reference to methylmercurya minireview[END_REF]. In salmonids, toxicity threshold is also reported to be lower for MeHg than for inorganic Hg [START_REF] Berntssen | Maximum limits of organic and inorganic mercury in fish feed[END_REF]) and a dietary level of 2 mg/kg MeHg has been shown to induce a pro-inflammatory response in juvenile Nile tilapia (Abu Zeid et al., 2021).

In addition to Hg, tunas accumulate high amount of selenium (Se) [START_REF] Yamashita | niacin, 10 mg; D-calcium pantothenate, 20 mg; pyridoxine-HCl, 3 mg; myo-inositol, 0.3 g; D-biotin, 0.2 mg; folic acid, 1 mg; cyanocobalamin, 0.01 mg; L-ascorbyl-2-polyphosphate, 50 mg; choline-HCl, 1 g; CaHPO4.2H2O (18% P; 22% Ca), 33 or 5 g in plantbased or tuna meal-based diets respectively; CaCO3 (40% Ca),•2.15 g[END_REF]. Thus, tuna by-products are expected to contain high Se concentration, probably above rainbow trout and salmonid Se requirement, defined between 0.15 and 0.65 mg/kg diet (NRC, 2011;[START_REF] Jesu Prabhu | Dietary selenium required to achieve body homeostasis and attenuate pro-inflammatory responses in Atlantic salmon post-smolt exceeds the present EU legal limit[END_REF]. On the contrary, plant-based aquafeeds are known to contain low Se level, below salmonid requirements [START_REF] Jesu Prabhu | Dietary selenium required to achieve body homeostasis and attenuate pro-inflammatory responses in Atlantic salmon post-smolt exceeds the present EU legal limit[END_REF]. This essential element plays also a great role in the protection against Hg toxicity as demonstrated in goldfish and zebrafish [START_REF] Bjerregaard | Dietary selenium reduces retention of methyl mercury in freshwater fish[END_REF][START_REF] Amlund | Dietary selenomethionine influences the accumulation and depuration of dietary methylmercury in zebrafish (Danio rerio)[END_REF]. These studies underlined also the importance of dietary Se concentration and chemical forms on Hg accumulation and detoxification.

The aim of this study was to investigate the impact of dietary MeHg and various Se chemical forms in alternative aquafeeds containing different basal Hg and Se concentrations.

The Hg and Se deposition linked with growth performance, pro-inflammatory and overall health status after a short and long-term dietary exposure was assessed in rainbow trout juveniles.

Material and methods

Ethical statement

The feeding trial was conducted in accordance with the European directive 2010/63/EU and the French decree n° 2013-118 on the protection of animals used for scientific purposes.

The protocol was approved by the Ethical Committee C2EA-73 and the French Ministry of Higher Education and Research (reference number APAFIS#27846-2020102812241350 v2).

Experimental diets

Diets were manufactured in the INRAE experimental facilities of Donzacq (Landes, France, https://doi.org/10.15454/GPYD-AM38), using a twin-screw extruder (BC 45,Clextral,Firminy,France). Twelve feeds were formulated with two different basal ingredient compositions (Table 1a). Plant-based diets were formulated with plant-derived proteins and tuna-based diets with FM derived from tuna by-products (Marine Biotechnology Products, Port-Louis, Mauritius). Contrary to tuna-based diets, plant-based diets were MeHg-free and known to contain low basal Se level. Control plant (PC) and control tuna (TC) diets were unsupplemented with MeHg and Se(IV) or SeMet either, containing thus only basal levels of Hg and Se (Table 1b). Two diets were supplemented with methylmercury(II) chloride (Sigma-Aldrich, Saint-Quentin-Fallavier, France): 2 mg Hg/kg diet for plant-based diet (PH) and 1.6 mg Hg/kg diet for tuna-based diet (TH). Four other diets were supplemented with 1.5 mg Se/kg diet, using either inorganic Se source (sodium selenite (Se(IV)), Sigma-Aldrich, Saint Louis, Missouri, USA) in diets PI and TI or organic Se source (L-selenomethionine (SeMet), Excential Selenium 4000, Orffa, Breda, Netherlands) in diets PO and TO, respectively. Two diets were supplemented with both Se(IV) and MeHg (PHI and THI diets) and two others with both SeMet and MeHg (PHO and THO diets).

Experimental design

A 6-month feeding trial was carried out in the INRAE experimental fish farm at Donzacq. All-female diploid rainbow trout (Oncorhynchus mykiss) from the same parental stock (n = 1800) with an initial body weight of 26 ± 1 g were randomly allocated to 50-L fiberglass tanks with 50 fish per tank for the first two months, then to 150-L fiberglass tanks with 26 fish per tank for the last four months of the trial. Water flow was set to ensure an oxygen concentration above 90% saturation. Tanks were supplied with flow-through (0.1 L/s, renewal 4.5 times/h at the beginning, then 0.25 L/s, renewal 7 times/h) spring water at 17 ± 1 °C. Fish were hand-fed twice a day to visual satiation under natural light regimen. Each diet was distributed to three replicate groups of fish over a 6-month growth trial. Mortality was recorded daily. Fish from each tank were bulk weighed every three weeks.

Sampling and data collection

Before every weighing and sampling (after 21 and 168 days), fish were overnight starved during 16 h. At the start, 21 fish in common, then 8 fish from each replicate tank (n = 24 fish per diet) at day 21 and day 168 were anaesthetized with benzocaine (30 mg/L) then killed with an overdose of benzocaine (60 mg/L). Fish were weighed and blood samples were collected from the caudal vein. Plasma was recovered from half of the centrifuged (5500 × g for 10 min) blood samples, immediately frozen and stored at -80 °C prior to analysis (n = 12 per diet). Three fish collected at the start and two fish per tank at day 21 and day 168 (n = 6 per diet) were frozen and stored at -20°C prior to proximate analysis. The liver of other collected fish (n = 18 at the start and n = 18 per diet at day 21 and day 168) were weighed for calculating hepatosomatic index (HSI). At the end of the feeding trial, remaining fish (from 3 to 10 per tank) were fed for another week, anaesthetized and killed 16 h after the last meal for faeces collection in distal gut for the determination of apparent digestibility coefficient (ADC) of Se and Hg. The samples of faeces were collected over ice, pooled per tank, frozen immediately and stored at -20 °C prior to Hg and Se analysis.

Proximate and mineral analyses in diets, whole fish and faeces

Dry matter content was determined by drying directly faeces samples or after grinding fish and diet samples at 105 °C for 24 h. Whole fish and faeces samples were freezed-dried before further analyses. Proximate composition of diets and freeze-dried fish was determined according to following procedures: ash by incineration at 550 °C for 10 h, protein (N × 6.25) by the Kjeldahl method after acid digestion, total lipid according to [START_REF] Folch | A simple method for the isolation and purification of total lipids from animal tissues[END_REF] using dichloromethane instead of chloroform and gross energy in an adiabatic bomb calorimeter.

Total Se and Hg concentrations in diet, freeze-dried fish and faeces samples were measured by inductively coupled plasma mass spectrometry (ICP-MS) according to [START_REF] Silva | Apparent availability of zinc, selenium and manganese as inorganic metal salts or organic forms in plant-based diets for Atlantic salmon (Salmo salar)[END_REF].

Determination of apparent digestibility coefficient (ADC) of minerals

The apparent digestibility coefficient (ADC) of Se and Hg was measured using vanadium (V) as an internal marker in faeces and diets according to [START_REF] Witkowski | Development and assessment of novel endogenous markers in commercial aquafeeds to measure apparent digestibility in large Atlantic salmon (Salmo salar) on salmon farms[END_REF].

Determination of plasma and blood metabolites

Plasma metabolites were determined in plasma of fish, n = 3 pooled samples per dietary treatment representing 4 fish each. Fish pro-inflammatory cytokines: tumor necrosis factor α (TNF-α), interleukine 1β (IL-1β) and interleukine 6 (IL-6) were determined with ELISA kit tests (Cusabio Biotech Co., Wuhan, Hubei, China) according to manufacturer's instructions using zebrafish TNF-α (cat. No. CSB-E13254Fh), zebrafish IL-1β (cat. No. CSB-E13254Fh) and Atlantic salmon (Salmo salar) IL-6 (cat. No. CSB-E13258Fh). TNF-α and IL-6 ELISA kits used a competitive inhibition enzyme immunoassay technique whereas IL-1β ELISA kit used a quantitative sandwich enzyme immunoassay technique. Kits provided cytokines biotinconjugated, avidin conjugated horseradish peroxidase and a substrate solution. Horseradish peroxidase transformed the substrate into a coloured product. In TNF-α and IL-6 ELISA kits, colour developed in opposite to the amount of pro-inflammatory cytokines in samples. In IL-1β ELISA kit, the colour developed in proportion to the amount of IL-1β in samples. The absorbance was measured at 450 nm with a microplate reader and converted into concentrations using the standard curve formula. Plasma lysozyme activity was determined according to [START_REF] Ellis | Lysozyme assays[END_REF] using a turbidimetric assay with lyophilized particles of Micrococcus lysodeikticus (Merck, Saint-Quentin-Fallavier, France). Alanine amino transferase (ALAT) and aspartate amino transferase (ASAT) activities were assessed in plasma by an end-point colorimetric test (AST GOT-ALT GPT Biolabo, France) at 505 nm with 2-oxoglutarate and 2,4dinitrophenylhydrazine according to the manufacturer's instructions using 40 µL of fish plasma. Total protein content in plasma was determined through the colorimetric Biuret method using bicinchoninic acid (BCA) solution and copper(II) sulfate solution (Interchim uptima, France), using 10 µL of plasma sample diluted in distilled water (1:100) mixed with 200 µL of working reagent (50 volumes of BCA with 1 volume of copper(II) sulfate solution). Absorbance was measured at 562 nm. Total immunoglobulin level in plasma was determined using 10 µL of plasma samples diluted in distilled water (1:100), mixed with an equal volume of polyethylene glycol 70 % and centrifuged at 10 000 g, for 30 min at 15 °C for immunoglobulin precipitation. Precipitated samples (10 µL) were mixed with 200 µL of a solution containing BCA and copper(II) sulfate (1:50) into a microplate and then incubated for 30 min at 37 °C.

The absorbance was measured at 562 nm and converted into concentration using a standard curve as for total protein determination. Albumin level in plasma samples was assessed by endpoint colorimetric test using bromocresol green method. A volume of 10 µL of plasma was used and absorbance was measured at 630 nm. Glycaemia was assessed at 504 nm using 5 µL of fish plasma and colorimetric method with glucose oxidase, following manufacturer's instructions (Glucose GOD-POD, Sobioda S.A.S, Montbonnot St Martin, France). Haemoglobin was measured in blood samples (n = 3 per dietary treatment) using a colorimetric method (Hb-Randox kit, Ref HG1539, United Kingdom) following the manufacturer's instructions with 20 µL of blood.

Statistical analyses

Data are expressed as mean ± standard error (SEM). Differences between dietary groups were analysed using a two-way ANOVA to test the effect of dietary Hg supplementation and dietary Se supplementation and their interaction. Prior to the two-way ANOVA, normality and homogeneity of variance of data were checked with a Shapiro-Wilk and a Levene test, respectively. When appropriate, analysis was followed with a Tukey post hoc test. Statistical analyses were performed using R software (version 3.6.1, R development Core Team, 2008).

Differences were considered significant when p-value was < 0.05.

Results

Dietary MeHg impact on growth performance, proximate body composition of rainbow trout juveniles and interactive effects of dietary Se

After 21 days of feeding, fish fed MeHg-supplemented plant-based diet PH displayed decreased body weight compared to fish fed control plant-based diet PC (Fig. 1A). Such effect of MeHg was not noticed in the presence of Se in diets PHI and PHO compared to control diets PI and PO (Fig. 1A). No significant effect of dietary MeHg supplementation was noticed on feed intake (FI) whereas a significant interaction was detected between MeHg and dietary Se forms on feed conversion ratio (FCR) and protein efficiency ratio (PER), but Tuckey's post hoc test did not allow to discriminate between plant-based dietary groups (Table 2). The highest FCR and the lowest PER were displayed in PH group and the lowest FCR and highest PER were noticed in PC group (Table 2). After 168 days of feeding, fish fed PH diet displayed decreased body ash retention compared to fish fed PC diet (Table 2). No other significant effect of MeHg supplementation in plant-based diets was observed on body weight (Fig. 1B), FI, FCR, PER, survival or proximate body composition (Table 2).

After 21 days of feeding, fish fed MeHg-supplemented tuna-based diets TH, THI and THO exhibited decreased body gross energy content compared to fish fed control diets TC, TI and TO (Table 3) without significant effect on growth (Fig. 1A). After 168 days of feeding, fish fed MeHg-supplemented diets TH, THI and THO displayed higher FI and reduced hepatosomatic index compared to fish fed TC, TI and TO (Table 3). A higher body weight was recorded in fish fed the MeHg and Se(IV)-supplemented diet THI compared to the control group TI (Fig. 1B) without significant difference on FCR and PER (Table 3). No significant effect of dietary MeHg was recorded on survival rate of fish fed tuna-based diets (Table 3).

Dietary Se impact on growth performance, proximate body composition of rainbow trout juveniles and interactive effect of dietary MeHg

After 21 days of feeding, fish fed Se-supplemented plant-based diets PI, PHI, PO and PHO displayed no significant differences in growth performance (Fig. 1A and Table 2) or proximate body composition compared to fish fed control diets PC and PH (Table 2). After 168 days of feeding, higher body dry matter, total lipid, gross energy content and lipid retention were noticed in fish fed Se-supplemented diets PI and PO compared to the control group PC (Table 2), but no significant effect of dietary Se supplementation was noticed on fish body weight (Fig. 1B) or other growth and survival parameters (Table 2).

After 21 days of feeding, fish fed Se-supplemented tuna-based diets TI, THI, TO and THO displayed decreased body weight compared to fish fed diets TC and TH (Fig 1A). After 168 days of feeding, reduced body weight was recorded in fish fed Se(IV)-supplemented diet TI compared to fish fed diets TC and TO (Fig. 1B). Fish fed SeMet-supplemented diets TO and THO displayed higher PER, protein retention and decreased FCR compared to Se(IV)supplemented diets TI and THI (Table 3). Fish fed Se-supplemented diets TI, THI, TO and THO exhibited reduced ash retention compared to fish fed control diets TC and TH (Table 3).

No significant effect of dietary Se was recorded on survival rate of fish fed tuna-based diets (Table 3).

Dietary MeHg impact on Hg and Se body composition, retention and digestibility in rainbow trout juveniles and interactive effect of dietary Se

MeHg supplementation in plant-based diets PH, PHI and PHO increased both shortterm and long-term body Hg content compared to fish fed control diets PC, PI and PO (Fig. 2A and Fig. 2B). After 168 days of feeding, fish fed diets PH, PHI and PHO displayed higher faecal Hg content compared to fish fed diets PC, PI and PO (Table 4). Fish exposed to diet PHO exhibited higher body Se content compared to fish receiving diet PO (Fig. 2D). Fish fed diets PHI and PHO presented reduced faecal Se content, increased Se digestibility and retention compared to fish fed diets PI and PO (Table 4).

In both the short and long term, higher body Hg content and lower Hg retention were recorded in fish fed MeHg-supplemented tuna-based diets TH, THI and THO compared to diets TC, TI and TO (Fig. 2A, Fig. 2B and Table 5). After 168 days of feeding, diets TH, THI and THO increased faecal Hg content and Hg apparent digestibility coefficient compared to diets TC, TI and TO (Table 5). After 21 days of feeding, fish fed THI diet exhibited reduced Hg retention compared to fish fed TI diet (Table 5). Fish fed diets TH, THI and THO displayed decreased Se retention (Table 5) without significant impact on body Se content (Fig. 2C) compared to fish fed control diets TC, TI and TO. However, in the long term, increased Se retention (Table 5) and body Se content (Fig. 2D) were recorded in fish exposed to diets TH, THI and THO compared to fish receiving diets TC, TI and TO.

Dietary Se impact on Hg and Se body composition, retention and digestibility in rainbow trout juveniles and interactive effect of dietary MeHg

In both the short and long term, fish exposed to Se-supplemented plant-based diets PI, PHI, PO and PHO displayed higher body Se content compared to fish fed control diets PC and PH (Fig. 2C and Fig. 2D). The highest body Se content was observed in fish fed SeMetsupplemented diets PO and PHO (Fig. 2C and Fig. 2D). These fish also exhibited higher Se digestibility compared to fish fed Se(IV)-supplemented diets PI and PHI and non Sesupplemented diets PC and PH with a higher Se retention and a reduced faecal Se content compared to fish fed PI and PHI (Table 4). Fish fed Se(IV)-supplemented diets PI and PHI displayed a higher short-term Se retention compared to fish fed PC and PH but a reduced longterm Se retention (Table 4). Se(IV) supplementation in MeHg-supplemented diet PHI increased faecal Hg content compared to diets PH and PHO (Table 4) without significant effect on Hg digestibility, retention (Table 4) or body Hg content (Fig. 2B).

Se supplementation in tuna-based diets TI, THI, TO and THO increased fish body Se content (Fig. 2C and Fig. 2D) and retention (Table 5) as early as 21 days of feeding with a superiority for SeMet, similarly to plant-based diets. No significant differences were observed on Se digestibility coefficient and faecal Se content between fish fed the Se(IV)-supplemented diets TI and THI and fish fed SeMet-supplemented diets TO and THO (Table 5). After 21 days of feeding, fish fed Se(IV)-supplemented diet THI displayed a reduced whole-body Hg content compared to fish fed diets TH and THO (Fig. 2A) with a significantly reduced Hg retention compared to fish fed diet THO (Table 5).

Dietary MeHg impact on plasma pro-inflammatory cytokines and global health parameters in rainbow trout juveniles and interactive effect of dietary Se

Short-term feeding with MeHg-supplemented plant-based diets PH, PHI and PHO induced higher plasma TNF-α and IL-1β levels compared to control diets PC, PI and PO (Fig. 3A and Fig. 3C). Long-term feeding with MeHg-supplemented plant-based diets also resulted in higher plasma TNF-α levels, however only fish fed the diet PHO supplemented with both MeHg and SeMet, exhibited significantly higher TNF-α levels than those fed the control diet PO (Fig. 3B). A long-term dietary supplementation with MeHg increased plasma total protein content and decreased immunoglobulin proportion when fed with Se(IV) (Table 6).

Short-term feeding with MeHg-supplemented tuna-based diets TH, THI and THO induced higher plasma IL-1β (Fig. 3C), glucose and albumin levels (Table 7) compared to fish fed diets TC, TI and TO. Plasma TNF-α level was also increased in MeHg-supplemented, non Se-supplemented diet TH compared to control diet TC (Fig. 3A). When MeHg was added concomitantly with both Se compounds (Se(IV) and SeMet) in diets THI and THO, no more significant increase of TNF-α level was observed compared to non MeHg-supplemented diets TI and TO (Fig. 3A). On the contrary, MeHg intake increased lysozyme levels only when fed with SeMet in diet THO compared to control diet TO (Table 7). In the long term, no more significant effect of MeHg supplementation in tuna-based diets was noticed (Fig. 3B, Fig. 3D, Fig. 3F and Table 7).

Dietary Se impact on plasma pro-inflammatory cytokines and global health parameters in rainbow trout juveniles and interactive effect of dietary MeHg

Short-term feeding with Se(IV)-supplemented diets PI and PHI resulted in decreased plasma IL-1β levels compared to other plant-based diets PC, PH, PO and PHO (Fig. 3C). In fish fed non MeHg-supplemented diets for 168 days, SeMet increased blood haemoglobin levels (Table 6) compared to control diet PC but when added concomitantly with MeHg in diet PHO, SeMet increased plasma TNF-α levels compared to diet PHI (Fig. 3B). Long-term Se(IV) intake in plant-based diets PI and PHI increased blood haemoglobin levels compared to non-Se supplemented diets PC and PH (Table 6).

Short-term feeding with SeMet-supplemented diets TO and THO reduced plasma TNFα and IL-1β levels compared to other tuna-based diets TC, TH, TI and THI (Fig. 3A and Fig. 3C). In absence of dietary MeHg supplementation, Se(IV)-supplemented diet TI led to higher TNF-α levels compared to control diet TC (Fig. 3A) and higher lysozyme levels compared to SeMet-supplemented diet TO (Table 7). Long-term SeMet supplementation decreased TNF-α level only when supplemented with MeHg in diet THO compared to diets TH and THI (Fig. 3B) whereas both Se(IV) and SeMet supplementation in diets TI, THI, TO and THO increased IL-6 levels compared to non Se-supplemented diets TC and TH (Fig. 3F).

Discussion

Short-term effect of dietary MeHg on growth, pro-inflammatory cytokines, overall health status and Hg deposition in rainbow trout juveniles and interactive effect of dietary Se

In MeHg-supplemented plant-based diet PH, containing low basal Se level (1.8 mg Hg/kg diet and 0.3 mg Se/kg diet), MeHg caused a transient growth reduction with higher FCR and plasma pro-inflammatory cytokine content observed only after 21 days of feeding without effect on survival. Such transient effect, after a 21-day exposition to dietary MeHg, is to our knowledge, not reported in the literature. Nile tilapia exposed to MeHg-supplemented FMbased diet (2 mg Hg/kg, 30 days of feeding) displayed higher pro-inflammatory cytokine transcript levels (TNF-α, IL-1β and IL-8) in the spleen (Abu Zeid et al., 2021). Our study confirm those observations but at a plasma metabolite level. Recently, a meta-analysis in Atlantic salmon underlined that fish growth performance decreased with increased severity of enteritis, a pathological state associated with important induction of pro-inflammatory parameters in intestines [START_REF] Agboola | A meta-analysis to determine factors associated with the severity of enteritis in Atlantic salmon (Salmo salar) fed soybean mealbased diets[END_REF]. Thus, the inflammation noticed in our study could explain the observed growth reduction. However, fish fed MeHg-supplemented tunabased diets displayed also higher pro-inflammatory cytokine levels and despite a decreased gross energy content, those fish displayed no growth alteration. So the transient growth reduction observed in fish fed MeHg in low Se plant-based diets might not only be related to the induction of inflammatory response but also to a toxic effect of Hg that would be emphasized in absence of Se such as the induction of oxidative stress [START_REF] Baldissera | Diphenyl diselenide dietary supplementation alleviates behavior impairment and brain damage in grass carp (Ctenopharyngodon idella) exposed to methylmercury chloride[END_REF].

Indeed we noticed increased transcript levels of antioxidant enzymes such as glutathione-Stransferase π and methionine sulfoxide reductase B3 in liver of trout fed the MeHgsupplemented plant-based diet PH for 21 days compared to the control diet PC [START_REF] Bidon | Dietary methylmercury and selenium interactions in rainbow trout juveniles (Oncorhynchus mykiss)[END_REF]. An increased transcript level of the selenoprotein P and glutathione peroxidase 1 in Sesupplemented diets PI, PHI, PO and PHO was also noticed, suggesting a better antioxidant protection with dietary Se supplementation that deserves further investigation for a better characterization and understanding.

The effects observed after 21 days of feeding on growth and inflammatory status by dietary MeHg in low Se plant-based diets was not supported by plasma parameters. Short-term effects of dietary MeHg were recorded but only in fish fed tuna-based diets with an increase of glucose and albumin levels. A 3-month feeding trial on Atlantic salmon established at 5 mg MeHg/kg the threshold at which the lowest toxic effect of dietary MeHg could be observed with a reduction of haematocrit and an increase of plasma protein [START_REF] Berntssen | Maximum limits of organic and inorganic mercury in fish feed[END_REF]. This concentration is above our dietary MeHg levels and could explain our results in rainbow trout.

The addition of MeHg in plant and tuna-based diets increased significantly the wholebody Hg level after short and long-term feeding. Despite the same level of dietary MeHg in plant and tuna-based diets, higher body Hg content were noticed in fish fed plant-based diets, after short (1.8 fold increase in PH diet compared to TH) and long-term exposure (1.3 fold increase in PH diet compared to TH). A negative linear correlation have been underlined between dietary molar ratio of Se/Hg and total Hg levels in Sacramento splittail larvae [START_REF] Deng | Effect of dietary methylmercury and seleno-methionine on Sacramento splittail larvae[END_REF]. Molar ratio of Se/Hg in MeHg-supplemented tuna-based diets was higher than in MeHg-supplemented plant-based diets (11.6 vs. 2.0, respectively) and might explain why fish fed MeHg-supplemented tuna-based diets displayed lower whole-body Hg level than fish fed MeHg-supplemented plant-based diets. However, despite the fact that dietary Se/Hg molar ratio was negatively correlated to whole-body Hg level in fish, it must be addressed that this parameter did not take into consideration chemical form of Se, another parameter that can influence Hg deposition. Indeed, despite a similar or even higher dietary Se/Hg molar ratio in THO diet compared to THI diet (13.0 vs. 11.9, respectively), fish fed THO displayed higher whole-body Hg level than fish fed THI in the short term (0.28 vs. 0.22 mg Hg/kg wet weight, respectively). However, this effect was no more significant after 168 days of feeding (0.78 vs. 0.91 mg Hg/kg wet weight). The reduced Hg digestibility (57% vs. 87% for MeHgsupplemented tuna and plant-based diets) associated with the reduced Hg retention after short (52% vs. 75% for MeHg-supplemented tuna and plant-based diets, respectively) and long term (54% vs. 64% for MeHg-supplemented tuna and plant-based diets, respectively) supports the reduced body Hg content for fish fed high Se tuna-based diets. It is noteworthy that, in fish fed MeHg-supplemented plant-based diets, Hg retention was higher after a short-term than a longterm exposure (75% after 21 days vs. 64% after 168 days of feeding). Similar trends were observed in muscle of zebrafish fed 5 and 10 mg MeHg/kg diet after 2 weeks by [START_REF] Amlund | Dietary selenomethionine influences the accumulation and depuration of dietary methylmercury in zebrafish (Danio rerio)[END_REF] and attributed to a variation in the uptake or in the elimination kinetic. It would have been interesting to also determine Hg digestibility after a short term exposure to know if there is variation in Hg uptake through time and describe better the Hg kinetic deposition in rainbow trout.

Interestingly, the short-term effect of dietary MeHg in diet PH containing low basal Se level on fish growth, was not observed in Se-supplemented diets PHI and PHO or in Se-rich tuna diets. Similar protective effect of high dietary Se on MeHg-induced growth reduction was reported in zebrafish exposed during 153 days to 10 mg/kg diet of SeMet and 12 mg/kg diet of MeHg [START_REF] Penglase | Selenium and mercury have a synergistic negative effect on fish reproduction[END_REF].

Effect of dietary MeHg on Se deposition in rainbow trout juveniles

No short-term effect of dietary MeHg was found on Se whole-body level. However, higher Se retention and digestibility were noticed after long-term exposure to MeHgsupplemented plant-based diets. Similarly, fish fed MeHg-supplemented tuna-based diets displayed higher Se retention, highlighting the effects of dietary MeHg on whole-body Se deposition in both dietary groups. The increase of Se digestibility observed in fish fed MeHgsupplemented diets contradicts the decreased SeMet digestibility described in juvenile white sturgeon by [START_REF] Huang | The interactive effects of selenomethionine and methylmercury on their absorption, disposition, and elimination in juvenile white sturgeon[END_REF]. The differences observed in both studies could be attributed to the dissimilar Hg and Se exposures. In the study of [START_REF] Huang | The interactive effects of selenomethionine and methylmercury on their absorption, disposition, and elimination in juvenile white sturgeon[END_REF], MeHg and SeMet were administered by intragastric gavage at lower concentration than in our study (0.85 mg Hg/kg body weight and 0.5 mg Se/kg body weight). On the other hand, the increase of wholebody Se level measured in fish fed MeHg-supplemented diets was reported in Sacramento spittail larvae exposed to dietary SeMet (0.64-35.0 mg/kg diet) and MeHg (0.01-11.7 mg/kg diet) with higher whole-body Se level when concomitantly exposed to SeMet and MeHg [START_REF] Deng | Effect of dietary methylmercury and seleno-methionine on Sacramento splittail larvae[END_REF]. The increase of body Se level in fish exposed simultaneously to MeHg and Se in comparison to the one only exposed to Se could be attributed to the formation of Se-Hg complexes such as mercury selenide recently identified in freshwater fish as Hg detoxification pathway [START_REF] Manceau | Demethylation of methylmercury in bird, fish, and earthworm[END_REF].

Effect of dietary Se on Hg deposition, pro-inflammatory cytokines, growth in rainbow trout juveniles and interactive effect of dietary MeHg

A short-term effect of Se(IV) was observed on Hg deposition with lower whole-body Hg level and retention measured in fish fed THI diet. This result highlights the superiority of Se(IV) over SeMet to reduce Hg level in agreement with data reported in rainbow trout and goldfish by [START_REF] Bjerregaard | Retention of methyl mercury and inorganic mercury in rainbow trout Oncorhynchus mykiss (W): effect of dietary selenium[END_REF][START_REF] Bjerregaard | Dietary selenium reduces retention of methyl mercury in freshwater fish[END_REF]. The lack of dietary SeMet effect on Hg deposition has also been reported in muscle of rainbow trout fed concomitantly MeHg and SeMet by [START_REF] Ribeiro | Assessment of the mercury-selenium antagonism in rainbow trout fish[END_REF], stressing the importance of Se chemical form on Hg detoxification. The lowering effect of Se(IV) supplementation in Se-rich tuna-based diets on body Hg accumulation was not noticed in Se-low plant-based diets, supporting the idea of a minimal Se threshold concentration to detect effects on Hg accumulation, as reported in an earlier study [START_REF] Bjerregaard | Dietary selenium reduces retention of methyl mercury in freshwater fish[END_REF].

A protective effect of dietary Se on the short-term pro-inflammatory effect of dietary MeHg was recorded in our study. Both Se(IV) and SeMet addition in tuna-based diets helped to alleviate the increase of TNF-α level by dietary MeHg addition after a short-term exposure whereas only SeMet reduced TNF-α level after a long-term exposure. This result highlights the superiority of SeMet to afford protection against MeHg pro-inflammatory effects in the long term in presence of high dietary basal Se level in tuna-based diets, as the lowering effect of SeMet on cytokine levels was not observed with plant-based diets. The greater capacity of SeMet over Se(IV) to reduce inflammatory response was also reported in head kidney leucocytes isolated from Atlantic salmon post-smolts after a 9-week feeding trial [START_REF] Jesu Prabhu | Dietary selenium required to achieve body homeostasis and attenuate pro-inflammatory responses in Atlantic salmon post-smolt exceeds the present EU legal limit[END_REF]. As described earlier, inflammation could be responsible for a reduction of fish growth [START_REF] Agboola | A meta-analysis to determine factors associated with the severity of enteritis in Atlantic salmon (Salmo salar) fed soybean mealbased diets[END_REF]. In fish fed plant-based diets, Se supplementation had no influence on the inflammatory state of fish, despite an improvement of growth in fish fed the Se-supplemented diets PHI and PHO compared to fish fed the MeHg-supplemented diet PH.

Thus, as mentioned before, inflammation alone cannot explain effects on fish growth.

On the other hand, despite the anti-inflammatory effect of Se discussed above, too high dietary Se level could also be detrimental. After a short-term feeding with the Se(IV)supplemented tuna-based diet TI, plasma TNF-α content was increased. Evidences of proinflammatory effects in presence of high dietary Se levels are scarce in fish. To our knowledge, only the study of [START_REF] Pérez-Valenzuela | Increased dietary availability of selenium in rainbow trout (Oncorhynchus mykiss) improves its plasma antioxidant capacity and resistance to infection with Piscirickettsia salmonis[END_REF] reported mononuclear cell infiltration in rainbow trout liver, a sign of early inflammation after an 8-week feeding trial using 10 mg Se/kg diet supplied as Se-yeast, an organic chemical form of Se. IL-6 levels were increased after a long-term exposure with Se-supplemented tuna-based diets compared to fish fed non Sesupplemented tuna-based diets, strengthening the possibility of pro-inflammatory response occurring after a Se supplementation in presence of high dietary Se level.

The growth reduction noticed with TI after 6 months of feeding suggests the supplementation with Se(IV) in tuna-based diet containing high basal Se level might be toxic for rainbow trout but not when supplemented as SeMet. Se toxicity threshold in fish depends on chemical form of Se [START_REF] Berntssen | Safe limits of selenomethionine and selenite supplementation to plant-based Atlantic salmon feeds[END_REF] and Se(IV) is considered more toxic than SeMet [START_REF] Berntssen | Sensitivity and toxic mode of action of dietary organic and inorganic selenium in Atlantic salmon (Salmo salar)[END_REF] with a lower toxicity threshold [START_REF] Berntssen | Safe limits of selenomethionine and selenite supplementation to plant-based Atlantic salmon feeds[END_REF]. These results are in accordance with our study as we did not observe adverse effects on growth with SeMet, despite the similar dietary Se level assessed in our tuna-based diets (9 mg Se/kg diet). However, it is important to note that, in tuna-based diets, basal Se level represents about 80% of the total Se concentration found in Se-supplemented tuna-based diets. The suspected principal chemical form of Se found in tuna is selenoneine, an organic chemical form of Se (Yamashita and Yamashita, 2010). Thus our results might rely on the chemical form added in the diet but also on the high basal Se level naturally present in tuna-based diets. It might be of great interest to perform a speciation analysis on tuna by-products and fish fed with these tuna-based diets to precisely characterize chemical form of Se.

When MeHg was added to TI diet, detrimental effects on fish growth performance were alleviated, underlying an antagonist effect of MeHg, maybe through the formation of Hg-Se compounds that are potentially associated with a reduction of Se bioavailability [START_REF] Raymond | Mercury: selenium interactions and health implications[END_REF].

Tuna by-products an interesting source of selenium for aquafeeds?

Tuna-based diets used in the present study displayed high Se levels, far above salmonid requirement [START_REF] Jesu Prabhu | Dietary selenium required to achieve body homeostasis and attenuate pro-inflammatory responses in Atlantic salmon post-smolt exceeds the present EU legal limit[END_REF]. Despite Se concentration in the TC diet equal to 7.5 mg Se/kg diet and thus below levels reported to reduce fish growth performance: 13 mg Se/kg diet supplied as Se(IV) for rainbow trout [START_REF] Hilton | Absorption, distribution, half-life and possible routes of elimination of dietary selenium in juvenile rainbow trout (Salmo gairdneri)[END_REF] and 11 mg Se/kg diet for Atlantic salmon [START_REF] Berntssen | Safe limits of selenomethionine and selenite supplementation to plant-based Atlantic salmon feeds[END_REF], it might be safer to reduce dietary Se level. Tuna, like other fish, accumulate Se mainly in liver and kidney [START_REF] Ruelas-Inzunza | Bioaccumulation of As, Hg, and Se in tunas Thunnus albacares and Katsuwonus pelamis from the eastern Pacific: tissue distribution and As speciation[END_REF][START_REF] Belmonte | Tissue distribution of mercury and its relationship with selenium in Atlantic bluefin tuna (Thunnus thynnus L.)[END_REF]. These organs are parts of tuna by-products, thus adjusting their level in by-products might be interesting to control Se level. Another possibility to reduce dietary Se level is to decrease the level of tuna by-products inclusion, in our study, we used an inclusion level of 60%, lower level might be suitable.

However, the main concern of FM prepared from tuna by-products used in aquaculture comes from the presence of contaminants, especially MeHg [START_REF] Kim | Tuna byproducts as a fish-meal in tilapia aquaculture[END_REF]. In Europe, the limit for Hg concentration in rainbow trout muscle must not exceed 0.3 mg/kg for human consumption (European Union, 2022). This threshold was not exceeded at whole-body level in fish fed the control tuna-based diet, even after 6 months of feeding, with whole-body Hg level concentration of 0.13 mg Hg/kg that might comply with the existing EU regulation, highlighting the potential of this ingredient for aquafeeds. However, Hg is known to accumulate in muscle [START_REF] Giblin | Pharmacodynamics of methylmercury in the rainbow trout (Salmo gairdneri): tissue uptake, distribution and excretion[END_REF] and so the Hg level in muscle is requested to conclude about the potential use of tuna by-products as aquafeed ingredient for rainbow trout aquaculture.

Conclusion

In conclusion, the present work highlights the importance of dietary chemical forms and concentration of Se on the understanding of MeHg and Se effects. MeHg accumulation was reduced by Se(IV) in high Se tuna-based diets after a short-term exposure and MeHg-induced pro-inflammatory response was hampered by SeMet in high Se tuna-based diets. On the other hand, growth performance and inflammatory status were impaired by Se(IV) in Se-rich tunabased diets, and paradoxically, antagonist effect by MeHg supplementation was displayed. Se digestibility, body content and retention were also higher in fish exposed to dietary MeHg, that deserves further investigation.

Abbreviations

Author's contributions

Marchand, T. Callet, F. Vallée, E. Plagnes-Juan, M. Delaygues and A. Soisson for their help during samplings. A special thought for the late F. Sandres who took care of the fish for this study and sadly passed away last year.

Table 1a

Experimental diet formulation and composition.

Diet

Plant 6.7 7.8 a Plant-derived proteins (% diet in plant-based or tuna meal-based diets respectively): wheat gluten, 18 or 0 (Roquette, France); corn gluten, 17 or 0 (Inzo, France); soybean protein concentrate, 15 or 0 (Estril®75 Sopropêche, France); soybean meal, 5 or 0 (Sud-Ouest Aliment, France); white lupin meal, 5 or 0 (Farilup500 Terrena, France); rapeseed meal, 5 or 0 (Primor 00 Sud-Ouest Aliment, France); dehulled pea mea, 3.8 or 10.8 (Primatex Sotexpro, France), whole wheat, 5 or 15 (Sud-Ouest Aliment, France).

b Tuna meal HighPro68 (Port-Louis, Mauritius).

c Crystalline amino acid premix (% diet): L-lysine, 1.4; DL-methionine, 0.3; glucosamine, 0.5; taurine, 0.3; betaine, 0.3; glycine, 0.2; alanine, 0.2. d Adivec (France).

e Vegetable oils (% diet): rapeseed oil, 4; linseed oil, 2.4; palm oil 1.6.

f Sopropêche (France).

g Vitamin and mineral premixes Se-free (per kg diet): retinyl acetate, 5000 IU; cholecalciferol, 2500 IU; DL-α-tocopheryl acetate, 50 IU; sodium menadione bisulfate, 10 mg, thiamin-HCl, 1 0.8 ± 0.0 0.7 ± 0.0 0.8 ± 0.0 0.8 ± 0.0 0.7 ± 0.0 0.8 ± 0.0 0.434 0.441 0.131 FI 1 D168 2.9 ± 0.1 2.7 ± 0.0 3.0 ± 0.1 2.9 ± 0.1 2.7 ± 0.1 2.9 ± 0.0 0.590 0.587 0.391 FCR 2 D21 0.79 ± 0.01 a 0.88 ± 0.02 a 0.85 ± 0.03 a 0.79 ± 0.01 a 0.81 ± 0.03 a 0.82 ± 0.01 a 0.400 0.630 0.023 FCR 2 D168 0.89 ± 0.01 0.92 ± 0.04 0.94 ± 0.01 0.94 ± 0.01 0.90 ± 0.02 0.93 ± 0.03 0.306 0.318 0.791 PER 3 D21 2.6 ± 0.0 a 2.3 ± 0.1 a 2.4 ± 0.1 a 2.6 ± 0.0 a 2.5 ± 0.0 a 2.5 ± 0.0 a 0.309 0.768 0.018

PER 3 D168 2.3 ± 0.0 2.2 ± 0.1 2.2 ± 0.0 2.2 ± 0.0 2.3 ± 0.0 2.2 ± 0.1 0.279 0.253 0.649 HSI 4 D21 1.2 ± 0.1 1.3 ± 0.1 1.0 ± 0.0 1.1 ± 0.1 1.1 ± 0.0
1.1 ± 0.0 0.937 0.072 0.373 HSI 4 D168 0.9 ± 0.0 0.9 ± 0.0 0.9 ± 0.0 0.8 ± 0.0 0.9 ± 0.0 0.9 ± 0.0 0.457 0.729 0.729 14 ± 0 13 ± 1 14 ± 0 13 ± 0 14 ± 1 13 ± 0 0.190 0.827 0.892 Lipid D168

SR
15 ± 1 b 16 ± 0 ab 18 ± 0 a 17 ± 1 ab 17 ± 1 a 18 ± 0 a 0.577 0.004 0.029 Energy D21

9.1 ± 0.1 8.9 ± 0.2 9.0 ± 0.2 8.7 ± 0.1 9.1 ± 0.4 9.0 ± 0.3 0.353 0.640 0.833 Energy D168 9.7 ± 0.4 b 10.5 ± 0.0 ab 11.2 ± 0.1 a 10.5 ± 0.2 ab 10.7 ± 0.2 a 10.9 ± 0.0 a 0.780 0.010 0.017 Ash D21

1.9 ± 0.0 2.0 ± 0.1 1.9 ± 0.0 2.1 ± 0.2 2.0 ± 0.1 1.8 ± 0.1 0.997 0.779 0.273 Ash D168

2.1 ± 0.0 2.0 ± 0.1 2.0 ± 0.0 2.0 ± 0.0 2.0 ± 0.1 2.0 ± 0.0 0.958 0.522 0.345

Body retention 7

Dry matter D21 significantly different (PHg×Se < 0.05) according to two-way ANOVA to test the effect of MeHg supplementation (PHg), Se supplementation (PSe) and the interaction (PHg×Se) followed by a Tukey's post hoc test. 1 FI, absolute feed intake expressed as g per fish per day = total dry feed intake per tank / (number of fish in tank × number of days over the experimental period). 2 FCR, feed conversion ratio = dry feed intake / wet weight gain. 3 PER, protein efficiency ratio = fish weight gain / crude protein intake. 4 HSI, hepatosomatic index expressed as % = liver weight / fish weight. 5 SR, survival rate expressed as %. 6 Body composition expressed as % for dry matter, crude protein, total lipid and ash and kJ/g for gross energy. 0.7 ± 0.0 0.6 ± 0.0 0.6 ± 0.0 0.6 ± 0.0 0.6 ± 0.0 0.6 ± 0.0 0.677 0.097 0.060 FI 1 D168 2.6 ± 0.0 2.6 ± 0.2 2.3 ± 0.1 2.8 ± 0.0 2.7 ± 0.0 2.7 ± 0.1 0.047 0.427 0.062 FCR 2 D21 0.73 ± 0.01 a 0.76 ± 0.01 a 0.88 ± 0.09 a 0.74 ± 0.02 a 0.75 ± 0.01 a 0.78 ± 0.02 a 0.878 0.427 0.028 FCR 2 D168 0.84 ± 0.01 ab 0.88 ± 0.01 a 0.88 ± 0.01 a 0.86 ± 0.01 ab 0.85 ± 0.01 ab 0.83 ± 0.00 b 0.960 0.012 0.010 PER 3 D21 2.7 ± 0.0 a 2.6 ± 0.0 a 2.3 ± 0.2 a 2.7 ± 0.1 a 2.6 ± 0.0 a 2.5 ± 0. significantly different (PHg×Se < 0.05) according to two-way ANOVA to test the effect of MeHg supplementation (PHg), Se supplementation (PSe) and the interaction (PHg×Se) followed by a Tukey's post hoc test. 1 FI, absolute feed intake expressed as g per fish per day = total dry feed intake per tank / (number of fish in tank × number of days over the experimental period). 2 FCR, feed conversion ratio = dry feed intake / wet weight gain. 3 PER, protein efficiency ratio = fish weight gain / crude protein intake. 4 HSI, hepatosomatic index expressed as % = liver weight / fish weight. 5 SR, survival rate expressed as %. 6 Body composition expressed as % for dry matter, crude protein, total lipid and ash and kJ/g for gross energy. 7 Body nutrient retention expressed as % = [(final weight × final body nutrient content) -(initial weight × initial body nutrient content)] / (total feed intake × feed nutrient content) × 100. 1.2 ± 0.0 1.1 ± 0.1 1.2 ± 0.1 1.1 ± 0.1 1.1 ± 0.1 1.1 ± 0.1 0.498 0.683 0.860 Glucose 5 D168 0.9 ± 0.1 0.8 ± 0.1 0.9 ± 0.1 0.9 ± 0.1 1.0 ± 0.0 0.9 ± 0. Values represent means ± SEM (n = 3). Means not sharing a common superscript letter are significantly different (PHg*Se < 0.05) according to two-way ANOVA performed in each dietary basis at each time to test the effect of methylmercury supplementation (PHg), selenium supplementation (PSe) and the interaction (PHg×Se) followed by a Tukey's post hoc test.

1 Lysozyme (mg/L), 2 total protein (g/L), 3 immunoglobulin (% total protein), 4 albumin (% total protein), 5 glucose (g/L), 6 ASAT, aspartate amino-transferase (UI/L), 7 ALAT, alanine aminotransferase (UI/L). 8 Haemoglobin (g/L).

Table 7

Plasma and blood health parameters in fish fed tuna-based diets for 21 (D21) and 168 (D168) days. Values represent means ± SEM (n = 3). Means not sharing a common superscript letter are significantly different (PHg*Se < 0.05) according to two-way ANOVA performed in each dietary basis at each time to test the effect of methylmercury supplementation (PHg), selenium supplementation (PSe) and the interaction (PHg×Se) followed by a Tukey's post hoc test.

Figure captions

  ALAT, alanine amino transferase; ASAT, aspartate amino transferase; Hg, mercury; IL-1β, interleukine 1β; IL-6, interleukine 6; MeHg, methylmercury; PC, control plant-based diet; PH, methylmercury-supplemented plant-based diet; PHI, methylmercury and selenitesupplemented plant-based diet; PHO, methylmercury and selenomethionine supplemented plant-based diet; PI, selenite-supplemented plant-based diet; PO, selenomethioninesupplemented plant-based diet; Se, selenium; Se(IV), selenite; SeMet, selenomethionine; TNFα, tumor necrosis factor α; TC, control tuna-based diet; TH, methylmercury-supplemented tunabased diet; THI, methylmercury and selenite-supplemented tuna-based diet; THO, methylmercury and selenomethionine-supplemented tuna-based diet; TI, selenitesupplemented tuna-based diet; TO, selenomethionine-supplemented tuna-based diet.

  768

  7 Body nutrient retention expressed as % = [(final weight × final body nutrient content) -(initial weight × initial body nutrient content)] / (total feed intake × feed nutrient content) × 100. Growth performance, proximate body composition and retention of rainbow trout juveniles fed 781 tuna-based diets for 21 (D21) or 168 days (D168).

  Values represent means ± SEM (n = 3). Means not sharing a common superscript letter are significantly different (PHg*Se < 0.05) according to two-way ANOVA performed in each dietary basis at each time to test the effect of methylmercury supplementation (PHg), selenium supplementation (PSe) and the interaction (PHg×Se) followed by a Tukey's post hoc test. 1 Hg retention = 100 × [(final body weight × final body Hg content) -(initial body weight × initial body Hg content)) / (total feed intake × dietary Hg content). 2 Hg faeces content (pg/kg wet weight). 3 ADCHg, apparent digestibility coefficient for Hg = 100 -[100 × (faecal Hg content / dietary Hg content) × (dietary vanadium content / faecal vanadium content)]. 4 Se retention = 100 × [(final body weight × final body Se content) -(initial body weight × initial body Se content)] / (total feed intake × dietary Se content). 5 Se faecal content (µg/kg wet weight). 6 ADCSe, apparent digestibility coefficient for Se = 100 -[100 × (faecal Se content / dietary Se content) × (dietary vanadium content / faecal vanadium content)].

Fig. 1 .

 1 Fig. 1. Mean body weight of rainbow trout juveniles fed plant-based diets (P, □) or tuna-based

Fig. 2 .

 2 Fig. 2. Hg (A and B) and Se (C and D) body contents in rainbow trout juveniles fed plant-based

Fig. 3 .

 3 Fig. 3. Plasma cytokine concentrations, TNF-α (A and B), IL-1β (C and D) and IL-6 (E and F),

Table 2 763

 2 Growth performance, proximate body composition and retention of rainbow trout juveniles fed 764 plant-based diets for 21 (D21) or 168 days (D168).

	765
	Plant based-diets	PC	PH	PI	PHI	PO	PHO	p Hg	p Se p Hg×Se
	Growth performance
	FI 1 D21

Table 5

 5 Hg and Se whole body retention, faecal content and apparent digestibility coefficient of in fish fed tuna-based diets for 21 (D21) and 168 (D168) days.

	Tuna based-diets	TC	TH	TI	THI	TO	THO	p Hg	p Se p Hg×Se
	Hg retention 1 D21	55 ± 3 b	57 ± 1 b	75 ± 2 a	40 ± 2 c 67 ± 8 ab 60 ± 3 b <0.001 0.156 <0.001
	Hg retention 1 D168	57 ± 3	55 ± 3	94 ± 21	54 ± 1	78 ± 2	52 ± 5 0.010 0.180 0.141
	Faecal Hg content 2 D168 62 ± 9 366 ± 34 81 ± 12 402 ± 35 63 ± 4 366 ± 49 <0.001 0.536 0.943
	ADCHg 3 D168	49 ± 4	58 ± 1	38 ± 8	61 ± 2	48 ± 2	51 ± 7 0.007 0.667 0.129
	Se retention 4 D21	17 ± 1	16 ± 1	18 ± 1	16 ± 1	25 ± 2	22 ± 2 0.026 <0.001 0.647
	Se retention 4 D168	9 ± 0	10 ± 1	10 ± 1	12 ± 1	16 ± 1	18 ± 1 0.036 <0.001 0.880
	Faecal Se content 5 D168 2264 ± 159 2247 ± 137 2571 ± 286 3026 ± 224 2464 ± 150 2388 ± 128 0.453 0.038 0.339
	ADCSe D168	23 ± 1	33 ± 6	40 ± 4	38 ± 2	37 ± 2	38 ± 1 0.352 0.009 0.191
	TC, not supplemented; TH, supplemented with MeHg; TI, supplemented with Se(IV); THI,
	supplemented with both MeHg and Se(IV); TO, supplemented with SeMet; THO,
	supplemented with both MeHg and SeMet.

Table 6

 6 Plasma and blood health parameters in fish fed plant-based diets for 21 (D21) and 168 (D168) days.

	Plant based-diets	PC	PH	PI	PHI	PO	PHO	p Hg p Se p Hg×Se
	Lysozyme 1 D21	23 ± 6	15 ± 6	20 ± 5	19 ± 6	17 ± 2	9 ± 4 0.120 0.349 0.742
	Lysozyme 1 D168	16 ± 7	9 ± 4	11 ± 3	5 ± 1	11 ± 2	7 ± 2 0.111 0.467 0.885
	Total protein 2 D21	23 ± 1	24 ± 1	24 ± 0	25 ± 1	24 ± 1	23 ± 2 0.399 0.702 0.666
	Total protein 2 D168	34 ± 1 b 31 ± 1 b 31 ± 2 b 37 ± 1 a 33 ± 1 b 31 ± 1 b 0.686 0.478 0.002
	Immunoglobulin 3 D21	17 ± 2	13 ± 1	14 ± 1	16 ± 1	16 ± 1	13 ± 2 0.149 0.931 0.134
	Immunoglobulin 3 D168 14 ± 0 ab 17 ± 1 ab 18 ± 1 a 14 ± 1 b 17 ± 2 ab 17 ± 1 ab 0.764 0.495 0.022
	Albumin 4 D21	66 ± 3	73 ± 3	68 ± 3	65 ± 2	70 ± 6	64 ± 3 0.833 0.703 0.147
	Albumin 4 D168	65 ± 2	73 ± 3	67 ± 2	65 ± 3	67 ± 2	70 ± 2 0.094 0.362 0.104
	Glucose 5 D21

Lysozyme (mg/L),

total protein (g/L),

immunoglobulin (% total protein),

albumin (% total protein),

glucose (g/L),

ASAT, aspartate amino-transferase (UI/L),

ALAT, alanine aminotransferase (UI/L).

Haemoglobin (g/L).

Acknowledgements

This study was supported by I-site E2S: Energy and Environment Solutions from the University of Pau and Pays de l'Adour, UPPA contract 2020-32 (M.B., PhD fellowship). The authors thank the Agence Nationale de la Recherche (MERSEL Project no. ANR-18-CE34-0004-01) and The Institute of Marine Research, Norway (TuneSel, Project no. 15745) for their financial support. This project has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement no. 101007962.

The authors wish to thank Marine Biotechnology Products (Port-Louis, Mauritius) and Orffa (Breda, The Netherlands) for the kind supply of tuna meal and selenomethionine, respectively.

They are also very grateful to F. Terrier and A. Lanuque for the preparation of diets and for the care of fish and A. Surget, L. Larroquet, C. Heraud, K. Dias, V. Véron, E. Baranek, M.

Data availability

Data will be made available on request

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supplementation level for sodium selenite, L-selenomethionine and methylmercury chloride 760 and elemental composition of tuna and plant-based diets.

761

Diet

Plant-based diets Tuna-based diets PC PH PI PHI PO PHO TC TH TI THI TO THO


Diego F Abreu
email: mecabreu@yahoo.com.br

Carlos Junqueira-Junior

Eron T V Dauricio

João Luiz

F Azevedo

LARGE-EDDY SIMULATIONS OF TURBULENT COMPRESSIBLE SUPERSONIC JET FLOWS USING DISCONTINUOUS GALERKIN METHODS

Keywords: Large-Eddy Simulation, Turbulent Flow, Jet Flow, Discontinuous Galerkin Methods

In this work, a discontinuous Galerkin scheme is employed to perform LES simulations of supersonic jet flows. A total of four simulations are performed with different meshes and order of accuracy. The number of degrees of freedom from the simulations varies from 50 × 10 6 to 400 × 10 6 . The results indicate that by increasing the resolution of simulation, in general, the results got closer to experimental data. The jet lipline is the only region in which this behavior is not observed. It investigated a procedure of using lower-order simulations to initialize high-order simulations and consequently reduce the total time of the simulation using high-order schemes. This strategy is successful and allows to perform high-order simulations with only 5% more computational effort than a complete second-order simulation.

INTRODUCTION

The Reynolds-Averaged Navier-Stokes (RANS) formulation has difficulty representing some types of fluid motions predominantly governed by free shear flows or wall-bounded flows with separated boundary layers. This difficulty is related to constructive assumptions of the formulation, characterized by the modeling of all turbulent quantities. The recent progress of computational power is enabling the employment of large-eddy simulations (LES) to simulate the problems that RANS formulation fails to model important aspects of the flow. Recent studies show the capability of LES simulations for reproducing free shear layer [START_REF] Brès | Modelling of jet noise: A perspective from large-eddy simulations[END_REF][START_REF] Kumar | Large eddy simulation of propeller wake instabilities[END_REF] and detached flows [START_REF] Ghate | Transonic lift and drag predictions using wall-modelled large eddy simulations[END_REF][START_REF] Masoudi | Large eddy simulation of incident flows around polygonal cylinders[END_REF]. Another advantage of using LES is its capability to produce high-frequency unsteady information, which is necessary for aerodynamics, acoustics, loads, and heat transfer analyses.

The authors are interested in the simulation of supersonic jet flows for performing aerodynamic analyses of the shear layer regarding velocity and pressure fluctuations to improve the design of nozzles and adjacent structures. Different numerical options are employed to obtain the solution of LES formulation for jet flows. For example, low-order accuracy [START_REF] Junqueira-Junior | Influence of different subgrid-scale models in low-order LES of supersonic jet flows[END_REF] and highorder accuracy [START_REF] Bogey | Influence of nozzle-exit boundary-layer conditions on the flow and acoustic fields of initially laminar jets[END_REF][START_REF] Debonis | Prediction of turbulent temperature fluctuations in hot jets[END_REF] finite difference schemes on structured meshes were employed to perform LES simulations of subsonic and supersonic jet flows. Low-order finite volume approach on unstructured meshes [START_REF] Mendez | Large-eddy simulations of perfectly expanded supersonic jets using an unstructured solver[END_REF][START_REF] Brès | Unstructured large-eddy simulations of supersonic jets[END_REF] is another option employed.

Due to the employment of structured meshes, the finite difference schemes have difficulty handling complex geometries. The finite volume schemes are applied to unstructured meshes, which make it easier to represent complex geometries, however, it is difficult to implement high-order discretizations with these schemes [START_REF] Hesthaven | Nodal Discontinuous Galerkin Methods -Algorithms, Analysis, and Applications[END_REF]. In this context, the discontinuous Galerkin schemes are gaining relevance, because they are easily implemented with high-order accuracy discretizations and can be employed with unstructured meshes. Some work is already simulating jet flows with discontinuous Galerkin schemes [START_REF] Abreu | A comparison of low and high-order methods for the simulation of supersonic jet flows[END_REF][START_REF] Corrigan | Jet noise simulation using a higher-order discontinuous galerkin method[END_REF] or using similar strategies, for example, the Flux Reconstruction schemes [START_REF] Shen | Validation of a high-order large eddy simulation solver for acoustic prediction of supersonic jet flow[END_REF].

The discontinuous Galerkin schemes have multiple options for implementation. For example, one may choose to represent the solution by nodal or modal polynomials. It is possible to choose between different options of test functions that could better suits different types of elements, which are utilized to discretize the computational domain. One set of choices for the discontinuous Galerkin formulation is named discontinuous Galerkin spectral element method (DGSEM) [START_REF] Kopriva | On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods[END_REF][START_REF] Hindenlang | Explicit discontinuous Galerkin methods for unsteady problems[END_REF]. The DGSEM, implemented in a numerical framework called FLEXI [START_REF] Krais | FLEXI: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws[END_REF], was investigated for performing LES of a supersonic round jet flows with Mach number equal to 1.4 and Reynolds number based on jet inlet diameter of 1.58 × 10 6 [START_REF] Abreu | A comparison of low and high-order methods for the simulation of supersonic jet flows[END_REF].

The simulations were performed with two numerical meshes with 6.2 × 10 6 and 1.8 × 10 6 elements with second-order and third-order accurate discretizations, respectively. The two simulations were performed with nearly 50 × 10 6 degrees of freedom (DOF). They presented similar results, with the simulation performed with third-order accuracy requiring twice the time to perform the same simulation time as the second-order accurate simulation. When comparing the results to experimental data, excessive dissipation is observed, which led to shorter potential cores. The potential core of the jet is the length in the centerline of the jet where the velocity reaches 0.95 of jet velocity. Other aspects of the flow, for example, the root mean square (RMS) of velocity fluctuations in the centerline and lipline of the jet, also presented some differences with experimental data.

In this work, the results obtained using a new mesh are presented. The new mesh has a larger refinement and improved topology than the meshes utilized in previous work. The new mesh is simulated with second-order and third-order accurate discretizations. Discussions regarding the quality and improvement of the simulations are presented. A discussion of computational efficiency utilizing discontinuous Galerkin methods is also performed to develop guidelines for future works.

NUMERICAL FORMULATION

GOVERNING EQUATIONS

The work has an interest in the solution of the filtered Navier-Stokes equations. The filtering strategy is based on a spatial filtering process that separates the flow into a resolved part (•) and a non-resolved part (•) ′ . Implicit filter size is obtained from the mesh size. The filtered Navier-Stokes equations in conservative form can be written by

∂ Q ∂t + ∇ • F( Q, ∇ Q) = 0, (1)
where Q = [ρ, ρũ, ρṽ, ρ w, ρ Ě] T is the vector of filtered conserved variables and F is the flux vector. The flux vector can be divided into the Euler fluxes and the viscous flux, F = F e -F v . The fluxes with the filtered variables may be written as

F e i =       ρũ i ρũũ i + δ 1i p ρṽũ i + δ 2i p ρ wũ i + δ 3i p (ρ Ě + p)ũ i       F v i =       0 τ mod 1i τ mod 2i τ mod 3i ũj τ mod ij -q mod i       , for i = 1, 2, 3, (2)
where ũi or (ũ, ṽ, w) are the Favre averaged velocity components, ρ is the filtered density, p is the filtered pressure and ρ Ě is the filtered total energy per unit volume. The terms τ mod ij and q mod i are the modified viscous stress tensor and heat flux vector, respectively, and δ ij is the Kronecker delta. The filtered total energy per unit volume, according to the definition proposed by Vreman [START_REF] Vreman | Direct and Large Eddy Simulation of the Compressible Turbulent Mixing Layer[END_REF] in its "system I" approach, is given by

ρ Ě = p γ -1 + 1 2 ρũ i ũi . (3)
The filtered pressure, Favre averaged temperature and filtered density are correlated using the ideal gas equation of state p = ρR T , and R is the gas constant, written as R = c p -c v . The properties c p and c v are the specific heat at constant pressure and volume, respectively. The modified viscous stress tensor may be written as

τ mod ij = (µ + µ SGS ) ∂ ũi ∂x j + ∂ ũj ∂x i - 2 3 (µ + µ SGS ) ∂ ũk ∂x k δ ij ( 4
)
where µ is the dynamic viscosity coefficient, calculated by Sutherland's Law, and µ SGS is the SGS dynamic viscosity coefficient, which is provided by the subgrid-scale model. The strategy of modeling the subgrid-scale contribution as an additional dynamic viscosity coefficient is based on the Boussinesq hyphotesis. The modified heat flux vector, using the same modeling strategy, is given by

q mod i = -(k + k SGS ) ∂ T ∂x i ( 5
)
where k is the thermal conductivity coefficient of the fluid and k SGS is the SGS thermal conductivity coefficient given by k SGS = µ SGS c p P r SGS [START_REF] Brès | Unstructured large-eddy simulations of supersonic jets[END_REF] and P r SGS is the SGS Prandtl number. The present work employs the static Smagorinsky model [START_REF] Smagorinsky | General circulation experiments with the primitive equations: I. The basic experiment[END_REF] in order to calculate the subgrid-scale contribution.

NODAL DISCONTINUOUS GALERKIN METHOD

The nodal discontinuous Galerkin method used in this work is based on the modeling called discontinuous Galerkin spectral element method [START_REF] Kopriva | On the quadrature and weak form choices in collocation type discontinuous Galerkin spectral element methods[END_REF][START_REF] Hindenlang | Explicit discontinuous Galerkin methods for unsteady problems[END_REF]. In this modeling strategy, the domain is divided into multiple hexahedral elements. This choice of elements permits the interpolating polynomial to be defined as a tensor product basis with degree N in each space direction. This set of options leads to an algorithm that can be easily implemented and also produce a high level of computational efficiency due to reduced calculations.

In this method, the elements from the physical domain are mapped onto a reference unit cube elements E = [-1, 1] 3 . The equations, presented in (1) need also to be mapped to this new reference domain, leading to

J ∂ Q ∂t + ∇ ξ • F = 0, (7)
where ∇ ξ is the divergence operator with respect to the reference element coordinates, ξ = (ξ 1 , ξ 2 , ξ 3 ) T , J = |∂x/∂ξ| is the Jacobian of the coordinate transformation and F is the contravariant flux vector.

The discontinuous Galerkin formulation is obtained multiplying [START_REF] Carpenter | Fourt-order 2N-storage Runge-Kutta schemes[END_REF] by the test function ψ = ψ(ξ) and integrating over the reference element

E E J ∂ Q ∂t ψdξ + E ∇ ξ • Fψdξ = 0. (8)
It is possible to obtain the weak form of the scheme by integrating by parts the second term in (8)

∂ ∂t E J Qψdξ + ∂E ( F • ⃗ N ) * ψdS - E F • (∇ ξ ψ)dξ = 0, (9)
where ⃗ N is the unit normal vector of the reference element faces. Because the discontinuous Galerkin scheme allows discontinuities in the interfaces, the surface integral above is ill-defined. In this case, a numerical flux, F * , is defined, and a Riemann solver is used to compute the value of this flux based on the discontinuous solutions given by the elements sharing the interface.

For the nodal form of the discontinuous Galerkin formulation, the solution in each element is approximated by a polynomial interpolation of the form

Q(ξ) ≈ N p,q,r=0 Qh (ξ 1 p , ξ 2 q , ξ 3 r , t)ϕ pqr (ξ), (10)
where Qh (ξ 1 p , ξ 2 q , ξ 3 r , t) is the value of the vector of conserved variables at each interpolation node in the reference element and ϕ pqr (ξ) is the interpolating polynomial. For hexahedral elements, the interpolating polynomial is a tensor product basis with degree N in each space direction

ϕ pqr (ξ) = l p (ξ 1 )l q (ξ 2 )l r (ξ 3 ), l p (ξ 1 ) = Np i=0 i̸ =p ξ 1 -ξ 1 i ξ 1 p -ξ 1 i . ( 11
)
The definitions presented are applicable to other two directions.

The numerical scheme used in the simulation additionally presents the split formulation [START_REF] Pirozzoli | Numerical methods for high-speed flows[END_REF], with the discrete form [START_REF] Gregor | Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations[END_REF], to enhance the stability of the simulation. The split formulation is employed for Euler fluxes only. The solution and the fluxes are interpolated and integrated at the nodes of a Gauss-Lobatto Legende quadrature, which presents the summation-by-parts property, that is necessary to employ the split formulation.

The Riemann solver used in the simulations is a Roe scheme with entropy fix [START_REF] Harten | Self adjusting grid methods for one dimensional hyperbolic conservation laws[END_REF] to ensure that the second law of thermodynamics is respected, even with the split formulation. For the viscous flux, since the discontinuous Galerkin scheme is not suitable for discretizing the high order derivative operator, the lifting scheme of Bassi and Rebay [START_REF] Bassi | A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations[END_REF] is used, which is also known for BR2. The time marching method chosen is a five-stage, fourth-order explicit Runge-Kutta scheme [START_REF] Carpenter | Fourt-order 2N-storage Runge-Kutta schemes[END_REF]. The shock waves that appear in the simulation are stabilized using the finite-volume sub-cell shock-capturing method [START_REF] Sonntag | Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells[END_REF]. The shock indicator of Jameson, Schmidt, and Turkel [START_REF] Jameson | Numerical solution of the euler equations by finite volume methods using runge-kutta time-stepping schemes[END_REF] is utilized.

EXPERIMENTAL CONFIGURATION

The experimental work [START_REF] Bridges | Turbulence associated with broadband shock noise in hot jets[END_REF] provides a good characterization of the flow properties for jet flows. Many configurations were analyzed. In this work, the interest is to simulate the fully expanded free jet flow configuration with a Mach number of 1.4. In this configuration the jet flow has a static pressure in the nozzle exit section that equals the ambient static pressure with a supersonic velocity, for this reason, it is possible to avoid the use of nozzle wall geometries and also the shock waves are weaker when compared to other operating conditions.

The experimental apparatus for analyzed configuration is composed of a convergent-divergent nozzle designed with the method of characteristics [START_REF] Bridges | Turbulence associated with broadband shock noise in hot jets[END_REF]. The nozzle exit diameter is 50.8 mm. The Reynolds number based on nozzle exit diameter is approximately 1.58 × 10 6 , which is large when compared to other jet experiments available in the literature.

The data acquisition in the tests applies Time-Resolved Particle Image Velocimetry (TRPIV) operated primarily with a 10 kHz sample rate. The experiment uses two sets of cameras, one positioned to capture the flow along the nozzle centerline and the other positioned to capture the flow of the mixing layer along the nozzle lipline.

NUMERICAL SETUP

GEOMETRY AND MESH CONFIGURATION

The geometry used for the calculations in the work presents a divergent shape and axis length of 40D, where D is the jet inlet diameter and has external diameters of 16D and 25D. Figure 1 illustrates a 2-D representation of the computational domain indicating the inlet surface in red, the far-field region in blue, the lipline in gray, and the centerline in black.

The computational grids used in the work are named M-1, M-2, and M-3. The M-1 and M-2 meshes are adaptations of the mesh utilized in previous work [START_REF] Junqueira-Junior | Influence of different subgrid-scale models in low-order LES of supersonic jet flows[END_REF] due to the different restrictions of each computational code. The M-3 mesh is generated with topological differences from M-1 and M-2 meshes. The M-3 mesh topology presents a high refinement level around the jet inlet boundary external diameter that transitions to a uniform distribution when moving forward in the longitudinal direction. In addition to the new topology, the M-3 mesh also presents a larger number of elements. The mesh generation uses a multiblock strategy since the FLEXI solver only handles hexahedral elements.

Fig. 2 exhibits a cut plane of the M-2 and M-3 meshes. M-2 mesh is presented to illustrate the topological differences between the two strategies. M-1 mesh is not presented because it only differs in the number of elements from M-2 mesh. The M-1 and M-2 meshes have a total of 6.2 × 10 6 and 1.8 × 10 6 elements that are simulated with second and third-order accuracy, respectively, resulting in simulations with 50 × 10 6 DOF. The M-2 mesh has 15.4 × 10 6 elements and is simulated with second and third-order accuracy, resulting in approximately 120 × 10 6 and 410×10 6 DOF. All the meshes utilized in the work are generated with the GMSH [START_REF] Geuzaine | GMSH: A three-dimensional finite element mesh generator with built-in pre-and post-processing facilities[END_REF] generator.

BOUNDARY CONDITIONS

different reference states to characterize the jet inflow, (•) jet , and the far-field, (•) f f . The inflow and the far-field surfaces are indicated in Fig. 1 in red and blue, respectively. A weakly enforced solution of a Riemann problem with a Dirichlet condition is enforced at the boundaries. The flow is characterized as perfectly expanded and unheated, i.e. p jet /p f f = T jet /T f f = 1, where p stands for pressure and T for temperature. The Mach number of the jet at the inlet is M jet = 1.4 and the Reynolds number based on the diameter of the nozzle is Re jet = 1.58 × 10 6 . A small velocity component with M f f = 0.01 in the streamwise direction is imposed at the farfield to avoid numerical issues. A sponge zone [START_REF] David G Flad | A discontinuous Galerkin spectral element method for the direct numerical simulation of aeroacoustics[END_REF] is employed close to all far-field boundaries to dump any oscillation that could reach the boundaries.

SIMULATION SETTINGS

A total of 4 simulations are compared in this work. The development of the simulations utilized 3 different meshes with two orders of accuracy obtained by changing the degree of the polynomial representing the solution. The S-1 simulation utilizes the M-1 mesh with secondorder accuracy. The S-2 simulation utilizes the M-2 mesh with third-order accuracy. The S-3 and S-4 simulations utilize the M-3 mesh with second and third-order accuracy, respectively. Table 1 summarizes the simulations performed and the total number of degrees of freedom in each of them.

CALCULATION OF STATISTICAL PROPERTIES

Two different approaches are taken to perform the 4 simulations. In the first approach, utilized for S-1, S-2, and S-3 simulations, the procedure involves three steps. The first one is to clean off the domain since the computation starts with a quiescent flow initial condition. The simulations run three flow-through times (FTT) to develop the jet flow. One FTT is the time required for one particle with the jet velocity to cross the computational domain. In the sequence, the simulations run an additional three FTT to produce a statistically steady condition. Then, in the last step, data are collected with a sample of approximately 250 kHz for another FTT to obtain the statistical properties of the flow. In the second approach, utilized for the S-4 simulation, the solution obtained from the S-3 simulation is utilized as the initial condition. The simulation is performed for 0.5 FTT to clean the second-order accuracy solution and allow it to provide a third-order accuracy solution. Then 2 additional FTT are simulated to extract data for the analysis. The cost of S4 simulation is higher than other simulations and the authors had some difficulties to stabilize the simulation, which consumed some available computational resources, for this reason it was not possible to run 3 FTT to obtain the statistics.

The mean and the root mean square (RMS) fluctuations of properties of the flow are calculated along the centerline, lipline, and different domain surfaces in the streamwise direction. The centerline is defined as the line in the center of the geometry y/D = 0, whereas the lipline is a surface parallel to the centerline and located at the nozzle diameter, y/D = 0.

RESULTS

ANALYSIS OF NUMERICAL RESULTS

The results from S1, S2, S3, and S4 simulations are presented in this section, which is divided into two parts to group different types of comparisons. In the first part, contours of mean longitudinal velocity, RMS longitudinal velocity fluctuation, and mean density are presented for each simulation. In the second part, the distribution of mean longitudinal velocity and RMS of longitudinal velocity fluctuation are presented along the jet centerline and lipline for the four simulations and compared to experimental data. In the final results, the mean longitudinal velocity, RMS of longitudinal velocity fluctuation, RMS of radial velocity fluctuation, and shear-stress tensor are presented in four spanwise lines for all the simulations and compared to experimental data.

In the first part, three main aspects can be analyzed from the different contours investigated and each contour is better to discuss one of the three aspects. The length of the potential core cannot be directly assessed from visual inspection, so the authors prefer to refer to the region of high velocity that can be easily inspected from the results of mean longitudinal velocity. The development of the shear layer can be visualized in all results, however, the one in which its intensity can be better visualized is in the results of RMS of longitudinal velocity fluctuation. The last aspect that can be assessed from the contours is the development of the series of shock and expansion waves in the early stages of the jet. Figure 4 presents the contours for the mean longitudinal velocity for all simulations. In Figs. 4a and 4b the contours of velocity are very similar, with the high velocity region in Fig. 4b being slightly longer. Analyzing the results in Fig. 4c, one can observe that the high-velocity region has increased significantly when compared to previous results. The improvement in the results obtained shows the importance of distributing elements where they are necessary. Finally, in Fig. 4d, the results from S4 simulation are presented. It is possible to observe that the high-velocity region is the longest among all the simulations, which is indicative that it was lacking resolution in previous simulations to adequately capture the development of the jet flow by adding too much dissipation. In Fig. 5 the contours of RMS of longitudinal velocity fluctuation is presented. Once more, the results presented in Figs. 5a and 5b from S1 and S2 simulations are similar, with the shearlayer development starting approximately 1D far from the jet inlet section. Just after the initial of the shear layer development, one can observe that the peak of RMS fluctuation occurs, which can be related to the large difference between the velocities and possibly the transition of the shear layer from laminar to turbulent. The results presented in Fig. 5c from the S3 simulation have significant differences from the other two previously discussed. The development of the shear layer is starting closer to the jet inlet section with smaller peaks of RMS of velocity fluctuation and with a smaller spreading. One can visualize that the two mixing layers are crossing in the center of the jet farther in Fig. 5c than in Figs. 5a and5b even presenting a sooner development. Analyzing the results in Fig. 5d, it can be observed that tendencies from the previous investigation continued to increase, which means that the beginning of the development of the shear layer got even closer to the jet inlet section and the crossing of the two mixing layers is happening farther from jet inlet section than the results from S3 simulation, Fig. 5c. S4 simulation is the one with smaller spreading and early development of the shear layer among all the simulations.

Finally, in Fig. 6, the contours of mean are presented for all simulations. In these In Fig. 6a only three sets of shocks and expansion waves are clearly visible, while in Fig. 6b it is possible to observe more than 6 sets. It is possible to observe also that the sets of shocks and expansion waves from the S2 simulation are stronger than those from the S1 simulation. Analyzing Fig. 6c, it is possible to observe that the S3 simulation produced even more sets of shocks and expansion waves than the S2 simulation, Fig. 6b, with larger intensity, that is evaluated by the level of variation of density produced by the shocks and expansion waves. Another aspect that can be observed is that the first set of shock and expansion waves in the S3 simulation is occurring closer to the jet inlet section than in S2 and S1 simulations, and appears to be a relation to the first set of shock and expansion waves with the beginning of the development of the shear layer. In Fig. 6d the results from S4 simulation is presented. One can observe the largest set of shock and expansion waves among all the simulations and also a thinner representation of the shocks and expansion waves, which can be closely related to the increased resolution of the simulation. It is also possible to observe a reduction in the intensity of the sets of shock and expansion waves when compared to the S3 simulation, Fig. 6c. The first part of this section is concluded with the comparison of the contours of mean longitudinal velocity, RMS of longitudinal velocity fluctuation, and mean density among the simulations. In the second part, the numerical results are compared with experimental data.

In the second part, in Fig. 7, the numerical results of all simulations are compared to the experimental data. In Fig. 7a the distribution of mean longitudinal velocity < U > /U j is presented in the centerline of the jet. One can observe in the figure that results from S1 and S2 simulations are almost equal. Results from the S3 simulation present a significant improvement when compared to previously performed simulations and the S4 simulation could almost capture the behavior observed in the experiments. In Fig. 7b the RMS of longitudinal velocity fluctuation u rms /U j is presented in the centerline of the jet. It is possible to observe once more in these results how well the resolution influenced the numerical results regarding the proximity to experimental data. The differences between S1 and S2 simulations are small, the S3 simulation got closer to experimental data and the S4 simulation once more presented the best match with experimental data. It can be observed in the results from the S4 simulation a double peak that does not appear in any other simulation or the experimental data. The authors believe that this result is a consequence of the fewer FFTs of the simulation in which data was gathered. Once more data could be used, authors believe that this characteristic would disappear and only one peak would be formed. While the results for the jet centerline present always improvements in the simulations with increased resolution, in the lipline that behavior is not always observed. In Fig. 7c, where the mean longitudinal velocity < U > /U j is presented in the lipline of the jet one may observe that far from the jet inlet section, the increased resolution produced a monotonic improvement in the numerical results, close to the jet inlet section, S3 simulation was the one that could better capture experimental data. However, it is not from the mean results where the greatest differences are observed. When analyzing the distribution of the RMS of longitudinal velocity distribution along the lipline of the jet, Fig. 7d, one can observe that monotonically the increased resolution pushed the results away from experimental data. While in the experimental data it is possible to observe a smooth growth of RMS of longitudinal velocity fluctuation and almost a plateau from x/D = 5 to x/D = 15, in all the simulations there is a sudden increase in the RMS of longitudinal velocity fluctuation and after the peak, it is possible only to observe a reduction on the values. The authors believe that the differences observed in these results are related to the choice of the boundary condition imposed for the jet inlet that represents neither the boundary layer profile from the nozzle nor the turbulent intensity in the nozzle exit section.

The results in Fig. 8 present different statistical properties of the flow in different longitudinal This result concludes our analysis of the numerical results from the simulations. It was possible to observe, in general, that the improved resolution of the simulations produced better results compared to experimental data. The simulation with the highest resolution, the S4 simulation, was the one that better matched the experimental data. Only in the jet lipline, this behavior is not observed. The authors have strong confidence that this has nothing to do with the effect of the resolution, instead, it may be strongly related to the choice of the boundary condition for the jet inlet condition, that does not reproduce the boundary layer developed inside the nozzle nor the turbulent intensity in the region. To improve the quality of the simulations in the jet lipline, a new boundary condition or a different simulation strategy should be adopted.

ANALYSIS OF COMPUTATIONAL EFFORT

At this point of the work, it is important to discuss some other aspects of computational effort to be able to improve the computational efficiency of the simulations. The main parameter utilized to measure the efficiency of a simulation is the Performance Index P ID, which can be calculated by

P ID = wall clock time n cores n DOF n time steps n RK-stages , (12)
where wall clock time is the time the simulation needed to perform n time steps time steps, n cores is the quantity of cores used in the simulation, n DOF is the number of DOF of the simulation and n RK-stages is the number of stages from the Runge-Kutta scheme. The PID was calculated for all four simulations and the results are presented in Tab. 2. It is important to clarify to the author that the numerical solver presented some improvements during the execution of the simulations and they can be related to the improvements in the P ID reduction from S3 and S4 simulations compared to S1 and S2 simulations. It is also possible to argue that with the increased number of degrees of freedom it is expected that more computation is performed with a similar number of cores, which also should increase the efficiency of the simulations. If we compare only S1 and S2 simulations, for the same number of DOF, the thirdorder accurate simulations cost almost twice the effort of a second-order accurate simulation. If these values are employed in the two simulations procedure performed in this analysis, the total cost of the simulation can be compared.

The first simulation procedure involves the whole calculation of the 9 FTT with a mesh of 50 × 10 6 elements that produces ≈ 400 × 10 6 DOF when simulated with second-order accurate discretization, which could produce a very similar result to those of S4 simulation. If the procedure for S4 simulation could be completely performed, it could initially start its 5 FTT with second-order accurate discretization with a total of 120 × 10 6 DOF. At this point, we do not consider the effect of the number of degrees of freedom in the PID, only the order of discretization. For this 5 FTT, the total time would be 3.34× smaller than those to perform the first simulation procedure due to the reduced number of degrees of freedom. Then, it is possible to consider the next 4 FTT calculated with third-order accurate discretization and a total of ≈ 400 × 10 6 DOF. In this 4FTT the cost of the third-order accurate discretization is twice of the second-order accurate simulation. If the total time of the second procedure is calculated, it costs ≈ 5% more than the procedure with second-order accuracy.

What is discussed here is that, once it is possible to start the high-order simulation with a previous result from another order of accuracy with the same mesh, it is possible to reduce the time required to obtain the desired data with high-order simulation and consequently reduce the cost of the total simulation. In the proposed procedure, the cost of the total third-order accurate simulation was only 5% larger than those of a second-order accurate simulation. This result is expressive and very interesting for high-order simulations.

Another important point to present is that the computational code utilized presented very good scalability with the number of cores. The tests for the S4 simulation varied the number of cores from a few hundred cores to a few thousand cores and the P ID was always close to 2µs.

CONCLUDING REMARKS

In this work, the employment of a discontinuous Galerkin framework called FLEXI was investigated for the LES simulation of supersonic free round jets. A total of four simulations are performed with 3 different meshes and second and third-order accuracy. The range of degrees of freedom from the simulations varies from 50 × 10 6 to 400 × 10 6 . All the simulations are performed for the same geometric model and with the same boundary conditions.

The results of the simulations are firstly compared visually between themselves to compare how they are capturing the main features of the flow: extension of the high-velocity region, development of the shear layer, and development of the sets of shocks and expansion waves. The results showed that with increased resolution the high-velocity regions got longer. The development of the shear layer starts closer to the jet inlet section and presents a smaller spreading. The number of sets of shocks and expansion waves increased and the visual of the shocks and expansion waves are thinner.

The numerical results showed that, in general, the increase in the resolution of the simulation, especially the number of degrees of freedom, produced better results when compared to experimental data. This behavior is observed in the results of mean longitudinal velocity distribution and RMS of longitudinal velocity fluctuation distribution in the centerline. It is also observed in the results from the four spanwise planes. The only results that do not follow this behavior are the mean longitudinal and RMS of longitudinal velocity fluctuation distributions along the jet lipline. In these regions, with increased resolutions, the results are pushed away from experimental data. The authors believe this behavior is related to the lack of resolution from the jet inlet boundary condition that could not reproduce the boundary layer and turbulent intensity from the experiments.

The analysis of the computational effort of the simulation showed that even utilizing a highorder method that costs more than a second-order method for the same number of degrees of freedom it was possible to reproduce a third-order simulation with only 5% more computational cost of total simulation by initializing the simulation with a smaller order of accuracy.

The work reached is objective of identifying the guidelines for performing LES simulations of supersonic jet flows using a discontinuous Galerkin scheme with adequate results with a reasonable computational cost. The open point on the jet inlet condition is the next step in the development of the work.

Figure 1 :

 1 Figure 1: 2-D schematic representation of the computational domain used on the jet flow simulations.

  (a) M-2 mesh.(b) M-3 mesh.

Figure 2 :

 2 Figure 2: Visualization of the half-plane longitudinal cut planes for the meshes used in the present work.

  5. The results from the lipline are an azimuthal mean from six equally spaced positions. The four surfaces in the streamwise positions are x/D = 2.5, x/D = 5.0, x/D = 10.0, and x/D = 15.0. Fig. 3 illustrates a snapshot of the jet flow with the lines and surfaces of data extraction. Mach number contours are presented in the figure.

Figure 3 :

 3 Figure 3: Snapshot of the jet simulation with two longitudinal lines and three crossflow lines along which data is extracted. Mach number contours are shown.

  (a) S1 simulation. (b) S2 simulation. (c) S3 simulation. (d) S4 simulation.

Figure 4 :

 4 Figure 4: Contours of mean longitudinal velocity component on cutplane in z/D = 0.

  S3 simulation. (d) S4 simulation.

Figure 5 :

 5 Figure 5: Contours of RMS of longitudinal velocity fluctuation on cutplane in z/D = 0.

  (a) S1 simulation. (b) S2 simulation. (c) S3 simulation. (d) S4 simulation.

Figure 6 :

 6 Figure 6: Contours of mean density on cutplane in z/D = 0.

Figure 7 :

 7 Figure 7: Results of mean streamwise velocity component distribution (left) and RMS of streamwise velocity fluctuation (right) in the jet centerline y/D = 0 (top) and lipline y/D = 0.5 (bottom).

  (a) x/D = 2.5 (b) x/D = 5 (c) x/D = 10 (d) x/D = 15 (e) x/D = 2.5 (f) x/D = 5 (g) x/D = 10 (h) x/D = 15 (i) x/D = 2.5 (j) x/D = 5 (k) x/D = 10 (l) x/D = 15 (m) x/D = 2.5 (n) x/D = 5 (o) x/D = 10 (p) x/D = 15

Figure 8 :

 8 Figure 8: Profiles of mean streamwise velocity component, RMS of streamwise velocity fluctuation, RMS of radial velocity fluctuation, and mean shear-stress tensor component (from top to bottom) at four streamwise positions x/D = 2.5, x/D = 5, x/D = 10 and x/D = 15 (from left to right).

Table 1 :

 1 Summary of simulations settings.

	Simulation Meshes Order of DOF/cell Cells Total # of DOF
			Accuracy		(10 6 )	(10 6 )
	S-1	M-1	2nd order	8	6.2	≈ 50
	S-2	M-2	3rd order	27	1.8	≈ 50
	S-3	M-3	2nd order	8	15.4	≈ 120
	S-4	M-3	3rd order	27	15.4	≈ 410

Table 2 :

 2 Summary of Performance Index P ID from all simulations.

	Simulation PID (µs)
	S1	8
	S2	15
	S3	5
	S4	2

ACKNOWLEDGMENTS

The authors acknowledge the support for the present research provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, under the Research Grant No. 309985/2013-7. The work is also supported by the computational resources from the Center for Mathematical Sciences Applied to Industry, CeMEAI, funded by Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP, under the Research Grant No. 2013/07375-0. The authors further acknowledge the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer. This work was also granted access to the HPC resources of IDRIS under the allocation 2020-A0092A12067 / 2021-A0112A12067 made by GENCI. The first author acknowledges authorization by his employer, Embraer S.A., which has allowed his participation in the present research effort. The doctoral scholarship provide by FAPESP to the third author, under the Grant No. 2018/05524-1, is thankfully acknowledged. Additional support to the fourth author under the FAPESP Research Grant No. 2013/07375-0 is also gratefully acknowledged. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001.