Philippe Colson

Yusuke Ominami

Akiko Hisada

Bernard La Scola

Didier Raoult
email: didier.raoult@gmail.com

Keywords: Mimivirus, giant virus, virophage, definition, defense, integration

Background. The discovery of mimivirus in 2003 prompted the quest for other giant viruses of amoebae. Mimiviruses and their relatives were found to differ considerably from other viruses. Their study led to major advances in virology and evolutionary biology. Aims. We summarized the widening gap between mimiviruses and other viruses. Sources. We collected data from articles retrieved from PubMed using as keywords "giant virus", "mimivirus", and "virophage", as well as quoted references from these articles. Content. Data accumulated during the last 15 years on mimiviruses and other giant viruses highlight that there is a quantum leap between these infectious agents which complexity is similar to that of intracellular microorganisms and classical viruses. Notably, in addition to their giant structures and genomes, giant viruses have abundant gene repertoires with genes unique in the virosphere, including a tremendous set of translation components. The viruses contain hundreds of proteins and many transcripts. They share a core of very central and ancient proteins but their genome sequences display a substantial level of mosaicism. Finally, mimiviruses have a specific mobilome, including virophages that can integrate into their genomes, and against which they can defend themselves through integration of short fragments of these invaders' DNA. Implications. Mimiviruses and subsequently discovered giant viruses have changed the virus paradigm and contradict many virus definition criteria delineated for classical viruses. The major cellular hallmark that still lacks in giant viruses is the ribosome, including both ribosomal protein and RNA encoding genes, which makes them bona fide microbes without ribosomes.

INTRODUCTION

Giant viruses of amoebae were discovered in 2003 (Table 1) [START_REF] Scola | A giant virus in amoebae[END_REF]. The characterization of their first representative, Acanthamoeba polyphaga mimivirus (APMV), prompted the quest for other similar infectious agents. During the last 15 years, nine new groups of giant viruses have been described [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF]. They include marseilleviruses, pandoraviruses, pithoviruses, faustoviruses, molliviruses, kaumoebaviruses, cedratviruses, pacmanviruses and orpheoviruses [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF][START_REF] Andreani | Orpheovirus IHUMI-LCC2: a new virus among the giant viruses[END_REF]. Giant virus names have been chosen by their discoverers for various reasons, due to specific features including morphological (as for the case of mimivirus, an acronym for Mimicking Microbe Virus in memory of "Mimi the amoeba", example of the story of the evolution told by his father to one of us (DR)), or to the geographical location of virus isolation or discovery (as for the case of Marseillevirus isolated in Marseille, France) [START_REF] Lagier | Naming microorganisms: The contribution of the IHU Mediterranee Infection, Marseille, France[END_REF]. Their particles have a size ranging between 200 and 2,300 nm and their genomes harbor 444-2,544 genes [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF][START_REF] Abrahao | Tailed giant Tupanvirus possesses the most complete translational apparatus of the known virosphere[END_REF]. Thus, giant viruses are as big or even bigger than some bacteria and they encode similar or greater number of genes. Beyond, data accumulated highlight that there is a quantum leap between these infectious agents and classical viruses, and some contain an almost comprehensive translation apparatus, although they lack ribosomes. In addition, the first viruses of virus to be discovered, named virophages, were found to replicate in mimivirus factories and their DNA can integrate into the genomes of mimiviruses, in addition to mimivirus-specific transposons named transpovirons. Mimiviruses and virophages strongly interact between each other, through sequence transfer, integration of virophages DNA into giant virus DNA, and defense mechanisms of mimiviruses against virophages. Therefore, giant viruses, virophages and their relationships represent new challenges in the field of virology. We focused here on the widening gap between mimiviruses and other viruses.

MIMIVIRUSES

APMV, the prototype virus of family Mimiviridae, was considered for years to be a Gram positive coccus because such large viruses were unknown at that time. Then, no PCR products were obtained using universal primers targeting bacterial 16S ribosomal DNA, but electron microscopy finally revealed ≈500 nm-large icosahedral viruses with ≈120 nm-long fibers. This first work inaugurated the world of bona fide "microbes" without ribosomal DNA [START_REF] Raoult | TRUC or the need for a new microbial classification[END_REF].

Since then, the family Mimiviridae has considerably expanded through the culture of mostly environmental water samples on Acanthamoeba spp. [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF][START_REF] Khalil | High-throughput isolation of giant viruses in liquid medium using automated flow cytometry and fluorescence staining[END_REF]. These mimiviruses have capsids with a diameter ranging between 370-600 nm and their genomes are 1.02-1.52 megabase pairs (Mbp) in length and encode 930-1,425 putative proteins [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF]. The main phenotypic and genotypic features of mimiviruses are described in Box 1. Three groups A, B and C of mimiviruses replicating in Acanthamoeba species were delineated based on phylogenomic analyses [START_REF] Colson | Reclassification of giant viruses composing a fourth domain of life in the new order Megavirales[END_REF]. These giant viruses are common in water and soil worldwide, and were in a few cases detected and even isolated from animals and humans [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF][START_REF] Moal | Mimivirus in the urine of a kidney-transplant recipient[END_REF][START_REF] Clouthier | Sturgeon nucleo-cytoplasmic large DNA virus phylogeny and PCR tests[END_REF].

Since 2010, distant relatives of mimiviruses of Acanthamoeba have been described, which infect common protists, flagellates and algae, mostly in marine waters [START_REF] Moniruzzaman | Diversity and dynamics of algal Megaviridae members during a harmful brown tide caused by the pelagophyte, Aureococcus anophagefferens[END_REF]. They include Cafeteria roenbergensis virus (CroV) [START_REF] Fischer | Giant virus with a remarkable complement of genes infects marine zooplankton[END_REF], the first one to be discovered, as well as Phaeocystis globosa virus and others [START_REF] Moniruzzaman | Diversity and dynamics of algal Megaviridae members during a harmful brown tide caused by the pelagophyte, Aureococcus anophagefferens[END_REF][START_REF] Santini | Genome of Phaeocystis globosa virus PgV-16T highlights the common ancestry of the largest known DNA viruses infecting eukaryotes[END_REF][START_REF] Gallot-Lavallee | Comparative genomics of Chrysochromulina ericina virus and other microalga-infecting large DNA viruses highlights their intricate evolutionary relationship with the established Mimiviridae family[END_REF][START_REF] Yan | The marine algal virus PpV01 has an icosahedral capsid with T=219 quasisymmetry[END_REF][START_REF] Sandaa | Isolation and characterization of two viruses with large genome size infecting Chrysochromulina ericina (Prymnesiophyceae) and Pyramimonas orientalis (Prasinophyceae)[END_REF][START_REF] Schvarcz | A giant virus infecting green algae encodes key fermentation genes[END_REF][START_REF] Yau | Virophage control of antarctic algal host-virus dynamics[END_REF][START_REF] Yutin | Mimiviridae: clusters of orthologous genes, reconstruction of gene repertoire evolution and proposed expansion of the giant virus family[END_REF]. Such mimivirus relatives are suspected to be paramount components of our biosphere [START_REF] Kerepesi | The "Giant Virus Finder" discovers an abundance of giant viruses in the Antarctic dry valleys[END_REF][START_REF] Mihara | Taxon richness of "Megaviridae" exceeds those of vacteria and archaea in the ocean[END_REF]. Recently, the 0.9-1.6 Mpb genomes of four putative giant viruses, named klosneuviruses and related to amoeba mimiviruses, have been assembled from environmental metagenomes [START_REF] Schulz | Giant viruses with an expanded complement of translation system components[END_REF]. Subsequently, a new giant virus (Bodo saltans virus) infecting Bodo saltans, an aquatic protozoan, was isolated and classified as a klosneuvirus [START_REF] Deeg | The kinetoplastid-infecting Bodo saltans virus (BsV), a window into the most abundant giant viruses in the sea[END_REF]. Two mimivirus-like strains were also isolated within or using Saccamoeba lacustris strains, from the bark of plane trees [START_REF] Michel | Experimental coinfection of Saccamoeba lacustris with Mimivirus-like giant virus and a small satellite virus[END_REF].

In 2018, two new mimiviruses, tupanvirus soda lake and tupanvirus deep ocean, were described [START_REF] Abrahao | Tailed giant Tupanvirus possesses the most complete translational apparatus of the known virosphere[END_REF]. They were isolated in Brazil from a "soda" lake and oceanic sediments, respectively. These viruses infect Acanthamoeba strains, but also Vermamoeba vermiformis and a wide range of protists in vitro. The viruses have icosahedral capsids similar to those of other mimiviruses of amoebae and a tail also covered with fibers that is the longest amongst viruses, since capsid and tail can reach together 2.3 μm in length. The genomes of these two tupanviruses harbor 1.44 and 1.52 Mpb and encode 1,276 and 1,425 genes, respectively.

VIROPHAGES AND THE MIMIVIRUS MOBILOME

The isolation of a second mimivirus in 2008 led to the discovery and description of a small (≈50 nm-large) icosahedral virus (strain Sputnik), the first virus of virus [START_REF] Scola | The virophage as a unique parasite of the giant mimivirus[END_REF]. It was named a virophage by analogy with bacteriophages. Indeed, it was unable to multiply in the absence of mimivirus, replicated in the mimivirus factories, slowed down the mimivirus replication and was commonly associated with production of morphologically abnormal viruses. Sputnik particles were found associated with mimivirus fibers [START_REF] Scola | The virophage as a unique parasite of the giant mimivirus[END_REF][START_REF] Desnues | Inside the lifestyle of the virophage[END_REF][START_REF] Boyer | Mimivirus shows dramatic genome reduction after intraamoebal culture[END_REF]. Both virophages and mimiviruses are produced within same viral factories. Sputnik appears to hijack the mimivirus factory, being detected inside it and often produced before the giant virus or at a distinct location. The 18,343 bp long circular dsDNA genome of Sputnik contains 21 genes including 14 ORFans and 7 ORFs with various putative origins including eukaryotic, bacterial, viral or plasmidic (Figure 1). Such chimeric gene repertoire and the presence of putative integrases and transposases led to hypothesize that this virophage might represent a vehicle of genes.

Another virophage, Mavirus (for Maverick virus) was isolated in association with CroV [START_REF] Fischer | A virophage at the origin of large DNA transposons[END_REF].

It also reduces amoebal cell lysis and production of its associated giant virus. Mavirus has a 19,063 bp circular dsDNA genome that encodes 20 proteins. Similar genome length and structure and a close evolutionary relationship were noticed between mavirus and the self-synthesizing maverick or polinton transposable elements [START_REF] Fischer | A virophage at the origin of large DNA transposons[END_REF]. The integration of provirophages in the genome of Bigelowiella isolates, an alga, was also described, suggesting that these cells may be infected with mimiviruses [START_REF] Blanc | Provirophages in the Bigelowiella genome bear testimony to past encounters with giant viruses[END_REF]. Overall, virophages have been isolated or detected by metagenomics in samples, mainly water, collected worldwide [START_REF] Zhou | Diversity of virophages in metagenomic data sets[END_REF][START_REF] Roux | Ecogenomics of virophages and their giant virus hosts assessed through time series metagenomics[END_REF][START_REF] Colson | Mimivirus: leading the way in the discovery of giant viruses of amoebae[END_REF]. They have 35-74-nm-large icosahedral capsids, and genomes encoding 16-34 genes. They were recently classified in a new viral family, named Lavidaviridae [START_REF] Krupovic | A classification system for virophages and satellite viruses[END_REF].

The mobilome represents all the kinds of mobile genetic elements, which are key players of genetic evolution: it comprises transposable elements, plasmids, introns and inteins, as well as viruses, [START_REF] Desnues | Provirophages and transpovirons as the diverse mobilome of giant viruses[END_REF]. The mimivirus specific mobilome corresponds to provirophages, transpovirons, inteins and introns. Whereas classical viruses are considered as a mobilome component, giant viruses have their own mobilome [START_REF] Desnues | Provirophages and transpovirons as the diverse mobilome of giant viruses[END_REF], another feature that they share with cellular organisms [START_REF] Sharma | Mimivirus inaugurated in the 21st century the beginning of a reclassification of viruses[END_REF] (Figure 2). Virophages are part of the mimivirus mobilome. They can integrate into mimivirus genomes as pro-virophages [START_REF] Desnues | Provirophages and transpovirons as the diverse mobilome of giant viruses[END_REF]. This is also the case for transpovirons, a new type of transposons specific to mimiviruses. They are composed of linear DNAs of about 7 kbp containing 6-7 genes, two of which are shared with virophages [START_REF] Desnues | Provirophages and transpovirons as the diverse mobilome of giant viruses[END_REF]. They depend on mimiviruses for their replication, being concentrated around the mimivirus factories during the replicative cycle, and they accumulate in the amoebal cytoplasm and the mimivirus and virophages virions.

MIMIVIRUS SYMPATRIC LIFESTYLE IN AMOEBAE THAT ARE SITES OF GENERALIZED SEQUENCE TRANSFERS

The tremendous size and composition of giant viruses that infect protists have been linked to their sympatric lifestyle, consisting in their survival and replication in a microbial community [START_REF] Raoult | Giant viruses from amoeba in a post-Darwinist viral world[END_REF]. The genomes of giant viruses are mosaics containing genes of eukaryotic, bacterial, and/or archaeal origin (Figure 1) and are considerably reshaped by lateral sequence transfers, in addition to gene duplication [START_REF] Boyer | Giant Marseillevirus highlights the role of amoebae as a melting pot in emergence of chimeric microorganisms[END_REF][START_REF] Filee | I am what I eat and I eat what I am: acquisition of bacterial genes by giant viruses[END_REF][START_REF] Moreira | Giant viruses, giant chimeras: the multiple evolutionary histories of Mimivirus genes[END_REF][START_REF] Suhre | Gene and genome duplication in Acanthamoeba polyphaga Mimivirus[END_REF][START_REF] Filee | Genomic comparison of closely related giant viruses supports an accordionlike model of evolution[END_REF]. This is exemplified by mimivirus (Figure 1), and by tupanvirus whose genes were inferred to have multiple origins, therefore evolutionary histories, warranting the representation of tupanvirus evolution as a rhizome rather than as a tree [START_REF] Abrahao | Tailed giant Tupanvirus possesses the most complete translational apparatus of the known virosphere[END_REF][START_REF] Raoult | The post-Darwinist rhizome of life[END_REF]. Acanthamoeba spp. and other free-living amoebae and phagocytic protists are cosmopolitan and predominant in the biosphere [START_REF] Rodriguez-Zaragoza | Ecology of free-living amoebae[END_REF][START_REF] Horn | Bacterial endosymbionts of free-living amoebae[END_REF][START_REF] Greub | Microorganisms resistant to free-living amoebae[END_REF][START_REF] Raoult | The discovery and characterization of Mimivirus, the largest known virus and putative pneumonia agent[END_REF]. They can harbor a variety of intracellular amoeba-resisting microorganisms [START_REF] Greub | Microorganisms resistant to free-living amoebae[END_REF]. As an illustration, an Acanthamoeba sp.

was isolated from a contact lens rinsing liquid together with a deltaproteobacterium (Candidatus Babela massiliensis), an alphaproteobacterium bacillus, a mimivirus and a virophage [START_REF] Cohen | Ameba-associated Keratitis, France[END_REF]. Cafeteria roenbergensis, the CroV host, also feeds on bacteria and viruses, and its genome was shown to harbor a 38-kbp fragment with 14 ORFs most similar to bacterial genes involved in carbohydrate metabolism [START_REF] Fischer | Giant virus with a remarkable complement of genes infects marine zooplankton[END_REF][START_REF] Massana | Crash of a population of the marine heterotrophic flagellate Cafeteria roenbergensis by viral infection[END_REF]. In addition, it was observed that obligate intra-amoebal parasites exhibit larger genomes than their intracellular relatives [START_REF] Raoult | Amoebae as genitors and reservoirs of giant viruses[END_REF].

Furthermore, subculturing the APMV prototype isolate 150 times in a germ-free amoebal host (in allopatry) was associated with a dramatic genome reduction (by ≈16%) [START_REF] Boyer | Mimivirus shows dramatic genome reduction after intraamoebal culture[END_REF].

In phagocytic protists, viruses and bacteria have to struggle for life, and they need a substantial and adapting gene armory to outcompete with, or at least resist to other microorganisms and genetic elements [START_REF] Raoult | Giant viruses from amoeba in a post-Darwinist viral world[END_REF]. Acanthamoeba spp. may therefore be viewed as an "adaptative zone" for giant viruses and virophages. The fight between microorganisms living in sympatry inside Acanthamoeba spp. and the host itself follows an evolutionary law described in 1973 by L. Van Valen [START_REF] Van Valen | A new evolutionary law[END_REF]. To illustrate this theory, he borrowed a scene from Lewis Caroll's book Through the looking-glass where Alice runs as fast as she can with the Red Queen through a chessboard, but nonetheless surprinsingly remains in the same place.

According to this "Red Queen hypothesis", co-existing organisms play a zero-sum game, where useful or necessary weapons and shields can vary from time to time, there is no single or chief competitor, and no victory is definitive as enhanced or new adversaries continue to emerge. In the setting of continuous sequence transfers promoted by contacts between genetic material from the intra-amoebal microorganisms during their multiplication or replication, each microorganism may act as a tinkerer [START_REF] Jacob | Evolution and tinkering[END_REF] by using sequence gains and losses to conceive new attack or defense tools. Moreover, new adaptations may occur at the expense of previous changes. This paradigm parallels that of the representation of genetic evolution as a rhizome, which is devoid of a center and can grow through gaining or loosing one or several elements [START_REF] Raoult | The post-Darwinist rhizome of life[END_REF][START_REF] Deleuze | Rhizome : introduction[END_REF]. It can be illustrated by several recently described defense mechanisms involving mimiviruses, including the defense of mimiviruses of amoebae against virophages.

MIMIVIRUS AND VIROPHAGE DEFENSE MECHANISMS

Following the observation that mimiviruses of group A, but not B-C, were resistant to the Zamilon virophage [START_REF] Gaia | Zamilon, a novel virophage with Mimiviridae host specificity[END_REF], the means by which mimiviruses A could defend against this virophage were investigated. This investigation was conducted by analogy with the defense strategy of bacteria and archaea against viruses through CRISPR-Cas systems, which consists in the integration into their genomes of fragments of these invaders' DNA ("cannibalism") [START_REF] Levasseur | MIMIVIRE is a defence system in mimivirus that confers resistance to virophage[END_REF]. Thus, short specific Zamilon DNA fragments were searched for in the genomes of mimiviruses A. Four copies of a 15 nucleotide-long Zamilon DNA fragment, named MIMIVIRE for "mimivirus virophage resistance element", were detected within an operon (Figure 1). This sequence was absent from the genomes of Zamilon-sensitive mimiviruses B-C. The mechanism of this resistance might rely on nucleic acid sequence recognition and confer immunity against virophages. The MIMIVIRE operon includes one gene that contains the 15 nucleotide-long Zamilon sequences and two genes annotated as a helicase and a nuclease, whose functions were experimentally validated. They may allow the cleavage of a foreign nucleic acid. The restoration of mimiviruses A sensitivity to Zamilon virophage was observed by independently inhibiting these three genes by RNA interference. Although it has been primarily underlined that the MIMIVIRE genes may not be related to a CRISPR-Cas system [START_REF] Mohanraju | Diverse evolutionary roots and mechanistic variations of the CRISPR-Cas systems[END_REF], it was shown later that it contained at least one Cas4-like protein based on structural and mechanistic analyses [START_REF] Dou | Structural and mechanistic analyses reveal a unique Cas4-like protein in the mimivirus virophage resistance element system[END_REF]. The integration of sequences from invaders as a defense mechanism appears to be a general phenomenon in biology. Interestingly, the presence of ribonucleases (RNases) H was recently detected in mimivirus genomes [START_REF] Moelling | RNase H as gene modifier, driver of evolution and antiviral defense[END_REF].

RNases H and RNase H-like enzymes are involved in most or all currently known defense mechanisms against transposable elements, viruses, and extracellular pathogens.

Mavirus integrated as a pro-virophage into the Cafeteria roenbergensis genome was recently shown experimentally, subsequently to host superinfection by CroV, to be transcribed, then to replicate without being directly detrimental to CroV replication [START_REF] Fischer | Host genome integration and giant virus-induced reactivation of the virophage mavirus[END_REF].

Nevertheless, CroV replication suppression and enhanced survival of the host population were thereafter observed, suggesting the acquisition of a protection conferred by Mavirus reactivation. Other putative defense mechanisms of mimiviruses against sympatric organisms were recently suggested for Bodo saltans virus [START_REF] Deeg | The kinetoplastid-infecting Bodo saltans virus (BsV), a window into the most abundant giant viruses in the sea[END_REF]. Competitive interference between different Bodo saltans virus strains or related viruses co-infecting a same host cell may occur through the site-specific homing endonucleases encoded by introns and inteins that have invaded essential genes of this mimivirus, including DNA-dependent RNA polymerase subunits. Indeed, these endonucleases can cleave the locus that is unoccupied in viral genomes lacking the intron or intein.

THE GROWING MISMATCH BETWEEN GIANT VIRUSES AND THE CRITERIA OF DEFINITION OF CLASSICAL VIRUSES

Mimivirus initially resisted identification for more than a decade because its phenotype did not match with that of viruses. It was considered as a microorganism (a Gram positive coccus), i.e. an organism visible only using optical microscopy [START_REF] Blanc | Lateral gene transfer between obligate intracellular bacteria: evidence from the Rickettsia massiliae genome[END_REF]. Similarly, pandoraviruses were considered as microorganisms and named Acanthamoeba endosymbionts due to their size (Figure 3) [START_REF] Scheid | An extraordinary endocytobiont in Acanthamoeba sp. isolated from a patient with keratitis[END_REF]. Later, its was shown that giant viruses of amoebae had hallmark features of cellular microorganisms and, de facto, most criteria of definition of viruses did not apply to them [START_REF] Sharma | Mimivirus inaugurated in the 21st century the beginning of a reclassification of viruses[END_REF].

The virus concept grew on the initial observations by Ivanowsky and Beijerinck that infectious agents smaller than microorganisms, not ultrafilterable themselves, may exist and transmit infections [START_REF] Ivanovski | Uber die Mosaikkrankheit der Tabakspflanze[END_REF][START_REF] Beijerinck | Uber ein contagium vivum fluidum als Ursache der Fleckenkrankheit der Tabaksblätter[END_REF]. Congruently, these infectious agents were not visible by light microscopy that allows seeing shapes larger than 200 µm. This paradigm was applied to viruses until the APMV discovery (Table 2). The modern concept of virus was delineated in 1957 by Lwoff [START_REF] Lwoff | The concept of virus[END_REF], although intracellular bacteria and viruses were grouped together in microbiology books until the 1970s. Lwoff stated that viruses contain only one type of nucleic acid, DNA or RNA; reproduce only from their genetic material, being unable to grow and divide; and do not harbor in their genomes information encoding an energy production system. The viral capsid was described a few years later [START_REF] Lwoff | A system of viruses[END_REF]. Messenger RNAs are in fact detected in giant viruses, many having been detected in APMV particles [START_REF] Raoult | The 1.2-megabase genome sequence of Mimivirus[END_REF]. Therefore, these viruses contain both DNA and RNA. While giant viruses do not multiply through binary fission, those with ovoid viruses (including pandoraviruses, pithoviruses and cedratviruses) have a weird assembly stage during which the viruses tegument seems to grow progressively while enclosing gradually its content [START_REF] Philippe | Pandoraviruses: amoeba viruses with genomes up to 2.5 Mb reaching that of parasitic eukaryotes[END_REF]. Moreover, giant viral factories look like morula from Chlamydia spp. [START_REF] Abdelrahman | Polarized Cell Division of Chlamydia trachomatis[END_REF]. The emblematic lack of enzymes involved in intermediate metabolism was recently challenged by the finding in a green alga-infecting mimivirus named Tetraselmis virus 1 of two key fermentation genes encoding a pyruvate formate-lyase and a pyruvate formate-lyase activating enzyme [START_REF] Schvarcz | A giant virus infecting green algae encodes key fermentation genes[END_REF]. Besides, some obligatory intracellular parasites among which the small bacteria Carsonella ruddii are devoid of a complete ATP generation machinery [START_REF] Nakabachi | The 160-kilobase genome of the bacterial endosymbiont Carsonella[END_REF]. Regarding the capsid, mimiviruses, as a majority of giant viruses, harbor one, which is pseudo-icosahedral [START_REF] Scola | A giant virus in amoebae[END_REF]. Nevertheless, pandoraviruses are devoid of recognizable capsid gene [START_REF] Philippe | Pandoraviruses: amoeba viruses with genomes up to 2.5 Mb reaching that of parasitic eukaryotes[END_REF], while pithoviruses harbor a capsid gene but no capsid protein detected by proteomics. They are also devoid of any known capsid morphology, as are cedratviruses and orpheovirus [START_REF] Andreani | Orpheovirus IHUMI-LCC2: a new virus among the giant viruses[END_REF][START_REF] Sharma | Pithovirus sibericum, a new bona fide member of the "Fourth TRUC" club[END_REF][START_REF] Andreani | Cedratvirus, a Double-Cork Structured Giant Virus, is a Distant Relative of Pithoviruses[END_REF]. Furthermore, emblematic elements that are lacking among classical viruses are protein synthesis components. Ten translation-related genes were described in the APMV genome [START_REF] Raoult | The 1.2-megabase genome sequence of Mimivirus[END_REF]. They corresponded to aminoacyl-transfer RNA (tRNA) synthetases or translation factors. In addition, six tRNA-encoding genes were present. It was later shown that RNA silencing of the gene encoding a putative translation initiation factor (R458) was associated with a prolonged eclipse phase and a delay in the appearance of the mimivirus factory, along with modulation of expression of 32 mimivirus genes [START_REF] Bekliz | The experimental analysis of mimivirus translation initiation factor 4a reveals its importance for viral proteins translation during infection of Acanthamoeba polyphaga[END_REF]. Recently, the mimivirus translation component set showed a dramatic expansion with the assembly of genomes of putative non-isolated mimivirus relatives, named klosneuviruses [START_REF] Schulz | Giant viruses with an expanded complement of translation system components[END_REF], then with the Bodo saltans virus discovery [START_REF] Deeg | The kinetoplastid-infecting Bodo saltans virus (BsV), a window into the most abundant giant viruses in the sea[END_REF]. Nevertheless, current record holders are tupanviruses whose genomes harbor the most complete set of translation-related genes of the virosphere, with all 20 aminoacyl-tRNA synthetases, and 67-70 tRNAs associated with 46-47 codons [START_REF] Abrahao | Tailed giant Tupanvirus possesses the most complete translational apparatus of the known virosphere[END_REF]. In addition, there are two different copies of an intronic region of 18S ribosomal RNA in the tupanvirus genome, and such sequences were shown to be present in other mimiviruses of amoebae. When excluding ribosomes, tupanvirus genomes harbor as many translation-related genes as Carsonella ruddii, a bacterium, Nanoarchaeum equitans, an archaeon, and, in the case of Tupanvirus deep ocean, Encephalitozoon cuniculi, an eukaryote. Thus, the major cellular hallmark that still lacks in giant viruses is the ribosome, including both ribosomal proteins and RNA-encoding genes. Overall, there is hence a quantum leap between classical viruses and mimiviruses and other giant viruses that have a complexity similar to that of intracellular microorganisms.

THE PRESENCE AND SIGNIFICANCE OF GIANT VIRUSES IN HUMANS

Beyond being currently considered as common in water and soils worldwide, giant viruses have been detected in human samples in several studies and by several teams. Notably, hints of their presence in humans have been increasingly reported through metagenomic analyses [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF][START_REF] Popgeorgiev | Marseillevirus-like virus recovered from blood donated by asymptomatic humans[END_REF][START_REF] Rampelli | ViromeScan: a new tool for metagenomic viral community profiling[END_REF][START_REF] Moustafa | The blood DNA virome in 8,000 humans[END_REF][START_REF] Arroyo Muhr | Viruses in cancers among the immunosuppressed[END_REF]. This involved sequences related to mimiviruses and virophages but also to marseilleviruses and more recently discovered giant viruses. Various other techniques have contributed to identify the presence of giant viruses in humans, including serologies, immunohistochemistry and immunofluorescence techniques, PCR and fluorescence in situ hybridization (FISH) [START_REF] Colson | Giant viruses of amoebae: a journey through innovative research and paradigm changes[END_REF][START_REF] Scola | Mimivirus in pneumonia patients[END_REF][START_REF] Dornas | Detection of mimivirus genome and neutralizing antibodies in humans from Brazil[END_REF][START_REF] Saadi | First isolation of Mimivirus in a patient with pneumonia[END_REF][START_REF] Aherfi | Marseillevirus in lymphoma: a giant in the lymph node[END_REF][START_REF] Popgeorgiev | Marseillevirus adenitis in an 11-month-old child[END_REF]. A critical step in studying the presence and significance of giant viruses in humans was their isolation from human samples. A marseillevirus was in 2012 the first giant virus of amoebae to be isolated from a human, in the feces from a young healthy Senegalese man [START_REF] Colson | Evidence of the megavirome in humans[END_REF]. Then, a mimivirus was isolated from the bronchoalveolar fluid and the feces of two pneumonia patients [START_REF] Saadi | First isolation of Mimivirus in a patient with pneumonia[END_REF][START_REF] Saadi | Shan virus: a new mimivirus isolated from the stool of a Tunisian patient with pneumonia[END_REF], and from the urine of a kidney-transplant recipient in whom no role of the giant virus could be speculated in the patient's symptoms that consisted in acute diarrhoea and dyspnoea [START_REF] Moal | Mimivirus in the urine of a kidney-transplant recipient[END_REF]. Based on serological assays, molecular tests and culture isolation, mimiviruses were suspected to be linked to pneumonia [START_REF] Saadi | First isolation of Mimivirus in a patient with pneumonia[END_REF], whereas marseilleviruses were mostly detected in the blood and the lymphoid tissues and associated with adenitis and Hodgkin lymphoma [START_REF] Aherfi | Marseillevirus in lymphoma: a giant in the lymph node[END_REF][START_REF] Popgeorgiev | Marseillevirus adenitis in an 11-month-old child[END_REF] . Besides, mice inoculated intracardially with APMV developed histopathologically proven lesions of pneumonia [START_REF] Khan | Pneumonia in mice inoculated experimentally with Acanthamoeba polyphaga mimivirus[END_REF] and a 30-day long persistence of Marseillevirus but no disease was observed in rats and mice inoculated parenterally, intraperitoneally or by aerosolization [START_REF] Aherfi | Experimental inoculation in rats and mice by the giant marseillevirus leads to long-term detection of virus[END_REF]. Overall, although the presence and clinical significance of giant viruses in humans are still controversial issues [START_REF] Sauvage | No evidence of marseillevirus-like virus presence in blood donors and recipients of multiple blood transfusions[END_REF][START_REF] Phan | Absence of giant blood Marseille-like virus DNA detection by polymerase chain reaction in plasma from healthy US blood donors and serum from multiply transfused patients from Cameroon[END_REF], they represent an emerging field that deserves broader analyses and increased consideration in future studies.

CONCLUSION

Mimiviruses and subsequently discovered giant viruses have changed the virus paradigm and contradict many virus definition criteria delineated for classical viruses. An opposite change recently occurred when ultrasmall bacteria were discovered, and found to lack genes involved in metabolic processes formerly considered as essential [START_REF] Brown | Unusual biology across a group comprising more than 15% of domain Bacteria[END_REF][START_REF] Luef | Diverse uncultivated ultra-small bacterial cells in groundwater[END_REF]. Mimiviruses can be currently considered as microorganisms lacking a canonical ribosome. Nevetheless, it is possible that an alternative translation device may have existed, discarded later on during the evolutionary process. Furthermore, future studies are warranted to gain a better knowledge on the presence and significance of giant viruses in humans.

BOXES Box 1. Main phenotypic and genotypic features of mimiviruses

The capsid of mimiviruses of amoebae is an almost perfect icosahedron, except at one of its vertices, which is a gateway for the liberation of the genome and is covered with a fivepointed star-shaped structure [START_REF] Scola | A giant virus in amoebae[END_REF][START_REF] Klose | The threedimensional structure of Mimivirus[END_REF]. This capsid comprises proteins having a structure of the type "double jelly roll fold". The viruses can carry on its surface highly glycosylated protein fibers, the constitution of which is not yet completely elucidated, that seem to intervene in viral entry into amoebae, and have a capacity of attachment to other organisms [START_REF] Andrade | Filling knowledge gaps for mimivirus entry, uncoating, and morphogenesis[END_REF]. Under the capsid, surrounded by an internal lipid membrane and fibers, there is a spherical compartment bounded by a double lipid layer and containing the genome and proteins [START_REF] Scola | A giant virus in amoebae[END_REF][START_REF] Klose | The threedimensional structure of Mimivirus[END_REF]. Mimivirus genomes are linear double-stranded DNAs that are very rich in A+T (≈72% of the bases for the Mimivirus prototype isolate) with a protein coding density of ≈90% [START_REF] Raoult | The 1.2-megabase genome sequence of Mimivirus[END_REF]. The gene repertoire of mimiviruses contains so-called "core" genes [START_REF] Raoult | The 1.2-megabase genome sequence of Mimivirus[END_REF], which have homologs in poxviruses, asfarviruses, phycodnaviruses, ascoviruses and iridoviruses joined together in 2001 in the group of large nucleocytoplasmic DNA viruses [START_REF] Yutin | Eukaryotic large nucleo-cytoplasmic DNA viruses: clusters of orthologous genes and reconstruction of viral genome evolution[END_REF]. Among the approximately 200 identified "core" genes, there are some that show the monophyly of all these viruses. Fifty core genes conserved in all or a part of these viruses have been assigned to the genome of a common ancestor [START_REF] Yutin | Eukaryotic large nucleo-cytoplasmic DNA viruses: clusters of orthologous genes and reconstruction of viral genome evolution[END_REF][START_REF] Yutin | Hidden evolutionary complexity of Nucleo-Cytoplasmic Large DNA viruses of eukaryotes[END_REF]. Phylogenetic and phyletic analyses of the mimivirus gene repertoires, particularly of genes that have homologs in cellular organisms, and of the protein folds detected in these viruses, support an early origin of the mimiviruses and other giant viruses [START_REF] Koonin | Origin and evolution of eukaryotic large nucleo-cytoplasmic DNA viruses[END_REF][START_REF] Boyer | Phylogenetic and phyletic studies of informational genes in genomes highlight existence of a 4 domain of life including giant viruses[END_REF][START_REF] Nasir | A phylogenomic data-driven exploration of viral origins and evolution[END_REF]. Moreover, mimivirus genomes harbor significant proportions of duplicated genes, of socalled "ORFans" (genes with no known homolog in sequence libraries) accounting for about 48% of all genes, and of genes that are predicted to have been involved in lateral exchanges of sequences with other organisms, including their amoebal host (Figure 1) [START_REF] Raoult | The 1.2-megabase genome sequence of Mimivirus[END_REF]. Promoters, introns and inteins have also been predicted. Functions not predicted before in viruses were revealed in mimiviruses. Emblematically, some mimivirus genes encode aminoacyl-RNA transfer (tRNA) synthetases, factors involved in translation, and tRNAs. Other unique genes amongst viruses are involved in nucleotide synthesis, amino acid metabolism, post-translational modifications, lipid and carbohydrate metabolism, or DNA repair. There are genes whose presence suggests a high degree of autonomy for replication, with respect to their host cell. These genes encode, in particular, DNA polymerases, helicases and primases associated with DNA replication, RNA polymerase subunits, transcription factors, Holliday junction resolvers and topoisomerases involved in the processing and maturation of DNA, ATPase pumps for packaging DNA, chaperone molecules involved in capsid assembly, and capsid proteins [START_REF] Yutin | Hidden evolutionary complexity of Nucleo-Cytoplasmic Large DNA viruses of eukaryotes[END_REF]. Polyadenylated messenger RNAs have been detected, often with stem-loop structures towards their terminal end [START_REF] Byrne | The polyadenylation site of Mimivirus transcripts obeys a stringent 'hairpin rule[END_REF].

Figure 1 .

 1 Figure 1. Schematics of the mosaicism of the Mimivirus and Zamilon virophage

Figure 2 .Figure 3 .

 23 Figure 2. Mobile genetic elements comprising the mimivirus mobilome

Acknowledgments

We are thankful to Adrien Teixera and Jacques Bou Khalil for their technical help with the generation of Figures 1 and3, respectively. We sincerely thank Takashi Irie, Kyoko Imai, Shigeki Matsubara, Taku Sakazume and the Hitachi team of Japan (Hitachi High-Technologies Corporation, Science & Medical Systems Business Group 24-14, Nishishimbashi 1-chome, Minato-ku, Tokyo 105-8717 Japan) for the collaborative study conducted together with IHU Méditerranée Infection, and for the installation of a SU5000 microscope at IHU Méditerranée Infection.

Funding

This work was supported by the French Government under the « Investissements d'avenir » (Investments for the Future) program managed by the Agence Nationale de la Recherche (ANR, fr: National Agency for Research) (reference: Méditerranée Infection 10-IAHU-03), 14 and by Hitachi High-Technologies Corporation, Tokyo, Japan.

Conflicts of interest

The authors have no conflicts of interest to declare. Funding sources had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; and preparation, review, or approval of the manuscript.


Umut Guven

Guillaume Ribert
email: guillaume.ribert@coria.fr

Impact of non-ideal transport modeling on supercritical flow simulation

Keywords: real gas, supercritical fluids, high pressure combustion, non-ideal transport

The simulation of a supercritical fluid flow requires sophisticated models for real gas thermodynamic and non-ideal phenomena. They both are presently addressed through the simulation of a non-reacting and reacting high pressure H 2 /O 2 splitter-plate configuration. In particular, the diffusion velocity of species is evaluated through the gradient of chemical potential (d NI l = X l (∇µ l ) T ) expressed with the Peng-Robinson equation of state, or with the classical low-pressure approach d I l = ∇X l , which only uses the gradient of the l th species molar fraction, X l . In addition, the high pressure binary diffusion coefficients are estimated by the correction of Kurochkin et al. or with the Takahashi approach. The results for the non-reaction case are consistent with the literature for mean and rms values using d I l . The use of d NI l has a limited impact but the temperature profiles become steeper. In the reactive case, the two approaches lead to a difference of 50 K on the average temperature just downstream of the injector and about 100 K further downstream. A non-ideal transport is then required for the modeling of supercritical flow simulation.

Introduction

The modeling and simulation of supercritical mixing and combustion requires attention to the problems usually encountered at low pressure, but also to the problems posed by the introduction of non-ideal phenomena related to high pressure [1]. It is now established that studying supercritical flows requires a dedicated framework [2][3][4] that includes a real-gas equation of state (EoS) and non-ideal transport fluxes. Such approach has been exploited by Bellan and co-workers in direct numerical simulations (DNS) of non-reacting mixing layer [5][6][7], and by Giovangigli et al. [8,9] for the computation of one-dimensional laminar flames. Only very recently a reactive mixing layer was performed by DNS [10] but with a single reaction for the oxidation of C 7 H 16 . It is indeed a scientific challenge to process with detailed high pressure chemistry since it has been shown that supercritical laminar diffusion or premixed flames can be less thick than one micron if the stretching of the flame becomes significant [11][12][13]. Dealing with supercritical flows also poses numerical challenges [14,15] linked to the presence of strong density gradients that can lead to spurious numerical oscillations. Hence, introducing detailed chemistry in the context of realistic high pressure configurations requires lowering the numerical cost of simulations but preserving the physical modeling of non-ideal phenomena. The numerical benchmark proposed by Ruiz et al. [16] for high-Reynolds-number supercritical non-reactive flow tends to satisfy this compromise. A splitter-plate configuration is studied with a two-dimensional DNS allowing a good description of the mixing of liquid oxygen (LOx) with hydrogen under high pressure.

In the present study, different modeling levels are evaluated for the combustion of hydrogen with LOx under supercritical conditions. In particular, the focus is on the modeling of the diffusion velocity of species, and the evaluation of binary diffusion coefficients at high pressure. A two-dimensional splitter plate configuration, inspired from [16] for computational cost considerations, serves as numerical reference for this reacting flow.

Theoretical formulation

Governing equations and thermodynamics

Simulations are carried out with the finite volume code SiTCom-B [17][18][19] which solves the reacting compressible Navier-Stokes equations in a cartesian mesh. The fully coupled conservation equations of momentum, species and energy for reactive flows is given by:

∂U ∂t + ∂F j c ∂x j + ∂F j d ∂x j = S (1)
where U = [ρu i , ρE, ρY k ] T is the vector of conservative variables. u i are the velocity components, E is the total non chemical energy decomposed as the sum of sensible energy and kinetic energy. Y k is the k th chemical species in a pool of N sp species. F j c represents the conservative variables flux vectors and is given by:

F j c = [ρu j u i + δ ji p, ρu j E + u j p, ρu j Y k ] T . F j d are the diffusive fluxes, F j d = [-τ i j , -u i τ i j + q j , -ρV k, j Y k ] T .
The source term vector S = (0, ωE , ωk ) T with ωk the chemical rate of species k and ωE , the heat release due to combustion. τ i j is modeled with the Newtonian viscous stress tensor and q j , the j th component of the heat flux vector, is given for a multi-component flow, by

q = λ∇T + ρ N sp k=1 h s,k Y k V k -p N sp k=1 D T k d k . (2)
λ is the thermal conductivity of the mixture, D T k , the thermal diffusion coefficient of species k related to the Dufour heat flux. The sensible enthalpy of species k, h s,k , is evaluated based on partial-density properties and departure functions [2,4,20]. In particular, the enthalpy, h, is calculated with the following relation,

h = N sp k=1 Y k h PG k (T ) + p p 0 ñ 1 ρ - T ρ 2 Å ∂p ∂T ã p ô T dp, (3)
where h PG k denotes the perfect gas specific enthalpy of the k th species. In Eq. (3) the partial derivative is estimated from the equation of state. Accurate highpressure relations proposed by Chung et al. [21] are used to evaluate the transport properties. The Peng-Robinson (PR) equation of state (EoS) links pressure, p, temperature, T and density, ρ, as

p = ρR u T W -bρ - ρ 2 aα(T, ω) W 2 + 2bWρ -b 2 ρ 2 , ( 4
)
where R u is the universal gas constant and W the molecular weight of the fluid mixture, W = N sp k=1 X k W k with X k the mole fraction of species k (among N sp species). The Van der Waals mixing rules are used for mixtures: aα

= N sp i=1 N sp j=1 X i X j √ α i α j a i a j (1 -κ i j ) and b = N sp i=1 X i b i
. κ i j is the binary interaction coefficient. The constants a i (attractive forces), b i (co-volume of particles) and α i are determined from universal relationships [START_REF] Poling | The properties of gases and liquids[END_REF], involving the critical temperature and partial pressure of species k, T c k and p c k , respectively, as well as the acentric factor.

Diffusion velocities and binary diffusion coefficient

Neglecting the baro-diffusion effects, the diffusion velocity of species k in the mixture is written for highpressure flows as [8,[START_REF] Oefelein | [END_REF]:

V k = - N sp l=1 D kl d l -D T k ∇T T (5)
with

d l = X l (∇µ l ) T = ∇X l + X l ∇µ sm l T , (6)
where the chemical potential of the l th species, µ l , is decomposed as µ l = ln X l + µ sm l [8]. The second term of Eq. ( 5) is named Soret effect. If the real-gas effects are neglected, the diffusion velocity for ideal gas is recovered and d l = ∇X l . The non-ideal part is given by the gradient of the dimensionless chemical potential ∇µ sm l T taken at constant temperature [8]. For PR EoS (Eq. ( 4)), µ sm l is written:

µ sm l = W l g PG l R u T - ρb l ρb -W + ln Å ρR u T p st (W -bρ) ã + W l 2 √ 2R u T Ç ∂aα ∂Y l b -aα W W l (b l -2b) b 2 W å • ln Ç W + (1 + √ 2)bρ W + (1 - √ 2)bρ å - aαρW bR u T √ 2 • b + √ 2b l - √ 2b Ä W + (1 + √ 2)bρ ä Ä W + (1 - √ 2)bρ ä g PG l
is the perfect gas Gibbs function of the l th species at standard pressure, p st .

Diffusion velocity modeling

Using Eq. ( 5) requires to evaluate the multicomponent diffusion coefficients, D kl , and the thermal diffusion coefficients, D T k . This task is performed in this study with the approach used in CHEMKIN-II [24] since it is the same approach than done in the solver REGATH, our reference code used to simulate real-gas flamelets [11][12][13]. Multicomponent properties are evaluated with the binary diffusion coefficients, D bin kl . This strategy will be used for the calculation of 1D premixed laminar flames (see section 4.2). However for 2D simulations, this strategy may be expensive in terms of CPU time because there is no explicit formula for D kl [25], and a simplest model is often used. The diffusion velocity of species k is then given by the classical approximation of Hirschfelder and Curtiss [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF], i.e.

V k = -D mix k Å d k + χ mix k ∇T T ã + V c . (7)
D mix k
is the diffusion coefficient of species k in the mixture, expressed with binary diffusion coefficients (D bin kl ),

D mix k = 1 -Y k N sp l =k X l /D bin kl , (8)
and χ mix k is the thermal diffusion ratio. V c is a correction velocity to ensure mass conservation. In literature, d k is always simply expressed by d k = ∇X k in Eq. (7). In this study, the Hirschfelder and Curtiss approximation is extended to high-pressure flows by using Eq. ( 6) for the simulation of supercritical premixed flamelets and the non-reacting case of the splitter plate configuration. The reacting case of the latter will be studied through the two approaches, multicomponent and zero order approximation.

Binary diffusion coefficients at high pressure

The evaluation of binary diffusion coefficients at high pressure, D bin kl , is based on kinetic theory considerations for dense gas mixtures. They are expressed as

D bin kl = F c × D bin,• kl , (9)
with D bin,• kl , the binary diffusion coefficients at standard pressure given by the kinetic theory of dilute gases [START_REF] Hirschfelder | Molecular theory of gases and liquids[END_REF], i.e. using polynomial fits, or coming from the empirical correlation of Fuller et al. [START_REF] Poling | The properties of gases and liquids[END_REF][START_REF] Fuller | [END_REF]. In Eq. ( 9), F c is a correction factor that takes into account for volume effects. Using the Takahashi approach [28], the scaling factor F c is tabulated as a function of the reduced temperature (T r = T/T c ) and pressure (p r = p/p c ) with

T c or p c given by [T, p] c = X k × [T, p] c,k + X l × [T, p] c,l
. Such approach has been used by many authors [11-13, 23, 29, 30] in various configurations. Using the Kurochkin et al. approach [31], F c = 1/χ kl with (10)

χ kl = 1 + N sp j=1 n j π 12 8(σ 3 k j + σ 3 l j ) -6(σ 2 k j + σ 2 l j )σ kl -3(σ 2 k j -σ 2 l j ) 2 σ -1 kl + σ 3
kl n j is the number concentration of the j th species and σ kl the collision diameter between the k th and l th species. The Kurochkin approach has been recently used by Giovangigli et al. [4,8] to simulate planar transcritical H 2 -O 2 -N 2 flames for which they founded that non-idealities in the EoS and in the transport fluxes have a strong influence on the cold zone of the flame. Additional strategies to model F c may be found in the literature [3], but they will not be used in this study.

Benchmarks configuration and modeling strategies

The case under study is the numerical benchmark proposed by Ruiz et al. [16]: a high-Reynolds-number supercritical flows exhibiting large density gradients is addressed by DNS in a 2D configuration. This test-case complies with relevant conditions for liquid rocket or diesel engines in terms of characteristic size, inlet velocity and temperature, and pressure level. This configuration is sketched in Fig. 1 with a detail for the boundary conditions. Additional information, in particular for the initial condition, is available in [16]. Ruiz et al. simulated this configuration with two numerical codes featuring real-gas thermodynamics and transport properties: AVBP [32] and RAPTOR [START_REF] Oefelein | [END_REF]. The diffusion velocity was modeled by Eq. ( 7), the Soret effect and the non-ideal part of the chemical potential (µ sm l ) were neglected, and both codes used the PR EoS. The models used for the evaluation of transport properties 1 in RAP-TOR and AVBP are summarized in Tab. 1 along with the different cases considered in this study with the solver SiTCom-B. In the benchmark proposed in [16], a set of simulations is performed with different mesh refinements, namely h x , where the subscript corresponds to the number of mesh cells used to discretize the lip height (h), in order 1 Using D mix k from Eq. ( 7) or obtaining the multi-component diffusion coefficients D kl from Eq. ( 5) are equivalent for binary fluids. Accordingly, V c = 0 in Eq. ( 7) for non-reacting cases.

to obtain grid-independent turbulence statistics. Numerical results are provided for mean and root mean square profiles of velocity, temperature and species mass fractions. Statistics are given for a period of 15 flow times (T FT ) after reaching a steady state solution computed after 10 flow times. T FT = 10h/U conv = 0.125 ms. Note that 10 × T FT is sufficient to recover mean profiles [16]. Finally, instantaneous flow fields are provided for the velocity components, oxygen mass fraction (Y O 2 ) and density for both codes RAPTOR and AVBP. In [16], the structures observed are similar for both codes for the case h 250 , and in agreement with literature [35] but the mean flow field streamlines show a small deviation in length and shape of the recirculation zone behind the lip. Nevertheless, both codes exhibit large-scale vortical structures having a characteristic length close to the lip height (h) and evolving as finger-like structures. Similar small-scale structures whose population increases with the mesh resolution are also found. The benchmark proposed by Ruiz et al. [16] is presently enriched by integrating a non-ideal part to d l (see Eq. ( 6)) and by assessing the modeling of binary diffusion coefficients (D bin kl ) through the Kurochkin et al. modeling. These new cases are listed in Tab. 1 as case #1, #2 and #3 and will only be addressed with SiTCom-B. Case #0 is the reference case mimicking the work of Ruiz et al. [16] and this will be the point of comparison of the three solvers. In addition, the splitter-plate configuration is fired (with SiTCom-B) using the chemical mechanism provided by Boivin et al. [36] (N sp = 8, 12 elementary reactions), along with the modeling used in case #0 for diffusion velocity. This reacting case is performed with the mesh h 250 because of computational cost considerations. A challenging case where the diffusion velocity of species k in the mixture follows Eq. ( 5) and ( 6), and diffusion coefficients have multi-component properties, is also presented. To assess this strategy, laminar premixed flamelets are also computed to validate the whole procedure.

Results and discussion

Non-reacting case

The results obtained with SiTCom-B and corresponding to the numerical benchmark proposed by Ruiz et al. (Case #0 in Tab. 1) are now detailed. Typical instantaneous fields of oxygen mass fraction and density are provided in Fig. 2 for the mesh resolution h 500 immediately downstream the LOx post. The overall fluid dynamics is in agreement with the results provided in [16] through a Kelvin-Helmholtz mechanism and this behavior is analogous to the one found for a flow over a backward facing step [37]. However, these eddies are able to penetrate the dense LOx stream entraining fluid portions into the hydrogen stream. Such elongated structures are observed for any case, but more smaller structures are observed if a finer mesh is used. Statistics from SiTCom-Bhave been recorded for the case h 250 following the recommendations given in [16]. Mean and root mean square (rms) temperature, axial and transverse velocities are compared with the results provided by RAP-TOR and AVBP in [16]. In recirculation zone disappears (Fig. 3(b)) and the flow accelerates faster with SiTCom-B because the level of fluctuations is higher at x/h = 1 than for the two other codes. The values of u rms are identical for x/h = 5 (Fig. 3(d)). The negative profiles of transverse velocity (v) in Fig. 4(a) show that the recirculation zone found with SiTCom-B is close to the RAPTOR results. However, the trend is similar to the one of AVBP at x/h = 5 (Fig. 4(b)) since the level of v rms is slightly less with SiTCom-B than with the two other codes (Fig. 4(c) and 4(d)). Finally, the temperature profiles (mean and rms) are in good agreement with RAPTOR (Fig. 5 kl . The impact of the modeling of the diffusion velocity and binary diffusion coefficients (see Tab. 1) is provided in Fig. 6. Using a non-ideal transport to model the diffusion velocity (d l ) changes the velocity profiles. At x/h = 1, the mean axial velocity has a larger negative value and a twice less important mean transverse velocity using d l = X l (∇µ l ) T instead of d l = ∇X l (Eq. ( 6)). Further downstream (x/h = 5), a similar observation can be done. The development of the mixing layer is thus slightly less pronounced with a non-ideal transport than with an ideal one. Also, the transverse velocity, v in Fig. 6(c), spreads over a larger domain, especially through the LOx stream, meaning that the species diffusion is more efficient with a non-ideal transport. The impact on temperature profiles is limited, but using the correction of Kurochkin for high-pressure binary diffusion coefficients yields shaper profiles than with the Takahashi approach.

Reacting case

Supercritical premixed flamelets. Following the work done by Giovangigli and co-workers [8,9] on H 2 /air laminar flames, the impact of non-ideal transport is assessed on stoichiometric H 2 /O 2 laminar premixed flames with SiTCom-B. First of all, a set of simulations was carried out under standard pressure and temperature conditions to validate that the results of SiTCom-B corresponded to the results of the REGATH reference test, in particular during the activation of the multicomponent modeling and Soret effect. In the present study the pressure is set to 10.0 MPa and the temperature of the fresh mixture is T f = 150 K. Supercritical flamelets are first computed using the models of case #0 (Tab. 1) and the CPU cost due to the activation of new or additional models is given in (.). In Fig. 7 (a) and (b), activating the Soret effect for light species (W < 5 g/mol) with case #0 leads to thinner flames with sharper profiles of species mass fractions and density with a diffusion of burnt gases towards the fresh mixture (CPU Soret = 0 %). In Fig. 7 (c) and (d), using Eq. ( 6) in Eq. ( 7) without Soret effects modifies the profiles of Y k and ρ near the dense mixture as in [9], contrary to our observations at 0.1 MPa (CPU X l (∇µ l ) T = +20 %). In Fig. 7 (e) and (f) the multicomponent (i.e. Eq. ( 5) replaces Eq. ( 7)) acts as the Soret effect (CPU D k j = +50 %). With case #0, evaluating D bin kl with the Takahashi method or the Kurochkin correction leads to similar results at 10.0 MPa. However, the second approach is preferred since it has no impact at standard pressure contrary to the Takahashi method. Finally, if the models for non-ideal transport are combined together (acronym NIT), i.e. using the multicomponent approach with Eq. ( 5) and ( 6) along with F c = 1/χ kl in Eq. ( 9), then all the profiles for species mass fractions, density and temperature are modified compared to case #0 (Fig. 7 (g) and (h)). According to these results the previous non-reacting splitter plate configuration (h 250 ) is fired with these two approaches. Only the adiabatic condition of the wall is changed to an isothermal one, fixed to 300 K.

Splitter plate. The instantaneous field of temperature is shown in Fig. 8 when using models for non-ideal transport (NIT). A diffusion flame develops in the mixing layer following the stoichiometric isoline and some pockets of burnt gases, still reacting, can diffuse in the streams of H 2 and LOx. Statistics are collected for 8T FT and the results are shown in Fig. 9 for mean variables at two downstream locations (x/h = 1 and 5). The impact of NIT on the profiles of axial velocity are small contrary to the differences observed for the transverse velocity, especially in the recirculation area where two contra-rotating vortices are found. The temperature profiles show that the mean flame begins to bend in x/h = 5 on the LOx side (y/h < 0) and that the maximum temperature is less than 50 K at x/h = 1 and 100 K at x/h = 5 if the non-ideal transport is modeled. This is confirmed on the profiles of Y H 2 O 2 where a clear difference occurs between the modelings as for supercritical flamelets. These results show that the classical approach used for low pressure flows cannot be used in a high pressure context.

Conclusion

The impact of non-ideal transport modeling has been addressed on 1D supercritical premixed flamelets and on the configuration of the 2D splitter-plate with and without combustion. With this modeling the diffusion velocity of species is described from the gradient of chemical potential coupled to the Peng-Robinson equation of state. A comparison with the classical lowpressure approach, which only uses the gradient of species molar fraction, is also performed. The results show that the non-ideal transport has an impact on the flame structure and consequently on the flame temperature in the case of supercritical flamelets. This behavior is also found in the flame developing right after the splitter-plate, which means that the non-ideal transport could have a stronger impact further downstream. This observation means that such an approach should certainly be taken into account in the case of realistic simulations at high pressure. The use of another EoS (Soave-Redlich-Kwong for ex.) or a dedicated highpressure chemistry remains to be done to quantify the relative difference between classical modeling and nonideal transport. Also, the multi-component approach with Soret effects are found non-negligible for the combustion of H 2 /O 2 . Finally, the development of highpressure models for large-scale simulations can now be achieved through the analysis of this database.

x p = 10 MPaFigure 1 :

 101 Figure 1: Description of the numerical benchmark proposed in [16].

  . The vortices shed from the top corner of the post Eq. (8)[28] [21] ∇X l µ/(ρS c,k ) F c = 1[21] ∇X l Eq. (8)[28] [33, 34] 1 ∇X l Eq. (8)[31] [21] 2 X l (∇µ l ) T Eq. (8)[28] [21] 3 X l (∇µ l ) T Eq. (8)[31] [21]

Table 1 :

 1 Modeling strategies used by the different numerical codes for non-reacting cases. S c,k is the Schmidt number of species k, with: S c,H 2 = 0.3 and S c,O 2 = 1.0.

Figure 2 :

 2 Figure 2: Instantaneous flow field from SiTCom-B for h 500 : (top) oxygen mass fraction, and (bottom) density. In black: LOx stream.

5 Figure 3 :

 53 Figure 3: Transverse cuts of mean (a,b) and rms (c,d) axial velocity in the case of the non-reacting mixing layer.

5 Figure 4 :

 54 Figure 4: Transverse cuts of mean (a,b) and rms (c,d) transverse velocity in the case of the non-reacting mixing layer.

5 Figure 5 :

 55 Figure 5: Transverse cuts of mean (a,b) and rms (c,d) temperature in the case of the non-reacting mixing layer.

  (a) to 5(d)) certainly because the two codes share the same modeling for D mix k and D bin

5 Figure 6 :

 56 Figure 6: Impact of modeling of the diffusion velocity and binary diffusion coefficients (see Tab. 1) on the development of the non-reacting mixing layer.

Figure 7 :

 7 Figure 7: Impact of diffusion velocity modeling on supercritical laminar stoichiometric premixed flames. p = 10.0 MPa and T f = 150 K.

Figure 8 :

 8 Figure 8: Instantaneous field of temperature with stoichiometric isoline (blue) with non-ideal transport (NIT).

Figure 9 :

 9 Figure 9: Transverse cuts in the case of the reacting mixing layer.

Acknowledgments

Umut Guven has been supported during his Ph.D. by the Region Haute-Normandie. Computing resources were provided by CRIANN. J. Oefelein is warmly thanked for providing numerical data from RAPTOR and AVBP.