Joseph Igbokwe

Violaine Nicolas

Adetunji Samuel Adesina
email: asadesina@yahoo.com

Michael Olufemi Awodiran

Elisabeth Fichet-Calvet

Ayodeji Olayemi
email: ayyolayemi@yahoo.com

MOLECULAR TAXONOMY OF CROCIDURA SPECIES (EULIPOTYPHLA: SORICIDAE) IN A KEY BIOGEOGRAPHICAL REGION FOR AFRICAN SHREWS, NIGERIA

Keywords:

The taxonomy of African shrew species is still unresolved due to their conserved morphology.

This also affects knowledge concerning their geographic distribution. In Nigeria, using mitochondrial Cytochrome b gene sequences, we carried out a survey for shrews from the genus Crocidura across various ecological zones to determine taxa that are present and also to assess their phylogeographic structure. Our analyses include 183 specimens collected with Sherman traps from 19 localities around the country. We detected six taxa: Crocidura olivieri lineages II, III and IV, C. hildegardeae, C. jouvenetae, and C. foxi. Among these, C. hildegardeae and C. jouvenetae are reported in Nigeria for the first time. Phylogenetic comparison of our genetic sequences to those generated from other parts of Africa demonstrate that all species in our study, as currently defined, are in need of taxonomic revision. Geographically, Nigeria seems to represent the easternmost boundary for C. olivieri lineage II and C. jouvenetae, and the western distribution limit of C. olivieri lineage IV and C. hildegardeae. The Niger River appears to be the most significant topographical barrier restricting these taxa. This information is vital to preserving the diversity but also managing the epidemiological potential of these small mammals.

Introduction

The shrew genus Crocidura (family Soricidae, order Eulipotyphla [1]) is the most speciose among African mammal genera [2]. These small mammals prey primarily on arthropods, earthworms, and molluscs [3], and are thus ecologically important as secondary consumers [4].

Shrews are relatively abundant, biologically and taxonomically diverse, have a restricted dispersal capacity, and are not subject to hunting pressure. Moreover, because of their short life span, they respond quickly to environmental changes. Thus they have been frequently used as model organisms for phylogeographic studies aimed at understanding factors driving faunal diversification in tropical Africa [START_REF] Jacquet | New status for two African giant forest shrews, Crocidura goliath goliath and C. goliath nimbasilvanus (Mammalia: Soricomorpha), based on molecular and geometic morphometric analyses[END_REF], [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF] and as bioindicators of habitat change [START_REF] Quérouil | ColynChronological prior to both other studies listed here Patterns of diversification in two African forest shrews: Sylvisorex johnstoni and Sylvisorex ollula (Soricidae, Insectivora) in relation to paleo-environmental changes[END_REF], [START_REF] Nicolas | ColynShrew species diversity and abundance in Ziama Biosphere Reserve (Guinea): comparison between primary forest, degraded forest and restoration plots[END_REF], [START_REF] Nicolas | Molecular and morphometric variation in two sibling species of the genus Praomys (Rodentia: Muridae): implications for biogeography[END_REF].

African shrews also bear epidemiological significance because they are increasingly being discovered to be hosts of potentially zoonotic hantaviruses. In Guinea, Crocidura theresae and Crocidura douceti were detected as the reservoirs of Tanganya virus and Bowe virus, respectively [START_REF] Klempa | Hantavirus in African wood mouse, Guinea[END_REF], [START_REF] Gu | YanagiharaComplete genome sequence and molecular phylogeny of a newfound hantavirus harboured by the Doucet's musk shrew (Crocidura douceti) in Guinea[END_REF]. In Ivory Coast, Crocidura obscurior was found to carry Azagny virus [START_REF] Kang | YanagiharaMolecular evolution of Azagny virus, a newfound hantavirus harbored by the West African pygmy shrew (Crocidura obscurior) in Côte d'Ivoire[END_REF]. Within Tanzania, other shrews such as Myosorex zinki and Myosorex geata have been reported to host the Kilimanjaro virus and Uluguru virus respectively [START_REF] Kang | YanagiharaaExpanded host diversity and geographic distribution of Hantaviruses in Sub-Saharan Africa[END_REF].

Identifying Crocidura specimens is notoriously difficult because of the high morphological similarity between species. The ensuing taxonomic uncertainties have resulted in the frequent grouping of taxa in so-called "species complexes" within which the number of species and their geographical distributions are highly debated. This lack of knowledge is a major problem for attempts to delineate appropriate units for biodiversity conservation and for investigations into the distribution ranges of species that may be carriers of zoonotic diseases. Nonetheless, contemporary studies using genetic sequences are beginning to contribute new insight [START_REF] Jacquet | New status for two African giant forest shrews, Crocidura goliath goliath and C. goliath nimbasilvanus (Mammalia: Soricomorpha), based on molecular and geometic morphometric analyses[END_REF], [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF], [START_REF] Jacquet | Forest refugia and riverine barriers promote diversification in the West African pygmy shrew (Crocidura obscurior complex, Soricomorpha)[END_REF], [START_REF] Vogel | DubeyGenetic identity of the critically endangered Wimmer's shrew Crocidura wimmeri[END_REF], [START_REF] Stanley | EsselstynPhylogeny, phylogeography and geographical variation in the Crocidura monax (Soricidae) species complex from the montane islands of Tanzania, with descriptions of three new species[END_REF].

Very little is known about the taxonomic diversity of shrews and their distribution ranges in Nigeria. In 1983, Hutterer and Happold [START_REF] Hutterer | HappoldThe shrews of Nigeria[END_REF] reviewed the bibliographical data and museum specimens available for this country. Since then, almost no work has been carried out on Nigerian shrews, and specimens from this country are only exceptionally included in recent regional phylogeographic or phylogenetic studies. Up to now, the few published shrew genetic sequences from Nigeria have been generated from a single locality in the southwestern part of the country, Ile Ife [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF], [START_REF] Igbokwe | AwopetuChromosomal analysis of small mammals from Southwestern Nigeria[END_REF]. In a recent small mammal survey across vast portions of Nigeria, Olayemi et al. [START_REF] Olayemi | Small mammal diversity and dynamics within Nigeria, with emphasis on reservoirs of the Lassa virus[END_REF] listed all their shrew specimens as Crocidura spp. in order to avoid taxonomic misinterpretation.

Nigeria possesses topographical features such as major rivers already shown to be involved in the speciation of other small mammals [START_REF] Olayemi | VerheyenSmall mammals, morphology and molecules: tale-bearing tenants of the Nigerian southwestern forest block[END_REF], [START_REF] Olayemi | Arenavirus diversity and phylogeography of Mastomys natalensis rodents, Nigeria[END_REF]. Therefore, this geographic region not only represents a significant knowledge gap, it also offers a distinct opportunity to contribute to earlier studies on the molecular biogeography of Afrotropical shrews. For instance, the distribution ranges of certain Crocidura clades described in Jacquet et al. [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF] that extend only up to the west or only to the east of Nigeria appear to have their boundaries within the country. Furthermore, high altitude could also potentially affect species distribution. That the Jos plateau is home to endemics as the Nigerian Gerbil Taterillus nigeriae, the Ochre Mole-rat Cryptomys ochraceocinereus and the Klipspringer Oreotragus [START_REF]HappoldThe mammals of Nigeria[END_REF] illustrates this point. Another example is the unique montane forest ecosystem on the Mambilla plateau, where a new shrew species Sylvisorex corbeti was described [START_REF] Hutterer | MontermannA large new species of Sylvisorex (Mammalia: Soricidae) from Nigeria and the first record of Sylvisorex ollula from the country[END_REF] and collection records were made for the first time in Nigeria of other shrews S. camerunensis, S. ollula, and Crocidura attila [START_REF] Hutterer | NikolausSmall mammals from forest islands of eastern Nigeria and adjacent Cameroun, with systematical and biogeographical notes[END_REF]. Therefore, geographical distribution records, including those for Crocidura shrews, need to be adequately described.

Our objectives in the present investigation are, using mitochondrial gene sequences, to survey the Crocidura taxa present within Nigeria and to describe their distribution according to main rivers and ecological zonation.

Materials and methods

Specimen collection and sequencing

Using Sherman live-traps, the 183 shrew specimens included in this study were collected during 2011-2017 in 19 localities around Nigeria. These localities are distributed across key ecological zones such as the western and eastern flanks of both the Niger and Benue Rivers and along the Guinea savanna and rainforest vegetative belts (Fig. 1). Jos (Jos Plateau, 1280 m above sea level; locality 19) and Ngel Nyaki (Mambilla Plateau, 1650 m above sea level; locality 15) are situated on highlands where several endemic and rare small mammal species have been recorded [START_REF]HappoldThe mammals of Nigeria[END_REF], [START_REF] Hutterer | NikolausSmall mammals from forest islands of eastern Nigeria and adjacent Cameroun, with systematical and biogeographical notes[END_REF]. During the period of the study, each locality was visited at least once in a session of three trap-nights, but certain localities were visited multiply. Traps were set in diverse habitats: inside houses (in kitchens, bedrooms and food storage areas), outdoors in domestic surroundings (including gardens and other sites close to the houses) and outdoors in wild vegetation (e.g., forest, savanna or river bank, depending on the locality). A broad designation of the habitat in which each specimen was captured appears in Appendix A. Our capture methods are described in detail in Olayemi et al. [START_REF] Olayemi | Small mammal diversity and dynamics within Nigeria, with emphasis on reservoirs of the Lassa virus[END_REF], with all voucher specimens preserved in ethanol at the Natural History Museum, Obafemi Awolowo University, Nigeria. Triangles designate localities (15 & 19) within highland. Broken lines separate vegetative zones (adapted from Federal Ministry of Environment, Nigeria [START_REF]NigeriaNational Biodiversity strategy and action Plan 2016-2020[END_REF]). It must be noted that patches of derived savanna are scattered over the area classed under rain forest.

No experiments were carried out on living animals. Kidneys were dissected from euthanized specimens and preserved in ethanol. Total DNA was extracted from the kidneys using the Nucleospin Tissue kit (Machery Nagel, Düren, Germany) and the DNeasy blood and tissue kit (QIAGEN, Valencia CA, USA). The cytochrome b gene (Cyt b) was amplified using the following primers: L7 (ACC AAT GAC ATG AAA AAT CAT CGT T) and H15915 (TCT CCA TTT CTG GTT TAC AAG AC) [START_REF] Ducroz | GranjonAn assessment of the systematics of Arvicanthine rodents using mitochondrial DNA sequences: evolutionary and biogeographical implications[END_REF]. Initial denaturation was carried out at 95 °C for 3 min, followed by 35 cycles of 94 °C for 30 s, 52 °C for 40 s, and 72 °C for 90 s. Amplicons were Sanger-sequenced and submitted to GenBank with accession numbers from MH996698 to MH996882 (Appendix A).

Phylogenetic analyses

The obtained sequences were compared to reference sequences in GenBank through a standard Nucleotide BLAST analysis (https://blast.ncbi.nlm.nih.gov/Blast.cgi?PAGE_TYPE=BlastSearch). As explained in the introductive section, the taxonomy of many Crocidura species is poorly known. Thus, the aim of our BLAST analysis was simply to be able to attribute each sequence to a given species complex. For each species complex, we then compared our sequences to all relevant published data and/or to unpublished sequences obtained by our team in recent years (details in Appendices B-E). Relationships among sequences were estimated by constructing phylogenetic trees using Neighbour Joining (NJ) phylogenetic analyses. NJ analyses were performed with PAUP 4b10 [START_REF]SwoffordPhylogenetic analysis using parsimony PAUP 4[END_REF] using the K2P genetic distance. Bootstrap analysis (100 replicates) was used to estimate the robustness of the internal nodes. Note that the aim of this study was not to resolve the phylogeny or taxonomy of the analysed groups, but to provide new information about the distribution ranges of well-differentiated evolutionary lineages using the classical barcoding approach based on mitochondrial sequences in combination with available integrative taxonomy data in the selected groups.

Results and discussion

Notes on individual taxa

C. olivieri species complex Lesson, 1827

The 149 sequences attributed to the C. olivieri species complex based on the BLAST analysis were compared to those published by Jacquet et al. [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF]. These authors highlighted the need for taxonomic revision of this complex: the species C. olivieri is polyphyletic and divided into five 2). In Nigeria specimens of clade II were only captured west of the Niger River, which seems to represent the easternmost limit of its distribution range. Specimens of this clade were captured both in the Guinea savanna and rainforest zones. We record for the first time the presence of clade IV in Nigeria. This clade was only captured in the Guinea savanna east of the Niger River, which seems to represent the westernmost limits of its geographical distribution. According to Jacquet et al. [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF], clade III is widely distributed from Senegal to Cameroon and Chad, but no specimen from Nigeria was previously sequenced. Our specimens fall within the genetic variability already recorded for that species. Clade III specimens were only captured in the

C. hildegardeae species complex Thomas, 1904

One specimen (NGE777) was attributed to the C. hildegardeae complex based on our BLAST analysis (88-89% identity with C. hildegardeae from Tanzania and Kenya recently published by Stanley et al. [START_REF] Stanley | EsselstynPhylogeny, phylogeography and geographical variation in the Crocidura monax (Soricidae) species complex from the montane islands of Tanzania, with descriptions of three new species[END_REF]). This species complex is in need for revision. Based on 16S mitochondrial sequences, Quérouil et al. [START_REF] Quérouil | A molecular insight into the systematics of African Crocidura (Crocidurinae, soricidae) using 16sRNA sequences[END_REF] and Dubey et al. [START_REF] Dubey | VogelBiogeographic origin and radiation of the Old World crocidurine shrews (Mammalia: Soricidae) inferred from mitochondrial and nuclear genes[END_REF] showed that C. hildegardeae from Burundi, Gabon and Republic of Congo and C. denti from Central African Republic, Cameroun, and Democratic Republic of Congo cluster together and do not form separate genetic clades. In our NJ tree, we included all C. hildegardeae sequences available in GenBank [START_REF] Sabuni | BryjaBiogeographic implications of small mammals from Northern Highlands in Tanzania with first data from the volcanic Mount Kitumbeine[END_REF] as well as unpublished C. hildegardeae and C. denti from Central Africa, and several representatives of the C. poensis species complex, which is known as the sister clade of the complex C. hildegardeae -C. denti [START_REF] Dubey | VogelBiogeographic origin and radiation of the Old World crocidurine shrews (Mammalia: Soricidae) inferred from mitochondrial and nuclear genes[END_REF]. Our analyses confirm that C. hildegardeae and C. denti are closely related and do not form two distinct monophyletic groups (Fig. 3). Moreover, within C. hildegardeae -C. denti, two main clades can be identified: one grouping specimens from Central Africa (Nigeria, Gabon, Congo Republic and Central African Republic) and one grouping specimens from East Africa (Tanzania, Burundi, Kenya). This analysis confirms the urgent need for an integrative taxonomic revision of C. hildegardeae and C. denti. Neither C. hildegardeae nor C. denti were previously known to occur in Nigeria. Nine specimens were identified as C. cf. jouvenetae (93% identity with C. cf. jouvenetae published by Vogel et al. [START_REF] Vogel | DubeyGenetic identity of the critically endangered Wimmer's shrew Crocidura wimmeri[END_REF] based on the BLAST analysis). Crocidura jouvenetae was referred to as a subspecies of C. crossei [START_REF]The mammals of Africa: an identification manual[END_REF], [START_REF]Mammal species of the world (Second Edition)[END_REF], [START_REF] Grubb | HillMammals of Ghana Sierra Leone and the Gambia[END_REF]. However, Hutterer [START_REF]Mammal species of the world: a taxonomic and geographic reference (Third Edition)[END_REF] considers the larger-sized jouvenetae to represent a separate species. According to Happold [2] C. jouvenetae is found in the rainforest biotic zone of West Africa, in southern Guinea, Liberia, and southern Ivory Coast, and it may also occur in Sierra Leone. Crocidura crossei has a larger distribution: it is known from the rainforest biotic zone, northern rainforestsavanna mosaic and Guinea savanna biotic zone from Guinea and Sierra Leone to western Cameroon. We compared our sequences to all previously published C. crossei and C. jouvenetae sequences [START_REF] Vogel | DubeyGenetic identity of the critically endangered Wimmer's shrew Crocidura wimmeri[END_REF], [START_REF] Dubey | VogelBiogeographic origin and radiation of the Old World crocidurine shrews (Mammalia: Soricidae) inferred from mitochondrial and nuclear genes[END_REF], [START_REF] Jacquet | molecular taxonomy, and exploration of the diversity of shrews (Soricomorpha: Soricidae) on Mount Nimba (Guinea)[END_REF] and Kang et al.

(unpublished sequences available in Genbank) (Fig. 4). Our results confirm that the complex C. jouvenetae-crossei is in urgent need for integrative taxonomic revision, none of these species being monophyletic. All specimens from Nigeria cluster together with a strong bootstrap support, and they form the sister clade composed of all specimens from Guinea and Ivory Coast. All Nigerian specimens occur in the rainforest zone (Fig. 1).

C. foxi Dollman, 1915

Twenty-six specimens were identified as closely related (99% identity) to two specimens from Burkina Faso available in Genbank (DQ305278 and DQ521043) (Fig. 5). These two specimens are identified as "Crocidura theresae" in GenBank and original publications [START_REF] Dubey | VogelUse of phylogeny to resolve the taxonomy of the widespread and highly polymorphic African giant shrews (Crocidura olivieri group, Crocidurinae, Mammalia)[END_REF], [START_REF] Dubey | VohralikCytogenetic and molecular relationships between Zarudny's rock shrew (Crocidura zarudnyi; mammalia: soricomorpha) and Eurasian taxa[END_REF], but they were later called Crocidura cf. foxi in subsequent studies [START_REF] Vogel | DubeyGenetic identity of the critically endangered Wimmer's shrew Crocidura wimmeri[END_REF], [START_REF] Quérouil | A molecular insight into the systematics of African Crocidura (Crocidurinae, soricidae) using 16sRNA sequences[END_REF]. Crocidura foxi and C. theresae both belong to the C. poensis complex, which was recently reviewed by Nicolas et al. [START_REF] Nicolas | Multi-locus phylogeny of the Crocidura poensis species complex (Mammalia, Soricomorpha): influences of the paleoclimate on its diversification and evolution[END_REF]. The comparison of our sequences with those from Nicolas et al. allowed us to unambiguously identify the Nigerian specimens as C. foxi. This species is widespread in Nigeria:

we caught it to the west and east of both the Niger and Benue Rivers, and both within the Guinea savanna and the rainforest (Fig. 1).

Biogeographical summary

The number of shrew taxa recorded in this study is small [START_REF] Jacquet | Phylogeography and evolutionary history of the Crocidura olivieri complex (Mammalia, Soricomorpha): from a forest origin to broad ecological expansion across Africa[END_REF] compared to what has been described for Nigeria in the past (24 species in Hutterer and Happold [START_REF] Hutterer | HappoldThe shrews of Nigeria[END_REF], for instance). A reason for our low diversity could be the fact that we used only Sherman traps, which possibly attracts only certain taxa. Surveys in Gabon [START_REF] Nicolas | ColynRelative efficiency of three types of small mammal traps in an African rainforest Belg[END_REF] and in the Congo Democratic Republic [START_REF] Gambalemoke | Shrew trap efficiency: experience from primary forest, secondary forest, old fallow land and old palm plantation in the Congo River basin (Kisangani, Democratic Republic of Congo) Mammalia[END_REF] demonstrated that pitfall traps are more efficient than Sherman traps for capturing shrews. Also, increasing our effort beyond the three trap-nights we spent in some localities might have yielded more variety. Nevertheless, our survey reports the presence of two taxa detected within Nigeria for the first time: C. jouvenetae and C. hildegardeae.

As could be expected, the Niger River appears to represent a significant physical barrier for several taxa, limiting C. olivieri lineage II and C. jouvenetae on its right bank to western Nigeria (and by extension, West Africa) and C. olivieri lineages III, IV, and C. hildegardeae on its left bank to central and eastern Nigeria (expanding into northern, central and eastern Africa) (Fig. 6).

Happold [START_REF]HappoldThe mammals of Nigeria[END_REF] reported 13 mammal species within Nigeria that occurred only on one side of the Niger River, but not on the other. The results of this study also show that the Benue River and/or the drier conditions towards the Sudan savanna in the North might play a combined role with the Niger River in limiting C. olivieri lineage IV and C. hildegardeae to eastern Nigeria. Elevated topography (represented by the Jos and Mambilla plateaus) apparently does not influence the distribution ranges of the taxa encountered in this study. None of the species was endemic to the Jos plateau. The only C. hildegardeae specimen from Nigeria was found in montane forest within the Mambilla plateau, but specimens from Gabon, Republic of Congo, and Central African Republic were recorded in the lowlands [START_REF] Nicolas | Multi-locus phylogeny of the Crocidura poensis species complex (Mammalia, Soricomorpha): influences of the paleoclimate on its diversification and evolution[END_REF].

With regard to habitat, specimens from this study belonging to the C. olivieri lineages and C. foxi were captured indoors, but also outdoors, in a wide range of domestic and wild vegetations (including lowland forest, savanna grassland, banana plants and fallow farmland; see Appendix).

Crocidura jouvenetae, on the other hand, was collected outdoors in domestic and wild vegetation (including lowland forest and grassland in forest clearings), while C. hildegardeae was captured only in wild vegetation (montane forest). Many Crocidura taxa have been described as commensal [2]. In Ekpoma, one of the localities sampled in this study, Olayemi et al. [START_REF] Olayemi | Widespread arenavirus occurrence and seroprevalence in small mammals, Nigeria[END_REF] detected two Crocidura specimens (later identified by Cyt b sequencing as C. olivieri and C. jouvenetae) with antibodies to the Lassa virus, which causes a deadly viral haemorrhagic fever in humans. They concluded that this was probably the result of a spill-over infection from proximity to the rodent Mastomys natalensis, which is known as the natural reservoir of this virus. These animals are usually found in the same peridomestic habitat. Again, this commensality along with the recent detection of hantaviruses [START_REF] Klempa | Hantavirus in African wood mouse, Guinea[END_REF], [START_REF] Gu | YanagiharaComplete genome sequence and molecular phylogeny of a newfound hantavirus harboured by the Doucet's musk shrew (Crocidura douceti) in Guinea[END_REF], [START_REF] Kang | YanagiharaMolecular evolution of Azagny virus, a newfound hantavirus harbored by the West African pygmy shrew (Crocidura obscurior) in Côte d'Ivoire[END_REF], [START_REF] Kang | YanagiharaaExpanded host diversity and geographic distribution of Hantaviruses in Sub-Saharan Africa[END_REF] and bacteria [START_REF] Halliday | Prevalence and diversity of small mammal-associated Bartonella species in rural and urban Kenya[END_REF] in Crocidura shrews highlights their zoonotic potential.

Overall our findings, like other recent studies employing molecular data, support the need for taxonomic revision of several taxa within the genus Crocidura. In addition, our survey demonstrates that Nigeria represents the geographical boundary of many Crocidura shrews, and is a region that must not be overlooked in the conservation and management of these animals.

Fig. 1 .

 1 Fig. 1. Geographic distribution of Crocidura species and lineages resolved in this study. To the left is a map of Africa, with Nigeria in inset. Colours within the circles indicate the presence of each taxon (but not its relative abundance). Numbers below the circles represent localities as listed: 1) Bwen, 2) Gwanara, 3) Abagboro, 4) Kako, 5) Okeluse, 6) Ifon, 7) Eguare Egoro, 8) Ekpoma, 9) Ebudin, 10) Opoji, 11) Okhuesan, 12) Ndubia, 13) Abakaliki, 14) Onmba Abena, 15) Ngel Nyaki, 16) Mayo Ranewo, 17) Lafia, 18) Obi, 19) Jos. Localities in close proximity (7,8,9) are grouped under the same circle. Geographical coordinates are listed in the Appendix.

  geographical clades showing allopatric or parapatric distributions, while specimens of C. viaria and C. fulvastra form a single genetic clade. Our Nigerian specimens appear in three different clades: C. olivieri clade II, C. olivieri clade IV and the C. viaria-fulvastra clade III (Fig. 1, Fig.

  Guinea savanna zone. According to Hutterer and Happold [17] C. viaria and C. fulvastra can be differentiated by ventral pelage and tail coloration. Based on these external characters, all our specimens from Nigeria fit more closely with C. fulvastra.

Fig. 2 .

 2 Fig. 2. Neighbour joining tree of the C. olivieri species complex based on 1140 bp of the Cyt b gene including the sequences used by Jacquet et al. [6] in their Fig. 2. a: Condensed tree displaying various taxa within the species complex; b: C. olivieri clade II, with Nigerian sequences encased in blue; c: C. viaria + C, fulvastra clade III, with Nigerian sequences encased in red; d: C. olivieri clade IV, with Nigerian sequences encased in yellow.

Fig. 3 .

 3 Fig. 3. Neighbour joining tree based on Cyt b sequences (1069 bp) of C. denti and C. hildegardeae specimens. Representatives of the C. poensis species complex (C. theresae, C. grandiceps, C. buettikoferi, C. wimmeri, C. turba, C. poensis, C. foxi) were also included in this analysis, and C. luna, C. lamottei and C. russula were used as outgroups. The specimen from Nigeria (NGE777) is indicated by an arrow.

Fig. 4 .

 4 Fig. 4. Neighbour joining tree based on all available Cyt b sequences (402 bp) of C. jouvenetae and C. crossei. The species C. lusitania and C. fuscomurina were used as outgroups. Specimens from Nigeria are encased in purple.

Fig. 5 .

 5 Fig. 5. Neighbour joining tree of the C. poensis species complex (1063 bp of the Cyt b gene), with a special emphasis on the species C. foxi. a: Condensed tree displaying various taxa within the species complex; b: C foxi, with sequences from Nigeria encased in green.

Fig. 6 .

 6 Fig. 6. Updated geographical distribution for Crocidura species detected in this study from Nigeria relative to molecular data compiled across Africa by Jacquet et al. [6] (to the left) and Nicolas et al. [38] (to the right).

Acknowledgements

We would like to thank Godwin Ehielu and Destiny Aigbomian for their immense assistance in the field. We are also grateful to various persons and institutions that facilitated our trapping around the country including Mallam Isa in Gwanara and Bwen, Drs Shiiwua Manu and Yahkat Barshep of the AP Levenetis Ornithology Research Institute (APLORI), Jos; and Drs Liman Usman and Adamu Ibrahim from the Nasarawa State Ministry of Health.

Funding

Fieldwork within Nigeria and part of the laboratory analyses were supported by the European Foundation Initiative for African Research into Neglected Tropical Diseases (EFINTD, grants 1/85/022 & 89 540); and the German Research Foundation (DFG, grant GU883/4-1). Further analyses were funded by the Belgian Science Policy (BELSPO). The funders had no involvement in the design, collection and interpretation of the data.

Disclosure of interest

The authors declare that they have no competing interest.

Supplementary data


Marie Saint-Sevin

Vincent Begoc
email: vincent.begoc@icam.fr

Sébastien Briot

Abdelhamid Chriette

Isabelle Fantoni

Vincent Bégoc

Design and Optimization of a Multi-drone Robot for Grasping and Manipulation of Large-size Objects

Keywords: Flying robot, grasping, manipulation, underactuated system, optimization, manipulability

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

Introduction

Researchers communities have shown an increasing interest in new uses of Unmanned Aerial Vehicles (UAVs), especially for interactions with the environment. Recent works have been devoted to drones able to grasp objects: [START_REF] Welch | Lightweight, low-cost, compliant grasper for UAV-based pick-and-place operations[END_REF][START_REF] Mellinger | Cooperative grasping and transport using multiple quadrotors[END_REF][START_REF] Pounds | Grasping from the air: Hovering capture and load stability[END_REF][START_REF] Orsag | Modeling and control of MM-UAV: Mobile manipulating unmanned aerial vehicle[END_REF] introduced UAVs under which a gripper was mounted. A drawback of this kind of solution is that it allows for very low dexterity during the manipulation process.

Further works explored solutions where a serial manipulator, equipped with a gripper, is attached to a UAV [START_REF] Thomas | Avian-inspired grasping for quadrotor micro UAVs[END_REF][START_REF] Kondak | Aerial manipulation robot composed of an autonomous helicopter and a 7 degrees of freedom industrial manipulator[END_REF]. However, such robots present a low payload and a reduced energy autonomy due to respectively the weight and the energy consumption of the embedded serial manipulator. To overcome those limitations, other works have explored the collaboration of several drones associated with cables [START_REF] Goodarzi | Stabilization of a rigid body payload with multiple cooperative quadrotors[END_REF][START_REF] Manubens | A motion planning approach to 6-d manipulation with aerial towed-cable systems[END_REF] or with rigid bodies [START_REF] Lee | Geometric control of multiple quadrotor UAVs transporting a cablesuspended rigid body[END_REF][START_REF] Six | Dynamic modeling and trajectory tracking controller of a novel flying parallel robot[END_REF]. However, these solutions have been designed for manipulation tasks and not for grasping.

[2] proposed a system named "the flying hand" which is basically a fleet of drones coming into contact with an object in order to manipulate it, each drone being considered as a finger. However, this system can not ensure the security of the grasp since it requires a very precise and robust control of each drone to continuously exert a force by each finger on the object, and the stability depends on contact friction between fingers and the object which can change with humidity for example.

In the present paper, we introduce a new aerial mechanism devoted to grasping and manipulation. This mechanism is basically an aerial hand in which the motors for closing the fingers have been replaced by drones. Fingers are underactuated so that it can automatically adapt to the object shape and size without adding actuators which burden the structure, decrease energetic autonomy and require complex control algorithms [START_REF] Birglen | Optimal design of 2-phalanx underactuated fingers[END_REF]. Our new flying manipulator ensures grasp stability, thanks to the use of non-backdrivable mechanisms which permit to achieve form-closure grasps [START_REF] Krut | Extension of the form-closure property to underactuated hands[END_REF]. Form-closure does not rely on friction forces and thus, requires no energy for the gripping task during the flight. In what follows, we introduce the robot architecture and its optimal design.

Presentation of the robot architecture

The robot is composed of a frame, four quadrotors and four two-phalanx planar fingers. In the proposed solution, all finger plane-of-motions are parallel (Fig. 1a). A four-bar mechanism (Fig. 2) is used to underactuate the fingers so that they can automatically adapt to the shape and size of the object and be less sensitive to positioning errors of the robot relative to the object to grasp. In Fig. 2(a), the finger is in its initial configuration and behaves as a rigid body. The bar (1) rotates until the proximal phalanx (3) comes into contact with the object Fig. 2: Closing sequence of a two-phalanx finger with a four-bar linkage transmission [START_REF] Birglen | Optimal design of 2-phalanx underactuated fingers[END_REF] (actuation bar in orange).

(Fig. 2(b)). The second phalanx (4) begins its rotation as soon as the torque produced by the actuation bar gets larger than the torque exerted by the spring, until it finally reaches the object (Fig. 2(c)).

The opening/closing motion of each finger is driven by the bar (1) which is actuated by a quadrotor linked to the frame by a revolute joint (Fig. 1b). This degree of freedom enables the drone to use its yaw motion to drive a nonbackdrivable worm-gear mechanism whose pulley is fixed to the actuation bar of the finger. As mentionned in [START_REF] Krut | Extension of the form-closure property to underactuated hands[END_REF], a two-finger planar gripper requires at least two unilateral mechanisms to produce 1st-order form-closed grasps of a cylindrical object in the plane (rotation of the object is not considered). Worm-gears are chosen with opposite hand (left and right) so that drones must turn in the opposite direction to close fingers during the grasping process. The resulting torque exerted on the frame along the vertical axis is null.

Since a quadrotor is underactuated (four propellers operate in a six-dimensional space), we introduce a tilting angle between both quadrotors in order to obtain a fully actuated mechanism in the plane. This allows the full manipulation of the grasped object in a vertical plane (Fig. 3a).

Optimization of the manipulability

In this section, we consider a planar manipulator actuated by two drones as presented in Fig. 3a and we optimize the position and orientation of drones with respect to the frame in order to maximize its capacity to manipulate an object in the plane. The aim of this study is to ensure that drones are able to exert forces on the frame along both directions of the plane. In our case, rotational motion is not needed, however, the manipulator must resist to disturbance torque about the orthogonal axis. The grasped object is supposed to be fixed relatively to the frame.

In [START_REF] Krut | Force performance indexes for parallel mechanisms with actuation redundancy, especially for parallel wire-driven manipulators[END_REF], the author introduces a force performance index: the maximum isotropic operational force, namely the maximal force the manipulator can exert in any direction of its operational space. It consists in computing the radius of the largest circle included in the convex hull of admissible operational forces. This latter is Fig. 3: Manipulability study obtained by mapping the admissible actuator space in the operational space by using the expressions given in [START_REF] Krut | Force performance indexes for parallel mechanisms with actuation redundancy, especially for parallel wire-driven manipulators[END_REF].

The admissible actuator space represents all realistic combinations of actuator forces. For the sake of simplicity, the four propellers of a quadrotor are modeled with two forces. The admissible actuator space is thus a 4-dimensional cube whose boundaries are defined by F min < F i < F max , i ∈ {1, ..., 4} derived from the propellers capabilities. Considering that each propeller can deliver a maximal thrust force of 5N, we obtain 0 < F i < 10 N, the admissible operational force convex hull represented in Fig. 3b can thus be obtained by using the expressions given in [START_REF] Krut | Force performance indexes for parallel mechanisms with actuation redundancy, especially for parallel wire-driven manipulators[END_REF].

Our force performance index is r, the radius of the largest circle included in the three polygons defined by the intersection of the operational force space with the three planes defined by M z = -1 Nm, M z = 0 Nm and M z = 1 Nm (chosen as limit values for the maximal accepted disturbance torque; see in Fig. 3b the convex hull obtained when using parameters of Tab. 1). Taking into account the gravity field of norm g, the circle is centered on (F x , F y ) = (0, m g), with m = 2.5 kg the weight of the system {quadrotors + gripper + object}.

The geometrical parameters of the manipulator's frame are α (characterizing the orientation of the propellers), h (the distance to the object center) and d (the distance between the two quadrotors) (Fig. 3a). α and h are the parameters to optimize. d = 770 mm is an input parameter set to, what authors consider, the minimal distance between the quadrotors in order to avoid aerodynamic disturbance.

The optimization process consists in varying α and h in a large interval (with small increments for high precision). For each couple of parameters, the performance index is calculated and we thus obtain the graphic presented in Fig. 4. Note that the operational forces are calculated at the object gravity center G, for a 300 mm radius cylindrical object. The best couple of design parameters based on the study of the Fig. 4 is specified in Tab. 1, with minimal h so as to reduce the mass of the manipulator. It leads to a force capacity of F x = F y = ±4.84 N for manipulating the aerial robot. Table 1: Optimization for manipulability: parameters and results

Form-closure optimization

Even if underactuated hands permit to produce enveloping grasp that should be, a priori, more robust than a two-contact grasp, in some configurations, such underactuated hands exhibit aberrant behavior leading to the ejection of the object [START_REF] Birglen | Optimal design of 2-phalanx underactuated fingers[END_REF]. To avoid this phenomenon, it is necessary to optimize the geometry of the gripper at the design stage.

In [START_REF] Krut | Extension of the form-closure property to underactuated hands[END_REF], the authors present a method to analyze the form-closure of an underactuated grasp. This type of stability is a purely geometrical property and thus, does not depend on actuators capability, friction forces, nor on the magnitude of external disturbances. Form-closure is thus an ideal property to attain with a flying gripper since it guarantees that the object will not fall.

Form-closure analysis

In [START_REF] Krut | Extension of the form-closure property to underactuated hands[END_REF], form-closure is reformulated for underactuated grasps as follows: "A grasp is said to be form-closed if, and only if, for any variation of the configuration of the grasp at least one of the unilateral kinematic constraints is violated." A 1st-order modeling of the relations between the configuration of the grasp and the unilateral kinematic constraints is given by matrix M defined as:

qc = M ẇ where M =   P -J 0 K 0 1 0   (1) with:
-qc is the unilateral constraints vector, including the contact constraints (between the object, the four phalanges and the palm) and the unilateral constraints imposed by worm-gear mechanisms. Each component of this vector has to be positive or null otherwise the corresponding constraint is violated. -ẇ = [ uT , θT ] T with u the vector of operational velocities of the object and θ the vector of joint velocities of the hand, -P is the projection matrix, J the hand Jacobian matrix and K the unidirectional mechanisms constraints matrix. Their expressions are given in [START_REF] Krut | Extension of the form-closure property to underactuated hands[END_REF]. The method presented in [START_REF] Krut | Extension of the form-closure property to underactuated hands[END_REF] is based on the study of the convex hull of matrix M. A grasp is first-order form-closed if and only if conv(M) strictly contains the origin of the configuration space of the grasp. Using this method shows us that form-closure depends on the position of the grasped object as depicted in Fig. 5a and Fig. 5b. In the same manner, form-closure also depends on the geometric parameters of the fingers depicted in Fig. 5c.

Optimization method

Since form-closure is solely a qualitative property, we introduce a quantitative performance index which characterizes the grasp robustness. This index corresponds to the maximum offset of the object's position δ x for which the grasp is form-closed (Fig. 6). It allows the system to overcome UAVs positioning errors.

Here, the pulley position is an input value deduced from the optimization made in Sec. 3. Concerning the grasped object, we consider two circles with different diameters (200 mm and 300 mm). The parameters to optimize completely define the geometry of the gripper. They are presented in Fig. 6.

In order to find the best values of these design parameters, we define a large range of values for each of them and test all potential combinations. For each set of parameters, δ x is increased incrementally from 0 to a maximum value δ xmax that still guarantees form-closure of the grasp. The following design constraints Fig. 7: Prototype made in plywood must be verified: no collision between distal phalanges, no collision between the actuating bar and the quadrotors and that the bars b 1 and c 1 should not be parallel in order to avoid singular configurations (Fig. 6). The best set of parameters is thus the one for which δ xmax is maximum. Final results are shown in Tab. 2. Table 2: Result of form-closure optimization A first prototype of the planar mechanism has been realized in 5 mm poplar plywood with a laser-cutting machine (Trotec Speedy 300) (Fig. 7). The finger's weight is about 1 kg and should be further reduced in order to increase the payload. This prototype is a first step before machining a 3D manipulator and it will be used to test grasp planning and control algorithms.

Parameters a[mm] b[mm] l1[mm] l2[mm] a1[mm]c1[mm] b1[mm] ψ[ • ] δxmax[mm]

Conclusion and future work

This paper presents a new flying manipulator equipped with four underactuated fingers and actuated by four quadrotors. An optimization method is proposed to determine the position and orientation of quadrotors for a two-finger planar mechanism in order to maximize its manipulability. A second optimization method is introduced to determine the geometric parameters of the underactuated finger, so as to maximize the capability of the gripper to produce first-order form-closed grasps and its robustness to positioning error of the UAV relative to the object. A first prototype of a planar mechanism was then presented.

Further works will consist in modeling the dynamics of the system and controlling it during the successive flying tasks (before contacting the object, while grasping and manipulation in free space). A study on the grasp planning for different shapes of object is contemplated too.

Fig. 1 :

 1 Fig. 1: Flying manipulator presentation

  (a) Geometric parameters and forces of the manipulator (b) Admissible operational force space for the optimal case

Fig. 4 :

 4 Fig. 4: Graphic resulting from the manipulability optimization

Fig. 5 :Fig. 6 :

 56 Fig. 5: Form-closure evolution.

Acknowledgement

We would like to thank the Icam for its financial support in the prototype manufacture.


M Bedel

A Sanitas

M El Mansori

Geometrical effects on filling dynamics in low pressure casting of light alloys

Keywords: low pressure casting, aluminum alloys, mold filling, fluid flow oscillations, oxide inclusions

In aluminum low-pressure sand casting process, filling oscillations are observed when the metal front reaches a section change in a part. The effect of geometry on the filling oscillations is primary considered experimentally, including both mold cavity and filling system geometries. To highlight the geometric parameters impacting the oscillations, the pressurized melt flow is secondly studied numerically and analytically. A new analytical model of oscillation is developed to quantitatively predict the oscillations. It links the resulting filling velocity to both the low-pressure casting parameters and the mold cavity geometry. Considering oxides inclusion criterion from casting literature, new rules to avoid bi-films defects are recommended for making reliable low-pressure castings.

Nomenclature

Introduction

When considering sand mold casting, the part quality depends mainly on the filling velocity. Indeed, if too slow, the filling will not be complete before solidification occurs, inducing misrun [START_REF] Campbell | Castings principles : the new metallurgy of cast metals[END_REF]. Moreover, filling too slowly may damage the sand mold which can be damaged if submitted to high temperatures for a long time. This leads to veining, scabs, or even mold erosion before the filling completion, directly impacting the final part mechanical properties [START_REF] Campbell | Castings principles : the new metallurgy of cast metals[END_REF]. Therefore, there is an incentive to fill a mold as fast as possible. However, a too rapid filling flow is known to induce higher oxide content in the melt, which deeply reduces the final mechanical strength of the part. Melt surface turbulence may lead to surface oxide film folding over [START_REF] Campbell | Castings principles : the new metallurgy of cast metals[END_REF]. The formed bi-films are then entrained into the metal bulk, acting later as cracks [START_REF] Campbell | Entrainment defects[END_REF].

To limit the entrainment of those oxides, Campbell proposed a maximal velocity criterion : it only depends on the melt properties and gives a maximal velocity of 0.5 m.s -1 in the case of aluminum alloys [START_REF] Campbell | Castings principles : the new metallurgy of cast metals[END_REF]. Runyoro et al. confirmed this criterion by experimentally studying the impact of metal ingate velocity on the final part bending properties, in the case of gravity casting of aluminum plates [START_REF] Runyoro | Critical gate velocities for film-forming casting alloys: a basis for process specification[END_REF].

A clear fall-off in bend strength was observed when considering in-gate entry velocities larger than 0.5 m.s -1 ; the melt rising as a jet could fall back, incorporating the oxides into the bulk. However, filling velocity was not the only oxide entrainment criterion ever considered. Kuo et al. proposed to consider the Reynolds number as an oxide entrainment criterion instead [START_REF] Kuo | Development of an interactive simulation system for the determination of the pressure-time relationship during the filling in a low pressure casting process[END_REF], while Cuesta et al. proposed to consider the Weber number [START_REF] Cuesta | Numerically modeling oxide entrainment in the filling of castings: The effect of the webber number[END_REF]. Indeed, analyzing fluid flow simulation of different alloys and channels geometries, they highlighted the additional influence of the channel geometry in the flow structure. Liu et al. attributed the surface crack formation to metal front backflow [START_REF] Liu | Formation Mechanism of Surface Crack in Low Pressure Casting of A360 Alloy[END_REF]. The surface oxide film would be folded by the flow back of the metal before rising again. However, the lack of experimental validation does not permit to favor one of those criteria. Nevertheless, they all depend on the metal velocity, which therefore needs to be quantitatively determined.

After choosing the appropriate criterion on velocity to avoid oxide film entrainment, the process parameters and filling system design have to be adapted to respect it. In gravity casting, the filling velocity cannot be controlled as the metal filling flow depends on the cast part geometry itself. A small fall height is sufficient to achieve the critical velocity [START_REF] Jolly | John Campbell's ten rules for making reliable castings[END_REF]. On the opposite, in Low Pressure Casting (LPC), the filling is controlled with tailored furnace pressurization. Indeed, in LPC, the gas pressure increase above the metal in the furnace forces it to rise through a rising tube toward the mold.

Therefore, it is theoretically possible to maintain the metal velocity below the critical value during the whole filling phase. This explains why LPC is regarded as an effective solution to avoid oxide film entrainment [START_REF] Campbell | Castings principles : the new metallurgy of cast metals[END_REF]. Liu et al. showed that the bending strength of an aluminum plate cast by LPC was significantly reduced when increasing the casting pressure ramp [START_REF] Liu | Characteristics of mold filling and entrainment of oxide film in low pressure casting of A356 alloy[END_REF]. Similarly, Puga et al. highlighted that the porosity content was increased and the tensile strength was reduced in an aluminum alloy industrial part cast by LPC when considering higher pressure ramps [START_REF] Puga | Low pressure sand casting of ultrasonically degassed AlSi7Mg0.3 alloy: Modelling and experimental validation of mould filling[END_REF] . Therefore, the relationship between the set gas pressure evolution and the induced metal filling flow is needed to optimize the process parameters.

By using the Pascal principle, a simple analytical expression was proposed by Hogg et al., linking linearly the metal front height to the gas pressure [START_REF] Hogg | Low pressure sand casting of magnesium alloys[END_REF]. They measured a filling height delay in comparison with this simple model in the case of a magnesium automotive part, that they explained by pressure losses. A more developed model based on Bernouilli's equation was proposed to link the pressure ramp and the system geometry to the metal gate velocity [START_REF] Fan | Low pressure lost foam process for casting magnesium alloys[END_REF]. Considering the filling of a lost-foam casting with a sudden section restriction, the experimental results were in good agreement with the proposed model [START_REF] Fan | Low pressure lost foam process for casting magnesium alloys[END_REF]. However, in the case of a plate-shape casting of aluminum alloy, some filling oscillations were experimentally identified, while they could not be explained based only on this analytical model [START_REF] Liu | Characteristics of mold filling and entrainment of oxide film in low pressure casting of A356 alloy[END_REF]. Similarly, several metal and water analog experiments highlighted this oscillatory phenomenon during filling by LPC [START_REF] Duan | Development of a 3D filling model of low-pressure die-cast aluminum alloy wheels[END_REF][13] [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF].

Recent work has been devoted to the understanding of the filling oscillations and their link with the process parameters in LPC. In [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF], the authors identified the geometric parameters responsible for those oscillations as the horizontal sections of the furnace, the rising tube and the mold cavity. Fixing the low pressure system geometry, the impact of a sudden section change in the mold cavity has been quantified both experimentally and numerically. Moreover, the pressure ramp was shown to have a linear impact on the oscillation intensity. Liu et al. similarly studied the impact of a sudden section restriction on the filling flow and final cast part quality and proposed a maximal section ratio of 0.5 to avoid backflow [START_REF] Liu | Formation Mechanism of Surface Crack in Low Pressure Casting of A360 Alloy[END_REF]. Section changes more representative of real casting geometries were studied in [START_REF] Liu | Effect of pressurizing speed on filling behavior of gradual expansion structure in low pressure casting of ZL205A alloy[END_REF] by comparing fluid flow simulation and water analog experiments in a progressive section enlargement. Fixing a constant transition angle, the transition height at which the critical velocity is reached was determined as a function of the pressure ramp and the expansion angle. Using the same method, Viswanath et al. studied the impact of three in-gate shapes on the filling dynamics, and showed that a cone-shape in-gate provided smoother filling flow than a flat bottomed in-gate [START_REF] Viswanath | Numerical simulation and experimental validation of free surface flows during low pressure casting process[END_REF].

Therefore, if the number of studies focusing on filling dynamics in LPC is increasing, there is still no general design rule permitting to properly fill a mold using this process.

The present work aims to define LPC design rules to fulfill this gap by studying the impact of the geometry on the filling dynamics. To do so, the effects of geometric parameters on filling velocity are experimentally and numerically studied. A new analytical model is proposed to characterize the melt flow and to deduce adapted design rules for the LPC process.

Experimental characterization of LPC filling flow

Experimental setup

The geometry of the low-pressure system considered in this study is illustrated in Figure 1 Therefore, the metal superheat is around 170°C. During filling, the metal is pushed through the tube toward the mold by increasing the air pressure in the furnace according to a chosen pressure ramp 𝑃 ̇, divided into five steps as described in [START_REF] Sanitas | Filling Characterization into a Section Restriction in Low-Pressure Casting[END_REF]. The step of part filling is commonly made with a constant pressure ramp. The authors showed that the pressure ramp has a linear impact on oscillations [START_REF] Sanitas | Filling Characterization into a Section Restriction in Low-Pressure Casting[END_REF].

Therefore, the same pressure evolution is considered in the whole study, with a unique and constant pressure ramp during mold filling of 𝑃 ̇=2500 Pa.s -1 . Indeed, by considering a pressure ramp at the upper limit of the machine range (0-2500 Pa.s -1 ), the oscillation phenomena are intentionally amplified in order to increase measurement accuracy. The pressure servo regulator system has an accuracy of 100 𝑃𝑎 • 𝑠 -1 .

In order to characterize the flow dynamics during filling, in-situ instrumentation was developed, as illustrated in Figure 1

2.2.

Geometric parameters impacting fluid flow

In order to study the geometry impact on filling dynamics, three geometric parameters potentially impacting the filling dynamics are identified: the total section change ratio defined as 𝑅 = 𝑆 𝑐 𝑆 𝑡 (total cavity cross section over tube internal cross section), the local shape of the section change and the section transition height ℎ 𝑡𝑟𝑎𝑛𝑠 . Those three parameters are experimentally tested and the metal height evolution with time below, inside and above the section change is presented for each case in Figure 2 (ℎ = 0𝑚 corresponds to the bottom of the section change).

Mold cavities with different section change ratio (R=0.125 and R=0.5) are considered in Figure 2-(a).

When the section restriction is stronger, the oscillatory phenomenon is clearly amplified, as already described in a previous study [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF]. This parameter must definitely be considered when studying the geometry impact on filling dynamics. In the following, both section restrictions (R<1) and section enlargements (R>1) are considered. In Figure 2-(b), three section change shapes are tested, for the same global section ratio R=0.24. Indeed, industrial part geometries can almost never be regarded as cylinders of varying diameter. The filling flow is often split into several channels due to the cavity geometry. Therefore, for a fixed global section ratio R=0.24, the case of a single central bar is represented in red, the case of 6 narrower bars is shown in blue and the case of a ring is shown in green. These experiments permit to observe that the metal height evolution is very similar in the three cases. Although the local geometry impacts the flow regime by modifying Weber or Reynolds numbers (due to characteristics dimensions), it does not affect the filling velocity. Therefore, the local geometry can be set aside as an impacting parameter on velocity. Only central cylinders of varying diameter are considered in the further study, and the results on velocity could be extrapolated to more complex geometries.

When considering those two first parameters, the section variation was always considered to be sudden. However, this is not often the case in parts designed for foundry processes; sudden section changes are conducive to defects formation during solidification such as hot tears [START_REF] Campbell | Castings principles : the new metallurgy of cast metals[END_REF]. Therefore, the third studied parameter is the transition height. The metal height evolution is given for two mold cavities of same section ratio R=0.24 and different transition heights in Figure 2-(c). The section change is either sudden (in red) or progressive with a total transition height ℎ 𝑡𝑟𝑎𝑛𝑠 = 67𝑚𝑚 with a constant transition angle of 75° (in green). The first oscillation is seen to be delayed and eased when the section change is more progressive. Therefore, this parameter is also taken into account in the following study. Out of the three selected geometric parameters, the section change ratio R and the section transition height h trans are observed to actually impact the filling dynamics, and are thus studied in the following.

Geometric parameters' selection

The preliminary experimental study permits to define the pertinent mold cavity geometries to study.

All the mold cavities are cylindrical in shape with a bottom of the section change at ℎ 𝑚 = 100𝑚𝑚

from the mold bottom. The section change is defined by a ratio 𝑅 = 𝑆 𝑐 𝑆 𝑡 and a section transition height ℎ 𝑡𝑟𝑎𝑛𝑠 . Here three different shapes are studied: (A) a constant transition angle, meaning a square variation of the section ratio in the transition zone, (B) a linear variation of the section ratio and (C) a square root variation of the section ratio. The ratio variation with height between the section transition bottom ℎ = 0 and the section transition top ℎ = ℎ 𝑡𝑟𝑎𝑛𝑠 is given for these three transition shapes in Eq.

(1):

𝑅 𝐴 (h) = S(h) S t = (1 -(1 -√R) h h trans ⁄ ) 2 𝑅 𝐵 (h) = S(h) S t = 1 -(1 -R) h h trans ⁄ 𝑅 𝐶 (h) = 𝑆(ℎ) 𝑆 𝑡 = (1 -(1 -𝑅 2 ) ℎ ℎ 𝑡𝑟𝑎𝑛𝑠 ⁄ ) 1/2 (1)
Examples of vertical cross-section view of studied mold cavities are given in By studying several system geometries, the authors showed in a previous work that the metal in the tube has an impact on the filling dynamics while the metal in the crucible and the air in the furnace can be neglected [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF]. Therefore, the modelled system is made of the mold cavity and the tube. The system geometry and boundary conditions are illustrated in Figure 4. The system is initially fully filled with air and a constant metal pressure ramp 𝑃 ̇ is applied at the bottom surface. Atmospheric pressure is imposed at the top surface and no mass exchange is allowed in the other system boundaries. A no-slip boundary condition is considered at the metal/mold interface. A 2D-axisymmetric system is considered and a 1 mm mesh size is used. As the free surface of the metal is not necessarily flat and horizontal during filling, the metal height evolution with time is considered along the symmetry axis.

Development of Lagrangian model

In order to characterize the geometry and the process parameters impact on the oscillatory phenomenon, an analytical model using the Lagrangian method is developed. This model was developed by the authors in the case of a sudden section change in [START_REF] Sanitas | Étude expérimentale et numérique de la coulée basse-pression de l'alliage de magnésium RZ5 dans des moules en sable imprimés en 3D, ENSAM[END_REF]. Here this model is extended to progressive sections changes, to quantify the metal height evolution inside and above a progressive section change. To do so, the continuous liquid metal media is divided into five volumes as illustrated in Figure 5: (1) the metal in the furnace below the tube bottom, (2) the metal in the furnace above the tube bottom, (3) the metal inside the tube, (4) the metal in the section restriction, and (5) the metal above the section restriction. In volumes ( 2), ( 3), ( 4) and ( 5), the metal is assumed to be incompressible and non-viscous. The volume (1) cannot be considered in the Lagrangian model as the boundary conditions with elements (2) and ( 3) are different. Therefore the metal in the crucible bottom is not considered in the following energy balance, which may be a strong simplification. The dynamic and dissipative effects as well as the effect of metal direction change are neglected. The validity of this assumption is hence studied in the following paragraph.

Using the energy minimization principle, the motion equations of the system submitted to an external force 𝐹 𝑝 (gas pressure in the furnace) is given by:

d dt ( ∂ℒ ∂h ̇) - ∂ℒ ∂h = F p with ℒ = E c -E p (2)
with ℒ the Lagrangian of the system. In each considered volume, the kinetic and potential energies are expressed as a function of the system geometry, the height h and the velocity h ̇ of the metal front.

When the metal front is in the transition zone (Step 1), h is the height of the metal above the bottom of the section change and when the metal front is above the section change top (Step 2), h is the height of the metal above the section change top, as shown in Figure 5. The different horizontal sections are expressed according to the furnace section and the section ratioβ and R (tube section S t = βS f and final cavity section S c = RβS f ). The volumes velocities are expressed according to the free surface metal velocity h ̇, simply considering the mass conservation. During Step 1, it corresponds to a metal velocity in the tube v t = R(h)h ̇ and a metal velocity in the furnace v f = R(h)βh ̇, with R(h) varying from 1 to final ratio R. During Step 2, it is simply v t = Rh ̇ and v f = Rβh ̇.

Therefore the kinetic and potential energies of the five volumes can be expressed during Step 1 and during Step 2 as functions of the geometrical parameters. In particular, the kinetic and potential energies depend on the metal height in the crucible ℎ 𝑓 , which decreases when the metal fills the mold cavity. The analytical expressions of the furnace height and the corresponding kinetic and potential energies of the five metal volumes are given in Table 1 during the two steps. When the transition shape is different, the terms h f (h), Ec 3 and Ep 3 are different, so only the (A) shape formula are given in At the beginning of Step 1, the metal front is supposed to be at the bottom of the section change and the metal front velocity is given by ℎ ̇(0) = 𝑃 ρ𝑔(1+𝛽) [START_REF] Liu | Characteristics of mold filling and entrainment of oxide film in low pressure casting of A356 alloy[END_REF]. Then when the metal front reaches the section transition top at t = t trans , equations of Step 2 are solved, with an initial front velocity from Step 1.

The external force is also expressed as it varies with the metal height in the furnace and the air pressure.

Volume

Step 1

Step 2 1

𝐸𝑐 1 = constant and 𝐸𝑝 1 = constant 2 𝐸𝑐 2 = 0.5𝜌𝑆 𝑓 𝛽 2 𝑅(ℎ) 2 ℎ 𝑓 (ℎ)ℎ ̇2 𝐸𝑝 2 = 0.5𝜌𝑆 𝑓 𝑔 ((ℎ 𝑓 (h) -ℎ 𝑡 ) 2 -ℎ 𝑡 2 ) 𝐸𝑐 2 = 0.5𝜌𝑆 𝑓 𝛽 2 𝑅 2 h 𝑓 (ℎ)h ̇2 𝐸𝑝 2 = -0.5𝜌𝑆 𝑓 𝑔 (2h 𝑡 + 2h 𝑡𝑟𝑎𝑛𝑠 -h 𝑓 (ℎ)) h 𝑓 (ℎ) (3)
3 (5)

𝐸𝑐 3 = 0.5𝜌𝑆 𝑓 𝛽𝑅(ℎ) 2 ℎ 𝑡 ℎ ̇2 𝐸𝑝 3 = -0.5𝜌𝑆 𝑓 𝑔𝛽ℎ 𝑡 2 𝐸𝑐 3 = 0.5𝜌𝑆 𝑓 𝛽𝑅 2 h 𝑡 h ̇2 𝐸𝑝 3 = 0.5𝜌𝑆 𝑓 𝑔𝛽(h 𝑡𝑟𝑎𝑛𝑠 2 -(h 𝑡𝑟𝑎𝑛𝑠 + h 𝑡 ) 2 ) ( 4
)
4 𝐸𝑐 4 = 0.5𝜌𝑆 𝑓 𝛽𝑅(ℎ)
5 𝐸𝑐 5 = 0.5𝜌𝑆 𝑓 𝛽𝑅ℎh ̇2 𝐸𝑝 5 = 0.5𝜌𝑆 𝑓 𝑔R𝛽ℎ 2 (6)

Validation of the Lagrangian model

The objective of developing the Lagrangian model is to analyze the effect of different process parameters and geometries on the filling dynamics. To do so, the model has to be validated by comparison with experimental and numerical results on defined cases. Figure 6 presents the metal height evolution with time in the case of a section restriction R=0.24 and the experimental pressure ramp 𝑃 ̇= 2500𝑃𝑎. 𝑠 -1 . Indeed, the section restriction is chosen to be representative of a standard section change in a part and the pressure ramp is taken at the upper limit of the system range in order to amplify the dynamics effects. Two section geometries are considered. In Figure 6-left the section change is sudden while in Figure 6-right, the transition angle is of 75°, corresponding to a transition height of 67 mm ((A) type). Those two section transitions are considered to be representative of the section changes that may occur in real parts.

A vertical cross-section of the considered cavity geometry is given in each graph. In both cases, the experimental results obtained from the tension acquisition system (in black) are compared with the Fluent simulation results (in blue) and the Lagrangian model results (in red). In addition, the continued metal rise in the case of no section change is given in black dashed line. The experimental points are presented with ∓2mm error bars corresponding to the position uncertainty of the contacts. In both cases, the experimental results show a linear rise of the metal below the bottom of the section change. Then when the metal crosses the section change zone, it starts to oscillate until the end of filling. As already commented by the authors in [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF], this behavior is qualitatively found back in both simulation and model results in the case of a sudden restriction. The present study permits to enlarge the conclusions to progressive section changes. The metal inertia is seen to be responsible for the oscillation formation. The discrepancies increase with time between experimental and numerical results can be explained by thermal effects: the viscosity, density and surface tension increase of the metal with cooling will tend to ease the oscillatory phenomena.

Going further, the oscillation period is found back and the first oscillation amplitude is even quantitatively predicted by the Lagrangian model, in both tested geometries. Moreover, the Lagrangian model results are seen to be very close to Fluent simulation results in the two tested configurations.

The period, amplitude and shape of the oscillations are almost identical. The developed Lagrangian model permits to quantitatively predict the first oscillations induced by a section change, and thus the maximal velocity reached by the metal during filling. Therefore, only the Lagrangian model will be used in the filling dynamics investigation presented in the remainder of the study. As the impact of pressure ramp on the oscillations was shown to be linear [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF], only one pressure ramp is studied in the following: 𝑃 ̇= 2500𝑃𝑎. 𝑠 -1 .

Geometry impact on filling dynamics

Sudden section change ratio effect

Using the Lagrangian model, the evolution with time of the metal front height is obtained above a section change of ratio R. It is illustrated in the case of R=0.125 in Figure 7. The graph origin corresponds to the moment when the metal front reaches the section change. This evolution is compared to the model of Liu et al. [START_REF] Liu | Characteristics of mold filling and entrainment of oxide film in low pressure casting of A356 alloy[END_REF], linking linearly the pressure ramp to the resulting vertical velocity in the cavity:

𝑣 0 = 1 𝜌𝑔(1 + 𝑅𝛽) 𝑃 ̇ (7)
The Lagrangian model does predict an average metal height evolution following the Liu model.

However, the filling velocity clearly oscillates around this average value, and the metal front even goes up and down during filling, even far from the section restriction. In order to analyze the effect of R value on this oscillatory phenomenon, the metal front over-height (ℎ -𝑣 0 𝑡) is given in Figure 8 for several R values. The impact of the section ratio R on the oscillatory behavior is clearly visible; the oscillation period increases with R and more importantly, the further is R from 1, the more the oscillation amplitude is important. The maximal velocity reached by the metal front during filling is larger when the section restriction is more important but this effect is less visible in the case of section enlargement. Therefore, in order to generalize these observations to the machine range of pressure ramp and to a large variety of section change ratios, the maximal metal front velocity is given as a function of 𝑃 ̇ for six R values in Figure 9.

As shown in [START_REF] Sanitas | Experimental and numerical study of section restriction effects on filling behavior in low-pressure aluminum casting[END_REF], the maximal velocity predicted by the Lagrangian model is proportional to the pressure ramp, but it additionally depends on the section change ratio. When considering a section restriction, the maximal velocity reached by the metal front strongly depends on R value. For example, the maximal velocity is multiplied by a factor 4 when the section restriction is 0.125 instead of 0.5.

The R value impact on the maximal velocity is lower in the case of a section enlargement. The maximal velocity is almost unchanged when R=8 instead of 4, in the whole considered pressure ramp range. In order to quantify the impact of section ratio on the maximal front velocity according to the Lagrangian model, equation ( 8) is modified in equation ( 8) as:

𝑣 𝑚𝑎𝑥 = 𝑓(𝑅) 𝜌𝑔(1 + 𝑅𝛽) 𝑃 ̇ (8)
With 𝑓(𝑅) a function of the section ratio. 𝑓(𝑅) = 1 when R=1 as 𝑣 𝑚𝑎𝑥 = 𝑣 0 , and𝑓(𝑅) is higher than 1

for any other R value as a section change always induces a metal front velocity increase. This function can be fitted almost perfectly by equation ( 9), as illustrated in Figure 10 :

𝑓(𝑅) = { 1 𝑅 𝑤ℎ𝑒𝑛𝑅 < 1 2 - 1 𝑅 𝑤ℎ𝑒𝑛𝑅 ≥ 1 (9)
The f(R) curve fitting by 1/R function when considering a section restriction highlights the predominant effect of inertia; flow rate conservation induces that the metal front velocity, initially equal to v 0 , is divided by the section ratio R when crossing the section change. When considering a sudden section enlargement, the metal is first slowed down at v min =v 0 /R before accelerating. The maximal velocity can therefore be approximated by v 0 +(v 0 -v min ), which justifies the shape of f(R) function when R ≥1. The f(R) function permits to link the maximal velocity reached by the metal front to the considered pressure ramp, knowing the section ratio value. Thanks to this improved model, it becomes possible to define the maximal pressure ramp permitting not to exceed a desired maximal metal front velocity, for any horizontal sudden section change.

Section change progressiveness effect

A rule has been defined to link the cavity geometry to the filling dynamics in the case of a sudden section change. In this section, the effect of the section transition smoothing is now considered. For a fixed section change ratio R, the impact of the transition height ℎ 𝑡𝑟𝑎𝑛𝑠 on the oscillations is studied in the case of a transition shape of (A) type presented in table 1 (constant transition angle). 11-(c). The evolution is given in dash line when the metal front is in the section transition zone and then in plain line when the metal front is above the section transition top.

Comparing the filling dynamics in the case of ℎ 𝑡𝑟𝑎𝑛𝑠 = 35𝑚𝑚 (in red, corresponding to 38° angle) to the sudden change case (in purple), one can see that the oscillations are very similar. Only a slight delay and a slight amplitude reduction are observed, but the oscillations period and general shape are conserved. The maximal velocity is reached in both cases at the transition zone top, during the first oscillation, as can be seen in Figure 11-(c). The transition height has to be as large as 105 mm (in orange, corresponding to 67° angle) to observe a noticeable impact. As the section transition zone is more progressive, the metal front acceleration inside and after the transition zone is reduced. The metal front velocity is lower and the transition zone is higher, which explains the delay to reach the transition top when increasing ℎ 𝑡𝑟𝑎𝑛𝑠 . Moreover, the maximal velocity is not reached at the transition zone top or during the first oscillation as previously, but above the transition top during the second oscillation, after 1.25s. Therefore, if the transition smoothing permits to reduce the metal acceleration inside the transition zone, the oscillations initiated inside are amplified above the section transition zone, justifying that considering the filling flow dynamics inside a section transition is not sufficient.

When the transition height is even higher with ℎ 𝑡𝑟𝑎𝑛𝑠 = 140𝑚𝑚(in green, corresponding to 72° angle), this phenomenon is amplified. A whole oscillation period occurs inside the transition zone and the oscillation amplitude is increased above the transition zone. The maximal velocity is reached just above the section transition top after 1.52s. Eventually, when ℎ 𝑡𝑟𝑎𝑛𝑠 = 200𝑚𝑚 (in dark green, corresponding to 77° angle), the oscillation amplitude increases inside the transition zone, to reach a maximal velocity at the transition top. By increasing more and more the transition height, one would reduce the maximal velocity until reaching the initial velocity 𝑣 0 given by eq.( 8) but also delay the maximal velocity reaching time to higher order oscillations. The maximal metal front velocity 𝑣 𝑚𝑎𝑥 being considered as the critical parameter to characterize filling, it is given in Figure 12-(a) as a function of both R and ℎ 𝑡𝑟𝑎𝑛𝑠 . The dotted line corresponds to 𝑣 0 , the metal front velocity in case of theoretical instantaneous adaptation to the new cavity section.

𝑣 𝑚𝑎𝑥 is observed to decrease when increasing ℎ 𝑡𝑟𝑎𝑛𝑠 , as expected. However, the impact of ℎ 𝑡𝑟𝑎𝑛𝑠 on 𝑣 𝑚𝑎𝑥 is seen not to be linear. Considering the case R=0.125, two inflexion points are observed at approximately ℎ 𝑡𝑟𝑎𝑛𝑠 = 100𝑚𝑚 and ℎ 𝑡𝑟𝑎𝑛𝑠 = 225𝑚𝑚. They correspond to the change of oscillation of the maximal velocity: for transition heights smaller than 100 mm, 𝑣 𝑚𝑎𝑥 is reached during the first oscillation, for transition heights between 100 mm and 225 mm, during the second oscillation, and so on. Therefore, adding a transition height has an impact for small ℎ 𝑡𝑟𝑎𝑛𝑠 values, but it seems that it is no use adding a very high transition height as its impact is more and more reduced.

For example for R=0.125, a transition height of 85 mm permits to divide 𝑣 𝑚𝑎𝑥 by a factor 2 compared to a sudden change. However, by considering a transition height twice larger, 𝑣 𝑚𝑎𝑥 is additionally reduced by only 30%.

As expected, when the section change ratio is larger and tends to 1, the maximal velocity is lower, as can be seen in Figure 12-(a). In order to analyze the ℎ 𝑡𝑟𝑎𝑛𝑠 impact for the different R values, the maximal velocity, function of ℎ 𝑡𝑟𝑎𝑛𝑠 , is normalized by the maximal velocity when the section change is sudden (noted 𝑣 max_0 ) in Figure 12-(b), noted 𝑣 𝑚𝑎𝑥 * = 𝑣 𝑚𝑎𝑥 /𝑣 max_0 . v 0 is the metal front velocity before the bottom of the section change and v max_0 is the maximal velocity reached by the metal in the case of a sudden section change. One can notice that increasing the transition height is less and less efficient in reducing the metal front velocity when the section ratio R is larger ; the transition height should be higher than 350 mm to divide the maximal velocity by a factor 2 when R=0.5 while ℎ 𝑡𝑟𝑎𝑛𝑠 = 88𝑚𝑚 would permit to reach this objective when R=0.125. When considering a section enlargement instead of a section restriction, the impact of the section change ratio on the maximal velocity is even more eased. For the three R>1 values tested in Figure 12 Contrarily to the case of a sudden section change, it is not possible to express analytically the maximal metal front velocity in a progressive section change by only considering the metal inertia. At each height, the metal acceleration is induced by competition between inertia (leading to acceleration in a section restriction) and gravity (leading to deceleration to fit the predefined pressure ramp setting).

The link between cavity geometry (through both section change ratio and transition height) and maximal front velocity, knowing the pressure ramp, is obtained numerically by solving the Lagrangian equations. The curves obtained for 𝑃 ̇= 2500𝑃𝑎. 𝑠 -1 in Figure 12-(a) can be obtained for any pressure ramp value by using the same method 4.3.

Section change shape effect

All the results presented in the previous section are obtained by the Lagrangian model considering a transition shape of (A) type (Figure 3), which means a constant transition angle. In this case, the section transition is not linear. When considering a section restriction, the section variation is stronger in the transition bottom part and weaker in the top part (Figure 3-(c)-left) and it is the opposite when considering a section enlargement (Figure 3-(c)-right). In order to characterize the impact of the transition shape on the filling dynamics, and potentially to identify an optimal section transition shape, three different shapes are studied, as presented in section 2.3. The (B) shape corresponds to a linear evolution of R(h) ratio from 1 at the transition bottom to final R ratio at ℎ = ℎ 𝑡𝑟𝑎𝑛𝑠 . The (C) shape corresponds to a square root evolution of R(h) ratio between the same limits. The impact of the transition shape on the maximal metal front velocity is illustrated in Figure 13 for two section change ratios: R=0.125 (Figure 13-(a)) and R=8 (Figure 13-(b)). In both cases, the results are very similar for the three section shapes. The impact of the transition height on the maximal metal front velocity, for a fixed pressure ramp and section ratio, is almost identical. In the case of the section restriction R=0.125 (Figure 13-(a)), the velocity decrease is only slightly faster when increasing the transition height for the (A) shape. This observation is only true when the transition height remains smaller than the tube diameter as for higher transition heights; the model noise is larger than the shapes discrepancy. In the case of R=8, the shape effect is even less visible, except for very high transition heights. Therefore, the transition shape does not impact significantly the filling dynamics, only the transition height has a visible effect.

(a) R=0.125 (b) R=8

Maximal filling velocity map

Thanks to the presented filling dynamics investigation, it is possible to define the relationship between the mold cavity geometry, the filling pressure ramp and the induced maximal velocity reached by the metal front during filling. If the filling criterion, not to have oxides defects, is chosen to be 0.5 m.s -1

for the maximal metal velocity, it is possible to directly link pressure ramp, section ratio and transition height, as shown in the map Figure 14.

The pressure ramp is limited at 3000 Pa/s in this study, corresponding to the machine extreme limit.

Moreover, only section ratios smaller than 0.5 are represented in the graph. Indeed, for larger values, the maximal velocity remains under 0.5 m/s, whatever the transition height is (in the studied pressure ramp range). This conclusion is also true for any section enlargement. From these results, one can see that when the section ratio is larger than 0.25, it is no use adding any transition height: the metal front velocity would never exceed 0.5 m/s, as can be seen by the red dashed line in Figure 14. On the opposite, when the section restriction is as small as 0.1, the transition height must be at least of 180 mm.

Design algorithm in LPC

The map given in Figure 14 is a precious tool in process parameters and design definition in LPC, as it permits to both determine the appropriate filling pressure ramp for any complex shape part and design the filling system adapted to low pressure casting. Therefore, the authors propose a specific methodology, presented in Figure 15. Knowing the geometry of a part cast in LPC, the casting parameters definition can be obtained by following the given algorithm:

-The N possible orientations of the part are selected by considering castability criteria. Indeed, the gates of the filling system, placed at the bottom of the part in LPC process, cannot be placed in any functional zone or in hot spots of the part. Moreover, some geometrical constrains can limit the access to certain zones of the part. Therefore, the possible casting orientations of a part are limited.

-For the N possible orientations, the maximal vertical section change R is determined, and the part orientation giving the smallest R value is selected.

-The height of this critical section change is determined.

-The section of the part bottom being known, the section change ratio of the filling system can be determined (for a known rising tube section).

-Given the R and h trans values of the part, the maximal filling pressure ramp can be found by using the 3D map given in Figure 14 (or equivalent Lagrangian model results adapted to any LPC system).

-Considering that the filling system and the part are filled with the same pressure ramp and knowing R value of the filling system, the minimal transition height of the filling system can be found by using the 3D map given in Figure 14. backflow is more critical than metal front velocity for oxide entrapment, as proposed by Liu et al [START_REF] Liu | Formation Mechanism of Surface Crack in Low Pressure Casting of A360 Alloy[END_REF],

the criterion applied to the Lagrangian model would simply be h ̇ positive. To accurately define the flow criterion adapted in the case of LPC, an extensive experimental study is needed to link geometry and process parameters to the final mechanical properties of the cast parts. Such an experimental study could also be used to validate a numerical model of oxide formation and entrapment [START_REF] Reilly | The present state of modeling entrainment defects in the shape casting process[END_REF].

Conclusions

In this study, the effects of the section variations on metal oscillations appearing during filling by low pressure have been experimentally and numerically investigated. The findings of this work are as follows:

-An industrial-size experimental study permits to highlight the major impact of pressure ramp and total horizontal section variation on fluid flow oscillations. Moreover, for a given section change ratio, the section transition height increase is shown to lower the oscillatory phenomenon, while the section transition shape does not significantly impact the filling dynamics.

-A new analytical expression linking pressure ramp, system geometry and resulting maximal metal front velocity is proposed. This model based on Lagrangian is validated by CFD simulation and experimental results.

-New design rules tailored to LPC are recommended to limit oxide inclusion defects. An algorithm is proposed to determine the maximal filling pressure ramp and the minimum filling system height. This algorithm can be applied to any other oxide inclusion criterion or LPC system.

Acknowledgements

  in red. Steel rods of 1 mm diameter are inserted in the mold cavity every 10 mm in height, with a position precision of  2 mm. Each contact is linked to the electrical circuit, of initial tension 11V. When the metal reaches a new contact, the output tension is reduced. The output tension data collected at a 100 Hz fixed frequency permits to measure the passage time of the metal at each rod during filling.

Figure 1 :

 1 Figure 1 : Vertical cross section view of the Low-pressure casting system and instrumented sand mold. Furnace and mold are in dark grey, liquid metal in light grey and air in the furnace in white.

Figure 2 :

 2 Figure 2 : Schematic mold cavity top view and vertical cross-section on the left and experimental metal height evolution with time on the right for 𝑃 ̇= 2500𝑃𝑎/𝑠 for (a) two different section ratio, (b) three shapes for the same section ratio R=0.24 and (c) two section transition heights h trans for the same section ratio R=0.24.(ℎ = 0𝑚 corresponds to the bottom of the section change).

Figure 3

 3 for two values of section change ratio R, for three values of transition height ℎ 𝑡𝑟𝑎𝑛𝑠 and for the three studied transition shapes (A), (B) and (C).

Figure 3 :

 3 Figure 3 : Illustration of studied mold cavity geometries for (A) transition shape in red, (B) transition shape in green and (C) transition shape in blue, for three different values of section transition height ℎ 𝑡𝑟𝑎𝑛𝑠 and for a section reduction defined by R=0.125 (on the left) and a section increase defined by R=8(on the right).

3 .

 3 Modelling of filling dynamics 3.1. Computational model In order to enlighten the filling dynamics origin, fluid flow simulation of LPC filling is performed using ANSYS Fluent® simulation software. The effect of metal cooling and solidification on the filling dynamics is neglected. Therefore, the model will be less and less accurate over time, and only the first oscillations of the metal front after section change will be considered. Continuity and Navier-Stokes equations are solved using finite volume discretization. As the fluid flow in the tube is turbulent, the 𝑘 -𝜖 turbulence model is used. Air and liquid metal are considered as non-miscible and the interface is tracked using the Volume Of Fluid method. More details about the model are given in Ansys Fluent Manual [17]. The two phases are considered as Newtonian fluids with constant density ρ and cinematic viscosity ν (respectively 2495 kg.m -3 and 1.13x10 -3 kg.m -1 .s -1 for liquid aluminum alloy [18] and 1.442 kg.m -3 and 0.10x10 -3 kg.m -1 .s -1 for air (Fluent 16.1 database)).

Figure 4 :

 4 Figure 4 : 2D axi-symmetric system geometry, initial and boundary conditions considered for Fluent simulations

(a) Step 1 (b) Step 2 Figure 5 :

 125 Figure 5 : Cross-section of the LPC system with the volumes considered for the Lagrangian model, (a) when the metal front is in the section change zone and (b) when the metal front is above the section change top.

Figure 6 :

 6 Figure 6 : Comparison of metal front height evolution with time obtained by experiment (black dots), by Fluent simulation (blue lines) and by Lagrangian model (red lines) for the case R=0.24 and 𝑃 ̇= 2500𝑃𝑎. 𝑠 -1 and for 2 transition heights: null on the left and 67mm on the right (75° transition angle)

Figure 7 :Figure 8 :

 78 Figure 7 : Evolution of the metal front height (from the mold bottom) with time for R=0.125, in the case of a sudden section change, by Lagrangian model

Figure 9 :Figure 10 :

 910 Figure 9 : Maximal reached velocity as a function of the pressure ramp and the section change ratio in case of a sudden section change, by Lagrangian model

  Five values of transition height are considered in Figure 11 in the case of R=0.125. The five top views (identical as the same ratio R is considered) and the corresponding vertical cross-sections are illustrated in Figure 11-(a). The transition height is varied from 0 (sudden change) to 200 mm, corresponding to almost three times the tube diameter. The over-height and the velocity evolutions with time are given for those five geometries, respectively in Figure 11-(b) and Figure

Figure 11 :

 11 Figure 11 : (a) Top view and vertical cross-section of the five considered cavity geometries, corresponding to five values of transition height (from 0 in purple to 200mm in dark green), and Lagrangian model results corresponding to those geometries, for R=0.125:(b) evolution of the metal front over-height with time and (c) evolution of the metal front velocity with time

  -(a), the transition height impact on 𝑣 𝑚𝑎𝑥 is almost identical and rather inefficient. Even considering a transition height of 350 mm, it is not possible to reduce the maximal velocity by a factor 2 (Figure 12-(b)). (a) (b)

Figure 12 :

 12 Figure 12 : (a) Maximal velocity 𝑣 𝑚𝑎𝑥 and (b) maximal relative velocity 𝑣 𝑚𝑎𝑥 * , for several R values, as a function of the

Figure 13 :

 13 Figure 13 : Maximal velocity 𝑣 𝑚𝑎𝑥 as a function of the transition height and for the three studied transition shapes, for (a) R=0.125 and (b) R=8. Dots correspond to the Lagrangian model results, and lines are 6 th -order polynomial fits.

Figure 14 :

 14 Figure 14 : Maximal pressure ramp not to exceed v=0.5 m/s during filling as a function of the section change ratio R and the transition height ℎ 𝑡𝑟𝑎𝑛𝑠

  This simple route is the first one, to our best knowledge, offering a cast part design method tailored to the low pressure casting process. It open the validation way to define new design rules tailored to LPC to cast more complex part geometries. Moreover, the oxide inclusions criterion of 0.5 m/s should be studied. Indeed, the Lagrangian model permits to characterize the fluid flow during filling. Therefore, a map equivalent to the one given in Figure 14 could be obtained for any other criterion. For example, if

Figure 15 :

 15 Figure 15 : Flow chart of the proposed design algorithm

  . The crucible diameter 𝜙 𝑓 is 545𝑚𝑚, the tube length ℎ 𝑡𝑢𝑏𝑒 is 953𝑚𝑚, the tube internal diameter 𝜙𝑖 𝑡𝑢𝑏𝑒 is 70𝑚𝑚 and the tube external diameter 𝜙𝑒 𝑡𝑢𝑏𝑒 is 100𝑚𝑚. Thus the furnace cross section is given

	by 𝑆 𝑓 =	Π 4	(𝜙 𝑓 2 -𝜙𝑒 𝑡𝑢𝑏𝑒 2	) and the tube internal cross section by𝑆 𝑡 =	Π 4	𝜙𝑖 𝑡𝑢𝑏𝑒 2	. 3D printed furan resin
	bonded sand molds, with different inner geometries, are placed at the top of the rising tube.
	About 100kg of Al-Si13% are melted in the crucible and held at 750°C  5°C by the electrical furnace.

Table 1 .

 1 The B and C shapes expressions are given in appendix.

Table 1 :

 1 Developed Langrangian motion model

The authors would like to acknowledge the contribution of colleagues. Thanks are due to J. BOURGEOIS, J. NEGRE and S. BUSSETTA of the Arts et Métiers ParisTech for their precious technical support. Prof. S.KHELLADI from DynFluid laboratory of the Arts et Métiers ParisTech is thanked for its precious help on fluid flow simulation.

Appendix Table 2 : Initial and boundary conditions used in the Lagrangian model

Step 1

Step 2

Initial conditions

ℎ(0) = 0; ℎ ̇(0) = 𝑃 ρ𝑔(1+𝛽) ℎ(0) = 0;ℎ ̇(0) = ℎ ̇(𝑡 𝑡𝑟𝑎𝑛𝑠 ) from step 1 (A1) Kinetic energy of Volume 3

Potential energy of Volume 3

Metal height evolution in the furnace ℎ 𝑓 (ℎ)