Carlos Rafael

Silva De Oliveira

Jéssica Mulinari

Marcos Antonio Batistella

Antônio Augusto Ulson De Souza

Selene Maria De Arruda

Guelli Ulson De Souza

Antimicrobial effect of cotton fabric functionalized with a kaolinite-titania nano-hybrid composite

Keywords:

The treated cotton fabric exhibited excellent antibacterial property.

• The samples showed better bactericidal performance against Bacillus cereus. • The multifunctionality of the kaolinitetitania composite was attested.

Introduction

A wide variety of pathogenic microorganisms can be transmitted through water, air, and contaminated surfaces. In recent years, the disease caused by COVID-19 has made evident the usefulness of textile masks in retaining the viral pathogen and has highlighted the importance of hygiene and correct sanitation of clothing and textile accessories as preventive care. Textile products, as they are organic, fibrous, and absorbent materials, in addition to being constantly exposed to human touch and atmospheric dirt, are conducive to microorganisms' adhesion, proliferation, and transmission. For these reasons, the development of textiles with antimicrobial activity that can help fight and prevent diseases has been a hot topic nowadays.

Various mineral particles and organic compounds were evaluated as antimicrobial additives for textiles [START_REF] Yang | Recent researches on antimicrobial nanocomposite and hybrid materials based on sepiolite and palygorskite[END_REF][START_REF] Hebeish | TiO2 nanowire and TiO2 nanowire doped Ag-PVP nanocomposite for antimicrobial and self-cleaning cotton textile[END_REF]. Among them, titania (TiO 2 ) is considered a promising antimicrobial agent due to its high effectiveness in inactivating various types of bacteria. In addition, TiO 2 is a non-toxic and low-cost compound with high chemical stability and photocatalytic properties [START_REF] Sallehudin | Preparation and characterization of TiO2-polysiloxane coated cotton yarn at different coating methods[END_REF]. Even under mild ultraviolet radiation, TiO 2 can show sufficient photocatalytic activity to eliminate xenobiotic compounds [START_REF] Koseki | Bactericidal performance of photocatalytic titanium dioxide particle mixture under ultraviolet and fluorescent light: an in vitro study[END_REF]. Akhavan et al. [START_REF] Akhavan | Synthesis of titania/carbon nanotube heterojunction arrays for photoinactivation of E. coli in visible light irradiation[END_REF] synthesized carbon-nanotubes/TiO 2 immobilized on Si (0 0 1) wafers for E. coli inactivation. Kalaiarasi et al. [START_REF] Kalaiarasi | Sensing and antimicrobial activity of polyaniline doped with TiO2 nanocomposite synthesis and characterization[END_REF] prepared a Polyaniline-TiO 2 nanocomposite, which exhibited antimicrobial activity against K. pneumoniae and P. mirabilis. Hebeish et al. [START_REF] Hebeish | TiO2 nanowire and TiO2 nanowire doped Ag-PVP nanocomposite for antimicrobial and self-cleaning cotton textile[END_REF] developed silver-doped TiO 2 nanowires, which they used to functionalize a PVP-treated cotton fabric and tested against S. aureus, B. cereus, E. coli, P. aeruginosa, and C. albicans.

The present research investigated the antimicrobial activity of a cotton fabric functionalized with a kaolinite-titania composite against gram-positive and gram-negative bacteria. This composite was recently successfully synthesized and exhibited excellent performance when applied in powder form to photocatalytic degradation of methylene blue in aqueous media, as reported in our previous work [START_REF] De Oliveira | Synthesis of superacid sulfated TiO2 prepared by sol-gel method and its use as a titania precursor in obtaining a kaolinite/TiO2 nano-hybrid composite[END_REF]. In another work [START_REF] De Oliveira | Functionalization of cellulosic fibers with a kaolinite-TiO2 nano-hybrid composite via a solvothermal process for flame retardant applications[END_REF], the same composite applied to cotton fabric exhibited superior fire-retardant behavior decreasing flame propagation due to its mineral nature when combined with phosphorus and nitrogen compounds. The present work shows that our composite also exhibited antimicrobial activity in addition to the photocatalytic and fire-retardant properties. Therefore, the results show the versatility of the applied treatment, proving the multifunctionality of the composite and the treated fabric.

Experimental

Preparation of functionalized fabric

A woven fabric (cotton 100%) was functionalized with a kaolinitetitania nanohybrid composite (denoted as KT) by solvothermal synthesis [START_REF] De Oliveira | Functionalization of cellulosic fibers with a kaolinite-TiO2 nano-hybrid composite via a solvothermal process for flame retardant applications[END_REF]. The KT composite consists of kaolinite microparticles containing TiO 2 nanocrystals adhered to its surface [START_REF] De Oliveira | Synthesis of superacid sulfated TiO2 prepared by sol-gel method and its use as a titania precursor in obtaining a kaolinite/TiO2 nano-hybrid composite[END_REF]. Details on the preparation method of the KT composite and the treated fabric were elucidated in the Supplementary Materials section.

Antimicrobial test

The antibacterial efficacy of the functionalized fabric was investigated under dynamic contact conditions on Escherichia coli and Bacillus cereus cells using ASTM E2149-13a (2014) with minor modifications explained as follows.

Both microorganisms were isolated from the biological sludge of a textile industry, which means that they were already used to textile chemicals. Bacterial cells were cultured in Tryptic Soy Broth (TSB) at 35 • C and agitation of 100 rpm for 18 h. After, the culture was diluted with sterile buffer solution (0.3 mM KH 2 PO 4 pH 7.2) until it reached an absorbance of 0.16 ± 0.02 and 0.67 ± 0.02 at 600 nm for E. coli and B. cereus, respectively. These absorbances represent concentrations of approximately 3.0 × 10 8 colonies forming units (CFU) × mL -1 . The solutions were then properly diluted to obtain the working solution containing a final concentration of about 3.0 × 10 5 CFU × mL -1 . The bacterial concentration of the working solution was determined by a serial dilution and plate count technique. For this, 0.1 mL of the different dilutions were spread on the surface of Tryptic Soy Agar plates and incubated at 35 • C for 24 h.

Fabric samples of 1.0 ± 0.1 g were used as test specimens; the treated and untreated fabric were tested. Each sample was placed in a 250 mL sterile Erlenmeyer flask and 50 mL of the working solution was added. A

To determine if the antimicrobial agent was leaching from the fabric, the parallel streak method AATCC 147 (2011) was used with minor modifications. E. coli was chosen as test organism. The bacterial inoculum was prepared by transferring 1.0 mL of a 24 h broth culture (grown in TSB) into 9.0 mL of sterile distilled water. Using a 4 mm loop loaded with the inoculum, five streaks of approximately 6 cm in length and spaced 1 cm apart were made on the surface of TSA plates. Rectangular pieces (2.5 × 5.0 cm) of coated and untreated fabrics were then placed transversely across the streaks, ensuring the contact between the microorganisms and the material. Subsequently, the plates were incubated at 37 • C for 24 h. After that, the plates were visually examined to observe if a clear zone of inhibition was formed beyond the fabric's edge. The test was performed in triplicate. 70000× magnification. It is possible to observe the details of the kaolinite crystal (structure of stacked hexagonal lamellae) containing the titania nanoparticles well distributed and adhered to the surface [START_REF] Pellenz | A comprehensive guide for characterization of adsorbent materials[END_REF]. The image showed the immobilization of nanoparticles in the basal and lateral planes of the clay mineral, as already reported in the literature [START_REF] Shao | Sol-gel synthesis of photoactive kaolinite-titania: effect of the preparation method and their photocatalytic properties[END_REF][START_REF] Li | Acetic acid functionalized TiO2/ kaolinite composite photocatalysts with enhanced photocatalytic performance through regulating interfacial charge transfer[END_REF].

Results and discussion

SEM-FEG analyzes

Fig. 2 shows the KT composite immobilized on the fibers' surface of the treated fabric (2B) and untreated fabric (2C). Untreated fabric fibers showed a smooth appearance containing slight twists, befitting the natural look of cotton. In contrast, the treated fabric fibers containing the mineral composite particles have a rough and irregular surface appearance. The micrographs confirmed the success of the composite synthesis [START_REF] De Oliveira | Synthesis of superacid sulfated TiO2 prepared by sol-gel method and its use as a titania precursor in obtaining a kaolinite/TiO2 nano-hybrid composite[END_REF] and its immobilization on cotton fibers [START_REF] De Oliveira | Functionalization of cellulosic fibers with a kaolinite-TiO2 nano-hybrid composite via a solvothermal process for flame retardant applications[END_REF].

EDX analysis of the treated sample was performed by SEM-FEG, using a JSM-6701F (Jeol) equipment with an EDS NanoTrace™ X-ray detector (Thermo Scientific) device. The qualitative result is shown in Fig. S2, and the estimated proportions of the elements present in the sample are shown in Table S1.

FTIR analyzes

Fig. 2 (A) shows the FTIR analyzes of the treated and untreated fabric samples. In both spectra, vibrational modes characteristic of cellulose were observed. In this case, the intense peak in the region of 3330 cm -1 corresponds to structural OH groups stretching vibration [START_REF] De Oliveira | Development of flexible sensors using knit fabrics with conductive polyaniline coating and graphite electrodes[END_REF], which reveals the continuity of the hydrophilic characteristic of cotton in the treated sample. The broader peak at 3260-3240 cm -1 in the treated sample can be ascribed to the formation of some intermolecular bonded OH stretching after the fiber treatment [START_REF] De Oliveira | Functionalization of cellulosic fibers with a kaolinite-TiO2 nano-hybrid composite via a solvothermal process for flame retardant applications[END_REF]. The peaks in the region between 1300 and 1400 cm -1 are related to the wagging vibration in the CH bond plane and the axial deformation mode of CH bonds [START_REF] Mistry | A Handbook of Spectroscopic Data -Chemistry[END_REF]. The absorption band around 1461 cm -1 may be related to the vibrational elongation of the -CN bonds, possibly coming from the free ends of the APTES molecules [START_REF] De Oliveira | Functionalization of cellulosic fibers with a kaolinite-TiO2 nano-hybrid composite via a solvothermal process for flame retardant applications[END_REF]. The band around 1000 cm -1 is characteristic of OH bonds and CO elongation.

The spectrum of the treated fabric showed peaks at 3690 and 3621 cm -1 , corresponding to structural OH (internal and external) vibration of aluminol groups (Al-OH) [START_REF] Li | Acetic acid functionalized TiO2/ kaolinite composite photocatalysts with enhanced photocatalytic performance through regulating interfacial charge transfer[END_REF], which indicates the presence of kaolinite. The peak at 1590 cm -1 may be related to the stretching vibration of Si-O bonds [START_REF] Li | Acetic acid functionalized TiO2/ kaolinite composite photocatalysts with enhanced photocatalytic performance through regulating interfacial charge transfer[END_REF] from the presence of kaolinite particles and APTES (adhesion agent used in the synthesis of KT immobilization on fibers). The absorption peak at 1622 cm -1 is related to N-H vibrational deformation [START_REF] Huang | A novel high whiteness flame retardant for cotton[END_REF], possibly from the APTES primary amine group. The peak around 900 cm -1 may be related to the vibrational elongation P-OH from the phosphorylation of some hydroxyl groups in the treated fiber [START_REF] De Oliveira | Functionalization of cellulosic fibers with a kaolinite-TiO2 nano-hybrid composite via a solvothermal process for flame retardant applications[END_REF]. The band observed at 671 cm -1 may be linked to the elongation of the Ti-O-Ti bonds [START_REF] Rashidzadeh | Synthesis of high-thermal stable titanium dioxide nanoparticles[END_REF][START_REF] Akram | Effect of reactant concentration on the physicochemical properties of nanosized titania synthesized by microwave-assisted continuous flow method[END_REF][START_REF] Andrés | Physical properties of high pressure reactively sputtered TiO2[END_REF] due to titania crystals immobilized in the kaolinite.

Antimicrobial properties

Table 1 shows the microbial activity (CFU quantification) of E. coli and B. cereus after contact with treated and untreated fabric samples. The fabric functionalized with KT composite showed excellent antimicrobial activity, both for E. coli (~99% reduction) and for B. cereus (100% reduction) compared to the control sample and the untreated fabric (see Fig. 3). Although mercerized and adequately rinsed, the nonfunctionalized fabric also showed some antimicrobial action, perhaps due to traces of sanitizing substances (e.g., surfactants) that may have remained in the fibers, even after several pre-washes. Considering that the composite contains TiO 2 , it is possible to assume that the antimicrobial action of the functionalized fabric occurs due to the attack of reactive oxygen species (ROS) [START_REF] Uyguner Demirel | A comprehensive review on the use of second generation TiO2 photocatalysts: microorganism inactivation[END_REF] photogenerated during the conditions of the dynamic test [START_REF] Godoy-Gallardo | Antibacterial approaches in tissue engineering using metal ions and nanoparticles: from mechanisms to applications[END_REF].

Table 1

Quantification of antibacterial activity of the untreated and treated fabric against E. coli and B. cereus.

KT particles immobilized on cotton fabric when in a liquid medium, under ambient light radiation for a sufficient time, can undergo photoexcitation and give rise to ROS. Although the dynamic method does not subject the working solution to specific high-energy lighting, it is well known that TiO 2 can be photoactivated even under natural light [START_REF] Spasiano | Solar photocatalysis: materials, reactors, some commercial, and pre-industrialized applications. A comprehensive approach[END_REF]. In our previous work [START_REF] De Oliveira | Synthesis of superacid sulfated TiO2 prepared by sol-gel method and its use as a titania precursor in obtaining a kaolinite/TiO2 nano-hybrid composite[END_REF], UV-vis DRS analyzes showed that the absorption energy band of KT (3.17 eV) is superior to that of TiO 2 (2.91 eV) alone (see Fig. S1 (b)). In this context, kaolinite possibly shifts the TiO 2 absorption edge to a higher energy region [START_REF] Shao | Sol-gel synthesis of photoactive kaolinite-titania: effect of the preparation method and their photocatalytic properties[END_REF], giving the composite superior optical properties, better redox capacity, and, consequently, better photocatalytic performance, which could explain the observed results.

The death outcome for B. cereus was slightly better than for E. coli, which may be related to gram-positive bacteria's lower cell wall complexity compared to gram-negative ones. Cell wall destruction depends on several factors, including the gram-positive or gram-negative nature of the bacteria. Many works report that the greater complexity of the cell wall of gram-negative bacteria can make it difficult to kill microorganisms under redox attack conditions, making them more resistant under certain conditions [START_REF] Godoy-Gallardo | Antibacterial approaches in tissue engineering using metal ions and nanoparticles: from mechanisms to applications[END_REF]. The bacterial cell wall is a multilayered structure composed mainly of proteins, lipids, and carbohydrates. The Gram-positive cell wall is formed of a thick layer of peptidoglycan (PGN) densely functionalized with anionic glycopolymers. The PGN layer is made up of N-acetyl glucosamine-N-acetyl muramic units cross-linked by pentapeptides [START_REF] Silhavy | The bacterial cell envelope[END_REF]. The Gram-negative cell wall contains a thinner layer of PGN located between the cell membrane and the outer membrane. The outer membrane is made up of lipopolysaccharides (LPS) (exclusive to Gram-negative bacteria). It serves as a strong barrier preventing the entry of hydrophobic substances and macromolecules, in addition to porins responsible for allowing the diffusion of selected molecules [START_REF] Godoy-Gallardo | Antibacterial approaches in tissue engineering using metal ions and nanoparticles: from mechanisms to applications[END_REF][START_REF] Silhavy | The bacterial cell envelope[END_REF]. Due to the low permeability of the outer membrane, Gram-negative bacteria are considered less sensitive, mainly to metal ions and nanoparticles. For these reasons, after the test, CFU quantification for E. coli (Gram-negative) was slightly lower than B. cereus (Gram-positive). Since TiO 2 nanoparticles are immobilized, and their size is much larger than that of bacterial cells, it is unlikely that the microbial inactivation mechanism is related to the adsorption and penetration of nanoparticles into the cytoplasmic membrane.

Fig. 4 shows the result of the parallel streak test. The test did not show the formation of microbial inhibition zone beyond the edges of the fabric, which corroborates the hypothesis of microbial inactivation by photocatalytic action of the treated fabric and not by leaching of KT particles. The analyzes assume that the antimicrobial activity of the functionalized cotton fabrics occurs by photocatalytic activation of TiO 2 , that is, under conditions of humidity and light radiation (with emission of photons with energy equal to or greater than the band-gap energy [START_REF] Hebeish | TiO2 nanowire and TiO2 nanowire doped Ag-PVP nanocomposite for antimicrobial and self-cleaning cotton textile[END_REF]), for the formation of ROS (see the Supplementary Materials section).

Mechanism of microbial inactivation

TiO 2 is widely reported as a semiconductor material with excellent photocatalytic performance when subjected to atmospheric and radiation conditions suitable for its photochemical activation [START_REF] Spasiano | Solar photocatalysis: materials, reactors, some commercial, and pre-industrialized applications. A comprehensive approach[END_REF][START_REF] Dědková | Antibacterial activity of kaolinite/nanoTiO2 composites in relation to irradiation time[END_REF]. A semiconductor material has two distinct regions between the layers of atoms, called valence band (VB) and conduction band (CB), with a distance between them called a bandgap. The bandgap region has no electronic states, and the bandgap energy can be defined as the minimum energy required for the excitation and promotion (leap) of an electron from a lower energy state (VB) to an unoccupied higher energy state (CB) [START_REF] Spasiano | Solar photocatalysis: materials, reactors, some commercial, and pre-industrialized applications. A comprehensive approach[END_REF]. When the semiconductor material (in this case, the TiO 2 crystals present in the composite) is exposed to light radiation with an energy equal to or greater than the bandgap energy, an electron (e -) in the filled VB is promoted to a vacant CB, leaving a positive gap (h + ) in VB (see Eq. ( 1)). The holes in the VB (h vb + ) give rise to a strongly oxidizing region, while the electrons in the CB give rise to a strongly reducing field. The electrons promoted from VB to CB can generate delocalized fields of energy on the crystalline structure of the material, providing electrical conductivity capacity similar the presented by metals. Thus, the composite containing TiO 2 acts as a heterogeneous photocatalysis material, mediating a redox process in the bacterial medium, promoting the formation of reactive oxygen species (ROS), such as ⋅O 2 -(Eq. ( 2)) and ⋅OH (Eq. ( 3)) [START_REF] Hebeish | TiO2 nanowire and TiO2 nanowire doped Ag-PVP nanocomposite for antimicrobial and self-cleaning cotton textile[END_REF][START_REF] Uyguner Demirel | A comprehensive review on the use of second generation TiO2 photocatalysts: microorganism inactivation[END_REF]. These species can react to give H 2 O 2 (Eq. ( 4)), hydroxide ions, and hydroperoxyl radicals (Eq. ( 5)).

TiO 2 + hv → e - cb + h + vb (Eq. 1b) O 2 + e - cb → • O - 2 (Eq. 2) h + vb + H 2 O → • OH + H + (aq)
(Eq. 3) Fig. 4. Results of the parallel streak method for the untreated (A) and treated (B) cotton fabric.

•OH + • OH→H 2 O 2 (Eq. 4)

•O - 2 + H + → • OOH (Eq. 5)

During the analyzes, the chemical species generated by the KT composite came into contact with the bacteria in the medium (working solution). The chemical attack of ROS promotes the oxidative degradation of lipids and proteins that form the cell wall of bacteria, increasing the permeability of ROS to the interior of the cells or causing the rupture of the membrane and leakage of the cytoplasm, culminating in the death of microorganisms [START_REF] Godoy-Gallardo | Antibacterial approaches in tissue engineering using metal ions and nanoparticles: from mechanisms to applications[END_REF][START_REF] Dědková | Antibacterial activity of kaolinite/nanoTiO2 composites in relation to irradiation time[END_REF]. Fig. 5 illustrates a possible mechanism of death of bacteria still inside the working solution.

Conclusion

The cotton fabric functionalized with the kaolinite-TiO 2 nano-hybrid composite exhibited excellent antimicrobial activity against Grampositive (~100%) and Gram-negative (~99%) bacteria. The observed microbial inactivation suggested a bacterial elimination mechanism guided by ROS photogenerated on the surface of KT-functionalized fabric while stirring the working solution. Although the method does not directly expose the samples to high energy radiation, previous analyzes of the composite suggest that the material has improved optical and photocatalytic properties compared to TiO 2 alone. In this context, the composite synthesized and immobilized in the cotton fabric seemed to fulfill the antimicrobial action well, even under weak radiation conditions. These results highlight the multifunctional behavior of the prepared textile which is promising for several applications.

Fig. 1 .

 1 Fig. 1. SEM-FEG micrograph of KT composite at 70000x.

Fig. 1

 1 Fig.1shows the micrograph of the KT composite on an image with

Fig. 2 .

 2 Fig. 2. FTIR analyzes and SEM-FEG micrographs of treated and untreated cotton fabric. (A) -FTIR analyzes of treated and untreated cotton fabric; (B) -Micrograph of treated fabric (it is possible to see the fiber covered by a mineral film); (C) -Micrograph of untreated fabric; (D) -Micrograph of KT composite immobilized on the surface of the fibers.

Fig. 3 .

 3 Fig. 3. Results of the dynamic contact test (ASTM E2149-13a) for (A) E. coli and (B) B. cereus.

Fig. 5 .

 5 Fig. 5. Mechanism of antimicrobial activity of KT functionalized cotton fabric. The cell wall scheme was adapted from Ref. [19], where, OMP: Outer membrane protein; IMP: Integral membrane protein; LPS: lipopolysaccharide; LTA: lipoteichoic acid; LP: lipoprotein; TA: wall teichoic acid; PGN: Peptidoglycan.

Acknowledgments

The authors are grateful to LABMASSA and LCME laboratories from the Federal University of Santa Catarina (UFSC). This study was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil -Finance Code 001.

Data availability

No data was used for the research described in the article.

CRediT authorship contribution statement

Declaration of competing interest

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

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.matchemphys.2022.127078.


Thomas Bergier
email: thomas.bergier@isae-supaero.fr

Romain Gojon

J Ér Émie Gressier

St Éphane Jamme

Laurent Joly

SWEEP EFFECTS ON A CANONICAL SHOCK WAVE/TURBULENT BOUNDARY LAYER INTERACTION

This study focuses on the effect of a sweep angle between the upstream mean flow direction and the shock plane normal in a canonical oblique shock wave/boundary layer interaction.

: an incident shock impinges on a turbulent boundary layer developing at free stream Mach number M = 2.7 and a Reynolds number Re θ = 3200. The sweep angle is implemented by adding a spanwise velocity component (crossflow) at the inflow and enforcing periodicity conditions on the side boundaries. Several sweep angles are investigated and compared to a canonical unswept case. A viscosity is selected for each case in an effort to keep a constant Re θ across the whole range of sweep angles. The mean flow structure is analyzed, showing a strongly skewed flow around the separation zone that increases in size compared to a reference unswept case. Pressure loads on the wall surface are also higher for swept cases; and the characteristic low-frequencies of the flow separation also slightly increase.

INTRODUCTION

Shock/boundary layer interaction (SBLI) is a phenomenon commonly found in supersonic airflows. Several different configurations have already been studied [START_REF] Clemens | Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions[END_REF]) over the last decades among which the interaction of an oblique shock impinging on a turbulent boundary layer (TBL) developing on a flat plate. This setup is known to lead to the formation of a separation bubble, due to the adverse pressure gradient created by the presence of the shock, as well as a "reflected" shock upstream of this bubble. This reflected shock/bubble system exhibits low frequency streamwise oscillations which can be the cause of detrimental pressure and load fluctuations. Efforts have been made to reduce the amplitude of these oscillations using control devices, among which micro-vortex generators. These devices and their impact on impinging SBLI configuration have been the focus of a recent work [START_REF] Grébert | Simulations of shock wave/turbulent boundary layer interaction with upstream micro vortex generators[END_REF]).

Even though SBLI and different control strategies have already been studied , most of these previous works were done on "canonical" setups, i.e cases not accounting for potential three-dimensional effects such as curvature of the wall or a sweep angle of the shock plane with respect to the incoming flow. These would however be more representative of a practical configuration of SBLI featuring vertical fins or swept ramps for instance. The objective of the present work is to address this question by investigating the effect of a sweep angle as shown in figure 1 using Large Eddy Simulations (LES).

NUMERICAL SETUP

The present LES were performed with the IC3 solver, which solves the spatially filtered compressible Navier-Stokes equation using, in our case, spectral difference methods applied on an unstructured mesh for the spatial discretization. Spectral difference methods (SD) are based on a polynomial representation of the solution inside the cell and of the numerical flow at the interface between cells [START_REF] Liu | Spectral dif-ference method for unstructured grids i: Basic formulation[END_REF]). Moreover, each control volume of the mesh is divided into several "spectral points" (also called "degrees of freedom", or "nDofs") where the solution is given and whose number depends on the order of the scheme used. A 4 rd order spectral scheme is used in the present work for the spatial part, meaning that each control volume (cv) contains 4 spectral points in each direction, giving a total of 64 solution points by cv. The temporal integration uses a 3 rd order Runge-Kutta method and no subgrid scale model is used. In order to deal with discontinuities, we use a limiter specially developed for high-order compact numerical schemes such as SD methods, named SWeP (Spatially Weighted Projections). This limiter is based on a reduction of the order of the polynomial used to describe the solution at the cells affected by discontinuities [START_REF] Lamouroux | A high-order compact limiter based on spatially weighted projections for the spectral volume and the spectral differences method[END_REF]). The size of the computational domain in our simulations corresponds to L x × L y × L z = 59.6δ i × 17.95δ i × 8.54δ i , δ i being the boundary layer thickness at the inlet of the domain 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)

Osaka, Japan, July 19-22, 2022 The SBLI configuration selected in this work is the one studied by [START_REF] Grébert | Simulations of shock wave/turbulent boundary layer interaction with upstream micro vortex generators[END_REF] and is based on [START_REF] Bo | Experimental investigation of the microramp based shock wave and turbulent boundary layer interaction control[END_REF] experiments. The physical parameters used in the inlet of the computational domain, as well as the shock features (angle of shock ψ), are summarized in Table 1. Regarding the boundary conditions (see figure 1 for their location), an adiabatic wall is used on the bottom boundary, a symmetry condition is used at the shock generator so that no boundary layer develops here and, on the upper boundary, value of the primitive variables of the flow are imposed. For the outlet, in the supersonic area (outside of the boundary layer) variables are extrapolated. For the subsonic area (inside the boundary layer), the value of static pressure is imposed equal to the mean of the pressure retrieved at the outlet for the supersonic area. At the inlet, the production of turbulence is achieved thanks to a "digital filtering" technique based on a filtering operation applied to statistical data [START_REF] Touber | Large-eddy simulation of low-frequency unsteadiness in a turbulent shockinduced separation bubble[END_REF]). It was first introduced by Klein et al. (2003) and then modified by [START_REF] Xie | Efficient generation of inflow conditions for large eddy simulation of street-scale flows[END_REF] and [START_REF] Touber | Large-eddy simulation of low-frequency unsteadiness in a turbulent shockinduced separation bubble[END_REF]. This method presents the advantage of not introducing any artificial low-frequency mode, as opposed to recycling or synthetic turbulence techniques. This is important in the case of SBLI as this phenomenon is known for displaying low-frequency dynamics. However, turbulence obtained thanks to digital filtering needs a certain length of development, around [15-20δ i ], to reach a physical state.

RESULTS

The aim of these simulations is to compare the behaviour of the mean flow, as well as the unsteady behaviour of the interaction system for different sweep angles. The sweep angles (β ) considered in this work are given in Table 2. The simulations are performed with what is called in the literature "infinite sweep", meaning that sweep is obtained introducing a spanwise (crossflow) velocity component for the incoming flow and using periodic conditions at the spanwise boundaries. Thus, in our computational domain, the shock plane stays the same as in the unswept case but the upstream flow is modified (figure 1). It should be noted that in the flow configuration of a swept shock impinging on a boundary layer, two flow configurations can be observed experimentally regarding the Table 2: Parameters for the different swept case upstream of the interaction. 2 is the axial Mach number (M x = u/c 0 ) : the added spanwise velocity component has no influence on the shock itself as its plane is aligned with the spanwise direction and tangential velocity is conserved. Thus, the incident shock features (angle ψ and flow deviation) are the same regardless of the sweep angle. It should also be noticed that as upstream velocity magnitude is increased to reach the desired sweep angle, the viscosity of the fluid is also increased, with the aim to keep a constant Reynolds number (as well as constant axial Mach number) across our sweep angle range. This can be verified in Table 2 that reports very close values for Re θ measured at the interaction location between our different cases.

β ( • ) w ∞ (m/s) µ ∞ (Pa • s) Re θ (x = X int ) M x 0 0 4.5 ×

Boundary layer validation

Before carrying out the swept SBLI computations, the state of the upstream turbulent boundary layer has to be assessed. Indeed, we have to make sure that the synthetic turbulence created at the inlet has developed well and that it is consistent between our different cases. The turbulent boundary layer characteristics are shown in figure 2 for the different sweep angles and compared to DNS data or correlations from the literature. The value of incompressible friction coefficient C f i is obtained thanks to the van Driest II transformation [START_REF] Van Driest | On turbulent flow near a wall[END_REF]) :

C f i = F c C f with F c = T w /T ∞ -1 arcsin 2 α and α = T w /T ∞ -1 T w /T ∞ (T w /T ∞ -1) (1)
with T w the wall temperature. This allow to compare our data, obtained from compressible simulation, with incompressible data or correlations, like Karman-Schoenherr 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)

Osaka, Japan, July 19-22, 2022

(KS) or Blasius (BL) [START_REF] Hopkins | An evaluation of theories for predicting turbulent skin friction andheat transfer on flat plates at supersonic and hypersonic mach numbers[END_REF]) :

C f KS = 1 17.08 log(Re θ i ) 2 + 25.11 log(Re θ i ) + 6.012

C f BL = 0.026 (Re θ i ) 1/4 , with Re θ i = µ ∞ µ w Re θ (2)
µ w being the dynamic viscosity at the wall. The shift in Re θ i observed on the upper image of figure 2 when the sweep angle increases can be explained by the fact that as β goes up, µ e increases more than does µ w (which is obtained from T w with a power law). The development length of the turbulence can clearly be seen looking at the undershoot of C f i tot near the inlet of the domain. More downstream, all curves can be found at reasonable C f i levels compared to the correlation, and pretty close to each other. On the bottom figure, the Reynolds stress tensor components are globally close to the DNS results. Differences can however be observed, particularly for the < u v > component which is overestimated over the whole profile compared to the reference data.

SBLI results and sweep effects

Regarding the SBLI simulations, the mean flow is studied first, especially near the interaction zone. Time-averaged skin friction lines are presented in figure 3, where they are superimposed to a colormap displaying the difference between the prescribed sweep angle and the actual angle of the flow with respect to the longitudinal (x-wise) direction. This measure was chosen because it provides a clear visualization of the separated area. This zone seems to grow in size as the sweep angle increases. This observation is comforted by the study of the x-wise skin friction coefficient (defined using the longitudinal component of the wall shear stress) along the bottom wall which shows a greater separated area (zone where C f x < 0) 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)

Osaka, Japan, July 19-22, 2022 when the sweep angle increases, as seen in figure 4 (bottom). A possible explanation for this phenomenon, also presented by [START_REF] Larsson | Large-eddy simulations of idealized shock/boundary-layer interactions with crossflow[END_REF], is that the wall being adiabatic and the overall Mach number increased by the added swept, the wall temperature at a given longitudinal location is higher for a higher sweep angle. This induces a decreased near-wall density, and thus decreased near-wall inertia, leading to an upstream shift of the separation line. The different separation lengths and wall average temperatures (given for x = 35δ i , at a location just upstream of the interaction) are specified in Table 3. As it stands, we cannot ensure that temperature alone plays the dominant role in the growing of the separated area. Indeed, a study involving constant wall temperature across the whole sweep angle range would be needed to discriminate the different possible effects (see [START_REF] Larsson | Large-eddy simulations of idealized shock/boundary-layer interactions with crossflow[END_REF] for such a study). In addition to the longitudinal size of the separation bubble, one can take an interest in the wall-normal size of said bubble. Figure 5 shows maps of time-averaged longitudinal velocity (u) in the xy plane around the interaction zone. The separation bubble is found to grow slightly in size as the the sweep angle increases, even if the differences remain very small and are not easy to discriminate on the figure.

In order to investigate the behaviour of the flow away from the wall, we present in figure 6 the streamlines at four y-locations distributed across the thickness of the inlet boundary layer (i.e. for 0 < y < δ i ) for the the swept cases β = 15 • and β = 20 • . It can clearly be seen that the flow is highly deviated near the separation and reattachment lines, and that the closer to the wall, the more important the deviation. This leads to a strongly skewed flow around the separation zone, which makes it prone to develop flow instabilities in this region. Further downstream, the flow tends to recover towards the expected post-shock direction, beyond x/δ i = 50, even though a full recovery is not reached before the end of the computational domain. Figure 7 displays the streamwise evolution of the angle of the flow with respect to the x axis (i.e. arctan(< w > / < u >)). The above-mentioned remarks are confirmed by theses curves that also show a complete reversal of the flow direction (obtained when arctan(< w > / < u >) > 90 • ) inside the separated region for the layers of the flow the closest to the wall. is greater between 20 and 15 degrees than the one seen between 0 and 15 degrees, despite a similar increase in wall temperature in both cases.

In addition to the effect on mean flow properties, it can be expected that the introduction of a sweep angle could also have an impact on the unsteady dynamics of the interaction. The intensity of the fluctuating pressure loads at the wall around the interaction area is also of particular importance in practical applications. To quantify this, we use a metric introduced by [START_REF] Grébert | Simulations of shock wave/turbulent boundary layer interaction with upstream micro vortex generators[END_REF], defined as follows:

I F S (x) = F 2 S (x) F S (x) with F S (x,t) = z P w (x, z,t)ds (3)
Figure 9 shows the evolution of I F S (x) along x axis for the 3 sweep angles studied. It can be observed that adding a spanwise velocity component induces higher intensity of pressure loads, even though the maximum level presented here for the β = 15 • case is higher than the β = 20 • one right after the reflected shock (around x/δ i = 38). Further downstream, the higher the sweep angle, the higher the I F S (x). The effect of a crossflow is thus potentially detrimental for the structural loading of the surfaces involved in this type of configurations. 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12) Osaka, Japan, July 19-22, 2022

SUMMARY

In this work, several LES simulations have been conducted in order to compare swept and canonical shock/boundary layer interaction configurations. Results show that the sweep angle affect both the average flow and the unsteady low-frequency dynamics of the SBLI. The size of separated flow grows with the sweep angle, which can be linked to an increased wall temperature due to the added transverse velocity and the adiabatic nature of the wall. Around the separated bubble, the flow is highly skewed for the swept cases, which is favorable to the development of instabilities. It then gently recovers the expected post-shock direction. Pressure loads on the wall surface are higher for swept cases, which can be detrimental in real-life configurations such as supersonic air-intakes. The well-known unsteadiness of SBLI configurations is also altered by the presence of sweep, its characteristic low-frequency being slightly shifted to higher values.

Figure 1 :

 1 Figure 1: Schematic representation of a swept configuration of SBLI and associated computational domain. Side view (top), top view (bottom).

Figure 2 :

 2 Figure 2: Top : Time and spanwise-averaged incompressible friction coefficient, based on longitudinal and spanwise velocity components (u and w) over the bottom wall, upstream of the interaction. Bottom : Reynolds stress tensor components (spanwise-averaged), values are made dimensionless by taking into account u and w.

Figure 3 :

 3 Figure 3: Time-averaged skin-friction lines superimposed to a colormap displaying the gap between the reference angle and the actual computed angle arctan(< w > / < u >) at the bottom wall. From top to bottom : β = 0 • , β = 15 • , β = 20 • .

Figure 4 :

 4 Figure 4: Top : Evolution of C p = (P w -P ∞ )/(γP ∞ M 2 x /2), time-averaged pressure coefficient. Bottom : evolution of C f x , time-averaged x-wise skin friction coefficient around the separated area. The horizontal dashed line corresponds to C f x = 0, used to delimit the extent of the separation bubble.

Figure 5 :

 5 Figure 5: Maps of time-averaged longitudinal velocity. Incident and reflected shocks locations (extrapolated inside the boundary layer) are marked with dashed lines. Mean separation location is located with white circle and mean reattachment point with white square. Scale is the same for the 3 maps and ranges from u = 0 to u = u ∞ . From top to bottom : β = 0 • , β = 15 • and β = 20 • .

Figure 6 :

 6 Figure 6: Streamlines for different wall-normal altitudes, ranging from the wall (skin-friction lines are plotted in that case) to y = δ i . Top : β = 15 • , bottom : β = 20 •

Figure 7 :

 7 Figure 7: Flow angle with respect to x axis (given by arctan(< w > / < u >)) for different wall-normal altitudes, ranging from the wall (angle of skin-friction lines are plotted in that case) to y = δ i . The horizontal full line situated at 90 • allow to see where the flow is reversed. Horizontal dashed line shows the upstream imposed sweep. Top : β = 15 • , bottom : β = 20 • .

  Figure 8 shows maps of spanwise-averaged Power Spectrum Densities (PSD) of wall pressure fluctuations. On the upper figure, the characteristic spectrum of a canonical unswept SBLI can be observed with low frequencies near the separation line. These frequencies are typically found to be two orders of magnitude below the ones associated with the upstream turbulent boundary layer. According to Piponniau et al. (2009), who developed a model for the low frequency unsteadiness of SBLI, a value of Strouhal Stl Lsep = f • Lsep/U ∞ = 0.03 should be observed for a flow with an upstream Mach number above 2. Downstream of the interaction, intermediate frequencies tend to dominate and are linked with shear layer vortices developing at the edge of the separation bubble. These observations are in line with several previous numerical and experimental studies ( Dupont et al. (2006), Touber & Sandham (2009), Priebe & Martn (2012), Grilli et al. (2012)). When a spanwise velocity is added, peaks associated with higher frequencies appear near the average separation location. As seen on figure 8, values of Stl Lsep of 0.1, 0.18 and 0.2 exhibits high energetic content. For β = 20 • , we can moreover see a shift of the lowest-frequency peak from Stl Lsep = 0.03 to Stl Lsep = 0.05.

Figure 8 :

 8 Figure 8: Spanwise-averaged PSD spectra of wall pressure fluctuations. From top to bottom : β = 0 • , β = 15 • , β = 20 • . PSD are normalized by local integral PSD(x, f ) d f . x sep and x r stands for the mean locations of separation and reattachment respectively. The horizontal dashed lines are located at Stl Lsep = 0.03 and Stl Lsep = 0.06

Table 1 :

 1 Physical parameters of the simulation

	M ∞	T ∞	P ∞	u ∞	ψ
	2.7 300 K 101 kPa 937 m/s 30.3 •
	(δ i = 1.12 × 10 -3 m). The grid is uniform along spanwise (z
	coordinate) and longitudinal (x coordinate) directions, except
	in the region near the interaction where the longitudinal size
	of the cells is reduced to better handle the strong adverse
	pressure gradient. With this meshing strategy, we have
	∆ + x = [11.5; 16.8] and ∆ + z = 10.6. The grid in the wall-normal
	direction (y coordinate) is gradually refined towards the
	bottom wall with ∆ + y = [0.6; 72.1]. As we do not use any wall
	model, this level of precision is needed near the wall to be able
	to resolve accurately the viscous sub-layer of the boundary
	layer. The mesh results in 1384 × 216 × 260 nDofs in x, y and
	z directions respectively, giving a total of around 77.7×10 6
	nDofs.

  [START_REF] Padmanabhan | Experimental study of swept impinging oblique shock/boundary-layer interactions[END_REF]). For low sweep angles, a cylindrical symmetry is expected, i.e separation and reattachment lines are parallel, whereas for higher sweep angles, conical symmetry appears, meaning that the separation and reattachment lines are no longer parallel. As previously mentioned, periodic boundary conditions are imposed in the simulations presented in this work, preventing conical symmetry of the interaction area, and making it irrelevant to study these cases with our current numerical setup. According to[START_REF] Padmanabhan | Experimental study of swept impinging oblique shock/boundary-layer interactions[END_REF], the limit between cylindrical and conical symmetries for their configuration, which is quite close to ours, is 24.7 • . This is why we chose to study the range of sweep angles presented in Table2, all belonging to the cylindrical symmetry. It can also be noted that the Mach number given in Table

			10 -5	3371	2.7
	15	251.27	4.681 × 10 -5	3367	2.7
	20	341.32	4.812 × 10 -5	3381	2.7
	topology of the interaction area depending on the value of
	the sweep angle (

Table 3 :

 3 Comparison between separation length and temperature upstream of interactionβ ( • ) L sep /δ i T w (x = 35δ i )/T ∞

	0	4.84	2.18
	15	5.01	2.25
	20	5.24	2.31

ACKNOWLEDGEMENTS

This research was supported by the French Ministry of Defense through the financial support of the DGA (grant #2020-650026). This work was performed using resources from GENCI [CCRT-CINES-IDRIS] (Grant 2021-[A0102A07178] and 2022-[A0122A07178]).