Renaud Ansart
email: renaud.ansart@ensiacet.fr

Florence Vanni

Brigitte Caussat

Carine Ablitzer

Méryl Brothier

Effects of reducing the reactor diameter on the dense gas-solid fluidization of very heavy particles: 3D numerical simulations

Keywords:

Very dense particles suspension

Euler-Euler modeling

Micro fluidized bed

In this study, 3D numerical simulations using an Eulerian n-fluid approach of a gas-solid fluidized bed composed of very dense particles of tungsten (19,300 kg m -3 ) were carried out to examine the behavior of this suspension, especially the effects of the reduction of the fluidization column diameter on the fluidization quality. Tungsten was selected as a surrogate material of U(Mo) (Uranium molybdene) which is of interest for new nuclear fuels with limited enrichment. Comparisons between experiments and computations for the axial pressure profile of a 5 cm diameter column demonstrate the capability of the mathematical models of the NEPTUNE CFD code to simulate the fluidization of this powder located outside the classification of Geldart. The numerical results show that the mobility into the bed of these very dense particles is very low. The reduction of the fluidization column diameter from 5 cm to 2 cm does not have significant effect on the local solid circulation but strongly decreases the axial and radial mixing of the particles due to wall-particles friction effects. These results confirm and allow to better understand the wall effects experimentally evidenced.

Introduction

Gas-solid fluidized beds (FB) are widely used in industrial applications such as drying, coal combustion [START_REF] Basu | Combustion of coal in circulating fluidized-bed boilers: a review[END_REF] and gasification [START_REF] Hofbauer | Six years experience with the FICFB-Gasification Process[END_REF], oil refining and nuclear application [START_REF] Kunii | Fluidization Engineering[END_REF]. This is due to the fact that FB reactors have excellent heat and mass transfer capabilities, high throughput rates, and can operate continuously, thus reducing operating costs [START_REF] Ydstie | Producing Poly-Silicon from Silane in a Fluidized Bed Reactor[END_REF][START_REF] Liu | Numerical simulations of particle growth in a silicon-CVD fluidized bed reactor via a CFD-PBM coupled model[END_REF].

In the nuclear field, new fuels, with limited enrichment in 235 U, are under development for research reactors. U(Mo) (Uranium molybdene) fuel powders dispersed in an aluminum matrix are among the most promising materials. But the coating of U(Mo) by a barrier material is necessary to limit interfacial interactions between the fuel and its matrix under irradiation [START_REF] Mazaudier | Further insight into mechanisms of solid-state interactions in UMo/Al system[END_REF]. Silicon seems to be a good candidate [START_REF] Zweifel | Crystallographic study of Si and ZrN coated U-Mo atomised particles and of their interaction with al under thermal annealing[END_REF]. Among other technics, the Fluidized Bed Chemical Vapor Deposition process (FB-CVD) is under study to deposit uniform silicon layers on U(Mo) particles (Vanni et al., 2015a). FB-CVD is an efficient technology to uniformly coat powders by a great variety of materials [START_REF] Vahlas | Principles and applications of CVD powder technology[END_REF]. There is an interest in being able to treat weights of U(Mo) as low as possible by the FB-CVD process. It is to http://dx.doi.org/10.1016/j.cherd.2016.11.008

Nomenclature

Roman symbols Ar

Archimede number (-) d p particle diameter (m) e c particle-particle normal restitution coefficient (-) g gravitational constant (m s -2 ) m p particle mass (kg m -3 ) P mean gas pressure (N m -2 ) q 2 p random kinetic energy (m 2 s -2 ) U k,i mean velocity of phase k (m s -1 ) U mf minimum fluidization velocity (m s -1 ) u k,i fluctuating velocity of phase k (m s -1 ) V f superficial gas velocity (m s -1 )

Greek symbols ˛k volume fraction of phase k (-) g gas viscosity (kg m -1 s -1 ) k density of phase k (kg m -3 ) p granular temperature (kg m -2 s -2 ) Subscripts g gas p particle be noted that for preliminary experiments a tungsten powder (19,300 kg m -3 , 75 m of median diameter) whose properties are very close to those of U(Mo) (17,500 kg m -3 , 50 m median diameter) has been used as a surrogate powder. Both powders are of very high density. The maximum dimensionless density is 10,000 in the Geldart's classification, but the dimensionless density of the tungsten particles clearly exceeds the upper limit (Fig. 1). First experiments have demonstrated that the FB-CVD technology can uniformly coat 1,500 g of tungsten powder with silicon in a reactor of 3.8 cm in diameter. Other experiments have shown that this weight cannot be decreased in the reactor of 3.8 cm because the target deposition temperature (650 • C) cannot be reached since heat exchange between the reactor walls and the bed of particles becomes too low (Vanni et al., 2015a). An experimental study has been conducted in glass and steel columns to specifically analyze the impact of decreasing the reactor diameter from 5 to 2 cm on the fluidization hydrodynamics of the tungsten powder (Vanni et al., 2015b). It was found that uniform silicon deposition could only be achieved if the fluidized bed hydrodynamics was of good quality, i.e. if it involves high thermal and mass transfer rates between the gas and the solid phases. This experimental study has shown that wall effects decreasing the quality of bed hydrodynamics appear in the reactor of 2 cm for 100 g and 180 g of powder. This was evidenced by an increase of the hysteretic behavior of the pressure drop curves, an increase of the minimum fluidization velocity and a decrease of the bed voidage. This was especially evident in a glass column where the electrostatic effects cannot be neglected (Vanni et al., 2015b).

The aim of the present study is to complement the experimental work by using 3D numerical simulations to analyze more precisely the influence of a decrease of the reactor diameter on some key local parameters of the fluidized bed hydrodynamics. The results are expected to be helpful in the FB-CVD process design and in the choice of its optimal gas flow parameters.

Very few studies are available in the literature about the numerical simulation of fluidized beds involving such dense particles. For UO 2 particles of 2 mm in diameter, Liu et al. (2015a) studied the impact of particle density up to 10,800 kg m -3 on the fluidization behavior of particles in spouting bed using 2D CFD-DEM coupling. The particle cycle time, spout behavior, dominant spout frequency and gas-solid contact efficiency was discussed and a flow pattern map under different densities and different gas velocities was obtained. [START_REF] Pannala | Simulating the dynamics of spouted-bed nuclear fuel coaters[END_REF] also studied conical spouted bed with heavy particles (up to 6,050 kg m -3 zirconia particles for nuclear fuel coaters) by 2-D Eulerian-Eulerian numerical simulations.

Miniaturization of chemical reactors, which is one of the most popular research areas in chemical engineering, has led to the concept of micro-fluidized bed reactors (Wang et al., 2011). Wang et al. (2011) have shown by CFD simulations that for Geldart A particles, the onset of turbulent fluidization is advanced significantly in micro fluidized beds. [START_REF] Zivkovic | On importance of surface forces in a microfluidic fluidized bed[END_REF] pointed out the importance of wall surface forces relative to volumetric forces, such as gravity, on micro-scale fluidized beds (the cross-sectional dimensions of the microchannels were 400 × 175 m 2 ). Liu et al. (2015b) performed several 2D Eulerian-Eulerian numerical simulations for a gas-solid micro-fluidized bed (channel width 3 mm) for Geldart A particles (53 m and 1,400 kg m -3 ) and compared the predicted minimum bubbling velocity and bed voidage to experimental measurements. They used very fine meshes (of approximately one particle diameter). Using the Gidaspow drag model, their simulations have shown that the predicted minimum bubbling velocities were significantly lower than their experimental data (Liu et al., 2015b). [START_REF] Wang | Gas-solid fluidization in mini-and micro-channels[END_REF] have established a flow regime map from experimental results obtained in column diameters starting from 0.7 mm to 5 mm in size for FCC particles. Their results revealed an increase in the minimum fluidization and bubbling velocities compared to those in large-scale fluidized beds. To the best of our knowledge, no numerical work has been reported concerning reduced diameter fluidized beds of heavy particles, which are studied in the present article.

The experimental fluidization set-up will be first presented before detailing the numerical model and presenting and discussing the results of the simulation. [START_REF] Thonglimp | Vitesse minimale de fluidisation et expansion des couches fluidisées par un gaz[END_REF] 3.2 cm s -1 Fig. 2 -Schematic of the experimental setup.

Experimental set up

The experimental set up is composed of three steel columns of 1 m height and 5, 3 and 2 cm of inner diameter (Vanni et al., 2015b). All are equipped with a similar Inox porous plate distributor (Poral TM 40). The tungsten powder used (CERAC, Inc. T-1220) is supplied by Neyco. Its grain density is claimed to be 19,300 kg m -3 . The Particle Size Distribution characteristics of the powder are summarized in Table 1 with its bulk density. The experiments were conducted at ambient temperature using argon as the fluidizing gas. Its flow rate was controlled by a mass flow controller (Aera FC-7710 C0, 0-20 slm). A differential fast response pressure sensor (GE Druck LPX 5380), with taps under the distributor and on top of the column, was used to measure the total pressure drop across the bed and determine the minimum fluidization velocity. Three other pressure sensors were set on the 5 cm column at 0 cm, 3 cm and 4.5 cm above the distributor to measure the axial pressure profile (Fig. 2). The sampling rate for pressure measurement is 2 Hz and the time-averages are realized during 2 min.

Numerical simulation description: Euler n-fluid approach

Three-dimensional numerical simulations are carried out using the code NEPTUNE CFD. This Eulerian n-fluid unstructured parallelized multiphase flow software has been developed in the framework of the NEPTUNE project financially supported by CEA (Commissariat à l'Energie Atomique et aux énergies alternatives), EDF (Electricite de France), IRSN (Institut de Radioprotection et de Sureté Nucléaire), and AREVA-NP [START_REF] Méchitoua | An unstructured finite volume solver for two-phase water/vapour flows modelling based on elliptic oriented fractional step method[END_REF]. The modeling approach for poly-dispersed fluid-particle flows is implemented by the Institut de Mécanique des Fluides de Toulouse (IMFT) in the NEPTUNE CFD V1.08 version. The numerical solver has been developed for High Performance Computing [START_REF] Neau | NEPTUNE CFD high parallel computing performances for particle-laden reactive flows[END_REF][START_REF] Neau | High performance computing (HPC) for the fluidization of particle-laden reactive flows[END_REF].

Mathematical models

The Eulerian n-fluid approach used is a hybrid method [START_REF] Morioka | Modeling of gas and solid particles two-phase flow and application to fluidized bed[END_REF] in which the transport equations are derived by phase ensemble averaging for the continuous phase and by use of the kinetic theory of granular flows supplemented by fluid effects for the dispersed phase.

The momentum transfer between gas and particle phases is modeled using the drag law of Wen and Yu [START_REF] Wen | Mechanics of fluidization[END_REF], limited by the Ergun [START_REF] Ergun | Fluid flow through packed columns[END_REF] equation for dense flows [START_REF] Gobin | Fluid dynamic numerical simulation of a gas phase polymerization reactor[END_REF][START_REF] Fede | 3D numerical simulation of a lab-scale pressurized dense fluidized bed focussing on the effect of the particle-particle restitution coefficient and particle-wall boundary conditions[END_REF]. The collisional particle stress tensor is derived in the frame of the kinetic theory of granular media [START_REF] Boëlle | Second-order prediction of the prediction of the particle-phase stress tensor of inelastic spheres in simple shear dense suspensions[END_REF]. In the present study the gas flow equations are treated as laminar because the gas Reynolds stress tensor in the momentum equation is negligible compared to the drag term. For the solid phase, a transport equation for the particle fluctuant kinetic energy, q 2 p , is solved. According to the large inertia of the particles and to the low inelasticity of particles (e c = 0.9), the spatial correlation between neighboring particle fluctuant velocities will remain negligible [START_REF] Fox | On multiphase turbulence models for collisional fluid-particle flows[END_REF][START_REF] Fevrier | Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study[END_REF][START_REF] Simonin | On the spatial distribution of heavy-particle velocities in turbulent flow: from continuous field to particulate chaos[END_REF]. The particle fluctuating motion may be assumed spatially uncorrelated obeying the so called molecular chaos assumption so that the product of the particle mass and particle fluctuant kinetic energy m p q 2 p can be identified to the granular temperature p defined in spatial granular flow theories [START_REF] Lun | The effects of an impact velocity dependant developed by sheared granular material[END_REF]).

The gas-particle turbulent correlation is negligible. The effects of the particle-particle contact force in the very dense zone of the flow are taken into account in the particle stress tensor by the additional frictional stress tensor [START_REF] Srivastava | Analysis of a frictional kinetic model for gas/particle flows[END_REF]. All the equations of the Euler-Euler approach are detailed in [START_REF] Fotovat | Sand-assisted fluidization of large cylindrical and spherical biomass particles: experiments and simulation[END_REF].

Numerical parameters

Geometry

The reference fluidized bed is a column of 5 cm in diameter and 40 cm in height with a conical portion at its top end. The influence of the column diameter reduction is analyzed by comparison with columns of 3 and 2 cm in diameter and of similar height.

Mesh

The 3D reference mesh (Fig. 3) is composed of 277,635 hexahedra, based on O-grid technique with 50 cells on the column diameter and approximately x = y ≈ 1 mm and z = 1.9 mm. It is noteworthy that a finer mesh, refined of 1.5 in each space direction, has been tested but no mesh refinement effect was observed on the bed height and on the time-averaged radial profiles of solid volume fraction, solid velocity and solid time variance velocity. The meshes for the 3 and 2 cm column diameter have exactly the same number of cells and were obtained by applying homothetic transformation.

Phase properties

The flow is composed of two phases: gas (argon) and tungsten particles. The phases' properties are summarized in Table 2. The particles are assumed to be spherical with a monodisperse diameter equal to the Sauter diameter. The authors have tested simulations with the median diameter but discrepancy with experimental results were observed especially for the prediction of the minimum fluidization velocity.

Boundary conditions

At the bottom (z = 0), the fluidization grid is an inlet for the gas with an imposed uniform superficial velocity (V f ) corresponding to the fluidization velocity and a wall for the particles. At the top of the fluidized bed, a free outlet for both gas and particles is defined. The wall-type boundary condition is no-slip for the gas and for the particles [START_REF] Fede | 3D numerical simulation of a lab-scale pressurized dense fluidized bed focussing on the effect of the particle-particle restitution coefficient and particle-wall boundary conditions[END_REF].

Initial conditions

The solid masses used in each column are detailed in Table 3. They correspond to a ratio between the fixed bed height and the column diameter H 0 /D close to 3.

Simulation progress

The numerical simulations have been performed on parallel computers with 20 cores. A numerical simulation is divided

Results and discussion

As shown in Fig. 4, Vanni et al. (2015b) have observed wall effects for a 2 cm glass column, consisting in an increase of the hysteretic behavior between increasing and decreasing pressure drop curves and of the minimum fluidization velocity in the glass column. This observation is less marked in the steel column due to the reduction of electrostatic forces. Defluidization curves in Fig. 5 present a comparison between numerical results and experimental measurements carried out of the total bed pressure drop at decreasing gas velocity in the steel column Vanni et al. (2015b). The horizontal dashed lines correspond to the theoretical bed pressure drop (equal to the bed weight per column surface area). A relative good agreement can be observed. However, the numerical results slightly underestimate the pressure in the fixed bed part. This leads to an overestimation of the minimum fluidization velocity as detailed in Table 4. This slight overestimation of the minimum fluidization velocity can be attributed to the non regular shape of particles (Fig. 6). It is noteworthy that the numerical results predict an increase of the minimum fluidization velocity for the column of 2 cm as the experimental ones, confirming the existence of wall effects. The [START_REF] Thonglimp | Vitesse minimale de fluidisation et expansion des couches fluidisées par un gaz[END_REF] correlation was used to calculate U mf . The value of 3.2 cm s -1 was found logically close to the experimental U mf value in the steel 5 cm column where the electrostatic and wall effects are minimum.

For the following simulations, the gas fluidization velocity has been fixed at 12 cm s -1 . The fluidization ratio is then close to 3 for the columns of 5 and 3 cm and to 2.8 for the column of 2 cm. The minimum fluidization velocities used to calculate the fluidization ratio are the experimental ones. They are extracted from Fig. 5 using the Davidson and Harrison method [START_REF] Davidson | Fluidized Particles[END_REF].

The predicted time-averaged gas pressure at the wall as a function of height for the three steel columns is presented in Fig. 7. The numerical data were extracted from the cells directly at the wall to plot these curves. For all cases, the gas pressure drop is linear inside the bed with almost the same slope. The pressure gradient is then constant and is not a function of the column diameter. Moreover, the experimental measurements for the column of 5 cm show a very good agreement with the numerical values.

Table 5 shows the time-averaged pressure gradient predicted at the wall. The values of the pressure gradient inside the bed for the different columns are almost the same as previously observed. Using this pressure gradient at the wall, the void fraction of the overall fluidized bed has been estimated by neglecting the friction forces of the particles at the wall and assuming an equilibrium between the buoyancy and the drag forces:

¯g = 1 - 1 ( p -g )g P L (1)
This estimation of the bed void fraction can be compared to the mean volume fraction obtained by integrating the local void fraction over the entire cells of the computational domain:

˛g = V bed ˛g dV (2)
This comparison (last line, Table 5) shows that the relative error increases with the reduction of column diameter. Hence, for the conditions tested, the friction forces at the wall can not be neglected anymore for a 2 cm column of fluidization. The smaller the column diameter is, the higher are the wallparticle friction forces. When the column diameter decreases, the ratio between the wall surface and the particles volume increases which generates a lifting effect of the bed. Thus, the reduction of the column diameter increases the void fraction causing the bed expansion. No experimental measurements Table 6 -Phases properties used for the simulation of sand particle.

Parameters Value

Gas density (Argon) 1.6 kg m -3 Gas viscosity 2.23 × 10 -5 Pa s Sand particle diameter 206 m Sand particle density 2,600 kg m -3 U mf [START_REF] Thonglimp | Vitesse minimale de fluidisation et expansion des couches fluidisées par un gaz[END_REF] 3.2 cm s -1 have been performed in the steel column to be compared with these predicted values. Some time-averaged radial profiles have been calculated at 2/3 of the bed height. The bed height has been determined (Table 5) from the changing slope of the axial profiles of the time-averaged gas pressure (Fig. 7). Consequently, the profiles were extracted on one cell at the position of z = 9.1 cm, 6.6 cm and 3.6 cm respectively for the columns of 5 cm, 3 cm and 2 cm. Fig. 8(a) shows the time-averaged radial profile of the solids volume fraction. Numerical predictions present a minimum at the center of the tube and a maximum near the wall. This trend is the same as that normally observed for classical Geldart group B particles. However, by performing specific simulations with sand particles (Table 6) of similar minimum fluidization velocity, we have verified that the fluidization of tungsten powder shows high solid volume fraction in comparison to results obtained for more conventional sand particles. Thus, the expansion of this powder is lower than for sand particles. Moreover, it is noteworthy that the reduction of column diameter induces a reduction of the extrema of the timeaveraged radial profile of the solids volume fraction and so an increase of the mean bed void fraction. This effect confirms the previous observations on the increase of the void fraction.

Fig. 8(b) and (c) shows respectively the time-averaged vertical component of solid phase velocity and the associated solid mass flux. The radial profiles are similar with a positive maximum value at the center and a negative minimum one close to the wall due to bubble rise in the center of the tube. Because the size and then the velocity of the bubbles are limited by the reduction of the column diameter, the maximum of the particle velocity decreases.

The particles rise at the center of the column is observed in Fig. 9 which shows the solid velocity vectors for the three columns. An upward solid flow in the center of the tube and a downward more concentrated solid flow near the wall are clearly observed with the formation of two 2D loops (resulting in torus in 3D cylindrical geometry) at the bottom and at the top of the fluidized bed. As can be noticed, the reduction of the column diameter does not influence the local behavior of the particles in the fluidized bed. Such a conical circulation pattern has already been observed in dense fluidized bed [START_REF] Fotovat | Sand-assisted fluidization of large cylindrical and spherical biomass particles: experiments and simulation[END_REF][START_REF] Werther | The local structure of gas fluidized beds-II. The spatial distribution of bubbles[END_REF]. Fig. 8(d) presents the time-averaged granular temperature of particles, which represents the frequency of particle-particle collisions. For the three columns, it presents a maximum at the center of the tube and a minimum near the wall. It is noteworthy that the granular temperature of tungsten particles is more than fifteen times lower than for the sand particles for a fluidization ratio of 4. This means that the high density of the tungsten particles tends to drastically reduce the frequency of particle-particle collisions. The granular temperature increases with the reduction of the column diameter due to an increase of the solid shear stress at the wall. The mean granular temperature for the column of 2 cm is twice higher than for the column of 5 cm. So, the reduction of the column diameter increases the frequency of particle-particle collisions but this remains notably lower than for conventional powders.

Fig. 10(a) and (b) presents the time-variance of the vertical and horizontal solid phase velocities. The time-variance of the vertical component of solid velocity is maximum at the center and minimum near the wall and the standard deviation is approximatively of the same order as the time-averaged velocity. The time-variance of vertical velocity of tungsten particles is of the same order as that of sand particles but the time-variance of horizontal velocity is three times lower. The time-variance of the vertical and the horizontal components of solid velocities decreases with the reduction of the column diameter due to the confinement effect. This means that the solid mixing in the fluidized bed decreases confirming the wall effects experimentally observed. This result can also explain that the heat transfer rates between the particles and the reactor walls decrease with the column diameter, as observed experimentally (Vanni et al., 2015b).

First CVD experiments have shown that the conversion rate of silane is lower than for conventional powders. This can be explained by the simulation results, indicating a lower particle mobility and a lower particle mixing for these very dense tungsten particles (Vanni et al., 2015a).

Conclusion

3D numerical simulations, using an Eulerian 2-fluid method, were performed in this work to analyze the hydrodynamics of very heavy particles of tungsten, located outside the classical classification of Geldart, in a dense gas-solid fluidized bed.

The aim was to study the influence of the reduction of column diameter.

The simulations are successful in reproducing the experimental measurements of axial gas pressure drop and the increase of minimum fluidization velocity by decreasing the column diameter from 5 cm to 2 cm. The numerical results pointed out that the reduction of column diameter increases the void fraction in the dense fluidized bed due to wall-particle friction effects. From 5 cm to 2 cm of column diameter, the particles have a conventional local circulation with the solids rising in an annular zone of increased bubble development in the column center and then descending near the wall.

However, the very high density of tungsten particles tends to drastically reduce their mobility inside the bed. Moreover, the reduction of column diameter decreases the solid mixing, confirming the wall effects experimentally observed.

As the measurements have shown that the tungsten particles can easily become electrostatically charged, future numerical simulations will take this fact into account, in order to improve the predictive capability of the model. Finally, future experimental research opportunities would be to carry out experiments on the local behavior of dense gas-tungsten particle suspension. It would be interesting to access to the bubbles size and velocity using appropriate probes and according to the particles trajectory from Radioactive Particle Tracking (RPT) or to Positron Emission Particle Tracking (PEPT) measurements to determine the particle velocity.

Fig. 1 -

 1 Fig. 1 -Representation of the tungsten particles with a diameter of 75 m in Geldart's classification modified by Yang (2007).

Fig

  Fig. 3 -3D mesh for the numerical simulation with 277,635 cells.

Fig. 4 -Fig. 5 -

 45 Fig. 4 -Experimental bed pressure drop curves in the glass and steel columns for H 0 /D = 3.

Fig. 6 -

 6 Fig. 6 -SEM view of tungsten particles.

Fig. 7 -

 7 Fig. 7 -Time-averaged axial profiles of gas pressure at the wall from numerical simulations and experimental measurements (P ref is a value above the dense fluidized bed), V f = 12 cm s -1 .

Fig. 8 -

 8 Fig. 8 -Effect of column diameter on the time-averaged flow variables radial profiles at z = 2/3× bed height, V f = 12 cm s -1 .

Table 1 -Particle properties and particle size distribution characteristics of the tungsten particles obtained with a Malvern Master Sizer Sirocco 2000 in dry mode.

 1

	Mean diameter	Value (m)
	d 3/2	70
	d 10	50
	d 50	75
	d 90	105
	Density	Value (kg m -3 )
	Particle	19,300
	Bulk	9,600
	U mf

Table 3 -Solid masses.

 3

	Column	5 cm	3 cm	2 cm
	Mass of solid (g)	2,827	741	181

Table 4 -Experimental and predicted minimum fluidization velocities.

 4

	U mf (cm s -1 )	D = 5 cm	D = 3 cm	D = 2 cm
	Exp. glass column	2.92	3.82	4.11
	Exp. steel column	3.14	3.02	3.19
	Simulation	3.41	3.50	3.82
	into two steps: a transitory step of 10 s corresponding to the
	establishment of the hydrodynamics of the fluidized bed and
	an established regime during which the statistics are com-
	puted for 100 s. The numerical radial profiles presented in this
	study are from the O-x direction but they are symmetrical with
	the profiles of the O-y direction. The authors have checked that
	all time-averaged bed values are axisymmetric.

Table 5 -Time-averaged gas pressure drop, bed height and solid volume fraction, V f = 12 cm s -1 .

 5

	Column	5 cm	3 cm	2 cm
	P/L (mbar m -1 )	1,006	1,012	1,017
	Bed height (cm)	13.79	10.05	5.55
	¯g	0.468	0.465	0.462
	˛g	0.497	0.512	0.517
	error( ¯g, ˛g )	6.1%	10.1%	11.9%

Acknowledgements

This work was granted access to the HPC resources of CALMIP under the allocation P11032 and CINES under the allocation gct6938 made by GENCI. The authors acknowledge helpful comments provided by Professor Olivier Simonin.


Paola Cavaliere

Françoise Norel

Christina Sizun
email: christina.sizun@cnrs.fr

H, 13C and 15N resonance assignments of σS activating protein Crl from Salmonella enterica serovar Typhimurium

in particular the possible role of Crl in triggering domain rearrangements in the multi-domain protein σ . Here we provide the H, C and N resonance assignments of Salmonella enterica serovar Typhimurium Crl, as a starting point for Crl structure determination and further structural investigation of the Crl -σ complex.

AQ1 AQ2

Salmonella Typhimurium Crl RpoS Sigma factor RNA polymerase Stress response Bacteria adapt to environmental perturbations like extreme stress conditions by entering into a stationary growth phase, altering their gene expression pattern, cell morphology and physiology. In enterobacteria like Escherichia coli and Salmonella, protection against multiple stress is controlled at the molecular level by the master transcriptional regulator during stationary phase, σ , encoded by the rpoS gene [START_REF] Battesti | The RpoS-mediated general stress response in Escherichia coli[END_REF][START_REF] Hengge | The general stress response in gram-negative bacteria[END_REF].

During exponential growth, the housekeeping σ factor σ associates with the multi-subunit core enzyme E (α ββ′ω) of the RNA polymerase to form the transcription initiation competent holoenzyme Eσ . However, in the stationary growth phase, σ is expressed and competes with σ . It then down-regulates σ -controlled genes involved in nutritional competence and promotes transcription of more than 10 % of the bacterial genome that is essential for cell survival under starvation and multiple stress conditions. In Salmonella enterica serovar Typhimurium, which causes typhoid fever symptoms in mice and gastroenteritis in humans, σ is moreover involved in virulence [START_REF] Hengge | The general stress response in gram-negative bacteria[END_REF].

To balance self-preservation and nutritional competence according to environmental cues, σ -dependent transcription is tightly regulated at multiple levels: transcription, translation, protein stability and activation ( [START_REF] Hengge | The general stress response in gram-negative bacteria[END_REF]. In E. coli and Salmonella, the Crl protein activates σ -dependent transcription and plays an important role in the biosynthesis of curli fibers, involved in adhesion to extracellular matrices and biofilm formation [START_REF] Hengge | The general stress response in gram-negative bacteria[END_REF]. Bacterial genomes containing the crl gene also contain the rpoS gene, underlining the close interplay between Crl and σ (Monteil et al. 2010a ). The transcription factor Crl binds directly to σ , but not to DNA, and stimulates formation of the Eσ holoenzyme, increasing the competitiveness of σ , which is otherwise the σ factor with the weakest in vitro affinity for E [START_REF] Hengge | The general stress response in gram-negative bacteria[END_REF].

Whereas the functions of Crl have been clearly established, the molecular mechanisms underlying the activation of σ by Crl are still poorly understood. Like all σ factors of the σ family, σ is multidomain protein [START_REF] Hengge | The general stress response in gram-negative bacteria[END_REF].

In contrast to housekeeping σ, high-resolution three dimensional structures are not available for σ . It might be speculated that Crl triggers σ conformational rearrangements that favor efficient binding to E. It has been shown that the conserved domain 2 of σ is the only domain that binds Crl, displaying the same Crl binding properties as full-length σ (Monteil et al. 2010b ;Banta et al. 2013 ;[START_REF] Cavaliere | Structural and functional features of Crl proteins and identification of conserved surface residues required for interaction with the RpoS/sigmaS subunit of RNA polymerase[END_REF]. In Crl, the conserved Arg51 was found to be essential for σ activation in E. coli [START_REF] Banta | Structure of the RNA polymerase assembly factor Crl and identification of its interaction surface with sigma S[END_REF] ), but in Salmonella additional critical aromatic and charged residues were identified [START_REF] Cavaliere | Structural and functional features of Crl proteins and identification of conserved surface residues required for interaction with the RpoS/sigmaS subunit of RNA polymerase[END_REF]. In both cases, the σ binding interfaces on Crl were analyzed in light of X-ray structures of a Crl homolog in Proteus mirabilis, Crl [START_REF] Cavaliere | Structural and functional features of Crl proteins and identification of conserved surface residues required for interaction with the RpoS/sigmaS subunit of RNA polymerase[END_REF][START_REF] Banta | Structure of the RNA polymerase assembly factor Crl and identification of its interaction surface with sigma S[END_REF]. Crl is much less conserved than σ , and sequence identity is less than 50 % between Crl and each E. coli Crl and S. enterica serovar Typhimurium Crl (Monteil et al. 2010a ). Neither Crl nor Crl could be crystallized, but the small size of Crl made it amenable to NMR spectroscopy. Here we provide the nearly complete H, C and N resonance assignments of Crl , as a prerequisite for structure determination of Crl and for further structural characterization of the Crl -σ complex.

The pVFC681 (pET-MCN-EAVNH) plasmid for overexpression of S. enterica serovar Typhimurium Crl in E. coli BL21(DE3) strain was described in [START_REF] Cavaliere | Structural and functional features of Crl proteins and identification of conserved surface residues required for interaction with the RpoS/sigmaS subunit of RNA polymerase[END_REF] in minimal M9 medium, supplemented with 100 µg mL ampicillin, 1 g L NH Cl (Eurisotop) and 3 g L unlabeled or C-labeled glucose (Cortecnet) and inoculated with 10 mL of saturated starter culture in Luria-Bertani broth, were grown at 37 °C until OD = 0.7. Induction was started with 1 mM IPTG at 30 °C for 4 h. For C N-80 % H-labeling, cells grown in 1 L of unlabeled M9 medium were collected by centrifugation at OD = 0.7. They were resuspended in 100 mL of triple labeled M9 medium, prepared in 99.8 % deuterium oxide (Eurisotop) and supplemented with 1 g L NH Cl (Eurisotop) and 2 g L C-labeled glucose (Cortecnet), and incubated for 1 h at 37 °C. Cells were collected again, resuspended in 900 mL triple labeled M9 medium and incubated for 30 min. Protein expression was induced with IPTG at 28 °C for 16 h. Cell pellets were harvested by centrifugation and lyzed at 4 °C in a Cell disrupter (Constant System Ltd.) in buffer A (50 mM sodium phosphate pH 8.0, 300 mM NaCl,10 mM imidazole, supplemented with anti-proteases and benzonase). After clarification by ultracentrifugation, the supernatant was loaded on to a Ni-NTA column (Protino Ni-NTA, 5 ml) and eluted with buffer B (buffer A added with 300 mM imidazole). After dialysis against buffer C (50 mM sodium phosphate pH 8.0, 300 mM NaCl), the protein was finally purified by size exclusion chromatography on a HiLoadTM 16/60 Superdex 75TM column (GE Healthcare) in buffer C. NOESY-HSQC, all other proton side chain assignments from 3D hCCH-TOCSY (15.6 ms spin lock) and 2D H-H NOESY spectra. The NOESY mixing time was 80 ms. H chemical shifts were referenced to DSS. Spectra were processed with Topspin 3.1 (Bruker Biospin) or NMRPipe [START_REF] Delaglio | NMRPipe: a multidimensional spectral processing system based on UNIX pipes[END_REF] and analyzed with CCPNMR 2.2 software (Vranken et al. 2005 ).

The N-HSQC spectrum and amide assignments of Crl at pH 8.0 and 293 K are shown in Fig. 1 . Assignment completeness for Crl was 82.0 % for amide resonances, 90.9 % for backbone resonances ( C , C , C′, H ) and 91.1 % for side chain protons. Taking the His-tag into account, completeness amounted to 81.0, 83.2 and 82.6 %. Exchangeable arginine and lysine side chain protons were not assigned. Assignments are completely missing for Asp30 and Glu89. Crl is a 133 residue protein containing 20 aromatic residues (4 tryptophans, 4 tyrosines, 10 phenyalanines and 2 histidines) that contribute to the core structure of the protein by stacking the two main helices α1 and α3 onto the central five stranded β-sheet (the topology of Crl is indicated in Fig. 2 ). A high proportion of H chemical shift outliers was found in the vicinity of these aromatic moieties, ranging from backbone atoms (Gly55-H , Thr68-H , Gly80-H , His104-H , Leu38-H , L107-H ) to methyl ( Val42-H , Leu60-H , L100-H ) and aromatic protons (Phe76-H ). Conversely the high amount of aromatic residues may explain the difficulty to assist backbone chemical shift assignment of Crl by prediction from homology models based on the X-ray structures of P. mirabilis Crl (47 % sequence identity, PDB IDs 4Q11 and 3RPJ). Nevertheless the secondary structure prediction of Crl by TALOS-N (Shen and Bax 2013 ) matches well with the X-ray structure of Crl , as shown in Fig. 2 . Severe broadening of amide signals constituted a major issue for assignment, even when lowering the pH from 8.0 to 6.5, at which Crl was considerably less stable. In the case of Glu89-Thr90, the lack of N-terminal capping of helix α3 explains line broadening. However most of the broadening occurred in the central β-sheet, in addition to the flexible loop 1 between helix α1 and strand β1 (Fig. 2 , residues in bold green and sky blue type). Amide resonances are missing downstream of and inside strand β1 (Asp30-Phe34, Cys37), in strand β3 (Phe73 and Leu75), but also in the central strand β2 (Trp56, Trp57 and Glu59), suggesting that conformational fluctuations at the millisecond time scale inside the β-sheet contribute to line broadening. Several Crl signals, mostly amides, were duplicated with a 60:40 intensity ratio. In the N-HSQC spectrum (Fig. 1 ) the corresponding peaks are marked "a" and "b". Although Crl crystallized as a dimer with a small intermolecular β-sheet formed by the β4′ extension, Crl dimerization in solution was ruled out by analytic ultracentrifugation [START_REF] Cavaliere | Structural and functional features of Crl proteins and identification of conserved surface residues required for interaction with the RpoS/sigmaS subunit of RNA polymerase[END_REF] as well as by N relaxation measurements. N R and R relaxation rates yielded an average effective rotational correlation time of 11.3 ± 1.0 ns and a hydrodynamic radius of 23 Å, compatible with a monomeric state of Crl . No evidence could be found either for significant proline cis-trans isomerization. Duplicated signals were prominently clustered in helix α3 (Glu94-Leu96, Tyr98-L100, Phe103-Glu105) and proximal to those displaying line broadening, i.e. in strands β1 (Phe35, Leu38-Ala39), β2 (Gly55) and β3 (Tyr69, Tyr71, Gly74). The equivalent regions in Crl are in close contact in the Crl X-ray structure [START_REF] Cavaliere | Structural and functional features of Crl proteins and identification of conserved surface residues required for interaction with the RpoS/sigmaS subunit of RNA polymerase[END_REF], indicating that a common perturbation might be responsible for the minor signals (Fig. 2 , residues in magenta). Subsequent NMR spectra of Crl samples purified only by affinity tag displayed a set of additional intense peaks corresponding to the C-terminal sequence Asp122-Ala133 (magenta box in Fig. 2 ), revealing a proteolytic site in the C-terminus. Proteolytic activity was mostly removed from the samples during purification, but full-length and truncated Crl co-eluted during size exclusion chromatography, accounting for signal duplication in differently labeled Crl samples.

The chemical shift assignments for Crl have been deposited in the BioMagResBank (http://www.bmrb.wisc.edu) under accession number 25476. This was supported by the French Research Agency (Grant ANR-11-BSV3-009) and the IR-RMN-THC (CNRS FR3050)

  ). Crl flanked by a 21-residue N-terminal His-tag was produced with N-, C N-and C N-80 % H-labeling. 1 http://eproofing.springer.com/journals/printpage.php?token=4aJKdVE...

Fig. 1

 1 Fig. 1 H-N HSQC spectrum at 800 MHz of 0.3 mM N-labeled Salmonella enterica serovar Typhimurium Crl at pH 8.0 and 293 K. Peak assignments are indicated according to numbering in the native sequence. N-terminal His-tag residues have negative numbers. In the case of duplicated signals related to partial cleavage of the C-terminus, major and minor species are indicated by letters a and b, respectively. Asn, Gln and Trp side chain resonances are denoted with δ and ε, and NH signals connected by horizontal lines

  http://eproofing.springer.com/journals/printpage.php?token=4aJKdVE...

Fig. 2

 2 Fig. 2 Sequence alignment of the Crl construct used for NMR measurements with Proteus mirabilis Crl. Secondary structure elements determined from the X-ray structure of Crl with PDB accession number 4Q11 (Cavaliere et al. 2014 ) are depicted on top for comparison with the secondary structure prediction of Crl by TALOS-N (Shen and Bax 2013 ). Crl residues with unassigned amide signals are shown in green; those located in the central β-sheet and for which line broadening by exchange precludes amide assignment are in green bold type. Residues with broad but assigned amide signals are in sky blue bold type. The C-terminal stretch that is partly cleaved by proteolysis is boxed in magenta. Residues that are spatially close to this stretch in the Crl structure, or can be relayed to it via side chain contacts, and display two amide signals, corresponding to the full-length and truncated forms, are shown in magenta bold type

  To accelerate back-protonation of amides, C N-80 % H-labeled Crl was treated with 8 M urea for 12 h at 4 °C, then dialyzed into 2 M urea and finally into buffer C. Samples for NMR experiments with aliphatic and aromatic H detection were exchanged on mMicro Bio-Spin 6 columns (Biorad) into buffer C in 100 % deuterium oxide. All other samples contained 7 % D O. 2 mM dithiothreitol was added to all samples. Protein concentrations were 300, 250 and 350 µM for N-Crl, C N-Crl and C N-80 % H-Crl samples, respectively. CO). To retrieve signals in solvent exposed regions like the N-terminal His-tag, a 3D HNCACB experiment was recorded on a N C-

		e.Proofing http://eproofing.springer.com/journals/printpage.php?token=4aJKdVE...
	NMR were carried out on a Bruker Avance III spectrometer equipped with a cryogenic TCI probe at a magnetic field of 18.8 T and a temperature of 293 K. Assignment of Crl backbone resonance frequencies was achieved by analyzing standard triple resonance experiments recorded on C N-Crl (3D HNCA, 3D HN(CO)CA, 3D HNCO, 3D CBCA(CO)NH) and C N-80 % H-Crl (3D HNCA, 3D HN(CO)CA, 3D HNCO, 3D -1 15 4 -1 1 3 600 13 15 2 600 -1 15 4 -1 13 13 15 2 1 2 15 13 15 13 15 2 STM 13 15 STM 13 15 2 STM HN(CA)-1 15 13
	1	1	15
	STM	α

Crl sample at pH 6.5. H assignments were obtained from a 3D H-N

  Conflict of interestThe authors declare that they have no conflict of interest.Banta Chumanov Yuan AH, Lin H, Campbell EA, Burgess RR, Gourse RL (2013) Key features of sigmaS required for specific recognition by Crl, a transcription factor promoting assembly of RNA polymerase holoenzyme. Proc Natl Acad Sci USA 110(40):15955-15960.

	e.Proofing http://eproofing.springer.com/journals/printpage.php?token=4aJKdVE...
	STM 15
	PM
			STM
	15	15
		1	2
			STM
		PM
	PM
		STM
			STM
	STM
	STM
	8 sur 10		03/05/2015 14:29

sur 10 03/05/2015 14:29

sur 10 03/05/2015 14:29