Banglun Zhou

Antoine Dazin
email: antoine.dazin@ensam.eu

Annie-Claude Bayeul-Laine
email: claude.bayeul-laine@ensam.eu

Jianping Yuan

Yaguang Heng
email: yaguang.heng@ensam.eu

Patrick Dupont
email: patrick.dupont@centralelille.fr

Najib Ouarzazi
email: najib.ouarzazi@univ-lille1.fr

Annie-Claude Bayeul-Lainé

Annie-Claude Bayeul-Lainé 2

Choosing the right model in

Keywords: Vaneless diffuser, Radial flow pump, Rotating instability, 2D numerical simulation, Experiment, Linear Stability Analysis

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INTRODUCTION

Instabilities could appear in pumps and compressors operating at off design conditions. They directly cause negative effects to them, such as vibrations, noise, mechanical damages. Consequently, they could lead to a reduction of the operating range of the machines. In the last decades, researchers [START_REF] Jansen | Rotating stall in a radial vaneless diffuser[END_REF][START_REF] Senoo | Influence of inlet flow conditions and geometries of centrifugal vaneless diffusers on critical flow angle for reverse flow[END_REF][START_REF] Frigne | Distinction between different types of impeller and diffuser rotating stall in a centrifugal compressor with vaneless diffuser[END_REF][START_REF] Dou | Analysis of the flow in vaneless diffusers with large width-to-radius ratios[END_REF] have developed theoretical analysis and experiment methods to investigate the mechanism of rotating stall in centrifugal machines. It seems that the physical mechanism associated with vaneless diffuser rotating stall is depending on its geometry. In narrow vaneless diffusers (h/R 3 <0.1 where h is the diffuser height and R 3 the inlet radius of diffuser), the occurrence of rotating stall is affected by the three-dimensional wall boundary layers [START_REF] Abdelhamid | Analysis of rotating stall in vaneless diffusers of centrifugal compressors[END_REF][START_REF] Fringe | A theoretical model for rotating stall in the vaneless diffuser of a centrifugal compressor[END_REF][START_REF] Ishida | Suppression of rotating stall by wall roughness control in vaneless diffusers of centrifugal blowers[END_REF]. In wide diffusers (h/R 3 >0.1), the wall boundary has no effect on the occurrence of rotating stall, and the instability develops in the core flow between the two SimHydro 2010:Hydraulic modeling and uncertainty, 2-4 June 2010, Sophia Antipolis Banglun ZHOU , Antoine DAZIN, Annie-Claude BAYEUL-LAINÉ, Jianping YUAN, Yaguang HENG, Patrick DUPONT, Najib OUARZAZI "Low Cost" approaches for the prediction of rotating instabilities in the vaneless diffuser of a radial flow pump.

boundary layers. In this case, the development of the instability is clearly linked to the value of the absolute flow angle at diffuser inlet [START_REF] Tsujimoto | Study of vaneless diffuser rotating stall based on two dimensional inviscid flow analysis[END_REF][START_REF] Moore | Weak rotating flow disturbances in a centrifugal compressor with a vaneless diffuser[END_REF]. It has been shown that a critical value of this angle exists, under which, the instability develops. More recent experiments, including PIV and pressure measurements, were performed, in order to obtain the characteristics of this unstable phenomenon, for many operating conditions [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF][START_REF] Dazin | High-speed stereoscopic PIV study of rotating instabilities in a radial vaneless diffuser[END_REF][START_REF] Pavesi | Experimental and numerical investigation of unforced unsteadiness in a vaneless radial diffuser[END_REF][START_REF] Wuibaut | PIV Measurements in the impeller and the vaneless diffuser of a radial flow pump in design and off design operating conditions[END_REF] and compared to 3D unsteady numerical calculations of the whole machine [START_REF] Pavesi | Experimental and numerical investigation of unforced unsteadiness in a vaneless radial diffuser[END_REF]. This last work has shown the ability of this kind of calculations to predict the occurrence and the characteristics of the rotating stalls (the number of cells, the structure of the rotating cells, the pattern and the amplitude of the phenomenon). The main drawback is that they are long and expensive calculations.

In recent years, simplified numerical approaches, based on a 2D numerical simulation of the radial diffuser, were used to predict the behavior of rotating stall in the vaneless diffuser (S. Ljevar [START_REF] Ljevar | Rotating stall in wide vaneless diffusers[END_REF][START_REF] Ljevar | Two-dimensional rotating stall analysis in a wide vaneless diffuser[END_REF] and Dazin et al [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF]). The calculations were based on the Reynolds Averaged Navier-Stokes (RANS) equations, assuming the hypothesis that the flow is two-dimensional in the core flow. The fluid is assumed viscous and incompressible. They showed the ability of such simplified approach to be able to predict the occurrence of the rotating instability. Besides, Tsujimoto et al [START_REF] Tsujimoto | Study of vaneless diffuser rotating stall based on two dimensional inviscid flow analysis[END_REF], and more recently Heng et al [START_REF] Heng | Experimental Study and Theoretical Analysis of the Rotating Stall in a Vaneless Diffuser of Radial Flow Pump[END_REF] have used linear stability analysis, assuming that the flow in the vaneless diffuser is 2D, incompressible and non viscous to predict the occurrence of unstable modes in vaneless diffusers.

The aim of the present paper is to evaluate the ability of a 2D simplified approach to predict the occurrence and the characteristics of the rotating stall in a vaneless diffuser. To do so, 2D numerical calculations, similar to the one proposed by S. Ljevar [START_REF] Ljevar | Rotating stall in wide vaneless diffusers[END_REF][START_REF] Ljevar | Two-dimensional rotating stall analysis in a wide vaneless diffuser[END_REF] and Dazin et al [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF], were managed to calculate the rotating instabilities inside a vaneless diffuser of a radial flow pump. A two-dimensional viscous incompressible flow model is used, so the influence of the wall boundary layers are consequently neglected. The boundary condition of the diffuser inlet was based on the flow field at the impeller outlet. A static pressure was set to the diffuser outlet. Monitoring points were located in the diffuser at different radius to acquire the pressure signals. The classical Fourier analysis was applied to identify the spectral characteristics of the developing rotating instabilities. The calculation results are compared to a 2D linear stability analysis results coming from [START_REF] Heng | Experimental Study and Theoretical Analysis of the Rotating Stall in a Vaneless Diffuser of Radial Flow Pump[END_REF] and from experimental results [START_REF] Dazin | High-speed stereoscopic PIV study of rotating instabilities in a radial vaneless diffuser[END_REF][START_REF] Pavesi | Experimental and numerical investigation of unforced unsteadiness in a vaneless radial diffuser[END_REF].

EXPERIMENTAL CONFIGURATION

Figure 1 The experimental configuration used in previous works by Dazin et al [START_REF] Dazin | High-speed stereoscopic PIV study of rotating instabilities in a radial vaneless diffuser[END_REF][START_REF] Pavesi | Experimental and numerical investigation of unforced unsteadiness in a vaneless radial diffuser[END_REF] The experimental measurements, support of the present work, have been carried out in air, in a radial flow pump with a radial impeller and a vaneless diffuser. The test rig used is shown in Figure 1. In order to ensure the axisymmetry of the pressure field at the diffuser outlet, no volute has been installed downstream of the diffuser. The vaneless diffuser walls are in transparent plexiglass, in order to have an optical access for the use of the particle image velocimetry (PIV) technique. Four Brüel & Kjaer condenser microphones (Type 4135) were used to acquire the unsteady pressure data. Their locations were set at two different radii (R=270mm and 370mm) and two different angle positions (an angle difference of 75°) on the diffuser wall. The experimental measurements is described in detail in [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF][START_REF] Dazin | High-speed stereoscopic PIV study of rotating instabilities in a radial vaneless diffuser[END_REF].

The characteristics of the impeller and of the diffuser are given in Table 1. The diffuser's radius ratio is R 4 /R 3 =1.5 . The vaneless diffuser is considered as a wide vaneless diffuser when h/R 3 >0.1.

Impeller characteristics

LINEAR STABILITY ANALYSIS

A 2D linear stability analysis diffuser was applied to study the stability of the flow in the diffuser. The analysis is based on the assumptions of a 2D, non-viscous flow with axisymmetric boundary conditions at the inlet and constant pressure at the outlet. The detail of the methodology used to predict the flow stability is available in the Tsujimoto's paper [START_REF] Tsujimoto | Study of vaneless diffuser rotating stall based on two dimensional inviscid flow analysis[END_REF]. According to the linear stability analysis, for a given diffuser's radius ratio R 4 /R 3 and a given number of unstable modes n (where n reprensents the number of unstable cells), the rotating stall occurs when the absolute flow angle at the diffuser's inlet is below a limit which is called the critical flow angle α cr .Figure 2 represents the evolution of the critical angle, for each mode, as a function of the radius ratio. In the experimental results, the radius ratio is R 4 /R 3 =1.5. For example, if we consider the flow rate Q/Q d =0.26, the inlet flow angle is estimated to be α=3 º, by the calculation of the velocity triangle at diffuser's inlet. The analysis of Figure 2 shows that, for this inlet flow angle, all modes (n=1-4) are predicted to be unstable. Moreover, the linear stability analysis, when the flow is unstable, is able to predict the propagation speed of the rotating cells. The results of this analysis will be compared to experimental results and to some numerical calculations that will be presented in the following paragraph.

SimHydro 2010:Hydraulic modeling and uncertainty, 2-4 June 2010, Sophia Antipolis Banglun ZHOU , Antoine DAZIN, Annie-Claude BAYEUL-LAINÉ, Jianping YUAN, Yaguang HENG, Patrick DUPONT, Najib OUARZAZI "Low Cost" approaches for the prediction of rotating instabilities in the vaneless diffuser of a radial flow pump.

NUMERICAL CALCULATIONS 4.1 Turbulence model

The calculations are based on the unsteady Reynolds Averaged Navier-Stokes (URANS) equations with the SST k-𝜔 turbulence model. In this case, the ratio between the diameter of diffuser's outlet and those of the diffuser's inlet is equal to 1.5, the same as in the experiments. The flow field calculated in the present work is 2D and limited to the vaneless diffuser.

The boundary condition at the inlet is an axisymmetric velocity. The tangential and the radial velocity's components at diffuser's inlet are given according to the the flow field at impeller's outlet. It is assumed that the outlet of the vaneless diffuser is connected to free air with a constant static pressure. The turbulence's intensities at the diffuser inlet and outlet are based on the Reynolds number at the inlet and the outlet respectively. For the discretization of the time-dependent terms, the second-order implicit time integration is used and the convergence criteria are 10 -5 . The time step is 0.00012 s (Corresponding to 360 time steps per impeller revolution). The flow field in the diffuser is considered viscous and incompressible. The velocities's triangle at the outlet of impeller (Figure 3) is determined to obtain the tangential velocity of the diffuser inlet considering the slip factor. The radial velocity of diffuser's inlet is calculated from the flow rate by equation ( 2). The slip factor is defined in equation( 1). The tangential velocity is evaluated by equation ( 3).

𝜎 = 1 - 𝜋 𝑍 𝑠𝑖𝑛𝛽 2 (1)
𝑣 𝑟 = 𝑄 𝜋𝐷 2 𝑏 2 (1- 𝑍𝑆 𝑢 𝜋𝐷 2 ) ( 2
)
𝑣 𝜃 = 𝑢 2 - 𝑣 𝑟 𝑡𝑎𝑛𝛽 2 -(1 -𝜎)𝑢 2 (3)
Where 𝜎 denotes the slip factor, Z the number of impeller's blades, Q the flow rate, 𝑆 𝑢 the thickness of impeller's blades at the outlet, D 2 the impeller's outlet diameter.

Mesh independence checking

The mesh used is a curvilinear orthogonal grid as shown in Figure 5. A mesh independence analysis has been conducted at flow rate Q/Q d =0.46. Two monitoring points, located at two radii (R=270mm and R=320mm) and at the same azimuthal position in the diffuser allow to acquire the static pressure evolution. A Fourier analysis is applied to identify the spectral characteristics of the fluctuating pressure. The dominant frequency of the spectrum as a function of the number of mesh-cells is shown in Figure 4. It can be seen that the value of the dominant frequency is constant when the grid size is larger than 95 000. The amplitude of the dominant peak in the spectrum is plotted as a function of the mesh size for the two sensor locations in Figure 6a and 6b. For a number of mesh cells higher than 125 000, the pressure's amplitude remains nearly constant. Finally, the best optimized mesh cells number is 125 000. This mesh will be used for the other simulations presented in this paper.

RESULTS AND DISCUSSION

Simulation results

Some of the numerical results obtained are presented in Figures 7 and8. These figures present the instantaneous flow structures after the development of the instability, in terms of vorticity fields (Figure 7) and velocity fields (Figure 8 and9). These results confirm, the ability of this kind of calculation to predict the arising of a rotating instability in a radial vaneless diffuser. This instability is characterised by a number of cells which is varying with the flow rate (n=3 for Q/Q d =0.26 and n = 4 for Q/Q d =0.31 and Q/Q d =0.61, in Figures 7, 8 and9). The unstable cell is characterised by a vortical core which is rotating around the diffuser at a velocity which is a fraction of the impeller velocity. This result is in a good agreement with results obtained Dzine et al, Ljvar et al [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF][START_REF] Ljevar | Rotating stall in wide vaneless diffusers[END_REF][START_REF] Ljevar | Two-dimensional rotating stall analysis in a wide vaneless diffuser[END_REF]. Considering the radial velocity of the flow, it can be seen that the vortical core is composed of one region of inward velocity next to a region of outward velocity (Figure 8). Between these two regions, a zone of high tangential velocity can be identified near to the diffuser inlet. (a

(a) Q/Q d =0.26 (b) Q/Q d =0.31 (c) Q/Q d =0.61
) Q/Q d =0.26 (b) Q/Q d =0.31 (c) Q/Q d =0.
61 Figure 8 The radial velocity for different flow rates conditions

(a) Q/Q d =0.26 (b) Q/Q d =0.31 (c) Q/Q d =0
.61 Figure 9 The tangential velocity for different flow rates conditions In order to deeply understand the mechanism of the stall, the classical Fourier analysis was applied to identify the spectral characteristics of the developing rotating instabilities. The static pressure coefficient 𝛹 is defined as:

𝛹 = 𝑝 1 2 𝜌𝑢 2 2
Where p is the static pressure, ρ is the flow density, u 2 is the impeller tip tangential velocity. Figure 10 shows the spectra of the rotating stall for the flow rate Q/Q d =0.26. The monitoring point of static pressure was located on radius R=270mm. The highest peack value of the spectral in simulation (shown in Figure 10 (b)) is in good agreement with the experimental one (shown in Figure 10 (a)). In the calculation, the dominant frequency is 20.4 Hz (the impeller rotation frequency is 20 Hz) for Q/Q d =0.26 condition, when the three stall cells are observed. So, the fundamental frequency of the rotating stall is 6.8 Hz. This result is quite close to the experimental one (the fundamental frequency of the rotating stall is 5.6 Hz) given by Dazin [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF]. The shape of the unstable cells are compared to the ones obtained the experimental results [START_REF] Dazin | High-speed stereoscopic PIV study of rotating instabilities in a radial vaneless diffuser[END_REF], in term of radial velocity distribution for Q/Q d = 0.26 (Figure 11). For this flow rate it seems that the results of the simulation are in a very good agreement with experiments, concerning the global shape of the unstable cell (it should be noticed that the color level are reversed in the experimental results compared to ths simulation ones because the frame was also reversed (the tangential velocity at the diffuser inlet is assumed to counterclockwise in the simulation. It is clockwise in the PIV map).

Figure 12

The radial velocity for radius R=320mm Figure 13 The radial velocity for radius R=370mm

Critical flow angle

The critical flow rate and the angle of rotating stall occurrence (flow angle at which the instability develops) for the three methods, the numerical simulation, the experiments and the linear stability analysis [START_REF] Heng | Experimental Study and Theoretical Analysis of the Rotating Stall in a Vaneless Diffuser of Radial Flow Pump[END_REF], are given in Table 2. The prediction of their value are very close for numerical and analytical approaches, but they both underestimate the value of the flow angle,and consequently they overestimate the flow rate at which the instability will first develops. These differences could be attributed to : -The hypothesis (2D flow, axisymmetric boundary condition at inlet) used for the analytical and the numerical approaches -A bad estimation of the experimental flow angle which is not measured but estimated by the calculation of the velocities' triangle at impeller outlet. An experimental campaign is programmed in the next future to evaluate its value.

Characteristics of rotating stall

The propagation speed and the number of stall cells are important characteristics of the rotating stall. The propagation speed of the rotating cells ω = 2π𝑓 𝑟𝑠 /𝑛. f rs is the dominated frequency, n the number of stall cells. The calculation results are once again compared with the experimental ones [START_REF] Dazin | Rotating instability in the vaneless diffuser of a radial flow pump[END_REF][START_REF] Dazin | High-speed stereoscopic PIV study of rotating instabilities in a radial vaneless diffuser[END_REF][START_REF] Pavesi | Experimental and numerical investigation of unforced unsteadiness in a vaneless radial diffuser[END_REF] and to those of the linear stability analysis [START_REF] Heng | Experimental Study and Theoretical Analysis of the Rotating Stall in a Vaneless Diffuser of Radial Flow Pump[END_REF] as shown in Figures 14 and15. It has to be noted that, in the experiments, in many cases, several concurrent modes could be observed simultaneously. The values reported in Figure 14 correspond to the dominant mode (the one with the highest amplitude). The linear stability theory could also predict the arising of several modes, depending on the flow rate; this is the most unstable mode which is reported on Figure 14 (the one with the greatest growth, that is the rate at which the mode develops, according to linear stability analysis). On the contrary, one single mode was observed in the numerical simulation. In Figure 14, it can be observed, that when the flow rate is decreased from stable to unstable conditions, the analytical prediction and the numerical simulation predict correctly that the first unstable mode developped is the mode n=4. But when the flow rate decreases, the simplified approach fails to predict correctly the correct number of modes, except for the lowest flow rates predicted. This means that, problably, the 3D effects, as well as the velocity profile at inlet could have an effect on the development of the instability. New simulations with more realistic velocity profiles will be managed in the next future. First of all, it has to be noted that the order of the propagation speeds predicted by the linear stability analysis and the 2D numercial simulations have the same order of magnitude as what is oberved in the experiments. But, for numerical simulations, the velocity is systematically overestimated and is nearly constant, whereas in the experiments, there is an increase of the velocity with the decrease of the flow rate. On the contrary, this trend is well predicted by the analytical approach, but the velocities are underestimated except fot the lowest flow rates. It has to be said that, in most experiments, there was not a single mode which was observed, but several competitive ones. On the contrary, the numerical simulations are predicting the arising of only one single mode. The linear stability analysis could predict the arising of several modes, but their evolution is supposed to be independent from the evolution of the others. The interaction of several unstable modes could have an influence on their velocities, in the experiments. Besides, the effect of the development of boundary layers, which does exist in the real case, are ignored by the two simplifed approaches.

CONCLUSIONS

In this paper, the ability of two simplified approaches to try to predict the arising of rotating stall in the vaneless diffuser of a radial flow pump are evaluated and compared to the existing experimental results [10- 11]. The first one is a linear stability analysis which is available in litterature [START_REF] Tsujimoto | Study of vaneless diffuser rotating stall based on two dimensional inviscid flow analysis[END_REF][START_REF] Heng | Experimental Study and Theoretical Analysis of the Rotating Stall in a Vaneless Diffuser of Radial Flow Pump[END_REF]. The second one is based on a 2D numerical simulations of the vaneless diffuser with a simplified boundary condition at inlet where the velocity is supposed to be axisymmetric. Both simplified approaches are able to predict the arising of rotating instability. The shape and the amplitude of the instability, obtained in a numerical simulation, are very close to the experiments. Concerning the arising of the instability, the critical flow angle (the inlet flow angle under which the instability develops) seems to be overestimated by the two simplified approaches. Both methods agree to predict that the first mode developped is the mode n=4. But, when the flow rate decreases, they fail to predict the correct dominant modes (except at very low flow rates).

The two simplified approaches are predicting the good order of magnitude for the propagation speed. But the numerical calculations are systematically overestimating the experimental data whereas the analytical method is underestimating them, except for the lowest flow rate tested experimentally. The main differences between the two simplified approaches compared to the experiments are the following : -The effect of the boundary layer are neglected, -

The velocity at the inlet is supposed to be axisymmetric, -

The interaction between the modes are not taken in account in the linear stability analysis and not observed in CFD, -There is a doubt about the value of the experimental value of the flow angle at diffuser inlet. To try to improve the simplied approaches, several new works are forecasted in the following months :

-An experimental campaign to measure the flow angle and the boundary layer thickness, -An extension of the linear stability analysis to non linear interaction between modes, -New CFD Calculations with more realistic inlet boundary conditions.

NOMENCLATURE

Figure 2 .

 2 Figure 2. Critical flow angle versus diffuser ratio.

Figure 3 4

 34 Figure 3 Velocities' triangle at impeller's outlet Figure 4 The dominant frequency of static pressure fluctuations for different mesh sizes at Q/Q d =0.46

Figure 5 Figure 6

 56 Figure 5 The diffuser's grid

Figure 7

 7 Vorticity magniture fields under different flow rates conditionsSimHydro 2010:Hydraulic modeling and uncertainty, 2-4 June 2010, Sophia Antipolis Banglun ZHOU , Antoine DAZIN, Annie-Claude BAYEUL-LAINÉ, Jianping YUAN, Yaguang HENG, Patrick DUPONT, Najib OUARZAZI "Low Cost" approaches for the prediction of rotating instabilities in the vaneless diffuser of a radial flow pump.

Figure 10

 10 Figure 10The spectral of pressure fluctuation

  (a) calculation results (b) experimental results [11] Figure 11 The radial velocity for the flow rate is Q/Q d =0.26The numerical and experimental values of radial velocities for the two radii (R=320mm and R=370mm) at the flow rate Q/Q d =0.26 are given in Figures12 and 13depending on the angle position. Three peaks can be observed for the two-dimensional simulations and for the experimental measurements, which are due to the presence of the three cells. It can be observed that these three peaks are of similar amplitude.

Figure 14

 14 Figure 14 Number of stall cells Figure 15 Propagation speed

Table 1 :

 1 Pump characteristics

	Units

Table . 2

 . SimHydro 2010:Hydraulic modeling and uncertainty, 2-4 June 2010, Sophia Antipolis Banglun ZHOU , Antoine DAZIN, Annie-Claude BAYEUL-LAINÉ, Jianping YUAN, Yaguang HENG, Patrick DUPONT, Najib OUARZAZI "Low Cost" approaches for the prediction of rotating instabilities in the vaneless diffuser of a radial flow pump. The occurrence of the rotating stall

		Critical flow rate	Critical flow angle	Number of stall cells
	Numerical simulations	Q/Q d =0.61	α ̃= 6.1°	n=4
	Experiments	Q/Q d =0.76	α ̃= 8.1°	n=4
	Linear stability analysis	Q/Q d =0.58	α ̃= 5.7°	n=4

  SimHydro 2010:Hydraulic modeling and uncertainty, 2-4 June 2010, Sophia Antipolis Banglun ZHOU , Antoine DAZIN, Annie-Claude BAYEUL-LAINÉ, Jianping YUAN, Yaguang HENG, Patrick DUPONT, Najib OUARZAZI "Low Cost" approaches for the prediction of rotating instabilities in the vaneless diffuser of a radial flow pump.

ACKNOWLEDGEMENTS

The researchers gratefully acknowledge the financial support extended by the Priority Academic Program Development of Jiangsu Higher Education Institutions and the China Scholarship Council as well as the academic support of Ecole Centrale de Lille and Arts et métiers ParisTech.


Vincent Escande

Tomasz K Olszewski

Eddy Petit

Claude Grison

] Eddy Petit

Biosourced Polymetallic Catalysts: An Efficient Means To Synthesize Underexploited Platform Molecules from Carbohydrates

Keywords: biomass, carbohydrates, green chemistry, plantbased catalysis, waste reuse

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

As the pressure on raw materials derived from fossil fuels continues unabated and environmental concerns become ever more pervasive, the chemical industry must increasingly focus on obtaining raw materials from renewable resources. [1] Thus, special emphasis should be put on developing protocols for transforming biomass into fine chemicals and chemicals with high added value. [1c, 2] There is already a considerable range of chemical building blocks derived from renewable resources, such as 5-hydroxymethylfurfural, [START_REF] Rosatella | [END_REF] g-valerolactone, [4] and lactic acid. [5] Because of their high synthetic potential, carbohydrates obtained from plant-derived biomass will make a valuable contribution to green chemistry of the future. [6] The Garcia Gonzalez reaction is a highly valuable route for the synthesis of polyhydroxyalkyl furans starting from carbohydrates (hexoses and pentoses) and b-dicarbonylated compounds (Scheme 1), but strangely it seems to have been largely forgotten. [7] By furnishing a number of useful properties including chirality, rigidity, lipophilicity, hydrophilicity, and flexibility in one system, polyhydroxyalkyl furans represent an interesting scaffold or platform molecule for synthetic chemists to use in the preparation of a variety of diverse structures (Figure 1).

Reported examples of their use include the preparation of free furanic acids having a polyhydroxylated alkyl side chain, [7] the synthesis of aldehydes by oxidative cleavage of the polyhydroxylated alkyl side chain, [8] oxidation/reduction of the carbonyl group, [9] and substitution of the terminal hydroxy groups to form oligomers. [9] The Garcia Gonzalez reaction has the potential to meet the modern criteria for green and sustainable chemistry. [10] This transformation is operationally simple, high yielding, and performed under environmentally friendly conditions (by using Polymetallic hyperaccumulating plants growing on wastes from former mining activity were used as the starting material in the preparation of novel plant-based Lewis acid catalysts. The preparation of biosourced Lewis acid catalysts is a new way to make use of mining wastes. These catalysts were characterized by X-ray fluorescence, X-ray diffraction, inductively coupled plasma mass spectrometry, and direct infusion electrospray ionization mass spectrometry. These analyses revealed a complex composition of metal species, present mainly as polymetallic chlorides. The catalysts proved to be efficient and recyclable in a solid-state version of the Garcia Gonzalez reaction, which has been underexploited until now in efforts to use carbohydrates from biomass. This methodology was extended to various carbohydrates to obtain the corresponding polyhydroxyalkyl furans in 38-98 % yield. These plant-based catalysts may be a better alternative to classical Lewis acid catalysts that were previously used for the Garcia Gonzalez reaction, such as ZnCl 2 , FeCl 3 , and CeCl 3 , which are often unrecyclable, require aqueous treatments, or rely on metals, the current known reserves of which will be consumed in the coming decades. Moreover, the plant-based catalysts allowed novel control of the Garcia Gonzalez reaction, as two different products were obtained depending on the reaction conditions.

Scheme 1. General concept of the Garcia Gonzalez reaction.

[a] V. a mixture of H 2 O/EtOH as the reaction medium); moreover, it requires a moderate temperature and short reaction time. The reaction is catalyzed by Lewis acids such as ZnCl 2 , [7] FeCl 3 , [START_REF] Nagarapu | [END_REF] and CeCl 3 . [8,12] However, these classical catalytic systems are unrecyclable, require aqueous treatment, rely on metals, the current known reserves of which will be consumed in the coming decades, [START_REF] Hunt | Element Recovery and Sustainability[END_REF] and do not permit control of the reaction selectivity (in some cases, the polyhydroxylated alkyl side chain undergoes further cyclization). [START_REF] Nagarapu | [END_REF] Owing to the depletion of metal resources [14] and the emergence of new more stringent regulations, [15] new catalysts are required that are inexpensive and that are not based on increasingly scarce metals. [START_REF]Catalysis without Precious Metals[END_REF] Earlier work by our group led to the development of a new range of plant-based Lewis acid catalysts that are derived from nonconventional biomass, that is, metal hyperaccumulator species. Metal-hyperaccumulating plants, or metallophytes, extract trace metals from soil and concentrate them in their shoots. [START_REF] Anderson | Element Recovery and Sustainability[END_REF] Exploring the utility of these plants led to the development of a phytoextraction technique that offers a means to remove the trace metals from contaminated soils, for example, contaminated mine sites, which cause major environmental problems worldwide. [18] Today, this environmentally compatible process has emerged as the preferred method to reclaim metal-contaminated sites. It is less costly than conventional remediation methods, has a lower environmental impact, and is better accepted by the public. [19] Potential and specific markets exist for phytoextraction, which also offers an alternative source of nonrenewable mineral materials. [START_REF] Raskin | Phytoremediation of Toxic Metals, Using Plants to Clean Up the Environment[END_REF] Field-scale trials of phytoextrac-tion by using the practices of farming systems proved the technology's potential on a large scale. It is now possible to access up to several tons of Ni-rich biomass in the USA and in Europe. As an example, crop yields of the nickel hyperaccumulator Alyssum murale can reach at least 20 t ha À1 or 400 kg Ni ha À1 with ordinary fertilizers and management practices. [START_REF] Chaney | Abstracts of the International Conference on the Biogeochemistry of Trace Elements[END_REF] Similar studies are in progress for zinc hyperaccumulator plants. We estimate that a possible biomass production of 5.2 t ha À1 would yield 60 kg ha À1 of Zn, and this is in agreement with the findings of Robinson et al. [START_REF] Robinson | [END_REF] However, numerous efforts are still necessary to exploit the ability to recover and recycle metals from contaminated biomass and fully develop the economic potential of phytoextraction. Innovative technologies are needed to obtain the full benefit of the remediation process. We have found that the unique polymetallic composition of the catalysts derived from metal hyperaccumulating plants allows them to efficiently mediate a diverse set of reactions to afford valuable products in good yields under mild reaction conditions. [18c, 23] Herein, we describe the use of a novel plant-based Lewis acid catalyst for the Garcia Gonzalez reaction, an innovation that will be of major interest for green chemistry. The key benefits of the proposed catalytic system are the use of a catalyst of plant origin, the possibility to recycle and reuse it, efficiency in terms of yield, the wide range of its applications, ease of control of the reaction outcome, and mild reaction conditions.

Results and Discussion

In this study, we used the two best zinc hyperaccumulator plants, Noccaea caerulescens (Brassicaceae) and Anthyllis vulneraria (Fabaceae), harvested in Les Avinires, a former zinc mining site in Saint-Laurent-Le-Minier, southern France. Both are included in a large program of ecological rehabilitation of this site; they are able to concentrate approximately 120 000 ppm of Zn II in calcinated shoots. [18c] The plant-based catalysts were prepared by heat treatment of leaves at 400 8C, followed by the addition of HCl (1 m). The potential of zinc hyperaccumulating plants for plant-based catalysis was based on the total mineral composition of contaminated biomass. X-ray fluorescence (XRF) was used to determine the exact chemical composition of the plant extract that was obtained (Table 1).

The XRF data were additionally confirmed by inductively coupled plasma mass spectrometry (ICP-MS). The mineral analysis clearly revealed that Zn was the major transition metal (6.75 %), accompanied by an amount of 2.75 % of Fe. An amount of 1.50 % of Al was also noted. The reproducibility of the composition of the catalyst was investigated, depending on the localization of the crops. Three different samples of leaves were collected at different points in the former mining site, and their content in Lewis acids was analyzed by ICP-MS after their transformation into the catalyst (Table 2). Whereas the contents of transition metals (Zn, Fe, Cd) and of Al and Pb were stable in the samples, larger differences were observed for Mg and Ca (see also data in Table 1). However, as the use of hyperaccumulating plants is intended as a source of Lewis acids, and particularly of transition metals, this variability in the Mg and Ca content should not compromise the catalytic activity. As a precaution, it is preferable to prepare the catalyst starting from the largest lots of collected plants to homogenize the composition and minimize variation. The biosourced catalyst obtained was characterized by X-ray diffraction (XRD) (Table 3). As the noncrystalline species were not detected by XRD, the plant-based catalyst was also characterized by direct infusion in electrospray ionization mass spectrometry (ESI-MS) in the negative mode after dilution in water. Metallic species were detected as chlorides and were identified by their isotopic distribution, as described in Table 4.

The concentration of the solution led to an unusual mixture of mineral species, such as potassium zinc tetrachloride. [18c] K 2 ZnCl 4 , the sole mixed zinc chloride that was observed, is a masked form of ZnCl 2 . [18c] First, we tested the ability of the plant-based catalyst to catalyze the Garcia Gonzalez reaction starting from d-glucose (1 a) and ethyl acetoacetate (2 a) by using different environmentally benign reaction media previously described in the litera- ture. [7,8,[START_REF] Nagarapu | [END_REF] Initially, the reaction was performed in water/ethanol, but significant leaching of the metallic elements was noted. To circumvent this problem, we attempted to support the plantbased catalyst on montmorillonite K10 and silica gel by using impregnation methodology. [24] Those experiments, however, led to a decrease in catalytic activity. To improve our methodology, we conducted the reaction in the solid phase by following methods previously used by Bartoli et al. [12] Silica gel was used to disperse the catalyst and the reagents. Gentle heating was necessary to achieve total conversion (TLC analysis). Subsequent easy workup was based on washing the solid with ethyl acetate to extract the reaction products (Figure 2). Insolubility of the metallic elements of the plant-based catalyst in this solvent was noted. This improved methodology was very efficient (Table 5, entries 1 and 2) and avoided contamination of the reaction products with the metallic residue. Bartoli and collaborators used NaI as an activating compound, [12] but no such additive was necessary if the reaction was catalyzed by the plant-based catalyst. The choice of conditions was also guided by the outcome of the experiment and was therefore considered conceivable for an economically feasible process, one that furthermore may permit reuse of the catalyst. [25] For all reactions, the amount of biosourced polymetallic catalyst was set at 4.0 mol % of Zn or 8.0 mol % of the sum Zn + Fe + Al. Owing to the complex composition of the catalyst, we chose to focus on Zn, Fe, and Al, as these elements have the most pronounced Lewis acidity of the elements present in the catalyst and are the most likely contributors to the catalytic activity. Loadings lower than 8.0 mol % of the sum Zn + Fe + Al resulted in a decrease in the reaction yield (Table 5, entry 3). In turn, higher loadings did not improve the reaction yield, even after prolonged heating.

Interestingly, if the reaction time was extended beyond 24 h, the formation of an epimeric mixture of desired polyhydroxyalkyl furans 3 a-3 a' was accompanied by the formation of cyclization products 4 a-4 a', which result from the cyclization-dehydration of the initial products. [26] If the reaction temperature was set at 85 8C, after 24 h only products 4 a-4 a' were formed in almost quantitative yield (Scheme 2). In turn, setting the reaction temperature at 50 8C gave the controlled formation of polyhydroxyalkyl furans 3 a-3 a' (Scheme 2). Therefore, the application of the plant-based catalyst enabled easy control of the process by simple adjustments of temperature and reaction time.

Therefore, this biosourced catalyst has unique flexibility and enables the control of the reaction sequence in comparison to "classical" catalysts and conditions, which lead only to one of the two possible products or to a mixture of 3 a-3 a' and 4 a-4 a'.

Additionally, the Garcia Gonzalez reaction of 1 a with 2 a performed in the presence of only SiO 2 led to products 3 a-3 a' in 8 % yield (Table 5, entry 4). Likewise, the use of commercial ZnCl 2 /SiO 2 in the same proportion as in the run with the plantbased catalyst (Table 5, entry 1) gave lower yield and selectivity (Table 5, entry 5). The combination of Zn II , Fe III , and Al III conveyed the catalytic activity, but with selectivity opposite to that obtained with the use of the plant-based catalyst (Table 5, entry 6). This is in accordance with previously published data, for which only the furan with a cyclic polyhydroxylic chain was [a] Reaction performed with d-glucose (10 mmol) and ethyl acetoacetate (12 mmol). [b] Zn (4.0 mol %), Fe (1.9 mol %), Al (2.2 mol %), SiO 2 (500 mg). [c] Zn (1.0 mol %), Fe (0.5 mol %), Al (0.6 mol %), SiO 2 (500 mg).

[d] SiO 2 (500 mg). [e] Commercial ZnCl 2 (4.0 mol %), SiO 2 (500 mg).

[f] Commercial ZnCl 2 (4.0 mol %), commercial FeCl 3 (1.9 mol %), commercial AlCl 3 (2.2 mol %), SiO 2 (500 mg).

obtained if FeCl 3 was used as the catalyst. [START_REF] Nagarapu | [END_REF] These results show that the catalytic activity lies in the polymetallic composition and in the original species present in the plant-based catalyst.

Subsequently, the optimized reaction conditions were applied to a selected spectrum of hexoses and pentoses and to b-dicarbonyl compounds to test the scope of the presented protocol (Table 6). The use of pentane-2,4-dione ( 2 6, entry 4). The use of 1,3-cyclohexanedione (2 c) in the Garcia Gonzalez reaction has not been previously reported. In our case, with the use of the plant-based catalyst we obtained cyclization products 4 c-4 c' in a low yield of 38 %, probably as a result of the known dimerization of 2 c (Table 6, entry 5). [27] A reaction with the use of d-galactose (1 b) and pentane-2,4-dione (2 b) did not follow the general pathway and furnished only cyclization products 4 d-4 d' in 98 % yield (Table 6, entry 6). As described in the literature, owing to the lack of anchimeric assistance of the OH group at the C2' position during the cyclization and probably because of steric effects, the two diastereomers were formed with a modest selectivity of 4 d/4 d' = 70:30. [START_REF] Nagarapu | [END_REF] The reaction of pentane-2,4-dione ( 2 6, entries 8 and9). The lateral chain was too short to undergo cyclization and, thus, only polyhydroxyalkyl furans were obtained.

In the case of cyclic products, the existence of those products as a mixture of diastereomers is well documented. [11, 26a] The ratio of diastereomers observed was moderate owing to the anchimeric assistance of the OH group at the C2' position or to its absence, depending on the starting carbohydrate. [START_REF] Nagarapu | [END_REF] However, in our case, after acetylation of the obtained uncyclized products, analysis by GC-MS revealed two signals with similar m/z values corresponding to two diastereomers. This fact was confirmed by 1 H NMR spectroscopy, for which the signals were doubled in various proportions, depending on the starting carbohydrate.

To avoid confusion by the formation of cyclic diastereomers, we studied the polyhydroxyalkyl furans obtained from pentoses, in which the lateral chain is too short to undergo cyclization. Starting from d-ribose, two diastereomers were observed by 1 H NMR spectroscopy for the products that had the linear polyhydroxyalkyl side chain. The diastereomers were most probably formed by epimerization at the C2' position (at which the dehydration is favored in the a position to the furan), following the formation of the carbocation by a mechanism proposed by Sµnchez and Roldµn, [26a] for which the linear epimers were until now hypothetical (Scheme 3)

To confirm the formation of those epimers with other catalysts, the synthesis was performed with the use of FeCl 3 and dribose as the carbohydrate. [START_REF] Nagarapu | [END_REF] Analysis of the reaction product by 1 H NMR spectroscopy clearly showed the existence of two diastereomers if the reaction was catalyzed by FeCl 3 .

The experimental results (Table 6) showed the following trends concerning the proportions of isomerized products: For uncyclized products, epimerization at C2' with rates of 8 to 25 % was observed. In contrast, the rates of isomerization were lower for the cyclized products, as most of the products were observed as b isomers (89-99 %). This is probably due to steric effects, as in the a isomer the furan and hydroxyl groups are on the same side of the tetrahydrofuran moiety. Indeed, higher proportions of the a isomer (30 %) were observed only for the cyclized product resulting from d-galactose in which the furan and the vicinal hydroxy group are on opposite faces of the tetrahydrofuran moiety (Table 6, entry 6). From a practical point of view, it should be noted that in each case, the different diastereomers of the uncyclized and cyclized products could be separated by fractional crystallization in ethyl acetate.

To test the potential for recycling and reuse of the catalyst, the catalyst was washed with ethyl acetate, dried (120 8C, 5 h), and used in a new run to yield the desired product. As summarized in Table 7, the polymetallic catalyst was used up to four cycles with a marginal decrease in catalytic activity. The batch-to-batch variability of the substrates was monitored by XRF; the mineral composition remained almost the same up to the fourth run. This was determined by comparing the amount Scheme 2. Controlling the selectivity of the Garcia Gonzalez reaction.

Table 6. Scope of the presented protocol. [a] Entry Carbohydrate b-Dicarbonyl T [8C]

Uncyclized products [b] Yield [c] [%] Cyclized products [b] Yield [c] [%] of Zn, Fe, and Al. These results thus illustrate the stability of the plant-based catalyst and show that there is no leaching of metallic species during the reaction and workup. Only the amount of iron decreased slightly. No trace amounts of cadmium or lead were detected during ICP-MS analysis of the final products. This result is important because these elements are known to be highly toxic.

Conclusions

In conclusion, we described the preparation of a novel plantbased Lewis acid catalyst starting form hyperaccumulating plants collected on former mining sites. The conception of this new type of catalyst can contribute to the recycling of mining wastes. The characterization of this biosourced catalyst revealed that it was composed of mono-and polymetallic species, particularly of transition-metal chlorides known for their Lewis acid character, such as K 2 ZnCl 4 . Reproducibility studies showed that the metal content of the catalyst was 4.80-9.65 wt % for Zn, 1.13-2.95 wt % for Fe, and 1.10-1.74 wt % for Al, depending on the localization of the plants used in the preparation of the catalyst. This catalyst proved to be highly efficient in the Garcia Gonzalez reaction by using solid-state methodology without the use of any additive, which improved the green potential of the reaction. Good to excellent yields (up to 98 %) of polyhydroxyalkyl furans were obtained. The plant-based Lewis acid catalyst showed unusual flexibility in catalyzing the Garcia Gonzalez reaction, as furans with an uncyclized or cyclized alkyl chain were obtained simply by adjusting the reaction temperature. Such an activity was not previously described for the catalysis of this reaction. Finally, this study highlighted the epimerization of uncyclized and cyclized polyhydroxyalkyl furans, which was only hypothetical on some points until now.

Experimental Section

General methods

Reagents and solvents were purchased from Sigma-Aldrich and were used without further purification. Flash column chromatography was performed by using Chromagel Carlo Erba Reactifs SDS silica 60A CC 35-70 mm. Reactions were monitored by using Merck Kieselgel 60 F254 aluminum. TLC plates were visualized by UV fluorescence (254 nm) and one of the following: KMnO 4 , ninhydrin, phosphomolybdic acid solution, or phosphotungstic acid solution. [a] 0.44 AE 0.0051 [b] [a] Complementary ICP-MS analysis revealed that less that 5 ppm of Cd was lost after the four runs. [b] Complementary ICP-MS analysis revealed that less that 5 ppm of Pb was lost after the four runs.

Preparation of the polymetallic plant-based catalyst

Leaves of Noccaea caerulescens and Anthyllis vulneraria were harvested before flowering in Les Avinires, a former zinc mining site in Saint-Laurent-Le-Minier, southern France (same mass of the two plants), air dried, and crushed. The obtained solid (150 g) was calcined at 400 8C for 5 h, and the resulting powder (24 g) was added to 1 m HCl solution (100 mL). The solution was heated at 60 8C and stirred for 2 h. The reaction mixture was filtered through Celite. The resulting solution, composed of different metal chlorides, was then concentrated under vacuum. The catalyst was kept in a desiccator under vacuum.

General procedure for the synthesis of uncyclized polyhydroxyalkyl furans

The carbohydrate (10 mmol), plant-based catalyst (390 mg, amount corresponding to 0.40 mmol of Zn, 0.19 mmol Fe, 0.22 mmol Al following ICP-MS dosing), and silica (500 mg, Chromagel Carlo Erba Reactifs SDS silica 60 A CC 35-70 mm) were mixed by grinding in a mortar. The b-dicarbonyl compound (12 mmol) was added, and the resulting solid was homogenized with a spatula. The solid was introduced in a sealed tube (Ace glass tube, 10.2 cm 25.4 mm) containing a magnetic stirring bar, and the vessel was heated to 50 8C in an oil bath for 24 h until completion of the reaction (TLC monitoring, toluene/acetone = 1:1). The solid mixture was then washed with ethyl acetate (2 5 mL) and filtered. The resulting solution was evaporated under reduced pressure to yield a grey powder. This powder was purified by crystallization in hot ethyl acetate to give the uncyclized polyhydroxyalkyl furan as a white solid. The previous catalytic solid (mixture of plant-based catalyst and SiO 2 ) was recycled by washing with ethyl acetate and drying in an oven (120 8C, 5 h) before being reused in the next run. See the Supporting Information for analytical data.

General procedure for the synthesis of cyclized polyhydroxyalkyl furans

The carbohydrate (10 mmol), plant-based catalyst (390 mg, amount corresponding to 0.40 mmol of Zn, 0.19 mmol Fe, 0.22 mmol Al following ICP-MS dosing), and silica (500 mg, Chromagel Carlo Erba Reactifs SDS silica 60 A CC 35-70 mm) were mixed by grinding in a mortar. The b-dicarbonyl compound (12 mmol) was added, and the resulting solid was homogenized with a spatula. The solid was introduced in a sealed tube (Ace glass tube, 10.2 cm 25.4 mm) containing a magnetic stirring bar, and the vessel was heated to 85 8C in an oil bath for 24 h until completion of the reaction (TLC monitoring, toluene/acetone = 1:1). The solid mixture was then washed with ethyl acetate (2 5 mL) and filtered. The resulting solution was evaporated under reduced pressure to yield a brown oil. This oil was purified by flash column chromatography (toluene/ acetone = 1:1) to yield the cyclized polyhydroxyalkyl furan as an off-white solid, which was recrystallized in hot ethyl acetate. The previous catalytic solid (mixture of plant-based catalyst and SiO 2 ) was recycled by washing with ethyl acetate and drying in an oven (120 8C, 5 h), before being reused in the next run. See the Supporting Information for analytical data.

Figure 1 .

 1 Figure 1. Polyhydroxyalkyl furans as platform molecules for synthetic chemists.

Figure 2 .

 2 Figure 2. Solid-phase catalytic process with plant-based catalyst.

  b) as the bdicarbonyl compound instead of ethyl acetoacetate (2 a) led selectively to expected polyhydroxyalkyl furans 3 b-3 b' in 72 % yield if the reaction was performed at 50 8C for 24 h (Table 6, entry 3). In turn, at 85 8C only expected cyclization products 4 b-4 b' were obtained in 91 % yield (Table

  b) with d-mannose (1 c) followed the same pathway and furnished only cyclization products 4 b-4 b' in 90 % yield (Table 6, entry 7). Finally, the biosourced catalyst was found to efficiently mediate the reaction performed with the use of pentoses. Polyhydroxyalkyl furans 3 e-3 e' were obtained in 70 % yield starting from pentane-2,4-dione (2 b) and d-ribose (1 d) or d-xylose (1 e; Table

  Reaction conditions: carbohydrate (10 mmol), b-dicarbonyl compound (12 mmol), plant-based catalyst (Zn + Fe + Al = 8.0 % mol), SiO 2 (500 mg), 24 h. [b] Proportions determined by 1 H NMR spectroscopy. [c] Yield of isolated product.

Scheme 3 .

 3 Scheme 3. Epimerization of the uncyclized and cyclized products.

Table 1 .

 1 Elemental composition of the plant-based catalyst, as established by XRF.

	Element	Composition [wt % AE standard deviation]
	Na	1.72 AE 0.021
	K	5.72 AE 0.078
	Mg	1.6 AE 0.080
	Ca	10.3 AE 0.17
	Fe	2.75 AE 0.063
	Zn	6.75 AE 0.021
	Cd	0.19 AE 0.0026
	Al	1.5 AE 0.014
	Pb	0.44 AE 0.0029
	O	15.97 AE 0.50
	Cl	43.27 AE 0.23

Table 3 .

 3 Characterization of the plant-based catalyst by XRD.

	Mineral	Formula (simplified)
	calcium magnesium chloride hydrate	CaMg 2 Cl 6 (H 2 O) 12
	anhydrite, syn	CaSO 4
	potassium zinc tetrachloride	K 2 ZnCl 4
	sylvite, syn	KCl
	magnesium phosphate	MgP 4 O 11

Table 4 .

 4 Characterization of the plant-based catalyst by direct infusion mass spectrometry (ESIÀ).[a]

	m/z (abundance [%])

À

[a] See the Supporting Information for a comparison of the experimentally observed and predicted isotopic distribution.

Table 2 .

 2 Mineral composition of different samples of plant-based catalysts, as established by ICP-MS.

	Sample of plant-based Latitude, longitude data of				Composition [wt % AE standard deviation]
	catalysts	sampling sites	Mg	Ca	Fe	Zn	Cd	Al	Pb
	sample 1	43.933031, 3.666407

3.76 AE 0.10 35.81 AE 0.50 1.80 AE 0.028 6.57 AE 0.059 0.35 AE 0.0040 1.74 AE 0.049 0.73 AE 0.0048 sample 2 43.933514, 3.667212 4.26 AE 0.16 31.15 AE 0.66 1.13 AE 0.030 4.80 AE 0.097 1.12 AE 0.036 1.10 AE 0.056 0.31 AE 0.0076 sample 3 43.932737, 3.666461 11.68 AE 0.18 25.75 AE 0.59 2.95 AE 0.030 9.65 AE 0.045 0.063 AE 0.00060 1.55 AE 0.088 0.11 AE 0.00067

Table 7 .

 7 Reusability of the plant-based catalyst in the Garcia Gonzalez reaction.

	Run	Yield [%]			Composition [wt % AE standard deviation]
		3 a-3 a'	Zn	Fe	Al	Cd	Pb
	first	65	6.75 AE 0.026	2.75 AE 0.042	1.50 AE 0.016	0.19 AE 0.0052	0.44 AE 0.0073
	second	60	6.70 AE 0.019	2.47 AE 0.028	1.47 AE 0.049	0.19 AE 0.0066	0.44 AE 0.0020
	third	58	6.70 AE 0.041	2.38 AE 0.037	1.45 AE 0.059	0.19 AE 0.0037	0.44 AE 0.0093
	fourth	55	6.68 AE 0.028	2.34 AE 0.055	1.45 AE 0.036	0.19 AE 0.0040

Acknowledgements

The authors would like to thank Agence Nationale de la Recherche (ANR) (11ECOT 011 01), Agence de l'Environnement et de la


Susan L Murphy
email: sumurphy@umich.edu

Alain Lescoat

Mary Alore

Michael Hughes

John D Pauling

Maya Sabbagh

Dinesh Khanna

OTR Susan L Murphy Scd

How do patients

Keywords: Raynaud's Phenomenon, Scleroderma, systemic sclerosis, qualitative analysis, connective tissue diseases

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Raynaud's Phenomenon (RP) is a vascular disorder characterized by painful episodes of digital discoloration and rapid blood flow back to the affected areas [1] which impacts about 5% of the population worldwide [START_REF] Maricq | Geographic variation in the prevalence of Raynaud's phenomenon: Charleston, SC, USA, vs Tarentaise, Savoie, France[END_REF]. RP has no cure, so treatment is focused on strategies that enable people to better manage symptoms, such as vasodilator medication and strategies to adapt to or avoid common triggers of cold exposure and emotional stress. However, optimal management is challenging. A main problem in establishing appropriate treatments is that RP itself is a blanket term describing heterogeneous disorders with different etiologies [START_REF] Hughes | Drug initiation and escalation strategies of vasodilator therapies for Raynaud's phenomenon: Can we treat to target?[END_REF][START_REF] Pauling | Raynaud's phenomenon-an update on diagnosis, classification and management[END_REF], and practice guidelines and research studies often fail to account for these differences [START_REF] Hughes | Drug initiation and escalation strategies of vasodilator therapies for Raynaud's phenomenon: Can we treat to target?[END_REF]. Additionally, the RP experience is not well-characterized and may differ between individuals [START_REF] Pauling | Multinational qualitative research study exploring the patient experience of raynaud's phenomenon in systemic sclerosis[END_REF], which hinders the ability to optimize treatment strategies.

A better understanding of how patients define their RP and its impact can better diagnose, assess (through understanding relevant outcome measure domains) and optimize treatment. Further, treatment targets may differ according to RP classification; whether it is 'primary' , a functional vasospastic disorder without underlying cause in an otherwise healthy person, or 'secondary' to another condition, such as systemic sclerosis (SSc) [START_REF] Denton | Systemic sclerosis[END_REF]. Despite shared use of the eponym, the pathophysiology of primary RP and SSc-RP differs markedly. Both are associated with macrovascular vasospasm of the digital arteries and arterioles, but in SSc, digital vasculopathy is also associated with an irreversible obliterative microangiopathy.

Differences in the lived experience of RP between primary and secondary RP has not been systematically studied, but could have implications for outcome measures and interventions. Previous studies have identified differences; with pain was a prominent feature of secondary (SSc -related) RP whereas numbness was more frequently associated with primary RP [START_REF] Maricq | Geographic variation in the prevalence of Raynaud's phenomenon: A 5 region comparison[END_REF][START_REF] Pauling | The patient experience of Raynaud's phenomenon in systemic sclerosis[END_REF]. We utilized a large international survey of people with RP (n = 1345) to examine and compare how patients defined their primary or secondary RP in their own words. Through a synthesis of qualitative data, we discuss experiences that may inform future research on RP management in these two patient populations. A c c e p t e d m a n u s c r i p t social media (including Facebook and Twitter), a scleroderma self-management website, Scleroderma Foundation website, and Scleroderma Raynaud's UK. Written consent was not needed based on IRB determination. The overall project objective was to examine signs and symptoms of RP including nature of digital color change and sensory symptoms, such as digital vasculopathy severity. Participants (≥18 years old) were invited to complete the survey if they had clinician-diagnosed RP. All participants self-reported RP classification (primary-not associated with another condition-or secondary). For secondary RP, the underlying disorder was specified by patients.

METHODS

Data

Analysis

To characterize the sample, descriptive analyses such as means and frequency counts were used. T-Tests and chi-square tests were used to examine differences between primary and secondary RP. Participants were asked to "define RP in your own words". Responses in languages other than English (e.g., Portuguese, Danish, French, Spanish) were translated into English prior to coding.

Qualitative data was analyzed using an open coding process. All raters (SLM, MA, AL) were blinded to patient RP classification and had no information concerning demographics and geographical origins of patients while coding. They were only provided with written responses of each patient's RP definition. Definitions varied in length from a few words to several sentences; most commonly , 1-2 sentences were provided. Two independent raters (clinician specialized in RP management and patient with SSc-related RP) independently coded each transcript and came together to reconcile discrepancies. In cases where agreement was not reached, co-author SLM provided final reconciliation. Throughout coding, the codebook was revised as needed in an iterative, collaborative process among the team. Once both raters completed coding independently (using a common version of the codebook), a single report of themes was created. Qualitative frequencies resulting from this coding were utilized to inform what domains were most salient to participants [START_REF] Guest | Applied Thematic Analysis[END_REF]. Frequencies of themes were compared across primary and secondary RP using chi-square tests and presented as odds ratios (OR) with 95% confidence intervals (CI). Statistical analyses were performed using SPSS 20.0.

All tests were performed with a significance level of p<0.05.

RESULTS

The survey was completed by 1718 people between April and May 2020. Of those, 1345 supplied an RP definition and self-reported primary or secondary RP. This sample was 93% female, A c c e p t e d m a n u s c r i p t mean age was 51.5 years (SD+ 13.4; range 18-83), and participants were from 45 countries (across 6 continents). With regard to RP classification, 17% (n=226) reported primary RP, 69% (n=927) reported SSc-RP, and 14% (n=192) reported other non-SSc-related, non-primary RP. Participants with primary RP were younger than those with secondary RP in this sample (41.8 years + 11.9 versus 53.3 years + 12.9 respectively, p < 0.0001, n = 1337). Of people with primary RP, 48% felt that their RP was not well-controlled. Slightly less than one third of the sample (31%) saw a specialist for RP, whereas the rest received care from a primary care provider. Use of vasodilators such as sildenafil, tadalafil or riociguat, was more frequently reported in patients with secondary RP versus primary RP (18.0% versus 2.6% respectively). The secondary RP group also more frequently reported usage of Endothelin receptor antagonists compared to the primary RP group (3.7% versus 1.3%).

Table 1 shows themes and patient descriptions. Regardless of RP classification, most people defined their RP by specific body parts affected, fingers and toes most frequently. Change in color of fingers and toes, and pain were mentioned by nearly half of the sample. Of people who identified triggers (n = 624, 46%), most were able to identify triggers that caused an episode (e.g., cold, stress, environmental conditions), although some mentioned it was unpredictable. Only 29 patients defined RP using "attack" (2%), and "episode" was only mentioned 13 times. Patients nonetheless frequently reported a similar succession of episodic color changes and sensations such as: "fingers turn white then blue then red, with pain". The impact on quality of life and function was described by over a quarter of the sample (27%). People mostly used negative descriptors such as "debilitating, lifechanging, or embarrassing". Some people provided descriptions that ranged in severity from "inconvenient", "limiting activities" to "makes my life a living hell.". Others provided more details such as: "It's horrible. My hands are always cold. I have to wear gloves most of the time." Another person defined RP stating: "It affects my daily life. I am always cold, my hands feel it the most. It can be depressing. It's not easy to manage. I have many aches and pains. I often ache."

Table 2 shows differences in how people define their RP based on primary or secondary classification. Of all themes identified, six were significantly different in proportions who endorsed each by group. People with primary RP more frequently mentioned RP's impact on function or quality of life compared to secondary (35% and 25% respectively, p=0.004). Pain was more frequently mentioned in primary compared to secondary RP (54% and 47% respectively, p=0.05). In contrast, patients with secondary RP more frequently cited specific body parts, color change, management of attacks and RP-related complications.

DISCUSSION

This large international study found patients defined RP most often by body parts involved, color change, and pain. Significant differences in frequency of these three main themes were found in patients with primary and secondary RP. Pain was more frequently mentioned in primary RP whereas color change and body parts involved were more frequent in secondary RP. These results suggest that the definition and perception of RP differ by classification. More than a quarter of the overall sample mentioned reduced quality of life as part of their definition.

The main themes identified are consistent with a previous focus group study of 40 patients with SSc-RP [START_REF] Pauling | Multinational qualitative research study exploring the patient experience of raynaud's phenomenon in systemic sclerosis[END_REF], although the findings of this survey are based on reports from a larger number of people with SSc across 6 continents. The core domains comprising the patient experience of RP were similar across primary RP and SSc, although the relative importance (based on frequency of reported themes) differs between these patient populations. For example, RP management was only mentioned by 7% of people with primary RP whereas 13% of patients with secondary RP mentioned this theme.

The theme "Constant vigilance and self-management" previously identified in SSc-related RP would thus be less applicable to primary RP [START_REF] Pauling | Multinational qualitative research study exploring the patient experience of raynaud's phenomenon in systemic sclerosis[END_REF][START_REF] Pauling | The patient experience of Raynaud's phenomenon in systemic sclerosis[END_REF].

Although all patients defined RP by its impact on quality of life, it was more frequently mentioned in primary RP. It may be that patients with secondary RP benefit from being more closely monitored by their provider for their primary condition or view RP as part of their overall disease . In patients with SSc-related RP, other symptoms, like digital ulcers or gastrointestinal involvement, may be more impactful on quality of life than RP itself [START_REF] Hughes | Patient experiences of digital ulcer development and evolution in systemic sclerosis[END_REF][START_REF] Lescoat | Combination of capillaroscopic and ultrasonographic evaluations in systemic sclerosis: results of a cross-sectional study[END_REF][START_REF] Lescoat | Ulnar artery occlusion and severity markers of vasculopathy in systemic sclerosis: a multicenter cross-sectional study[END_REF]. Previous studies mentioned that pain was more frequently reported in SSc-associated RP, but our results show a trend for more pain in primary RP [START_REF] Maricq | Geographic variation in the prevalence of Raynaud's phenomenon: A 5 region comparison[END_REF][START_REF] Pauling | The patient experience of Raynaud's phenomenon in systemic sclerosis[END_REF]. Recent advances in management of RP-related complications such as digital ulcers may have helped to limit pain in secondary RP [START_REF] Hachulla | Efficacy of sildenafil on ischaemic digital ulcer healing in systemic sclerosis: The placebo-controlled SEDUCE study[END_REF]. Many patients from both groups also reported an impact of RP on functioning. Several patients also mentioned the impact of how others reacted to their RP as "embarrassing" or "misunderstood". For some patients, it may be important to consider other therapies such as use of psychologists to address mental health and mood issues that may coincide with RP. Others mentioned lack of clinician education concerning RP. Education of clinicians about RP and addressing its complications may help improve patient quality of life. This may include referral to rehabilitation services to help people learn adaptive strategies for situations where RP is triggered.

A c c e p t e d m a n u s c r i p t

Only one third of patients with primary RP included color change in their definition whereas this theme was mentioned by more than half of patients with secondary RP. Such findings could have implications for outcome measure development. For example, including color change in a combined index or outcome measure may not have the same clinical relevance to patients with secondary and primary RP. Interestingly, the concept of "episode" or "attack" was only included in definitions by less than 5% of the sample. This result challenges the concept of discrete "attacks" and number of "attacks" that has formed the basis of previous clinician-derived outcome measures in RP trials [START_REF] Denton | Efficacy and safety of selexipag in adults with raynaud's phenomenon secondary to systemic sclerosis: a randomized, placebo-controlled, phase II study[END_REF].

Our findings are consistent with previous studies highlighting that number of RP attacks may be unreflective of RP activity. Previous studies have observed that some patients are not "100% sure what an attack is" [START_REF] Pauling | Multinational qualitative research study exploring the patient experience of raynaud's phenomenon in systemic sclerosis[END_REF][START_REF] Pauling | Patient perceptions of the raynaud's condition score diary provide insight into its performance in clinical trials of raynaud's phenomenon: comment on the article by Denton et al[END_REF]. Therefore, the concept of "attacks" may not properly reflect RP from the patients' perspective.

Our study does have some limitations. Participants were recruited through RP-related patient associations or foundations which has the risk of inherent selection-bias of more severe and wellinformed patients. Diagnosis and classification of RP as primary or secondary was based on self-report which may have led to misclassification. However, our data suggest that classifications were trustworthy as people with secondary RP more frequently reported cutaneous complications such as telangiectasia or digital ulcers which are frequently seen in secondary RP related to SSc. The qualitative analysis was only based on a single open-ended question and thus saturation of themes was not possible. However, a particular strength is that this study has much more generalizability given the size and international representation of the sample. Also utilization of a mixed qualitative & quantitative approach allowed analysis of themes derived from patient data instead of preconceived definitions of themes and domains.

To conclude, our study highlights differences in relative importance of themes used for RP definitions of patients with secondary and primary RP and suggests that these two populations may differ in terms of feeling or functioning regarding their condition.

1.

Wigley F, Flavahan N. Raynaud's Phenomenon. N Engl J Med. 2016;375(6):556-65. What I find that works are white cotton gloves at night."  "I have to run (my fingers) under warm water then they turn purplish blue before returning to their normal color. I keep gloves/ mittens with me at all times and hand warmers..."

COMPLICATIONS

Reporting complications of RP, such as chilblains, telangiectasias, digital ulcers, sores, cracking, or infections  "…Now in my feet with occasional chilblains"

 "…The ulcers are the most painful side effect."

INFLUENCE OF WEATHER

Discussing differences in RP due to seasons or weather  "(White freezing fingers and toes) happens more in winter but also spring if I'm outside and not moving"

 "Winter very difficult, summer air conditioning a nightmare"

A c c e p t e d m a n u s c r i p t

  were taken from the PAtient Survey of experiences of RAynaud's Phenomenon (PASRAP) Survey Project. The study was approved with exempt status by the University of Michigan IRB (Study ID: HUM00175143; OHRP IRB Registration Number(s): IRB00000246). An online survey was sent through several methods to tap a sample with primary or secondary (SSc -related) RP:

A c c e p t e d m a n u s c r i p t A c c e p t e d m a n u s c r i p t

A

  c c e p t e d m a n u s c r i p t  "My body's overreaction to cold temperatures, almost a faulty defense mechanism to protect against cold weather"  "Restricted circulation which leads to episodes of discoloration & pain in the extremities" ONSET/ DURATION Discussing timing of an episode, whether it was gradual or sudden onset or duration  "Sleeping fingers that turn white in color, and then go to purple. It usually lasts around 20-30 minutes."  "Fingers suddenly loose blood supply..."MANAGE SYMPTOMSMentioning strategies to try to manage, prevent, or stop episodes  "Hands will swell in size and is very uncomfortable. Have tried meds and creams nothing works.

A

  c c e p t e d m a n u s c r i p t

Table 1 . Examples of Responses Under Each Theme

 1 Embarrassing around people who don't know what it is. Limiting to day to day life. Impacts me every day"  "Horrible! It is triggered by more than just temperature. Often just using the bathroom or eating in the morning will set it off. And it feels like my whole body is impacted. Sometimes I have just give in and lie down under an electric blanket" MECHANISM Explaining the mechanism, pathogenesis, how the body works or doesn't work

	Defines RP by…
	EFFECTS ON BODY PARTS
	Stating number and/or type of body parts affected
	 "Decreased circulation to extremities. For me it is fingertips."
	 "(it's) like having all the blood drained from your fingers."
	Stating color change and/or describes how colors change
	 "Hands and feet become very cold with redness, white and blue color."
	 "Finger gets cold, turns white, individually, maybe just one, and feel numb and can't be warmed up
	with warm water, etc. Eventually warm up, turn red and stung a little."
	SYMPTOMS
	Reporting pain
	 "Throbbing pain at night, particularly before starting medication."
	 "Irritating and painful"
	Mentioning other symptoms such as numbness, cold, head, loss of sensation, cramps, spasms
		"Burning sensation in the fingers and/or toes from lack of blood flow"
	Reporting tingling, pins and needles
	 "Taking all the blood flow and replacing it with lava burning pins and needles"
	TRIGGERS
	Identifying a trigger/situation(s) in which it occurs, or unpredictable nature of episodes
	 "(RP) can be triggered by cold weather, opening freezer, a breeze..."
	 "Mine is triggered by stress & cold…"
	IMPACT AND EFFECTS ON QUALITY OF LIFE
	Describing impact on quality of life, by expressing negative emotions, how others react to RP, or specific
	functional limitations, such as loss of hand function
	 "Debilitating to so many different aspects of everyday life. It was become increasingly worse every
	year!"
	 "

Table 2 . Differences in RP Definition based on Primary or Secondary Diagnosis (n = 1345)

 2 Phenomenon, OR=Odds Ratio; CI=Confidence interval Univariable associations assessed through Chi 2 square test, level of significance P<0.05

	Themes from RP	Primary RP (N = 226)	Secondary RP (N = 1119)	OR	95% CI	P value
			n (%)		n (%)
	EFFECTS ON BODY PARTS
	Number and types of body parts affected	140	(61.9)	788	(70.4) 0.684	0.508-0.921	0.01
	Color change	81	(35.8)	615	(55.0) 0.458	0.34-0.62	0.0001
	SYMPTOMS
	Pain	122	(54.0)	524	(46.8)	1.33	1.00-1.77	0.05
	Other symptoms	19	(8.4)	109	(9.7)	0.85	0.51-1.42	0.53
	Tingling, Pins and Needles	56	(24.8)	248	(22.2)	0.86	0.62-1.21	0.39
	TRIGGERS
	Identifying triggers	94	(41.6)	530	(47.4)	0.79	0.59-1.06	0.11
	IMPACT AND EFFECTS ON
	QUALITY OF LIFE
	Impact on function or Quality of Life	78	(34.5)	283	(25.3)	1.56	1.14-2.11	0.004
	MECHANISM
	Explaining Mechanism	63	(27.9)	307	(27.4)	1.02	0.74-1.41	0.89
	ONSET/DURATION
	Timing/Onset of Episodes	51	(22.6)	270	(24.1)	0.92	0.65-1.29	0.62
	MANAGE SYMPTOMS
	Strategies to manage and prevent episodes	15	(6.6)	148	(13.2) 0.466	0.27-0.81	0.006
	COMPLICATIONS
	Complications	11	(4.9)	111	(9.9)	0.465	0.25-0.88	0.02
	INFLUENCE OF WEATHER
	Season or Weather	19	(8.4)	79	(7.1)	1.21	0.72-2.04	0.48
	RP=Raynaud's

Funding: Dr. Lescoat was funded by the French network of the University Hospitals HUGO (Hôpitaux Universitaire du Grand Ouest) (AAP JCM2020) and a grant from Rennes University Hospital (CORECT Visiting Grant 2020). Dr. Khanna's work was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases at National Institutes of Health [K24-AR-063129]. Conflicts of interest/Competing Interests: Dr. Pauling reports personal fees from Boehringer Ingelheim; Grants, personal fees and non-financial support from Actelion Pharmaceuticals; Personal fees from Sojournix Pharma, all outside the submitted work. Dr. Hughes reports speakers fees from Actelion Pharmaceuticals. Dr. The study was approved with exempt status by the University of Michigan IRB (Study ID: HUM00175143; OHRP IRB Registration Number(s): IRB00000246).

data underlying this article will be shared on reasonable request to the corresponding author.