V Clary

T Oudart

P Larroudé

J Sommeria

T Maître

An optimally-controlled RANS Actuator force model for efficient computations of tidal turbine arrays

Keywords:

A steady-state Actuator force model using the RANS equations is developed to calculate the power production and the flow through arrays of tidal or river Darrieus turbines. It uses detailed three dimensional force distributions depending on the position on the turbine, obtained beforehand by a set of blade-resolved URANS simulations of the turbine. New power coefficient and force coefficient laws depending on the local velocity instead of the upstream velocity are established and appear to be independent from the local turbine blockage in an array. Those laws are used to construct a model that adapt the Actuator force distributions to the local velocity of the flow reaching each turbine, in order to simulate each turbine functioning close to its maximum efficiency point. The model is validated against experimental measurements on a reduced-scale Darrieus turbine. A fence farm configuration and a two row farm configuration are investigated and compared to results of the same model adapted in two dimensions. The local blockage effect is more favorable for fences than for staggered turbine configurations, increasing the local velocity and the power production for each turbine.

Introduction

Tidal energy is currently undergoing fast progress, and the first deployment projects of several machines are planned at different places in the world. In the future, simplified models will be needed for choosing the location of several tens of turbines in an array and studying their influence on the hydrodynamic currents in the vast oceanic areas impacted. The wake interaction between turbines must be considered, with the influence of the velocity deficit and turbulence created by the upstream turbines in an array. The influence of the upstream turbulence intensity was clearly shown by [START_REF] Mycek | Experimental study of the turbulence intensity effects on marine current turbines behaviour. Part I: One single turbine[END_REF] for horizontal axis tidal turbines. They measured experimentally that the wake of a turbine placed in a zone of high turbulence (15% turbulence intensity) recovered much faster than for low turbulence (3% turbulence intensity).

Our study focuses on vertical axis water turbines, which have the main advantage of being insensitive to the direction of the upstream flow. They are also less sensitive to the upstream turbulence level, as [START_REF] Boudreau | Comparison of the wake recovery of the axial-flow and cross-flow turbine concepts[END_REF] showed comparing the CFD results of various turbine models. A large eddy simulation (LES) conducted by [START_REF] Guillaud | Large Eddy Simulations on Vertical Axis Hydrokinetic Turbines and flow phenomena analysis[END_REF] showed in details the different vortices created in all parts of a Darrieus vertical axis turbine, including the arm-shaft connections and the blade tips. Those vortices lead to a big reduction of the turbine efficiency. This simulation model is the more accurate to describe the turbine behavior, yet it requires huge computational resources which is prohibitive for array optimization.

Different approaches have been used to reduce the computational costs. For axial turbines, analytical methods based on the Betz-Joukowsky law (the Actuator Disk method) have been improved to take into account the confinement of stream thierry.maitre@legi.grenoble-inp.fr (T. Maître) turbines, due to the presence of the bathymetry, free surface and the other adjacent turbines [START_REF] Garrett | The efficiency of a turbine in a tidal channel[END_REF][START_REF] Whelan | A free-surface and blockage correction for tidal turbines[END_REF]. The models were extended to an array of tidal stream turbines by [START_REF] Vennell | Exceeding the Betz limit with tidal turbines[END_REF] or [START_REF] Draper | Centred and staggered arrangements of tidal turbines[END_REF]. Simplified CFD models seem promising. At the oceanic scale, large domains and long duration are computed thanks to 2D models, in order to simulate properly the effects of the tides at a potential site all along the year. Two different approaches exist to compute the effect of a tidal turbine: it can be modeled by a friction force on the bottom [START_REF] Kramer | A correction to the enhanced bottom drag parameterisation of tidal turbines[END_REF], or by adding a force source term in the momentum equations [START_REF] Thiébot | Modelling the effect of large arrays of tidal turbines with depth-averaged Actuator Disks[END_REF], both methods representing the action of the turbine on the mean flow in the vertical water column with significantly the same results. Three-dimensional simulations might be useful to take into account the 3D characteristic of the flow and the bathymetry more precisely as in [START_REF] Nguyen | Three dimensional tidal turbine array simulations using OpenFOAM with dynamic mesh[END_REF] or [START_REF] Thiébot | Wake field study of tidal turbines under realistic flow conditions[END_REF]. [START_REF] Wimshurst | Tidal power extraction on a streamwise bed slope[END_REF] showed using an Actuator Disk (AD) approach that a turbine at a location where water depth is diminishing (in the current direction) produces less power than the same turbine at a location with increasing water depth. This is due to modifications in the boundary layer, as turbines are often placed at elevations that are still impacted by the velocity reduction in the bed boundary layer.

To improve AD models, the blade-element method embedded in a RANS solver (RANS-BE) can be used for the different types of turbines, to calculate the forces to impose in the so-called Actuator Line models. A force distribution depending on the position on the turbine and depending on time is used instead of the uniform force distribution of AD models. Such simulations were done for axial turbines using the RANS approach for modeling turbulence [START_REF] Edmunds | An enhanced disk averaged CFD model for the simulation of horizontal axis tidal turbines[END_REF], with a good accuracy. The method to obtain the force distribution seems crucial, especially for Darrieus turbines where the stall phenomenon occurs. In their Actuator Line Method, [START_REF] Shamsoddin | Large eddy simulation of vertical axis wind turbine wakes[END_REF], [START_REF] Mendoza | Near-wake flow simulation of a vertical axis turbine using an actuator line model[END_REF] and [START_REF] Grondeau | Wake of a ducted vertical axis tidal turbine in turbulent flows, lbm actuator-line approach[END_REF] calculated the force distribution on Darrieus turbine blades with a semiempirical dynamic stall model. They used the LES turbulence model and were able to calculate the wake of one turbine with a great accuracy.

In array configurations, the flow reaching each turbine is modified due to the local blockage defined as the fraction of the channel section occupied by the turbines. The behavior of the turbine for those different flow conditions will determine the distribution forces that have to be imposed. The turbine regulation is important and will act on the operating point used. Equipping the turbines with variable speed technology seems the most promising issue and allows the use of a maximum power point tracking (MPPT) system, in order to always take advantage of the best efficiency point of the turbine. The local velocity that is striking each turbine of an array must be used to calculate the best efficiency point for this flow configuration. For axial turbines, [START_REF] Nishino | Local blockage effect for wind turbines[END_REF] used the RANS k-model to obtain the velocity in each cell of their Actuator Disk volume. The turbine forces are deduced using the drag coefficient value corresponding to the best efficiency point of the turbine. An elaborate Actuator cylinder method based on the RANS k-SST model was developed by [START_REF] Shives | A tuned actuator cylinder approach for predicting cross-flow turbine performance with wake interaction and channel blockage effects[END_REF] for cross flow turbines. The drag coefficient and power coefficient values were also depending on the upstream Reynolds number and turbulence intensity, in order to be accurate for different flow conditions. Satisfactory velocity deficits are achieved in the wake, thanks to the SST eddy-viscosity limiter that prevents a too fast velocity recovery.

A few array layout behaviors have been investigated in the literature. A power production law for turbines side by side in a channel (the fence configuration) was proposed by [START_REF] Garrett | The efficiency of a turbine in a tidal channel[END_REF]. They found out that turbines in a fence benefit from local blockage effects if they are working at their optimal operating point. Vogel andWillden (2017, 2019) used a BEM model with the forces and power production adapting to several tested advance parameters. They found out a maximal power production increase of 26% for a fence of eight machines compared to the power production of the same isolated machines in free-stream conditions, with a mean power coefficient Cp=0.608 instead of 0.484. [START_REF] Dominguez | Fast power output prediction for a single row of ducted cross-flow water turbines using a bem-rans approach[END_REF] considered 2D fences of ducted cross-flow water turbines. A power increase factor equal to 2.6 was found for a fence containing 15 turbines with a lateral spacing of 1 turbine width and a blockage ratio of 0.4. More recently an experimental study [START_REF] Mcnaughton | Experimental study on interactions between two closely spaced rotors[END_REF] showed that two side-by-side axial turbines witness a power production increase if they are placed close to each other and operate at their new optimal advance parameter. Concerning staggered configurations, the URANS farm simulation realized by [START_REF] Nuernberg | Three dimensional tidal turbine array simulations using OpenFOAM with dynamic mesh[END_REF] showed a small increase of the production of turbines placed closely downstream and on the side of a first one, with a maximum 11% power increase. [START_REF] Ordonez-Sanchez | Experimental evaluation of the wake characteristics of cross flow turbine arrays[END_REF] did experi- The present study aims at developing a 3D steady-state method for turbine array modelings that does not need aerodynamic foil coefficients nor empirical data for taking into account the rotating blades and the possible stall phenomenons. Moreover, the proposed method allows one to calculate the turbine power production with a good accuracy, and different farm configurations are tested. The turbine used is a three-bladed (n=3) reduced-scale Darrieus turbine, that had already been experimented by [START_REF] Maître | Modeling of the flow in a Darrieus water turbine : Wall grid refinement analysis and comparison with experiments[END_REF]. Its characteristics are presented in Figure 1. It has a diameter D=175 mm and a height H=175 mm. The blades are NACA0018 profiles, with a camber following a rotating circle of diameter 175 mm. Its chord value is c=32 mm, leading to a solidity 2nc/D=1.1. The upstream flow direction is represented by the vector ∞ , and the rotational speed Ω is controlled. The turbine advance parameter is defined in a classical way as = Ω ∕(2 ∞ ). The origin of all coordinates in this work is the intersection of the rotation axis and the mid-height plane of the turbine. The x axis is along the inlet flow direction, z is the vertical axis and y the transverse axis.

The force distributions used are obtained from a few unsteady RANS rotor-stator simulations of the turbine done for different upstream flow conditions. An interpolation from those force distributions is performed for intermediate cases.

The model developed adapts the force values to the upstream flow velocity, with an equation linking those forces to the local velocity calculated for each turbine. Therefore simulations of any configuration of turbine array can be easily performed without having to tune any parameter. The method can be extended to axial turbine or others. In any case the mesh used is cartesian, which will be an advantage in the future to calculate the influence of the masts or external parts of the turbine not represented in this study. Those parts could be modeled by adding the corresponding drag force in the affected cells, or by the use of IBM methods that prove to be efficient on cartesian meshes [START_REF] Constant | An immersed boundary method in OpenFOAM : Verification and validation[END_REF].

Methodology

Preliminary URANS simulations

The force distributions imposed in the adaptive model are results obtained beforehand from unsteady blade-resolved simulations of the Darrieus turbine. These simulations are done with the open source software OpenFoam4.1. A RANS turbulence closure model is used with the k-Omega Shear Stress Transport linear eddy viscosity equations [START_REF] Menter | Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications[END_REF][START_REF] Menter | Ten Years of Industrial Experience with the SST Turbulence Model[END_REF]. This model has two equations on k and , and allows to capture correctly the flow separation. It has been widely used to calculate the performances and loads of cross-flow turbines. [START_REF] Maître | Modeling of the flow in a Darrieus water turbine : Wall grid refinement analysis and comparison with experiments[END_REF] used this turbulence model and did a mesh sensitivity analysis for a 2D simulation of a Darrieus turbine. To capture the boundary layer flow near the turbine, they found out that the maximum dimensionless wall distance y+ has to be lower than 5 (with good results obtained for values always lower than 2), and the mean y+ value has to be less than 1. [START_REF] Kramer | Three-dimensional numerical simulations of straight-bladed vertical axis tidal turbines investigating power output, torque ripple and mounting forces[END_REF] showed that a 3D URANS simulation with a mean y+ value less than 1 is able to reproduce correctly the geometry effects like the arm-blade connections. In our simulations, the wall refinement used has a cell height of 1.0 × 10 -5 m near the wall and is extended within 15 layers, with a growth rate of 1.17. After convergence, a maximum y+ value of 2.4 and a mean value always lower than 0.2 are obtained for the different positions during one turbine revolution and for all the simulated advance parameters. The inlet conditions are a flow velocity of 2.3m/s, a turbulence intensity of 2.5%, and a value = 1 -1 , which is low and creates no turbulence decay along the domain. Wall laws are used as lateral, top and bottom boundary conditions. The outlet conditions are a constant pressure condition and a zero gradient velocity condition. The dimensions of the simulation domain are 0.60 m wide, 0.55 m high and 2.5 m long in the direction of the flow (0.5 m upstream, and 2 m downstream of the turbine). A view of this domain is presented in Figure 2. To reduce the number of cells, a symmetry is used on the median plane (z=0), therefore only the upper half of the domain in Figure 2 is simulated. The turbine rotation is taken into account using a dynamic mesh interface between the tunnel domain and a cylinder containing the turbine. These specifics lead to a full mesh composed of about 14 million cells, with 9 million cells in the rotor domain. The turbine shaft and its support structures are not modeled.

The pimpleDyMFoam solver is used to get accurate results in acceptable time. It is a large time-step transient solver for incompressible, turbulent flow, using the PIMPLE (merged PISO-SIMPLE) algorithm. It is able to take into account dynamic meshes. The numerical schemes used are second order (backward) for the time, and second order for pressure, velocity, k and omega (Gauss linear) with a limiter for k and omega. Classical time step values are used, depending on the advance parameter simulated for the turbine. At ≥2, which is larger or close to the optimal advance parameter in the present study, the time step is chosen to correspond to a rotation of the turbine of 1 degree. This value was recom- [START_REF] Maître | Modeling of the flow in a Darrieus water turbine : Wall grid refinement analysis and comparison with experiments[END_REF]. A smaller time step corresponding to 0.5 degree of rotation is chosen for lower values. A maximum of 30 subiterations is chosen for each time step. Results are obtained only once the two following criteria are met: at least 12 revolutions of the turbine have been completed, and the flow is converged in the wake. Doing only 6 revolutions has led to differences with the final force and power values less than 1%. Using a coarser mesh containing 6 million cells with the same near wall grid has also led to differences of the same order of magnitude.

The URANS simulation results are compared to experiments using the same reduced-scale Darrieus turbine. New experiments were conducted in the CERG hydrodynamic tunnel TH2 in Grenoble, whose test section is approximately 2 m long with a constant rectangular shape that is 60 cm wide by 55 cm high. Three different flow velocities are used in the test section: 1.8 m/s, 2.3 m/s and 2.8 m/s. The turbine is not centered and is shifted 5 cm towards negative y values, but simulations showed that this has no influence since the walls are far enough away from the turbine.

A turbulence grid is located 1 m upstream of the turbine, and creates homogeneous isotropic turbulence. It has rectangular bars of thickness 1 cm regularly spaced each 5 cm in the two transverse directions. The turbulence intensity has been measured beforehand without turbine along the tunnel, and an extrapolation at the turbine location (where the absence of window is hindering measurements) gives the turbulence intensity value of 5.5 %. This value is different from the URANS inlet turbulence intensity value, but no significant effect is expected because the flow through vertical axis turbines has a low sensitivity to turbulence. Three different flow velocities have been tested. The instrumentation of the turbine is detailed in the work of [START_REF] Maître | Modeling of the flow in a Darrieus water turbine : Wall grid refinement analysis and comparison with experiments[END_REF].

The power production of the turbine is measured via the electrical torque, and the corresponding power coefficient Cp is deduced. Cp is equal to the turbine kinetic power P divided by the maximum extractable power from a free stream flow of velocity ∞ , considering the projected section S of

= 1∕2 3 ∞ (1)
In this equation, is the density of the water, chosen to 1000 ∕ 3 . The Cp curves for each flow velocity are compared to the numerical Cp values obtained with the URANS blade-resolved simulation of the turbine in Figure 3. All experimental curves are close which means that there are few Reynolds effects for those tunnel velocities. The URANS curve is in good agreement with the experimental ones, with the highest error for = 2. Forces along the streamwise (x) and lateral (y) directions are measured via piezoelectric sensors, and the corresponding dimensionless force coefficients Cx and Cy are deduced. In order to compare them with the results of the URANS blade-resolved simulation that was done without the turbine shaft, the drag created by this part is estimated using the drag coefficient curve of an infinite fixed cylinder of the same diameter. The value of 12.3 N is calculated and is added to the total simulated drag. The comparison of the experimental and simulation results is presented in Figure 4. The Cx results are very close, but there are discrepancies in term of Cy values, with high relative errors since the turbine transverse force values are small. However the URANS simulation is validated against the experiments and its results are used to construct the simplified model as explained in the following section.

A force conservative simplified model

In our simplified model, a classical representation of the turbine is used: force source terms are added in the momentum equations for each cell of the domain swept by the turbine. The method used to obtain a time-averaged force field from the URANS simulation results consists of two steps. mesh, which geometry is adapted to represent the Darrieus force distribution. It is more suitable than using a cartesian mesh that might lead to a loss of information if the mesh is too rough, or to discontinuities if the cell sizes are too close to the URANS cell dimensions. The cylindrical mesh used is presented in Figure 5. Its cells are the basic volume elements of a fixed cylindrical coordinate system (O, r, , z), which does not rotate with the turbine. The decomposition is done here for the half of the turbine simulated, and will be extended later by symmetry to the whole turbine. The zone where blade forces are present is decomposed into one cell in the radial direction r, 10 cells in the z-direction and 72 cells along the 360°of ( = 5°). The arm forces are extracted in a domain that contains 10 cells in the radial direction and 1 cell in z-direction, with = 5°. When the simulation is converged, during one turbine revolution, both arm and blade forces are extracted for each cell of this cylindrical mesh, for each time step equivalent to 1°or 0.5°of rotation. This referential being fixed, at each time step, cells of the cylindrical mesh intersect either a part of the blades or arms (in this case the corresponding forces are extracted) or only a fluid part (no forces are extracted). At last, a time-averaging of those force distributions during the whole turbine revolution is performed for each cell to obtain a steady-state spatial distribution of the forces.

The second step is a projection of those forces on a new cartesian mesh, of which the cell size can be adapted to have a proper representation of the turbine. This projection step has been chosen for its simplicity to model whatever number of turbines in an array without having to take care of the turbine positions to construct the mesh. Forces from the cylindrical steady-state force distribution are projected in the simplified model mesh. The cell forces imposed in the simplified mesh are obtained from a weighting of the forces of all the neighbor cells of the cylindrical mesh whose center is comprised within a distance lower than a constant distance of the code, named _ . This is illustrated in Figure 6 for a two dimension mesh. In the following equations, the index i is taken for numbering the cells of the simplified mesh (noted ℎ . ), and the index j for cells of the cylindrical mesh (noted ℎ . ). is a linear function of the distance between the cells i and j, and is defined as:

= _ - ≤ _ (2) = 0 > _ (3)
In order to have the conservation of the total forces applied in the mesh, a factor has to be used to calculate the part of the force on a cell i due to the influence of the cell j. It is the function calculated as:

= ∑ ∈ ℎ . ( 4
)
The total force vector applied on the cell i of the simplified mesh is defined as a function of the cylindrical mesh

= ∑ ∈ ℎ . = ∑ ∈ ℎ . × ∑ ∈ ℎ . ( 5
)
It can be easily seen that the addition of the forces for all cells of the simplified mesh is equal to the total force applied on the cylindrical mesh. Another advantage of this method is that a smoothing is automatically done close to the borders of the turbine area. Indeed, even if cells are not comprised in the turbine swept volume, they witness a force contribution from cells comprised in a distance _ . The factor _ is therefore a smoothing factor of our simulations that has to be chosen carefully.

The force distribution obtained after projection for = 2 is presented in Figure 7 in the horizontal plane z=-2 cm ( ∕ =-0.23) (under the turbine arms), and the vertical plane y=0.

A grid sensitivity study has been done. It is linked to the smoothing parameter _ presented before, and both the cell size dx and this parameter have been tested. In order to be sure to have at least one cell in the radius direction for Transverse profile at 8D Ux-dx0.02m-dist0.02m Ux-dx0.01m-dist0.02m

Ux-dx0.01m-dist0.01m Ux-dx0.005m-dist0.02m

Figure 8: Velocity proles 2D and 8D downstream of the turbine for the dierent cell sizes dx and _ tested modeling the blades, the parameter _ can not be lower than dx. The velocity deficits at 2 diameters (2D) and 8 diameters (8D) downstream of the turbine are plotted versus y at the altitude z=-2 cm, for different values of the tested parameters. They are presented in Figure 8. We observe that the curves are converging towards the curve with dx=0.005 m. The case with dx=0.01 m and _ =0.02 m gives the same velocity profiles and it will be used in the simulations. It gives better results than using _ =0.01 m, because in this last case the arms are badly represented with only one cell in the z-direction and no vertical forces imposed, and the near-wake is slightly impacted. The chosen parameters dx=0.01 m and _ =0.02 m lead to a small over estimation of the turbine drag and power of respectively 2.4% and 3.6% compared to the converged values.

Research of a maximum efficiency operating point independent of the confinement

A classical representation of the turbine performances is the power coefficient versus curve, already presented in Figure 3. This curve presents a maximum of efficiency for close to 2, and can be used to calculate the turbine power production in free stream conditions knowing the upstream flow velocity ∞ . With a turbine placed in a restricted section, for example in a natural channel or between other turbines in an array, the flow just upstream of the turbine is generally accelerated compared to an isolated configuration. This effect is due to the straightening of the streamlines upstream the turbine. It induces an increase of the turbine extractable power. As a consequence, the power production can not be calculated with the performance coefficient of equation 1 anymore.

The confinement number is usually defined as ∕ ℎ , with ℎ the cross section of the channel simulated. In the present simulations, the domain height is kept constant and the confinement is changed in the horizontal direction, to correspond to turbines close to each other always located at the same water depth. A lateral confinement is defined as = ∕ , with D the turbine diameter and b the horizontal dimension of the channel chosen for each simulation. Three different confinement geometries are simulated with the URANS model: =0.29, =0.44 , and =0.58. Different advance parameters are used to draw the power coefficient curves. For each simulation, a mean local velocity is calculated to obtain a new local advance parameter * , defined as:

* = Ω ∕(2 ) (6)
The local velocity is calculated as the mean streamwise velocity value in all cells of the cylinder swept by the vertical axis turbine, that is time-averaged over one turbine revolution.

The local power coefficient Cp* is defined using the local velocity instead of the free stream velocity, as:

* = 1∕2 3 (7)
The local force coefficients for each components of forces (the local thrust coefficient Cx* and the equivalent coefficients in the 2 other directions Cy* and Cz*) are defined in the same way, using the local velocity instead of the free stream velocity, and depending on the three components of the total forces applied on the turbine , , : *

, , = , , 1∕2 2 (8)
The Cp versus curves are presented for each confinement in Figure 9.a, and compared to the corresponding * versus * curves in Figure 9.b. The labels added on this last plot correspond to the respective values used for each calculation point. The Cp versus curves are different for each confinement, and the maximum efficiency values are increasing as the confinement is increasing. The maximum of efficiency is also slightly shifted towards larger values as the confinement is raised. However the Cp* versus * curves are all superimposed. A 4 ℎ order polynomial fitting curve has been drawn, using the method of least squares with all the Cp* calculated points. All points are very close to the fitting curve, in regard to the simulation uncertainties. A justification is proposed for the existence of this unique curve. The turbine performances are increased if the velocity triangles on its blades are favorable. It means that the angle of attack on the blades has to be optimized. This angle depends on the relative velocity, and the * parameter is a good spatial average representation of this velocity for the whole turbine volume. Therefore a same * parameter leads approximately to the same power coefficient.

The classical and local force coefficients on the x and y axes are drawn in Figures 10 and11 Finally, time-averaged force values at several turbine locations have been monitored in the cylindrical mesh. The chosen locations are shown in Figure 5. The positions 1 and 2 are located in the zone of strong radial and tangential forces, at the angle =207.5 °. Position 1 is at the turbine center altitude (z=0), and position 2 is located at ∕ =0.46 where there is no influence of the arms. Position 3 is located at ∕ =0.46, at the most upstream position of the turbine ( close to 180°). The cell forces for those monitored cells are also made dimensionless using the local velocity to get the coefficients , , * . The values * and * are plotted versus * for the three different confinement configurations in Figure 12. Only three values have been simulated. The piecewise linear curves are drawn with the three points obtained for the confinement case = 0.29. For each position, the points obtained for the other confinement cases are located on these curves, even if small discrepancies occur. The monitoring on all the other cells gives the same order of accuracy. Excepted the calculation uncertainties, a source of discrepancies can be the fact that the mean local velocity over the whole Darrieus turbine is used, and forces can be locally slightly different for some confinement cases if the flow velocity and angle of attack are locally modified, for example by the presence of nearby channel walls. However, it is shown that those dimensionless force coefficients obtained for each cell of the cylindrical mesh are also independent from the confinement. They will be used later in the adaptive model without any additional confinement correction.

Each Cp versus curve in Figure 9.a has a different point of maximum efficiency. Those points are found using the different polynomial fitting curves. For each confinement, the order of the fitting polynomial is the number of simulated points minus one. The corresponding Cp* and * are calculated and presented in Table 1. It appears that the Cp* and * values found are close to each others. Taking the average of those points is a good approximation of a maximum efficiency operating point, independent from confinement. The maximum differences in terms of * and Cp* between two points are noted respectively Δ * and Δ * . The uncertainty analysis for the maximum power output is done as following:

= 1∕2 3 * = (Ω ∕2) 3 * 2 * 3 (9) ⟹ Δ = -3 Δ * * + Δ * * (10)
By using values found in Table 1, the relative error Δ * ∕ * is lower than 2.7% and the relative error Δ * ∕ * lower than 3%, which gives a total error on the maximum power production always lower than 11.7%. Therefore, using * =3.6 and Cp*=1.98 is a good approximation for imposing the best efficiency operating point in the simulations, for any possible flow configuration.

The adaptive model implementation

In real operating cases, the turbine performances and the forces applied on the turbine depend on the configuration of the flow through the turbine. The aim here is to develop an adaptive model that calculates automatically the forces and performances depending on this flow using the * parameter.

The calculation loop steps for the so-called adaptive model are summarized in Figure 13. Dimensionless URANS force distributions (the * and * distributions from Figure 12, and the corresponding * ) have been extracted on the cylindrical mesh for three * values: 1.4, 4.25 and 9.7. A linear interpolation is done for each cell if the chosen * is located in-between those values. The force coefficients are then multiplied by the term 1∕2 2 to get the force distributions that will be projected on the cartesian mesh, according to the previous paragraph. Those forces are added in the Navier-Stokes equations, then the flow and the new local velocity are calculated for the current iteration. After convergence, the final value is calculated and the * versus * curve of Figure 9.b is used to calculate the corresponding power production of the turbine.

The adaptive model is tested for different configurations: for the CERG test case in next section, and for array calculations in section 4. The CERG test case simulation is performed as a model validation. The adaptive model in which the force distribution is an unknown is compared with the force conservation model using the forces given by the URANS calculations. Moreover a 2D version of these two models removing the z-direction has been implemented to measure the effect of the 2D assumption on the results. The same software and setup are used (and the same cell size dx=dy=0.01 m in the central zone). The only differences are the domain size which is modified to keep the same turbine confinement, and the force distribution which is adapted in 2D. The confinement in 3D is ∕( ℎ) = 0.0928. In 2D, the value b=188.6 cm is chosen to have the same confinement value ∕ = 0.0928. The z-component of force vanishes in 2D. Because the turbine height is set equal to 1m, the x and y components 2 , are calculated for each ( , ) position in the cylindrical mesh as the sum of the 3D cell forces 3 , along z (with cell altitude indices ranging from to ) divided by the height of the turbine H: In the case of array calculations, the low array confinement is enough to have no influence on the results anymore, therefore the same x and y-domain lengths are used both in the 2D and 3D models.

2 , ( , ) = ∑ = 3 , ( , , ) (11
= 1 = 1.5 = 2 = 2 = 2 = 2.5 = 2.5 = 2.6 = 3 b) C * x _ _29% C * x _ _44% C * x _ _58% C * x _fit

Simulation results for a single machine

The test-case setup

To check the validity of the simulation results, PIV measurements have been realized on the experimental hydrodynamic tunnel downstream of the turbine, in several horizontal planes of different altitudes. The reference plane is located at the altitude z=1 cm, then 5 planes are located above it and 5 planes below it. Each of the consecutive planes are separated by a 4 cm increment in the z-direction. Vertical profiles of the axial velocity are reconstructed at several xpositions downstream of the axis of the turbine with the values obtained on the horizontal planes. The experimental values present a shift of approximately 3 cm towards the top of the tunnel compared to the simulations. It has been observed that the peculiar geometry of the flume with an upstream half-convergent section placed only in the lower part of the tunnel creates a z-component of velocity close to 0.05 m/s. This deviates progressively the wake of the turbine towards the top. Hence all measurement points altitudes are shifted of -3 cm when compared to the numerical results. The reference plane will therefore be described as the plane of altitude z=-2 cm when compared to numerical results.

The simulation domain is the domain already presented in Figure 2, that corresponds to the experimental setup. The k-Omega Shear Stress Transport turbulence model is used. The uniform inlet velocity of 2.3 m/s is chosen, and the turbulence inlet values are chosen to = 0.0711 2 ∕ 2 and = 90 -1 in order to have the turbulence intensity value of 5.5 % and the correct turbulence decay at the turbine location.

Wake results

The advance parameter = 2 is first simulated with all models. It is slightly different from the point of maximum efficiency presented in Table 1. The corresponding forces calculated via the URANS simulation are imposed for the force-conservation model, and * = 4.25 is now imposed in the adaptive model, that was the local advance parameter calculated in the URANS simulation at = 2. The wakes obtained are compared to the experimental one. The transverse velocity profiles are plotted in Figure 14 in the horizontal plane of altitude z=-2 cm ( ∕ =0.23), at several positions downstream of the turbine (at the distances 2D, 3D,... downstream of the turbine axis). The available vertical velocity profiles are plotted at the same positions downstream of the turbine in Figure 15, at the lateral position y=0 cm. We observe that both 3D models give sensibly the same results, even if the forces imposed are slightly different: the turbine drags are respectively equal to 80,2N and 84,3N for the force-constant and the adaptive cases though the experimental drag without the axis drag is equal to 79,9N. The velocity in the wake is indeed little sensitive to the imposed force values. Regarding the vertical profiles, results are more accurate in the lower part where the shaft of the turbine is not present in the experiments, than in the upper part where the shaft is present in the experiments but not in the simulations. In both Figures, the 3D simulation results are in good agreement with the experiments in the far-wake, at distances larger or equal to 4D or 6D. There are discrepancies in the near-wake, that are common with the use of Actuator force models. The eddies generated by the turbine blades are not calculated with those models but may influence the velocity field in the near-wake. Therefore we can not expect to have accurate predictions in the near-wake, but the model is validated for modeling turbine arrays with distances higher than 4D between consecutive turbines.

The turbulent kinetic energy (k) profiles are also plotted at the same positions in the horizontal plane of altitude z=-2 cm, in Figure 16. The differences found between the two models are insufficient to act on the velocity profiles. The turbulent kinetic energy is over-estimated in both simplified models compared to the experiments. It causes the wake to decay fast enough, which was not the case for axial turbine in classical Actuator Disk models for which authors tried to add extra turbulence source terms at the disk position [START_REF] Nguyen | Modelling turbulence with an Actuator Disk representing a tidal turbine[END_REF]. Our vertical axis Actuator force model creates this extra turbulent kinetic energy by itself, which makes the velocity recover fast enough in the wake.

Regarding the horizontal profiles obtained with the 2D simulations, the velocity deficit does not decrease fast enough and there are big discrepancies in the far-wake. In the turbulence theory [START_REF] Pope | Turbulent Flows[END_REF], the velocity deficit decay of an axisymmetric wake as a function of the position x is following the function -2∕3 in 3D, whereas it is following the function -1∕2 in 2D that decreases slower. This is due to geometrical aspects, as the wake limits where the mixing occurs are an area circling the wake in 3D, and only two lines in both sides of the wake in 2D. Therefore 2D models are not expected to give correct results for the wake prediction without adding any extra correcting force or turbulence source term.

However 2D models require much smaller calculation efforts. To quantify the discrepancies that can be introduced by these models, the 2D version of the developed model has

0 0.5 1 1 1 1 1 1 <U>/U -1 -0.5 0 0.5 y/D 2D 3D 4D 6D 8D 12D Exp 3D-force-cons. 3D-adaptive 2D-force-cons. 2D-adaptive 0 2 3 4 6 8 12
x/D Figure 14: Transverse velocity proles for each model and the experiment at several positions x/D downstream of the turbine, in the horizontal plane of altitude z=-2 cm ( ∕ =-0.23)

0 0.5 1 1 1 1 1 1 <U>/U -1 -0.5 0 0.5 1 z/H 2D 3D 4D 6D 8D 12D Exp-RG force-cons. adaptive 0 2 3 4 6 8 12
x/D

Figure 15: Vertical velocity proles for each model and the experiment at several positions x/D downstream of the turbine, in the vertical plane y=0 cm been compared to the 3D one in terms of power production and velocity deficits, in the next sections.

Power production results

The force conservation model results are presented for the cases = 1, = 2 and = 3, as well as the corresponding adaptive model results for * = 1.4, * = 4.25 and * = 9.7. The Table 2 summarizes the experimental, URANS, and the two aforementioned models results with the calculated local velocity, , * , * , power (P) and relative error on power (Er. P). The URANS simulation is taken as reference because its force values are used rather than the experimental ones in the two Actuator force models.

For the case = 2 (close to the optimal advance parameter), both 2D models present high power production discrepancies and are not accurate for calculating this value. In 3D as well as in 2D, results are more accurate for the adaptive model. The local velocity calculated is closer to the URANS calculated one. The power production is hence better calculated, with errors of 3.5% (14.3% in 2D) for the adaptive model and 21.5% (56.4% in 2D) for the force conservation model. The larger error value obtained with the force conservation model is due to an overestimation of the local velocity leading to an overestimation of the power using equation 7. The force conservation approach is the classical approach and implies a conservation of the total forces. But this approach might not be the best to model the flow through the turbine and its wake. Another approach would be to enforce the flow rate through the turbine, which might create a more accurate wake in the simulation. The adaptive model is a compromise between those two approaches. In this model, neither the force values nor the local velocity are conserved, but the * value is imposed. It gives a relation linking the local velocity and the forces imposed, that leads to a compromise between the conservation of those two values.

For the lower advance parameter = 1, corresponding to the case of a high stream velocity or a low turbine rotation speed, the power production is correctly estimated with both 3D models, because the local velocity is always correctly predicted. For the higher advance parameter = 3 that corresponds to a high turbine rotation speed or a low stream velocity, results are less accurate. But this case is extreme with even a negative turbine power production that is small in magnitude. As a result, small discrepancies on the local velocity lead to high relative errors on the power. However the adaptive model produces less than 9 % error on the power production, and this model is suitable to estimate the power production for a wide range of advance parameters between 1 and 3.

Tidal turbine array calculations

The different configuration setups

The aforementioned adaptive model is used in this section to compute several configurations of turbine arrays. The 2D and 3D models are considered. The lateral spacing (distance between two consecutive turbine centers in a row) is first tested in a fence configuration, with 8 turbines side by side. A configuration of two rows of turbine with staggered positions (8 turbines in the first row, and 7 turbines in the second row) is also studied, with different lateral spacing and distances between the two rows (denoted axial spacing). The same turbine reduced-scaled model of height 17.5 cm is kept.

For all cases, a same mesh refined in the central zone around the turbines is used. It is presented in Figure 17. The constant cell height dz=1 cm is used in the whole domain. Cubic cells of size dx=dy=dz=1 cm are used in the central zone. The domain height is 55 cm and the turbines are lo- The distance L=7D is introduced as the distance between the two extreme turbine centers of a 8-turbine fence if no space is left between two adjacent turbines. An inflation of maximum growth rate 1.2 is used in the x and y directions along an upstream distance of 5L, a downstream distance of 20L, and a lateral distance of 6.6L. With this mesh the boundary conditions are far away and are not influencing the calculations anymore. The total mesh size is about 26 million cells. Symmetry conditions are used in the two lateral, the upper and the lower domain boundaries. The inlet velocity of 2.253 m/s in the x-direction is chosen. The inlet turbulence intensity is set to 2.5 %, with a value = 1 -1 that ensures almost no turbulence decay all along the farm. The same outlet conditions as for the single machine simulations are used. A number of iterations of 20 000 is required to obtain a convergence in terms of local velocity and power production. It leads to calculation times of about 4600 core hours (on nodes Intel Sandy Bridge EP E5-2670, 8c/2.6 GHz/20M/8 GT/s with 4GB RAM/core), which is an acceptable time lower than for a single rotor URANS simulation. Moreover the domain length influence and the cell refinement in the array wake (more than 1L downstream of the array) have not been tested and it is more than likely that the cell number could be drastically reduced without significant differences in the results.

The simulations are realized with the values * = 3.6 and Cp*=1.98 in order to stay close to the optimum of power production, as explained in the former sections. All the tested farm cases are summarized in Table 3.

Fence configuration results

The velocity colormap and the streamlines in the horizontal plane of altitude z=-2 cm are presented in Figure 18 A slight global deviation of the wake towards negative yvalues occurs. The velocity deficit is highly overestimated in the far-wake for the 2D model. It is in agreement with the behavior of this model that overestimates the velocity deficit for a single turbine wake (as already shown in Figure 14).

Results in term of power production are analyzed hereafter. The dimensionless farm power (DFP) is defined to compare the total power production to the one produced by the same number N of isolated turbines with the same inlet velocity, as:

= ∑ =0 × 1∕2 3 ∞ (12)
= 0.273 is the maximal power coefficient value obtained from the URANS simulations for the less confined case in Table 1 (that is close to the non confined case). The results for the different lateral spacing are presented in Fig- ure 21. The results for the same simulations using the 2D model are also shown.

In the fence, the closer the turbines are to each other, the higher the extracted power is. The same behavior is observed both in 2D and 3D. The 2D model overestimates the local blockage effect because the stream can not flow above or under the turbines. When the lateral spacing is lower than 3D, a 10 to 24 % power increase is obtained compared to turbines in free stream conditions. This is coherent with results presented by [START_REF] Mcnaughton | Experimental study on interactions between two closely spaced rotors[END_REF], that found out a power increase of 20 % for an experimental fence of two axial tidal turbines. The local blockage effect in our study is higher due to the higher number of turbines and certainly increases again the power production. [START_REF] Vogel | Improving Tidal Turbine Performance Through Multi-Rotor Fence Configurations[END_REF] found out a maximum power increase of 16 % for their 8-turbine fence simulated with a BEM method adapting to the flow conditions. The trend is respected in our simulations. However this extra-power extracted from the fluid creates a stronger velocity deficit in the wake, that might decrease the production of a potential second turbine row that

Staggered configuration results

The staggered configuration wakes are presented in Figure 19 for the lateral spacing of 1.5D and the axial spacing of 15D, and in Figure 20 for the lateral spacing of 4D and the axial spacing of 15D. Both 3D model results (case a) and 2D model results (case b) are presented. In the first configuration, the velocity deficit in the wake of the first line is far higher than in the second case, where the low local blockage allows the flow in-between the turbines. The flow reaching the second row has a decreased velocity and a lower power production is expected. The global farm wake recovers also slower than for the higher lateral spacing case. In Figure 19, the velocity deficit just upstream of the second row is far higher for the 2D model. The power production of the second row calculated with this model is expected to be small compared to the 3D model one. In Figure 20.b, the wakes of the first row turbines extend in-between the second-row turbines for the central turbines. But the first row wakes are partially impacting the 4 turbines of the second row located the most at the outsides. Therefore their power production are decreased.

The power production results of the staggered configurations are presented in Figure 22. The 3D model results are first analyzed. The solution maximizing the power production is to put all turbines on the same line (the staggered case with the axial spacing of 0D and lateral spacing of 4D is then equivalent to a 15-turbine fence with a lateral spacing of 2D). It is also noticed from Figures 21 and22 that in this case, the DFP is 1.18, higher than the one obtained in the fence of 8 turbines with 2D lateral spacing (DFP=1.14). Adding turbines in a row increases the local blockage effect and the DFP. In the staggered cases, the lateral spacing of 1.5D hinders the flow to pass through the first row, and the flow reaching the second row witnesses a big velocity deficit. As a result, the power production of the second row is highly decreased and the dimensionless farm power is impacted, with values lower than 1. Consequences are less grave if the second row is far enough from the first one, with a dimensionless farm power higher than one for the distance 15D. For the lateral spacing of 4D, the flow is reaching the second row without any velocity deficit, and the second row witnesses even a slight local velocity increase. The farm power increase is close to 10 % for all axial spacing of the second row between 5D and 15D. The staggered configuration benefits less from the local blockage effects than the fence configuration with the same number of turbines placed close to each other. For more rows in a staggered disposition, the power harnessed is also expected to decrease if rows are too close, with better results if a bigger lateral spacing is kept between all turbines. Keeping a lateral distance sufficient enough for the stream to flow besides the first row turbines, and an axial spacing of 15D between two consecutive rows, seems enough to have a global farm wake recovery, and to enable one to put extra turbine rows without huge power decrease.

Regarding the 2D model, the same behavior is observed but there are big discrepancies on the calculated DFP values. With the lateral spacing of 1.5D, the second row power production is always highly reduced because the velocity deficit created by the first row is overestimated with the 2D model. The DFP calculated are lower than 0.8 for all those cases. The axial spacing of 15D is not enough to have a velocity deficit recover in 2D, contrary to the 3D model. For the lateral spacing of 4D, the first row wakes are expanding inbetween the second row turbines when the two rows are close enough and the power production is not decreased compared to the 3D model. It starts to decrease when the axial spacing is higher than 10D. An explanation can be that some of the first row wakes are impacting the second row turbines and decreasing their power production, as already presented be-

Conclusions

Different URANS blade-resolved simulations of a vertical axis Darrieus turbine have been performed to feed a steady-state 3D Actuator force model. The calculated turbine forces are time averaged over one turbine revolution to obtain a detailed spatial force distribution, instead of the uniform force distribution of standard Actuator Disk models or their equivalent for vertical axis turbines. This method replaces the classical BEM approach to obtain the force distribution.

The URANS computations have been performed for different turbine lateral confinements, in order to draw several classical power coefficient and force coefficient curves. When the coefficients are plotted as a function of the local velocity instead of the free-stream velocity, the curves become independent of the confinement. Those curves are used to construct an adaptive model independent of the turbine confinement or the local blockage effect. It gives a good estimation of the power production of a single turbine with only 3.5 % relative error at advance parameters close to the maximum efficiency point, and less than 9 % for extreme operating points. The model is also calculating correctly the farwake flow at distances higher than 4D or 6D, but presents discrepancies for the near-wake velocity profiles.

An operating point close to the maximum efficiency point has been found for the simulated turbine. For this point, the turbine power production is calculated with an error always lower than 11.7 %, whatever the local blockage is. It is used in several farm configurations and could be a starting point for future optimization simulations, which could be performed with the model presented here that requires relatively low computational efforts.

Amongst the tested farm configurations, the fence configuration with the lowest inter-turbine spacing gives the highest farm power production. A maximum power increase of 24 % is found for the 8-turbine fence with a lateral spacing of 1.2D. Staggered farm configurations benefit less from local blockage effects even if an optimization of the lateral and axial inter-turbine spacing still has to be done. A compromize has to be found between having closely spaced first row turbines harvesting a lot of power, and still a sufficient power production in the next rows.

The same calculations have been performed using 2D models. For the single turbine simulation, the local velocity is calculated with large discrepancies, that lead to large power production discrepancies. 2D models might be sufficient to deduce general trends concerning the turbine positioning in an array, but they prove to produce large errors to calculate the array power production.

Finally the 3D model seems promising for calculating arrays of vertical axis water turbines. A comparison to measurements in the case of wake interactions between several turbines still has to be done to confirm the model. The whole methodology could also be applied to axial tidal turbines of any shape. The model validity still has to be checked for those turbines, for which the wake decay mechanisms are different.

Figure 1 :

 1 Figure 1: Reduced-scale Darrieus turbine tested and modeled in the simulations

Figure 2 :

 2 Figure 2: View of the domain and the turbine position in the simulations. The turbine center (x=y=z=0) corresponds to the middle of the section

Figure 3 :

 3 Figure 3: Comparison of the experimental and URANS bladeresolved simulation Cp curves

Figure 4 :

 4 Figure 4: Comparison of the experimental and URANS bladeresolved simulation Cx and Cy curves

Figure 5 :

 5 Figure 5: Cylindrical mesh used to compute the time-averaged forces to be used in the Actuator model simulations, with the blade domain mesh on the top and the arm domain mesh on the bottom. The monitoring cells used in this work are presented in red

Figure 6 :Figure 7 :

 67 Figure 6: 2D view of the force projection: the orange cells are all the neighbor cells j of the cylindrical mesh used to get the force applied on the cell i of the simplied model mesh

  . The force values in the z-direction are not presented. 4 ℎ order polynomial fitting curves have been plotted using all the simulated Cx* and Cy* points. The dimensionless local force coefficients are also independent from the confinement in Figures 10.b and 11.b.

Figure 9 :

 9 Figure 9: a) Cp versus curve and b) * versus * for the three connement cases

Figure 10 :

 10 Figure 10: a) Cx versus curve and b)* versus * for the three connement cases

Figure 11 :

 11 Figure 11: a) Cy versus curve and b)* versus * for the three connement cases

Figure 12

 12 Figure 12: a) * versus and b) * versus * for the three connement cases and the three monitored positions of Figure 5

Figure 13 :

 13 Figure 13: Computation loop of the adaptive model

Figure 16 :

 16 Figure 16: Transverse turbulent kinetic energy proles for each model and the experiment at several positions x/D downstream of the turbine, in the horizontal plane of altitude z=-2 cm ( ∕ =-0.23)

Figure 17 :

 17 Figure 17: 2D view of the farm mesh and the turbine positions for the staggered conguration with 4D lateral spacing and 15D axial spacing

Figure 18 :

 18 Figure 18: Axial velocity colormap and streamlines in the horizontal plane of altitude z=-2 cm for the fence conguration with a lateral distance of 1.2D between the dierent turbine axis, with: a) 3D model result ; b) 2D model result

Figure 20 :

 20 Figure 20: Axial velocity colormap and streamlines in the horizontal plane of altitude z=-2 cm for the staggered conguration with an axial distance of 15D and a lateral distance of 4D between the dierent turbine axis, with: a) 3D model result ; b) 2D model result

Figure 21 :

 21 Figure 21: Fence dimensionless power production depending on the lateral spacing used

Figure 22 :

 22 Figure 22: Staggered conguration dimensionless farm production depending on the axial spacing used, for the two lateral spacing tested

Table 1

 1 Interpolated local parameters corresponding to the points of maximum eciency for the 3 connement cases

			Cp		*	*
	= 0, 29	1.825	0.273	1.19	3.53	1.932
	= 0, 44	1.925	0.301	1.23	3.61	1.982
	= 0, 58	2.05	0.341	1.27	3.70	2.036

Table 2

 2 Comparison of the main criteria for the experiments, the URANS simulation and the two Actuator force models for three advance parameters

	Model = 2		*	*	P (W) Er. P
	URANS (ref) 1.094 2	4.25 2.32 48.9
	Experiment	2			44.3	-9.4%
	for.-cons. 3D 1.239 2	3.71 2.04 59.4	21.5%
	adaptive 3D	1.125 2.08 4.25 2.32 50.6	3.5%
	for.-cons. 2D 1.421 2	3.24 1.75 76.5	56.4%
	adaptive 2D	1.163 2.15 4.25 2.32 55.9	14.3%
	Model = 1		*	*	P (W) Er. P
	URANS (ref) 1.644 1	1.4	0.29 19.7
	Experiment	1			21.4	8.6%
	for.-cons. 3D 1.657 1	1.4	0.29 18.8	-4.6%
	adaptive 3D	1.649 1.01 1.4	0.29 19.9	1.0%
	Model = 3		*	*	P (W) Er. P
	URANS (ref) 0.709 3	9.7	-1.92 -10.5
	Experiment	3			-4.4	-58.1%
	for.-cons. 3D 0.964 3	7.2	2.12 29.1	-377%
	adaptive 3D	0.743 3.12 9.7	-2.03 -11.4	8.6%

Table 3

 3 Inter-turbine distances for the fence farm cases and the staggered farm cases

			Fence conguration
			lateral spacing
	1.2D	1.5D	2D	3D	4D
		Staggered conguration
	lateral spacing		axial spacing
	1.5D			5D	10D	15D
	4D		0D	5D	10D	15D

Acknowledgment

This work is part of the ANR 3DMMTA project funded by the french "Agence nationale de la recherche". The simulation results were obtained with the help of the GRICAD calculation mesocenter at Grenoble.


Agnès Moisan

Yamina Lazzoun

David Naudin
email: david.naudin@aphp.fr

Iade Yamina Lazzoun

Importance des fonctions exécutives cognitives dans la prise de décision en anesthésie-réanimation

Keywords: fonction exécutive, métacognition, prise de décision, théorie du double processus

diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Les progrès technologiques, l'évolution des connaissances et les recommandations des sociétés savantes ont permis de réduire considérablement les risques périanesthésiques. Ces risques sont à présent bien connus et identifiés. Ils sont même anticipés de façon proactive grâce à la consultation d'anesthésie. Ainsi, les antécédents du patient, la nature de la chirurgie, la position du patient en peropératoire, la technique d'anesthésie, les stratégies de réveil et, bien entendu, l'environnement et le contexte (urgence ou programmé) vont directement impacter la prise en charge peropératoire.

Un des points essentiels de l'activité d'anesthésie repose sur le fait de devoir maintenir et suppléer les principales fonctions vitales aussi bien cardiocirculatoires, respiratoires que neurologiques. La mise en oeuvre de techniques spécifiques, les postures, l'administration de médicaments d'anesthésie peuvent engendrer des perturbations homéostatiques importantes. Pour le neuroscientifique Antonio Damasio, « la vie exige qu'une collection de fourchettes paramétriques soit maintenue constante à tout prix pour des dizaines de composantes à l'intérieur de la dynamique du corps » [START_REF] Damasio | L'autre moi-même. Les nouvelles cartes du cerveau, de la conscience et des émotions[END_REF]. Tout l'enjeu de l'activité anesthésique tient au maintien de cet équilibre physiologique au regard des suppléances mises en oeuvre. Dans le contexte de prise en charge d'urgence, cet équilibre peut être largement dégradé avant même la prise en charge, par exemple dans un contexte préhospitalier chez un patient polytraumatisé. Il s'agit alors de restaurer et de contrôler au maximum cette homéostasie.

Une des particularités de l'activité de l'infirmier anesthésiste diplômé d'État (Iade), aussi bien au bloc opératoire que dans le contexte de l'urgence, repose sur la nécessité de prises de décisions rapides. Ces décisions sont parfois conservatoires puisque l'essentiel des suppléances mises en place implique des fonctions vitales ne supportant pas un retard de traitement (cardiovasculaire, respiratoire et neurologique). La question est de savoir sur quels mécanismes se basent ces prises de décisions et comment elles sont appliquées. Notre objectif est de décrire, sous l'angle de la psychologie cognitive et des neurosciences, les différents chemins cognitifs pour agir.

T1 Les différents chemins pour agir : la théorie du double processus

Pour agir, nous activons des règles disponibles en mémoire et facilement récupérables, que nous mobilisons dans des situations routinières mais aussi dans des situations inédites. Pour juger, inférer, décider, nous appliquons ces règles dès lors qu'elles sont acceptables au regard du contexte de la situation. Par exemple, lors de l'ouverture du site d'anesthésie, nous appliquons, parce que nous connaissons parfaitement notre environnement, des règles et des procédures très élaborées et automatisées. L'ouverture du site s'effectue sans avoir besoin de réfléchir à chacune des actions mises en oeuvre. Cependant, ces automatismes n'ont pas toujours existé puisqu'ils se sont élaborés progressivement, à force de répétition et d'apprentissage. Ainsi, l'étudiant Iade lors de son cursus va progressivement "routiniser" des procédures qu'il aura apprises. L'autre possibilité réside dans notre capacité à réaliser un effort cognitif et à dépenser une certaine énergie afin d'élaborer des réponses inédites plus adaptées. Par exemple lorsque l'Iade hésite face à une situation et qu'il est obligé de faire appel à un raisonnement hypothético-déductif, comme dans le cas d'une chute brutale de la valeur de dioxyde de carbone (CO2) expiré (EtCO2). L'Iade va émettre diverses hypothèses pour comprendre le problème (ventilatoire, circulatoire ou métabolique), puis agir en conséquence.

Sur ces deux mécanismes repose la théorie du double processus, largement documentée dans la littérature, concernant la prise de décision [START_REF] Stiegler | Cognitive processes in anesthesiology decision making[END_REF][START_REF] Kahneman | Système 1/Système 2. Les deux vitesses de la pensée[END_REF].

T2 Système 1 et système 2, deux niveaux de raisonnement Selon cette théorie, deux niveaux de traitement peuvent être mis en oeuvre pour réaliser une action, qui correspondent au modèle décrit par les sciences cognitives (figure 1). Daniel Kahneman [START_REF] Kahneman | Système 1/Système 2. Les deux vitesses de la pensée[END_REF] a reçu le prix Nobel pour la description de ces deux systèmes :

• la reconnaissance rapide, de faible coût cognitif, qui est basée sur des schémas rapidement disponibles en mémoire ; ce que Kahneman appelle le "système 1" (S1) ;

• l'analyse détaillée passant par des processus logiques et des hypothèses reposant sur des données disponibles et mobilisant de nombreux processus et ressources cognitifs, ce que Kahneman appelle "système 2". Le S1, intuitif, utilise des modes de raisonnement rapides appelés "heuristiques". Il est mobilisé avec « peu ou pas d'effort et aucune sensation de contrôle délibéré », parfois de manière irrépressible [START_REF] Houdé | [END_REF]. Il s'agit de la voie que nous empruntons par habitude, sans aucune réflexion, de manière routinière. Selon Olivier Houdé, le système 1 après entraînement (ou exposition récurrente à des situations) « peut fournir des réactions intuitives compétentes (voire expertes) » [START_REF] Houdé | [END_REF] : par exemple, lorsqu'une infirmière diplômée d'État (IDE) ou Iade reconnaît immédiatement des signes de détresse ventilatoire, imposant une prise en charge spécifique.

Ainsi, que ce soit dans un contexte d'urgence ou dans un contexte programmé, le soignant opère une catégorisation 1 qui repose en grande partie sur la reconnaissance de situations prototypiques plurielles 2 (canevas, patron, pattern en sont des synonymes). Cette reconnaissance de forme ou de prototype aboutit rapidement à des prises de décisions avec la mise en route de connaissances procédurales. Cette première phase, non analytique, est souvent qualifiée d'"intuitive". Elle est d'ailleurs plus spontanée que réellement intuitive puisqu'elle renvoie à une construction antérieure, consciente ou inconsciente, et repose sur un maillage de la pratique, du vécu, de l'expérientiel et de la théorie. Cette construction antérieure, si elle suppose de solides assises théoriques, est nécessairement renforcée par l'expérience clinique qui permet à l'Iade de se créer des répertoires de scripts venant s'enrichir au cours de l'exercice professionnel.

La limite réside dans le fait que ce système 1 comporte parfois des biais qui sont des altérations du raisonnement ou de la perception ; intervenant avant les traitements conscients, ceux-ci ne sont donc pas contrôlables. Or, ces heuristiques sont parfois indispensables pour "routiniser" certaines actions et nous permettre de décider rapidement. Pour Amos Tversky et Daniel Kahneman, « elles peuvent aussi conduire à des erreurs graves et systématiques » [START_REF] Tversky | Prospect theory: an analysis of decision under risk[END_REF]. Ces erreurs, ou biais, résultent donc de raccourcis pris par la pensée lors d'un raisonnement et pouvant conduire l'Iade à s'écarter d'une vision rationnelle et logique.

T2 Biais cognitifs

Pour Olivier Houdé, le système 1 « […] néglige l'ambiguïté et supprime le doute, il est biaisé pour croire et confirmer ; il exagère la cohérence émotionnelle ; il se concentre sur les preuves existantes et ignore les preuves manquantes ; il surestime les probabilités faibles ; […] il réagit plus fort aux pertes qu'aux gains » [START_REF] Houdé | [END_REF]. Houdé définit les biais de raisonnement comme des tendances systématiques à prendre en considération des facteurs non pertinents pour la tâche à résoudre et à ignorer les facteurs pertinents [START_REF] Houdé | [END_REF]. Le tableau 1 résume quelques-uns de ces biais cognitifs [START_REF] Naudin | Éducation thérapeutique du patient et concept de vicariance. L'exemple du diabète de type 1[END_REF].

Comme le démontrent les travaux de Daniel Kahneman, le système 1 gouverne la majeure partie de nos actions. Le système 2 est sollicité dans des conditions spécifiques comme l'incertitude ou lorsque les routines ne sont pas opérationnelles. S'articulent alors les deux grands principes antagonistes permettant la réalisation d'une action : l'activation d'automatisme (système 1) mais porteur également de nos préconceptions, préjugés et biais cognitifs, ou la mise en oeuvre d'une démarche de réflexion logique (système 2). Comment cette articulation est-elle effective dans la mesure où ces deux systèmes semblent en opposition ?

T2 Système 3 et fonctions exécutives

Selon Olivier Houdé [START_REF] Houdé | [END_REF], cette articulation est sous le contrôle d'un "système 3" qui permet d'inhiber les automatismes et de basculer vers un raisonnement logique mobilisant des capacités cognitives. Progressivement, parce qu'il est confronté à l'erreur ou à l'insuccès, ou parce qu'il est entraîné, le cerveau peut utiliser d'autres voies. Les automatismes (système 1) vont alors être inhibés grâce à un système spécifique (le système 3), et laisser la place aux efforts cognitifs et à la réflexion du système 2. Olivier Houdé postule que nous pouvons apprendre à inhiber les automatismes, les préjugés, les biais cognitifs, même si l'enseignement de règles logiques (système 2) ne suffit pas toujours à améliorer les performances. Houdé et al. [START_REF] Houdé | Evidence for an inhibitory-control theory of the reasoning brain[END_REF][START_REF] Houdé | Shifting from the perceptual brain to the logical brain: the neural impact of cognitive inhibition training[END_REF] ont montré qu'en enseignant, en même temps que la règle, des notions sur les biais et les modalités pour les contourner, les sujets obtenaient de meilleurs résultats. Par exemple, il est possible de travailler des biais en formation (initiale ou continue) via la simulation. Pour Olivier Houdé, « ce contrôle exécutif, assuré par le cortex préfrontal, est un opérateur subtil de détour cognitif […] qui lui seul peut permettre -s'il est bien exercé -la flexibilité (ou shifting) d'un mode de raisonnement à un autre : du système 1 au système 2 » [START_REF] Houdé | [END_REF].

Dans certaines situations, nous devons inhiber la réponse qui se présente spontanément à nous pour basculer vers une action plus adaptée. Par exemple, lors d'une induction à séquence rapide, la succinylcholine est le curare de choix ; pourtant dans certaines situations (en cas de patient à estomac plein et de rhabdomyolyse notamment), il faut absolument inhiber ce choix et procéder d'abord à des vérifications (kaliémie) ou choisir un autre curare (rocuronium).

Le système 3 ainsi décrit renvoie à l'inhibition, qui est une fonction exécutive du cortex préfrontal, très développée chez l'homme. Ces fonctions exécutives permettent le contrôle, l'exécution des conduites, le choix des stratégies, la prise de décision.

Plusieurs grandes fonctions ont été identifiées qui sont synthétisées sur la figure 2.

TEG1 L'inhibition doit permettre de résister aux habitudes ou automatismes, aux tentations, aux distractions ou interférences.

TEG1 La flexibilité sert à changer la perspective ou l'approche d'un problème. Elle permet de s'adapter, de passer d'une tâche à une autre selon les exigences de la situation. Elle est en lien avec des stratégies d'action alternative. Un manque de flexibilité mentale aura pour conséquence une forme de rigidité et des persévérations, une difficulté à changer de routine et d'habitude.

TEG1 La mémoire de travail a pour rôle de stocker et de manipuler des informations pendant de courtes périodes et lors de la réalisation d'une tâche donnée. Elle permet de résister aux distractions et aux interférences, de formuler des objectifs, de planifier une action (ou série d'actions), et de réguler celle-ci pour atteindre les objectifs fixés [START_REF] Diamond | Executive functions[END_REF][START_REF] Miyake | The unity and diversity of executive functions and their contributions to complex "Frontal lobe" Tasks: a latent variable analysis[END_REF][START_REF] Friedman | Unity and diversity of executive functions: individual differences as a window on cognitive structure[END_REF][START_REF] Aron | Progress in executive-function research: from tasks to functions to regions to networks[END_REF].

TEG1 La planification incorpore l'élaboration d'un plan d'action et les différentes étapes [START_REF] Koechlin | Prefrontal executive function and adaptive behavior in complex environments[END_REF]. La replanification permet de reprogrammer des objectifs en fonction de différentes circonstances.

TEG1 L'attention est un terme générique qui réfère à de multiples processus psychologiques différents. Ce n'est pas une fonction exécutive mais une fonction cognitive en interaction avec les autres fonctions.

T2 Focus sur l'attention

Michael Posner et al. [START_REF] Posner | Chapter 22 -Developing attention and self-regulation in infancy and childhood[END_REF] ont décrit, sur la base d'études d'imagerie, trois réseaux impliqués dans les différents aspects de l'attention. Ces derniers sont en charge d'assurer des fonctions bien spécifiques comme l'alerte, l'attention sélective et l'attention exécutive.

TEG1 Le système dit d'alerte permet de moduler la vigilance en fonction des périodes de la journée et des circonstances. Il correspond à l'état de vigilance et peut varier également au décours de la journée. L'alerte rend compte de la modulation de l'intensité de l'attention en fonction de la fatigue. Elle permet de détecter les modifications de l'environnement [START_REF] Mazeau | Chapitre 5 -Attention et fonctions exécutives[END_REF]. Selon Stanislas Dehaene [START_REF] Dehaene | Apprendre ! Les talents du cerveau, le défi des machines[END_REF], les systèmes cérébraux d'alerte et de vigilance signalent quand il convient de faire attention. Ainsi, l'alerte est en lien avec les circonstances et, par exemple, un danger, une émotion. Ce système d'alerte est également un puissant stimulus de l'apprentissage selon Dehaene [START_REF] Dehaene | Apprendre ! Les talents du cerveau, le défi des machines[END_REF]. Les signaux d'alerte peuvent être "imprimés" par le cerveau, ce qui pourrait expliquer une mode d'apprentissage rapide (appelé now print) [START_REF] Cahill | Enhanced human memory consolidation with post-learning stress: interaction with the degree of arousal at encoding[END_REF]. Cela démontre la force de l'expérience vécue d'une situation "grave" en termes d'apprentissage, face à un état de choc anaphylactique, par exemple. TEG1 L'attention sélective permet de choisir un objet ou une information. Toujours selon Stanislas Dehaene, elle correspond à ce à quoi nous prêtons attention [START_REF] Dehaene | Apprendre ! Les talents du cerveau, le défi des machines[END_REF], c'est-à-dire l'orientation de l'attention. Par exemple, lorsque l'Iade sélectionne des éléments qu'il considère pertinents dans le dossier d'anesthésie du patient (comme un reflux gastro-oesophagien), au détriment d'autres informations jugées moins importantes (un score d'Apfel à un quart).

Là encore, Stanislas Dehaene [START_REF] Dehaene | Apprendre ! Les talents du cerveau, le défi des machines[END_REF] souligne le rôle de cet aspect de l'attention dans l'apprentissage, tout comme Jean-Philippe Lachaux [START_REF] Lachaux | Le cerveau attentif. Contrôle[END_REF]. Il est impératif que l'apprenant soit en capacité de savoir à quoi il doit faire attention pour apprendre. TEG1 L'attention exécutive, également appelée "système attentionnel superviseur" (SAS), permet la surveillance et la résolution de conflits, la vigilance face aux distractions. Ce réseau est impliqué dans la régulation des émotions, des pensées et des actions. Pour Michael Posner et al., « il est en charge de la surveillance des conflits via la mémoire de travail, la surveillance des émotions et la réaction aux erreurs » [START_REF] Posner | Chapter 22 -Developing attention and self-regulation in infancy and childhood[END_REF].

Pour éviter de possibles saturations, notre organisme dispose d'un mécanisme de sélection des informations. Ce contrôle sélectif est indispensable au maintien des actions orientées vers des objectifs, en dépit de possibles distractions. Plus le plan d'action est complexe et présente des exigences importantes et plus l'effort mental pour maintenir l'attention à son niveau optimal sera coûteux sur le plan cognitif.

Dans le cas de l'anesthésie d'un patient polypathologique, l'Iade sélectionne et hiérarchise les informations les plus pertinentes pour prévenir et agir au mieux en fonction des risques de l'intervention (terrain, chirurgie, anesthésie), ce qui lui demande un effort et un coût cognitif certain. TEG1 L'attention est en lien avec les efforts mentaux pour réaliser une tâche. Ce concept porte le nom de "théorie des ressources" qui considère qu'il existe un seuil à la capacité d'un individu à réaliser un travail mental. Dans certaines circonstances routinisées, l'Iade peut accomplir sans effort plusieurs actions, vérifier le site d'anesthésie et parler avec son étudiant, par exemple. Dès que l'attention doit être soutenue, en raison de la survenue d'un événement indésirable, l'Iade va focaliser son attention sur celui-ci. Pour Brandon J. Schmeichel et Roy F. Baumeister [START_REF] Schmeichel | Effortful attention control[END_REF], le contrôle de l'attention est une forme de maîtrise de soi qui implique l'inhibition des comportements et des émotions. Ainsi, plusieurs études tendent à prouver que les efforts engagés dans le contrôle de l'attention réduiraient considérablement la capacité de maîtrise de l'individu [START_REF] Schmeichel | Effortful attention control[END_REF][START_REF] Schmeichel | Attention control, memory updating, and emotion regulation temporarily reduce the capacity for executive control[END_REF]. Cela peut expliquer, sans les excuser pour autant, certains comportements humains au bloc opératoire, comme un changement d'humeur, de ton, des propos inadaptés dans le contexte du travail. L'effort d'attention est parfois dicté par la situation, mais peut être tout aussi bien régulé volontairement. La question de l'effort est importante puisqu'elle dépend à la fois du niveau de motivation pour la tâche à accomplir, mais aussi du degré de contrôle attentionnel que l'on doit allouer pour la réaliser. Cette allocation d'attention peut être anticipée. TEG1 L'effort cognitif évolue en fonction du niveau de maîtrise de la compétence et de l'acquisition d'automatisme. Dès lors, le niveau de contrôle de l'attention requis pour l'exécution de la tâche devient de moins en moins important. Ce qui est tout l'inverse quand la compétence est en cours d'acquisition. Un novice alloue une grande partie de son attention à la réalisation de la tâche nouvelle qu'il exécute. S'il ne peut allouer cette attention à cette tâche, alors son niveau de performance sera beaucoup moins important [START_REF] Decaro | The benefits and perils of attentional control[END_REF]. Cela explique notamment pourquoi un étudiant infirmier anesthésiste exprime une certaine inertie après avoir accompli un geste qui lui a demandé une forte attention, lors de ses premières intubations orotrachéales, par exemple. Son action lui a demandé un coût cognitif, à laquelle s'ajoute une saturation émotionnelle, et il subit une sorte de black-out provisoire.

TEG1 Une autre possibilité, à laquelle chacun de nous est confronté, est le fait d'oublier ce que nous venons de faire tellement cette tâche est automatisée. Cela peut poser problème, notamment dans le cas de l'administration d'un médicament (un antibiotique au moment de l'induction, par exemple). D'où l'importance de laisser les seringues vides étiquetées dans le plateau d'induction pour se rappeler ce qui a été injecté.

On comprend ici toute l'importance de ces fonctions attentionnelles et exécutives qui permettent le contrôle cognitif. Ces fonctions exécutives sont à rapprocher du concept de métacognition (ou réflexivité) (figure 3).

T1 Les fonctions exécutives : socle de la métacognition

Selon la définition de Flavell, la métacognition est la connaissance que nous avons de nos propres processus cognitifs ainsi que des processus permettant leur régulation [START_REF] Flavell | Metacognitive aspects of problem solving[END_REF]. Or, nous avons montré que ce sont ces mêmes fonctions exécutives qui permettent de réguler l'action. Ce que confirment Thomas O. Nelson et al. : « En mettant l'accent sur la régulation du traitement de l'information nécessaire pour produire des fonctions cognitives d'ordre supérieur, les fonctions exécutives sont étroitement liées à la métacognition, en particulier à l'aspect contrôle des processus métacognitifs. » [START_REF] Nelson | Metamemory: a theoretical framework and new findings[END_REF] La métacognition, via les fonctions exécutives, permet l'autorégulation des comportements, comme le proposent Dieudonné Leclercq et Marianne Poumay [START_REF] Leclercq | La métacognition[END_REF], avant, pendant et après l'action.

Ce contrôle proactif repose sur l'anticipation, la prédiction, la planification et l'élimination préventive des interférences (avant même qu'elles n'aient lieu). Ce que fait l'Iade lorsqu'il "préconditionne" son attention sur les risques liés à l'anesthésie, à la chirurgie et au terrain du patient après avoir pris connaissance de l'intervention et de la consultation d'anesthésie (par exemple, toutes les actions anticipées lors d'une intubation difficile prévue).

Le contrôle interactif est un système de correction retardé qui repose sur la détection et la résolution des interférences quand celles-ci apparaissent [START_REF] Braver | The variable nature of cognitive control: a dual mechanisms framework[END_REF][START_REF] Braver | Explaining the many varieties of working memory variation: dual mechanisms of cognitive control[END_REF]. Tel est le cas lorsque l'Iade adapte son action en corrigeant un risque réel : dans le cas d'une intubation difficile imprévue, par exemple.

Le système rétroactif consiste en l'évaluation des conséquences des actions et de leurs efficacités, l'évaluation de l'efficacité de la curarisation d'un patient, par exemple.

T1 Former des professionnels proactifs et réactifs

La compréhension des trois systèmes tels que nous les avons exposés permet de travailler au sein des programmes de formation des professionnels un ensemble de stratégies adaptatives permettant une meilleure régulation des décisions. Ainsi, l'acquisition d'heuristiques (système 1) utiles et robustes pour le professionnel, car peu coûteuses en ressources cognitives, est essentielle. Il s'agit par exemple de routiniser certaines actions pour les rendre presque invisibles dans le quotidien du soignant.

Parallèlement, le travail de renforcement de la logique, et donc du système 2, doit être soutenu dans les programmes de formation. Il s'agit là de travailler sur les biais possibles inhérents aux heuristiques intervenant dans le système 1. Cette démarche, qui passe par le renforcement des fonctions exécutives en lien avec le système 3, permettrait également un meilleur contrôle des automatismes en favorisant la bascule entre les systèmes 1 et 2. Des outils d'aide à la décision peuvent être modélisés, comme les supports de guidage cognitif (appelés "aides cognitives"), pour sortir des biais inhérents aux heuristiques du système 1. Ces outils viennent en support du choix en cas de problème au bloc opératoire [START_REF] Dupanloup-Meistelman | Aides cognitives : un atout en situation d'urgence[END_REF].

Sur le plan pratique, cette démarche consiste à permettre l'émergence d'un réel travail sur les fonctions exécutives grâce aux activités développant la métacognition, l'inhibition et le contrôle attentionnel chez les professionnels. Cet "apprendre à résister" est aussi en lien avec un travail sur une meilleure connaissance de soi et de l'autre, socle de compétences non techniques essentielles en anesthésie. Des outils comme la simulation et l'analyse de pratique sont, de ce point de vue, essentiels.

Nous savons que l'ensemble de ces fonctions exécutives peut être entraîné. Ces apprentissages peuvent s'automatiser, de sorte que nous puissions porter une attention particulière à des signes spécifiques et saillants, que nous puissions récupérer un souvenir prospectif pour agir, ou une tâche que nous avons planifiée. Il s'agit peut-être d'une revisite du concept d'expert. Dans notre proposition, l'expert n'est pas seulement "intuitif" dans l'action. Il est à la fois capable de mettre en oeuvre des procédures automatisées, mais aussi de s'en dégager dans une sorte de "pas de côté" cognitif. Il est probable que les fonctions exécutives régulant l'action de manière proactive, interactive et rétroactive sont contributives de cette expertise.

Enfin, la compréhension de ces processus cognitifs ouvre des possibilités importantes dans le développement des supports neurotechniques permettant de soutenir l'activité pédagogique. Les nouvelles technologies (informatiques, tablettes, téléphones portables) [START_REF] Mcevoy | A smartphone-based decision support tool improves test performance concerning application of the guidelines for managing regional anesthesia in the patient receiving antithrombotic or thrombolytic therapy[END_REF], si elles sont utilisées dans une démarche éthique, peuvent également l'être dans le travail de fonctions exécutives telles que l'attention. Elles pourraient également être des techniques de support destinées à suppléer ou à étendre les capacités perceptives ou cognitives des professionnels, notamment par l'apport de la réalité augmentée et de l'intelligence artificielle [START_REF] Brocker | L'intelligence artificielle en médecine : intérêts et limites[END_REF].

T1 Conclusion

Essentielles, les fonctions exécutives permettent la mise en oeuvre de stratégies métacognitives, qui sont des mécanismes d'autorégulation du fonctionnement cognitif. Ces stratégies générales sont impliquées dans de nombreuses situations, telles que l'apprentissage (scolaire ou en situation professionnelle), mais aussi dans les expériences de la vie quotidienne. La planification et la supervision, l'inhibition des distractions et des tâches concurrentes, l'activation de la mémoire de travail permettent ainsi de contrôler la décision. Cette proposition ouvre des pistes nouvelles, notamment concernant la neuroéducation, ou éducation cognitive, qui favorise la découverte de ses propres mécanismes de prise de décision et d'apprentissage. La connaissance du modèle des trois systèmes, que nous avons exposé, en constitue la base. Le professionnel en situation de travail présente une combinaison unique de points forts et de points faibles résultant des interrelations entre les facteurs cognitifs, métacognitifs, environnementaux et psychoaffectifs. Ces facteurs influencent la prise de décision individuelle, mais aussi collective. Ce modèle permet également de redéfinir l'expertise qui ne peut être limitée à une activation efficace de routines d'action au bon moment. La véritable expertise repose à la fois sur des routines robustes (système 1) et sur la capacité d'activer le système hypothético-déductif (système 2). Précisément, ce "pas de côté" est sous la dépendance des fonctions exécutives. L'expert serait donc celui qui non seulement possède un réseau de connaissances, des prototypes et des routines efficaces, mais aussi cette capacité à les inhiber pour basculer vers la réflexion et la création de réponses nouvelles et adaptées à la situation. La prise de conscience de cette bascule, au moment où elle se produit, étant le signe d'une régulation experte des processus cognitif et métacognitif.

Notes

1 Il faut entendre par catégorisation un principe de classement des phénomènes perçus (pour nous, les situations en anesthésie-réanimation) selon leurs caractéristiques communes. 2 Étymologiquement prôtotupos : "type, modèle premier" ; le prototype présente l'avantage de ne pas nécessiter beaucoup de comparaisons pour classer une nouvelle donnée.

Accroche possible

L'expert est à la fois capable de mettre en oeuvre des procédures automatisées, mais aussi de s'en dégager dans une sorte de "pas de côté" cognitif Texte suivant à placer dans la marge en au dessus de la déclaration de liens d'intérêt Ce travail a fait l'objet d'une thèse en science de l'éducation de David Naudin, sous la codirection des Prs Gérard Reach et Rémi Gagnayre, au sein du Laboratoire éducations et pratiques en santé (LEPS EA 3412) Université Paris 13.

Déclaration de liens d'intérêts

Les auteurs déclarent ne pas avoir de liens d'intérêts.

Tableau 1. Les principaux biais cognitifs selon Naudin et al. [6] et quelques exemples chez les soignants.

Biais cognitifs Définition et exemples

Biais de confirmation

Il s'agit pour le praticien de la tendance à rechercher des informations qui confirment les attentes. Ici, le cerveau a tendance à négliger les informations contradictoires. Ce biais conduit à l'interprétation des informations dans le sens des attentes.

Biais d'ancrage

Le cerveau prend pour référence la première information dont nous avons eu connaissance à propos d'un sujet (que ce soit une personne, une action, un événement, un produit, une technique, une procédure, une solution, etc.). Dans ce cadre, le soignant néglige alors les nouvelles informations à venir, d'autant plus qu'elles sont en contradiction avec cette première information ou impression. Dans le doute, nous procédons à des estimations à partir d'un point de repère, même si celui-ci est suggéré.

Biais de primauté

Le clinicien ne se fonde que sur les premières informations, sans chercher à réactualiser des données.

Biais de disponibilité

Seules les informations directement disponibles sont utilisées et jugées probables et fiables et ne conduisent pas le soignant à aller chercher d'autres informations plus fines ou plus précises. Le biais de disponibilité correspond donc à un jugement émis en fonction de la facilité avec laquelle un exemple vient à l'esprit. Ce biais est également présent au regard de la facilité avec laquelle on peut s'imaginer le cours d'un événement. Fermeture prématurée Croire avoir identifié/diagnostiqué avec certitude sans même vérifier les alternatives.

Biais de statu quo

Ce biais incite l'individu à préférer, du fait des résistances au changement, un statu quo. Dans ce biais, les individus se montrent critiques et opposants. La peur de la perte (ou aversion à la perte) dans le cerveau humain est toujours dominante par rapport à l'attrait au gain. Le cerveau se montre donc peu enclin à risquer de perdre. Cette aversion aux pertes explique pourquoi le cerveau préfère les solutions immédiates aux solutions différées même si les bénéfices immédiats sont moins importants.

Biais de cadrage

La façon de présenter des informations conditionne le choix. Par exemple, si on indique au patient le taux de succès d'un traitement, les probabilités d'adhésion à ce traitement seront plus fortes que si on lui indique un taux d'échec.

Biais d'attention

Il montre notre capacité à trier l'information en fonction de nos propres centres d'intérêt. Nous ne captons donc les informations (visuelles ou intellectuelles) qu'en fonction de ce que nous recherchons.

Biais d'échantillonnage

Le cerveau est un très mauvais statisticien et le jugement se fonde la plupart du temps sur des échantillons peu représentatifs. Les informations statistiques (comme des données épidémiologiques) sont ignorées au profit d'exemples frappants ou des cas dits extrêmes.

Biais de représentativité

Il s'agit de la tendance à attribuer une caractéristique à une population. Dans le cadre de la douleur, cela peut se traduire par le fait de considérer des réactions exagérées ou des résistances à la douleur pour une population donnée.

Fausses croyances

Nous possédons parfois de fausses croyances sur un sujet. Le maintien de ces croyances est toujours très important et explique que, malgré des preuves tangibles et rationnelles, le cerveau demeure imperméable ou use d'informations invérifiables pour les maintenir.

Biais de dissonance cognitive

Il s'agit de la tendance à interpréter une situation pour éliminer les contradictions. Il est basé sur le concept de la dissonance cognitive, c'est-à-dire le fait de penser deux choses contraires en même temps, et qui amène un inconfort dont on essaye de se débarrasser en éliminant les contradictions. Biais de généralisation d'une règle Dans ce cas précis, la règle est rendue générale alors qu'elle a été produite à partir d'un fait spécifique.

Biais de conformisme

Tendance à penser et agir comme les autres le font.

Biais d'autocomplaisance

Chercher toujours à s'attribuer les réussites, ou encore à faire porter les échecs sur les autres.

Biais d'attribution

Tendance générale des individus à sous-évaluer, dans l'explication du comportement d'une personne, l'effet lié à la situation dans laquelle elle se trouve et à surestimer, au contraire, l'effet associé à son caractère. Les gens font constamment des attributions concernant la cause de leur propre comportement et celui des autres ; cependant, les attributions ne reflètent pas toujours fidèlement la réalité.

Biais de faux consensus

Le fait de croire que les autres acteurs sont majoritairement en accord avec notre système de pensée. Chaque individu suppose que l'autre est rationnel et agira comme lui serait amené à le faire.

Figure1_Naudin. eps ©Figure 1 .

 eps1 Figure1_Naudin.eps

Figure 2 .

 2 Figure2_Naudin.eps © Elsevier Masson SAS Figure 2. Les fonctions exécutives et attention(s) selon Adèle Diamond [9].

Figure3_Naudin. eps ©Figure 3 .

 eps3 Figure3_Naudin.eps © Schéma d'après Naudin et al. [6] Figure 3. Les trois systèmes de la pensée selon Olivier Houdé [4].