 Mi je Anna Brunetti, phd. student at the university of Trieste. My topic of my talk is the larger dissimulation of marine turbine in a stable stratified flow condition. In the last years, the development of an efficient renewable energy technology has become a priority for worldwide politics. And in this scenario marine turbines is a promising technology and it's at an early stage of development. Marine turbines produces electricity mostly from the exploitation of tidal currents. And in fact, many tidal sites has been identified and where it seems possible that in the next decade thousands of turbines will be installed in situ with a total installed capacity of up to or free gigawatt. The working principle of a marine turbine is similar to the wind devices, but little research has been done in the marine environment. So for these reasons we decided to study the interaction between the turbine and the flow field, evaluating efficiency and power production. And moreover our aim is to study out the certification influence the flow in presence of the marine turbine and vice versa how the effect of the turbine mixing influence the stratification. In order to model the presence of the turbine we decided to choose the actuator disk method and this choice was made with intention to address our study not only toward the pure research but also to make this instrument of numerical simulation used for the applied field. And we could have chosen to use other methods like the result geometry or the actuator line method but compared to the actuator disk method they are much more computationally expensive. So they exclude the possibility to simulate a cluster of turbines. The turbine model works in this way. The presence of the turbine give rise to normal and tangential forces that act in opposition to the flow. So these forces are calculated through the actuator disk model and then applied to the flow field as a body force. As you can see these are the LES equations, the Navier-Stokes equation plus the body force. There are two versions of the actuator disk model. The actuator disk model without rotation and with rotation. The simpler one is the actuator disk model without rotation and is based on the one dimensional momentum theory for which the rotor is represented by a uniform actuator disk which creates a jump of pressure into the stream that flows through it. And in this case the normal forces are applied uniformly over the disk. Instead in the case of the actuator disk model with rotation the rotation of the wake is taken to account actually the flow behind the wake the rotor rotates in the opposite direction to the rotor rotation. This method is based on the blade element momentum theory that it merges the one dimensional momentum theory with the blade element theory. The blade element theory consists in analysis of forces at every blade section as a function of blade section characteristics. The blade element momentum equations are these and the normal and tangential forces are calculated through these formulas. As you can see they are function of phi that is the angle of relative wind but also the relative velocity and the lift coefficient and the drag coefficient are function of phi. And so in order to find phi it's necessary to perform an iterative method. But it arose the known issue of blade element momentum equations convergence. The methods widely used for the converters of axial and tangential induction factors suffer from a lack of robustness. So we solved the problem of convergence using the approach suggested by Ning et al that consists in reducing the two variable two equation fixed point problem into one variable root finding problem that is allow us to use a robust method of convergence and that is in this case the brand method. But for to have a guaranteed convergence that's not enough because it's necessary fundamental to bracket a region where to find a zero of the residual function that does not contain any singularities in the interior. In fact the turbine have different state of working so between one region for example the momentum and the empirical and the propeller break there is a singularity. The blade element momentum equations describe the momentum region. So after we solved the problem of convergence we validate the model in the experimental data of Baji et al the test was carried out in a town in tank with a free surface on the top and the turbine submerged into the fluid. We performed largely simulation coupled with the after this model with rotation and also without rotation and then we compared the results with the experimental data. This is the comparison with the power coefficient that is the ratio between the rotor power and the power in the wind. Actually the power coefficient is a very important coefficient because it's an esteem of the power that can be extracted. The tip speed ratio in this plot the power coefficient is as a function of tip speed ratio that in this case it's as a function of just the angular velocity. So there is a good agreement between the results and the measurement data the experimental data except from high numbers of tip speed ratio. We did the same for the truss coefficient that is the ratio between the truss force and the dynamic force and this is important for the loads of the rotor and again this is against the tip speed ratio and these are the plots of the wake downstream the rotor. This is the case of the after this model without rotation and in particular this is the time average of the streamwise velocity in the vertical plane and this is for the after this model with rotation. The difference is clear that for the after this model with rotation the wake is symmetric and it's similar to the experimental measurements. After that since the turbines are submerged into the marine environment to represent as close as possible the real physical flow it's important to take into account the phenomena that characterizes the marine environment like it could be the marine certification. So our purpose is to determine whether marine stratification influence the energy production and efficiency and the wake behind the rotor that's important especially for a cluster of turbines for the arrangement of a cluster of turbines and also we want to evaluate the effect of turbine mixing on stratification. The stable stratified condition is the thermocline that is an abrupt separation between the superficial cold warm layer and less denser between the colder and dense layer deeper. In many tidal sites it could be observed a sharp thermocline that is superficial near the surface with a jump of density. So we perform largely simulation and with a jump of density to recreating the thermocline for two different conditions a weak stratification and a strong stratification. The characteristics of the simulation and the domain of simulation were calculating according to the Richardson bulk to the real Richardson bulk for the weak condition and this is the dimensionalized temperature profile that we imposed and these are the results, this is the contour plot of temperature for a vertical plane and in the middle of the channel it is possible to see the internal that forms and the plot of density profile and the Vizala frequency that has its maximum value obviously in the middle of the channel than the ms of temperature fluctuation and in the following plots streamwise velocity profile that is fluctuation and velocity shear stress you can see that turbulence is suppressed by the presence of the internal ways that exchange the available potential energy with kinetic energy. A strong stratification and the Richardson bulk number is almost one and in this case we imposed a jump of salinity this is the salinity profile dimensionalized as the other plots the density profile and the Brun-Vizala frequency that has a higher value compared to the weak condition and the rms of salinity fluctuation and of velocity fluctuation that is this shape because of the internal waves so the next step is to introduce the turbine and to see what happened to the stratification and also to the wake and the efficiency of a turbine. OK, Sina. Thank you. Thank you. Thank you.