## 2 Materials and Methods
### Numerical Modelling  
After the application of the synthesized mechanism to the globe valve, a valve with a new design was exported to the simulation tool, ANSYS Release 16.2, for the position, force, and flow analysis of the valve. Position analysis was performed to study the displacement of the valve disc with respect to the input displacement. Force analysis was done to calculate the actuation force required to operate the valve with the new mechanism. Flow analysis was carried out to see the effect of the new mechanism on the flow efficiency of the valve. A 3D CAD model of the globe valve developed using Autodesk Inventor was imported to ANSYS using the STEP file format. Joints and contacts were defined in the rigid dynamics module of ANSYS. The mechanism and all valve components were assumed to be rigid to study the dynamic behavior of the mechanism. Rigid dynamics analysis can be used to determine the dynamic response of an assembly of rigid bodies linked by joints and springs using implicit, Runge-Kutta functions. In a rigid body solver, no stresses and strain results are produced, and the solver only take forces, displacement, moments, velocities, and acceleration into account. Input displacement is applied at the push link at regular intervals to measure the output displacement at the disc. The simulation model for position analysis is shown in Figure 4.  
Figure 4: Simulation model for position analysis.  
Figure 3: (**a**) Globe valve with designed mechanism. (**b**) Isometric view of mechanism.  
The extending mechanism does produce the magnified motion, as is obvious from its name, but comes at a price. The extending mechanism also reduces the force at the output compared to the force applied at the input. Therefore, the next step was to perform the force analysis on the designed mechanism to calculate the force required to actuate the mechanism. For this purpose, the valve design with applied mechanism was subjected to rigid dynamics analysis. Boundary conditions were applied to represent the real-life conditions including the fluid pressure in the valve acting on the disc, and the input force required to move the disc.  
For the flow analysis, a 3D model of the flow path through the valve was extracted. Meshing for the extracted model was done using ANSYS meshing. The grids used were a combination of structured and unstructured. A structured grid was generated for sweep able bodies which are the upstream and downstream flow across the valve, whereas an unstructured (tetrahedron) grid was used for the valve flow. Investigation for grid independence was performed using a grid with 200,000 elements. All valve and pipe boundaries were denoted as no slip velocity conditions, which implies that the relative to boundary fluid velocity was zero. The inlet and outlet of the flow profile were set as the pressure type, and pressure difference was assigned between the inlet and outlet. Initial conditions were set to standard temperature and pressure conditions (Pressure: 1 atm, Temperature: 25 \({}^{\circ}\)C). Steady state analysis was performed using incompressible flow type. The turbulence model was used to study the flow behavior in the governing equations. In this study, the standard k-epsilon (K-\(\epsilon\)) turbulence model with two equations was used. The process to select the turbulence model was based on a comparison of the various available studies on turbulence models for engineering applications. In the model under consideration here, the flow was turbulent with a high Reynolds number and our point of interest was the outlet flow velocity. The k-epsilon model is the most suitable model for the said case as studies have shown that the model is the most widely used for fully turbulent flows. It is also easy to implement and computationally cheap. In contrast to the k-epsilon model, the k-omega model is more suitable for near wall functions and low Reynolds number models. The flow velocity profile through the valve is shown in Figure 5 with an applied pressure difference of 50 kPa across valve.