# Wall-Climbing Mobile Robot for Inspecting DEMO Vacuum Vessel
## 4 Aerodynamic Study and Finite Element Analysis  
### Aerodynamic Study  
To assess the payload capability of the WMR, the dynamic analysis of the impeller must be conducted to optimize the WMR's performance. The impeller is the most important component and will determine the capacity of the WMR. It is made of 1 mm-thin aluminium to reduce the weight of the robot. The airflow dynamic model is built up and shown in Figure 7. The simulation was carried out in computational fluid dynamic (CFD) software [30,31]. The analysis optimised the design factors, such as the radius of the impeller, rotational speed, power consumption, and adhesion force. The impeller was covered by a round-shaped cover manufactured from carbon fibre. The simulation results showed no significant dependency on the shape of the cover or the gap between the cover and the impeller.  
From the airflow simulation, the flow pattern of the streamlines around the impeller and vector plot in the X-Z plane is shown in Figure 8. The simulation results revealed that the flow pattern is similar to the theory, and the gas is accelerated by the centrifugal force and ejected from the impeller's nozzles. The gas is sucked into the impeller's centre area from the bottom, forming the recirculation pattern depicted in Figure 8. The low-pressure region in the central cavity of the impeller and the low static pressure of the recirculation flow under the impeller are major sources of the adhesion force.  
Figure 5: The timing diagram for WMR trajectory tracking; (**a–d**) show the position of the WMR at 0, 33, 66, and 100% of the tracking path, respectively.  
Figure 6: Angle displacement curve (**a**) and angle velocity curve (**b**) of the trajectory-tracking process.  
Two sets of simulations were conducted to assess the effect of rotational speed, impeller radius, and impeller height on the adhesion force produced by the impeller. The adhesion force was defined as a gas-dynamic force acting on the rotating impeller, pushing it to the surface. In the first simulation, the impeller radius was \(R\), and the impeller height was \(h=\)10 mm. The adhesion force for different speeds at different impeller radiuses is shown in Figure 9a. In the second simulation, the motor speed was \(n\), and the impeller radius was \(R=\)100 mm. The adhesion force for impeller height at different speeds is shown in Figure 9b. From the results of the previous two sets of simulation results shown in Figure 9, we concluded that the height of the impeller has less impact on the adhesion force. Therefore, small perturbations such as welding seams, bolt heads, and cavities between walls will not cause many changes in the generated adhesion force. The rotational speed impacts the adhesion force, but the trend is relatively steady compared with the impact of impeller radius on the adhesion force.  
The required motor power is shown in Figure 10a when only gas-dynamic forces were considered, and no friction losses or other forces and losses were considered. The power is related to the rotational speed and the impeller radius; therefore, it has a similar trend as the adhesion force. The efficiency is measured as the ratio of the generated adhesion force to the required power and is shown in Figure 10b. From the simulation results, the impeller with a radius of \(R=\)90 mm needs lower power to generate the same adhesion force, with a relatively smooth variation trend. The structure might have caused the impeller's increased  
Figure 8: The flow pattern of the impeller.  
Figure 7: Impeller and CFD model.  
efficiency with \(R=\)50 mm; in other words, the radius of the impeller was too small for this application.