## 3 Results and Discussion
### Optimization Results  
In the response surface method of the response surface optimization module, the values of the output parameters can be seen according to the values of the input parameters. The values of the parameters for the efficiency of the output parameters are shown in Figure 15.  
As seen from Figure 15, the efficiency value is at its highest at the point where the X value is one. It is seen that the efficiency is at its lowest value when the x value is three. It is seen that the C value has the lowest value of efficiency at an angle of 5 degrees. It can be seen from the graph that the highest efficiency values are between 1-2 and 8-9. For the L parameter, it is seen that the efficiency is highest at 15 mm. It is understood from the graph that as the L value increases, the efficiency decreases. For the theta angle, it is seen that the efficiency is at its highest value at an angle of 85 degrees, and the efficiency is at its lowest at an angle of 60 degrees, which is the initial value. The graphs of the values of these parameters in the same module, corresponding to the total pressure ratio, are also shown in Figure 16.  
Figure 14: Experimental results and analysis results. Figure 15: _Cont._In Figure 16, the X value takes values between the lower and upper limits we determined and the total pressure ratios corresponding to these values can be seen from the graph. Even though it does not increase linearly, it is seen that the total pressure ratio  
Figure 15: Efficiency result curves of X, C, L, and \(\theta\) parameters, respectively. decreases as the distance between the inducer and exducer increases. If we examine the clocking C value, it is expected that there will be a curve that constantly repeats itself at angles, since it is the horizontal distance between the inducer and the exducer. It is seen that the pressure compression ratio decreases as the inducer height value increases, starting from 15 mm. It is seen that it has its lowest value at the upper value of 25 mm. It is seen that the total pressure ratio first increases and then decreases as the theta degree increases. It can be seen from the graph that it has the highest value at a cutting angle of 85 degrees. In the optimization module, the last module of the response surface method, optimization processes were started by targeting the values with the highest pressure compression ratio and efficiency. The multi-objective genetic algorithm (MOGA) method was used as the optimization method. The MOGA method is a variant of NSGA-II based on controlled elitism. This method supports multiple objectives and constraints and aims to find the global optimum. In this study, we aim to find the maximum values of the output parameters when there are no restrictions. With this method, 4000 design points were created initially, and continued with 800 design points in each iteration. Three optimum designs were obtained in a maximum of 20 iterations. The values of the optimum design points are shown in Table 6. The design points with the parameter values in Table 6 are the optimum points that give the highest total pressure ratio and efficiency. Figure 16: _Cont._  
Since the values and results were very close, design number 1 was selected from these design points, geometry was created accordingly, and analyses were made at different flow rates. The geometry of design number 1 is shown in Figure 17.  
Analyses at different flow rates were carried out using the analysis method, whose accuracy we have previously confirmed through the experimental results. The flow rates used in the analyses and the values obtained from the analysis results are shown in Table 7.