# Effect of Impeller Trimming on the Energy Efficiency of the Counter-Rotating Pumping Stage
## 4 Discussion  
After obtaining the pressure and energy characteristics of the counter-rotating stages with different trimmings, the following conclusions were made. They had different pressure characteristics compared to the reference impeller. They could both increase and decrease. Particularly, the pressure head and power consumption increased and reached their maximum for a trimming of about 8 mm. After this, these characteristics decreased.  
After comparing two studies (for \(D_{4}\) = constant and \(h\) = constant), the difference in the pressure and energy characteristics could be seen. For the case of \(D_{4}\) = constant, these characteristics were higher than for the case of \(h\) = constant.  
On the other hand, for the case of \(h\) = constant, the pressure head did not change significantly for trimmings less than 5 mm. However, for higher trimmings, the pressure head decreased significantly.  
The energy characteristics also increased for trimmings up to 7-8 mm; however, after this, they decreased too. Due to the high power, the energy efficiency decreased, reaching its minimum at about 7.8 mm, then slowly increased.  
After comparing the case of the replaced counter-rotating stage without trimming, the pressure head for trimming about 15 mm was equal to the pressure head of the reference impeller. This fact decreased energy efficiency. Under trimming of about 16 mm, the power consumption would already be the same. In this case, the pressure head and energy efficiency changed.  
For the case of the elongated counter-rotating stage, for trimming 15.5 mm, the energy efficiency would be the same as for the impeller without trimming. However, with trimming of about 17 mm, the pressure head and power consumption were the same too. This was the optimal option for trimming, as the power consumed was the same and the pressure was higher compared to the impeller without trimming. In this regard, the main advantage was that the efficiency of the counter-rotating stage increased, and its overall dimensions decreased from 151 mm to 134 mm. This allowed us to reduce the material consumption of the impeller by up to 20%.  
The following facts also highlighted the significance of the obtained results. Firstly, when trimming the impeller by 15 mm, the same characteristics as without trimming at a smaller diameter were reached. This led to a smaller diameter of the pumping equipment and reduced material consumption.  
Secondly, in [26], an increase in the pressure head of the pump stage occurred due to the improvement of the design of the impeller blade system. The primary disadvantage of that method was the presence of a sinking shape of the head characteristic. This led to a breakdown of the pump parameters in off-design operation modes. However, the proposed counter-rotating state avoided this problem.  
In paper [4], an increase in the pressure head of the pump stage was achieved by changing the width of the inter-vane channel at the outlet. However, this changed the flow rate, which was not satisfactory in the designing of pumping units.  
Finally, paper [20] showed that cutting only the impeller's cover disk led to a deterioration in the tangential momentum of the fluid flow at the impeller outlet. Thus, we can conclude that trimming should be performed on both disks simultaneously.