The affinity laws determine a pump's characteristics parameters of impeller diameter, pressure (p), rotational speed (N), flow rate (m), and power (Hp). The laws predict the relationship between these parameters, showing the impact of a change in the impeller diameter on the flow rate, pressure, and power of the pump (Shankar et al., 2017). For instance, if the pump's performance curve is known at one point, the affinity laws can be used to determine the pump's performance with a different impeller diameter or at a different rotational speed. The below formulas highlight the Affinity laws:
The laws are only applicable if the pump's efficiency remains constant at all times. This paper assumes that the pump runs at a 100% efficiency level, and no changes occur to the impeller diameter. Moreover, the analysis will utilize data from the Safety Injection pump test and the Generic Pressurized Water Reactor Simulator from Module 3. The information will be used to test three scenarios on the effect of the pump's characteristic parameters.
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In the first scenario, the pump's discharge pressure is assumed to decrease by 50% while the speed remains the same. The graph below demonstrates the impact of reducing pressure on the pump's horsepower.
Since the pump's speed is constant, the first Affinity law demonstrates that the flow rate will remain constant. Horsepower is the only characteristic parameter that is affected in this first scenario. A limitation of using the Generic Pressurized Water Reactor Simulator is that it does not produce the horsepower discharge values. As such, the below formula is utilized to calculate the horsepower at each level of the increment:
Decreasing the system's pressure means that the pump consumes less energy to attain the same rotational speed and flow rate. In a real-life scenario, a reactor inside an SI pump, which mandated a long-term DHR, would not achieve adequate cooling due to the decreasing pressure values (Shankar et al., 2017). Nevertheless, no substantial damage would be done to the entire system.
The second scenario utilizes a variable speed pump. Changes in horsepower and flow rate were calculated following a 10% total speed increase in increments of 2%. In this scenario, pressure remains constant, and the calculations adopt the same horsepower value used within the first scenario. The two graphs below illustrate how flow rate and horsepower change with the changing speed, respectively.
The results depict a linear increase between the rotational speed and flow rate using the first Affinity law to calculate the flow rate(Li, 2020). Simultaneously, the pump's horsepower and rotational speed increase exponentially. The resultant changes from this scenario produce two significant effects. One, the increase in flow rate would also increase the flow accelerated corrosion (Esayah, 2018). In essence, the more the fluid passing through the pipe, the more the entire system suffers from erosion. Two, an incremental power increase in the pump's electric motor may ultimately damage the component, further increasing the chances of a fire outburst.
In the third scenario, the assumption is that the discharge value is restricting the discharge flow at a 25% decrease rate. The graph below shows how this effect has on the horsepower on a 5% increment level.
Arriving at the above results followed a series of steps. First, changes in speed were calculated using the first Affinity law and the decreasing flow rates. The new speed value was then substituted into the third Affinity law to obtain the new horsepower. The above graph depicts how power reduces as the flow rate decreases. The changes in the characteristic parameters of the pump have little impact on the pump. If the situation were to occur in a damaged core needing long-term DHR, adequate cooling would not be achieved in the long run.
In conclusion, the Affinity laws effectively calculate the responsiveness of a pump when its parameters are changed. The estimates from the calculations can provide a clear picture of the pump's health and its components, aiding in the preservation of these components. However, the pump's efficiency is not considered first due to the assumption the Affinity model takes. As such, the above scenarios are based on a less effective model. Regardless, the Affinity laws are useful in providing information on pumps and other hydraulics. Simultaneously, Excel and other similar programs can manipulate the data to generate graphs, such as those listed above, to demonstrate the effects of speed, flow rate, pressure, and horsepower within the entire system.
References
Esayah, A. G. (2018). Flow accelerated corrosion of the heat exchanger carbon steel tubing in air cooled condensers (Doctoral dissertation, Colorado School of Mines. Arthur Lakes Library). Retrieved from https://mountainscholar.org/bitstream/handle/11124/172269/Esayah_mines_0052E_11475.pdf?sequence=1
Li, W. G. (2020). Affinity laws for impellers trimmed in two partial emission pumps with very low specific speed. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science , 0954406220936313. DOI: 10.1177/0954406220936313
Shankar, V. A., Umashankar, S., Paramasivam, S., & Norbert, H. (2017). Real time simulation of variable speed parallel pumping system. Energy Procedia , 142 , 2102-2108. https://doi.org/10.1016/j.egypro.2017.12.612
