Physical Modelling of the Set of Performance Curves for Radial Centrifugal Pumps to Determine the Flow Rate
Abstract
:1. Introduction
2. Derivation of the Physical Model of the Set of Performance Curves
2.1. Derivation of the Physical Model Equations
2.2. Identification of the Tuning Parameters
Algorithm 1: Identification of the tuning parameters |
FOR WHILE Calculation of Calculation of Calculation of IF END END IF END IF [W] BREAK END END |
2.3. Algorithm for Calculating of the Flow Rate by Using the Physical Model
Algorithm 2: Flow rate determination |
WHILE Calculation of Calculation of LOOP |
2.4. Experimental Setup to Measure the Set of Performance Curves by Varying the Prewhirl Angles
3. Analysis and Validation of the Physical Model
3.1. Parameter Identification and Regression Analysis
3.2. Validation with Varying Speeds and Prewhirl Angles
3.3. Evaluation of the Physical Model in the Flow Rate Calculation Algorithm
4. Conclusions
- The physical model relies on established empirical equations. The model can be adapted to specific pump performance curves via parameter tuning. A modified Levenberg–Marquardt method is used to fit the tuning vectors.
- The accuracy of mapping the performance curve by the physical model is in the range of fourth-degree polynomial accuracy. However, in comparison to the polynomial approximation, the model can be parameterized with significantly fewer measurement points.
- Due to the separate consideration of the mechanical losses of the pumps, the physical model offers superior accuracy in flow rate determination compared to the affinity laws. Deviations of less than 2% can be achieved. It can be concluded that the need for additional measurements can be avoided using a physical model.
- It is possible to calculate the changes in the set of performance curves resulting from prewhirl. This also resulted in deviations of less than 2% when determining the flow rate. The improved accuracy of the physical model in determining the flow rate is due to its ability to reproduce the set of performance curves with minimal deviation despite the large number of influencing variables.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Parameter | PO001 | PO002 | PO003 |
---|---|---|---|
specific speed () | |||
outer diameter inlet () | |||
inner diameter inlet () | |||
diameter outlet () | |||
width impeller outlet () | |||
number of blades () | |||
blade angle outlet () | |||
mechanical power at () | |||
flow rate at BEP () | |||
head at BEP () | |||
pump power at BEP () | |||
nominal speed () | |||
power factor () |
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Reeh, N.; Manthei, G.; Klar, P.J. Physical Modelling of the Set of Performance Curves for Radial Centrifugal Pumps to Determine the Flow Rate. Appl. Syst. Innov. 2023, 6, 111. https://doi.org/10.3390/asi6060111
Reeh N, Manthei G, Klar PJ. Physical Modelling of the Set of Performance Curves for Radial Centrifugal Pumps to Determine the Flow Rate. Applied System Innovation. 2023; 6(6):111. https://doi.org/10.3390/asi6060111
Chicago/Turabian StyleReeh, Nils, Gerd Manthei, and Peter J. Klar. 2023. "Physical Modelling of the Set of Performance Curves for Radial Centrifugal Pumps to Determine the Flow Rate" Applied System Innovation 6, no. 6: 111. https://doi.org/10.3390/asi6060111