Numerical Study of the Energy Flow Characteristics of Multi-Stage Pump as Turbines
Abstract
:1. Introduction
2. Methodology
2.1. Definition of Hydraulic Loss
2.2. Entropy Production Theory
2.3. Pearson Correlation Coefficient and p-Value
3. Experimental Research
3.1. Experimental Setup and Process
3.2. Geometric Parameters
4. Numerical Analysis
4.1. Computational Model and Mesh Generation
4.2. Solution Modeling
4.3. Comparison of Experimental and Numerical Simulation Results
5. Energy Loss Analysis
5.1. Comparison of Energy Loss Calculation Methods
5.2. Distribution of Entropy Production of Each Component with Flow Rate
5.3. Distribution of Entropy Production in Flow Field
5.4. Correlation Analysis
6. Conclusions
- (1)
- Based on entropy production theory, the energy loss calculation method can statistically investigate each component of the multi-stage PAT. Unlike the traditional methods, entropy production theory can predict the locations where losses occurred accurately. The guide vane, impeller, inlet and outlet volute, front and back chambers, and the balance disc are the main sources of energy loss in multi-stage PAT. The total entropy production rate of the impellers and the guide vanes increases dramatically as the flow rate increases. The total entropy production rate of each component under design flow conditions is listed in decreasing order: impeller, guide vane, front and back chamber, a balance disk, and inlet and outlet volute. The energy loss is commonly observed near the leading edge of both the impeller blades and the positive guide vanes. The entropy production of each factor is referenced in decreasing order as turbulent entropy production, wall entropy production, and direct entropy production. The entire energy loss is larger at the first stage because there is no reverse guide vane. The entropy production rate of each impeller is not clearly distinguishable. Therefore, using the entropy production theory can effectively identify the characteristics of the flow field and the location of energy losses. It provides a reference for the targeted optimization of multi-stage PAT.
- (2)
- The flow domain versus entropy production of impellers and guide vanes indicates that the energy loss is closely related to other physical quantities in the flow domain. The distributions of streamlines with the impellers and guide vanes versus VEPR prove that higher relative velocity accompanies larger energy loss. Furthermore, the distribution of streamlines and vortex cores at the impellers reflects that flow domain stability increases from the first stage impeller to the fifth stage impeller. When the distributions of WEPR and skin friction coefficient at the impeller are compared, the WEPR is discovered to be significantly relevant to the wall friction distribution.
- (3)
- There is a correlation between hydraulic loss and entropy production. The Pearson correlation coefficient is used to evaluate the relationship between the hydraulic loss and entropy production of the impellers. According to the findings, viscous entropy production has the strongest correlation with the dissipation effect, followed by turbulent entropy, total entropy, and wall entropy. The dissipation and transportation effects are also strongly associated.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parson Correlation Coefficient Range | Correlation Level |
---|---|
0.8–1.0 | Very strong correlation |
0.6–0.8 | Strong correlation |
0.4–0.6 | Medium correlation |
0.2–0.4 | Weak correlation |
0.0–0.2 | Very weak or no correlation |
p-Value Range | Significance Level |
---|---|
<0.05 | Significant |
<0.01 | Very significant |
Measurement Apparatus | Range | Accuracy (%) |
---|---|---|
Flow meter | 2.121–106 m3/h | ±0.3 |
Pressure transmitter 1 | 0–5 MPa | ±0.2 |
Pressure transmitter 2 | 0–2.5 MPa | ±0.2 |
Torque sensor | 0–70 N m | ±0.3 |
Speed sensor | 0–13,000 rpm | ±0.01 |
Parameter | Value |
---|---|
Nominal rotating speed n, r/min | 2900 |
Nominal flow rate Qd, m3/h | 27.5 |
Specific speed ns | 56.7 |
Blade number Z | 5 |
Impeller inlet diameter D1, mm | 146 |
Impeller outlet diameter D2, mm | 56 |
Impeller inlet width b, mm | 6 |
Inlet volute diameter, mm | 40 |
Outlet volute diameter, mm | 50 |
Blade inlet angle β, deg | 27 |
Parameters | |||
---|---|---|---|
Number of cells (million) | N1/N2/N3 | 14.6/10.8/7.0 | 14.6/10.8/7.0 |
Grid refinement factor | r21/r32 | 1.106/1.156 | 1.106/1.156 |
Computed variables | 203.01/202.46/201.49 | 54.01/53.87/53.59 | |
Apparent order | P | 1.647 | 2.654 |
Extrapolated value | 206.65 | 54.94 | |
Approximate relative error | 0.27% | 0.26% | |
Extrapolated relative error | 1.76% | 1.69% | |
Grid convergence index | 1.87% | 1.06% |
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Ye, S.; Li, X.; Zhu, Z.; Li, L.; Lin, T. Numerical Study of the Energy Flow Characteristics of Multi-Stage Pump as Turbines. Processes 2022, 10, 2488. https://doi.org/10.3390/pr10122488
Ye S, Li X, Zhu Z, Li L, Lin T. Numerical Study of the Energy Flow Characteristics of Multi-Stage Pump as Turbines. Processes. 2022; 10(12):2488. https://doi.org/10.3390/pr10122488
Chicago/Turabian StyleYe, Sikun, Xiaojun Li, Zuchao Zhu, Linmin Li, and Tong Lin. 2022. "Numerical Study of the Energy Flow Characteristics of Multi-Stage Pump as Turbines" Processes 10, no. 12: 2488. https://doi.org/10.3390/pr10122488