Analysis of Applicability of CFD Numerical Studies Applied to Problem When Pump Working as Turbine
Abstract
:1. Introduction
2. Materials and Methods
- The product of filtered velocities is
- The subgrid stress tensor is
- The filtered stress tensor rate is
- The filtered viscous stress tensor is
- 1.
- Collection of information. Recent studies related to PATs research were found. A deep search was developed to do a great database, which helps to analyze the different published CFD analyses applied to pump working as turbine.
- 2.
- Selection of relevant information for this study. The papers of interest should be related to numerical simulation CFD applied to PATs: experimental studies, theoretical, mathematical models, new proposals for obtaining the characteristic curves of the pumps, studies of optimization of component elements, state of the art, studies of PATs for machine speeds fixed or variable, among others.
- 3.
- Information Analysis. The information consulted and collected from the studies analyzed is described below:
- Step 3A. From the CFD numerical simulation studies, the information obtained was: pump type-axial, radial or mixed; fixed or variable speed; rotational speed value; specific speed value; CFD package; boundary conditions at the entrance or exit of the machine; the turbulence closure model; mesh-type; and simulation results.
- Step 3B. The main results of the experiments were obtained from the experimental research.
- Step 3C. From the other studies, the results and conclusions obtained from different investigations were used to discover more about new applications and optimizations.
- Step 3D. Calculation of the relative error. In cases where both numerical simulation and experimental test results were obtained for the same conditions, the maximum relative error between the experiment and the numerical simulation was calculated according to the following equation:
It should be noted that this calculation of the parameters with the maximum dispersion were considered to obtain the significant values. For some cases, the papers directly reported these values. - 4.
- Concurrency and diagonalization. Based on the information collected and the results of the calculations, a concurrency and diagonalization analysis was performed to identify the number of investigations according to the type of PATs and to identify the main CFD modelling parameters used in successful experiences.
3. Results and Discussion
3.1. CFD Model Applied in PATs Simulations
3.2. Analysis of CFD Simulation When PAT Operated under Fixed Rotational Speed
3.3. PATs under Variable Rotational Speed
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
H | head |
P | power |
p | pressure |
Q | flow rate |
Ns | specific speed |
n | rotational speed |
D | external machine diameter |
Greek symbols | |
ψ | |
η | efficiency |
ω | specific kinetic energy dissipation rate |
ε | turbulent kinetic energy dissipation rate |
Δ | change |
Subscripts | |
BEP | Best Efficient Point |
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Type of Machine | Published Research | Consulted References |
---|---|---|
Axial | 7 | [5,11,26,27,28,29,30] |
Mixed | 5 | [8,31,32,33,34] |
Radial | 44 | [10,15,19,20,28,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74] |
ID | Reference | Boundary Conditions | Study-Variable | Relative Max Error (%) | |
---|---|---|---|---|---|
Inlet | Outlet | ||||
1 | [10] | stagnation pressure | static pressure | - | - |
2 | [15] | static pressure | mass flow | H | 10 |
3 | [20] | constant total pressure | constant static pressure | η | 2.18 |
4 | [19] | - | - | H | 4 |
5 | [20] | constant total pressure | constant static pressure | η | 2.18 |
6 | [35] | mass flow | static frame total pressure | H | 5.56 |
7 | [36] | mass flow | static pressure | η | 5.19 |
8 | [41] | volume flow rate | average static pressure | η | 2.6 |
9 | [42] | flow rate | static pressure | Q | 10 |
10 | [44] | - | - | H | 2.2 |
11 | [45] | uniform velocity distribution | constant static pressure | H | 9.0 |
12 | [46] | mass flow | static pressure | H, η | - |
13 | [47] | static pressure | mass flow | η | 6.8 |
14 | [49] | uniform velocity | constant static pressure | H | 9 |
15 | [51] | - | - | Q | 0.82 |
16 | [52] | velocity inlet | static pressure | η | 8.70 |
17 | [53] | total pressure | mass flow | H | 3.70 |
18 | [54] | static pressure | mass flow | η | 7.69 |
19 | [55] | velocity inlet | pressure outlet | η | 3.99 |
20 | [56] | velocity inlet | pressure outlet | - | - |
21 | [69] | total pressure | environmental pressure | - | - |
22 | [58] | mass flow | - | - | - |
23 | [50] | mass flow | - | H | 4.81 |
24 | [59] | pressure | mass flow | η | 4.64 |
25 | [60] | constant total pressure | variable static | ψ | 4.00 |
26 | [61] | pressure inlet | pressure outlet | p | 28.60 |
27 | [62] | static pressure | mass flow | P | 12.31 |
28 | [63] | static pressure | mass flow | - | - |
29 | [64] | mass flow | static pressure | P | 14.71 |
30 | [65] | static pressure | mass flow | η | 4.17 |
31 | [66] | - | - | H | 10.00 |
32 | [67] | velocity | static pressure | H | 10.70 |
33 | [68] | volumetric flow rate | average static pressure | ψ | 5.00 |
34 | [70] | enviromental pressure 1bar | mass flow | - | - |
35 | [71] | static pressure | mass flow | - | - |
36 | [72] | mass flow | static pressure | ψ | - |
37 | [73] | total pressure | flow rate | η,ψ (design point) | 4.9 |
38 | [43] | mass flow, velocity direction, turbulence kinetic energy k and turbulent dissipation ε | static pressure | ψ | 22.9 |
38 | [76] | static pressure | mass flow | PSHAFT | 3.51 |
n | Package | Numerical Simulation | Boundary Condition | Error Calculation | Reference | |||
---|---|---|---|---|---|---|---|---|
rpm | Closure M | Grid | Inlet | Outlet | Variable-Study | Relativemax Error (%) | ||
300–2200 | PumpLinx | k-ε | hexagonal not deformed cells | flow | pressure | p | 3.10 | [74] |
520–1500 | FloEFD | k-ε | structured hexaedral | flow rate | pressure | ΔH, η | (1,7–44,48), (0–52,4) | [39] |
810–1500 | FloEFD | k-ε with wall functions | structured hexahedral | flow rate | static pressure | H | 9 | [38] |
1500–2910 | ANSYS-FLUENT | k-ε | structured hexahedral/unstructured tetrahedral | Unif. velocity | static pressure | η | 34.62 | [37] |
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Plua, F.; Hidalgo, V.; López-Jiménez, P.A.; Pérez-Sánchez, M. Analysis of Applicability of CFD Numerical Studies Applied to Problem When Pump Working as Turbine. Water 2021, 13, 2134. https://doi.org/10.3390/w13152134
Plua F, Hidalgo V, López-Jiménez PA, Pérez-Sánchez M. Analysis of Applicability of CFD Numerical Studies Applied to Problem When Pump Working as Turbine. Water. 2021; 13(15):2134. https://doi.org/10.3390/w13152134
Chicago/Turabian StylePlua, Frank, Victor Hidalgo, P. Amparo López-Jiménez, and Modesto Pérez-Sánchez. 2021. "Analysis of Applicability of CFD Numerical Studies Applied to Problem When Pump Working as Turbine" Water 13, no. 15: 2134. https://doi.org/10.3390/w13152134
APA StylePlua, F., Hidalgo, V., López-Jiménez, P. A., & Pérez-Sánchez, M. (2021). Analysis of Applicability of CFD Numerical Studies Applied to Problem When Pump Working as Turbine. Water, 13(15), 2134. https://doi.org/10.3390/w13152134