Pressure Drop and Energy Recovery with a New Centrifugal Micro-Turbine: Fundamentals and Application in a Real WDN
Abstract
:1. Introduction
2. Experimental Tests
3. Numerical Model
3.1. Turbine Geometry and Boundary Conditions
3.2. Numerical Results
4. Application to the Water Distribution Network (WDN) of Funchal City—Madeira, Portugal
4.1. The Optimization Procedure
4.1.1. The Variables
4.1.2. Non-Linear Constraints
4.1.3. Linear Constraints
4.1.4. The Objective Function
4.1.5. The Mathematical Model
4.2. Optimization Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
List of Symbols
Runner thickness | |
Maximum runner thickness | |
Minimum runner thickness | |
β | Leakage exponent |
γ | Fluid specific weight |
Wall lift-off | |
Binary variable of flow direction through the k-th link | |
Discount rate | |
Turbine efficiency | |
μ | Flow viscosity |
ρ | Flow density |
τ | Non-dimensional torque |
φ | Non-dimensional discharge |
ψ | Non-dimensional head drop |
Roughness coefficient of the k-th link | |
Total cost of turbine | |
Total cost of valve | |
Water unit cost | |
Turbine diameter | |
Diameter of the k-th pipe | |
Maximum turbine diameter | |
Minimum turbine diameter | |
Energy income | |
External force | |
Leakage coefficient at the i-th node | |
Gravity acceleration | |
Head drop | |
Head at i-th node | |
Maximum head drop within the devices | |
Head drop within turbine | |
Positive component of head drop within turbine | |
Negative component of head drop within turbine | |
Head drop within valve | |
Positive component of head drop within valve | |
Negative component of head drop within valve | |
Binary variable for turbine location | |
Binary variable for valve location | |
, | Indices for nodes |
Set of nodes linked to the i-th node | |
Index for links | |
Length of pipe connecting nodes i and j | |
Length of the k-th link | |
Number of links | |
Rotational speed | |
Net present value | |
Number of nodes | |
Experimental coefficient | |
Hydraulic power | |
Produced power | |
Pressure | |
Maximum allowable pressure | |
Minimum allowable pressure | |
Experimental discharge | |
Total leaked discharge | |
Discharge through the turbine | |
Discharge through the k-th link | |
Maximum discharge through the k-th link | |
Demand of the i-th node | |
Leaked discharge at the i-th node | |
Positive component of discharge through k-th link | |
Negative component of discharge through k-th link | |
Experimental coefficient | |
Resistance term at the k-th link | |
Torque | |
Flow velocity | |
Water saving | |
Number of years | |
Index for years | |
Node elevation |
Appendix A
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D (mm) | 150 | |||||
H (m) | 32.8 | |||||
Q (L/s) | 19.49 | 27.98 | 34.1 | 39.19 | 43.72 | 46.26 |
Q (%) | 42 | 60 | 74 | 85 | 95 | 100 |
η (%) | 33 | 40 | 52 | 55 | 62 | 65 |
N (rpm) | 767 | 1064 | 1489 | 1580 | 1792 | 1843 |
P (W) | 2040 | 3590 | 5680 | 6930 | 8710 | 9690 |
V (m/s) | 0.97 | 1.39 | 1.70 | 1.95 | 2.17 | 2.30 |
T (N m) | 25.40 | 32.22 | 36.43 | 41.88 | 46.41 | 50.21 |
Ph (W) | 6265 | 8994 | 10,961 | 12,597 | 14,053 | 14,870 |
NPV (€) | N° Turbines (-) | N° Valves (-) | Av. Power (kW) | Water Saving (m3/day) | Invest. Cost (€) | |
---|---|---|---|---|---|---|
(I) 1 | 7,169,083 | 5 | 4 | 68 | 8507 | 482,298 |
(II) 1 | 11,942,920 | 6 | 1 | 65 | 13,673 | 55,786 |
D (mm) | HT (m) | QT (L/s) | N (rpm) | ηT (%) | |
---|---|---|---|---|---|
Link 89 | 187 | 52 | 11 | 2748 | 75 |
Link 795 | 540 | 50 | 91 | 933 | 81 |
Link 1358 | 500 | 5 | 25 | 319 | 75 |
Link 1375 | 940 | 13.5 | 144 | 278 | 80 |
Link 2485 | 165 | 161 | 15 | 5480 | 77 |
D (mm) | HT (m) | QT (L/s) | N (rpm) | ηT (%) | |
---|---|---|---|---|---|
Link 8 | 685 | 5.95 | 51 | 254 | 77 |
Link 14 | 70 | 50 | 1.6 | 7200 | 68 |
Link 108 | 170 | 119 | 14 | 4573 | 76 |
Link 1241 | 535 | 41.5 | 82 | 858 | 80 |
Link 1242 | 747 | 11.5 | 84 | 323 | 79 |
Link 2485 | 220 | 122.5 | 24 | 3585 | 78 |
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Morani, M.C.; Simão, M.; Gazur, I.; Santos, R.S.; Carravetta, A.; Fecarotta, O.; Ramos, H.M. Pressure Drop and Energy Recovery with a New Centrifugal Micro-Turbine: Fundamentals and Application in a Real WDN. Energies 2022, 15, 1528. https://doi.org/10.3390/en15041528
Morani MC, Simão M, Gazur I, Santos RS, Carravetta A, Fecarotta O, Ramos HM. Pressure Drop and Energy Recovery with a New Centrifugal Micro-Turbine: Fundamentals and Application in a Real WDN. Energies. 2022; 15(4):1528. https://doi.org/10.3390/en15041528
Chicago/Turabian StyleMorani, Maria Cristina, Mariana Simão, Ignac Gazur, Rui S. Santos, Armando Carravetta, Oreste Fecarotta, and Helena M. Ramos. 2022. "Pressure Drop and Energy Recovery with a New Centrifugal Micro-Turbine: Fundamentals and Application in a Real WDN" Energies 15, no. 4: 1528. https://doi.org/10.3390/en15041528