Entropy Production Evaluation within a Prototype Pump-Turbine Operated in Pump Mode for a Wide Range of Flow Conditions
Abstract
:1. Introduction
2. Methodology and Numerical Model
2.1. Governing Equations and Turbulence Model
2.2. Entropy Production Theory
2.3. Geometric Model
2.4. Grid Generation
2.5. Numerical Settings
2.6. Grid Independence Validation
3. Results and Discussion
3.1. Experimental Validation
3.2. Analysis of Three Hydraulic Loss Compositions
3.3. Analysis of Hydraulic Loss for Each flowing Domain
3.4. Distribution and Variation of Entropy Production
4. Conclusions
- As the flow rate increased, the total hydraulic losses significantly decreased, before gradually increasing with the flow rate. Generally, recorded hydraulic losses through the whole flow passage were primarily caused by flow separations, backflows, and vortices. In the near-wall regions, they could be approximated as friction losses. Three types of entropy production exhibited the same variation pattern as the TEP. EPTD and EPDD were dominant, with EPTD contributing the most to TEP, followed by EPDD. The TEP at the draft tube, GV, SV, and the spiral casing followed the aforementioned variation pattern of the total hydraulic losses, but the TEP at the runner continuously decreased as flow rate increased.
- The location and distribution mode of high hydraulic losses along the pump-turbine’s full flow passage significantly depended on the machine flow conditions. Under low-flow conditions, high hydraulic losses occurred primarily in the GV and draft tube flow domains. On the other hand, under high-flow rate conditions, high hydraulic losses were mostly concentrated in SV, the spiral casing, and GV;
- The pump-turbine hydraulic losses in pump mode primarily originated from the poor flow state in the mainstream region, and they significantly increased in the span-wise direction from the hub to the shroud side. Under low-flow conditions, hydraulic losses mainly came from flow separations in the GV flow channels, vortices in the vaneless region, and flow shocks on the runner blade’s leading edge. Under high-flow conditions, hydraulic losses mostly originated from the flow separations that took place within the flow channels in GV and SV flow domains, GV wake flows, and unsteady flows within the spiral casing. As to BEP, the hydraulic losses mainly derived from the vortices in flow channels between GV and SV, the blade wakes, and the elongated vortices in the runner’s inter-blade flow channels near the shroud side.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
i, j, k | Indices denoting the x, y, and z directions |
Time-averaged velocity components | |
Cartesian coordinate component(m) | |
Velocity fluctuation components (m/s) | |
ρ | Density (kg/m3) |
t | Physical time (s) |
Time average pressure (Pa) | |
μ | Dynamic viscosity (Pa·s) |
Subgrid-scale stress | |
Hamilton operator | |
Turbulence production rate due to viscous forces | |
Specific turbulence dissipation rate | |
k | Turbulence kinetic energy (m2/s2) |
ω | turbulence frequency (s−1) |
μeff | Effective dynamic viscosity (Pa·s) |
μt | Turbulent viscosity (Pa·s) |
ν | Kinematic viscosity (m2/s) |
νt | Eddy viscosity (m2/s) |
S | Strain tensor (s−1) |
y | Distance to the nearest wall |
y+ | Dimensionless wall distance |
Energy dissipation rate | |
Total entropy production (W/K) | |
Entropy production rate caused by direct dissipation (W·m−3·K−1) | |
Entropy production rate caused by turbulence dissipation (W·m−3·K−1) | |
Entropy production rate caused by wall shear stress(W·m−2·K−1) | |
T | Temperature (K) |
Velocity near the wall (m/s) | |
Shear stress near the wall (Pa) | |
hep | Hydraulic loss obtained by entropy production method (m) |
hp | Hydraulic loss obtained by differential pressure method (m) |
g | Gravity acceleration (m/s2) |
Mass flow rate (kg/s) | |
r | Mesh refinement factor |
hcoarse | Size of the coarse grid |
hfine | Size of the fine grid |
H | Delivery head (m) |
pTot | Total pressure (Pa) |
M | Torque of the impeller blades (N·m) |
n | Rotational speed (r/min) |
Pt | Total input power (W) |
Q | Flow rate (m3/s) |
η | Pump efficiency (%) |
Abbreviations
PIV | Particle Image Velocimetry |
DNS | Direct Numerical Simulation |
LES | Large Eddy Simulation |
RANS | Reynolds-Averaged Navier-Stokes |
EPDD | Entropy Production Rate caused by Direct Dissipation |
EPTD | Entropy Production Rate caused by Turbulence Dissipation |
EPWS | Entropy Production Rate caused by Wall Shear stress |
TEP | Total Entropy Production |
GV | Guide Vanes |
SV | Stay Vanes |
SST | Shear Stress Transport |
SIMPLEC | Semi-Implicit Method for Pressure-Linked Equations-Consistent |
RMS | Root Mean Square |
RE | Richardson Extrapolation |
GCI | Grid Convergence Index |
ASME | American Society of Mechanical Engineers |
GVO | Guide Vane Opening |
BEP | Best Efficiency Point |
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Parameter | Value |
---|---|
Runner inlet diameter D1/m | 2.37 |
Runner outlet diameter D2/m | 4.20 |
Number of runner blades | 9 |
Number of guide-vanes | 20 |
Specific speed nq | 41 |
Rated speed nr/(rpm) | 428.6 |
Rated working head Hr/m | 442.82 |
Rated discharge Qr/(m3/s) | 61.87 |
Rated power input/(MW) | 298.6 |
Part | Mesh1 | Mesh2 | Mesh3 | |||
---|---|---|---|---|---|---|
Nodes | Quality | Nodes | Quality | Nodes | Quality | |
Spiral casing with extended tube | 4.20 | 0.68 | 82.7366 | 0.63 | 37.0997 | 0.62 |
Stay vanes | 2.37 | 0.35 | 113.5939 | 0.33 | 50.7443 | 0.32 |
Guide vanes | 9 | 0.57 | 279.7729 | 0.57 | 126.5364 | 0.56 |
Runner | 20 | 0.33 | 381.3327 | 0.34 | 178.1229 | 0.34 |
Draft tube with extended tube | 41 | 0.60 | 138.4717 | 0.60 | 59.305 | 0.59 |
Sum | 428.6 | - | 995.9078 | - | 451.8083 | - |
Parameter | φ = H (m) | φ = η (%) |
---|---|---|
N1 | 22,553,199 | |
N2 | 9,959,078 | |
N3 | 4,518,083 | |
Mesh refinement factor r21 | 1.3132 | |
Mesh refinement factor r32 | 1.3014 | |
Numerical value φ1 | 477.5352 | 87.1648 |
Numerical value φ2 | 474.7498 | 86.3246 |
Numerical value φ3 | 469.9528 | 84.9235 |
Apparent order p | 2.11672 | 1.98787 |
Extrapolated value φext21 | 481.1052 | 88.3335 |
Relative error ea21 | 0.5833% | 0.9638% |
Extrapolated error eext21 | 0.7421% | 1.3231% |
Grid convergence index GCIfine21 | 0.9344% | 1.6761% |
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Yan, X.; Kan, K.; Zheng, Y.; Chen, H.; Binama, M. Entropy Production Evaluation within a Prototype Pump-Turbine Operated in Pump Mode for a Wide Range of Flow Conditions. Processes 2022, 10, 2058. https://doi.org/10.3390/pr10102058
Yan X, Kan K, Zheng Y, Chen H, Binama M. Entropy Production Evaluation within a Prototype Pump-Turbine Operated in Pump Mode for a Wide Range of Flow Conditions. Processes. 2022; 10(10):2058. https://doi.org/10.3390/pr10102058
Chicago/Turabian StyleYan, Xiaotong, Kan Kan, Yuan Zheng, Huixiang Chen, and Maxime Binama. 2022. "Entropy Production Evaluation within a Prototype Pump-Turbine Operated in Pump Mode for a Wide Range of Flow Conditions" Processes 10, no. 10: 2058. https://doi.org/10.3390/pr10102058