Investigation on the Impact of Air Admission in a Prototype Francis Turbine at Low-Load Operation
Abstract
:1. Introduction
2. Prototype Site Measurements
2.1. Prototype Unit and Experimental Setup
2.2. Measurement Procedure and Plant Behavior
3. Numerical Model
3.1. Geometry and Mesh
3.2. CFD-Setup
3.3. FEM-Setup
3.3.1. Modal Analysis
3.3.2. Transient FEM Analysis
3.4. Life Expectancy
4. Results and Discussion
4.1. Cavitation Behavior and Pressure Oscillations
4.2. Trailing Edge Vortex Shedding
4.3. Modal Analysis of the Draft Tube
4.4. Fatigue Damage and Dynamical Stress
5. Conclusions
- A huge draft tube vortex, with a frequency corresponding to approximately , is the most concerning fact in terms of high dynamical stress and runner fatigue damage.
- Both turbulence models showed quite similar behavior and a good agreement with the measurement. However, in contrast to single flow analysis the pressure amplitudes of the simulation tend to be higher than the ones obtained by the sensor.
- An improved runner model, targeting separation effects, showed the appearance of trailing edge vortex shedding.
- A simplified modal analysis of the draft tube confirmed that the vibrations of the machine set are related to vortex shedding.
- The air injection not only significantly reduced the vibrations of the machine set and might have a positive effect on cavitation, but also improved runner fatigue life.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
Acronyms | |
CDS | Central deference scheme |
CFD | Computational fluid dynamics |
CFL | Courant number |
D | Pressure side |
DES | Detached Eddy Simulation |
DT | Draft tube |
GGI | General grid interface |
FEM | Finite element method |
FFT | Fast-Fourier-Transformation |
FSI | Fluid-structure-interaction |
GV | Guide vanes |
GVA | Guide vanes with inlets for air injection |
LES | Large Eddy Simulation |
MP | Monitor point |
RANS | Reynolds averaged Navier-Stokes equations |
R1 | T-rosette |
RMS | root mean square |
Acronyms | |
RN | Runner |
RNVS | Refined runner domain |
RP | Rated point |
S | Suction side |
SAS | Scale Adaptive Simulation |
SBES | Stress Blended Eddy Simulation |
SC | Spiral casing |
SRS | Scale-Resolving Simulation |
SST | Shear stress transport |
SV | Stay vanes |
URANS | Unsteady RANS |
VIV | Vortex-induced-vibrations |
Greek Symbols | |
Rayleigh-Parameter, () | |
Rayleigh-Parameter, () | |
Water density, () | |
Vapor density, () | |
Stress amplitude, () | |
Yield strength, () | |
Damping ratio, (-) | |
Frequency limit, () | |
Frequency limit, () | |
Latin Symbols | |
Acceleration measured at the draft tube cone, () | |
Acceleration measured at the hollow hub, () | |
Acceleration measured at the turbine bearing, () | |
Damping marix, () | |
C | Damage factor, (-) |
D | Outer diameter of the runner, (m) |
Empirical factor for condensation, (-) | |
Empirical factor for vapor, (-) | |
f | Frequency, () |
Rotational frequency, () | |
Vortex shedding frequency, () | |
g | Gravity constant, () |
H | Turbine head, (m) |
Stiffness marix, () | |
k | Turbulent kinetic energy, () |
L | Characteristic lateral dimension, (m) |
Mass marix, () | |
Interphase mass transfer rate, () | |
Number of load cycles until the S-N curve is reached, (-) | |
Speed factor, (-) | |
Number of load cycles, (-) | |
P | Power, () |
Rated power, () | |
p | Pressure, () |
Pressure amplitude, () | |
Draft tube cone pressure amplitude, () | |
Pressure in the bubble, () | |
Draft tube cone pressure, () | |
Draft tube outlet pressure, () | |
Dynamic pressure (RN outlet), () | |
Latin Symbols | |
Bubble radius, (m) | |
Nucleation site radius, (m) | |
Nucleation volume fraction, (-) | |
Bubble volume fraction, (-) | |
Strouhal number, (-) | |
Relative displacement measured at the turbine bearing, (m) | |
Circumferential velocity (RN outlet), () | |
v | Velocity, () |
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Domain | SC | SV | GV | RN | DT | GVA | RN VS |
---|---|---|---|---|---|---|---|
Number of cells (million) | 20 | ||||||
Minimum determinant (-) | |||||||
Minimum angle () | 27 | ||||||
(-) | 32 |
Description Parameters | Parameters |
---|---|
Damping ratio (-) | |
Low limit frequency (Hz) | 1 |
Upper limit frequency (Hz) | |
Rayleigh coefficient (-) | |
Rayleigh coefficient (-) |
Description Parameters | Parameters |
---|---|
Material (-) | 13 4 |
Survival probability (%) | |
Mean stress (N/mm) | 150 |
Logarithmic standard deviation of (-) | |
Stress ratio (-) | 1 |
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Unterluggauer, J.; Maly, A.; Doujak, E. Investigation on the Impact of Air Admission in a Prototype Francis Turbine at Low-Load Operation. Energies 2019, 12, 2893. https://doi.org/10.3390/en12152893
Unterluggauer J, Maly A, Doujak E. Investigation on the Impact of Air Admission in a Prototype Francis Turbine at Low-Load Operation. Energies. 2019; 12(15):2893. https://doi.org/10.3390/en12152893
Chicago/Turabian StyleUnterluggauer, Julian, Anton Maly, and Eduard Doujak. 2019. "Investigation on the Impact of Air Admission in a Prototype Francis Turbine at Low-Load Operation" Energies 12, no. 15: 2893. https://doi.org/10.3390/en12152893
APA StyleUnterluggauer, J., Maly, A., & Doujak, E. (2019). Investigation on the Impact of Air Admission in a Prototype Francis Turbine at Low-Load Operation. Energies, 12(15), 2893. https://doi.org/10.3390/en12152893