This paper presents results of sediment and cavitation erosion through Tunnel 2 and Tunnel 3 of Tarbela Dam in Pakistan. Main bend and main branch of Tunnel 2 and outlet 1 and outlet 3 of Tunnel 3 are concluded to be critical for cavitation and sediment erosion. Studies are also performed for increased sediments flow rate, concluding 5 kg/sec as the critical value for sudden increase in erosion rate density. Erosion rate is concluded to be the function of sediment flow rate and head condition. Particulate mass presently observed is reasonably low, hence presently not affecting the velocity and the flow field.
In recent studies, it is highlighted that sediments are gradually accumulated in Tarbela Dam reservoir, resulting in gradual decrease in reservoir water storage capacity, increased load on embankment wall, and damage to tunnels and turbines [
Tunnels parameters.
Parameters  Tunnel 2  Tunnel 3 

Length (m)  846.51  907.41 
Inlet Elevation (m)  373  360.43 
Outlet Elevation (m)  337.11  340.46 
Inlet Diameter (m)  10.96  48.87 
Outlet Branches Diameter (m)  4.87  7.32 
Average Volume Flow Rate of Water (m^{3}/sec)  978.63  2415.64 
Average Available Head (m)  950.91  918.15 
Power Generation Capacity (MW)  1050  1728 
Constant and coefficients used in RS Model.
Anisotropic Diffusion Constant 

0.09 


Turbulent Schmidt Number 

1.00 


Reynolds’ Stress Coefficients 

1.80 

0.60  

1.44  

1.92 
Finnie erosion model given in (
Cavitation is a phenomenon that results from a pressure drop of the liquid phase below saturation pressure of the liquid under the conditions. Based on the tunnels geometry, S bend and outlet branches sharp bends, pressure drop of water is expected along these locations. Therefore, erosion due to cavitation phenomenon is studied. RayleighPlesset’s model given in (
Variables used in RayleighPlesset’s cavitation model.

4240 Pa 

0.01 

50 

1000 

5 

0.25 

1 
Both tunnels are modeled in ProEngineer software [
Mesh sensitivity analysis.
Equations  Mesh size  

1  2  3  5  
UMomentum Bulk  1.06 
1.42 
1.66 
2.46 
VMomentum Bulk  5.56 
5.35 
4.46 
3.49 
WMomentum Bulk  7.62 
7.99 
5.68 
8.05 
Mass of Water  1.19 
1.72 
1.87 
2.47 
uuRS  5.12 
4.47 
9.12 
1.00 
vvRS  6.16 
4.06 
5.19 
4.16 
wwRS  1.03 
4.98 
4.98 
4.67 
uvRS  9.94 
5.43 
1.96 
2.49 
uwRS  1.90 
2.54 
1.91 
2.04 
vwRS  2.71 
1.19 
6.00 
6.25 
EDissipation K  1.71 
1.20 
9.42 
4.88 
Computational time (sec)  4310  1900  1104  1623 
Various constants and coefficients used in simulation.
Parameter  Detail  Tunnel 2  Tunnel 3 

Erosion  Finnie Model 


Particles injection  Uniform injection  Twoway coupled  Twoway coupled 
Restitution Coefficient  Perpendicular and parallel  0.9 and 1, respectively  0.9 and 1, respectively 
Drag Coefficient  Schiller and Neumann Correlation  0.44 for 
0.44 for 
Particle Integration  Tracking distance and time  1200 m, 300 sec  1200 m, 300 sec 
Boundary conditions, initialization condition, and sediment flow rates at different heads.
Type  Head  Tunnel 2  Tunnel 3  

Boundary conditions  Pressure (kPa)  High  1323.53  1290.76 
Medium  950.91  918.15  
Low  578.30  545.53  


Initial conditions  Velocity (m/sec)  High  11.55  2.05 
Medium  10.33  1.70  
Low  7.57  1.31  


Sediment flow rates at different heads (kg/sec)  5 × 10^{−5}, 5 × 10^{−4}, 5 × 10^{−3}, 5 × 10^{−2}, 5 × 10^{−1}, 5, and 50 
Modeling of Tunnel 2: (a) main bend, (b) main branch, (c) outlets: Tunnel 3, (d) S bend, and (e) outlets.
Meshing: Tunnel 2 (a–c) and Tunnel 3 (d–f).
The velocity of water at different critical locations of Tunnel 2 and Tunnel 3 for different head condition and sediments flow rate is summarized in Tables
Velocity at different locations of Tunnel 2 under different head and varying sediment flow rates.
Head  Sediment flow rate (kg/sec)  Main bend  Main branch  Out1  Out2  Out3  Out4  Out5  Out6 

High  0.00005  41.4  54.8  38.7  17.0  20.4  32.9  43.7  30.2 
50  41.4  54.8  38.7  17.0  20.4  32.9  43.7  30.2  


Low  0.00005  31.0  41.0  29.0  12.8  15.3  24.6  32.8  22.6 
50  31.0  41.0  29.0  12.8  15.3  24.6  32.8  22.6 
Velocity at different locations of Tunnel 3 under different head and varying sediment flow rates.
Head  Sediment flow rate (kg/sec)  S1  S2  Out1  Out2  Out3  Out4 

Medium  0.00005  30.4  25.0  22.5  19.9  20.9  26.5 
50  30.4  25.0  22.5  19.9  20.9  26.5  


Low  0.00005  22.4  18.4  16.6  14.7  15.5  19.5 
50  22.4  18.4  16.6  14.7  15.5  19.5 
Erosion rate density is observed to be increased with increase in sediment flow rate. For high head condition, the change can be easily attributed to the increase in velocities at all critical locations of both tunnels. Figures
Erosion rate density (kg/m⋅sec) in Tunnel 2 under various head conditions and at fixed sediment flow rate of 50 kg/sec.
Head  Main bend  Main branch  Out1  Out2  Out3  Out4  Out5  Out6 

High  45  324  269  34  49  52  62  107 
Medium  28  237  198  30  38  34  60  62 
Low  17  130  98  15  17  20  27  40 
Erosion rate density (kg/m⋅sec) in Tunnel 3 under various head conditions and at fixed sediment flow rate of 50 kg/sec.
Head  S1  S2  Out1  Out2  Out3  Out4 

High  28  2.3  16  23  60  11 
Medium  20  1.3  11  15  42  7 
Low  12  1.0  7  8  24  2 
Erosion rate density at main branch for all head conditions and different sediment flow rate in Tunnel 2 (BM: main branch; H: high head; M: medium head; L: low head).
Erosion rate density at outlet 3 for all head conditions and different sediment flow rate in Tunnel 3 (Out: outlet; H: high head; M: medium head; L: low head).
It is observed from water and sediment flow through the tunnels that pressure at the inside of the bends or sharp corners drops below saturation pressure resulting in water vapors formation. Analyses were performed for the various head conditions, that is, high, medium, and low. A significant pressure drop is observed at the main bend, main branch, and outlet branches in Tunnel 2 and S bend and outlet branches in Tunnel 3. The volume fraction of water vapors is on the higher side at the critical locations of the tunnels, highlighting the notion that these locations are prone to erosion, and is concluded due to the cavitation effect. Cavitation erosion is therefore further superposed on the sediments erosion already observed. The presence of water vapors will bring these locations under a greater threat. The maximum water vapor volume fraction gradient, maximum volume fraction of water vapors, and Euler or cavitation numbers at different heads are summarized in Tables
Volume fraction of water vapors and volume fraction gradient in Tunnel 2 under various head conditions.
Head  Main bend  Main branch  Outlet branches 
Max. water vapor volume fraction gradient (m^{−1})  Max. volume fraction of water vapors 

Volume fraction of water vapors and volume fraction gradient  
High  0.75  0.98  0.98  1.729  0.980 
Medium  0.73  0.97  0.97  1.792  0.977 
Low  0.72  0.96  0.96  1.764  0.967 


Euler or cavitation numbers  
High  0.09  0.24  0.13  —  — 
Medium  0.43  1.11  0.63  —  — 
Low  0.41  1.23  0.36  —  — 
Volume fraction of water vapors, volume fraction gradient, and Euler or cavitation numbers in Tunnel 3 under various head conditions.
Head  S1  S2  Out1  Out2  Out3  Out4  Max. water vapor volume fraction gradient (m^{−1})  Max. volume fraction of water vapor 

Volume fraction of water vapors and volume fraction gradient  
High  0.95  0.95  0.48  0.82  0.82  0.97  1.746  0.971 
Medium  0.86  0.95  0.91  0.73  0.76  0.95  1.916  0.958 
Low  0.87  0.72  0.67  0.45  0.57  0.74  1.416  0.906 


Euler or cavitation numbers  
High  0.86  1.09  0.41  0.39  0.51  0.96  —  — 
Medium  0.97  1.12  0.49  0.68  0.80  1.12  —  — 
Low  1.09  1.38  0.69  1.00  1.88  2.40  —  — 
Cavitation erosion (water vapors) at different locations of Tunnel 2.
Cavitation erosion (water vapors) at different locations of Tunnel 3.
Flow profile is observed to be not affected by the increase in sediment flow rate through the tunnels because of small particulate mass and negligible particletoparticle interaction. The tracks followed by particles remained unchanged and any rise in erosion rate density is concluded as a direct consequence of head and sediment flow rate. Main branch of Tunnel 2 and outlet 3 of Tunnel 3 are concluded to be critical for sediment erosion.
Keeping in view the expected increased sediment flow rate in the tunnels due to sediment delta movement towards main embankment wall, for both tunnels, until 5 kg/sec sediment flow rate, almost zero erosion rate density is observed which however started increasing rapidly after this and became prominent at the sediment flow rate of 50 kg/sec. Hence, the possibility of catastrophic failure of the tunnels due to increased sediment flow rate cannot be ignored.
Cavitation is observed to be threatening at several locations. Main bend of Tunnel 2 and outlet 1 of Tunnel 3 are concluded to be critical for cavitation erosion. The combined effect of both erosion due to sediments and cavitation further increases the erosion rate density.
The authors declare that they have no competing interests.