# Sediment and Cavitation Erosion in Francis Turbines—Review of Latest Experimental and Numerical Techniques

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## Abstract

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## 1. Introduction

^{9}tons of sediment reach oceans in a year. Every year, reservoir sedimentation causes an estimated 1% reduction [2] in the total capacity of the reservoirs. Figure 1 shows the aerial view of a large dam located in Itaipu, Brazil.

^{3}/km

^{2}a year [3]. The flushing of gravel and rocks carried through Sichuan in the Yangtze could not be removed because of their weight and size, and it is predicted that the reservoir would deposit up and become unusable within the next ten 10 years.

_{ff}), was used for the clearance gap of several hydrofoils to compare the possible leakage flow, starting from the reference case. It is shown that L

_{ff}is reduced by 4.45 times for the NACA-4412 profile and the average value of the circumferential velocity, at the runner inlet only by 1.31%, compared to the base case. The drop in intensity and size of leakage flow and passage vortex shows minimization of the coalesced impact of secondary flow and sediment erosion. Comparison of various studies show that efficiency of FT varies between 3% and 6% based on changes in sediment concentration and secondary flow phenomena. However, around 2 to 3.5 mm loss in thickness of runner is observed. In all of the discussed studies it is found that cavitation phenomena need the latest equipment for its detection and visualization. Moreover, a lot of work is needed to assess the cavitation numerically.

## 2. Experimental and Numerical Investigation for Sediment Erosion

#### 2.1. Introduction

#### 2.2. Experimental Approaches

#### 2.3. CFD Work

^{3}/s, respectively for design point.

#### 2.4. Effect of Surface Roughness

#### 2.5. FSI as a Multiphysics Approach

## 3. Experimental and Numerical Investigation for Cavitation Erosion

#### 3.1. Introduction

#### 3.2. Experimental Techniques

#### 3.3. Cavitation Research by CFD

#### 3.4. Vortex Rope Formation

## 4. Experimental and Numerical Investigation for Coalesced Effect of Sediment and Cavitation Erosion

#### 4.1. Introduction

#### 4.2. Use of Cavitation Inducers

## 5. Current Status and Future Prospects

- Appropriate testing time should be utilized in which the true behavior of erosion can be obtained during the experiments. It is possible to “speed up” the events in the model which may occur over a relatively long time in the prototype by utilizing the time scales appropriately.
- Selection of suitable similarity formulae and conditions, such as dynamic, kinematic, and geometric similarity requirements should all be satisfied.
- Avoid using distorted models, and if they are utilized, interpretation of the results should be done carefully.

## 6. Conclusions

- Sediment erosion severely damages turbine parts in hydroelectric power plants. It is observed that the size, shape, and concentration of sediment particles are important erosion parameters. Water flowrate and head are significant flow properties. Surface of the erodent is yet another important parameter. Sediment erosion not only deteriorates the surface of the turbine components, but it also causes efficiency loss and high maintenance cost is required periodically. The technology advancements have led to extensive use of computational tools for solving sediment erosion problems.
- Cavitation inducers and some latest visualization techniques like PIV, LDV etc. are used by several researchers as experimental means to study the cavitation phenomena. In the last decade, numerical methodology has been used extensively and tangible results have been achieved.
- Study of the coalesced effect of sediment and cavitation erosion in hydroelectric power turbines is a challenging issue for future research. Therefore, it is recommended to develop an appropriate CFD methodology validated through experimental techniques for the quantification of combined effect.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Number of dams higher than 30 m in major countries [3].

**Figure 3.**Aerial view of Tarbela Dam Hydroelectric Project [5].

**Figure 4.**(

**a**) Rotating disc apparatus (RDA) apparatus; (

**b**) apparatus components; (

**c**) erosion behavior observed on the blade [13].

**Figure 5.**Inlet velocity triangle at Best Efficiency Point (BEP) [15].

**Figure 7.**Runner at Tarbela dam hydroelectric project (TDHP), (

**a**) at actual site, (

**b**) erosion rate density profile [17].

**Figure 8.**Turbine efficiency measurements at TDHP [17].

**Figure 9.**Erosion rate behavior for different particle sizes [20].

**Figure 10.**Stress distribution on the blade from two-way FSI [25].

**Figure 12.**Cumulative mass loss as a function of test duration without and with the cavitation inducers [29].

**Figure 14.**Vapor core rope development for σ = 0.380 [41].

**Figure 15.**Pressure recording locations in spiral casing, runner blade, and draft tube [42].

**Figure 16.**Hill chart for showing cavitation and non-cavitation operating points [43].

**Figure 18.**(

**a**) Tribometer configuration, (

**b**) boundary conditions: slurry pot tester cavitation and erosion simulation [46].

**Figure 19.**Velocity profile and sand particles angle of attack on the sample with 15° Cavitation Inducers (CI) and 3500 rpm in the tribometer [46].

**Figure 20.**(

**a**) Weight loss curves for the cavitation; (

**b**) weight loss curves of the sediment erosion; (

**c**) weight loss curves for the coalesced effect [47].

Model | Equation | Parameters |
---|---|---|

Thapa et al. [6] | ${E}_{r}=C.{K}_{hardness}{K}_{shape}{K}_{m}{K}_{f}.a{\left(size\right)}^{b}$ | K_{m} = the material factor and K_{f} = the flow factorC = silt concentration kg/m ^{3}K _{shape} and K_{hardness} = shape and hardness factors respectively. |

Rajkarnikar et al. [12] | $e=\frac{{W}_{0}-{W}_{i}}{{W}_{0}}\times 100$ | e_{i} = cumulative erosion after test i in mg/gm, W_{0} is weight of test specimen at the beginning of the experiment in gm, W_{i} is weight of test specimen after test i in gm. |

Teran et al. [16] | ${E}_{r}=E\ast N\ast {m}_{p}$ | E = Dimensionless mass loss, N is the rate of number of particles, m_{p} is average particle mass. |

Aponte et al. [20] | ${N}_{E}=\frac{{E}_{r}}{{V}_{j}{A}_{0}{\rho}_{{H}_{2}O}\left(\frac{C}{1-C}\right)}$ | N_{E} is the dimensionless normalized erosion, E_{r} is the erosion rate in kg/s, V_{j} is the average velocity of jet in m/s, A_{0} is the jet outlet cross-sectional area, C is concentration of sand, and ρ_{H2O} is density of water in kg/m^{3}. |

Investigators | Details of Tests/Models | Major Conclusions |
---|---|---|

Franc et al. [31] | $N=\frac{8}{\pi {\delta}^{2}\tau}{e}^{-\left(2D/\delta \right)}$ | Cavitation rate depends on: pitting rate, coverage rate, and depth of deformation rate |

Gohil et al. [35] | $\begin{array}{c}\hfill \dot{{m}_{cav}}=0.0081536{T}^{0.9726}H{s}^{0.3573}{V}^{4.9927}\hfill \\ \hfill {\eta}_{los{s}_{cav}}=1.4550{T}^{0.2247}H{s}^{0.1724}{V}^{-5.1779}{e}^{\left[3.2497{\left(lnV\right)}^{2}\right]}\hfill \end{array}$ | Correlations developed for cavitation rate and normalized efficiency loss, useful for the plant operators. To predict the degradation rate of performance. |

Celebioglu et al. [43] | $\begin{array}{c}\hfill \psi =\frac{2gH}{{\omega}^{2}{R}^{2}}\hfill \\ \hfill \phi =\frac{Q}{\pi \omega {R}^{3}}\hfill \end{array}$ | Head coefficient and discharge coefficients are used to plot a numerical hill chart. The methodology developed for the minimization of cavitation at off-design. The cavitation limit is determined by using the cavitating and non-cavitating operating points. |

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**MDPI and ACS Style**

Noon, A.A.; Kim, M.-H. Sediment and Cavitation Erosion in Francis Turbines—Review of Latest Experimental and Numerical Techniques. *Energies* **2021**, *14*, 1516.
https://doi.org/10.3390/en14061516

**AMA Style**

Noon AA, Kim M-H. Sediment and Cavitation Erosion in Francis Turbines—Review of Latest Experimental and Numerical Techniques. *Energies*. 2021; 14(6):1516.
https://doi.org/10.3390/en14061516

**Chicago/Turabian Style**

Noon, Adnan Aslam, and Man-Hoe Kim. 2021. "Sediment and Cavitation Erosion in Francis Turbines—Review of Latest Experimental and Numerical Techniques" *Energies* 14, no. 6: 1516.
https://doi.org/10.3390/en14061516