**5. Estimated justification resource of hydro turbines**

Standard operating life of hydraulic units is established by project documentation and for most units are 30–40 years. Currently, a significant part of hydraulic units of powerful hydroelectric power plants is carried out outside the standard operating time. This leads to a decrease in the overall level of reliability of the structure as a whole and its individual elements and to an increase in the probability of failures and financial costs for technical diagnostics and repairs. The exhaustion of the standard operating life of the elements of hydro turbines raises the question of the assessment of the residual resource as one of the priorities in the field of ensuring the safety of hydraulic structures [7–9]. At the same time, as noted in [8], there are no generally accepted methods for assessing the residual life and the regulatory framework that defines the procedure for extending the service life of the impellers and making decisions about their replacement.

Taking into account the specified circumstances, the authors formulated the basic provisions for the calculation of the residual life of hydraulic turbine elements. The calculation of the resource before the formation of cracks is carried out on the allowable stresses:

$$\left[\sigma\right] = \min\left\{\frac{R\_{02}}{n\_{02}}; \frac{R\_{\text{m}}}{n\_{\text{m}}}\right\} \tag{10}$$

where *R*<sup>02</sup> and *Rm* are regulatory design resistances of the metal and *n*<sup>02</sup> and *nm* are dimensionless safety margins.

The estimated allowable number of loading cycles of the elements of the turbine at the stage of the occurrence of cracks, for the "start-stop" mode and mode control with the transition through the "forbidden" zone of operation modes, is determined by the formula:

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety… DOI: http://dx.doi.org/10.5772/intechopen.88306*

$$\begin{aligned} [N] &= \frac{1}{4n\_N} \left[ \frac{E e\_\circ}{\sigma\_d - \sigma\_{r0}/(1 + \sigma\_{r-1}r)} \right]^2, \\ \sigma\_{r0} &= \frac{\gamma \varepsilon \beta}{K\_\sigma} \sigma\_{-1} \sqrt{1 - \sigma\_m/[\sigma]} \end{aligned} \tag{11}$$

where *σ*�<sup>1</sup> is fatigue limit of given loading mode; *σ<sup>m</sup>* is stress average of cycle; *σ<sup>a</sup>* is stress amplitude of cycle; *r* is the asymmetry coefficient of the loading cycle; *γ*, *ε*, and *β* are dimensionless coefficients that take into account the influence of the medium, scale factor, and surface quality; and *Kσ* is stress concentration factor.

The estimated allowable number of loading cycles at blade and blade frequencies is determined by the following formula:

$$\left[\mathrm{N}\right] = \frac{\mathrm{N}\_0}{\mathrm{n}\_N} \left(\frac{\sigma\_{r0}}{\sigma\_a}\right)^m \tag{12}$$

where *N*<sup>0</sup> is the base number of loading cycles and *m* is dimensionless fatigue pattern indicator.

The influence of the multifrequency component of the loading mode from Karman vortices is taken into account through the reduced stress amplitude:

$$\sigma\_{\mathfrak{a}} = \sum\_{i=1}^{n} \sigma\_{ai} (o\_i / o\_1)^a \tag{13}$$

where *σai* is stress amplitude at the frequency *ωi*, *ω*<sup>1</sup> is the frequency of reduction, *α* is dimensionless coefficient taking into account the influence of the multifrequency nature of loading*,* and *nN* is the safety factor by the number of loading cycles.

The total accumulated fatigue damage for the considered loading modes is defined as the sum of the ratios of the actual *Nei* and the calculated loading cycles:

$$d = \sum\_{i} \frac{N\_{ei}}{[N]} \le \mathbf{1} \tag{14}$$

The number of cycles *Nl* at the stage of crack growth is determined by the following formulas:

For single-frequency loading mode

$$N\_l = \frac{1}{n\_l} \frac{2}{(m-2)C Y^{\frac{m}{2}} \sigma^m} \left[ \frac{1}{I\_0^{\frac{m-2}{2}}} - \frac{1}{l^{\frac{(m-2)}{2}}} \right] \tag{15}$$

For multifrequency loading mode

$$\frac{d\boldsymbol{l}}{d\boldsymbol{N}} = q \frac{\pi}{8} \left(\frac{\boldsymbol{K}\_{th}}{\boldsymbol{R}\_{0.2}}\right)^{2} \left\{ \mathbf{1} + (\boldsymbol{1} - \boldsymbol{\beta}) \frac{\left(\boldsymbol{1} - \boldsymbol{\widetilde{K}}\_{th}^{2}\right)^{2} - \left(\boldsymbol{\widetilde{K}}\_{\max}^{2} - \boldsymbol{\widetilde{K}}\_{th}^{2}\right)^{2} \boldsymbol{o}\boldsymbol{\mu}^{2}}{\left(\boldsymbol{\widetilde{K}}\_{\max}^{2} - \boldsymbol{\widetilde{K}}\_{th}^{2}\right)^{2} \boldsymbol{o}\boldsymbol{\mu}^{2}}\right\}^{1/(\boldsymbol{\beta} - 1)}\tag{16}$$

where *q*, *β*, and *μ* are parameters of the cyclic crack growth diagram, *K*e*th* ¼ *Kth=KC* and *K*e*max* ¼ *Kmax=KC* are relative threshold and maximum stress intensity factors, *Kc* is the crack resistance characteristic of steel, *ω* is relative frequency of loading, and *Kth* is the threshold stress intensity factor.

The nature of the defects and damage is presented in **Figures 3**–**5**. Similar defects were detected and investigated previously in the impellers of the Sayano-

Statistical analysis of the nondestructive testing results for cavitation erosion zones allowed determining the main geometrical parameters for these defects: the

Standard operating life of hydraulic units is established by project documentation and for most units are 30–40 years. Currently, a significant part of hydraulic units of powerful hydroelectric power plants is carried out outside the standard operating time. This leads to a decrease in the overall level of reliability of the structure as a whole and its individual elements and to an increase in the

probability of failures and financial costs for technical diagnostics and repairs. The exhaustion of the standard operating life of the elements of hydro turbines raises the question of the assessment of the residual resource as one of the priorities in the field of ensuring the safety of hydraulic structures [7–9]. At the same time, as

Taking into account the specified circumstances, the authors formulated the basic provisions for the calculation of the residual life of hydraulic turbine elements. The calculation of the resource before the formation of cracks is carried out on the

½ �¼ *<sup>σ</sup>* min *<sup>R</sup>*<sup>02</sup>

The estimated allowable number of loading cycles of the elements of the turbine at the stage of the occurrence of cracks, for the "start-stop" mode and mode control with the transition through the "forbidden" zone of operation modes, is

*n*<sup>02</sup> ; *R*<sup>m</sup> *nm* 

where *R*<sup>02</sup> and *Rm* are regulatory design resistances of the metal and *n*<sup>02</sup> and *nm*

(10)

noted in [8], there are no generally accepted methods for assessing the residual life and the regulatory framework that defines the procedure for extending the service life of the impellers and making decisions about

Shushenskaya HPP and Krasnoyarskaya HPP [6, 7].

*Distribution corrosion damages of length (a) and depth (b).*

**5. Estimated justification resource of hydro turbines**

length, width, and depth (**Figure 6**).

*Probability, Combinatorics and Control*

**Figure 6.**

their replacement.

allowable stresses:

are dimensionless safety margins.

determined by the formula:

**46**

**Figures 7**–**9** show the comparison of the results of the resource calculation according to the above procedure for the elements of hydro turbines of the

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety…*

frequencies of the Karman vortices.

*DOI: http://dx.doi.org/10.5772/intechopen.88306*

modern units.

**6. Conclusion**

**49**

Krasnoyarskaya HPP. The calculations were carried out on the basis of the results of a comprehensive diagnosis of the technical condition, with an assessment of the characteristics of the stress-strain state, the characteristics of the mechanical properties, and the defectiveness of the structural elements. The calculations took into account loading cycles: "start-stop," mode control, on blade frequencies, and at the

As can be seen from the figures, the resource has a wide range of values. This is due to the different levels of metal damage detected during technical diagnostics

The calculation results show that the hydraulic units surveyed using modern means of technical diagnostics and nondestructive testing have a resource reserve sufficient for planning and carrying out work to replace the impellers with more

It can also be assumed that an integrated approach to the problem of ensuring the reliability and safety of hydraulic units makes it possible to reliably predict the

Analysis of domestic and foreign studies and the practice of operating hydraulic equipment of large hydroelectric power plants indicate the need for the development of more advanced computational methods for estimating the life of hydro turbines that have completed their standard (design) service lives. When solving problems of resource assessment, special complex methods of technical diagnostics and modern computational and experimental technologies should be applied. These methods should be based on a combination of engineering design models that take into account the individual characteristics of hydraulic units based on routine monitoring and diagnostics and systems of reasonable safety factors (fatigue, crack length, stress, etc.) reflecting the uncertainty of the task with the required degree of

It should be emphasized that the purpose, role, and place of technical diagnostics and assessment of the hydraulic equipment resource should be linked to the task of assessing the protection of hydropower stations from severe accidents and disasters according to risk criteria. In technical assignments for the design of hydroelectric power plants, new quantitative safety indicators should be introduced that implement the design-experimental complex "strength—resource—reliability—

and the initial dimensions of crack-like defects in structural elements.

possibilities, terms, and conditions for their further operation.

accuracy design loads, material properties, and modes of operation.

survivability—safety—risk—security".

**Figure 7.** *Estimated cumulative damage for impeller blades.*

**Figure 8.** *Estimated residual life of impeller blades by the criterion of cracking.*

**Figure 9.** *Estimated residual life of impeller blades at the stage of crack development.*

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety… DOI: http://dx.doi.org/10.5772/intechopen.88306*

**Figures 7**–**9** show the comparison of the results of the resource calculation according to the above procedure for the elements of hydro turbines of the Krasnoyarskaya HPP. The calculations were carried out on the basis of the results of a comprehensive diagnosis of the technical condition, with an assessment of the characteristics of the stress-strain state, the characteristics of the mechanical properties, and the defectiveness of the structural elements. The calculations took into account loading cycles: "start-stop," mode control, on blade frequencies, and at the frequencies of the Karman vortices.

As can be seen from the figures, the resource has a wide range of values. This is due to the different levels of metal damage detected during technical diagnostics and the initial dimensions of crack-like defects in structural elements.

The calculation results show that the hydraulic units surveyed using modern means of technical diagnostics and nondestructive testing have a resource reserve sufficient for planning and carrying out work to replace the impellers with more modern units.

It can also be assumed that an integrated approach to the problem of ensuring the reliability and safety of hydraulic units makes it possible to reliably predict the possibilities, terms, and conditions for their further operation.

## **6. Conclusion**

**Figure 7.**

**Figure 8.**

**Figure 9.**

**48**

*Estimated cumulative damage for impeller blades.*

*Probability, Combinatorics and Control*

*Estimated residual life of impeller blades by the criterion of cracking.*

*Estimated residual life of impeller blades at the stage of crack development.*

Analysis of domestic and foreign studies and the practice of operating hydraulic equipment of large hydroelectric power plants indicate the need for the development of more advanced computational methods for estimating the life of hydro turbines that have completed their standard (design) service lives. When solving problems of resource assessment, special complex methods of technical diagnostics and modern computational and experimental technologies should be applied. These methods should be based on a combination of engineering design models that take into account the individual characteristics of hydraulic units based on routine monitoring and diagnostics and systems of reasonable safety factors (fatigue, crack length, stress, etc.) reflecting the uncertainty of the task with the required degree of accuracy design loads, material properties, and modes of operation.

It should be emphasized that the purpose, role, and place of technical diagnostics and assessment of the hydraulic equipment resource should be linked to the task of assessing the protection of hydropower stations from severe accidents and disasters according to risk criteria. In technical assignments for the design of hydroelectric power plants, new quantitative safety indicators should be introduced that implement the design-experimental complex "strength—resource—reliability survivability—safety—risk—security".
