# The Effect of Unsteady Water Discharge through Dams of Hydroelectric Power Plants on Hydrodynamic Regimes of the Upper Pools of Waterworks

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Development of a Hydrodynamic Model in a Two-Dimensional Formulation

#### 2.2. Model of Unsteady Flow in a Two-Dimensional Formulation of RiverFlow2D, Basic Equations

#### 2.3. Construction of a Two-Dimensional Hydrodynamic Model of a Section of the Kama Reservoir and Initial Data Assignment

^{3}/s is the maximum allowed through hydraulic units during routine operation of the HEPP and 300 m

^{3}/s is the minimum sanitary pass established for the Kamskaya HEPP. Material processing was carried out in the ArcGIS v.10.4 software package. The data obtained in the form of Esri shapefiles (coasts, contours, depth points) were finally processed and converted into a digital elevation model in the form of TIN (Triangulated Irregular Network). Then, in the SMS v.11.1 software package in a special module “Map”, the obtained data were converted into the internal format of the program for further use in creating the model. Hydrological and meteorological data were obtained from official sources of the Federal State Budgetary Institution Perm TsGMS of Roshydromet and the Kama Hydroelectric Power Plant, a branch of PJSC RusHydro. Their processing was carried out using Microsoft Excel.

#### 2.4. Initial Data for 2D Modeling

- -
- The flow rate of water entering the Kama reservoir (Kama River—1675 m
^{3}/s, Chusovaya—226 m^{3}/s and Sylva—159 m^{3}/s) was considered constant at 2060 m^{3}/s for 5 days. This is taken on the basis of the average annual summer inflow of water entering the Kama reservoir along its main tributaries, the Kama, Chusovaya and Sylva rivers; - -
- The discharge flow rate of water at the Kamskaya HEPP (Kama river) for 5 days was varied according to the following scheme: the initial discharge flow rate of 350 m
^{3}/s for 10 h, then after 2 h the discharge flow rate rose to 3770 m^{3}/s, then within 10 h constant flow rate of 3770 m^{3}/s, then decrease in 2 h of discharge flow rate to 350 m^{3}/s, then again after 10 h rise to 3770 m^{3}/s and so on within 5 days. A two-hour drop in water discharge flow rate occurred in the time interval from 7 to 9 p.m., and a rise in water discharge flow rate occurred in the time interval from 7 to 9 a.m. These flow rates were taken from the conditions of maximum and minimum load on the Kama hydroelectric station in summer conditions. The maximum and minimum peaks were taken as constants. In real conditions, the discharge flow rate of water during the day can vary quite strongly. The schedule of water discharge flow rates by tributaries of the Kama reservoir and water discharge from the Kamskaya HEPP is shown in Figure 2, the beginning of the day (0 a.m.) is taken as “0”; - -
- The flow rates of water intake and discharge at the Permskaya TPP (the Kama River, city of Dobryanka) were considered constant and equal to 42.5 m
^{3}/s for 5 days. This value was obtained from the average long-term data of the Permskaya TPP in the summer period with the continuous operation of two power units.

#### 2.5. Three-Dimensional Hydrodynamical Model

#### 2.6. Model of Unsteady Flow in a Three-Dimensional Formulation, Basic Equations

#### 2.7. Boundary Conditions for 3D Modeling

- -
- at the bottom of the river and on its banks, the no-slip conditions and constant temperature were set ${u}_{1}={u}_{2}={u}_{3}=0,T={T}_{0}$;
- -
- at the input of the computational domain, the time-variable velocity of the main flow, determined in two-dimensional modeling was set the temperature was set as equal to the background temperature of the river ${u}_{i}={V}_{i}(t),T={T}_{0}$;
- -
- in places of water intake and discharge, a constant water velocity and a constant temperature were set: at the inlet of the working channel ${u}_{i}={V}_{1},T={T}_{0}$ and at the outlet of the working channel ${u}_{i}={V}_{2},T={T}_{2}$;
- -
- the upper boundary of the fluid was considered free, the wind effect was taken into account—shear stresses were set in accordance with the formula $\tau ={\rho}_{air}C{W}^{2}$ presented in [32], where ${\rho}_{air}$ is the air density, $C$ is the dimensionless coefficient of wind stress and $W$ is the wind velocity at a distance of 10 m from the water surface. According to [32], for wind velocities from the range 1 m/s < $W$ < 15 m/s, the dimensionless parameter has the form $C=0.0005{W}^{0.5}$. The calculations were made for wind velocity $W=8$ m/s, so the value $C=1.11\times {10}^{-3}$ was used. For the temperature on the surface of the water, a linear law of heat transfer was set; taking into account the heating of the surface from the surrounding air, the heat transfer coefficient was selected on the basis of field measurements.

#### 2.8. Construction of a Three-Dimensional Hydrodynamic Model of a Section of the Kama Reservoir

## 3. Results

#### 3.1. The Results of Two-Dimensional Numerical Simulation

#### 3.2. Results of 3D Numerical Modeling

^{3}/s, the temperature of the discharge water was 32.4 °C, and the temperature of the water of the reservoir receiver was 21.8 °C. The calculation time was five days. Based on the simulation results, an assessment was made of the zone of influence of heated water masses on the reservoir at a change in the hydrological regime of the river.

^{3}/s. As can be seen from the figures, under all wind conditions, at a variable discharge flow rate, the thermal pollution spot covers a larger area than at a constant discharge flow rate equal to 2000 m

^{3}/s.

^{3}/s, the thermal spot propagates to a smaller distance upstream, but it does not reach the water intake channel.

^{3}/s, the thermal spot propagates against the river flow and warm water enters the intake canal. At a non-stationary discharge flow, the area of the thermal spot is larger; it reaches the intake channel earlier.

^{3}/s, a thermal spot propagates downstream to the Kamskaya HEPP dam and warm water does not enter the water intake canal.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Abbaspour, A.H.J.; Moghimi, P.; Kayhan, K. Modeling of thermal pollution in coastal area and its economical and environmental assessment. Int. J. Environ. Sci. Technol.
**2005**, 2, 13–26. [Google Scholar] [CrossRef] [Green Version] - Madden, N.; Lewis, A.; Davis, M. Thermal effluent from the power sector: An analysis of once-through cooling system impacts on surface water temperature. Environ. Res. Lett.
**2013**, 8, 035006. [Google Scholar] [CrossRef] - Hester, E.T.; Bauman, K.S. Stream and retention pond thermal response to heated summer runoff from urban impervious surfaces. J. Am. Water Res. Assoc.
**2013**, 49, 328–342. [Google Scholar] [CrossRef] - Raptis, C.E.; Pfister, S. Global freshwater thermal emissions from steam-electric power plants with oncethrough cooling systems. Energy
**2016**, 97, 46–57. [Google Scholar] [CrossRef] - Issakhov, A.; Mashenkova, A. Numerical study for the assessment of pollutant dispersion from a thermal power plant under the different temperature regimes. Int. J. Environ. Sci. Technol.
**2019**. [Google Scholar] [CrossRef] - Alcamo, J.; Flörke, M.; Märker, M. Future long-term changes in global water resources driven by socio-economic and climatic changes. Hydrol. Sci. J.
**2007**, 52, 247–275. [Google Scholar] [CrossRef] - Directive 2006/44/EC of the European Parliament. 2006. Available online: https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=uriserv:OJ.L_.2006.264.01.0020.01.ENG (accessed on 4 May 2020).
- Van Vliet, M.T.H.; Franssen, W.H.P.; Yearsley, J.R.; Ludwig, F.; Haddeland, I.; Lettenmaier, D.P.; Kabat, P. Global river discharge and water temperature under climate change. Glob. Environ. Chang.
**2013**, 23, 450–464. [Google Scholar] [CrossRef] - Ptak, M.; Sojka, M.; Kałuża, T.; Choiński, A.; Nowak, B. Long-term water temperature trends of the Warta River in the years 1960–2009. Ecohydrol. Hydrobiol.
**2019**, 19, 441–451. [Google Scholar] [CrossRef] - Webb, B.W.; Nobilis, F. Long-term changes in river temperature and the influence of climatic and hydrological factors. Hydrol. Sci. J.
**2007**, 52, 74–85. [Google Scholar] [CrossRef] - Ptak, M.; Sojka, M.; Choiński, A.; Nowak, B. Effect of environmental conditions and morphometric parameters on surface water temperature in Polish lakes. Water
**2018**, 10, 580. [Google Scholar] [CrossRef] [Green Version] - Ling, F.; Foody, G.M.; Du, H.; Ban, X.; Li, X.; Zhang, Y.; Du, Y. Monitoring thermal pollution in rivers downstream of dams with Landsat ETM+ thermal infrared images. Remote Sens.
**2017**, 9, 1175. [Google Scholar] [CrossRef] [Green Version] - Issakhov, A. Mathematical modeling of thermal process to aquatic environment with different hydro meteorological conditions. Sci. World J.
**2014**, 2014, 678095. [Google Scholar] [CrossRef] [PubMed] - Issakhov, A. Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant. Int. J. Nonlinear Sci. Numer. Simul.
**2015**, 16, 229–238. [Google Scholar] [CrossRef] - Miara, A.; Vorosmarty, C.J. A dynamic model to assess tradeoffs in power production and riverine ecosystem protection. Environ. Sci. Process. Impacts
**2013**, 15, 1113–1126. [Google Scholar] [CrossRef] - Stewart, R.J.; Wollheim, W.M.; Miara, A.; Vörösmarty, C.J.; Fekete, B.; Lammers, R.B.; Rosenzweig, B. Horizontal cooling towers: Riverine ecosystem services and the fate of thermoelectric heat in the contemporary Northeast US. Environ. Res. Lett.
**2013**, 8, 025010. [Google Scholar] [CrossRef] [Green Version] - Miara, A.; Cohen, S.M.; Macknick, J.; Vorosmarty, C.J.; Corsi, F.; Sun, Y.; Tidwell, V.C.; Newmark, R.; Fekete, B.M. Climate-Water Adaptation for Future US Electricity Infrastructure. Environ. Sci. Technol.
**2019**, 53, 14029–14040. [Google Scholar] [CrossRef] - Issakhov, A.; Zhandaulet, Y. Numerical Study of Technogenic Thermal Pollution Zones’ Formations in the Water Environment from the Activities of the Power Plant. Environ. Model. Asess.
**2020**, 25, 203–218. [Google Scholar] [CrossRef] - Durán-Colmenares, A.; Barrios-Piña, H.; Ramírez-León, H. Numerical Modeling of Water Thermal Plumes Emitted by Thermal Power Plants. Water
**2016**, 8, 482. [Google Scholar] [CrossRef] [Green Version] - Hester, E.T.; Doyle, M.W. Human Impacts to River Temperature and Their Effects on Biological Processes: A Quantitative Synthesis. J. Am. Water Resour. Assoc.
**2011**, 47, 571–587. [Google Scholar] [CrossRef] - Issakhov, A. Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities. Appl. Math. Model.
**2016**, 40, 1082–1096. [Google Scholar] [CrossRef] - McGuirk, J.J.; Rodi, W. A depth-averaged mathematical model for the near field of the side discharge into open-channel flow. J. Fluid Mech.
**1978**, 86, 761–781. [Google Scholar] [CrossRef] - Park, S.W.; Chung, M.K. Prediction of 2-dimensional unsteady thermal discharge into a reservoir. J. Korean Soc. Mech. Eng.
**1983**, 7, 451–460. [Google Scholar] - Lyubimova, T.; Lepikhin, A.; Konovalov, V.; Parshakova, Y.; Tiunov, A. Formation of the density currents in the zone of confluence of two rivers. J. Hydrol.
**2014**, 508, 328–342. [Google Scholar] [CrossRef] - Lyubimova, T.; Lepikhin, A.; Parshakova, Y.; Lyakhin, Y.; Tiunov, A. The modelling of the formation of technogenic thermal pollution zones in large reservoirs. Int. J. Heat Mass Transf.
**2018**, 126 Pt A, 342–352. [Google Scholar] [CrossRef] - Lyubimova, T.; Lepikhin, A.; Parshakova, Y.; Lyakhin, Y.; Tiunov, A. Application of hydrodynamic modeling in 2D and 3D approaches for the improvement of the recycled water supply systems of large energy complexes based on reservoirs-coolers. Int. J. Heat Mass Transf.
**2019**, 140, 897–908. [Google Scholar] [CrossRef] - Faulkner, A.; Bulgin, C.E.; Merchant, C.J. Coastal Tidal Effects on Industrial Thermal Plumes in Satellite Imagery. Remote Sens.
**2019**, 11, 2132. [Google Scholar] [CrossRef] [Green Version] - Pivato, M.; Carniello, L.; Viero, D.P.; Soranzo, C.; Defina, A.; Silvestri, S. Remote Sensing for Optimal Estimation of Water Temperature Dynamics in Shallow Tidal Environments. Remote Sens.
**2020**, 12, 51. [Google Scholar] [CrossRef] [Green Version] - Vreugdenhil, C.B. Numerical methods for shallow-water flow. In Water Science and Technology Library; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994; Volume 13. [Google Scholar]
- Reference Manual “RiverFlow2D Two-Dimensional River Dynamics Model” August, 2016, Hydronia LLC. Available online: http://www.hydronia.com/riverflow2d (accessed on 4 May 2020).
- Launder, B.E.; Spalding, D.B. Lectures in Mathematical Models of Turbulence; Academic Press: London, UK; New York, NY, USA, 1972; 169p. [Google Scholar]
- Wu, J. Wind stress and surface roughness at sea interface. J. Geophys. Res.
**1969**, 74, 444–453. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Morphometry of the considered section of the Kama reservoir. The brown rectangle shows the area of interest in the vicinity of Dobryanka town.

**Figure 2.**Change in the discharge flow rate of water from the Kamskaya Hydroelectric Power Plant (HEPP) and the flow rate of water inflow into the Kama reservoir.

**Figure 3.**A map of the morphometric peculiarities of the bottom of the Kama reservoir in the region of the Permskaya Thermal Power Plant (TPP). Red lines show the boundaries of the computational domain for three-dimensional modeling.

**Figure 4.**Scheme of the computational domain. Computational grid. For sufficient visualization, the vertical size is increased by 40 times.

**Figure 5.**The velocity vector field in the vicinity of Dobryanka town at 4 days, 13 h from the start of calculations, which corresponds to 1 h of the day (stock flow, calm conditions).

**Figure 6.**The velocity vector field in the vicinity of Dobryanka town at 4 days, 1 h from the start of calculations, which corresponds to 1 h at night (back flows, calm conditions).

**Figure 7.**Change in the velocity module in the area of the water intake channel of Permskaya TPP (blue line), in comparison with the change in discharge flow rate of water from the Kamskaya HEPP (green line) and in comparison with the velocity module at a constant discharge of water through the Kamskaya HEPP (red line).

**Figure 8.**Temperature fields in the near-surface layer for southeasterly wind; the time from the start of calculations (t). The calculations were carried out for the period starting from midnight.

**Figure 9.**The velocity vector field in the horizontal plane near the surface (

**a**) and at a depth of 6 m (

**b**) for the southeasterly wind. The time after the start of calculations is 20 h.

**Figure 10.**Temperature fields in the surface layer for northwesterly wind; the time from the start of calculations (t). The calculations were carried out for the period starting from midnight.

**Figure 11.**Temperature fields in the near-surface layer for calm conditions; the time from the start of calculations (t). The calculations were carried out for the period starting from midnight.

**Figure 12.**The temperature distributions in depth at different verticals for calm conditions at t = 97 h.

**Figure 13.**Temperature fields for Wind SE 8 m/s for 95 H. (

**a**,

**c**,

**e**)—under the influence of a discharge from HEPP, regular mode in a changing discharge of water; (

**b**,

**d**,

**f**)—under minimum influence of a discharge from HEPP, continuous discharge mode.

**Table 1.**The average monthly values of air temperature according to observations at a meteorological station in Dobryanka.

Value | Month | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

I | II | III | IV | V | VI | VII | VIII | IX | X | XI | XII | |

Cp. T, °C | −13,0 | −9,6 | −3,0 | 2,6 | 10,4 | 14,8 | 16,7 | 15,6 | 9,5 | 1,7 | −6,0 | −9,7 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lyubimova, T.; Parshakova, Y.; Lepikhin, A.; Lyakhin, Y.; Tiunov, A.
The Effect of Unsteady Water Discharge through Dams of Hydroelectric Power Plants on Hydrodynamic Regimes of the Upper Pools of Waterworks. *Water* **2020**, *12*, 1336.
https://doi.org/10.3390/w12051336

**AMA Style**

Lyubimova T, Parshakova Y, Lepikhin A, Lyakhin Y, Tiunov A.
The Effect of Unsteady Water Discharge through Dams of Hydroelectric Power Plants on Hydrodynamic Regimes of the Upper Pools of Waterworks. *Water*. 2020; 12(5):1336.
https://doi.org/10.3390/w12051336

**Chicago/Turabian Style**

Lyubimova, Tatyana, Yanina Parshakova, Anatoly Lepikhin, Yury Lyakhin, and Alexey Tiunov.
2020. "The Effect of Unsteady Water Discharge through Dams of Hydroelectric Power Plants on Hydrodynamic Regimes of the Upper Pools of Waterworks" *Water* 12, no. 5: 1336.
https://doi.org/10.3390/w12051336