Simulation of water temperature distribution in Fenhe Reservoir

Water Science and Engineering, 2009, 2(2): 32-42doi:10.388/j.issn. 1674-2370.2009.02.004http://kkb.hhu.edu.cne-mail: wse@hhu.edu.cnSimulation of water temperature distribution in FenheReservoirShu-fang FAN*, Min-quan FENG, Zhao LIUKey Laboratory of Norhwest Water Resources and Environmental Ecology of Ministry of Educaion,Xi'an University of Technology, Xi 'an 710048, P R. ChinaAbstract: In order to evaluate the need of controlling the temperature of water discharged fromthe Fenhe Reservoir, the reservoir water temperature distribution was examined. Athree-dimensional mathematical model was used to simulate the in-plane and vertical distributionof water temperature. The parameters of the model were calibrated with field data of thetemperature distribution in the Fenhe Reservoir. The simulated temperature of discharged water isconsistent with the measured data. The difference in temperature between the discharged water andthe natural river channel is less than 3"C under the current operating conditions. This will notsignificantly impact the environment of downstream areas.Key words; three-dimensional mathematical model; reservoir water temperature; watertemperature distribution; water temperalure simulation; discharge; Fenhe Reservoir1 IntroductionThe difference of temperature between reservoir water and a natural river channel willimpact the water quality and ecology of the river. In order to obtain the temperaturedistribution in a reservoir and its degree of impact on the environment, it is necessary tosimulate and predict the reservoir's temperature. Reservoir water temperature has beenstudied since the 1930s. At present, a large number of one- and two-dimensionalmathematical models have been developed and applied in actual projects, achieving someacceptable results. However, because the one-dimensional vertical temperature model doesnot consider the longitudinal changes of temperature, it is not applicable to longer reservoirs.A two-dimensional vertical temperature model can better simulate the temperaturedistribution; It can therefore be applied extensively in many reservoirs (Ferrarin andUmgiesser 2005; Jiang et al. 2000; Xiong et al. 2005; Deng et al. 2004), but it is empiricaland not universal. The traditional depth- or width-averaged models of temperaturedistribution cannot accurately capturethe temperature transport and mixing inthree-dimensional flows, so it is necessary to simul中国煤化Ibution with athree-dimensional model. Politano et al. (2008)MHC N M H G-dimensional*Corresponding author (e-mail: tj_ fanfan@l63.com)Received Jan. 6, 2009; accepted May 25, 2009non-hydrostatic model to predict the temperature dynamics for the McNary Dam. The modeltook into account the short and long wave radiation and heat convection at the free surface. .Unes (2008) developed a three dimensional model that simulated the temperaturedistribution of a reservoir. Jing et al. (2002) used a three-dimensional model to simulate thetemperature distribution of a large reservoir over a long period. Qiu et al. (1997) used aturbulence model to simulate the three dimensional stratified flow. The simulation reflectedthe effect of non-homogeneous density and the computed results agreed with theexperimental data. Ren et al. (2008) developed a three-dimensional mathematical model onthe basis of analysis of the characteristics of large reservoirs and the regulation of watertemperature distribution in the Three Gorges Reservoir. In addition, Ren et al. (2007)developed a simple and convenient three-dimensional temperature simulation model toshorten the amount of computer processing time in temperature field calculation for deeplake reservoirs. Liu (2004) used the MIKE3 model to simulate the temperature distribution.In this study, a three-dimensional turbulent model was used to simulate and calculate thetemperature distribution of the Fenhe Reservoir, presently the largest reservoir in ShanxiProvince. The Fenhe Reservoir has a total design storage of 0.721 km' and a controlled drainagearea of 5268 km'. It is a Class II hydroproject mainly used for flood control, irrigation andpower generation. The Fenhe Reservoir is located in a narrow valley and has a width rangingfrom 200 m to 2200 m. It has a backwater with a maximum length of 18 km and a 32-km2backwater area with water flowing in mainly from the Fenhe River, Lanhe River and JianheRiver. The discharge is diverted by a power station (Fig. 1). The height, crest elevation, crestwidth, and length of the earth dam are 61.4 m, 1 131.4 m, 6 m, and 1002 m, respectively. Thesedimentation has already exceeded half of the storage capacity of the reservoir due to the highsediment concentration of the inflow. While the reservoir brings enormous social and economicbenefits, it may also impact the ecological environment and water use downstream. Changes inwater temperature may destroy the environment of natural aquatic animals, especially fish, andinfuence irrigation and domestic water use. In order to better develop and utilize waterresources and improve reservoir efficiency, it is necessary to predict the temperature structureof the reservoir and take appropriate measures for temperature control,In the three-dimensional model, topography, meteorological conditions, and changes ofdensity and water level are fully considered, so that simulation conditions accord with theactual conditions. The temperature distribution under different hydrological conditions wasanalyzed and the simulated results were verified with the measured data. The range of variationbetween discharge temperature and the natural river temperature under current operatingconditions was determined according to the simulated results. This allowed us to evaluate theneed for taking measures to control the discharge temperature.中国煤化工MHCNMHGShu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No.2, 32-423AFenhe Reservoir? Intake towerHydropower\gEstaton5 SilwyuneayFig. 1 Layout of Fenhe Reservoir2 Numerical model2.1 Governing equationsThe governing equations are as follows:the continuity equation:2u.=0(1)axthe momentum equation:Ou, e(u,u)__ 1 ap(2)ar ax,ρ ax,[(台管)Sm = Bg,ST(3)the convection-diffusion equation of temperature: ;aT、a(Tu)_ a( v, oTa(.haa ax,ax,(στ ax;) ax,(ρC ax,)+Sr(4)Sr=__18(5)ρCax,and the k - & equation:ak0k_ a|v，akau, 。u)\ou,_ RY aT-8-ε(6)atax; ax;(σ ax;))+{(ax, ax, Jax,σ ax;ac0E__ a(v aeσ,ah FCa2k;2(7)a。 a(oa,)"eanwhere x ( =1,2,3) is the coordinate system, in which不is the longitudinal direction,名isthe transverse direction, and x is the vertical direction: y. is the velocitv component in thexj direction;I is the time; ρ is the density of wat中国煤化工the tubulentYHCNMHG34Shu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No. 2, 32-42viscosity coefficient, which is equal to v, =_cqk2, C is the empirical constant; 8y is theKronecker function; h is the coefficient of molecular thermal diffusivity (W/(m:"C)); C is thespecific heat capacity (J/(kg:"C)); T is the temperature; k is the turbulent energy; ε is theturbulent kinetic energy dissipation rate; g, is the component of the gravitational accelerationin the x; direction; β is the volumetric expansion coefficient; Sm and Sp are the sourceitems of the momentum equation and the convection-diffusion equation, respectively; φ is theflux of solar radiation (W/m2) through the x plane; Ce, Ce2, σr, σ, and σr are theempirical constants (Table 1); and Co3 is the ratio of the velocity functions in the vertical andu,|longitudinal directions: Ce3 = tan", and Ce3 =0 when the flow direction is perpendicular|u4to the direction of gravity.Table 1 Empirical constantsCpCaCe2σστ0.091.921.1.3.92.2 Numerical simulationThe solution of the mathematical model employs the alternating-direction implicit (ADI)method for integration of the flow continuity equation and the momentum equation, whosemathematical matrix is solved with the double sweep method.2.3 Boundary conditionsThe boundary conditions of the three dimensional model are:(1) The topographical boundary: According to the geometry of the Fenhe Reservoir, arectangular grid is used to divide the reservoir area into units. The topography produced in thisway should accord with the characteristic curves of water-storage capacity.(2) The heat exchange boundary: The heat exchange at the reservoir surface generated byoutside temperatures and solar radiation should be determined. In particular, such data astemperature, humidity and precipitation during the simulation year should be collected.(3) Upstream boundary conditions: The inflow and temperature of every month of thesimulation year should be determined.(4) Downstream boundary conditions: The reservoir operation schedule and outflow forthe simulation year should be determined.(5) The resistance boundary of the river bottom: Because the gradient of the riverbed is aconstant, the resistance cofficient of each grid cell, which is determined by the roughness ofthe riverbed, is a constant.(6) The wind speed and wind direction of every中国煤化工/ear should bedetermined from measured data.YHCNMHGShu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No. 2, 32-4233 Parameter calibrationIn order to calibrate model parameters, the temperature distribution of the FenheReservoir was monitored at the end of April and July of 2008. The measurement points werearranged on three perpendicular lines in five sections in the range of 6 km in front of the dam.The results are presented as weighted averages of the data measured at the threeperpendiculars in a section.The temperature distribution of May, June and July of 2008 was simulated. The initialtemperature field was chosen according to the measured value of 9.5C from the 28th of April,2008. Some boundary conditions for temperature distribution simulation from May to July of2008 are shown in Table 2. The parameters were calibrated by comparison of simulated andmeasured values at the end of July.Table 2 Boundary conditions for temperature simulation from May to July of 2008Monthly mean inflowMonthly mean inflow Monthly mcan outflowMonthly mean waterMonthtempcrature (C)(m/s)level (m)May10.97.86 .10.721 120.36June14.814.329.391 119.88July17.911.596.461 120.63Fig. 2 shows the vertical temperature distribution in sections 1, 2, and 3 of the FenheReservoir, which are located, respectively, 0.98 km, 2.33 km, and 3.58 km in front of the dam, atthe end of July, 2008. The simulated results and the measured data were compared.Water temperature (9;)Water temperaure (C)Water temperature (C)1618202224262830161820 22262830_161820222426283012i 10- +Simulated= 12+ Measured14[12L(a) Section I(b) Section2(C) Section 3Fig 2 Comparison of temperaure distribution in sections 1, 2, and 3 at end of July, 2008As seen from these figures, the vertical distribution of the water temperature simulatedin each section follows a distribution pattern similar to the measured result, but thesimulated value is lower than the corresponding measured data at the surface. The cause ofthis phenomenon is as follows: the field monitoring was always carried out at noon, whenthe temperature at the surface reached 25"C, while the monthly mean temperature of theinflow boundary, which averaged the daily solar radiation for the length of the simulation,was only 17.9C，so the simulated value is lower than the corresponding measured value.The agreement between the measured data and simulated results of the temperaturedistribution validated the model's applicability. Th中国煤化工: model afercalibration are shown in Table 3.YHCNMHG36Shu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No.2, 32-42Table 3 Main parameter values of modelHorizontal diffusionVertical diffusionLight absorptionLight cxtinctionSun constant "WindCoemcrientcefficientcoefficicntcoefficientcofficicntcoffcient)0.20.60.2950.375Note: ") sun constant was determined by Angstrom's law; 2) wind ceofficient was determined by Dalton's law.4 Results and discussion4.1 Calculation conditionsAfter calibration, the model was adopted to simulate the temperature distribution ofthe Fenhe Reservoir in 1985, a normal year with a runoff probability P of 50%. There aretwo difficulties in simulating the temperature of the Fenhe Reservoir. One is the formationof a distorted cone region (70 m long, 55 m wide, and with a maximum depth of 15.2 m)due to serious sedimentation. The other is the influence of water diversion ftom the YellowRiver to the Fenhe River on water temperature distribution in the reservoir, which, due tothe high sediment concentration in water from the Yellow River, produces density flow infront of the dam.Based on elevation data provided by the Fenhe Reservoir Administration Bureau, wemade a topographical map. The rectangular grid system was adopted for partition of thecalculation range, and the calculation range of the reservoir mainly consisted of thebackwater area (about 10 km upstream of the dam). Based on the mean value of the monthlywater level, the vertical grid size was set at 1 m in each layer; the maximum layer numberwas 31, and the minimum layer number was 20; the horizontal grid was 100 mx100 m, themaximum number of cells being 11 076 and the minimum number of cells being 2110; thelength of time steps was 60 seconds; and the simulation period was a full year.The meteorological conditions adopted in the simulation were obtained by statisticalaverage of the long-term measured data of the Loufan weather station, which are shown inTable 4.Table 4 Statistical data from Loufan weather stationMonthTemperature (C)Rainfall (mm)January-8.01.8July21.7101.9February-5.14.August19.8105.4March1.49.2September14.465.3April9.720.5October8.27.6May16.4 .36.8November0.10.3June20.156.7December-6.5The heat exchange in the water during the freezing and thawing period was notconsidered, and 0"C was assumed to be the boundary of the water temperature during thefreezing period. The monthly mean temperature o中国煤化Ileservoir wascalculated by means of weighted statistical methodsYHCNMH Gm the JingleShu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No. 2, 32-423station and Shangjingyou station. The calculated inflow water temperature and monthlymean inflow to the Fenhe Reservoir for the normal year are shown in Table 5. The averageinflow and the runoff to the Fenhe Reservoir for the normal year are 8.3 m'/s and 0.26km',respectively. The calculated monthly mean outlow from the Fenhe Reservoir for the normalyear is shown in Table 6. The average outflow and the runoff from the Fenhe Reservoir forthe normal year are 4.86 m'/s and 0.15 km', respectively.Table 5 Monthly mean water temperature and mean infow to Fenhe Reservoir in 1985MonthWater temperatureMonthly meanWater lemperatureof inflow(C)inflow (m/s)of inflow (C)lanuary1.25July18.88.41February0.12.50August17.414.70March).15.08September11.826.10April3.95.44October6.110.00May2.115.40November4.74June15.3.86December2.07Table 6 Monthly mean outflow from Fenhe Reservoir in 1985outlow (m/s)outlow (m'/s)January0.034.020.070.043.970.0531.107.817.S39.770.064.2 Simulation resultsThe initial temperature field in early May was chosen to be 10°C, according to themeasured value of 9.5C from April 28, 2008 and the monthly mean temperature of 12.1Cfrom May, 1985. The calculation's starting time was May 1. The initial state was a uniformtemperature field with a temperature of 10°C. The linear interpolation algorithm was used tocalculate the flow rate and water temperature at the boundaries. The vertical distribution ofmonthly mean water temperature in the reservoir area was obtained along the central line ofthe longitudinal profile. We drew graphs for January, April, July and October of 1985 to serveas typical examples.In January, the reservoir water level was 1 116 m, the maximum depth in front of the damwas 26 m, the scouring funnel had a depth of 15 m, and the actual maximum depth of thereservoir was 11 m. As can be seen in Fig. 3, the reservoir showed a typical stratification ofwater temperature. Because of lower air temperature and colder water inflow, the surface ofthe reservoir froze. However, a thermocline existed 1-4 m below the water surface and thewater temperature rose from 1.1C to 3.6C. A constant temperature of 3.7C existed4 mbelow the surface. The monthly mean water temperature of the outflow was 3.75C.In April, the reservoir operated with a low water level, whose actual maximum depth wasonly 5 m, and the water temperature distribution in the中国煤化工aixed (Fig 4).，The water temperature in front of the dam reached 8YHCNMHGhilethewater38Shu-fang FAN et al. Water Science and Engineeing. Jun. 2009, Vol. 2. No. 2. 32-42temperature in the reservoir tail was lower because the monthly mean temperature of inflowwas only 3.9C. The monthly mean temperature of outflow in April was 8.32"C, higher thanthe temperature of inflow, so it was beneficial to the environment downstream.11181114Mean temperature(C1110g Above041 1061102|品01-02m -010三1098m -02--0,↓1 0941090Below-049876543210Below0410987654321Upstream distance from dam (km)(a) Vertical distribution(b) Surface distributionFig. 3 Water temperature distribution in January of 19851 1101106(化、310981094■Below4.5■Below 3609876543210109876543210Upstrcam distance from dam (km)Fig. 4 Water temperature distribution in April of 1985In July, the operating level rose to 1 113 m due to an increase in water inflow. At this time,the actual maximum depth of the reservoir was 8 m. There was stratification of watertemperature in front of the dam (Fig. 5). The temperature of the surface layer (within a depthof about 3 m) reached 20°C. A thermocline existed 3-5 m below the water surface, and therewas a constant temperature of 17C below 5 m. The monthly mean water temperature of theoutflow was 17.17C in July, which was 1.6°C lower than the water temperature of the inflowfrom upstream. Thus, the temperature would not significantly influence the ecologicalenvironment downstream.ean temperature(C)身1106号1102高1098= Below 17.0i Bclow 18010987654321 0Fig. 5 Water temperature distribution in July of 1985In October, the storage level rose to 1121 m and中国煤化工th was 16 m.MYHCNMHGShu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No. 2, 32-4239Because the season had changed, the temperature of the inflow decreased. The distribution ofthe water temperature changed after that. The water temperature mixed clearly and reached7-8C due to the changes in the surface layer and the deep layer (Fig. 6). The hot water in thereservoir was discharged by the drive of colder inflow and the outflow had a mean tempeatureof8.1 C, which was 2C higher than that of the inflow.1 122; Mean temperatureMean temperaure1118(C)百1144。Above 8004厂g Above 7?511107.50-7.751106-1 102-三1098-1094Below5.75109010 987654321 (109876543210Upstream distance from dam (km )Upstrcam distance from dam (km)(a) Vertical distribution(b) Surface distributionFig. 6 Water temperature distribution in October of 1985The vertical water temperature distribution in the normal year is shown in Fig. 7. Theresults indicate that the reservoir maintain steady stratification of temperature during thesummer and winter.- + January✧February 七 March- 0Apil-+May-士July- + September-号 October-七November-一 Decenber110110510 11416 18 20Water temperature (C)Fig. 7 Vetical temperature distribution in front of dam in each monthThe surface layer of the reservoir froze in December, January and February. Ice thicknesswas about 0.5 m, and the water temperature rose rapidly with increasing depth below the ice.The water temperature was about 1.3C at a depth of 1 m, and about 3"C at a depth of3 m.There was a constant temperature of 3.8-4C below 5 m. A clear thermocline existed 1-5 mbelow the water surface, as observed from the vertical stratification. In March, the ice of thereservoir warmed up and the vertical temperature structure gradually mixed.The operating water level of the reservoir in April, May and June was low because asubstantial amount of water was discharged during this period. Therefore, solar radiation andtemperature directly affected the bottom of the reservoir, causing the vertical temperaturestructure to mix completely. The water temperature in front of the dam reached 8.3°C in April, .中国煤化工11.8C in May, and 15C in June.IYHCNMHG40Shu-fang FAN et al. Water Science and Engineering, Jun.2009, Vol. 2, No. 2, 32-42 .In July, with the influence of high water temperature on the boundary, a stratifiedphenomenon of an upper and lower zone appeared in the reservoir. However, the watertemperature of the deep layer was higher when the water storage capacity was smaller. Ittherefore lessened the stratification. The water temperature at the reservoir surface was 20C,while the water temperature at the reservoir bottom was 17.5"C.The cooling period began in August. The weak stratification of the reservoirdisappeared gradually, and water temperature tended to mix in the vertical direction. Thewater temperature at the reservoir surface was 17.3C, while the water temperature at thereservoir bottom was 16.8C.The water level rose in September and October. The reservoir started rolling at the sametime, so the water temperature structure re-mixed. The water temperature in front of the damreached 12C in September and 7.9°C in October.The air temperature and water temperature decreased significantly in November, so thewater temperature showed stratification again. The water temperature at the reservoir surfacewas between 2C and 3C, while there was a constant temperature of about 4.3C below 3 m.Fig. 8 compares the monthly mean water temperature of the natural river channel and thereservoir outflow, and the two curves demonstrate a similar trend. From May to August, thetemperature of discharged water was lower than that in the natural river channel, and themaximum difference was less than 3 C, which would not have a great impact on downstreamareas. The temperature of discharged water was higher than that of the inflow water in otherperiods of this year, which would be beneficial to the downstream ecological environment.+ Inflow walter temperaluret Outlow walter temperatureot01234567891011 12MonthFig. 8 Comparison of monthly mean water temperature of reservoir inflow and outlow water5 Conclusions(I) A three-dimensional numerical model was employed to simulate the distribution ofwater temperature in the Fenhe Reservoir using a long-term hydrologic data series as well asmeasured data of reservoir water temperature in 2008. Results of model validation andparameter calibration show that the model is applicable for long-term simulation of a largedrainage basin.(2) As we can see from the simulation of the no中国煤化工ervoir showstemperature stratification in the summer and winter.:fYHCNMHGbetweentheShu-fang FAN et al. Water Science and Engineering, Jun. 2009, Vol. 2, No. 2, 32-4241inlet and the outlet was 1.6C in the summer and 3.6C in the winter. In the autumn and spring,the water temperature of the reservoir mixed and there was a constant water temperatureacross different depths.(3) The results showed that in 1985 the temperature of the reservoir outflow was thelowest in March, only 2.4C, but this was higher than the natural inflow temperature, whichwas 0.1"C. The temperature difference between the inlet and the outlet was 1.6C in thesummer, which was less than 3C, and would therefore not significantly influence thedownstream ecological environment.ReferencesDeng, Y, Li, J., and Luo, L.2004. Simulation on thermal stratification of the river-like deep reservoir. JourmalofHydrod)ynamics (Ser A), 19(5), 604 609. (in Chinese)Ferrarin, C, and Umgiesser, G 2005. Hydrodynamic modeling of a coastal lagoon: The Cabras Lagoon inSardinia, Italy. Ecological Modelling, 188(2- 4), 340-357. 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A 3-D numerical method for stratified flow with k-ε model.Journal of Hydraulic Engineering, 28(7), 7-12. (in Chinese)Ren, H. T, Chen, Y. C. Liu, Z. W., Shen, M. B., and Zhu, D. J. 2007. Study on water temperature simulationmodel for deep lake and reservoir. Journal of Hydroelectric Engineering, 26(3), 99-105. (in Chinese)Ren, H. T, Chen, Y. C., and Liu, Z. W. 2008. Study on water temperature prediction in Three GorgesReservoir. Journal of Hydrodynamics (Ser. A), 23(2), 141-148. (in Chinese)Unes, F. 2008. Analysis of plunging phenomenon in dam reservoirs using three-dimensional density flowsimulations. Canadian Journal of Civil Engineering, 35(10), 1138-1151. [doi:10.1139/ L08-061]Xiong, W, Li, K. F, Deng, Y, and Li, J.2005. Application of 1-D and 2-D coupling temperature model in theThree-Gorge Reservoir. Journal of Sichuan University (Engineering Science Edition), 37(2), 22-27. (inChinese)中国煤化工MHCNMHG42Shu-fang FAN et al. Water Science and Engineering, Jun.2009, Vol. 2, No.2, 32- 42