INFLUENCE OF LONG AND DEEPLY-BURIED DIVERSION TUNNELS ON THE WATER TEMPERATURE

695Journal of Hydrodynamics Ser. B 2004 ,16( 6 ) 695 -700China Ocean Press , Beijing - Printed in ChinaINFLUENCE OF LONG AND DEEPLY-BURIED DIVERSION TUNNELS ON .THE WATER TEMPERATURELI Ran ,LI Ke-feng ,LUO Lin , DENG YunState Key Hydraulics Laboratory of High Speed Flows , Sichuan University , Chengdu 610065 , China ,e-mail liran@ china. com( Received Sept. 12 ,2003 )ABSTRACT: A 3-D temperature model for diversion tunnel was ple , the diversion tunnel of the Nanya Hydropower Sta-developed by combining k-ε model and energy transport equation. .tion , located on the tributary of the Dadu River ，isThe aclual geometry data of the tunel was used to constuet a 7016m long and its buried depth is about 630m ; the di-three-dimensional computational domain including the concrete lin-version tunnels of the 1st and 2nd cascade hydropowering. As the interaction between temperature and velocity fields canstations of the Yuzixi River , a tributary of the Minjangbe taken into account , the model can be employed to accuratelyRiver , are 8429m and 7750m long respectively and theirsimulate the temperature and velocity field. The model was valida-ted with the field data observed in the diversion tunnel of the Nanyaburied depth are about 650m , the diversion tunnel of theRiver. The water temperature of the diversion tunnel of the Second2nd cascade hydropower station of the Jinping Station , toJinping Cascade Hydrpower Station to be built was predicted. lItis be built on the Yalongjiang River , is as long as 18km andshown that the temperature increase is not observable due to the its buried depth is as large as 2500m , being the longestlarge diameter of the tunnel ,the big flow rate and the short contact and deepest-buried tunnel in China. From the environ-time. The result can provide scientific foundation or reference formental and ecological consideration , the study on the in-the design of hydropower station , and protection strategy of aquaticfluence of long and deeply-buried diversion tunnel on theorganisms and aquatic ecosystem.water temperature is of theoretical and practical necessi-KEY WORDS : diversion tunnel , water temperature , numericalty.Many researchers studied the modeling of heat andsimulationmass transfer in engineering environmental problems 121,but most studies on turbulent flow are about reservoirs and1. INTRODUCTIONrivers' 371. At present the study about the influence of the .The construction of hydropower stations will influ- long and deeply-buried diversion tunnel on the water tem-ence the water temperature of natural streams and it is a perature is limited. CHDf 8 J observed temperature chan-very important issue for the protection of aquatic organ-ges of flow through natural diversion tunnels. Chen' 9isms and aquatic ecosystem. Many diversion hydropower simulated the water temperature in a diversion tunnel withstations are being built , in which the natural water flows numerical model. In Chen' s study , the von Karman lawthrough the diversion tunnels buried in mountains and was adopted and axial symmtrical advection and heatgoes into the generating chamber. The temperature of the transport equation was solved. The influence of the tem-inflowing water in those tunnels will be mainly affected by perature on the velocity field is neglected and the geome-the terrestrial heat. The longer and deeper the tunnel is，try of the tunnel is simplified to be a straight cylinderthe more the increase of the temperature will be.which中国煤化工tably. In recent years ,There are more than 10 diversion hydropower sta- the dev:HC N M H Gmerical simulation pro-tions in China in which the diversion tunnels are longer vides a new approach to the study of terrestrial heatingthan 4000m and the buried depths are large. For exam- offcts on the water temperature.。Pr品市齐据red by the National Natural Science Foundation of Chind( Grant No :50279025 ).696A 3-D temperature model for diversion tunnel was( 2 ) Momentum equation :established by combining the h-ε model and energy trans-port equation'1] The actual geometry data were used_ a( ρU;U;) =-+ [(μ+μ)to determine the computational domain including the con- d2crete lining. As the interaction between temperature andvelocity fields can be taken into account , the model canaU;、aU;(3 )(x+)]accurately simulate the temperature and velocity fields.The model was validated with the field observed data inRef.[ 8 ] The water temperature of the diversion tunnelwhereμ is the dynamic viscosity , and μ, is the turbulentof the second Jinping cascade to be built is predicted.viscosity ,given as :2.3~D TEMPERATURE MODEL FOR DIVER- μ, = ρC。k?(4)SION TUNNELThe concrete is usually used as lining material of di-(3 )k equation :version tunnels. In view of the difference of heat transferproperties between concrete and rock , the outer boundaryof the concrete lining is treated as the outer boundary of(pU;k);是[(μ+出)路]+C-pe(5)σT, )ax,the computational domain.The concrete lining region in the computational do-where G is the generation term and is given by :main is defined as the solid paot and solved with the heattransportation equation. The water flow region is definedas the fluid paot and solved with the fluid heat transporta- G = μaU， aU\aU;(6)x + x,)axtion model.2.1 Numerical model(4 )ε equation :2.1. 1 Heat transportation equation of concrete liningregionThere is no fluid flow in the concrete lining region ,dρU;)__ g+华)验]+C。aX= &[(u+σ。aX;Jonly is the convection effect is considered. The governingequation is written asEG-C2ep(7)g2T,=0(1)aX}( 5 ) Temperature equation :where T is defined as temperature of the concrete( C ) ,x( U;T)and X; represents the coordinate in the i direction( m ).ax,lc, +,)axJ(8)2.1.2 Fluid heat transportation modelThe fluid heat transportation model includes the con-whereλ is the heat conductivity( W/( m 9C ) ,and C, is .tinuity equation , momentum equation ,k equation ,ε e-the heat capacity at constant pressure( J/kg°C ).quation and temperature equation.In the above equations ,C。,σk ,σ。,C。and C2。are( 1 ) Continuity equation :the empirical constants and given as 0.09 ,1.44 ,i(pU;)=0(2)中国煤化工model are listed in Ta-0X;ble 1.TYHCNMHGAs the density is treated as the function of tempera-where U; represents the velocity component in the i direc-ture in the model , the interaction between the tempera-tion( m/s ) , and ρ the density of water which is the func-ture and the velocity fields can be considered.tion of ten而亦数据697Table 1 The material propertiesMaterialp( kg/m3 )C,[J/(kg C)]λ( W/(m C))Concrete .2700. 01130.01.28Wate( 4C )998. 24182. 00.62.2 Boundary conditionswhere Cks denotes the roughness constant and h:" is theThe boundary conditions include those at the inlet ，roughness height.outlet and wall boundaries.2.3 Solving method2.2. 1 Inlet boundaryThe typical finite volume method is adopted to solveThe inlet of the diversion tunnel is defined as the ve- the problem.locity-inlet where the velocity and temperature are provid-ed. The values of k and 8 are determined by empirical for- 3. THE MODEL VALIDATIONmulae.The Nanya Hydropower Station is a diversion power2.2.2 Outlet boundarystation located on the Nanya River , a tributary of theThe outlet of the diversion tunnel is defined as the Dadu River. Its diversion tunnel is 7016m long and thefree outflow boundary where the zero normal gradient for buried depth is about 630m. In order to understand theall scalar variables and normal velocity components are thermal effect of the diversion tunnel , the Chengdu Hy-applied. .droelectric Investigation and Design Institute carried out a2.2.3W all boundaryfield invesitigation in 1993. The inflow and outflow tem-The outer boundary of the solid zone is defined as peratures of the tunnel were observed respectively. 0wall boundary where the temperature is given by the fol- Feb. 13 , 1993 , the averaged water temperature at the in-lowing empirical formula :let is 8.2C and at the outlet is 8. 4C.T = 0.025( H-40 )+ 17(9)where H is the buried depth of the tunnel.The inner boundary of the solid zone is defined as-2808the wall boundary of the fluid zone. As the wall is madeof concrete , the Law-of-the-Wall modified for roughness-281is applied. The modified wall function has the form282 Ht品= L(erx,U2)-.- AB( 10)83 tU。K9.=8.5_-2844whereK E Up o。,U,are the Karman' s constant( =0.Y/m42 ) , empirical constant( = 9. 81 ) , mean velocity of thefluid at point P , distance from point P to the wall , fric-中国煤化工tion velocity , respectively ,and△B is the roughess func- Fig. 1MHC N M H Gitlet of Nanya Rivertion given byThe temperature changes through the tunnel weresimulated by use of the model developed above. The tem-△B = In(1 +cgh, )( 11 ) perature contours of the outlet boundary depicted arek.shown in Fig. 1. The averaged temperature computed of698the outlet boundary is 8. 44C. From Table 2 it can be the observed and simulated data. It shows that the resultseen that there is a small difference , 0.04C , between calculated is quite satisfactory and the model is capableTable 2 Comparison of field observed and computed temperature at the outlet of Nanya RiverInflowOutlowTemperatureErrorRelativeItemtemperatureincreaseerror(C)( C)Observed8.28.40.042%Computed8.440.24Table 3 Predicted temperature at the outlet of tunnel No. 1 Cascade of Jinping StationFlowVelocityMonthrate( m'/s)( m/s)1348.93. 679.4119. 4580.0472360.453.798.7768. 8270.0513374. 453.948. 9879.0350. 0483904.1111. 40511. 4410. 0362943.1014.51214.56063703.9016. 141 .16. 1780. 03774204.4216. 18516. 2230. 038817. 19617.232916. 32516. 3530.02903353.5314. 62014.6640. 043113483. 6612. 77612. 8243403. 5810. 83210. 8780. 045of predicting temperature for diversion tunnels to be built. side the_ lining is 11m. The maximum flow rate for eachtun中国煤化工vlocity is4. 42m/s.4.TEMPERATURE PREDICTION FOR JING-YHC N M H G of heat transfer proper-PING DIVERSION TUNNELties between concrete and surrounding rock , the predic-There are four diversion tunnels for the 2nd Jingping tion for the temperature changes through the tunnel NO. 1cascade to be built , the averaged length of which is 16. is carried out by using the model developed above.6km. The 2裂掩d diameter is 12m and the diameter in- 4. 1 Computational domain and mesh setup699Taking the concrete lining zone as part of the com- biggest increase of water temperature occurs in Feb. andputational domain , the three-dimensional computational the value is 0.051 C. The temperature increases in otherdomain is determined.months varies from 0. 029C to 0. 050C. The tempera-The mesh is uniform in the longitudinal direction and ture increase affected by the terrestrial heat is not obviousthe interval length is 50m. The mesh on the cross section in general( see Fig.4 ).is non-uniform on which the interval length range from 0.25m-1.5m. The mesh sketches are shown in Fig. 2 andFig.3.24日40.0N-26-280.0020-30L/km-32Fig. 4 Sketch of the terrestrial temperature along tunnel axisThe temperature contours in February ，when the34 Elargest temperature increase occurs , are depicted in Fig-4712 -47 10广/m5. It is concluded that the high temperature gradient ex-ists in the concrete lining zone and the temperature de-creases rapidly within the fluid zone. The water tempera-Fig.2 Mesh sketch on cross-section of Jinping Stationture on the axis of the tunnel changes litle compared withthat of the inlet.-24FZ联-26-\y-28-30Fig. 3 Mesh sketch on longitudinal-section of Jinping Station-344. 2 Boundary conditions-4712 47 10十The temperature of the flow discharged from the 1stX/mJingping cascade is taken as the inlet boundary in themodel. The velocity of the inlet is obtained from the gen-eration flow rate through the tunnel , and the values of k Fig. 5中国煤化工rlet in Februaryand ε are taken from the empirical formulae.ItYHCNMHGincrease of the water4.3Predicted resultstemperature Is8 attected by many tactors , such as the tem-The temperature changes of each month in a normal perature of surrounding rock , the temperature of the in-year are predicted by mean of the numerical model. Table flow water , the tunnel diameter ,the flow rate , etc. Since3 present芳数物putation results. It can be seen that the the large diameter and the big flow rate of the Jinping tun-700nel , the water stays very short time in the tunnel and thatdrodynamics ,Ser. B 2003 ,15(3 ):17-21.results in small temperature increase.[4] DENG Yun ,LI Jia ,LUO Lin ,ZHAO Wen-qian. Tempera-ture prediction model for reservoirs[ J ] Journal of Hy-draulic Engineering ,2003 ,( 7 ):7-11.( in Chinese )5. CONCLUSIONA 3-D temperature model for diversion tunnel has[5 ] NI Hao-qing. The application and development of turbulencemodel in buoyance back flow[ J ] Journal of Hydrody-been developed in this paper. The model was validatednamics ,Ser. A ,1994 ,9( 6 ) :651-665.( in Chinese )with the field data. The water temperature of the Jinping[6] DENG Yun. Study on the water temperature prediction mod-diversion tunnel to be built was predicted. It shows thatel for the huge and deep reservoir[ D ] PH. D. Thesis ,the inflow temperature increased through the tunnel is notChengdu : Sichuan University , 2003.( in Chinese )obvious due to the large diameter , the big flow rate and [7] KARPIK s. R. , RAITHBY G. D. Laterally avernged hy.the short conduct time in the tunnel. The result can pro-drodynamics model for reservoir[ J ] Journal of Hydraulicvide scientific foundation and/ or reference for the designEngineering , 1990 ,116( 6 ) :793-798.of similar projects and the protection of aquatic organisms[8] CHENGDU HYDROELECTRIC INVESTIGATION AND DE-SIGN INSTTTUTE( CHDI ). Study on the influence of longand aquatic ecosystem.diversion tunnels on water temperature , Technical Report ,1994.[9 ] CHEN Ming-qian. Mathematical model for the system of ter-REFERENCESrestrial heat , surrounding rock and fluid about undergroundtunnel<[ D ]. Mather Thesis , Chengdu : Chengdu University[1 ] NI Hao-qing , SHEN Yong-ming. Numerical modeling ofof Science and Technology , 1991.( in Chinese )turbulent flows， heat and mass transfer in engineering [ 10 ] WOLFGANG Rodi. Turbulent models and their applica-environmental problemC[ M ] Beijing : W ater Conservan-tions in hydraulics[ M ] Delft , The Netherlands IAHRcy and Hydroelectric Power Press , 1996. ( in Chinese )Publication , 1984.[2] JIN Haisheng ,ZHANG Shu-nong. Numerical simulationof [11] PATANKAR s. v. Numerical heat transfer and fluidstratified flow with both vertical temperature gradient andflows[ M ] New York : MeGraw Hill , 1980.vertical salinity gradien[ J ]. Journal of Hydrodynamics ,Ser. A ,1991 ,6( 4 ) :72-78.( in Chinese )Biography :LI Ran( 1968- ) , Female ,Doctor , Associate[3] HU Zhen-hong , SHEN Yong ming. Calculation of thermal .Professorand saline turbulent flow by k-ε mode[ J ] Journal of Hy-中国煤化工MYHCNMHG