The TI8 tunnel will house a proton beam transfer line of 450 GeV from the SPS to the LHC collider. This line will comprise 340 classical compact design magnets which are expected to dissipate about 120 W/m to the air along the tunnel. As the ventilation injection and extraction points are separated by approximately 2.5 Km (the length of the tunnel), a significant increase in the air bulk temperature is expected along the distance. This report presents an estimation of the air temperature evolution with time at the end of the tunnel

Pimenta dos Santos, M A

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHORGANISATION EUROPÉENNE POUR LA RECHERCHE NUCLÉAIRECERN - ST DivisionCERN-ST-2000-061CERN-ST/CV-2000-27713 July 2000THERMAL TRANSIENT ANALYSIS OF TI8 TUNNELM. A. Pimenta dos SantosAbstractThe TI8 tunnel will house a proton beam transfer line of 450 GeV from the SPS tothe LHC collider. This line will comprise 340 classical compact design magnets whichare expected to dissipate about 120 W/m to the air along the tunnel. As the ventilationinjection and extraction points are separated by approximately 2.5 Km (the length of thetunnel), a significant increase in the air bulk temperature is expected along the distance.This report presents an estimation of the air temperature evolution with time at theend of the tunnel.2T, air temperatureTROCK, geothermal fixed temperaturedc, outer wall thicknessdiw, inner wall thicknessdr, distance from rock-concrete interface to point offixed temperature TROCK.Rtotal, Conduction resistance from inner wall to pointof fixed temperature TROCKR, equivalent cylinder radiusP, perimeter of contact air-wall for one tunnel sectionr, radial coordinatez, axial coordinatew, air average axial velocitydz, control volume lengthTPULSION, tunnel inlet air temperatureTEXTRACTION, tunnel outlet air temperatureVair, volumetric rateVCV, moving control volumehCONV, heat transfer convection coefficientTiw, inner wall temperatureCiw, inner wall specific heatriw, inner wall volumetric massKiw, inner wall thermal conductivityTow, outer wall temperatureCow, outer wall specific heatrow, outer wall volumetric massKow, outer wall thermal conductivityCp, air specific heatr, air volumetric massK, air thermal conductivity1. INTRODUCTIONThe TI8 tunnel will house a large number of conventional magnets dissipating heat ata considerable rate during periods of several hours with short pauses in between. Otherthan the magnets, other heat sources such as cables, water return pipes, lights, etc willgenerate heat continuously. Starting from fixed ventilation parameters of inlettemperature 17ºC and a flow rate of 22500m3/h, the calculations presented in this paperseek to estimate the transient air temperature evolution at the end of the tunnel for twodifferent magnet operating cycles.List of Symbols2. PROBLEM DESCRIPTION2.1 GeometryFig.1 – TI8 tunnel wall and interior cross-sectionalviews3Fig.1 represents a cross-section of the TI8 tunnel. In this report, the mass ofconcrete interior to the surface defined by the drainage membrane will be referred to asInner wall. Conversely, Outer wall will refer to all the mass of concrete exterior to thesurface defined by the drainage membrane. As indicated in Fig.1, the outer wallthickness, dc, is variable from point to point thus unknown. The 5cm gap between thetwo walls contains a 1cm thick plastic drainage membrane and the rest of the volume isfilled with air. For the purpose of thermal calculations, this membrane will be ignoredand the gap will be assumed as containing only air and referred to as air gap.2.2 Ventilation data and Thermal LoadsVentilation data:Volumetric rate, Vair = 22500m3/h = 6.25m3/sArea tunnel (free), A=5.55m2  Þ air speed, w=1.13m/sTpulsion=17°CThere are four different types of magnets, each one dissipating heat at a differentrate as shown in Table 1. Approximately 90% of this heat is assumed to be transferred tothe appropriate water cooling circuit incorporated in each magnet, whereas the remaining10% is assumed to be transferred to the air. The magnets are the only variable heat loadsin the tunnel and follow a time history as shown in Fig.2. Constant heat loads includeelectrical cables, water pipes and other equipment. Table 1 - Thermal loads1)Magnet Type Power per magnet QuantityMBI 1.1 kW ´ 236 = 2596 kWMQI 2.2 kW ´ 86 = 189.2 kWB340 7 kW ´ 12 = 84 kWB280 8.5 kW ´ 6 = 51 kWtotal power 2920.2 kWPower loss to the air: 0.1 ´ total power            292.01 kWPower/meter 116.8 W/mConstant thermal loads:Cables 57 kWWater pipes 11 kWOthers 11 kWtotal 79 kWPower/meter 31.6 W/m1) Data kindly provided by Mr. Volker Mertens  from SL/BT Group.4Fig.3 – TI8 tunnel and equivalent cylinder having the same free and concrete areaFig.2 – Heat load time historyIn the current paper, calculations will be carried out for three different magnetoperating patterns: continuous operation, 6 hours operation followed by a 2 hours pauseand 8 hours operation followed by a 2 hours pause.3. GOVERNING EQUATIONS OF THE THERMAL PROBLEMThe air temperature at the end of the tunnel is highly dependent on the rate of heattransfer to the walls along the distance. In the worst case, if walls were adiabatic thetemperature at the end of the tunnel for continuous operation of the magnets would becalculated as follows:Total power into the air (variable+constant), Q =   292.01+79 kW = 371.02 kWFor air at 40°C (average temperature along the distance), the following properties apply: r  = 1.122Kg/m3Cp =1004 J/Kg.KCpVQTTairPULSIONEXTRACTION ××+=rTEXTRACTION » 69.5°CTo render the problem computationally affordable, some simplifications must bemade. The first is to consider an equivalent cylindrical tunnel having the same free andwall cross-sectional area as the real tunnel, asshown in Fig.3. The radius R of such acylinder is calculated in appendix I. The areaof contact wall-air for convective heat transferpurposes remains the same as in the realtunnel.3 07 01 1 01 5 0t ime  P o w e r  ( W  /  m )magnets ON magnets OFFVariable + Constant Loads= 116.8 W/m +31.6 W/m= 148.4 W/mConstant  Loads= 31.6 W/m5Another important simplification is to assume uniform air temperature at a givencross-section and moment in time i.e. to consider the flow as being 1-Dimensional. Underthese hypotheses, a heat balance can be written for a control volume VCV of air movingalong with the flow at speed w (see Fig.4):( ) ( )),,(),()(),(),(),(),( tzRrWtzCONVtEtztztzCVtz TThdzPdzqzTwtTCpV =-××-×=÷÷øöççèæ¶¶+¶¶×× &r      ( 1 )whereR is the equivalent cylinder radiusP.dz is the area of contact air-wall (see Appendix I)( )),,(),( tzRrWtzCONV TThdzP =-××  is the heat transferred to the wall by convectionqE(t) is the heat dissipated per meter by the equipment (magnets, cables, etc)Vcv , the moving control volume is given by Vcv = 2pR.dzzTwtT¶¶+¶¶ is known as the substantial derivative and accounts for the fact that thecontrol volume follows the flow, i.e., T=T(z,t) Þ zTwtTdtdT¶¶+¶¶=Fig.4 – Moving control volume considered for the heat balanceThe temperature in the wall is a function of r, z and t and obeys the followingequation (in cylindrical coordinates and symmetry with respect to the axis):6mWKKRdiwRRiwiW./025.037.12329.132.0329.1ln2ln=×÷øöçèæ +=×÷øöçèæ +=ppmWKKdiwRdiwRRag ./182.002624.0232.0329.105.032.0329.1ln205.0ln=×÷øöçèæ+++=×÷øöçèæ+++=pptTCzTKrTrKrTKrtzrWrWrWtzrWrWtzrWrWtzrWrW ¶¶×=¶¶+¶¶×+÷÷øöççèæ¶¶¶¶×),,()()(2),,(2)(),,()(),,()( r      ( 2 )and the coupling between wall and air temperature being given by:( )RrWWtzRrWtzCONV rTrKTTh== ¶¶-=- )(),,(),(      ( 3 )3.1 Some justified simplificationsAlthough equation (2) is the exact description of the temperature evolution in thewall, it complicates considerably the solution of the whole system of equations (1), (2)and (3). However, the problem can be simplified significantly if the following hypothesesare made:i) Conduction resistance is ignored for the inner wall, i.e. the temperature isconsidered uniform at any given instant for R¢r¢R+ diwii) Temperature is fixed to the geothermal temperature (Trock) at a certain point inthe rock (see Fig.5)iii) Thermal heat capacity is ignored for the outer wall and for the rock.iv) Conduction along z is neglectedThe type of simplification made in (i) is called the lumped-heat-capacity method.Such system is obviously idealized because a temperature gradient must exist in theconcrete if heat is to be conducted into or out of the inner wall. The assumption ofuniform temperature distribution throughout each cross-section of the inner wall isequivalent to saying that the surface-convection and air gap resistance are large comparedwith the internal-conduction resistance as shown below:Internal- conduction resistance per meter lengthof equivalent cylinder is:Air gap resistance per meter of length ofequivalent cylinder is:Convection resistance per meter of length of tunnel (see Appendix II)0.020 K/ W.m £CONVCONV hPR×=1  £ 0.06 K/ W.m7so Riw compared witht Rag+Rconv is:12.01.0 £+£CONVagiwRRRSimplification (ii) is equivalent to assuming that at a certain distance from theouter wall, the mass of rock is large enough to absorb heat without having its temperatureincreased in the process.Simplification (iii) stems from (ii) and means that none of the heat conductedfrom the inner wall through the air gap is absorbed and used to raise the temperature ofthe outer wall and rock.Conduction along z can be neglected since wall temperature gradients in thisdirection are very small. Fig. 5 shows the simplified thermal model and the equivalentelectrical circuit.Fig.5 – Simplified thermal model and equivalent electrical circuitWith the simplifications introduced above, equation ( 2 ) and (3) are replaced by:totalROCKtziwtziwtzCONViwiwiwiwRTTTThdzPtTVC---××=¶¶××× ),(),(),( )(r                     ( 4 )83.2 Discretization of the  Governing EquationsEquations (1) and (4) can now be discretised using the following approximationstTTtT ntnttzD-»¶¶-1),( (5a)zTTzT ntnttzD-»¶¶ -1),( (5b)ntiwnttzRriwtz TTTT 111),,(),( ---= -»- (5c) tTTtTntiwntiwiwD-»¶¶ -1 (5d)to become, after some rearrangements,( ) úûùêëé×××D+-×××D-+= ----- 211111221RCpqtTThRCptTTT EntiwntCONVntntnt prr                   (6)and( ) ( ) ntiwntiwtotalwwiwntiwntCONViwiwiwntiw TTrockTRVCtTThVCtwRT 1111122----- +-D--××D××=rrp         (7)A computer code in FORTRAN77 was written to solve this system of equations.As justified in Appendix III, Rtotal ranges from 0.0093 K/W to 0.013 K/W. Likewise, asjustified in Appendix II, hconv ranges from 1.8 W/K.m2 to 5.4 W/K.m2. Taking intoaccount the geothermal gradient, the rock temperature Trock, at the TI8 tunnel averagedepth (75 m), is in the vicinity of 12ºC. It is also shown in Appendix IV that with acontrol volume length of dz = 25m, convergence of solution is secured.94. RESULTS4.1 Case 1: Magnets Operating ContinuouslyFig.6 and Fig.7 represent air temperature evolution at the end of the TI8 tunnel forthe two extreme values of hCONV. It can be seen that temperature reaches 22°C to 29°C inafter one day and stabilises between 40.5°C and 47°C after 23 to 26 days. It can also benoticed that in the short term hconv is the major influence on the temperature variabilitywhereas the influence of Rtotal becomes important only in the short to long term.Fig. 6 – Air temperature evolution at the end of tunnel TI8 for magnets operating withoutinterruption and hCONV =1.8 W/Km2Fig. 7 – Air temperature evolution at the end of tunnel TI8 for magnets operating withoutinterruption and hCONV =5.4 W/Km217.522.527.532.537.542.547.51 6 11 16 21 26 31time (days)T(C)hconv=1.8W/Km2, Rtotal=0.0093 K/Whconv=1.8W/Km2, Rtotal=0.013 K/W17.522.527.532.537.542.547.51 6 11 16 21 26 31time (days)T(C)hconv=5.4W/Km2, Rtotal=0.0093 K/Whconv=5.4W/Km2, Rtotal=0.013 K/W104.2 Case 2: Operation Cycle 8h ON + 2h OFFFig. 8 – Air temperature evolution at the end of the tunnel for a cycle 8h + 2h and  hconv = 1.8 W/K.m2Fig. 9 – Air temperature evolution at the end of the tunnel for a cycle 8h + 2hand hconv = 5.4 W/K.m22022.52527.53032.53537.54042.5451 6 11 16 21 26 31time (days)T(C)hconv=1.8 W/K.m2, Rtotal=0.0093K/Whconv=1.8 W/K.m2, Rtotal=0.013K/W2022.52527.53032.53537.5401 6 11 16 21 26 31time (days)T(C)hconv=5.4 W/K.m2, Rtotal=0.0093K/Whconv=5.4 W/K.m2, Rtotal=0.013K/W114.3 Case 3: Operation Cycle 6h ON + 2h OFFFig. 10 – Air temperature evolution at the end of the tunnel for  a cycle 6h +2hand  hconv = 1.8 W/K.m2Fig. 11 – Air temperature evolution at the end of the tunnel for for  a cycle 6h +2hand  hconv = 5.4 W/K.m22025303540451 6 11 16 21 26 31Time (days)T(C)hconv=1.8 W/Km2, Rtotal=0.0093 K/Whconv=1.8 W/Km2, Rtotal=0.013 K/W2025303540451 6 11 16 21 26 31Time (days)T(C)hconv=5.4 W/Km2, Rtotal=0.0093 K/Whconv=5.4 W/Km2, Rtotal=0.013 K/W125. SUMMARY OF RESULTSTable 2 summarises results from Fig.6 to 11. It can be seen that the uncertaintiesin the wall thermal behaviour as well as in the air-wall heat transfer coefficient lead towide limits for the expected temperature in the tunnel. Nevertheless, the calculationsshow that pauses of two hours cause only a reduction of about 4°C from the steady statetemperature reached with continuous operation. Moreover, when shortening the time ‘ON ‘ from 8h to 6h, the temperature drop achieved in the steady state is merely 1°C.Table 2 – Summary of estimated limits for temperature at the end of TI8 tunnelMagnets’Operating PatternTemperature after 1 dayStabilised TemperatureCase 1:ContinuousOperation22°C£T£29°C 40.5°C£T£47°Creached after 22 to 28 daysCase 2:8h ON + 2h OFF 22°C£T£28.5°CWhen Magnets are ON  37°C£T£43.6°CWhen Magnets are OFF  32.5°C£T£38.5°Creached after 25 to 30 daysCase 3:6h ON + 2h OFF 22°C£T£28.5°CWhen Magnets are ON  35.9°C£T£42.7°CWhen Magnets are OFF  31.8°C£T£37°Creached after 25 to 30 daysIt also stands out from the same plots that an increase in the convection heattransfer coefficient reduces the amplitude of temperature variation between periods ONand OFF. This can be explained by the fact that when magnets are ON, heat is transferredfrom the air into the walls whereas when magnets are OFF part of this heat is returnedback to the air. A higher heat transfer coefficient means more heat being returned to theair during the period OFF and thus a smaller drop in air temperature from the precedingperiod ON.Only the temperatures at the tunnel outlet were presented in this report. Thecorresponding values for any other point at any instant can be obtained by with goodapproximation by interpolating linearly between the inlet and outlet temperatures for thatsame instant.136. CONCLUSIONSFor an inlet temperature of 17°C and volumetric rate 22500m3/h, air temperaturesat the end of TI8 tunnel are expected to range between 22°C and 29°C after 24 hours ofoperation. For cycles of 6 to 8 hours of magnet operation followed by 2 hours pauses, theair temperature is expected to stabilise between 36°C and 44°C after a transient monotoneevolution of 25 to 30 days.If magnets are operated without pauses, temperature at the end of the tunnelstabilises between 41°C and 47°C after 22 to 28 days.7. ACKNOWLEDGEMENTI wish to acknowledge the help of Dr. Guillermo Peon from ST/CV in themathematical formulation of this problem.14APPENDIX I - Calculation of equivalent cylinderTI8 Tunnel area = 6.27 m2TI8 Tunnel free area: (blue area on Fig. AI.1) = 5.55 m2Inner wall area :(red area + green area on  Fig. AI.2) »2.99 m2Equivalent cylinder radius: mR 329.155.5 ==pThe equivalent cylinder inner wall thickness, diw, iscalculated to maintain the same volume of concrete:( )[ ] 222 99.2 mRdiwR =-+p  ® diw = 0.32mNote: the inner wall thickness for the real tunnel variesfrom 0.25m (red area) to 0.5m (green area).For convection heat transfer calculation purposes, the areaused was that of the real tunnel, i.e. P.dz where P is thewall exposed perimetermwP 15.9360)1802(5.12236.2 =+´´+= pwith w » 42°Note: the exposed perimeter for the equivalent cylinder is 8.35mFig. AI.1Fig. AI.215APPENDIX II - Calculation of hconvCalculations are based on the equivalent cylindrical tunnel defined in APPENDIX IReynolds number: Prandtl number for air at 300K:5510002.2105.1329.1213.1.2.Re ´=´´´== -airRwuPr=0.707For fully developed turbulent flow, convection heat transfer can be calculated by theexpression recommended for smooth pipes by Dittus and Boelter1:3.08.0 PrRe023.02××=Rkhconv23.08.05 57.3)707.0()10002.2(023.0329.1202624.0mKWhconv ×=´×××=However, the assumption of smooth pipe is somehow idealistic, as the tunnel ispartially obstructed with equipment (see Fig.1) and is not cylindrical. This modifiesconsiderably the velocity profile and introduces uncertainty on the value of hconv howeverit is reasonable to assume an error margin of 50%, i.e.1.8 W/K.m2 £ hconv £ 5.4 W/K.m21) Dittus, F.W., and L.M.K. Boelter: Univ. Calif. (Berkeley) Pub. Eng.,vol.2, p.443,1930.16APPENDIX III – Variability of RtotalFig. AIII-1 – Simplified Thermal model and equivalent electrical circuitThe total conduction resistance is Rtotal  = Rag + Row + Rcontact+ Rrock and isgiven, for a tunnel segment of length dz, by the formulae below. Note that R=1.329 mand diw=0.32 m as calculated in appendix I. The outer wall thermal conductivity, Kow =Kiw =1.37 W/m.K  (conductivity of concrete obtained from  Holman J.P., 1997, HeatTransfer, McGraw-Hill, New York). The inner wall thermal capacity is given by M=riw 3Ciw 3p{(R+diw)2-R2) }.dz .Table 3   - Components of RtotaldzKdiwRdiwRRag××÷øöçèæ+++=p205.0lnAir gap conduction resistancedzKdiwRdcdiwRRowOW ××÷øöçèæ+++++=p205.005.0ln Outer wall conduction resistancedzKdcdiwRdcdiwRRcontact××÷øöçèæ+++++++=p205.001.005.0lnContact resistance between the outer walland the rock was assumed as beingequivalent to 1cm of airdzKdcdiwRdrdcdiwRRrockROCK ××÷øöçèæ+++++++++=p201.005.001.005.0ln Rock conduction resistance to the pointwhere temperature is fixed at TrockThe outer wall thickness dc, the length dr of rock to the point of fixed temperatureTrock and the rock conductivity Krock are needed to calculate Rtotal. The two former1700.0050.010.0150.020.0250.030 1 2 3 4Krock (W/m.K)Rtotal (K/W)dc=0.5m,dr=5.0mdc=0.1m,dr=0.5mparameters vary from point to point yet it is reasonable to assume the following limits fortheir variation:0.1m < dc <  0.5m 0.5m < dr < 5.0mThe type of rock found at the typical depth of CERN tunnels is known as ‘greensandstone’ (‘molasse’ in French) and is a mixture of sedimentary rock of compressedsand and marl ( mixture of clay and lime). Table 4 shows the thermal conductivity valuesfor this particular green sandstone, obtained from O. Johansen : Thermal Conductivity ofsoils. Ph.D. Thesis – Trondheim 1975.Table 4 – Thermal conductivity for each component of green sandstonetype Conductivity (W/ m. K) % in Geneva’s green sandstonesandstone 3.560.9 45marl sandstone 3.060.8 26marl 2.660.7 29weighted average 3.160.8 100Thus, the value of Krock will be considered to vary in the interval2.3 W/m.K < Krock < 3.9 W/m.KRtotal  for Krock = 2.3 W/m.Kdc = 0.1m dc = 0.5mdr = 0.5m 0.0096 0.01dr = 5.0m 0.013 0.013Rtotal   for Krock = 3.9 W/m.Kdc = 0.1m dc = 0.5mdr = 0.5m 0.0093 0.0099dr = 5.0m 0.011 0.011Fig. AIII-2 – Dependence of Rtotal on the value of Krockfor extreme values of dc and drSo calculations will be done forRtotal= 0.0093 K / W and 0.013 K / W to cover the whole range of values

Thermal transient analysis of TI8 tunnel

Abstract

Similar works

Full text

Available Versions

CERN Document Server