Fully coupled numercal smulaton of fre n tunnels: from fre scenaro to structural response F. Pesavento 1 B.A. Schrefler 1 D. Gawn 2 J. Prncpe 3 1 Dept. of Cvl Envronmental and Archtectural Eng. Unversty of Padua Padua Italy 2 Dept. of Buldng Physcs and Buldng Materals Tech. Unversty of Lodz Lodz Poland 3 CIMNE Unverstat Poltècnca de Catalunya Barcelona Span Keywords Tunnel fre scenaro coupled smulaton multphase porous materal damage pressure Abstract In ths paper we present an effcent tool for smulaton of a fre scenaro n a tunnel. The strategy adopted s based on a 3D-2D couplng technque between the flud doman and the sold one. So the thermally drven CFD part s solved n a three dmensonal cavty.e. the tunnel and the concrete part s solved on 2D sectons normal to the tunnel axs at approprate ntervals. The heat flux and temperature values whch serve as couplng terms between the flud and the structural problem are nterpolated between the sectons. Between the sold and the flud doman an nterface layer s created for the calculaton of the heat flux exchange based on a wall law. In the analyss of the concrete structures concrete s treated as a multphase porous materal. Some examples of applcaton of ths fully coupled tool wll be shown. 1. Introducton The avalablty of an effcent tool for smulaton of a fre scenaro n a tunnel s of paramount mportance for fre safety management n emergency stuatons for tranng of fre brgades pror to emergency cases n order to be able take the rght decsons when needed and to evaluate measures geared to ncrease the resstance of exstng tunnel vaults aganst spallng. We have developed such a tool whch takes the thermal flud-structural couplng n a tunnel fre fully nto account [1]. It appears as one of the largest coupled problems actually solved n the communty of computatonal nteracton problems. The smulaton of a realstc fre scenaro s stll a tme consumng task and the tool s not yet completely ready for the frst of the above mentoned three goals. One of the bottlenecks s the heavy computatonal burden lnked wth the three fluds model for concrete. It s not possble to dsregard the enormous heat snk the tunnel vault represents wth the phase changes and chemcal reactons gong on n heated concrete. Such an omsson can yeld temperature felds also some 1000 C above measured ones n an experment. On the other hand smplfcatons of these phenomena are not possble as hghlghted n two recent companon papers [23]. In the exstng model [1] we have chosen a 3D-2D couplng strategy where the thermally drven CFD part s solved n a three dmensonal cavty.e. the tunnel and the concrete part s solved on 2D sectons normal to the tunnel axs at approprate ntervals. The heat flux and temperature values whch serve as couplng terms between the flud and the structural problem are nterpolated between the sectons. Wth ths approxmaton the heat transfer n the tunnel vault n the drecton of the tunnel axs s dsregarded. As an example wth such an approach the fully coupled smulaton on a realstc 1
tunnel for a fre of 20 MW of the duraton of one hour lasts more than three days on a hghend workstaton. The am of our current research effort s twofold: realze a true 3D-3D couplng on one hand and reduce drastcally the computng tme on the other hand. The way for achevng ths s through adopton of an extremely fast equaton solver whch can acheve a speed-up of up to 3600 tmes [4]. At the same tme the on-gong research ams also at the assessment of varous methods to lmt the consequences of a fre n the tunnel. In partcular n the framework of HYDROFIRESHOCK project the research team s evaluatng the effectveness of an nnovatve fre suppresson system. 2. Interface condtons and couplng strategy To solve the thermo-mechancal problem on the doman Ω we consder a geometrc doman decomposton of the problem by means of a non-overlappng subdoman approach. We splt the doman nto the flud and structural subdomans as Ω = Ω S Ω F. The condtons to be satsfed at the nterface are the contnuty of the temperatures and veloctes as well as the normal components of heat fluxes and tractons. If we denote by Γ SF (t) the surface of the tunnel walls these condtons read v F Γ SF = u S Γ SF n σ F Γ SF = n σ S Γ SF T F Γ SF = T S Γ SF n q F Γ SF = n q S Γ SF (1) where t s explctly noted that Γ SF (t) s actually a movng surface and ts poston depends on the soluton of the structural problem. The approxmatons proposed n [15] are based on two assumptons: 1. The veloctes of the sold medum are small (compared to the dmensons of the tunnel). 2. The mechancal tracton produced by the flud on the sold s small. These assumptons result n u S 0 and n σ F 0 and therefore the boundary Γ Γ SF (t) SF remans fxed and the nterface condtons become: v F Γ SF = 0 n σ F Γ SF = 0 T F Γ SF = T S Γ SF n q F Γ SF = n q S Γ SF (2) Thus the couplng between the sold and the flud s due to the thermal problem only. A further approxmaton was developed n [5] to consder the problem of the strong boundary layers present n a turbulent flow. Ths second approxmaton s based on a non-overlappng 2
doman decomposton of the problem n three subdomans one n the sold regon and two n the flud regon. One of the flud subdomans wll be a thn regon of thckness δ near the sold surface and the other wll be the rest of the flud doman. Usng the well-known wall functon approach [6] the problem n boundary layer s approxmately solved and an teraton strategy between the remanng subdomans s proposed. Therefore ths second approach also nvolves two subdomans but the nterface condtons now read: t ΓSF = γ v F Γ SF n F v F Γ SF = 0 n S σ S Γ SF = 0 (3) and n S q S = n Γ SF F q F = α Γ SF c ( ϑ F ϑ Γ SF S Γ SF ) (4) where t s now the tangental stress actng on the flud t = n σ F ( n σ F n)n ΓSF (5) and γ and α c are parameters that depend on the wall functon coeffcents. The frst one s computed from the unversal velocty profle assumed n the wall functon approach as usual [6]. The second one could also be computed n a smlar fashon but t s estmated from expermental values n ths work. It s also mportant to remark that we do not consder any mass exchange between the sold and the flud. Consderng a geometrc doman decomposton of the problem by means of a nonoverlappng subdoman approach we expect to construct the soluton problem from the soluton of local problems for the flud and the structure usng the nterface condtons above descrbed. Ths s carred out by teratvely solvng local problems on each doman untl convergence on the nterface condtons s satsfed that s to say we use an teraton-bysubdoman strategy. The descrpton of the local problems for the concrete structure (.e. the sold doman) and the flud doman s beyond the scope of ths paper. In the followng we just descrbe brefly the couplng strategy between the local problems. If L denotes the dfferental operator on the doman and B the dfferental operator on the boundary the stuaton s as follows. On the flud regon we solve at the teraton of each tme step: L F ( T F ) = f F n Ω F B F ( T F ) = g F n Ω F Γ SF 1 B FS ( T F ) = B FS ( T F ) n Γ SF (6) where boundary condtons on Γ SF depend on the soluton of the structural problem at the prevous terate. On the structural doman we solve at the -th teraton 3
L S ( T S ) = f F n Ω s B F ( T S ) = g F n Ω S Γ SF k B SF ( T S ) = B SF ( T F ) n Γ SF (7) where we can take k = or k = 1. In the frst case the soluton of ths problems s sequental whereas n the second one t can be parallel. The choce of the boundary condtons of the local problems should be such that presented nterface condtons are satsfed when convergence s acheved. It s well known from the theory of doman decomposton methods that n the case of non-overlappng subdomans we can choose Drchlet-Neumann(Robn); Neumann(Robn)-Drchlet or Robn-Robn. In ths work we apply the nterface condtons already descrbed. One mportant pont of ths strategy s that we already have programs that solve the flud dynamcs problem and the structural problem. Then a master/slave algorthm was mplemented by developng a thrd code (the master code) n order to control the teratve process. The MPICH2 lbrary an mplementaton of the MPI-2 standard provdes functons for process communcatons that are used to nterchange the data needed to apply boundary condtons on each dedcated (slave) code. Some mnor modfcatons on these codes are needed n order to exchange data wth the master. In order to perform a calculaton nput data for each subproblem needs to be generated and the master code starts the calculaton by startng the slave process (ths s only possble under MPI-2 standard). Durng the calculaton the master code needs to defne the boundary condtons to be appled on each subproblem. A partcular aspect of ths mplementaton s the need of couplng a two dmensonal code wth a three dmensonal one. On the one hand due to the hgh number of state varables of the structural model only two dmensonal calculatons are performed usng the structural code. On the other hand three dmensonal calculatons can be performed usng the flud dynamcs code. Therefore the three dmensonal concrete tunnel vault s approxmated by several two dmensonal sectons and varables are lnearly nterpolated to generate boundary condtons on the flud. Ths task s also performed by the master code. The values of the temperature or heat flux to be appled as boundary condton on an nterface node need to be calculated from the temperature on the other subdoman. Ths s done by fndng the host element and nterpolatng. The element search strategy used s based on the quad-tree algorthm. 2.1 Tunnel fre: example of the 3D-2D couplng strategy The structure under consderaton s the tunnel of Vrgolo close to Bolzano (Italy) that has been also used for an expermental test n the framework of UPTUN project [7]. We have consdered the central part of the tunnel 80 m long. Its geometry s decomposed n the flud and the sold domans see Fg.s 12. The sold doman conssts n the cross secton of the tunnel vault. In the smulatons fve cross sectons are consdered at 0 30 40 50 80 meters along the longtudnal axs z. The locaton of fre s the secton at 40 m. The flud s consdered as an deal gas and has the followng propertes: dynamc vscosty µ=1.8x10-5 kg/ms specfc heat c p =1006 J/kgK thermal conductvty λ f =0.026 W/mK densty ρ=1.225 kg/m 3. Concrete used for the sold doman (.e. the sectons of the concrete tunnel) s C60 concrete (wth a fnal compressve strength equal to 60 MPa) and has the followng man propertes at ambent temperature (20 C): elastc modulus E=40000 MPa porosty n=0.082 ntrnsc permeablty k=2 10-18 m 2 sold densty ρ s =2564 kg/m 3 sold thermal conductvty λ s =1.92 W/mK sold specfc heat c ps =855.52 J/kgK. The volumetrc heat source 4
correspondng to the fre s located at the coordnates (xyz)=(1.00.540.0) and has a volume equal to 8 m 3. Ths means that the fre s located n the central secton of the tunnel at 0.5 m from the longtudnal axs and at a heght of 1 m from the road pavement. The total thermal power nvolved by the fre s ncreasng n 10 mnutes up to 20MW followng a lnear law and then kept constant. For ths analyss 15300 hexaedral elements are used n the flud doman whle each cross secton s dscretzed wth 640 quadrlateral elements wth eght nodes. Fgure 1 Global geometry of the tunnel. A B Fgure 2 Geometry of the tunnel: (A) 3D flud doman (B) 2D sold doman (.e. tunnel cross secton) The ntal and the boundary condtons selected for ths case are: For the flud doman: the atmospherc pressure s mposed at the ends of the tunnel the ntal flud velocty s equal to zero close to the tunnel vault the flud can exchange heat wth the concrete structure surface accordng to the unversal profles ( wall law ) descrbed n [1] wth a heat exchange coeffcent equal to α c =500 W/m 2 K. The ntal temperature s set to 298.15 K for the whole flud doman. For the sold doman: on the nner sde of the cross secton.e. the vault surface n contact wth the flud two convectve (.e. Robn) boundary condtons are mposed. The convectve heat exchange s governed by the same unversal profles descrbed for the flud doman wth the same exchange coeffcent α c. As far as the mass exchange between the surface of concrete and the surroundng envronment s concerned a water vapour pressure equal to 1300 Pa and an exchange coeffcent of 0.02 m/s are set. The ntal condton for the concrete structure are p g =101325 Pa p c =7 10-7 Pa T=298.15 K. Ths set of values corresponds to an ntal relatve humdty equal to 58%. On the outer sde of the cross sectons the values of gas pressure capllary pressure and temperature are fxed (.e. Drchlet bc.s) to the ntal ones. 5
Fgure 3 Velocty feld (m/s) at t= 600 s (C) (A) cross-secton and (B) longtudnal secton. Fgure 4 Temperature dstrbuton (K) at t = 3600 s n the flud doman and n sectons S2 S3 (fre) S4. The total tme of smulaton s 1 hour. The case under consderaton corresponds to a real fre case n terms of the total thermal power nvolved the duraton of the fre and the value of the heat exchange coeffcent selected. Fgure 3 shows that the velocty of the ascensonal flux close to the fre source s hgher than 9 m/s whle the horzontal fluxes flowng toward the ends of the tunnel have a velocty equal to 3 m/s (t=600 s). The temperature dstrbuton n the flud doman and n the top part of the sectons S2 S3 (the secton of the fre) and S4 are shown n Fgure 4. 6
A B Fgure 5 Temperature and rel. humdty dstrbuton (A) and gas pressure and total damage dstrbuton (B) n the top of the central secton S3 (fre) at t = 3600 s. The central secton that s the most stressed one s the most exposed to spallng rsk. Indeed the peak of gas pressure (2.4 MPa) n the external layer of the concrete vault (10 cm thck) the formaton of the mosture-clog (the relatve humdty reaches n ths zone a value hgher than 90%) and fnally the total damage ( 55%) can lead to a progressve spallng startng from that layer see Fg. 5. Fnally Fgure 6 shows the dstrbuton of maxmum temperature n the cross sectons along the longtudnal axs and a comparson between the heat source temperature evoluton n tme and the temperature profles most used n lterature. The case consdered corresponds to a fre wth a temperature profle between an ISO-Fre and a Hydro-carbon Fre. A B Fgure 6 Dstrbuton of the maxmum temperature of the cross-sectons along the z -axs (A) and comparson of the source temperature evoluton wth the man heatng profles avalable n the lterature (B). 3. Fre mtgaton strateges In ths secton we present an applcaton of the FIT tool descrbed n secton 2 wthn the HYDROFIRESHOCK Project. The project ams at the development testng and deployment of an nnovatve automatc system for the suppresson of fre n tunnels. The system conssts of (see Fg. 7): nterventon and control statons at regular ntervals (typcally every 42 m); each control staton s equpped wth two cameras n the vsble range and two n the I.R. (Infra Red) range; the control statons are nterconnected va a ppe under pressure ( 10 bar) for supply of water or ant-fre foam; moble structures (.e. overhead trolley located every 800 m) connected to the control/dockng statons (42 m); 7
each moble structures has two extngushng devces (remotely controlled) wth a capacty of 1000 lt/mn. A Fgure 7 General scheme of the suppresson system (A) and a partcular of the moble structures (B) (Courtesy of Caccalanza & C S.p.A.). The work s n progress and the numercal tool wll be employed for the analyss of the effectveness of the extngushng system. In partcular varous confguratons of the system wll be studed wth and wthout force convecton and wth dfferent fre scenaro expecally n terms of total thermal power nvolved and ts evoluton n tme. B 4. References [1] Schrefler B.A. Codna R. Pesavento F. Prncpe J. Thermal couplng of flud flow and structural response of a tunnel nduced by fre Int. J. Numer. Meth. Engng Vol. 87 361-385 2011. [2] Gawn D. Pesavento F. and Schrefler B.A. What physcal phenomena can be neglected when modellng concrete at hgh temperature? A comparatve study: Part 1: physcal phenomena and mathematcal model Int. J. Solds Struct. Vol 48 1927-1944 2011. [3] Gawn D. Pesavento F. and Schrefler B.A. What physcal phenomena can be neglected when modellng concrete at hgh temperature? A comparatve study: Part 2: comparson between models Int. J. Solds Struct. Vol. 48 1945-1961 2011. [4] Bertoldo A. Banco M. and Pucc G. A fast multfrontal solver for non-lnear multphyscs problems Computatonal Scence ICCS 2004 PT 2 Book Seres: Lecture Notes n Computer Scence 3037 614-617 2004. [5] Prncpe J. and Codna R. A numercal approxmaton of the thermal couplng of fluds and solds Internatonal Journal for Numercal Methods n Fluds Vol. 59 1181-1201 2009. [6] Sagaut P. Large eddy smulaton for ncompressble flows Scentfc Computng Sprnger 2001. [7] EU Research Project UPTUN Cost-effectve Sustanable and Innovatve Upgradng Methods for Fre Safety n Exstng Tunnels fnal report 2006. 8