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RADIATIVE HEAT EXCHANGE MODELING OF QUENCH EXPERIMENTS

RADIATIVE HEAT EXCHANGE MODELING OF QUENCH EXPERIMENTS. A.Vasiliev Nuclear Safety Institute of Russian Academy of Sciences, Department of Severe Accidents Modeling B.Tulskaya 52, 115191 Moscow, Russia. Why is Adequate Radiative Heat Exchange Modeling Important?.

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RADIATIVE HEAT EXCHANGE MODELING OF QUENCH EXPERIMENTS

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  1. RADIATIVE HEAT EXCHANGE MODELING OF QUENCH EXPERIMENTS A.Vasiliev Nuclear Safety Institute of Russian Academy of Sciences, Department of Severe Accidents Modeling B.Tulskaya 52, 115191 Moscow, Russia 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  2. Why is Adequate Radiative Heat Exchange Modeling Important? The temperatures in a bundle reach high values (1000K and higher) at which taking into account of radiative heat exchange between the rods and other structures of the test section gets important. Radiative heat transfer dominates the high-temperature stages because radiative heat fluxes (proportional to T4, where T is the temperature) are generally comparable with or greater than convective and conductive heat fluxes in a system. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  3. Modeling of Radiative Heat Exchange in Existing Code Systems Existing models of radiative heat exchange use many limitations and approximations: • Approximate estimation of view factors and beam lengths; • The geometry change in the course of the test is neglected; • The database for emissivities of materials is not complete; • Absorption and emission of radiation by steam-noncondensable medium is taken into account approximately. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  4. Reasons for Development of Advanced Model of Radiative Heat Exchange • Non-correct taking into account of radiative heat exchange does not allow assess adequately other important models of such processes as thermal expansion, mechanical behavior, chemical interaction, melting, flowing, candling, dissolution and other phenomena. • Thus, the development of detailed model of radiative heat exchange which adequately takes into account the change of geometry, the axial radiative heat transfer, the emissivity change for SFD in VVER and experiments like PARAMETER, QUENCH is a very actual problem. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  5. Advanced Model MRAD of RATEG/SVECHA code The module MRAD was developed to model radiative heat exchange in VVER-type reactor vessel both inside the core and between the core and in-vessel structures under severe accident conditions The approach used for radiative heat exchange problem was developed on the basis of classical principles and special methods which allow to evaluate radiation heat fluxes in steam-noncondensables medium in cases of intact geometry, and partial and total degradation of structures. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  6. Purpose of Presented Work Application of advanced module of radiative heat exchange developed in IBRAE for VVER-type reactor SAto simulation of tests like QUENCH. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  7. Basic Features of Radiative Heat Exchange for Test and Reactor geometry 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  8. Reactor upper lid Upper block of protective tubes (BPT) BPT middle plate BPT baffle Reactor pit Lower BPT BPT lower plate Downcomer CORE Core baffle Bypass POROUSDEBRIS Support grid FA supports Lower plenum QUENCH Test Section and VVER under SA conditions 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  9. QUENCH and VVER cross-sections 163 Fuel Assemblies in VVER-1000 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  10. Why is the Exact Solution Complicated? It is necessary to note that the exact solution of radiative heat exchange problem is very complicated due to the following circumstances: ·         the construction of reactor core and in-vessel structures itself is rather complicated for rigorous statement and solution of radiative heat exchange problem; ·         non-uniform, non-stationary temperature field spatial distributions arise in the course of an accident; the calculation of these temperature fields should be fulfilled self-consistently with radiative heat exchange problem; ·         severe accident evolution is accompanied by change of emissivity of surfaces and the dramatic change of geometry of construction elements up to their total degradation; ·         surrounding gas absorption and emission has considerable effect to radiative heat exchange problem; the parameters of steam-noncondensables medium (density, temperature, concentration of noncondensables) change also considerably during an accident. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  11. Requirements to Radiation Module Radiative heat exchange module should ensure: ·         sufficient accuracy of the radiative heat exchange problem’s solution when the extent of detailed description of core and in-vessel structures is given by external thermal hydraulic code; ·         high computational speed and stability of running in the integral code designed for severe accident description; ·         some universality which would allow to apply the module to different types of reactors and to different nodalizations within the bounds of one type of reactor; • ability of the model to be verified on smaller scale facilities (QUENCH, PARAMETER…). 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  12. Method of Advanced Model Radiative heat exchange is computed using dividing on zones (zonal method) as in existing radiation models implemented to severe accident numerical codes such as ICARE, SCDAP/RELAP, MELCOR but improved in following aspects: • New approach to evaluation of view factors and mean beam length. • Detailed evaluation of gas absorptivity and emissivity. • Account of effective radiative thermal conductivity for the large core. • Account of geometry modification in the course of SA. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  13. Basic Assumptions We deal with homogeneous, absorbing, emitting and nonscattering gas in a system of surfaces. When the radiation exchange from one surface to another is considered the gas between these surfaces is assumed to have uniform temperature, pressure and concentrations of mixture components. The gray medium model is used that is absorption coefficient is averaged on spectrum and independent of wave length or only wave length interval with constant absorption coefficient is considered. The emissivities of surfaces are also averaged on spectrum. The radiation exchange between surfaces takes a diffusive character. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  14. Distinctive Features of Model MRAD (View Factors and Mean Beam Length) The main MRAD characteristics are: ·         the special logic for computation of view factors and mean beam lengths taking into account the complicated character of changing of these parameters as far as geometry is changed in the course of an accident; ·         the precise analytical expressions were derived for view factors and mean beam lengths for complex systems of interacting surfaces; ·         the geometrical distinctive features of VVER-type reactor are taken into account (for example, triangular set of fuel rods in the core); ·         the principal taking into account of axial radiative heat transfer along with radial transfer which corresponds to tensor character of radiative thermal conductivity; ·         the non-stationary heat transfer is modeled in the core periphery (where large temperature gradients are present) which makes possible to estimate more adequately the radiative heat fluxes from the core periphery to surrounding structures. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  15. Distinctive Features of Model(Method of Solution) • The radiative heat exchange problem is solved in the module MRAD both for intact (initial) geometry and for new geometry which is changed from initial one as a result of thermal expansion, melting, flowing, degradation, slumping of elements in the course of an accident which is described by following means: • All participating surfaces are included in the system of equations for heat fluxes from the very beginning of computation (even if some surfaces do not participate in the radiative exchange yet); • At every time step new view factor and mean beam lengths are estimated taking into account modified dimensions during thermal expansion, melting and candling; • If, as a result of degradation or relocation, some radiation surface disappears and the visibility arises between two other surfaces then non-zero view factors are calculated for these surfaces; • If some surface has disappeared (relocated) then view factors of this surface get equal to zero. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  16. Governing System of Equations for Radiation Heat Transfer Exchange - outgoing radiative heat fluxes - gas emissivity - gas absorption coefficient - optical thickness - mean beam length 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  17. nk βk rik Sk E ni βi Si T Basic Definitions Si andSk – arbitrary areas ni andnk – unit vectors normal to SiandSkrespectively E– projection of Sk onto unity sphere T around the point on Si i andk – angles between niandnkrespectively and rik 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  18. View factor between Si andSk Reduced view factor Mean beam length Geometric optical length Gas absorption coefficient, m-1 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  19. Rb Si zu zd Rd Sk Rc Why is it Difficult to Get Analytical Expressions for Mean Beam Length? These formulas for the case include 3-dimensional integrals 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  20. Im - C C  Re C1 C2 C3 S2 S1 U2 U1 T2 T1 We Need the Integrals of the Form n=0,1,2 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  21. Evaluation of Gas Absorption Coefficient Integral steam emissivity on full spectrum is approximated as From we determine steam absorption coefficient 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  22. 1 1.1 0.079 0.523 2 1.38 0.116 13.4 3 1.87 0.214 16.4 4 2.7 0.447 204 5 6.3 2.51 284 6 20 38.7 95 Absorption Bands for Steam Specific absorption coefficient Kai, 1/(mMpa) Absorption band number i ai, m ai, m 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  23. Absorption Bands for Hydrogen In infrared range of spectrum the hydrogen (H2) has one absorption band with the following parameters (Kamenshchikov et al., 1971): characteristic wavelength of absorption band at center =2.22 m, integrated on band spectrum specific absorption coefficient of hydrogen where pH2 is the partial pressure of hydrogen, bar; T is its temperature, K. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  24. Effective Radiative Thermal Conductivity Approach The distinctive feature of temperature field distribution in the core is the existence of large temperature gradients in the vicinity of core boundaries (top, bottom and side). Indeed, in the course of core heat-up the considerable heat fluxes arise from the core periphery to surrounding structures. At these conditions the strong temperature drop on some characteristic distance is inevitable from the centre to the periphery. This local temperature profile at the core boundary will result in the lowering of radiative heat fluxes to surrounding structures and to rising heat-up rate of the core itself. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  25. Effective Radiative Conductivity in Radial Direction for the Case of Triangular Set of Rods Stefan-Boltzmann constant pitch rod radius emissivity 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  26. THERMAL PROBLEMOF INTEGRAL CODE Geometry of radiating surfaces (modules of thermal expansion, melting, flowing, оdegradation, convection mass transfer, corium level in lower plenum) Temperatures andemissivitiesof radiating surfaces (modules of temperature calculation in heatelements andcorium in lower plenum) RADIATION MODULE MRAD View factor and reduced view factor calculation for “standard geometries” Calc_View Determination of radiative heat fluxes in a system Calc_Rad Taking into account of non-uniform temperature profile (effective radiative conductivity approach) View factor and reduced view factor calculation forheat elements, participating in radiative exchange Read_Rad 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  27. Model Verification(1) Due to extremely complicated character of analysis in most general formulation the verification of model was conducted in several directions encompassing separate aspects of the phenomenon considered. At first, the investigation was made on the basis of simplest configurations allowing the analytical solution. The use of reciprocity and closeness laws for radiation exchange favors the achievement of this goal. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  28. Model Verification(2) At second, the model was justified on the basis of integral experiments with comparably simple geometries (tests like PHEBUS SFD B9+, CORA W2, QUENCH-03,QUENCH-06) and the computations of severe accidents at VVER-1000. All integral tests without exception showed extremely high importance of adequate description of radiative heat transfer for thermal behavior analysis. Beside that, these tests simulate in small dimension the geometrical features of pressurized water reactors and their analysis is important for understanding of radiation behavior in the reactor. Severe accident analysis at VVER-1000 was also important from the point of view of “radiation energy” conservation in numerical calculations. At third, the results were compared with sparse experimental data on thermal behavior of fuel assemblies located in container TK-13 designed for storage and transportation of fuel assemblies. Here the special attention was paid to adequate simulation of effective thermal conductivity parameter and of temperature profile in fuel assembly. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  29. 41 A 1 2 61 31 B 51 Illustration of the Method of Strings R – rod radius 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  30. View Factor Between Two Rods of Finite Length d H L1,L2 – lengths of strings (L1>L2) 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  31. View Factors in QUENCH Geometry D C A B 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  32. Two Rods of Finite Length The generalized method of strings allows to estimate view factors for surfaces placed at different levels AE=0.0011 A Only if AB(TA-TB)>> AE(TA-TE) axial radiative transfer is small E 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  33. Axial Temperature Profile for TFS2 in QUENCH-03 t=2250s 1 –experiment, 2 –RATEG/SVECHA 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  34. Axial Temperature Profile for Shroud in QUENCH-03 t=2570s 1 –experiment, 2 –RATEG/SVECHA 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  35. QUENCH-03 Integral Radiative and Convective Fluxes to Shroud 1 – Radiative flux, 2 – Convective flux 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  36. QUENCH-03 Heat Balance 1 – electrical power, 2 – radiative flux to shroud, 3 – heat transferred by gas, 4 – convective flux to shroud 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  37. Radiation Absorption in QUENCH-03 Wg(1-)B(T4-T4g)S – power absorbed in the bundle emissivity of gas S surface of heat elements Optical thickness is about 0.025 at 1000K and 0.01 at 2000K W1001000 W during the test 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  38. Application of RATEG/SVECHA to QUENCH-06 QUENCH-06 2000 1500 1000 Temperature, K 500 0 0 2000 4000 6000 8000 Time, s TFS 5/9 calculation Temperature at the level 550mm 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  39. Application RATEG/SVECHA to QUENCH-06 QUENCH-06 50 40 30 H2 generation, g 20 10 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time, s experiment calculation Hydrogen generation 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  40. CORA-W2 (Experiment versus RATEG/SVECHA) Temperature of shroud at 650mm Temperature of rods (periphery) at 650mm 1 – without radiation, 2 - with radiation, 3 – experiment 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  41. Conclusions (1) The universal module for numerical modeling of radiative heat exchange in reactor vessel during in-vessel stage of severe accident is developed. The basic purpose of the module is its using in best estimate codes for severe accident analysis at VVER-type reactors. The application of known classical principles and introducing of some special methods allowed to describe the radiative heat transfer self-consistently in the following cases: ·         Intact geometry; ·   Partially or totally degraded core and in-vessel structures; ·        Energy exchange in the cases of considerable zones of degradation including the exchange with the melt in core and in lower head. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  42. Conclusions (2) Currently, radiation exchange module MRAD is implemented to Russian best estimate code RATEG/SVECHA/HEFEST. The numerical code RATEG/SVECHA/HEFEST developed for modeling of thermal hydraulics and the late phase of severe accident at nuclear power plant with VVER. As a part of integral code RATEG/SVECHA/HEFEST the module MRAD was tested on a broad range of problems: ·         By comparison with known analytical solutions; ·       On the basis of computations of integral experiments and severe accidents at VVER-type reactor; ·     On experiments on temperature behavior of fuel assemblies in vertical containers. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

  43. Conclusions (3) Radiation plays important role at high-temperature phases of QUENCH experiments. The analysis showed, that at temperatures higher than 1000K, radiation heat fluxes play important role in a system. The developed model of radiative heat exchange allows take into account the change of geometry, the axial radiative heat transfer, the emissivity change and absorption and emission in steam-noncondensables medium in QUENCH experiments. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005

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