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

2. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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 T 4, where T is the temperature) are generally comparable with or greater than convective and conductive heat fluxes in a system.

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

4. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Reasons for Development of Advanced Model of Radiative Heat Exchange n n 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. n n 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.

5. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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 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.

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

7. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Basic Features of Radiative Heat Exchange for Test and Reactor geometry PhenomenonQUENCHVVER Axial radiative heat transfer ++ Radiation from upper and lower boundary -+ Radiation absorption and emission in steam-noncondensables media ++ Absorption and scattering on aerosoles -+ Effective tensor radiative thermal conductivity at periphery -+

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

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

10. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

11. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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…). ability of the model to be verified on smaller scale facilities (QUENCH, PARAMETER…).

12. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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: 1. New approach to evaluation of view factors and mean beam length. 2. Detailed evaluation of gas absorptivity and emissivity. 3. Account of effective radiative thermal conductivity for the large core. 4. Account of geometry modification in the course of SA.

13. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

14. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

15. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Distinctive Features of Model (Method of Solution) n 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: n 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); n At every time step new view factor and mean beam lengths are estimated taking into account modified dimensions during thermal expansion, melting and candling; n 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; n If some surface has disappeared (relocated) then view factors of this surface get equal to zero.

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

17. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Basic Definitions S i and S k – arbitrary areasn i and n k – unit vectors normal to S i and S k respectively E – projection of S k onto unity sphere T around the point on S i SiSi SkSk nini nknk βiβi βkβk rikrik E T  i and  k – angles between n i and n k respectively and r ik

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

19. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Why is it Difficult to Get Analytical Expressions for Mean Beam Length? These formulas for the case include 3-dimensional integrals RbRb RcRc RdRd zdzd zuzu SiSi SkSk

20. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 We Need the Integrals of the Form n=0,1,2 Im  Re  -- C1C1 C2C2 C3C3 S2S2 S1S1 T2T2 T1T1 U2U2 U1U1 CC

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

22. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Absorption Bands for Steam 11.10.0790.523 21.380.11613.4 31.870.21416.4 42.70.447204 56.32.51284 62038.795 Absorption band number i ai,  m  ai,  m Specific absorption coefficient K ai, 1/(mMpa)

23. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Absorption Bands for Hydrogen In infrared range of spectrum the hydrogen (H 2 ) 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 p H2 is the partial pressure of hydrogen, bar; T is its temperature, K.

24. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

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

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

27. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

28. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

29. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Illustration of the Method of Strings 1 4141 6161 5151 3131 2 A B R – rod radius

30. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 View Factor Between Two Rods of Finite Length H d L 1, L 2 – lengths of strings (L 1 > L 2 )

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

32. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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 E Only if  AB (T A -T B )>>  AE (T A -T E ) axial radiative transfer is small

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

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

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

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

37. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Radiation Absorption in QUENCH-03 W  g  (1-  )  B (T 4 -T 4 g )S – power absorbed in the bundle emissivity of gas Ssurface of heat elements W  100  1000 W during the test Optical thickness is about 0.025 at 1000K and 0.01 at 2000K

38. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Application of RATEG/SVECHA to QUENCH-06 0 500 1000 1500 2000 0 400060008000 Time, s Temperature, K TFS 5/9 calculation QUENCH-06 Temperature at the level 550mm

39. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 Application RATEG/SVECHA to QUENCH-06 0 10 20 30 40 50 010002000300040005000600070008000 Time, s H2 generation, g experiment calculation QUENCH-06 Hydrogen generation

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

41. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

42. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.

43. 11th International QUENCH Workshop, Karlsruhe, October 25-27, 2005 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.