Heikki Suikkanen GEN4FIN 3.10.2008 1/ 27 Coolant Flow and Heat Transfer in PBMR Core With CFD Heikki Suikkanen Lappeenranta University of Technology Department of Energy and Environmental Technology GEN4FIN
Heikki Suikkanen GEN4FIN 3.10.2008 2/ 27 Contents 1 Pebble-Bed Modular Reactor (PBMR) 2 Computational Fluid Dynamics (CFD) 3 Modeling Approach 4 Example Case 5 Discussions
Heikki Suikkanen GEN4FIN 3.10.2008 3/ 27 Pebble-Bed Modular Reactor (PBMR) Contents 1 Pebble-Bed Modular Reactor (PBMR) 2 Computational Fluid Dynamics (CFD) 3 Modeling Approach 4 Example Case 5 Discussions
Heikki Suikkanen GEN4FIN 3.10.2008 4/ 27 Pebble-Bed Modular Reactor (PBMR) The PBMR Project PBMR-400 Figure source: http://metnet.files.wordpress.com/2008/06/pbmr.jpg Pebble-Bed Modular Reactor (Pty) Limited Founded by Westinghouse, Eskom Holdings Limited, and the Industrial Development Corporation of South Africa Limited in 1999 Headquarters in Centurion, South Africa Mission is to develop commercial high-temperature reactors for the production of electricity and process heat Demonstration plant to be built in Koeberg near Cape Town (2010 )
Heikki Suikkanen GEN4FIN 3.10.2008 5/ 27 Pebble-Bed Modular Reactor (PBMR) Spherical Fuel Elements PBMR fuel design TRISO coated particle Figure sources: http://blogs.princeton.edu/chm333/f2006/nuclear/trisoball.jpg http://www.ne.doe.gov/images/trisofuelpellet.gif Fuel design together with the use of gas coolant and non-metallic core structures allows high operating temperatures
Heikki Suikkanen GEN4FIN 3.10.2008 6/ 27 Pebble-Bed Modular Reactor (PBMR) Power Plant Design PBMR Brayton cycle layout Demonstration plant Reactor thermal power 400 MW (165 MW e) Recuperative helium gas-turbine cycle Dedicated for electricity generation Figure source: http://www.schillerinstitute.org/graphics/conferences/070915 _Kiedrich/ferreira/pbmr_schematic.jpg
Pebble-Bed Modular Reactor (PBMR) Reactor Unit PBMR reactor unit 6.2 m diameter, 28 m high Fixed centre and side reflectors constructed from graphite blocks Graphite structures supported by a steel core barrel Three de-fueling chutes connected to core unloading devices Reactivity control system and reactivity shutdown system Two coolant flow inlets and one outlet Figure source: http://www.schillerinstitute.org/graphics/conferences/070915 _Kiedrich/ferreira/power_conversion_unit.jpg Heikki Suikkanen GEN4FIN 3.10.2008 7/ 27
Heikki Suikkanen GEN4FIN 3.10.2008 8/ 27 Pebble-Bed Modular Reactor (PBMR) Reactor Core Core vertical cross section Annular core region surrounded by graphite reflectors Control rod channels in the side reflector Channels for small absorber spheres in the centre reflector High thermal capacity and other design features make passive decay heat removal possible Figure sources: Venter, P. J. et al. Integrated design approach of the pebble bed modular reactor using models. Nuclear Engineering and Design, 2007. Vol. 237: 12-13. pp. 1341-1353.
Pebble-Bed Modular Reactor (PBMR) Reactor Core Main parameters Reactor thermal power Reactor inlet temperature Reactor outlet temperature System pressure Coolant mass flow rate Core outer diameter Core inner diameter Core height 400 MW 500 C 900 C 9.0 MPa 192 kg/s 3.7 m 2.0 m 11 m Core horizontal cross section Number of fuel pebbles 452 000 Source: Venter, P. J. et al. Integrated design approach of the pebble bed modular reactor using models. Nuclear Engineering and Design, 2007. Vol. 237: 12-13. pp. 1341-1353. Heikki Suikkanen GEN4FIN 3.10.2008 9/ 27
Heikki Suikkanen GEN4FIN 3.10.2008 10/ 27 Computational Fluid Dynamics (CFD) Contents 1 Pebble-Bed Modular Reactor (PBMR) 2 Computational Fluid Dynamics (CFD) 3 Modeling Approach 4 Example Case 5 Discussions
Heikki Suikkanen GEN4FIN 3.10.2008 11/ 27 Computational Fluid Dynamics (CFD) Basics of CFD Geometry under investigation is defined The geometry is discretized (meshed) Boundary conditions are defined Governing equations are written for each cell in algebraic form Numerical methods are used to obtain the solution Results are post-processed and analyzed Discretized flow region Source: Lectures of numerical methods in heat and mass transfer by Professor Timo Hyppänen (LUT 2008)
Heikki Suikkanen GEN4FIN 3.10.2008 12/ 27 Computational Fluid Dynamics (CFD) Computer Software A UDF for defining inertial resistance profile DEFINE_PROFILE(inertial_res,t,i) { cell_t c; begin_c_loop(c,t) { F_PROFILE(c,t,i) = 3.5*(1 - C_POR(c,t)) /(d_p*pow(c_por(c,t),3)); } end_c_loop(c,t) } A variety of commercial and free software for pre-processing, solving and post-processing exists In this work a commercial software Fluent by Ansys Inc. is used for solving and post-processing Fluent has a good range of built-in models and schemes User coding via user defined functions (UDFs)
Heikki Suikkanen GEN4FIN 3.10.2008 13/ 27 Modeling Approach Contents 1 Pebble-Bed Modular Reactor (PBMR) 2 Computational Fluid Dynamics (CFD) 3 Modeling Approach 4 Example Case 5 Discussions
Heikki Suikkanen GEN4FIN 3.10.2008 14/ 27 Modeling Approach Porous Medium Approximation Packing fraction = V spheres V total A random pack of spheres Figure Source: http://cherrypit.princeton.edu/rcp64.gif The large number of fuel pebbles makes it impossible to model the whole core with individual pebbles (computing power limitations) A Porous medium approximation is used Pebble-bed can be considered a packed bed of spherical particles Parameter that describes the packing s properties is the void/packing fraction A constant value or a position dependent profile can be used for the packing/void fraction Fluent includes a simple porous medium model by default
Heikki Suikkanen GEN4FIN 3.10.2008 15/ 27 Modeling Approach Core Flow and Heat Transfer Details It is not necessary to take pebble motion into account in coolant flow and heat transfer calculations (very slow speed) Coolant gas flows through the pebbles Pebbles generate heat Convection heat transfer (coolant-pebble) Conduction heat transfer (pebble-pebble, pebble-reflector, all solids) Radiation heat transfer (pebble-pebble, pebble-reflector walls, core barrel-rpv wall) Heat transfer details
Heikki Suikkanen GEN4FIN 3.10.2008 16/ 27 Example Case Contents 1 Pebble-Bed Modular Reactor (PBMR) 2 Computational Fluid Dynamics (CFD) 3 Modeling Approach 4 Example Case 5 Discussions
Heikki Suikkanen GEN4FIN 3.10.2008 17/ 27 Example Case Computational Domain Axisymmetric geometry used in the computations The active core region bounded by the pressure vessel is studied A simplified geometrical representation of the core Axisymmetric geometry without additional cooling or leakage flow paths Constant temperature boundary condition at the pressure vessel outer wall Porous medium approximation of the fuel region
Heikki Suikkanen GEN4FIN 3.10.2008 18/ 27 Example Case Material Properties Thermal conductivity of H-451 graphite Thermal conductivity [W/m K] 160 140 120 100 80 60 40 0 200 400 600 800 1000 1200 1400 1600 Temperature [ C ] Original data (axial) Original data (radial) Polynomial fit (axial) Polynomial fit (radial) Appropriate material properties are issued Helium: density(ideal gas law), specific heat f(t), thermal conductivity f(t), viscosity f(t) Graphite (both reflector and fuel): constant density, specific heat f(t), thermal conductivity f(t), constant emissivity Steel (core barrel and RPV): constant density, specific heat f(t), thermal conductivity f(t), constant emissivity
Heikki Suikkanen GEN4FIN 3.10.2008 19/ 27 Example Case Fluid Flow Equations Fluid flow in a domain is governed by the conservation laws of mass and momentum Fuel pebbles form a volume blockage that is taken into account by adding loss terms to the momentum equations Continuity equation ρ t + (ρu) = 0 Momentum equation in x-direction t p (ρu)+ (ρuu) = (µ u) +Bx +Vx x Viscous losses p visc = µ K U + Inertial losses = p iner = F ρ U U K Pressure drop over the pebble-bed p = 150µ (1 ɛ) 2 L dp 2 d p ɛ 3 u + 1.75ρ (1 ɛ) ɛ 3 u 2
Heikki Suikkanen GEN4FIN 3.10.2008 20/ 27 Example Case Porosity Variation Porosity profile 1 0.9 0.8 Increase in void fraction near the reflector walls is taken into account by using a correlation suggested in literature Larger void fraction near the walls affects flow and heat transfer Void fraction 0.7 0.6 0.5 0.4 0.3 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 r [m] Radial variation of void fraction h i ɛ (r) = ɛ 1 + c 1 e c 2(r r i )/d p, r i r ro+r i, 2 h i ɛ (r) = ɛ 1 + c 1 e c 2(r o r)/d p, ro+r i < r r 2 o
Example Case Energy Equation in the Pebble-Bed A mixture model is used for heat transfer in the fuel/flow region Local thermal equilibrium between fuel and coolant is assumed Correlation suggested in literature is used for conduction + radiation heat transfer between the fuel pebbles Energy equation in porous medium ˆ(ρcp) s (1 ɛ) + (ρc p) f ɛ T + (ut ) = (k t eff T ) + S h, k eff = ɛk f + (1 ɛ) k s Correlation for pebble-bed thermal conductivity (conduction + radiation) k s = 4σT 3 d p (`1 α 0.5 (1 α) + α0.5 2 10/9 B z = 1.25 α 1 α h i» Bz +1 1 + ε 1 B z ) 1 1, ( ε 2 1)kp Heikki Suikkanen GEN4FIN 3.10.2008 21/ 27
Example Case Nuclear Heat Source Chopped cosine power profile Heat generation rate per unit volume [MW/m 3 ] 7 6 5 4 3 2 Nuclear heat source is added to the energy equation as an additional source term A chopped cosine approximation for vertical power distribution No available data about what the "real" profile would be like Total heating power of 400 MW 1 0 1 2 3 4 5 6 7 8 9 10 11 Axial position [m] Heikki Suikkanen GEN4FIN 3.10.2008 22/ 27
Heikki Suikkanen GEN4FIN 3.10.2008 23/ 27 Example Case Results of Steady-State Computations Contours of temperature in C Velocity profile 10 9 8 7 Velocity [m/s] 6 5 4 3 2 1 0 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Radial position [m] Pressure drop over the core 401 kpa Average outlet temperature 897 C
Heikki Suikkanen GEN4FIN 3.10.2008 24/ 27 Discussions Contents 1 Pebble-Bed Modular Reactor (PBMR) 2 Computational Fluid Dynamics (CFD) 3 Modeling Approach 4 Example Case 5 Discussions
Heikki Suikkanen GEN4FIN 3.10.2008 25/ 27 Discussions Improving the Accuracy and Reliability Use of a more detailed 3D geometry Power profile mapped from a reactor physics code Studying the validity and accuracy of correlations Using a two energy equation model in the fuel region (especially in time-dependent cases) Energy equation for the fluid phase ɛ (ρc p) f T f t + (ρc p) f [ (ut f )] = (k f T f ) + h fs a fs (T s T f ) + S h,f Energy equation for the solid phase (1 ɛ) (ρc p) s T s t = (k s T s) + h fs a fs (T f T s) + S h,s
Heikki Suikkanen GEN4FIN 3.10.2008 26/ 27 Discussions Further Research Interests Randomly packed pebbles Using Discrete Element Method (DEM) to study the packing behavior near the walls Using the two energy equation model in computations (already done but there are some problems in implementing the model properly to Fluent) Figure: Doctor Payman Jalali (LUT)
Heikki Suikkanen GEN4FIN 3.10.2008 27/ 27 Discussions Thank you for listening! Any questions?