Transcript Slide 1
By S. Saeidi Contribution from: S. Smolentsev, S. Malang University of Los Angeles August, 2009 Introduction Motivation/Goals Problem Definition Mathematical model Numerical Code Test Results Conclusion and Future Investigation Liquid metal, such as PbLi has so many advantages using as heat transfer fluid Corrosion behavior of ferritic steel exposed to PbLi is not well understood Maintaining acceptable limits for material loss is an important goal in blanket development For ferritic steel/PbLi, corrosion is controlled by convection, diffusion and dissolution at the solid-liquid interface Mass, heat and momentum transfer are coupled The main purpose is to develop a numerical code to access corrosion of ferritic steel in PbLi under either experimental or real blanket conditions There are no commercial codes available for corrosion analysis under fusion blanket conditions Experimental data are available on ferritic steel/PbLi corrosion, but no good interpretation exists We need a code, which would help us to perform some initial corrosion analysis under blanket conditions We want to help experimentalists to understand the data, and to understand the corrosion phenomenon itself Use of code for benchmarking with more sophisticated software, which is planned to be developed in future (HIMAG) Corrosion is a result of dissolution of wall material, which is then transported by the flow Transport mechanism are convection and diffusion Flow is either laminar or turbulent. MHD effects should be included We consider only one component (Fe) diffusing into PbLi We also consider deposition phenomenon, which occurs in the cold part of the loop Heat, mass and momentum transfer are coupled. The mathematical model should include energy equation, flow equations (including MHD effects), and mass transfer equation The boundary condition at the solid-liquid interface assumes saturation concentration at given wall temperature m=0 – plane geometry m=1 – pipe Flow U U U 1 P 1 m U 1 U V m y t ( j B) t x y x y y y t, kt, Dt=0 – laminar t, kt, Dt>0 – turbulent U 1 m ( y mV ) 0 x y y Turbulence closures are used to calculate t, kt, Dt Heat Transfer: MHD effects are included through jxB, P/x, t, kt, Dt T T T 1 m T C p U V m y k kt q' ' ' More equationsare used to x y y y y introduce MHD effects t Mass Transfer: C C C 1 m C U V y D D t y t x y y m y Mass diffusion coefficient plotted as a function of the wall temperature Saturation concentration Csat of iron atoms in PbLi as function of temperature Borgstedt, H.U and Rohrig, H.D:1991, Journal of Nuclear Materials 181-197 •Saturation concentration equation expressed in mole fraction (percentage) MODULE DESCRIPTION STATUS MAIN Switches between the modules Included INPUT Reads input data Included VELO Calculates velocity profile Included TEMP Solves the energy equation Included CONC Solves the admixture transport equation Included OUTPUT Prepares and organizes data output Included • Velocity distribution can be calculated for both laminar and turbulent flow regimes for simple geometries (pipe, rectangular duct, parallel channel) with or without a magnetic field •Finite-difference computer code •Non-uniform meshes with clustering points near the walls •Implicit method for solving equations (Tri-diagonal solver) Plot of Nusselt number along x direction in Plane channel with parabolic velocity profile Flow Plane channel, slug flow Plane channel, parabolic velocity profile Plane channel, parabolic velocity profile Pipe, slug flow Pipe, parabolic velocity profile Pipe, parabolic velocity profile BC type Nu (calc.) Nu (theory) Const. T (C) Const. T (C) 4.94 4.94 3.77 3.77 Const. Q 4.12 4.12 Const. T (C) Const. Q 5.78 5.78 3.66 3.66 Const. Q 4.36 4.36 The comparisons have been made for a laminar flow Temperature profile Concentration profile Flow Length: 2m Channel Width: 20cm Twall= 500 C Laminar flow= U=3 cm/s Cwall=0.01 Kg/m3 Plot of Sherwood number along the X direction: Rate of mass transfer along the X direction: •Sh decreases along the x until the flow become fully developed Initials steps towards a mathematical model and numerical code for modeling of corrosion/deposition processes have been performed We will keep working on the code and use it to analyze the effect of the flow regime, MHD, flow geometry, inlet conditions, etc. on corrosion/deposition of ferritic steel in PbLi under either experimental or real blanket conditions We will look for experimental data and run the code trying to reproduce the experimental data In the future, the code will be used for benchmarking with more sophisticated software (HIMAG)