IAEA Technical Meeting on Re-evaluation of Maximum Operating Temperatures and Accident Conditions for High Temperature Reactor (HTR) Fuel and Structural Materials Uncertainty of the pebble flow to power peak factor Fu LI, Chen HAO INET, Tsinghua University, China lifu@tsinghua.edu.cn IAEA Headquarters, Room F0811 10 12 June 2013
Outline 1 Uncertainty of pebble bed flow 2 Modeling of pebble bed flow 3 Modeling of flow uncertainty 4 Uncertainty to power peak factor 2
1 Uncertainty of pebble bed flow Pebble flows in a random way S.Y. Jiang, Experimental and numerical validation of a tworegion-designed pebble bed reactor with dynamic core, Nuclear Engineering and Design 246 (2012) 277 285 3
1 Uncertainty of pebble bed flow But the degree of randomness is limited Many experiments Can be simulated by DEM It is reasonable Kadak, A.C., Bazant, M.Z., Pebble flow experiments for pebble-bed reactors. HTR- 2004, Beijing, China., 2004. 4
1 Uncertainty of pebble bed flow How to define the randomness of the pebble flow? How to model the randomness? What is effects of random of pebble flow to core parameters, such as the power distribution, keff, maximum fuel temperature? 5
1 Uncertainty of pebble bed flow Random is limited Flow down almost as a whole Especially in straight flow region for tall cylindary core Constrained by boundary: reflector One pebble deviation along whole height? 6
1 Uncertainty of pebble bed flow Stable flow line is obvious Ignore the random deviation in reactor model Random can be treated by uncertainty analysis 7
2 Modeling of pebble bed flow Real flow Smoothly, continuously charge and discharge Random drop position in top Different flow line + random deviation Multiple pass Discriminated by pebble burnup Controlled by shuffling speed Some pebbles are discharged as spent fuel Some pebbles return to top of the core, as a whole 8
2 Modeling of pebble bed flow VSOP flow mode Averaged in top: charging Fixed flow line Flow channel Region in each channel Pebble flow as region move Multiple pass Multiple batch in each region Different batch, different pass, different burnup Discharging, burnup measurement 9
2 Modeling of pebble bed flow VSOP flow mode Fuel shuffling All regions move downward in each time step Batch represent number of pass Same material property for same batch Mixing in discharge box Fixed number of pebble pass 10
2 Modeling of pebble bed flow VSOP flow model In reality Different number of pass Variant burnup value, in shuffling, in discharging, in spent fuel Smooth slow movement 11
2 Modeling of pebble bed flow VSOP flow model Verified by Monte Carlo simulation Trace single pebble movement To random channel Different burnup increment in each channel Certain number of pass, according to discharging burnup threshold Millions of pebble can be sampled, is enough Statistic on the pebble Burnup distribution, spent fuel burnup, number of pass 12
2 Modeling of pebble bed flow VSOP flow model Verified by Monte Carlo simulation Variation on parameters are found Average values agree well with VSOP result Simplified VSOP model is good choice Hao Chen, Li Fu, Investigation on the pebble bed flow model in VSOP, Proceedings of the HTR 2012, Tokyo, Japan, October 28 November 1, 2012, Paper HTR2012-5-007 13
3 Modeling of flow uncertainty Fixed flow line + random deviation VSOP flow model Fixed flow line With average model (good enough) How to model the random deviation? How to combine with VSOP? 14
3 Modeling of flow uncertainty VSOP flow model Flow channels Regions Batches How to model random deviation Interexchange between channels Mixing coefficient between channels 15
3 Modeling of flow uncertainty VSOP flow model + mixing coefficients =>Flow channels with random deviation Can be implemented into VSOP model 16
3 Modeling of flow uncertainty How much for mixing coefficient? Depend on channel size Depend on deviation distance Can be defined from pebble flow experiment or simulation One pebble size along core height=> <1% Uncertainty analysis Can evaluate the result of larger coefficients Sensitivity analysis 17
4 Uncertainty to power peak factor Add mixing coefficient to VSOP flow model To simulate the random deviation besides fixed flow line Exchange pebbles along channels Change the material property in each region/batch 18
4 Uncertainty to power peak factor Evaluate the core parameter with different mixing coefficients 0 means no random deviation(original VSOP flow model) 1% coefficient is reasonable Larger coefficient can be evaluated Different core condition can be evaluated Different number of pebble pass Based on unperturbed equilibrium core condition power peak factor is the target parameter Affect the decay heat peak, and the max fuel temperature under accident condition 19
4 Uncertainty to power peak factor Power peak vs. number of pass, different mixing coefficient 20
4 Uncertainty to power peak factor Results: After taking into account of mixture among channels by introducing mixing coefficient in VSOP model Pebbles are mixed among channels Fission material are changed Power distribution is changed Power peak factor/maximum power density is changed The degree of change is limited Much less than 1 percent Even assuming much mixing among channels 21
4 Uncertainty to power peak factor Results: The change of power peak factor because of mixing effect Decrease along the increase of the number of pebble pass Decrease along the decrease of mixing coefficient Because the difference of fissile material among the channels is limited Especially for the multiple pass operation mode of pebble bed HTR 22
Conclusion remarks Flow of pebble shows some degree of random, besides the deterministic average flow lines Reactor analysis code, like VSOP, must simplifies the pebble flow model as: Fixed flow line, large time step, averaging in top, This simplification is inevitable, and good enough, as shown by Monte Carlo simulation 23
Conclusion remarks Random of pebble flow can be simulated by introducing mixing coefficient into fixed flow lines in VSOP code The effect of pebble flow random to power distribution can be evaluated with modified VSOP code with mixing coefficient in pebble flow mode 24
Conclusion remarks The change of maximum power density because of pebble flow random is very small Because the degree of random is limited Because the difference of fissile material content in different channels is limited, especially for multiple pass shuffling mode of pebble bed HTR 25
Conclusion remarks Therefore, the effect of pebble flow random to maximum fuel temperature under accident condition is limited The power density determines the decay heat The decay heat determines the max fuel temperature under accident condition This result can be treated as the one part of IAEA CRP on HTGR UAM One special issue for pebble bed HTGR The result is not so bad 26