Criticality Excursion ANALYSIS
TRACY Benchmark I
IDENTIFICATION NUMBER: TRACY-LEU-SOL-STEP-001, 002, 003, 004, 005
KEY WORDS: Low enrichment, Solution, Step reactivity insertion
1.0 DETAILED DESCRIPTION
Many experiments1-7) have been performed to study criticality accident with solution fuel, however, obtained data have been not available in useful form for long time. TRACY Benchmark problem was made to provide experimental condition and obtained data of fission yield, power, temperature and pressure in organized form, which should be useful for the calculation by various criticality accident evaluation codes. The benchmark is expected to be beneficial to evaluate and/or improvesuch numerical codes through its analysis and to give the basis of the common knowledge of criticality accident.
The feature of TRACY benchmark problem is as follows;
-Low enriched uranyl nitrate solution,
-Co-axial double cylinders tank,
-Three methods of reactivity insertion.
In this benchmark, the experiments of pulse reactivity insertion are provided, that is the simplest method of reactivity insertion for TRACY experiments. The selected experiment and its ID number are tabulated in Table 1.1.
Table 1.1 Benchmark case and its excess reactivity.
ID number / Run number / Excess reactivity ($)001 / 100 / 0.30
002 / 143 / 0.70
003 / 72 / 1.10
004 / 196 / 2.00
005 / 203 / 2.97
1.1 Overview of Experiment
Low enriched Uranyl nitrate aqueous solution is contained in a cylindrical core tank made of SUS304L stainless steel. There is a guide tube in its vertical center line for a transient rod, Tr-rod, which contains B4C inside it. After pumping fuel solution into the core tank, the transient rod is withdrawn from the core in order to insert reactivity. Desired reactivity is achieved by tuning the height of fuel solution. During free excursion, power, temperature and core pressure are measured. At the end, Tr-rod was inserted to shutdown.
1.2Description of Experimental Configuration
The core tank has an annular shape with 52cm outer and 7.6cm inner diameter. The effective cross section area for solution fuel is 1918 cm2. For more information, see Fig.1.1, 1.2 and 1.3. In Fig.1.3, the position 0.0mm of the Tr-rod means that the bottom of B4C inside the Tr-rod is 90mm below of the bottom of the fuel solution. The solution height is measured a needle type level gauge with accuracy of 0.25mm.
Figure 1.1: Schematic view of TRACY core tank.
Figure 1.2: Schematic view of TRACY core tank cross section (detail).
Figure 1.3: Schematic view of cross section of TRACY core tank and Tr-rod.
1.3Description of Material Data
The fuel solution is uranyl nitrate solution, which consists of uranyl nitrate [UO2(NO3)2], free nitric acid [HNO3], and water [H2O]. The enrichment of 235U is 9.98 wt.%. Tables 1.2 through 1.6 give standard value of composition and atomic number density of materials.
Table 1.2: Solution fuel conditions at 25C.
Table 1.3: Fuel conditions and kinetic parameters at 25.5C.
Table 1.4: Atom number densities of the fuel solution with
the concentration of 390 gU/L at 25.5C.
Table 1.5: Atom number densities of SUS304L at 25.5C.
Table 1.6: Atom number densities of air at 25.5C.
1.4Description of External Neutron Source
No external neutron source was used for each experiment.
1.5Description of Initial States
In each experiment, the reactivity is inserted by pulse withdrawal of the transient rod, and there was no external neutron source. Initial conditions are tabulated in Table 1.7.
Table 1.7: Selected experiments and their initial states.
1.6Description of Reactivity Insertion
In each experiment, a transient rod (Tr-rod) was fully inserted initially and was fully withdrawn within 0.2 seconds. Desired reactivity was achieved by following procedure;
1)The criticality solution height for which Tr-rod was fully withdrawn, Hc1, is measured.
2)The solution level, h, corresponding to desired reactivity for the experiment was determined by solving following formula;
where I is desired reactivity, Hcl: critical level of solution, C: constant;, and extrapolation length.
3)Solution level was tuned to the level h with Tr-rod fully inserted.
4)Tr-rod was withdrawn pneumatically at the time 0.
1.7 Description of the Detector or Measurement Systems and Measured Results
Reactor power, fuel solution temperature and core pressure were measured.
1.7.1Measurement of Power Levels – There were three neutron detectors. Two were linear channels and one was log channel. They were on ceiling of the core room right above the core tank as shown in Fig. 4. As the log detector, a cadmium covered 235U fission chamber was employed, which was covered with 10mm-thick polyethylene and 1mm-thick cadmium in order to detect epi-thermal neutrons. It was placed in a lead shielding of 10cm-thick to reduce the noise due to gamma rays, which was about 2.5m far from the core.
1.7.2Measurement of Temperature Levels and Distributions – Almel-chromel thermocouples were used to measure the temperature distribution in fuel solution. There were two types of thermocouple groups, they have different configuration of thermocouples to each other. Type-1 group was used for all experiments. Type-2 was used for R196 and R203 experiments. Type-1 has response time of about 1s and type-2, 0.1s.
1.7.3Measurement of Pressure Levels – Core pressure was measured with a pressure gauge installed to the side wall of the core tank. The pressure was observed for more than 1.5$ of reactivity insertion.
2.0 EVALUATION OF DATA
2.1 Evaluation of Power Levels and Distributions
There is a difference in measured values between linear channel and log channel. Such difference is less than 5% for reactivity lower than 1.5$. However, it increases as inserted reactivity increases. The difference is about 17% for R196(2.0$), about 48% for R203(2.97$).
2.2 Evaluation of Temperature Levels and Distributions
Thermocouples have response of 0.1 to 1 second. The accuracy is 1.5C.
2.3 Evaluation of Pressure Levels and Distributions
The base line of the pressure decreases after the first peak power. That may be due to temperature change of solution fuel and the noises due to radiation. Amount of uncertainty is unknown.
3.0 CALCULATION MODEL OF KINETICS CODES
Four kinetics codes, AGNES8), CRITEX9), INCTAC10), TRACE11) were used for sample calculations of the benchmark problems. AGNES, CRITEX and TRACE are based on one-point approximation and INCTAC solves neutron transportation equation by the finite element method. Brief summary of those codes are described hereinafter.
3.1AGNES
This code models the transient criticality of a fissile solution contained in a cylindrical vessel with vertical walls. Temperature, radiolytic gas void and boiling void feedback are taken into account. Cooling by natural convection of air outside of core or forced cooling by water can be calculated. Total number of fission is calculated based on the power profile.
3.1.1Neutronics – One-point kinetics equation is solved.
The calculation geometry consists of three regions such as fuel, container and coolant. The calculation regarding neutron is done in fuel region only. The basic equation of AGNES2 is the one-point kinetics equation as follows;
Nuclear solution fuel region is assumed to be homogeneous and only cylindrical shape can be calculated by using R-Z coordinate.
As temperature reactivity feed back, many effects such as Doppler effect, scattering cross section effect, density effect, and volume expansion effect can be taken into account, if the reactivity coefficients of those are evaluated beforehand.
3.1.2Thermodynamics –Average temperature is considered in fuel, container and coolant region.
The fuel and coolant regions connect each only to the container region, and the energy released by fission in the fuel region goes to the coolant region through the container region. The temperatures denoted byTi are calculated as follows;
where i denotes region number; 1 for fuel, 2 for container and 3 for coolant region. The first term of the right hand side is the energy released in the region i, and the second and third are the energy transferred from or to the adjacent regions. The heat transfer from the container region to the structural materials connected directly to the container and to the natural convection of air can be calculated.
3.1.3Radiolysis –Modified energy model is adopted. It assumes followings;
1)Radiolytic gas is created in proportion to the power.
2)Concentration of radiolytic gas beyond a threshold gives rise to void which gives reactivity feedback.
3)Growth rate of gas void is proportional to the power and excess radiolytic gas concentration.
4)Gas void moves to the solution surface and disappears.
Main parameters are Ci,j; the mol density of radiolytic gas, the gas void fraction Fij in a mesh (i,j) ,t; void-energy transfer coefficient, C0, the saturation mol density of dissociation gas, G; gas production rate.
3.1.4Calculation Procedure – The atomic number densities calculated using SST12) formula are shown in Table 3.1. Using those values, kinetics parameters shown in Table 3.2, (eff = 0.0076, = 0.00004864s) and reactivity temperature effect (t(cent) = -3.7578T - 0.00544T2) and its void effect (v(cent) = -43.7%V - 0.946%V2) are estimated using SRAC13) and TWODANT14) codes with JENDL-3.215) library.The reactivity insertion time was assumed to be 0.15s, which is almost the same as the time for the transient rod passes through the full height of the fuel solution. The initial power density was assumed to be 1x10-5W/m3, which is based on a measurement by neutron detectors for start up with no external neutron source condition. In each simulation, the temperature and void feedback reactivity coefficients were used with a weight which denotes the effect of the no-uniform distribution of the temperature and the void, and its value was 1.6 at the first. It changed to be unity exponentially with a time constant, TCT, which denotes the effect of convection driven by buoyancy or void. TCT was determined to be the same order as the peak power profile for each case, and TCT = 500s for R100, 80s for R143, 30s for R72 and 5s for R196 and R203. For the parameters which affect the creation of radiolysis dissociation gas void, the saturated concentration of dissociation gas, CD, was 15 mol/m3. The generation rate of dissociation gas, G, was 6x10-7 mol/J for the case with less than 1$ and 3x10-7 mol/J for the case greater than 1$. Those values are determined so that the power profile is reproduced for the best. The energy-void transfer coefficient, , was determined so that the experimental data could be reproduced for the best and was 1x10-7 m6/J/mol through all cases.
Table 3.1: Atom number density of the fuel solution with
the concentration of 390 gU/L at 25.5C.
Table 3.2: Delayed neutron fraction and decay constant with
the concentration of 390 gU/L at 25.5C.
Delayed Neutron Fraction / Decay Constant[1/s]
1 / 2.5490E-04 / 1.2703E-02
2 / 1.6521E-03 / 3.1704E-02
3 / 1.4940E-03 / 1.1525E-01
4 / 3.0053E-03 / 3.1161E-01
5 / 8.9084E-04 / 1.4003E+00
6 / 3.2420E-04 / 3.8740E+00
eff
(total) / 7.6213E-03 / ---
3.2CRITEX
This code models the transient criticality of a fissile solution contained in an open cylindrical vessel with vertical walls, so that the solution is able to expand vertically (thermal dilatation, production of radiolytic gas bubble). The solution vertical extent is divided with axial meshes into a number of volumes that allows to calculate the axial movement of the solution and the following reactivity effect. The energy deposited in the volumes is calculated based on the power profile (assuming fundamental neutronic mode), coupled with the central power calculated with the point kinetic equation.
3.2.1Neutronics – One-point kinetics equation is solved.
3.2.2Thermal – hydraulics – Heat conduction and natural convection are considered.
3.2.3Radiolysis – Radiolytic gas bubble migration is modeled by means of a conservation equation with bubble migration velocity and a source term.
3.2.4Calculation procedure – Kinetics parameters such as neutron life time, delayed neutron constants, Doppler coefficients and etc. are tabulated as internal data, they have been evaluated with WIMS or APOLLO deterministic neutronics code.
3.3INCTAC
INCTAC is applicable to the analysis of criticality accident of aqueous homogeneous fuel solution system. Neutronic transient model is composed of equations for the kinetics and for the spatial distributions, which are deduced from the time dependent multi-group transport equations with the quasi steady state assumption.Thermo-hydraulic transient model is composed of complete set of the mass, momentum and energy equations together with the two-phase flow assumptions.
3.3.1Neutronics – Quasi-steady state approximation or transport theory is used.
3.3.2Thermal – hydraulics – Heat conduction is solved with pseudo 3 dimensional calculation. Two phase flow model with liquid and gas is adapted.
3.3.3Radiolysis – Gas concentration is calculated as follows;
: before saturation ( C < C0 )
: liquid flow velocity [m/s]
: radiolysis gas generation rate [(mol/m3)/s]
C < C0 : after the saturation( C C0 ) and gas (void) generation rate is
where,
: radiolysis gas (void) generation rate [(kg/ m3)/s]
Ma: molecular weight of radiolysis gas [kg/mol]
G: energy to generate radiolysis gas [mol/J]
N: power density [watt/ m3]
C: radiolysis gas concentration [mol/ m3]
C0: radiolysis gas saturation (threshold) concentration[mol/ m3]
Mass conservation of non-condensable gas (void) is denoted as follows;
: void fraction [-]
g: density of void [kg/m 3 ]
g: void flow velocity [m/s]
3.3.4Calculation procedure– The atomic number densities calculated using SST12) formula are shown in Table 3.3. Based on those values, evaluated kinetics parameters are tabulated in Table 3.4. Neutron cross sections used are based on SCALE-4.4 44 group library. Delayed neutrons are evaluated using SRAC9513) with JENDL-3.214) library.
Table 3.3: Atom number density of the fuel solution with
the concentration of 390 gU/L at 20C.
H / 5.7917E-02N / 2.3371E-03
O / 3.7765E-02
U-235 / 9.9723E-05
U-238 / 8.8814E-04
At base state: 20 deg-C and no void.
Table 3.4: Delayed neutron fraction and decay constant with
the concentration of 390 gU/L at 20C.
Delayed NeutronFraction / Decay Constant
[1/s]
1 / 2.5084E-04 / 1.2710E-02
2 / 1.6285E-03 / 3.1704E-02
3 / 1.4697E-03 / 1.1525E-01
4 / 2.9606E-03 / 3.1162E-01
5 / 8.7734E-04 / 1.4003E+00
6 / 3.1936E-04 / 3.8740E+00
eff
(total) / 7.5064E-03 / ---
3.4TRACE
3.4.1Neutronics – TRACE code adopts the point kinetics approximation with 6 group neutron precursors. The code assumes that calculations begin when the system attains delayed criticality (keff=1) at time zero. The spatial power distribution is assumed constant during transients. Fuel solution temperature feedback and void feedback reactivities were taken into account. The fuel solution region is divided into coarse meshes in 2-D cylindrical geometry. The feedback reactivity induced by fuel solution temperature change and void generation are calculated by using a spatial weighting function. For the present benchmark calculations the power weighting function was adopted, i.e. cosine and Jo Bessel functions for axial and radial dimensions, respectively.
3.4.2Thermal – hydraulics – The heat transfer model in the fuel solution is treated by a transient heat conduction model in 2-D cylindrical coordinates. The spatial distribution of the heat generation from neutron fission reactions is assumed constant during simulation (represented by cosine and Jo Bessel function in axial and radial dimensions, respectively). The effect of complex fluid motion on the distribution of solution temperature is modeled by a temperature mixing parameter. The vessel is divided only into two lumped regions, i.e. the side wall and the bottom wall. The heat transfer from the vessel walls to the surrounding air is also approximated by air natural convection. The natural heat transfer coefficients (at the inner and outer sides of the vessel walls) are calculated inside the code. Different coefficients are used for horizontal and vertical walls.
3.4.3Radiolysis – The radiolytic gas modeling of TRACE code mainly consists of two models, one for the radiolytic gas bubble nucleation formation and another for the gas bubble velocity. The main parameters for this model are the G value (proportional to the number of product molecules formed for each 100 eV of energy absorbed by the system; input in mol/J) and the critical number of moles of radiolytic gas per unit void volume (mol/m3). It should be noted here, although the fuel solution region is divided into coarse meshes in 2-D cylindrical geometry, the bubble movement is treated in the axial direction only (no bubble movement in the radial direction). For gas bubble velocity a model which is originally based on the CRITEX code empirical model is adopted, where a continuous function of bubble velocity is developed based on the absolute value and the sign of the inverse period. The absolute value of the inverse period is a measure of how fast the power changing and the sign of the inverse period is set to -1, 0, and 1 for negative (decreasing power), zero (local minima or maxima) and positive inverse period (increasing power), respectively.
3.4.4Calculation Procedure – For TRACY benchmark calculations, atomic number density of fuel solution, TRACY vessel (SUS-304L), and the surrounding air were taken from Tables 4, 5, 6, and 7 of the Specification of TRACY Benchmark I.The kinetic parameters (delayed neutron fractions, prompt neutron lifetime, neutron generation time, temperature coefficients and void coefficients) were determined by using SRAC code system and JENDL-3.2 library and shown in Table 3.5 and 3.6. First, using SRAC’s PIJ module (1-D collision probabilistic method) transport group constants were prepared in 107 neutron energy group for each region, i.e. the fuel, vessel and the surrounding air. Second, using SRAC’s ANISN module (1-D neutron transport approximation, S8 P1, cylindrical geometry) 16 group diffusion constants were prepared. SRAC’s CITATION module (neutron diffusion approximation, cylindrical geometry) was then used for estimating the delayed neutron fractions, prompt neutron lifetime and neutron generation time.The temperature coefficients were calculated using SRAC’s TWOTRAN module by varying the fuel solution temperature (adjusting also its density; 5 temperature points; maximum temperature 100C) and 2-nd order polynomial fitting was applied to obtain the coefficients. Similarly, the void coefficients were calculated by varying the fuel density (but keeping the fuel solution temperature constant, i.e. fixed at the room temperature) (4 points; maximum void ratio 60 %) and 2-nd order polynomial fitting was applied to obtain the coefficients.
Table 3.5 Kinetic parameters for TRACY
benchmark calculations by TRACE code
Parameter / TRACY experimentsDelayed neutron fractions / 2.5140E-04
1.6199E-03
1.4689E-03
2.9505E-03
8.7515E-04
3.1892E-04
Precursor decay constant (s) / 1.2703E-02
3.1704E-02
1.1524E-01
3.1160E-01
1.4003E+00
3.8739E+00
Generation time (s) / 4.8585E-05
Prompt neutron lifetime (s) / 4.7624E-05
Table 3.6 Temperature and void reactivity coefficients for
TRACY benchmark calculations by TRACE code
Feedback reactivity / TRACY experimentsTemperature (T, Kelvin) /
Void (V, % volume) /
Note: Reactivity is given in $ unit.