GENERAL OVERWIEW
Motivation of the thesis
After carrying out successfully full core conversion from HEU to LEU fuels, the calculation tools or computer codes in neutronics and thermal hydraulics for LEU core are required for core and fuel management purposes Furthermore, design calculation to set up new experiments on the DNRR inside or outside the reactor core also needs fidelity, and reliable computer codes for different applications or basic research In refueling procedures, besides carrying out experiments to determine characteristics of the DNRR in neutronics and thermal hydraulics, calculations also need to be done in advance to confirm in safe operation and effective utilization. Through these tasks, the computer codes are played a very important role in management, safety operation, and utilization.
To ensure the accuracy of computer codes employed for neutronics and thermal hydraulics in the DNRR's management and utilization, validation is crucial This validation process involves comparing code results with experimental data or benchmark problem calculations from established codes With the transition to LEU fuel, numerous neutronics and thermal hydraulics parameters of the DNRR underwent alterations, necessitating code validation both during start-up and the design phase Furthermore, the codes applied to full core conversion calculations were utilized for HEU and mixed cores in core and fuel management The official computer codes employed for LEU core management were successfully validated within the dissertation's scope.
The safety analysis for the DNRR in design calculation to establish the LEU core was performed mainly with RELAP5Mod3.2 or Mod 3.3 [38] In the code, the whole reactor core can be modeled as point kinetics together with a thermal hydraulics module to solve momentum, mass, and energy equations The disadvantage of the code is based on point kinetics then output results do not give as much detail as 3-D of the reactor core In the reactor core event having a small core in space, the effect of spatial power is not ignored or affects neutron or power distribution The 3-D kinetics code PARCS that supplied group constants by Serpent
2 code was used in the preliminary calculation for transients and reactivity insertion accident (RIA) of the DNRR.
The MCDL burn-up code couples the MCNP code for accurate neutron flux and reaction rates with a burn-up module using the implicit Runge Kutta Method (RADAU II), resulting in errors in atomic number density of actinide and fission product isotopes below 10^-12 MCDL can handle HEU and LEU cores, with simple input for MCNP and specific input for burn-up cells, beryllium cells, and control rod positions Its library includes data on 71 isotopes, including names, atomic masses, half-lives, and fission yields.
The beryllium poison evaluation [32] was also integrated into the MCDL code to determine the atomic number density of isotopes H-3, He-3, Li-6, and Be-9 under reactions (n, l), (n, t) and (n, p) following burn-up time steps calculation as well as cooling time The effect of beryllium poisoning is direct to excess reactivity and neutron flux distribution For the DNRR, the main effect is excess reactivity during operation time from HEU cores to LEU cores.
The new research direction can be established by coupling calculations between the 3-D kinetics code PARCS and thermal hydraulics system code RELAP5 for safety analysis The coupling calculation of these codes can be performed for safety analysis in 3-D space by changing the power peaking factor when withdrawing any control rod such as the ShR or ReR The specific of each RIA analysis can be modeled and simulated in a practice of the DNRR scenario The tool can also be used for the design calculation of new research reactor with high power and multipurpose applications.
General introduction about the DNRR
1.2.1 History, structure and reactor core arrangement
The DNRR has been upgraded and expanded from the TRIGA Mark II research reactor with a power of 250 kW, so some components are retained such as a graphite reflector, thermal column, four horizontal beam tubes, and thermalizing column During the start-up phase in 1983, the reactor core was loaded with HEU (36% U-235) VVR-M2 fuel type and then LEU (19.75% U-235) VVR-M2 fuel type as present [29, 30] The reactor core has a cylindrical shape with a diameter of 44.2 cm and a height of 60 cm It is surrounded by a graphite reflector with a thickness of
35 cm and a height of approximately 55.8 cm All FAs are fixed at the bottom by two grid plates, one having 12.5 cm in thickness and the other 14 cm The entire core is immersed in the reactor pool, which has a height of 6.2 m and a diameter of 1.98 m. Horizontal beam tubes have of 17 cm diameter and the center line of all beam tubes is
7 cm below the center of the reactor core Fig 1.1 illustrates the specifics of the DNRR in axial and radial directions.
Fig 1.1 Cross sections of the DNRR in axial and radial directions
The research reactor's core configuration consists of a FA fixing grid plate with 121 triangular holes for fuel assemblies, beryllium corona, and control rod driving tubes The secondary reflector, formed by beryllium blocks outside the core, creates a neutron trap in the seven central cells surrounded by six beryllium blocks and an irradiation location The graphite reflector encases the core with a diameter of 30.5 cm and a height of 55.9 cm.
Six control rods consisting of boron carbide in stainless steel sheaths (two of which are safety rods (SaR) and the other four are shim rods (ShR)) and another control rod called the automated regulating rod (ReR) composed of stainless steel manage the reactor and ensure its safety Each control rod is suspended from a flexible cable that is attached to its own electric motor drive The rods move vertically within tubes of aluminum that penetrate the core To stop the chain reaction, the safety and shim rods (if the latter are partially removed) can be fully inserted into the core in less than one second by free fall under the effect of gravity. The control rods have an absorption length of 65 cm, which is adequate to cover the entire active height of the reactor core.
Outside the reactor tank, a reinforced concrete structure of 8.6 m in length and 6.55 m in height is installed for radiation shielding The shielding structure of the reactor is in the shape of a ladder, with a bottom width of approximately 6.69 m and an octagonal top width of around 3.81 m The normal concrete density of shielding material is 2.35 g/cm 3 and the concrete density at the thermal column door is 3.5 g/cm 3 A 3.6 ton steel plate is installed on the top of the reactor tank for shielding after renovating and enlarging the DNRR.
The reactor tank of the DNRR is kept from the former TRIGA reactor which is
6061 aluminum with a thickness of 6.4 mm, a height of 6.25 m, and a diameter of 2 m; it is surrounded by concrete shielding Currently, the reactor core has three wet irradiation channels including 1-4, 5-6, and 9-6; especially the modified neutron trap has the capacity to load 9 containers with TeO2 target to produce I-131 isotope [7,
25] Two dry irradiation channels of 7-1 and 13-2 are mainly used for neutron activation analysis of short-lived isotopes The rotary specimen has 40 irradiation holes with a diameter of 31.75 mm and a height of 274 mm for each hole These irradiation holes are used for radioisotope production and neutron activation analysis.
Four horizontal beam tubes from the TRIGA reactor were still retained in the DNRR, including three penetration radial beam tubes and one tangential beam tube. The inside of the beam tubes is made of aluminum and separated into two sections; the first section, with an inner diameter of 15.2 cm, is welded to a protective concrete layer, while the second section, with a diameter of 16 cm, is welded to the reactor's aluminum tank All horizontal beam tubes are utilized for fundamental research, such as nuclear data, structure, and other applications The thermal column of the TRIGA reactor is still kept and used for neutron activation analysis purposes and is filled with graphite blocks of 10.210.2127 cm 3
Since the DNRR was originally constructed as the TRIGA Mark II reactor,primary materials used in the core structure such as graphite reflector, horizontal beam tubes, reactor tank, and other auxiliary components were all American-made The majority of aluminum used in the structure of the DNRR was aluminum alloy 6061.During the upgrading and enlarging of the DNRR from 1981 to 1984, the aluminum used in the core structure was SAV-1 produced by the former Soviet Union Graphite material used mainly in the reflector, thermal column, and thermalizing column was almost 100% pure C-12 isotope Since 1984, the core has been added to the beryllium blocks in the center and periphery to create neutron traps and a secondary reflector, and a number of beryllium rods have been placed into the core when FAs can not occupy all positions inside the reactor core The detailed material of the DNRR used for neutronics calculation to determine the characteristics parameters for the working core using HEU or LEU fuels is given in Table 1.1.
Table 1.1 Material in structure of the DNRR
No Material Unit Atom/cm 3 × 10 24
3 Aluminum Al-27 5.91015E-02 Si-Na 5.49973E-04 Mg-Na 4.51430E-04
(Fresh Fe-56 1.80028E-05 Fe-57 4.31820E-07 O-16 1.23360E-03 without Mn-55 3.99050E-06 Cu-63 1.79053E-06 Cu-65 7.98070E-07 poisoning) Ni-58 1.27510E-06 Ni-60 4.87500E-07 Ni-61 2.11100E-08
Ni-62 6.70500E-08 Ni-64 1.70000E-08 Cr-50 2.75150E-07 Cr-52 5.30069E-06 Cr-53 6.00910E-07 Cr-54 1.49280E-07 H-1 1.63150E-03 Si-Nat 7.80490E-05 Mg-Nat 2.27460E-06
Fe-58 1.96970E-04 Ni-58 5.46539E-03 Ni-60 2.11317E-03 Ni-61 9.58700E-05 Ni-62 2.94861E-04 Ni-64 8.70080E-05 Cr-50 7.05444E-04 Cr-52 1.37095E-02 Cr-53 1.56311E-03 Cr-54 3.89549E-04 Mg-55 1.29090E-03
Al-27 5.85997E-04 Ca-Nat 2.99509E-03 Ti-Nat 1.62777E-05 Fe-Nat 5.88764E-02
Nat 1.95300E-03 Si-Nat 3.47400E-5 Fe-54 1.70300E-6 Fe-56 2.67100E-05 Fe-57 6.17100E-07 Fe-58 8.15100E-08
(Note: Nat means Natural) The DNRR can be operated with variable power up to a maximum of 500 kW without pulse mode as a TRIGA reactor The average thermal neutron flux in the reactor core is approximately 3.6×10 12 to 4.0×10 12 n/cm 2 /s at steady-state nominal power Natural convection is used to remove heat produced by fission from the reactor core The extracting well with 2 m height was installed directly above the reactor core to increase the flow rate through the reactor core by the "chimney effect." In the reactor pool, water is heated as a result of fission, thermalization of neutrons, and decay of fission products The heated water then ascends to the extraction well and is mixed with the pool water The primary cooling system removes the hot water from the reactor pool towards the top of the pool The removal of heat is accomplished using a secondary cooling loop The heat exchanger transfers heat from the primary coolant to the secondary coolant, which is then released into the atmosphere via a fan-forced air cooling tower.
The DNRR is the unique research reactor operating in Vietnam for training, neutron activation analysis, radioisotope production, and fundamental research From
2019 to the present, the DNRR has operated an average of 4,300 hours per year, mostly to produce I-131 isotope to supply about 25 hospitals in the country From
1983 until now, the reactor core arrangement of the DNRR as following:
- 88 HEU FAs with the central neutron trap at start-up;
- 89 HEU FAs with the central neutron trap from 1984 to April 1994;
- 100 HEU FAs with the central neutron trap from April 1994 to March 2002;
- 104 HEU FAs with the central neutron trap from March 2002 to June 2004;
- 104 HEU FAs with the central neutron trap, reshuffling 16 fuel assemblies in the core with 16 fuel assemblies at the core periphery, from June 2004 to December 2005;
- 104 HEU FAs with the central neutron trap, one beryllium block inserted into the cell 13-2, from December 2005 to July 2006;
- 104 HEU FAs with the central neutron trap, dry channel at cell 7-1, two beryllium blocks inserted into the cells 13-2 and 1-4, from July 2006 to November 2006;
- 106 HEU FAs with the central neutron trap, two fresh beryllium blocks inserted into the cells 13-2 and 1-4, from November 2006 to September 2007;
- 98 HEU and 6 LEU FAs with the central neutron trap, dry channel at cell 7-1, temporary wet channel at cell 13-2, and wet channel at cell 1-4 from September 2007 to July 2009;
- 92 HEU and 12 LEU FAs with the central neutron trap, dry channel at cell 7-1, temporary wet channel at cell 13-2, and wet channel at cell 1-4 from July 2009 to May 2011;
- 92 LEU FAs, with the central neutron trap, dry channel at cell 7-1, temporary wet channel at cell 13-2, and wet channel at cell 1-4, 12 beryllium rods around neutron trap from December 2011 to April 2012 In August 2012, a new pneumatic transfer system was installed in cell 13-2 In September 2019, two new wet irradiation channels at cells 5-6 and 9-6 were installed to use for radioisotope production purpose; only 10 beryllium rods around the neutron trap.
- 94 LEU FAs, with central neutron trap, dry channels at cells 7-1, 13-2, wet channels at cells 4-1, 5-6 and 9-6, 8 beryllium rods around neutron trap from April
- 96 LEU FAs, with central neutron trap, dry channels at cells 7-1, 13-2, wet channels at cells 4-1, 5-6, and 9-6, 6 beryllium rods around neutron trap from June
- 98 LEU FAs, with central neutron trap, dry channels at cells 7-1, 13-2, wet channels at cells 4-1, 5-6, and 9-6, 4 beryllium rods around neutron trap from June 2023 to present.
Historically, the TRIGA reactor was operated from 1963 to 1968 and under extended shutdown until March 1975 At the end of March 1975, all TRIGA fuels were unloaded and then shipped back to the United States In October 1979, Vietnam signed a contract with the former Union of Soviet Socialist Republics (USSR) to reconstruct and upgrade the TRIGA reactor The upgraded reactor named the DNRR using the VVR-M2 HEU fuel type In November 1983, the reactor reached criticality during the physical start-up phase with the critical core loading of 69 FAs without neutron trap and 72 FAs with neutron trap The initial working core consisted of 89 HEU FAs with neutron trap and 18 beryllium rods From September 2007 to May
2011, the DNRR conducted partial conversion employing 6 to 12 LEU FAs in the mixed cores as part of the RERTR program In November 2011, the DNRR archived criticality one more with 72 LEU FAs and a neutron trap, and in January 2012 the working core was established with 92 LEU FAs and 12 beryllium rods around the neutron trap In addition, the DNRR has completed some projects such as upgrading the control system of the reactor in 2007, installing and operating security system in
2008, and expanding the radioactive waste storage facility in 2019.
The DNRR has a complicated operating history with different periods and various fuels using from it was the former TRIGA reactor to the present stage [10].
At its first launched in 1963, the reactor used TRIGA fuel with a hydrogen retarder and uranium fuel mixed into a U-ZrH mixture, which has the characteristics following: has a very high value of temperature response coefficient, the temperature of the stainless steel fuel cladding is greater than 450 0 C, the coolant in the core is usually at high temperature and there is a boiling phenomenon of the coolant (light water) In 1984, the DNRR was restarted using 36% U-235 HEU VVR-M2 fuel type,operating in a mixed cores configuration with both HEU and LEU fuels fromSeptember 2007 to May 2011 In February 2012, the DNRR officially operated with the configuration of 92 LEU VVR-M2 fuel type From 1984 to 2019, the average annual operating time is about 1,300 hours; however, since 2020, the average annual operating time was exceeded 4,400 hours [10], with the primary purpose of radioactive isotope production.
O p er at io n t im e (h ou r)
Fig 1.2 Annual operation time of the DNRR from 1984 to 2011 (the core configuration using HEU fuel and mixed cores)
O p er at io n t im e (h ou r)
Fig 1.3 Annual operation time of the DNRR from 2012 to 2022 (using LEU fuel)
Due to the COVID-19 pandemic outbreak from 2019 to 2021, the DNRR has been operating almost every week to meet the domestic isotope demand In addition, by installing two new wet irradiation channels at cells 5-6 and 9-6 in the core, the output of the I-131 isotope produced on the DNRR each month can reach more than
The development of computer codes for reactor calculation in the world 38 1.4 The research situation about research reactor in Vietnam
Calculation programs for core and fuel management to determine physics, thermal hydraulics, and safety parameters for research reactors have been long of interest since they have a direct impact on the design calculation process as well as the operation, utilization, and application safety Currently, for neutronics calculations, created computational programs tend to employ the Monte Carlo method since it yields accurate, high-fidelity results, and contemporary computer resources satisfy this demand in terms of calculation speed or memory In kinetics and refueling optimization, for example, deterministic computer programs are still applicable when fast results or huge numbers of calculations are necessary The majority of the world's research reactors employ computation programs that must be checked against experimental data or findings from benchmark issues, such as Monte Carlo code results The world's current neutronics calculation codes, especially those employing the Monte Carlo method, produce very dependable calculation results In addition, the calculating library is constantly updated and improved, which is a prerequisite for approaching the experimental value A quick calculation algorithm, such as paralell calculation, that combines many methodologies is being developed to suit the requirements of the reactor's design calculation and operation management However, validating the calculation algorithms is always an issue due to the varying characteristics of reactors, their diversified exploitation and use, and the design requirements for new fuel types.
For nations with developed nuclear engineering, computational programs in physics or neutronics and thermal hydraulics have been verified and validated for application in many types of research reactors and fuels Different types of research reactors with different fuels, such as MTR fuel [33 ], TRIGA fuel [34], and Russian- made coaxial fuel types such as VVR-M2, VVR-KN, and IR-4M [35] have distinct primary functions Almost programs that use the Monte Carlo approach in physics calculations, such as MCNP, MVP, Serpent 2, and Tripoly [36] have no trouble describing the problem's geometry It is highly specialized in thermal hydraulics calculation programs since the codes depend on the geometry and a reasonable thermal hydraulics correlation.
The MCNP code has traditionally been regarded as the most suitable for physics calculations of practically all research reactors, and the code's numerous calculation libraries can be applied to a variety of reactor calculation applications. The MCNP code and calculation libraries can be updated based on the findings of the global scientific community After the combination of the MCNPX [37] and MCNP codes, the MCNP6 code can calculate burn-up and solve the transport equation for over 34 charged particles To increase the calculation performance of the MCNP code, Message Passing Interface (MPI) [14] or Parallel Virtual Machine (PVM) [15] environments can be used to build super-computer or PC-cluster with distributed memory for parallel processing.
On the basis of the kind of fuel, such as a plate or pin type, and the heat removal mechanism, such as forced or natural convection, thermal hydraulics codes can be built to accommodate safety analysis at steady-state with varying inlet coolant temperatures or reactor power levels For the validation of the thermal hydraulics codes, experimental data is necessary.
Calculation of three-dimensional kinetics is a crucial challenge, particularly for high-power research and power reactors The PARCS code is utilized as a tool in the system codes of the U S Nuclear Regulatory Commission (NRC) for licensing, with comprehensive calculation functions ranging from safety analysis incorporating 3-D kinetics to fuel burn-up computation Kinetics calculations are typically of little relevance for research reactors and are frequently employed in power reactors. Nevertheless, 3-D kinetics calculations are always essential for precisely assessing the reactor's transition or accident conditions with the rapid update of the detailed power distribution in the core based on the computational model The 3-D kinetics code can be applied effectively to the optimal core lifetime modeling of a reactor For safety analysis, programs such as the RELAP5 code can also integrate with the PARCS code to calculate 3-D kinetics and thermal hydraulics.
Fuel burn-up computation programs in Europe, the United States, and Japan can be adapted effectively to the DNRR Nevertheless, these codes must be modified to account for the construction, kind of fuel, and beryllium poisoning as the DNRR. The REBUS-MCNP system code is deemed adequate for calculating the DNRR's fuel burn-up Alternately, alternative calculating programs, such as MVP-Burn [39], MCNP6, or Serpent 2, may be used with the necessary modifications to adequate the DNRR practice conditions.
The advancement of computation programs for nuclear reactors necessitates continuous development and validation to meet the evolving needs of diverse reactor designs and fuels Rigorous evaluation against experimental data and comparison with other programs ensure accuracy and reliability A comprehensive computational library evaluation is also crucial for optimizing program selection For research reactors, a calculation program system encompassing physical calculations, thermal hydraulics, fuel burn-up analysis, and safety assessment is essential for design, operation, and management.
3-D kinetics combined with thermal hydraulics calculations, and possibly additional computational fluid dynamic (CFD) as OpenFOAM open source code [16].
1.4 The research situation about research reactor in Vietnam
Since 1984, the DNRR has been upgraded and enlarged to use HEU VVR-M2 fuels, and since 2012 LEU fuels have been used Numerous studies involving the assessment of physical and thermal hydraulics parameters of the core using two different fuels have been conducted Experimental data have been not only used in the management, operation, and exploitation of the DNRR but also used to validate calculation programs and the self-developed in-house programs The group constants were prepared by using cell code WIMS-D5 [40], and whole core calculation codes with the finite difference method (HEXAGAII, III [41, 42]), the nodal method (HEXNOD23 [43]) were applied for reactor 2-D or 3-D calculation of the DNRR. Neutron fluxes by energy groups and multiplication factor of the HEU core were determined by using these computer codes In addition, the codes HEXA-BURNUP
Various calculation programs were employed for the DNRR, including PIJ, CITATION, CORE-BN for core management, WIMS-5D and CITATION for physics calculations, MCNP and MVP for high-fidelity physics results, and WIMS-ANL, REBUS, and REBUS-MCNP for LEU core design For thermal hydraulics, the in-house code and COOLOD were initially used, but PLTEMP4.2 proved more suitable for the DNRR's natural convection, Russian-made fuel, and extracting well The PLTEMP4.2 code's reliability was validated using an instrumental FA with thermocouples, demonstrating minimal discrepancy between calculated and experimental results.
Fuel burn-up calculation for the DNRR performed by the CORE-BN code in the SRAC2006 system code and yielded relatively good results, but lacking the correction for beryllium poisoning, was also performed by updating the group constants of the materials, regardless of whether beryllium was exposed to neutrons during reactor operation WIMS-ANL, REBUS, and REBUS-MCNP codes were utilized to compute fuel burn-up for the DNRR while taking beryllium poisoning into account When these programs are applied to a research reactor with multiple fuels, the user must compute the library for the REBUS code by using WIMS-ANL code, the code is quite difficult-to-use software To eliminate this issue, MCDL's self- developed in-house code was built with a simple input that can handle various research reactor fuels The MVP-Burn, MCNP6, and Serpent codes are also used for fuel burn-up calculations, but the Serpent code is the most effective due to its simplicity and effectiveness in reactor calculation The measurement data of the burn- up of 106 burnt HEU FAs before transferring to the Russian Federation are crucial for validating the burn-up calculation systems applying to the DNRR.
Dr Ha Van Thong's 1990 dissertation, "Experimental research on neutron physics features in the DaLat nuclear research reactor" [3] was conducted to determine the physics parameters of the HEU fuel core In the dissertation, the author examined the challenges of reactor kinetics, which primarily involve the existence of photo-neutrons caused by the presence of beryllium material at the reflecting ring,neutron trap, and beryllium rods The static parameters of the reactor core during the initial startup phase were primarily determined through experiments involving the neutron field distribution in relation to the height and radius of the core, the unequal neutron field distribution, Laplacien, effective size, and extrapolated length The results of the thesis lead to a greater understanding of the reactor and its uses, such as radioisotope production, study of neutron activation analysis, and safe operation.
Dr Do Quang Binh's 1996 research thesis for the HEU core, "Study on kinetic characteristics and optimal fuel loading pattern for the DaLat nuclear research reactor" [4] also focused on experimental kinetics study, including determining the optimum core configurations of the reactor, the control rod positions required for the reactor to reach critical state, the minimum critical power level, the source power level, and the response of neutron density in subcritical and critical states These information were crucial for guaranteeing the DNRR's safe operation From there, it was also proposed to FA burn-up in the core based on the linear relationship between reactivity and depletion In addition, the dissertation discusses the development of algorithms to calculate physics, fuel burn-up in 2-D, fuel burn-up prediction, and optimal fuel loading patterns for the DNRR The results concentrate predominantly on HEU cores.
Dr Phan Thi Thuy Giang's 2020 dissertation, titled "Development of a computational model of physics and optimization of core fuel management (HEU) of the DaLat nuclear research reactor" [5] implementing the following contents:
Building and validating calculation model on neutron physics for critical analysis and fuel burn-up of the DNRR using the SRAC2006 system code Evaluation of the influence of the ENDF/B-VII.0 [46], JENDL-3.3, and JENDL-4.0 [47] data libraries to the critical calculation results and the ReR worth in comparison with the calculation results from MCNP5 code and experimental data Development of a new core and fuel management code using a discrete evolutionary algorithm (DE) applied to the HEU VVR-M2 fuel-loading core [48] The results of the dissertation have laid the groundwork for the computation of physics, fuel consumption, and optimal fuel loading patterns for HEU-fueled cores.
These dissertations have done research towards the DNRR's primary objective,including calculations and experiments for the core using HEU fuel between 1984 and 2007 The outcomes of these researches are the following: Fundamental steps for approaching and mastering reactor engineering In addition, these results are valid for LEU-fueled cores from 2012 until the present.
Reactor kinetics in three dimensions
Reactor kinetics studies of behavior, characteristics, and states of a reactor evolving with time Kinetics problems can be categorized according to the following time scales: fast transitions with microseconds to seconds (nuclear explosions, pulse reactors, reactor accidents), short transitions with minutes to hours (reaction start-up, effect of reactivity, required power level changes, poisoning of isotopes produced during operation), and slow transitions with days or months (fuel burn-up, production of heavy isotopes, effects of radiation on materials) Calculation of neutron flux distribution, power distribution, and reactivity coefficients of moderator and fuel during the time-dependent evolution of a reactor is a crucial topic that has a direct relation with operation and utilization of reactor To adapt to the fluctuating reactivity during operation, the intrinsic safety of a reactor with negative temperature feedback coefficients must be ensured When a reactor is operating at a particular power level, changing the power level results in a non-critical condition, which is accompanied by changes in the neutron flux distribution and power of the reactor core This is also the subject of the reactor kinetics study The critical power level of the reactor is attained by changing the control rod positions or adding/removing burnable poisons like boron The temperature during reactor operation must also be considered since the reactor will approach a critical limit or a predetermined power level will be multiplied by a temperature-dependent factor.
Included in the fundamentals of reactor kinetics are issues pertaining to reactivity with varying reactivity due to several causes, neutron production time, and delayed neutron The major action reactivity modifies the factor of multiplication so that it is no longer equal to 1; otherwise, the reactor will no longer be in critical status The reactivity is highly dependent on the size of the core, the density of the material, and the neutron reaction cross-section The fuel and moderator's reactivity feedback affects the kinetics of the reactor and must therefore be carefully examined.
Neutron generation time for thermal reactors is only approximately 10 -3 seconds; this is the time required for neutrons to diffuse in the thermal energy area prior to initiating a chain reaction Even though less than 1% of neutrons are created by fission, delayed neutrons play a crucial role in the functioning of the reactor It is only because of delayed neutrons that the operator may manage the increase in the reactor's power according to the period without accident happens.
It is required to consider and employ a 3-D kinetics program when there are specific criteria regarding the spatial distribution of neutron flux, it is applicable in reactors with a large core, and it can evaluate the continuous power distribution over time steps In fact, despite the small core size of reactors, the influence of space is still rather apparent, such as the distribution of flux or power according to the height and radius of the FAs from the core's center to its periphery.
Reactor kinetics and thermal hydraulics are crucial in determining reactor safety during accident scenarios By analyzing detailed thermal hydraulics of the reactor core and considering how reactor kinetics influence power and neutron fluxes in response to accidents (e.g., reactivity insertions, coolant/flow loss), the safety analysis of reactor systems is guided Thus, reactor kinetics remains a paramount concern throughout the design, operation, and safety evaluation of reactors.
Early calculations of reactor kinetics led to the development of numerous 3-D kinetics calculation tools, including PARCS, KIOD3D [49], DYN3D [50], TRIKIN
[51], NESTLE [52], and NODAL3 [53] In increasingly improved computer technology, kinetics calculation coupling with thermal hydraulics programs such asRELAP5 [38], COBRA-EN [54], and TRACE [55] are increasingly utilized in reactor safety calculations Programs for safety analysis that incorporate 3-D kinetics are frequently utilized, particularly for high-temperature, high-pressure nuclear power reactors These programs may also apply to research reactors with low temperature and low pressure but need to be modified.
Calculations and analysis of reactor kinetics and safety for the DNRR are generally based on point kinematic models such as the RELAP5 code or self- developed or in-house DRSIM calculation program [56] To test the usefulness of the PARCS program in the safety and transition analysis of reactivity insertion incidents, it is required to apply the PARCS program to 3-D kinetics calculations for theDNRR It is then conceivable to use PARCS for the study and safety evaluation of the DNRR and future new research reactor.
Burn-up calculation for core and fuel management
The burn-up of fuel is a crucial process that directly impacts the performance and security of a reactor The change in the nuclear concentration of the fuel in the fuel regions when creating heavy isotopes, the fission products, and the concentration of U-235, while simultaneously reducing the excess reactivity, are two characteristics directly affected by fuel burn-up In addition, there are additional key characteristics that fluctuate, and the rate of fuel depletion is estimated on a daily, monthly, or even annual basis, such as the DNRR.
One of the most significant tasks directly related to the management of the fuel and reactor core is determining the fuel burn-up of a reactor during operation Variables such as excess reactivity, neutron flux distribution, power distribution, fuel macro- sections, neutron spectra, and safety parameters change when a reactor burn-up The complicated transformation involving numerous physical phenomena that occurs during fuel combustion is a problem that must always be tackled thoroughly and precisely In addition, it is required to estimate the change in isotopic composition in the core as a function of time and space in order to have precise solutions in the event that the burn-up exceeds the regulation or other safety restrictions For research reactors, an evaluation of excess reactivity must be performed after each operation cycle to assure continuing operability in subsequent cycles.
The fuel burn-up is measured in terms of the percentage of burnt U-235 mass to initial mass, or in terms of the total power generated per initial ton of heavy nuclear mass (MWd/ton) Experiments such as assessing the effective reactivity of the FA according to a linear relationship of reactivity and burn-up, gamma scanning method measuring the activity of Cs-137 isotopes, or ratio number of Cs-134/Cs-137 or other correlated isotopes can be used to measure fuel burn-up Using 2-D or 3-D whole core calculation programs, theoretical calculations are performed to determine flux or power distribution as well as parameters of fission, absorption, reaction cross- section, and scattering matrix of the fuel at the time of interest, thus determining the change in nuclear concentration or burn-up with time step For group or cross- sectional constants that fluctuate with burn-up, the transport program or the lattice cell program is typically used to calculate them In conjunction with the program that calculates the fuel burn-up by solving the Bateman equation, parameters linked to fuel burn-up are computed, such as the nuclear concentration of isotopes and the effective multiplication factor The predictive skills of a fuel burn-up calculation program are crucial for determining the fuel consumption strategy and the ideal fuel loading patterns that satisfy safety criteria while maximizing fuel consumption.
Using experiments and theoretical calculations, researchers examined the three-dimensional fuel burn-up of the DNRR, particularly for the core fueled with Highly Enriched Uranium (HEU) They employed the gamma scanning method to investigate the burn-up of HEU fuels, utilizing a gamma probe to measure the isotope activity of Cs-137 or the ratio of Cs-137 to Cs-134.
134 to Cs-137 This method is quite precise when measuring fuel use, however, the experimental design and implementation time are both lengthy Moreover, this method still requires data to compute the ratio of Cs-134 to Cs-137 isotopes based on burn-up In theoretical calculations, the SRAC2006, REBUS-MCNP, or MVP-Burn codes are utilized to determine the 3-D fuel burn-up Recently, it is possible to calculate fuel burn-up using either MCNP6 or Serpent codes Before being utilized to compute fuel burn-up, calculation programs have been validated For HEU and LEU cores of the DNRR, the programs produced relatively accurate calculation results that varied from experimental data by no more than 10%.
For the DNRR core, there are beryllium blocks surrounding the neutron trap and outside the core, which influences the burn-up calculations The inclusion of beryllium poisoning calculations is a true correction for the calculation findings of the core's excess reactivity and neutron flux distribution With a low working power of 500 kW, the water temperature in the hottest channel does not reach 55 0 C, so the beryllium blocks and beryllium rods in the reactor core of the DNRR are unaffected by hardness or structural changes.
CALCULATION MODELS FOR THE DALAT NUCLEAR
Neutronics calculation models
Typically, the lattice cell problem for fuel and other non-fuel components to be included in the entire core computational model is performed initially The most challenging aspect of this topic is to create a model that corresponds to the lattice cell that will be constructed for the entire core problem For the VVR-M2 fuel type of the DNRR, the calculation model in the conserved area must be hexagonal, cylindrical, or concentric circular The complexity of creating a computational model for the lattice cell problem depends on the capabilities of the lattice cell program For the DNRR, the FA was calculated using a rational model (hexagonal or concentric circular) followed by the neutron traps, irradiation positions, control rods, lattice cells at the core edge, and the remaining lattice cells in the model as horizontal beam tubes, graphite reflector, and thermal column The outputs of the lattice cell computation are group constants or micro or macro cross-sections depending on the program according to the number of neutron energy groups (at least 2 energy groups). Particularly for the fuel lattice cell, if utilizing in the calculation of whole core burn- up, it is necessary to calculate additional data of group constants dependent on fuel burn-up usually as percentage of U-235 burnt or consumption.
The fuel lattice cell of the DNRR was computed using a 2-D model that included the portions with the fuel elements, the head, and the tail, which are homogenized according to the materials with varied weight ratios, mostly aluminum and water materials listed in Table 2.1 The area of VVR-M2 FA is subdivided into thirteen distinct layers from center to outer From the center out, the water portion will be followed by the fuel element, and the process will be repeated three times,corresponding to three fuel elements, the outer layer of water adjacent to other FA, or the structure of the core, such as beryllium rods, irradiation channels For the WIMS-ANL and the WIMS-D5 codes, the outer hexagonal fuel element is transformed into a cylindrical or coaxial annular shape while maintaining the same volume or surface area The configuration of the model created with the SRAC code (PIJ program) is identical to the LEU FA, although the hexagonal corners of the outermost fuel rod are not rounded in Fig 2.1 If the codes using Monte Carlo method are employed to calculate the group constants, it is assumed that the geometry of HEU and LEUVVR-M2 FAs will be identical to the real thing as in Fig 2.1 The primary result of the programs that solve the lattice issue is the precise determination of the group constant parameters, such as the diffusion coefficient, macroscopic cross-sections, and the energy group scattering matrix In order to verify that 2-D computational models can use the same model of deterministic programs as the one that employs the Monte Carlo approach, the multiplication factors will be evaluated to determine the adquacy of the two specified models. a) b) c)
Fig 2.1 Calculation model for VVR-M2 FA of the DNRR (a- Model using MCNP code; b- PIJ code and c- WIMS-ANL or WIMS-5B codes)
The bottom and top materials of the FA are homogenized and composed of water and aluminum in varying weight proportions Due to the complicated geometry of these components, the calculation model in the MCNP code is used the same as a model in deterministic code The ratio of materials in weight of the pieces contained aluminum from 10 to 40%, the remaining light water from 60 to 90% If using the deterministic codes for fuel burn-up calculation, the group constants of FA must be assessed in terms of fuel burn-up in order to be employed in the computation of the complete core with the updated burn-up percentage of U-235.
Table 2.1 Length and material of LEU FA in axial direction
Length from top to the
50 SAV1 and water Shape of aluminum as fuel element
600 Fuel meat: U-Al (HEU) and Cylinder and hexagonal
50 SAV1 and water Shape of aluminum as fuel element
(Note: SAV1 means Russian aluminum type)
The neutron trap's group constants were estimated using the homogenized FA material and concentric circles models to conserve the area of water and beryllium Homogenized fuel composition, including uranium, serves as a fission source for determining the multiplication factor and group constant characteristics Area estimation proceeds inward, starting with water-filled hexagonal lattice cells, followed by water in adjacent cells and beryllium components Group constants are derived from lattice cells containing water only or water and beryllium, necessitating corrections for H-3, He-3, and Li-6 production in poisoning calculations due to beryllium presence.
Fig 2.2 Calculation model for group constants of the neutron trap
(a- in practice and b- calculation model in PIJ code) The lattice cells determined including wet and dry irradiation channels as well as group constants of control rods based on a model consisting mostly of concentric cylinders with area conservation similar to FA and structural materials, the outermost of which is homogenized of FA For the PIJ code, the entire core region of the reactor can be homogenized of FA, and the lattice cells to be calculated are placed in equivalent positions within the core to determine the group constants Particularly for the SaRs and ShRs of the DNRR, the component containing the B4C material has a very significant neutron absorption capacity, making it nearly hard to establish the group constants with precision Thus, the outermost boundary condition for these lattice cells is defined as the ratio of neutron current to neutron flux by group neutron energy in Fig 2.3 Using calculation programs such as ANISN, TWOTRAN (SRAC2006), or the MCNP code, the boundary condition parameters can be computed and included in a full core calculation program such as the CITATION or the REBUS-PC codes The follower of the control rods consists of aluminum material (54.5 cm in length), hence the group constant was computed similarly to the non-fuel lattice cells.
A computation model for lattice cell codes when determining non-fuel group constants is usually performed in the presence of a FA to solve the problem with a neutron source in the form of fission or a fixed source This FA can be given outside the lattice cell to be calculated, or homogenize the entire core and move the lattice cells to their respective positions in the core In the case of using the SRAC system code, it is possible to construct a 2-D core region using a 2-D in the CITATION code and output the group constant data for the corresponding lattice cells.
Fig 2.3 Calculation model for lattice cells in side the DNRR core
(a- Model to calculate group constant of non-fuel cells; b- Cross section of two
SaRs and four ShRs; c- Model of SaR or ShR in PIJ code) Due to the complicated geometries of the reactor, the non-fuel lattice cells outside the core were divided in radii from outside the core to the end of the graphite reflector Due to the four horizontal beam tubes, the cells holding air were also calculated and included in the whole core calculation model According to the calculation, the number of lattice cells utilized in the calculation for the DNRR is in the range of 40 to 45 cells without fuel, depending on the configurations employing different materials in the core such as aluminum chock rods, irradiation channels, beryllium rods.
Non-fuel lattice cells outside the core were considered to be the same when they were symmetrically positioned and had no different materials Typically, a hexagonal animation zone, such as a hexagonal core, is surrounded by six lattice cells arranged symmetrically The exterior lattice cells are often made of aluminum, water, beryllium, or graphite, whereas the beam tube or dry irradiation position lattice cells are primarily formed of air and graphite Because there are forty irradiation holes in the graphite reflector, the computing model is also complicated.
For control rod has strong absorption material as ShRs of the DNRR, the values of neutron currents to fluxes at the boundary depend on few energy groups in whole core calculation that determined as boundary condition for neutron diffusion problem.
Fig 2.4 Calculation model for lattice cells outside the DNRR core
As descriped in Fig 2.4, almost lattice cells outside the reactor core can be calculated by using the CITATION code in the SRAC2006 system code in 2-D or simply by adding only homogeneous material cells in PIJ code to get group constants. The other cells of horizontal beam tubes can get group constants in this way.
Approximately 40 to 45 lattice cell types are required for whole-core calculations These cells include fuel assemblies (FA) with top and bottom structures, neutron traps, beryllium rods and blocks, control rods and followers, irradiation channels, horizontal beam tubes, and thermal columns These components ensure the accurate modeling of a nuclear reactor's core, considering fuel assemblies, neutronics, and experimental facilities.
For the DNRR, when using deterministic codes with finite difference or nodal methods, the complete reactor core is simulated as a material homogeneous hexagonal lattice in the computation model Depending on the calculation programs employed, such as the REBUS-PC, the HEXNOD23, or the CITATION codes, the DNRR's primary applied geometry for the entire core was hexagonal cells The model's radius was extended to the end of the graphite reflector, and horizontal beam tubes number 2, 3, and 4 were added Since beam tube number 1 is located outside of the graphite reflector, it does not affect the neutron flux distribution within the core region The computation model from the codes using the Monte Carlo method is identical to the computation model using the deterministic method, except that it is uniform and straightforward. a) b)
Fig 2.5 Calculation model for the DNRR using the REBUS-PC and CITATION codes (a- model in REBUS-PC and b- model in CITATION)
In the axial direction, the REBUS code's computing model is flexibility- determined based on the height of each lattice cell with different homogeneous materials; hence, it is totally identical to the geometrical features in Monte Carlo codes For the CITATION code model, the height portion typically devides the fuel in the core evenly, whereas the non-fuel portion is proportional to the height For fuel with a height of 60 cm as fuel type VVR-M2 of the DNRR, the height of the FA was divided into 30 equal volumes, each of which corresponds to 2 cm This calculation model guarantees the entire core height, including the head and tail of FA The position of the control rods may not correspond to the height of the divided fuel in the computed model Using this fuel height division, the COREBN code can be used for performance fuel burn-up calculations of each fuel zone.
Fig 2.6 Calculation model in axial direction using the CITATION code
Using deterministic methods to compute neutronics for the DNRR has disadvantages, particularly when the structure must be simplified such as horizontal beam tubes, or when creating new irradiation channels then group constants of these components must be prepared When a configuration is altered or new materials are introduced, it is required to establish group constants and incorporate them into the deterministic codes.
2.1.2 Calculation model for computer codes using Monte Carlo method
Depending on the required computation in fuel depletion or power peaking factor, the FA length can be divided into five to thirty equal volumes, or more if necessary In the computation of depletion, three fuel meat sections of each node in the axial direction, comprising one circular and two hexagonal forms, were homogenized by mixing under the union operator of the MCNP code In the detailed power peaking factor calculation (Fig 2.7 c), the two inner rings of the FA were subdivided into six parts with equal volumes of fuel meat, while the outermost ring has two different types of volume: one in the side and one in the corner In the almost cases, the hottest part of the FA is the corner outermost fuel element of the FA. Except for the need to homogenize the material in the top and bottom of FA, the fuel meat and 5 cm of aluminum in both sides in the axial direction were modeled as practical geometry. a) b) c)
Thermal hydraulics calculation for the DNRR
The LEU VVR-M2 FA has three coaxial annular tubes (fuel elements) The outermost fuel element has a hexagonal shape and is 32 mm, with 35 mm of FA pitch in width across parallel sides The other two, inner fuel elements have circular shapes of outer diameters of 22 mm and 11 mm, respectively The thickness of the fuel meat of the UO 2 -Al dispersion is 1.00 mm and that of the aluminum clad is 0.75 mm on each side There exists a gap of about 2.5–3 mm between adjacent fuel elements for coolant flow In the PLTEMP code, the VVR-M2 fuel was modeled with three coaxial cylinders as detailed in Fig 2.10 In the calculation model, the outermost cylinder preserves the conversion area of the original hexagonal tube The LEU working core of 92 LEU FAs was modeled with 2 hot channels (at cell 10-5 and cell 4-5) and 90 average channels, with a 2-m height ―chimney‖ also taken into account.
At the design calculation stage, the channel in cell 13-2 was considered a full-water channel The 12 beryllium rods were arranged in such a way as to avoid the high power density of the FAs located near the neutron trap and to increase neutron thermalization for radioisotope production IRT-4M fuel type was also calculated in detail for thermal hydraulics by using the PLTEMP code [58, 59].
Fig 2.10 The DNRR model calculation for the PLTEMP/ANL code and LEU core with 92 FAs (a: Fuel assembly, b: Fuel assembly model, c: Reactor coolant system model for
PLTEMP/ANL code and d: LEU core with 02 hottest cells) The PLTEMP/ANL4.2, with a ―chimney‖ or extracting well model and Collier‘s heat transfer correlation [60], is quite adequate for the DNRR which operates at low pressure and uses natural convection for heat removal The laminar, turbulent, and transient modes of mixed convection are included in the code:
Nu 0.023R 0.8 Pr 0.4 , if Re ≥ RE1
Nu Nu , if RE1 ≤ Re ≤ RE2 (2.1)
RE2 RE1 T where the recommended values are: CL1 = 4.0, CL2 = 0.17, CL3 = 0.33, CL4 = 0.43,
CL5 = 0.25, CL6 = 0.1, RE1 = 2000, and RE2 = 2500 The subscript b refers to bulk coolant and w to coolant at the wall temperature Re is the Reynolds number (VD e /
), Pr is the Prandtl number (C p /k), b is the dynamics viscosity of the bulk liquid coolant (kg/(m.s)), w is the dynamics viscosity of the coolant at the wall temperature (kg/(m.s)), k b is the bulk coolant conductivity, D e is the hydraulic diameter (m), β is the gap of the rectangular channel or annulus (m), s is the span of the channel (m), and g is acceleration due to gravity (9.80665 m/s 2 ).
The Shah’s CHF correlation was employed to adapt the code for DNRR thermal hydraulic analysis Additionally, the Forster-Greif correlation was utilized to calculate the ONBR in conjunction with hot channel factors for safety analysis considerations.
= +∆ where q is heat flux in W/m 2 , P is the pressure of the coolant in bar, and T or T (w: water and sat: saturation) is the temperature in o C.
In this version of the PLTEMP code, the hot channel factors can be applied in thermal hydraulic analysis to estimate safety margin parameters such as the ONBR,
DNBR, and FIR [62] When using the hot channel factors, three steps of calculation are carried out The first step is done as a normal calculation The second step is a repeat of the first step with an increase in reactor power and a decrease in reactor flow to determine the uncertainty in the Nusselt number correlation The last step applies the hot channel factors to the bulk coolant, film temperature, and cladding surface heat fluxes obtained in the second step In this step, the cladding surface temperature and heat fluxes with the effect of the hot channel factors are evaluated and compared under some limiting criteria The hot channel factors of the code have two parts: global and local In the global hot channel factors, the reactor power, flow rate, and heat transfer coefficient (correlation of the Nusselt number) are presented, while the local hot factors include bulk coolant temperature rise, local coolant film temperature rise, and heat flux from the cladding surface The determination of the global hot channel factors is based on the design calculation data or experiments on the reactor using the operation data To estimate the local hot channel factors, the characteristics of the geometry and material, as well as the thermal hydraulic parameters of the hottest FA are considered The combined random errors and the combined systematic errors are used to estimate the local and global hot channel factors, respectively, in the PLTEMP/ANL4.2 code.
In each node at an axial direction of the hottest or average channel, the output of the code includes the temperature, the ONBR, as well as the temperature of water saturation, and the ONB temperature condition of the fuel cladding Other safety parameters, including the ONBR, DNBR, and FIR, are also calculated and shown in the output file The minimum DNBR factor at the determined power is also printed at the end of the output file, together with the coolant pressure and flow rate, with the calculation model as FA-only or full reactor core.
Reactor kinetics application for the DNRR
2.3.1 Preparation group constants for the PARCS code
To meet the requirements of the 3-D kinetics calculation in the reactivity insertion accident for the DNRR, the PARCS code was used The code is combined with the PIJ program of the SRAC2006 or the Serpent codes or GENMAXS code
[63] to generate the lattice cell grouping constants The Serpent code was chosen because the program for reactor physics and burn-up calculations is based on the 3-D continuous using the Monte Carlo method developed by VTT Technical Research Center of Finland The Serpent code provides simulations of complex reactor geometry for critical calculations, fuel cycle investigations, and other applications In addition, the Serpent has many potent features, such as an automatic burnup sequence for spatial homogenization, coupled multi-physics calculations, computational simulations (transient simulations), sensitivity calculations, features that permit pre- checking of geometry, and a quick computation time The Serpent 2 code has been extensively utilized in the calculations of nuclear reactors and TRIGA reactors in particular.
The Serpent code includes the capacity to generate group constants of lattice cells based on the two energy groups, making it a very practical tool for updating information regarding burn-up and beryllium poisoning The lattice cells are defined in 3-D space, which makes it highly practical for calculating the group constants of lattice cells, such as horizontal channels, based on the height of the beryllium rods. For the two SaRs, four ShRs have strong absorption neutron material, and the super- cell option in the Serpent code was used to create a macro cross-section using in calculation model of the DNRR using the PARCS code. a) b) c)
Fig 2.11 Super-cell model in the Serpent code to create group constants of ShR
(a- cross section, b- vertical and c- control rod model)
2.3.2 Calculation model for the DNRR using the PARCS code
The calculation model for the DNRR using 92 LEU FAs was similar to the model of the REBUS-PC code in the radial direction and the CITATION code in the axial direction with 2 neutron energy groups and 6 delayed neutron groups. a b
Fig 2.12 Calculation model of the DNRR using the PARCS code
(a-cross section model and b-vertical model)
A main disadvantage of the PARCS code is only applied for nuclear power plants (PWR, BWR, or VVER-1000) in thermal hydraulics calculation and the code uses almost default data that is measured or calculated from other codes Therefore, it is not adequate for the research reactor operation in the conditions as low power, low pressure, and low temperature The calculation 3-D kinetics model for the DNRR is quite good in geometry when applying a hexagonal prism shape.
Burn-up calculation for the DNRR
The evaluation of fuel burn-up plays a very important role in nuclear reactors because safety, utilization, and core lifetime are dependent on the depletion process during reactor operation The determination of fuel burn-up in a nuclear reactor can be performed by experiments or theory calculations Many experiment methods have been applied to estimate fuel burn-up such as the gamma scanning method, reactivity measurement method, etc [64] Although experimental burn-up data are very accurate conducting experiments is complicated and difficult The calculation method is more simple, more economical, and good enough for optimization in fuel using and core lifetime estimation.
Depletion calculations require integration with core analysis codes to obtain reaction rates and flux distributions These calculations are solved numerically using data on fission yields, isotope half-lives, and reaction types While Monte Carlo simulations offer accurate results, they can be computationally demanding However, modern high-performance computing capabilities and parallel computing techniques have reduced run times significantly Additionally, the MCNP code provides versatile calculation libraries that can be updated or modified using the latest nuclear data from the NJOY2016 code.
The MONTEBURN [65], MOCUP [66], and MCODE codes [67] are popular computational codes for burn-up calculation coupling between the ORIGEN code
[68] and the MCNP codes The disadvantages of these codes are depending on the ORIGEN code and need numerical methods like predictor and corrector method to achieve small errors of burn-up calculation results such as in the MCODE code but the time step in the code is limited The SRAC system code uses the CITATION code to solve the neutron diffusion equation and the diffusion code is only good for simple geometry of reactor core For depletion calculation, COREBN based on CITATION and burn-up package (DCHAIN: Code for analysis of build-up and decay of nuclides) using the analytical method to solve the depletion equation The main problem here is the lumped fission product and the data are not easy to create by users The REBUS-MCNP linkage system code is quite good for depletion calculation but the same problem with data libraries is not also convenient for users Besides the lumped fission product that has been created by WIMS-ANL, pseudo libraries for the REBUS code with many isotopes (about 21 isotopes) are also needed to prepare for the
REBUS-MCNP system code The number density of U-235 for each type of fuel also needs to be prepared for interpolation using a polynomial equation or spline third or sixth order following burn-up time steps BURNCAL [69] code has been developed by SANDIA National Laboratory (USA) and is a simple code for depletion calculation using the Euler method and users need to supply the power density of the depletion cell This code is simple but provides a good idea for improvement in depletion calculation.
The 21 actinide and 50 fission product isotopes in the MCDL code (Monte Carlo Depletion for Light water reactor) were considered to suffice for depletion calculation Reaction chains including reaction types used in the MCDL code have been taken from the SRAC2006 system code The library of the MCDL code contains data of isotope labels in the MCNP5 code, the user‘s defined name of 71 isotopes, decay constants, and fission yield products of 21 actinide isotopes to 50 fission product isotopes Radau IIA method [70] has been applied for solving the burn-up equations to ensure the accuracy of calculation results with long time steps of about
The MCDL code includes three parts: main control of the code, receiving calculation results from MCNP running, and depletion calculation The data library for depletion was taken in SRAC code and WIMSD-5 codes for all isotopes Only five reaction types are considered for depletion including (n, fission), nu-bar reaction to calculate for number of neutron released per fission of 21 heavy isotopes, (n, 2n), (n, ), and (n, p) for Sm-49 only In beryllium poisoning calculation, three reactions (n, l), (n, p), and (n, t) have been considered FORTRAN90 programming language is chosen for composing the code and allocation array mode is applied So the limit of running memory of the code is only dependent on the memory of user‘s computer. The MCDL code can be run both on Linux or Windows operating systems with MPI environment for parallel calculation of the MCNP code.
The MCDL code structure is described in Fig 2.13 including 5 important subroutines for depletion cycle calculation Detail function of each subroutine is as follows:
1 Main subroutine is to control all depletion calculation following time steps and read all input and library files: Input for depletion, modified input for MCNP, library data.
2 RunMCNP subroutine is to submit running case of the MCNP code with the modified input The modified input is added data for tallying neutron flux, reaction rate of each active cell in original MCNP input file The MCDL code will be executed after the MCNP code is finished.
3 ReadMCTAL subroutine is to read tallied results from MCNP and then transfer all these information to the depletion subroutine.
4 Depletion subroutine carries out depletion calculation and writes burn-up time, number densities to a temporary file called burnup.dat.
5 Update subroutine has main function for updating calculation number densities of each isotope to create new input file for the MCNP code for the next running step. Number density of all isotopes in depletion node and total number densities of isotopes in each material card are updated after having new calculated number densities from ―depletion‖ subroutine.
The ―be-poisoning‖ subroutine is implemented to evaluate the number densities of Be-9, Li-6, He-3, and H-3 isotopes after finishing the burn-up calculation In the case of cooling calculation, all reaction rates have to be assigned equal to zero; this means that only decay is considered.
Input files for the MCNP5 and the MCDL codes need to be prepared by users. The name of the input file for the MCDL code has to be set as INPUT.inp and arbitrary for name of input of the MCNP code The order of depletion and beryllium poisoning cells in the MCDL code must be matched with depletion cells from the top to the bottom in input for the MCNP code The material card in the MCNP input file needs to put all 71 number densities for each depletion cell and other materials like aluminum, silicon, and oxygen This means the MCDL code can be used for many kinds of fuel types with different enrichments or material compositions The name of cells and material cards must be used 5 digits and in formatted form for easy assess in reading and writing data by the FORTRAN programming language.
The MCDL code input file requires specific data, such as depletion cell labels (matching MCNP input), depletion cell volumes, burn-up steps, burn-up power (MW), and time steps (days) Additionally, it necessitates surface cards illustrating changing control rod positions after burn-up stages and the name of the depletion model.
MCNP input file, directory of MCNP, and output file name All declared data will be read in free format by the MCDL code Notice that the last step for burn-up calculation is only input for the next step in MCNP code but not running at all.
After running the MCNP code, the MCTAL file recorded the main data needed for solving the depletion equation of each isotope and each active cell This MCTAL file is kept after each burn-up calculation step.
The output file of the MCDL code contains the number density of each isotope, burn-up of each depletion cell, and multiplication factor of all time steps Information about the standard deviation of multiplication factor and the relative error of reaction rates after reading the MCTAL file is also printed in the mctest file One temporary file records data about the mass of uranium and plutonium isotopes.
The rate of change in concentration or number density of an isotope is determined by its production and removal rates Production can occur via fission, neutron reactions with a parent isotope, or decay of a parent isotope Removal can occur through fission if the isotope is fissionable, neutron reactions, or self-decay into a daughter isotope.
Summary of Chapter 2
The chapter presents calculation models for neutronics of the DNRR using LEU fuel In neutronics calculation with the deterministic method, group constants of fuel and other non-fuel lattice cells were prepared before carrying out whole core calculation to get multiplication factor, and neutron fluxes or power distribution The nearly practical shape of FA and the reactor core was modeled using computer codes with the Monte Carlo method, the advantages of these codes are easy to generate calculation models in real situations, the modern calculation method and continuous calculation libraries These codes can give fidelity, reliable obtained results. However, the requirement of computer resources is needed to reduce calculation time by parallel calculation using super-computer or PC-cluster under MPI or PVM environment.
For thermal hydraulics calculation in steady state of the DNRR, the PLTEMP4.2 code was used because of adequate in the calculation model (fuel type, extracting well, and natural convection), correlation of Russian fuel type as well as for uncertainty analysis The PLTEMP code was frequently modified to meet requirements for Russian fuel types such as VVR-M2, IRT-4M, or VVR-KN.
In the DNRR 3D reactor kinetics calculation, the hexagonal shape in the radial direction and axial free calculation model were utilized with the PARCS code The Serpent 2 code was employed to generate group constants in two neutron energy groups, including specific handling of control rods in super-cell mode This flexible control rod movement facilitates RIA analysis based on the reactor core's space.
The development of the MCDL code was presented with the ability to apply for the DNRR using HEU and LEU fuels and the code was integrated beryllium poisoning calculation as well The code has advantages in burn-up calculation depending on control rod positions during burn-up time steps The 71 heavy and fission product isotopes of each depletion region were archived with high fidelity results using the MCNP code to calculate neutron flux and reaction rates coupling with a burn-up module (Implicit Runge Kutta – RADAU II) and the calculation error was about 10 -12 of the atomic number density.
RESULTS AND DISSCUSSIONS
Neutronics and thermal hydraulics for LEU core
3.1.1.1 Neutronics characteristics of the HEU and LEU VVR-M2 fuel types.
Table 3.1 presents the calculation results for the infinite multiplication factors of HEU and LEU VVR-M2 FAs by different computer codes and geometries of hexagonal or extruded hexagonal corners of the outermost fuel element Fig 3.1 shows the neutron spectra of these FAs with 107 neutron energy groups using PIJ code (SRAC2006) with ENDF/B.VII.0 library and the MCNP code for the average power of HEU and LEU FAs during the start-up periods of the cores containing 89 HEU FAs and 92 LEU FAs respectively.
Table 3.1 Infinite multiplication factor of the VVR-M2 HEU and LEU fuels
Computer code HEU FA LEU FA
Geometry as PIJ (SRAC) 1.64143 0.00005 1.63457 0.00005 and WIMS-ANL
The infinite multiplication factor of LEU fuel is less than HEU fuel primarily because the moderation volume (water region) remains unchanged while the ratio of fast neutrons is slowed down less compared to the thermal neutron flux produced by HEU fuel Obviously, the higher enrichment of HEU fuel makes the higher ratio of mass or atomic density of U-235 to U-238, which increases the probability of thermal neutron production The ratio of atomic number density of U-238 to U-235 in HEU and LEU fuels is 1.74 and 4.0, respectively Therefore, the resonance absorption cross section at epithermal energy of LEU fuel is significantly greater than HEU fuel, which has a significant impact on the neutron spectrum in the thermal energy region.
The calculation libraries also affect the calculation results of infinite multiplication factors because the micro cross-section of isotopes in these libraries is quite different The obtained calculation of infinite multiplication factors using the MCNP code with different libraries are shown in Table 3.2 The difference results between the multiplication factors of HEU and LEU FAs with two different libraries were not significant and were approximately 6 pcm and 5 pcm, respectively. However, a better calculation library must be validated when comparing calculation results to experimental data In the case of the DNRR using LEU fuel, the ENDF/BVII.1 library [72] is suitable for neutronics and burn-up calculations.
Table 3.2 Calculation results of infinite multiplication factors with different calculation libraries
Fuel type HEU FA LEU FA
Calculation ENDF/B-VII.0 ENDF/B-VII.1 ENDF/B-VII.0 ENDF/B-VII.1 library
The neutron spectrum of HEU fuel is higher in the thermal energy region compared to LEU fuel due to U-235 enrichment This difference impacts the utilization of a nuclear reactor when using HEU or LEU fuels, leading to up to 20% variation in neutron flux at irradiation positions The disparity in neutron spectra primarily affects the thermal energy region, resulting in higher neutron flux in the HEU core than the LEU core Beryllium rods placed around the neutron trap enhance thermal neutron flux, compensating for the reduced thermal neutron flux in the LEU core, making its flux comparable to HEU or mixed cores previously used.
The main differences between HEU and LEU fuels are the density of uranium
LEU fuel consumes more slowly than HEU fuel, extending its usage time Though thinner than HEU fuel cladding, LEU fuel cladding effectively releases fission products at a U-235 burn-up exceeding 60% Despite this capability, the maximum burn-up of discharged LEU fuel in the DNRR is estimated at around 30%, well below the recommended criteria Nevertheless, the successful 2011 full core conversion demonstrated the safe operation of LEU fuel in the DNRR at 500 kW.
Fig 3.1 Neutron spectrum of HEU and LEU VVR-M2 fuels with 108 neutron energy groups in average power (89 HEU FAs core and 92 LEU FAs core) Because the size and dimensions of HEU and LEU fuels remain unchanged, the primary advantage is that there is no need to modify the core structure of the DNRR, and LEU FAs can be loaded into the core using the existing grid plates Since the mass of the U-235 isotope in LEU fuel is greater than in HEU fuel, the mass of U-
235 will increase when LEU fuels are loaded in the same core configuration as HEU fuel Thus, the effective multiplication factor or excess reactivity of the LEU core will be greater than the HEU core Due to the high mass of U-235 in the LEU fuel,loading LEU fuels close to the neutron trap (at the third ring from the center of the core to the outside) could lead to thermal hydraulics safety violations with the fuel cladding temperature limit (operating at 500 kW at the manufacturer-recommended
103 0 C) Primarily, the temperature violation can be avoided by loading LEU fuels away from the neutron trap and beginning in ring number four.
Variations in computational libraries have minimal impact on neutron spectra for LEU fuel, except in the fast energy region This is attributed to discrepancies in cross-sectional data among libraries.
N eu tr on f lu x / l et h ar gy
D iff er en ce (E N D F /B -V II 0 -E N D F /B -V II 1
Fig 3.2 Neutron spectrum of LEU VVR-M2 fuel type with different calculation librariesThe source of error contributing to the infinity multiplication factor was mostly determined by geometric characteristics, such as the thickness of the aluminum cladding and the fuel meat, as well as material parameters, such as the mass of uranium isotopes and enrichment The distinction was also represented in the computation model or in the use of distinct calculation techniques, such as deterministic or Monte Carlo methods Frequently, issues solved with the MonteCarlo approach are regarded as the standard or benchmark against which deterministic methods are evaluated The utilized computation library also contributes to the inaccuracy, as discussed above Typically, the FAs employed in the calculation are averaged against characteristics such as mass, enrichment, and shape.
The computation for the HEU core containing 89 FAs was performed using the SRAC and MCNP codes Comparing the obtained results from two codes with experimental data revealed a very good agreement This would confirm the DNRR's safe operation and utilization capability when using HEU fuels [74].
3.1.1.2 Criticality, reactivity, control rod worths
During the design calculation of the full core conversion, LEU core characteristics parameter values were evaluated The MCNP5 or MCNP6 codes, along with the REBUS-PC linkage code, are predominantly applied for neutronics and burn-up calculation The SRAC2006 code was also utilized, but only to calculate few fundamental parameters In design calculations, there are numerous modifications in the implementation process, thus the MCNP code was frequently used because the code met the changing requirements during the physical start-up and energy start-up [75, 76, 77] In addition, the MCNP code was easy to carry out for core and fuel management because the LEU core with 92 FAs utilized 12 slightly burnt LEU fuels from the mixed core that operated from September 2007 to May
2011 The calculation libraries of the MCNP code should be continuously updated in order to produce reliable calculation results when compared with experimental data. For the LEU core, a direct comparison between the calculated results and experimental data revealed that the difference is negligible and entirely acceptable. Based on the results of the REBUS-MCNP program system's calculations, the applicability of this program for fuel and core management is acceptable.
The DNRR used beryllium blocks to locate around the neutron trap and at the periphery of the core as additional reflector, it is necessary to evaluate beryllium poison before proceeding to establish critical configurations in the physics and energy start-up Since 1984, the reactor has been operated with a number of beryllium rods and blocks at the core‘s center and periphery to improve neutron reflectivity.Beryllium is irradiated by neutrons with energies greater than 0.7 MeV, producing isotopes Lithium (Li-6), Tritium (H-3), and Helium (He-3) by reactions (n, l) and (n,
2n) These isotopes have large neutron absorption cross sections; the formation of He-3, Li-6, and H-3 produced a significant negative reactivity that causes changes in the distribution of neutron flux, power, and excess reactivity.
The Beryl program was modified to utilize MCNP code results for input, and MCNP reaction rates were utilized to determine nuclear concentrations of He-3, Li-6, and H-3 MCNP assessed the poison effects of these isotopes on reactor excess reactivity The beryllium poisoning effect was evaluated over the DNRR's operational history since 1984 Calculations and measured data for irradiated DNRR beryllium rods showed excellent agreement (within 10%), confirming the negative reactivity contribution of these rods Six beryllium rods were employed in the measurements, including two new rods and four irradiated rods (two from 1994 and two from 2002) Cells 9-6 and 5-6 measured effective reactivity through control rod position changes (ReR), with an estimated error of 0.4 cents from the ReR indicator.
Kinetics calculation results for LEU core
3.2.1 Calculation results from the Serpent and PARCS codes at steady state condition
The Serpent code was used to evaluate kinetics parameters and obtained results were compared with experimental data The results showed that it was not significant difference between experimental data and calculation results from Serpent code.
Table 3.16 Calculation results and experimental data for decay constant
Calculation Difference (%) neutron Experimental Error of (Cal- results group data Serpent code Exp)/Cal*100
Table 3.17 Calculation results and experimental data of delayed neutron fraction.
Serpent data (Serpent (Cal-Exp)/Cal*100 code) code
Calculation results from the Serpent and PARCS codes to excess and shutdown margin reactivities in Table 3.18 of the working core with 92 LEU FAs were in very good agreement with the difference was less than 500 pcm.
Table 3.18 Calculation results of multiplication factors from the Serpent and PARCS codes
Position of control rods (cm) Effective multiplication factors (k eff )
Four ShRs ReR Serpent 2 PARCS/Serpent Difference
Using the Serpent/PARCS codes, safety analysis of some transient processes and reactivity insertion accidents of the LEU core with 92 FAs were performed The transient/accident scenarios included increasing the power from 80% to 100%, changing in the power of the DNRR when inserting positive reactivity less than 10 cents The results of simulation calculations with PARCS were compared to
106 experimental data and previously performed calculation results from the RELAP5 code.
3.2.2 Calculation and experiment results during increasing power of the DNRR from 80% to 100%
Fig 3.14 demonstrates that when feedback reactivity temperature coefficients of water and fuel were not taken into account in calculation by the PARCS code, the calculated reactor power increased rapidly during 400 s investigation even fully insertion of the ReR causing the core to return to a critical state When the feedback temperature coefficients of water and fuel were taken into account in the calculation, it can be seen in Fig 3.15 that the reactor power increased more slowly than if the feedback temperature coefficients were ignored Fig 3.15's reactivity curves provide the explanation for this disparity It can be seen that when the feedback temperature of water and fuel were considered, a positive reactivity inserted into the reactor by the upward movement of the ReR was partially compensated by the negative reactivity from the feedbacks reactivity temperature of water and fuel If the feedback of reactivity temperature were not taken into consideration, the rate of increase of the reactor power would be substantially slower.
Figure 3.14 indicates a power value calculation of 90% nominal power upon reactor criticality, which subsequently decreased to 83% This contrasts with the experimental data in Figure 3.16, which displays 100% power after the completion of the reactor power increase process These discrepancies can be attributed to the following factors:
(1) The thermal hydraulics parameters used in the PARCS model were defaulted for the pressurized water reactor (PWR) type, while for the DNRR, the pressure and temperature of the water and the temperature of the fuel were much lower than PWR Therefore, the thermal hydraulics in the current PARCS model used to simulate the DNRR had significantly different from the actual thermal hydraulics of the DNRR This difference can be solved by combining the PARCS model with a thermal hydraulics calculation program such as the RELAP5 code and this was also a research direction that expecting to be carried out in the future for the DNRR In addition, Fig 3.17 and Fig 3.18 show simulation results for a scenario in which reactor power increased from 80% to 100% using PARCS to illustrate the ability to simulate the power changing of the DNRR in terms of neutronics;
(2) The second reason is that the experimental data depicted in Fig 3.18 were carried out in 2020, while the PARCS calculation model was only used in start-up time and the following data can be added later To accurately determine these parameters requires a lot of time and effort, so within the scope of this research, we only compared the results of the transitional simulation and the safety of the insertion reactivity accident with experimental data in neutronics aspect It can be seen that these preliminary transitional calculation results were an important premise for carrying out further studies on new research reactor and the DNRR as well by using the PARCS code coupling with another thermal hydraulics calculation program.
Fig 3.14 Calculation results of the increasing power of the DNRR from 80 to 100%
Fig 3.15 Experimental data of the changing position of ReR (TD) when increasing reactor power from 80% to 100%
Experimental Thựcnghiệm data nâng during công increasing suâttừ power 80lên from 100% 80to
Fig 3.16 Position of ReR (TD) and power when increasing reactor power from
Fig 3.17 Reactivity and reactor power when increasing reactor power from 80 to 100%
Fig 3.18 Calculation results the changing position of ReR (TD) when increasing power from 80 to 100%
3.2.3 Simulation of the accident when uncontrolled withdrawal of one control rod at nominal power
During the normal operating state of the DNRR, a safety rod (ShR) was uncontrollably withdrawn from the reactor core at a maximum speed of 3.4 mm/sec A similar calculation was performed for the ReR, with the speed set at 20 mm/sec Figure 3.19 presents the calculation and simulation results for the accident caused by the uncontrolled withdrawal of ShR number 1 of the DNRR, both with and without feedback reactivity temperature coefficients of water and fuel.
3.20 describes the simulation results that have been calculated using the RELAP5 code The accident scenarios for an uncontrolled withdrawal of a control rod of theDNRR in simulation calculations using the PARCS and RELAP5 codes [30] were identical Fig 3.21 shows the results of calculation and simulation of the accident of uncontrolled withdrawal of the ReR from of the DNRR using the PARCS code in instances with and without feedback temperature coefficients of water and fuel.
Figs 3.19 and 3.21 illutrate that when impacts of feedback temperature coefficients of water and fuel were not taken into account in the calculation, power increased more rapidly than when these effects were considered as an uncontrolled control rod withdring These feedback temperature coefficients of water and fuel are an inherent safety element of the DNRR, with the function of preventing a fast increase in power under transient or accident conditions In addition, because the effective worth of the ReR is less than a ShR, but the speed withdrawal is greater, it was possible to insert a positive reactivity equivalent to ShR number 1 (approximately 2 cents per second) and the transient time was relatively short (Fig.
3.21) As depicted in Fig 3.19, the influence of the feedback temperature coefficients of water and fuel was unclear when compared to transients or accidents that can occur over a longer time.
Comparing Fig 3.20 and Fig 3.21 reveals that the calculation results from the PARCS and RELAP5 codes were in good agreement in the case simulation of the uncontrolled withdrawal of shim rod number 1 from the DNRR for both the cases of over power limit to 110% and reactor shutdown after 15.03 seconds from the beginning of the accident The input settings values in the simulation computations using the PARCS and RELAP5 codes were comparable at the same time that the LEU working core was started up This illustrates the potential of simulating the uncontrolled withdrawal of a control rod using the PARCS code for the DNRR The differences in values between Figs 3.20 and 3.21 can be explained as follows: (1) the distinction between the spatially dependent 3-D space kinetic model used in PARCS and the point kinetic model used in RELAP5; (2) the thermal hydraulics model used in the PARCS code for PWR type while using thermal hydraulics system of the DNRR in RELAP5.
For the overpower limit for reactor shutdown of 110% nominal power, the scram time was calculated to be around 3.4 seconds using the PARCS and RELAP5 programs (see Figs 3.20 and 3.21) This can be explained by the substantial positive reactivity insertion; consequently, the influence of feedback temperature is negligible in a short period of time, so the power gain in the PARCS and RELAP5 codes are comparable However, if the reactor is shut down at 15.03 seconds after the onset of the accident, the difference in the influence of water and fuel feedback temperature coefficients in the PARCS and RELAP5 models becomes more apparent At the time of reactor shutdown, there was a significant disparity between the power values calculated by the PARCS and RELAP5 codes Integration of the PARCS and RELAP5 codes for the analysis of transitions or accident conditions, such as the uncontrolled removal of a control rod, will be required coupling kinetics and safety analyses of the DNRR or a new research reactor.
Fig 3.19 Power and reactivity in the accident of uncontrolled withdrawal of the
ShR number 1 with and without feedback reactivity temperature coefficients of water and fuel
Fig 3.20 Reactor power transient of one ShR withdrawal from operating power 100%
P_noFB -2 ro_withFB -4 ro_noFB
Fig 3.21 Reactor power and reactivity transient of ShR number 1 uncontrolled withdrawal from operating power 100%
3.2.4 Simulation of the changing of power when inserting positive reactivity smaller than 10 cents
Fig 3.22 depicts the simulation results of the power variation of the DNRR using LEU fuel when inserting 10 cents reactivity and feedback temperature of water and fuel were taken into account Fig 3.23 depicts the changing in position of theReR when modeling a transient with insertion of a positive reactivity less than 10 cents using the PARCS code Fig 3.24 shows the experimental data of the power change of the DNRR when inserting positive reactivity less than 10 cents to increase the reactor power from 0.5% to 50% The transient scenario using the PARCS code shown in Figs 3.22 and 3.23 is similar to the experimental data depicted in Fig 3.24.
The PARCS code simulation (Fig 3.22) yielded a power output of only 24%, significantly lower than the experimental data in Fig 3.24 (50%) This discrepancy stems from differences in thermal hydraulic parameters and feedback reactivity temperature coefficients between the PARCS model and the DNRR Additionally, the 2011 PARCS calculation model requires updates to account for fuel burn-up and beryllium poisoning, which were present in the 2020 experimental measurements.
Fig 3.22 Power and reactivity changing when inserting 10 cents reactivity
Fig 3.23 The changing of the ReR (TD) when inserting 10 cents
Experiment Thựcnghiệm to increase nângcông power suât from từ0 0 5 5% lên to 50% 50%
Fig 3.24 Experimental data of power (D1) and ReR (TD) position when inserting 10 cents
Burn-up calculation results
3.3.1 Validation of the MCDL code
Calculation model of FA is nearly the same between the MCDL and the SRAC codes This means that the active volume taking the same with outermost layer having hexagonal shape The library ENDF/B-VII.0 was applied for both the MCNP and SRAC codes calculations Total burn-up percent in calculation of HEU and LEU FAs were about 36% U-235 and 29% U-235, respectively Output data including neutron flux, reaction rate and multiplication factor were obtained with errors under 0.1% and standard deviations under 0.005% with the total particles in the problem were 12 millions Difference of multiplication factors between the MCDL and the SRAC codes is smaller than 115 pcm for both cases (see Table 3.19) Maximum difference of atom densities of all isotopes is under 10% to actinide isotopes Cm-243, Cm-245 and Cm-246 Figs 3.25 and 3.26 depict calculated results of infinite multiplication factors and atom densities of heavy isotopes at last burn-up step by the MCDL and SRAC codes.
Table 3.19 Infinite multiplication factors of HEU and LEU FAs depending on burn-up
BU (%) MCDL SRAC Difference BU
Fig 3.25 a) Infinite multiplication factor of HEU fuel depending on burn-up steps and b) atom density of actinide isotopes at the end of burn-up step (~ 36% burn up of
Fig 3.26 a) Infinite multiplication factor of LEU fuel depending on burn-up steps and b) atom density of actinide isotopes at the end of burn-up step (~ 29% burn-up of
U-235) The difference in the initial infinity multiplication factor between the MCDL and SRAC codes from initial condition to 15% burn-up for both HEU and LEU fuels is mainly due to the fact that two codes solve the neutron transport equation using different methods In the PIJ (SRAC) code, the deterministic method of collision probability has been simplified in calculation neutron energy group (107 groups) and the geometry (2-D) as compared to the MCNP code, which uses Monte Carlo method with real geometry and continuous computation libraries Calculation results of neutron flux, reaction rate, and multiplication factor of the MCNP code are always higher fidelity, reliability than the SRAC code and are considered as benchmark problem Because of using the same burn-up chain and similar burn-up reactions, when the presence of heavy and fission products isotopes as well as the decrease in mass of U-235 with burn-up to yield equivalent atomic concentration number densities between both codes, then the calculation results of multiplication factors have less difference.
To calculate the burn-up distribution of the entire core, all FAs and beryllium rods or blocks are divided into five equal-volume nodes in axial direction With 12 million particles in a single running case, the error of neutron flux and reaction rates derived from the MCNP code is less than 0.12% and 2.1%, respectively, and the standard deviation of the multiplication factor is less than 0.008% In average, using
64 cores processing for parallel calculation, the time consuming fore each running case is about 1.5 hours.
Depletion calculation of fresh core using 89 HEU FAs and 15 beryllium rods of the DNRR at start up working core in 1984 was implemented by the MCDL code and the REBUS-MCNP linkage system code 538 full power days (FPD) continuous operating of the DNRR under nominal power of 500 kW and 100 days for cooling were modeled in both codes The maximum discrepancies of active nodes and cells are under 2% and 1%, respectively The excess reactivity at the end of fuel cycle of the MCDL code is higher than those of the REBUS-MCNP code about 0.215 %k/k.
Fig 3.27 shows calculated results of both codes The main reason of the difference of multiplication factor values between two codes is different library data used forMCNP code In REBUS-MCNP linkage system code, ENDF/B6.0 was applied and the calculated multiplication factor is smaller Library ENDF/B6.0 of MCNP code has coarse meshes of energy while ENDF/B-VII.1 has fine meshes of energy and evaluated data in ENDF/B-VII.1 are updated with latest experimental data.
Fuel assembly Beryllium Water Dry and wet channels
Fig 3.27 Burn-up (% U-235) distribution of fresh HEU core after 538 FPDs operation (REBUS-MCNP system code at upper values and MCDL code at lower values) Fresh LEU core using 92 FAs and 12 poisoned beryllium rods is calculated for burn-up distribution Total time for depletion scheme is 600 full power days and 100 days for cooling Maximum difference between two codes in active nodes and cells is about 5% and 2%, respectively The difference of excess reactivity at the end of cycle
Fuel assembly Beryllium Water Dry and wet channels
Fig 3.28 Burn-up (%U-235) distribution of fresh LEU core after 600 FPDs operation (MCNP_REBUS code at upper values and MCDL code at lower values)
The MCDL code was used to investigate burn-up of HEU and LEU VVR-M2
FAs with the total burn-up of 36.29% and 28.50% of U-235, respectively, as shown in Table 3.19, Figs 3.25 and 3.26, and the results performed by the MCDL and the
SRAC codes indicate that the difference of multiplication factors between the codes is of 114.61 and 107.9 pcm for HEU and LEU FA, respectively The difference of atomic number densities of all isotopes less than 10% to actinide isotopes Cm-243,
Cm-245 and Cm-246 as shown in Figs 3.25 and 3.26.
The burn-up distribution of whole fresh HEU and LEU cores of the DNRR was also analysed The results show that the excess reactivity at the end of fuel cycle with the MCDL code is higher than those with the MCNP_REBUS linkage code about 0.215 %k/k.
3.3.2 Calculation results of the HEU core
The changing of atomic number density of heavy isotopes of HEU and LEU fuels of the DNRR were evaluated by using MCNP code The calculation results showed that the total operation time of LEU fuel is longer than those of HEU fuel with the main reason related to U-235 mas and uranium density difference of both fuel types. a) b)
Fig 3.29 The changing of heavy isotopes of a) HEU and b) LEU fuels of the DNRR
The fuel burn-up of the HEU core was computed from the 89 FAs configuration to the 100 FAs configuration to the 104 FAs to the shuffling of 12 FAs and replaced channel 1-4, channel 13-2 with 2 FAs to create the core using 106 FAs.
In September 2007, the mixed-core was established so that full core conversion might be implemented gradually later In May 2011, all burnt 106 HEU FAs were moved out from the core and stored in the intermediate stage of the reactor tank In August
2011, they were transferred to the spent fuel storage pool and then shipped back to the Russian Federation in July 2013 Up to May 2022, the DNRR has refueled 7 times for the core using HEU fuels and the mixed core; 02 times conducted to refueling for the core using LEU fuels The time for fuel burn-up calculation of HEU core and mixed-core from 1984 to 2011 as in Table 3.20.
Table 3.20 Operation time and excess reactivity of the HEU cores and mixed-cores
Core configuration time (day at excess excess (C- power 500 reactivity reactivity E)/C*100 kW) (β eff ) (β eff )
104 HEU FAs (2 beryllium rods at channels 13-2 and 1- 31.75 3.36 3.35 0.30
106 HEU FAs (2 new FAs at
Employing the MCDL code, the fuel burn-up of the remaining 106 HEU FAs in the mixed-core was calculated, considering beryllium poisoning Gamma scanning was conducted to measure Cs-137 isotope activity and the Cs-134/Cs-137 ratio These measurements were compared to the calculated results, validating the burn-up estimation of the 106 HEU FAs.
The two measurement methods showed significant differences in accuracy, with the method using the ratio yielding a 20% difference between calculation and experimental data, while the method using only Cs-137 had a smaller difference of 15.5% Despite these differences, both methods exhibited a strong correlation between calculated and measured data, indicating that the calculations could reliably estimate the experimental results.
Cs-137 and about 6.8% for the method using the isotope ratio Cs-134/Cs-137 Fig.
3.30 shows the difference of calculation results and experimental data when using Cs-
137 isotope Previously in 2000, gamma scanning method was also performed for the
100 HEU FAs core configuration The results show that there is a good agreement between the calculated results and the experimental data. d if fe re n ce b et w ee n c al cu la ti on an d ex pe ri m en ta l d at a P er ce nt ag e (% ) re su lt s
Identify number of 106 HEU FAs
Summary of Chapter 3
The chapter presents calculation results of neutronics, thermal hydraulics,primary RIA analysis, and fuel burn-up for core and fuel management for the DNRR using fully LEU fuels The obtained results were compared with experimental data to confirm about the high fidelity and good calculation model that have been built for the DNRR.
In neutronics, the characteristics of the DNRR using LEU fuel were investigated to determine parameters related to reactivity, control rod worths, neutron flux distribution, power peaking factor, feedback coefficients and kinetics These obtained data were used for core management and assured ability for safe operation as well as effective utilization Then, MCNP5 or 6 codes and ENDF/BVII.1 library were used as official codes for core management of the DNRR in neutronics calculation.
The thermal hydraulics analsysis was carried out to estimate safety factors at steady state operation of 500 kW Under normal operation condition with inlet temperature 32 0 C, the maximum fuel cladding was under 91 0 C far below limitation of 103 0 C When adding hotpot enginerring data in thermal hydraulics analysis, the cladding temperature was still under melting temperature of aluminum and the fuel cladding integrity was ensured.
The primary safety analysis for the Reactivity Insertion Accident (RIA) of the Dual-fluid Natural-circulation Reactor (DNRR) using Low-Enriched Uranium (LEU) fuel was executed utilizing the 3-D kinetics code PARCS The computational results demonstrated that under the accident scenario involving positive reactivity insertion, the DNRR remained in a safe state, and the fuel cladding integrity was preserved.
The MCDL code was applied to calculate for burn-up as well as refueling to the DNRR using effectively 10 fresh remained LEU FAs After establishing 98 LEU FAs core configuration, the ability to extend operation time of the DNRR up to 2030 if adding 28 LEU FAs with more than 32000 hours running at full power of 500 kW. The burn-up and refueling calculations for the DNRR were conducted with ability to enhance radioisotope production of I-131 isotope When adding two new irradiation channels at cell 5-6 and 9-6 together with accumulated irradiation of target containers by moving position from rotary specimen to inside the core at each operating cycle in week, the activity of each irradiated container after 3 cycles can be reached more than
5 Ci and each month the DNRR can produce more than 100 Ci of I-131 isotope.
Utilizing MCNP for neutronics calculations, PLTEMP4.2 for thermal hydraulics analysis, and MCDL for burn-up calculations, this dissertation addressed three significant issues Firstly, it calculated and analyzed neutronics and thermal hydraulics for a LEU core with 92 fuel assemblies Secondly, it employed the PARCS code for preliminary DNRR applications with 3-D kinetics calculations Lastly, it developed the MCDL code, integrating beryllium poisoning for burn-up calculations, to explore HEU and LEU cores.
To optimize neutronics and thermal hydraulics on the Dynamic Neutron Research Reactor (DNRR), sensitivity analysis (SA) methods were employed to optimize refueling loading patterns using 10 fresh Low Enriched Uranium (LEU) fuels This analysis aimed to enhance radioisotope production of the I-131 isotope Major findings included:
1 The detailed investigation of VVR-M2 LEU and HEU fuels was conducted with a focus on multiplication factors, spectrum, and determining the most suitable library for DNRR as ENDF/BVII.
2 Using the MCNP code and other computer codes such as SRAC2006, WIMS- ANL and REBUS-PC to evaluate all neutronics characteristics of the LEU core with
92 LEU FAs The obtained results were compared to experimental data or calculation results from other codes and the discrepancy between calculation results and experimental data was found to be a maximum of 10% The effective multiplication factors of twenty-five distinct core configurations were computed, and the average values from three codes and experimental data were within 20 pcm of one another In comparison to experimental data, the effective reactivity of FAs, beryllium rods, and the control rods' value for LEU core were estimated with a maximum 10% variance. Neutron flux distribution at each FA in the core and irradiation positions were also calculated for radioisotope production and other applications The power peaking factor was an essential value for the thermal hydraulics analysis and was determined following the positions of control rods Other parameters including feedback
135 temperature coefficients and kinetics parameters for the LEU core were evaluated and using for thermal hydraulics and safety analysis.
3 The validation of the PLTEMP/ANL4.2 code was carried out by comparing the calculation results of the LEU core to experimental data of the HEU core of the DNRR with very good consistency The LEU working core with 92 FAs and 12 beryllium rods was evaluated and subjected to steady-state thermal hydraulic analysis without hot channel factors at the nominal thermal power of 500 kW The obtained results show that at the hottest FA, the fuel cladding temperature was only 90.4 o C, which was far below the limitation of the VVR- M2 fuel cladding temperature of 103 o C, the ONB temperature was about
115.6 o C, according to the Forster-Greif correlation, and the minimum DNBR value was about 32.0 When the systematic uncertainties were taken into account, the maximum fuel cladding temperature was predicted to be 98.4 o C, which again was well below the limit value of 103 o C, the DNBR value was 17.79, and the coolant temperature at the outlet of the hottest FA was very low compared with the saturation temperature of 107 o C This means that the DNRR met the thermal hydraulics safety at steady-state condition with application of the global hot channel factors When all systematic as well as random uncertainties were applied to a limiting calculation, the maximum fuel cladding temperature obtained was 114.3 o C, which was several degrees below the ONB point of 116.2 o C The minimum DNBR value, according to Shah‘s correlation, was estimated as 15.2, which was much higher than the acceptable criterion of 1.5 for the DNRR.
To the second purpose, the PARCS code was used for preliminary calculations in kinetic and transient analysis of LEU core with 92 FAs and calculation results were compared with experimental data or calculation results from the RELAP5 code.The Serpent code was used to generate multi-group cross-sections for 3-D kinetics calculations of the DNRR in PARCS code model The DNRR calculation model,completely specified with the Serpent 2 code, was also utilized to validate the steady- state and using in transient/accident investigation The calculation results showed the limitation of applying the PARCS code to the research reactor so to have a tool for 3-
D kinetics coupling with system code as the RELAP5 code The main reason of disadvantage of the PARCS code in thermal hydraulics is that safety analysis factors are default parameters for PWR type.
The final objective of this research was to develop the MCDL code to calculate burn-up for the DNRR using HEU and LEU fuels The specific outcomes are as follows:
1 The MCDL code was validated for HEU and LEU fuels, as well as the initial HEU and LEU core with 89 and 92 FAs, respectively The generated calculation results were compared with the REBUS-MCNP code, and the burn-up percentage difference between the two codes was less than 5%.
2 Detailed examination for HEU and mixed cores including fuel burn-up and beryllium poisoning estimation to isotopes He-3, H-3, Li-6 The burn-up distribution of 106 HEU FAs were calculated by the MCDL code and compared to experimental data using gamma-scanning method The maximum difference between calculation results and experimental data was under 18% The poisoned beryllium blocks and rods were updated for using in design calculation for LEU core in neutronics.
with and without feedback reactivity temperature coefficients of water and
SRAC2006 MVP and WIMS-ANL REBUS- critical core MVP-Burn and REBUS MCNP
MCNP code exhibits exceptional accuracy and fidelity, rendering it an optimal choice for modeling complex structures and historical operations, such as those associated with DNRR Its computational prowess enables it to manage core and fuel for established LEU cores with high precision, making it an invaluable tool for nuclear engineering applications.
The error of experimental data of effective multiplication factors was based on the position of control rods and changing of water temperature inside the reactor tank. The effective reactivity error in position of ReR in linear range from 200 mm to 400 mm was about 1.15 cents in each mm Then the standard deviation of experimental data of multiplication factor was 0.0115%.
3.1.1.3 Excess reactivity, control rod worth, beryllium rods
The excess reactivity evaluated by the MCNP code for the working core configuration was approximately 7.8% and was similar to the experimental result It was ensured that the shutdown margin reactivity of the working core would be greater than -1%k/k The effective of control rods worth were determined and compared to experimental data using the asymptotic period method for measuring ReR and compensation method for ShRs or SaRs The highest discrepancy between the calculation results and the experimental data was under 7% In the calculation, control rod worths were estimated by changing positions of each considered control rod (fully insertion or withdraw) at critical condition of core configurations in Table.
Table 3.5 The effective control rods worth of the working core using 92 LEU FAs
Difference (%) Control rod Experimental Calculation
(Cal-Exp)/Cal*100 data results
The error of reactivities in theoretical calculations is less than 0.5% and depended on standard deviation of the effective multiplication factor from 0.005% to
0.009% The error of experiment is mainly depended on the position of ReR, which in the linear region from 200 mm to 400 mm is equivalent to 1.15 cents per mm.
Based on the error of the ReR‘s worth is approximately 5%, the measured error of
SaRs and ShRs worths is between 5% to 10% The asymptotic periodic method was applied to measure effective worth of ReR, the power of the reactor would increase following the asymptotic period as N(t) = N(l)e t/T after transient time l T is reactor period, which is the time that reactor power increases e (2.73) times The reactivity can be determined by inhour equation with asymptotic period corresponding T as follow:
( where, i is decay constant of delayed neutron group i (s -1 ) = ln2/t1/2 β) in the thermal energy range of material, suchi is delayed neutron fraction for group i, l is prompt neutron lifetime (s), and T is reactor period
Control rod worths of four shut-off rods (ShRs) were calculated using the compensation method based on the effective reactivity profile of reactivity regulators (ReRs) Additionally, effective reactivities of fuel assemblies (FAs) and beryllium rods were determined via calculations and experiments on the working core employing 92 FAs Comparison between calculated and experimental data revealed a maximum difference of approximately 5 cents.
Table 3.6 The effective reactivity of LEU FAs
No Experimental Calculation Difference position data results (Exp.-Cal.)
The method measurement of effective reactivity based on the changing position of ReR when loading and unloading measured FAs from the reactor core.
The error of calculations was negligible and under 0.5% while experiment errors were in the range from 5% to 10%.
Table 3.7 Effective reactivity of beryllium rods
No Experimental Calculation Difference position data results (Exp.-Cal.)
The beryllium rods in the calculation have been evaluated for beryllium poisoning to compare with experimental data The measurement of the effective reactivities of the FAs and the beryllium rods was based on the position of the ReR and the error was only about 5 to 6 cents.
During physical start-up, the reactor core was devoid of photo-neutrons Experiments to measure reactivity were conducted at a low power of 5.10 -5 % nominal power (~ 25 W), ensuring negligible photo-neutron effects This low power level allowed for highly accurate and reliable experimental data, given the absence of photo-neutron interference.
87 to beryllium produced photo-neutron and then slowed down to thermal neutron as a neutron source, the presence of beryllium material within the reactor core is advantageous for a second start-up reactor without using an external neutron source. Nonetheless, beryllium material can impact a reactor's beryllium poisoning, excess reactivity, and neutron field within the reactor core.
The radial thermal neutron flux distribution of the entire LEU working core was determined by measuring the neutron flux at the position located 30 cm above the bottom of FA as the centerline of FA The difference between the calculation results and experimental data is less than 3%, with the exception of cells 6-4 and 12-2 towards horizontal beam tubes, where the differences were 8.13% and 8.56%, respectively The relative flux measurements were normalized to 1.0 in the neutron trap, where the neutron flux is the highest.
Table 3.8 The calculation results and experimental data of relative thermal neutron flux in radial direction
Experimental Calculation (Cal-Exp)/Cal*100 data results
Calculation results and experimental data of thermal neutron flux distribution in axial direction at the center of the FAs, beginning at 0 cm from the bottom of FA.
In the axial range from 15 cm to 65 cm in the middle of FA, the difference between calculated results and experimental data was approximately 4%, whereas for the other ranges, the difference was approximately 10% The activation method was applied to evaluate relative thermal neutron flux at irradiation positions and in FAs, beryllium rods by using Lutecium foil with enriched 2.59% of the Lu-176 isotope Gold foil was used to estimate the absolute thermal neutron fluxes at irradiation positions within the reactor core and at rotary specimens Thermal neutron flux can be determined using the activated foils in the thermal neutron field of the reactor under irradiation time t i , waiting time t w , and measured time t m , following the formula:
√ √ where is decay constant of active nuclei [s -1 ], m – mass of foil [g], - enrichment of taget isotope, A – Mass number of target isotope [g], N A = 6.02×10 23 - Avogadro constant; 0 – active micro cross-section [m 2 ] at room temperature T 0 = 20 0 C (with velocity 2200 m/s, equivalent energy 0.025 eV), T n – neutron temperature at irradiation position, - measurement efficiency, B(t m ) – total count number with measured time t m , G th – self shielding factor, - branching efficiency.
The error of neutron activation method applying to the DNRR has a value less than 10% with contribution from mass and shape of foil, time irradiation or measurement, and detector efficiency The Cd cover of foil is also needed in order to eliminate thermal neutron and pay attention to epithermal neutron flux.
Table 3.9 The calculation results and experimental data of relative thermal neutron flux in axial direction
Calculation results and experimental data of thermal neutron flux distribution in axial direction of the neutron trap at the core center are shown in Table 3.10; position 0 cm is at the bottom of the irradiation channel The maximum discrepancy between calculation results and experimental data was under 5%.
Table 3.10 Calculation results and experimental data of thermal neutron flux at the neutron trap of LEU working core
The maximum thermal neutron flux position in axial direction is 20 cm from the bottom to the top with a cosine shape and the maximum peak will be shifted to the higher position following changing position of control rods as reactor operation time For irradiation to enhance the ability to produce I-131 isotope, the neutron trap was modified to load 9 containers by 3 irradiation channels In the LEU core, 12 beryllium rods located around neutron trap have two roles including increasing moderation material to thermalization of fast neutron in the reactor core and avoiding high power density of FAs close to the neutron trap.