Fragmentation of a Single Molten Metal Droplet Penetrating Sodium Pool I Copper Droplet and the Relationship with Copper Jet

The progression of hypothetical core disruptive accidents in metallic fuel fast breeder reactors is strongly affected by the fragmentation of molten metallic fuels due to the molten fuel-coolant interaction (FCI). As a basic study of FCI, the present paper focuses on the fragmentation of a single molten copper droplet with mass from 1 to 5 g, whichpenetrated a sodium pool at instantaneous contact interface temperatures (T_i) from 995 to 1,342°C. Intensive fragmentation of a single molten copper droplet was clearly observed even if T_i values are below the melTsing point (1,083°C) of copper besides the higher T_i range. The intensive fragmentation shows that the mass median diameters (D_m) of copper droplets with a fivefold difference in mass or the same mass have little difference, i.e., they are nearly the same. Under the lower T_i condition, the D_m data of droplet fragments of both the same and different masses scatter widely. It is found that the present D_m/D₀ data of mass median diameter normalized by the diameter before touching sodium (D0) give a distribution with larger values than those of molten copper jets with large mass from 20 to 300 g under the lower T_i condition, which were previously reported by the authors, because of the limited amount of heat of droplets. The present Dm=D0 data under the higher T_i condition are found to show an effecTive fragmentation compared with those of molten copper jets with a large mass of 4 kg.     

Break up time of fragmentating-solidifying UO2 spheres when quenched in sodium

When molten UO₂ is quenched in sodium, a sand-like debris results containing about 80% of fractured particles and 20% of smooth particles and spheres. The production of the fractured particles is normally explained by the thermal stress fragmentation model. Previously brittle fracture mechanics was applied to the complete solid shell of a freezing UO₂ drop, i.e. where 954°C < T < 2850°C; a calculation of fragmentation time was not possible. In this contribution the solid shell is continuously subdivided in a plastic or ductile layer for 1300°C < T < 2850°C and a brittle one for 945°C < T < 1300°C. Cracking occurs in the brittle layer only. In the present model a layer of a predescribed depth is assumed to ablate instantaneously, when the temperature reaches the transition point of elastic of ductile behavior (T = 1300°C) at its inner boundary. A new layer is formed within a time step, governed by the heat conduction equation. The discontinuous ablation process is thus related to the continuous progression of the solidification front. A calculation of the fragmentation time is possible: in principle it comprehends the summation of a large number of time steps for the formation of brittle layers. The thickness of the cracked brittle layer is parametrized to 20, 10, 5 and 1 μm. The concept of instantaneous ablation was suggested by the experience that the violent boiling forces of sodium are very effective on the UO₂ surface. The introduction of these minor changes makes the thermal stress model more realistic, because it can explain now, why UO₂ does not fragment in argon and water. The fragmentation time assessed for a UO₂ drop of 7.2 mm diameter in sodium, brittle layer 10 μm, is 250 ms.     

Fragmentation of continuous molten copper droplets penetrating into sodium pool

The progression of hypothetical core disruptive accidents (CDAs) in metal fuel cores is strongly affected by exclusion of molten metal fuel from the core region due to molten fuel–coolant interaction (FCI). As a basic study of FCI, the present paper focuses on the fragmentation characteristics of continuous molten copper droplets with a total mass from 20 to 50 g penetrating into a sodium pool. The results show that the fragmentation of the continuous molten copper droplets is sensitive to the change of the hydrodynamic and thermal conditions when the instantaneous contact interface temperature (T_i) is lower than the turning point (T_tp) and insensitive at T_i > T_tp. Compared with the fragmentation of a single droplet, the fragmentation of continuous droplets is accelerated and enhanced due to the collision between the droplets and the upward microjets. The present mass median diameter (D_m) or dimensionless mass median diameter (D_m/D₀) of continuous copper droplets shows a distribution with smaller values than those of single copper droplet, and larger values than those of copper jets under similar thermal and hydrodynamic conditions. These results are promising to assure the termination of accidents in CDAs and useful to the core design with enhanced safety in FBRs.     

Fragmentation of a single molten metal droplet penetrating into sodium pool. IV. Thermal and hydrodynamic effects on fragmentation in copper

To characterize the relationship between thermal and hydrodynamic effects on fragmentation of molten metallic fuels, with the interaction of the sodium coolant under a wide range of thermal and hydrodynamic conditions, in this paper, we focus on the fragmentation characteristics of a single molten copper droplet (1 and 5 g) with an ambient Weber number (We _a) from 102 to 614 and superheating conditions from 15 to 574°C, which penetrates into a sodium pool at an initial temperature from 298 to 355°C. In our experiments, fine fragmentations of the single molten copper droplets with a high We _a were clearly observed even under a supercooled condition that is well below the copper melting point of 1083°C. The dimensionless mass median diameters (D _m /D ₀) of molten droplets with a high We _a are less than the molten droplets with a low We _a under the same thermal condition. When We _a was approximately >200, the hydrodynamic effect on fragmentation became dominant over the thermal effect under a relatively low superheating condition. For a higher We _a range, the comparisons indicated that the fragment sizes of the molten copper droplets had similar distributions to those of copper and metallic fuel jets and stainless steel droplets even with different thermophysical properties and a 1000-fold mass difference, which implied the possibility that the fragment size characteristics of the molten metal jets could be evaluated by the interaction of a single droplet with the sodium coolant without consideration of dropping modes and mass.     

Melting attack of solid plates by a high temperature liquid jet — effect of crust formation

When a molten UO₂ jet impinges on a steel structure in a reactor vessel during a severe accident, the erosion rate of the steel by the molten UO₂ jet is expected to be limited considerably by a UO₂ crust layer forming on a molten steel substrate at the jet/steel plate interface. A series of simulation experiments was performed to study the melting behavior of solid plates by high temperature liquid jets and the effects of crust forming at jet/structure interface. In the first series of experiments, salt (NaCl) was selected as the jet material and tin (Sn) as the solid structure. The experiments were conducted with varying the jet diameter (10 30 mm) and jet temperature (900 1100°C). The jets were accelerated to a range of 3 5 m/s at the nozzle outlet by gravitational force and impinged perpendicularly to the solid plate underneath. Furthermore, to check the effects of the thermo-physical properties on the erosion behaviors, preliminary experiments were performed by using a molten Al₂O₃ jet ( 2200°C) impinging on stainless steel plate at room temperature. The erosion rates obtained in the present experiments were far less than the values predicted by an analytical solution that neglects the existence of a crust layer and its thermal effects. With the inclusion of the crust behavior in the model, the experimental results were predicted fairly well. From the present experiments, a Nusselt number of the turbulent heat transfer, which takes into account simultaneous melting and freezing in the impingement region of a molten jet, is correlated by a Reynolds number and a Prandtl number as follows: Nu_m = 0.0033 Re---Pr.In conclusion, the existence of a crust layer plays an important role in the erosion process of a solid plate by the molten fuel jet with high melting point as in a reactor situation.     

Boiling fragmentation of molten stainless steel and copper in sodium

Approximate measurements were made on fuel fragmentation of stainless steel/sodium and copper/sodium systems: the surface area of stainless steel increased by a factor of 260 to 3.1 and that of copper by a factor of 300 to 2.7 m²/kg. The number of particles obtained was about 10⁸ per kg fuel. The conditions were: stainless steel 1600°C, copper 1927°C, sodium 400°C at 1 bar ambient pressure (argon cover gas); no detectable pressures accompanied the interaction.A violent sodium boiling model is used for the explanation of the results. A specified number of sodium vapor bubbles grow and collapse with high frequency on the contact surface. The collapse effectively increases the fuel (=heating) surface, and an appropriate energy transfer coefficient is assumed. Contact temperatures, nucleation, bubble statistics, mechanical energy transfer, surface increase and heat transfer are coherently treated and describe the fragmentation transient. The copper surface area is calculated to increase by a factor of about 750 to 6.6 m²/kg within very short times of 1 ms or even less, the stainless steel surface by 200 to 2.4 m²/kg.     

Numerical analysis of fragmentation mechanisms in vapor explosions

Fragmentation of molten metal is the key process in vapor explosions. However, this process is so rapid that the mechanisms have not yet been clarified in experimental studies. In addition, numerical simulation is difficult because we have to analyze water, steam and molten metal simultaneously with boiling and fragmentation. The authors have been developing a new numerical method, the moving particle semi-implicit (MPS) method, based on moving particles and their interactions. Grids are not necessary. Incompressible flows with fragmentation on free surfaces have been calculated successfully using the MPS method. In the present study, numerical simulation of the fragmentation processes using the MPS method is carried out to investigate the mechanisms. A numerical model to calculate boiling from water to steam is developed. In this model, new particles are generated on water–steam interfaces. A two-step pressure calculation algorithm is also developed. Pressure fields are separately calculated in both heavy and light fluids to maintain numerical stability with the water and steam system. The new model and algorithm are added to the MPS code. Water jet impingement on a molten tin pool is calculated using the MPS code as a simulation of collapse of a vapor film around a melt drop. Penetration of the water jet, which is assumed in Kim–Corradini’s model, is not observed. If the jet fluid density is hypothetically larger, the penetration appears. Next, impingement of two water jets is calculated. A filament of the molten metal is observed between the two water jets as assumed in Ciccarelli–Frost’s model. If the water density is hypothetically larger, the filament does not appear. The critical value of the density ratio of the jet fluid over the pool fluid is ρ_jet/ρ_pool=0.7 in this study. The density ratios of tin–water and UO₂–water are in the region of filament generation, Ciccarelli–Frost’s model. The effect of boiling is also investigated. Growth of the filament is not accelerated when the normal boiling is considered. This is because normal boiling requires more time than that of the jet impingement, although the filament growth is governed by an instant of the jet impingement. Next, rapid boiling based on spontaneous nucleation is considered. The filament growth is markedly accelerated. This result is consistent with the experimental fact that the spontaneous nucleation temperature is a necessary condition of vapor explosions.     

Thermal Fragmentation of a Molten Metal Jet Dropped into a Sodium Pool at Interface Temperatures below Its Freezing Point

In order to verify the thermal fragmentation of a molten jet dropped into a sodium pool at instantaneous contact interface temperatures below its freezing point, a basic experiment was carried out using molten copper and sodium. Twenty grams of copper was melted in a crucible with an electrical heater and was dropped through a 6 mm nozzle into a sodium pool of 553 K, in the form of a jet column. Thermal fragmentation originating inside the molten copper jet with a solid crust was clearly observed in all runs. It is verified that a small quantity of sodium, which is locally entrapped inside the molten jet due to the organized motion between the molten jet and sodium, is vaporized by the sensible heat and the latent heat of molten copper, and the high internal pressure causes the molten jet with a solid crust to fragment. It is also found that the fragmentation caused in the molten copper-sodium interaction was severer than that in the molten uranium alloy jet-sodium interaction, which was reported by Gabor et al, under the same superheating condition and lower ambient Weber number condition of molten copper.     

Fuel elements of the high temperature pebble bed reactor

This work is devoted to spherical fuel elements for the high temperature pebble bed reactor, their manufacture and the conditions which they must satisfy for use in a process-heat reactor with an average gas outlet temperature T_{G, out} of 950°C. The positive results known from the operation of the AVR with T_G,out = 950°C and from extensive irradiation tests of the THTR-300 element with BISO coated mixed-oxide particles, even beyond the range of design specifications, and possible damage mechanisms are described in detail. They show that a spherical fuel element already exists, for which only a short-term development is needed to produce a coolant temperature of 950°C in a process-heat reactor. Further developments will be characterized by the use of a pebble bed HTR for high conversion rates (c ≈ 0.95) or for average gas outlet temperatures of more than 950°C. At higher temperatures the increased demands, mainly with regard to the release of fission products, can be fulfilled through the application of TRISO-coated fuel particles and the doping of the fuel kernels with . The reprocessing programme for fuel elements in the Federal Republic of Germany is mentioned briefly.     

LWR fuel rod behavior during severe accidents

Chemical interactions between UO₂ fuel and Zircaloy cladding up to 2350°C are described. UO₂/Zircaloy single effects tests have been performed with short LWR fuel rod segments in inert gas and under oxidizing conditions. The reaction kinetics of molten Zircaloy cladding with solid UO₂ fuel has been investigated with UO₂ crucibles containing molten Zircaloy. The UO₂/Zircaloy reactions obey parabolic rate laws. The oxygen uptake by solid Zircaloy due to chemical interaction with UO₂ occurs nearly as quickly as that from the reaction with steam or oxygen.To study the competing effects of the external and internal cladding oxidation under realistic boundary conditions and the influence of the uncontrolled temperature escalation due to the exothermic steam/Zircaloy reaction on the maximum cladding temperature, single rod and bundle experiments have been performed. Electrically heated fuel rod simulators, including absorber rod material (Ag, In, Cd alloy), guide tubes and grid spacers are used. The maximum measured cladding temperature during the temperature escalation was about 2200°C. The failure temperature of the absorber rods and the extent of bundle damage depends on the guide tube material (Zircaloy or stainless steel) and varies between 1200 and 1350°C. The molten materials and liquid reaction products can relocate and form large coherent lumps on solidification, which may result in complete blockage of the fuel rod bundle cross section. In the future, 7 × 7 bundle experiments of 2 m overall length will be performed in the new CORA facility to study, in addition, the influence of quenching on fuel rod integrity.     

Results on research of templates from Kozloduy-1 reactor pressure vessel

The studies on the specimens manufactured from the templates cut out from the weld 4 of Kozloduy NPP Unit 1 reactor vessel have been conducted. The data on chemical composition of the weld metal have been obtained. Neutron fluence, mechanical properties, ductile to brittle transition temperature (DBTT) using mini Charpy samples have been determined. The phosphorus and copper content averaged over all templates is 0.046 and 0.1 wt.%, respectively. The fluence amounted up to 5×10¹⁸ n cm⁻² within 15–18 fuel cycles, and about 5×10¹⁹ n cm⁻² for the whole period of operation. These values agree well with calculated data. DBTT was determined after irradiation (T_k) to evaluate the vessel metal state at the present moment, then after heat treatment at the temperature of 475°C to simulate the vessel metal state after thermal annealing (T_an), and after heat treatment at 560°C to simulate the metal state in the initial state (T_k0). As a result of the tests the following values were obtained: T_k, +91.5°C; T_an, +63°C; and T_k0, 54°C. The values of T_k and T_an obtained by measurements were found to be considerably lower than those predicted in accordance with the conservative method accepted in Russia (177°C for T_k and 100°C for T_an). Thus, the obtained results allowed to make a conclusion that it is not necessary to anneal Kozloduy NPP Unit 1 reactor vessel for the second time. The fractographic and electron-microscopic research allowed to draw some conclusions on the embrittlement mechanism.     

Distance for fragmentation of a simulated molten-core material discharged into a sodium pool

A series of experiments has been carried out to obtain experimental knowledge on the distance for fragmentation of a molten core material discharged into the sodium plenum during postulated core disruptive accidents of sodium-cooled fast reactors. In the current experiments, 0.9 kg of molten aluminum (initial temperature: around 1473 K) was discharged into a sodium pool (diameter: 0.11 m, depth: 1 m, initial temperature: 673 K) through a nozzle (inner diameter: 20 mm). Visual observation of the fragmentation behavior was performed using an X-ray imaging system. The following experimental results were obtained. (1) Liquid column of molten aluminum was intensively fragmented almost simultaneously with a rapid expansion of sodium vapor in the vicinity of the column. (2) Due to the intensive fragmentation, penetration of the liquid column was limited to approximately 100 mm or so from the sodium level. (3) The molten aluminum was rapidly cooled after the intensive fragmentation. Based on these results, the distance for fragmentation of the liquid column was estimated to be 100 mm in the experiments. Through the current experiment, useful knowledge was obtained for the future development of an evaluation method of the distance for fragmentation of the molten core material.     

Molten fuel-coolant interaction during a reactivity initiated accident experiment

The results of a reactivity-initiated accident experiment, designated RIA-ST-4, are discussed and analyzed with regard to molten fuel-coolant interaction (MFCI). In this experiment, extensive amounts of molten UO₂ fuel and zircaloy cladding were produced and fragmented upon mixing with the coolant. Coolant pressurization up to 35 MPa and coolant overheating in excess of 940 K occurred after fuel rod failure. The initial coolant conditions were similar to those in boiling water reactors during a hot startup (that is, coolant pressure of 6.45 MPa, coolant temperature of 538 K, and coolant flow rate of 85 cm³/s). It is concluded that the high coolant pressure recorded in the RIA-ST-4 experiment was caused by an MFCI and was not due to gas release from the test rod at failure, Zr/water reaction, of UO₂ fuel vapor pressure. The high coolant temperature indicated the presence of superheated steam, which may have formed during the expansion of the working fluid back to the initial coolant pressure; yet, the thermal-to-mechanical energy conversion ratio is estimated to be only about 0.3%.     

A thermal stress mechanism for the fragmentation of molten UO2 upon contact with sodium coolant

An important aspect of fuel-coolant interaction problems relative to various hypothetical LMFBR accidents is the fragmentation of molten oxide fuel on contact with sodium coolant. In order to properly analyze the kinetics of such an event, an understanding of the breakup process and an estimate of the size and dispersion of such fragmented fuel must be known. A thermal stress initiated mechanism for fragmentation is presented using elastic stress theory for the cases of both temperature-dependent and independent mechanical properties. Included is a study of the effect of the choice of surface heat transfer boundary condition and the compressibility of the unsolidified inner core. Results of parametric calculations indicate that the thermal stresses induced in the thin outer shell and the pressurization of the inner molten core are potentially responsible for the fragmentation. For UO₂ in Na the calculated stresses are extremely high, while for aluminum in water they are much smaller and a strong function of the surface heat transfer boundary condition. Qualitatively, these results compare favorably with small scale dropping experiments, that is, molten UO₂ quenched in Na undergoes fragmentation while aluminum in water usually results in little breakup. The experimentally observed increase in breakup with decreasing coolant temperature is also in qualitative agreement with the thermal stress-induced mode of fragmentation.     

Verification of rod safety via confidence intervals for a binomial proportion

The probabilistic safety assessed to a set of N fuel rods assembled in one core of a nuclear power reactor is commonly modelled by ∑_i≤N X_i, where X₁, …, X_N are independent Bernoulli random variables (rv) with individual probability p_i = P (X_i = 1) that the ith rod shows no failure during one cycle. This is the probability of the event that the ith rod will not exceed the failure limit during one cycle. The safety standard presently set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) requires that the expected number of unfailed rods in the core during one cycle is at least N − 1, i.e., E(∑_i≤N X_i) = ∑_i≤N p_i ≥ N − 1, whereby a confidence level of 0.95 for the verification of this condition is demanded. In this paper, we provide an approach, based on the Clopper–Pearson confidence interval for the proportion p of a binomial B(n, p) distribution, how to verify this condition with a confidence level of at least 0.95. We extend our approach to the case, where the set of N fuel rods is arranged in strata, possibly due to different design in each stratum.     

On the mechanism of aluminum ignition in steam explosions

An available theory [Epstein, M., Fauske, H.K., 1994. A crystallization theory of underwater aluminum ignition. Nucl. Eng. Des. 146, 147–164] of the ignition of aluminum melt drops under water, which is based on the assumption that the aluminum oxide (Al₂O₃) drop-surface skin first appears in a metastable molten state, is compared with existing experimental data on the ignition of aluminum drops behind shock waves in water [Theofanous, T.G., Chen, X., DiPiazza, P., Epstein, M., Fauske, H.K., 1994. Ignition of aluminum droplets behind shock waves in water, Phys. Fluids 6, 3513–3515]. The predicted and measured ignition temperature of about 1770 K coincides approximately with the spontaneous nucleation temperature of supercooled liquid Al₂O₃ (1760 K). This suggests that the crystallization of the oxide layer represents a strong ‘barrier’ to aluminum drop ignition under water. Apparently a similar interpretation is applicable to aluminum drop ignition in gaseous oxidizing atmospheres. We conclude from the theory that the low-temperature aluminum ignitions (in the range 1100–1600 K) that have been observed during steam explosions are a consequence of the short aluminum drop oxidation times in this environment relative to the characteristic time for Al₂O₃ crystallization. Several aspects of the aluminum drop/shock interaction experiments besides ignition are discussed in the paper. In particular, the experiments provide strong evidence that during the course of a vapor explosion metal fragmentation occurs via a thermal mechanism at low pressure and precedes the development of a high-pressure shock.     

Molten fuel-coolant interaction phenomena with application to carbide fuel safety

This paper reviews the major phases occurring during an energetic molten fuel/coolant interaction (MFCI), the categories of interaction and modes of contact between molten fuel and liquid coolant, the film boiling destabilization and collapse mechanisms, and the important fragmentation mechanisms of the melt. Two major models that describe the processes involved in an MFCI event are discussed: the spontaneous nucleation model and the pressure detonation model. Finally, the MFCI experiments involving carbide fuel and liquid sodium are reviewed and the potential for an energetic interaction between molten carbide fuel and liquid sodium is discussed. Recommendations are given for future work on MFCI phenomena relative to the carbide fuel/sodium system.     

Increased fuel burn up in a CANDU thorium reactor using weapon grade plutonium

Weapon grade plutonium is used as a booster fissile fuel material in the form of mixed ThO₂/PuO₂ fuel in a Canada Deuterium Uranium (CANDU) fuel bundle in order to assure the initial criticality at startup.Two different fuel compositions have been used: (1) 97% thoria (ThO₂) + 3%PuO₂ and (2) 92% ThO₂ + 5% UO₂ + 3% PuO₂. The latter is used to denaturize the new ²³³U fuel with ²³⁸U. The temporal variation of the criticality k_∞ and the burn-up values of the reactor have been calculated by full power operation for a period of 20 years. The criticality starts by k_∞ = 1.48 for both fuel compositions. A sharp decrease of the criticality has been observed in the first year as a consequence of rapid plutonium burnout. The criticality becomes quasi constant after the second year and remains above k_∞ > 1.06 for 20 years. After the second year, the CANDU reactor begins to operate practically as a thorium burner.Very high burn up could be achieved with the same fuel material (up to 500,000 MW·D/T), provided that the fuel rod claddings would be replaced periodically (after every 50,000 or 100,000 MW·D/T). The reactor criticality will be sufficient until a great fraction of the thorium fuel is burnt up. This would reduce fuel fabrication costs and nuclear waste mass for final disposal per unit energy drastically.     

Assessment of Fuel Coolant Interactions (FCIs) in the FBR Core Disruptive Accident (CDA)

Application of general behavior principles (GBPs) and consideration of relevant contact modes suggest that only incoherent small-scale fuel coolant interactions (FCIs) with negligible damage potential appear possible with the molten oxide fuel-liquid sodium system as the fuel disperses away from the core into a coolable non-critical array.

In contrast to the SPERT-1, BORAX-1 and SL-1 nuclear transients that ultimately led to energetic vapor or steam explosions, the presence of molten fuel and liquid sodium in the FBR core always requires the presence of solid cladding which separates the fuel and coolant and, hence prevents energetic FCIs prior to coolant escape.

Furthermore, unlike the CORECT-II experiments which examined dynamic re-entry of liquid sodium on molten fuel pools that resulted in unstable interfaces leading to significant sodium entrapment and relatively energetic FCIs, the prevailing contact mode in the FBR core disruptive accident (CDA) scenario is displacement of the lighter and less viscous liquid sodium by the heavier and more viscous molten fuel resulting in stable interfaces with no significant sodium entrapment and FCIs. Dynamic re-entry of liquid sodium into the core is not possible with the two-component steel vapor-liquid sodium system, since the interface contact temperature upon steel vapor condensation is well in excess of the sodium boiling temperature. A pressure reduction in the steel vapor region due to condensation is immediately compensated for by an equivalent pressure increase due to sodium evaporation.

Finally, considering that the molten oxide fuel-liquid sodium interface contact temperature is well below the sodium homogeneous nucleation temperature which in turn is well below the fuel melting temperature, not only eliminates the potential for large-scale vapor explosions as molten fuel streams are injected into liquid sodium pools, but also implies that small scale superheat explosions are possible which are consistent with the usually observed incoherent sharp pressurization events (amplitudes up to the order of 10 MPa and duration of the order of 1 ms). These general behavior characteristics are also consistent with complete fuel fragmentation with fragment sizes ranging from 100 to 1,000 μm, and the absence of significant or damaging FCIs.     

Reactivity feedback coefficients of a material test research reactor fueled with high-density U3Si2 dispersion fuels

The reactivity feedback coefficients of a material test research reactor fueled with high-density U₃Si₂ dispersion fuels were calculated. For this purpose, the low-density LEU fuel of an MTR was replaced with high-density U₃Si₂ LEU fuels currently being developed under the RERTR program. Calculations were carried out to find the fuel temperature reactivity coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It is observed that the average values of fuel temperature reactivity feedback coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient from 20 °C to 100 °C, at the beginning of life, followed the relationships (in units of Δk/k × 10⁻⁵ K⁻¹) −2.116 − 0.118 ρ_U, 0.713 − 37.309/ρ_U and −12.765 − 34.309/ρ_U, respectively for 4.0 ≤ ρ_U (g/cm³) ≤ 6.0.