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.     

Ductile–brittle transition of polycrystalline iron and iron–chromium alloys

Fracture toughness of polycrystalline Fe, Fe–3%Cr and Fe–9%Cr was measured by four-point bending of pre-cracked specimens at temperatures between 77 K and 150 K and strain rates between 4.46 × 10⁻⁴ and 2.23 × 10⁻² s⁻¹. For all materials, fracture behaviour changed with increasing temperature from brittle to ductile at a distinct brittle–ductile transition temperature (T_c), which increased with increasing strain rate. At low strain rates, an Arrhenius relation was found between T_c and strain rate in each material. At high strain rates, T_c was at slightly higher values than those expected from extrapolation of the Arrhenius relation from lower strain rates. This shift of T_c was associated with twinning near the crack tip. For each material, use of an Arrhenius relation for tests at strain rates at which specimens showed twinning gave the same activation energy as for the low strain rate tests. The values of activation energy for the brittle–ductile transition of polycrystalline Fe, Fe–3%Cr and Fe–9%Cr were found to be 0.21, 0.15 and 0.10 eV, respectively, indicating that the activation energy for dislocation glide decreases with increasing chromium concentration in iron.     

Effect of pressure on critical heat flux in uniformly heated vertical annulus under low flow conditions

Critical heat flux (CHF) experiments have been carried out in a wide range of pressure for an internally heated vertical annulus. The experimental conditions covered a range of pressure from 0.57 to 15.01 MPa, mass fluxes of 0 kg m⁻² s⁻¹ and from 200 to 650 kg m⁻² s⁻¹, and inlet subcoolings from 85 to 413 kJ kg⁻¹. Most of the CHFs were identified to the dryout of the liquid film in the annular-mist flow. For the mass fluxes of 550 and 650 kg m⁻² s⁻¹, the CHFs had a maximum value at a pressure of 2–3 MPa, and the pressure at the maximum CHF values had a trend moving toward the pressure at the peak value of pool boiling CHF as the mass flux decreased. The CHF data under a zero mass flux condition indicate that both the effects of pressure and inlet subcooling on the CHF were smaller, compared with those for the CHF with a net water upflow. The Doerffer correlation using the 1995 CHF look-up table and the Bowring correlation show a good prediction capability for the present CHF data.     

An experimental and analytical study of the effect of axial power profile on CHF

The effect of axial heat flux distribution (AFD) on the critical heat flux (CHF) was investigated. CHF measurements were obtained with HFC-134a cooled vertical tubes having four non-uniform and one uniform AFD profiles. The HFC-134a test conditions covered a pressure range from 1.6 to 2.4 MPa, a mass-flux range from 2.8 to 4.7 Mg m⁻² s⁻¹, and an inlet-quality range from −0.9 to 0. The water-equivalent pressure and mass-flux ranges are 10–14 MPa and 4–6.5 Mg m⁻² s⁻¹, respectively.In general, the observed AFD effect on critical power is small at high inlet subcoolings. At low inlet subcoolings, the critical power for the inlet-peak profile is up to 15% higher than that for the outlet-peak profile. A local conditions analysis showed that the AFD has the strongest effect on CHF at high dryout qualities. CHF values for non-uniform AFDs could be 50% lower than those for the uniform AFD. The AFD effect on CHF becomes diminished with decreasing dryout quality.Four different approaches to account for the effect of AFD on CHF were assessed against the experimental values from the current experiment. The boiling-length-average heat-flux approach with the boiling-length starting point at the onset of annular flow (OAF) provided the best prediction of the critical power and the CHF location.     

Transformation and fragmentation behavior of molten metal drop in sodium pool

In order to clarify the fragmentation mechanism of a metallic alloy (U–Pu–Zr) fuel on liquid phase formed by metallurgical reactions (liquefaction temperature = 650 °C), which is important in evaluating the sequence of core disruptive accidents for metallic fuel fast reactors, a series of experiments was carried out using molten aluminum (melting point = 660 °C) and sodium mainly under the condition that the boiling of sodium does not occur. When the instantaneous contact interface temperature (T_i) between molten aluminum drop and sodium is lower than the boiling point of sodium (T_c,bp), the molten aluminum drop can be fragmented and the mass median diameter (D_m) of aluminum fragments becomes small with increasing T_i. When T_i is roughly equivalent to or higher than T_c,bp, the fragmentation of aluminum drop is promoted by thermal interaction caused by the boiling of sodium on the surface of the drop. Furthermore, even under the condition that the boiling of sodium does not occur and the solid crust is formed on the surface of the drop, it is confirmed from an analytical evaluation that the thermal fragmentation of molten aluminum drop with solid crust has a potential to be caused by the transient pressurization within the melt confined by the crust. These results indicate the possibility that the metallic alloy fuel on liquid phase formed by the metallurgical reactions can be fragmented without occurring the boiling of sodium on the surface of the melt.     

The study of reduced transition probabilities for E2 transitions in the decays of Os and Pt nuclei

The ratios of E2 transition rates, i.e., B(E2; I_i − I_f)/B(E2; I_i − I_f) were computed for gamma to ground state band transitions in ¹⁹²Os and ¹⁹²Pt. The reduced transition probabilities for the E2 transitions evaluated on the basis of Interacting Boson Approximation (IBA-I) model and those measured experimentally are compared. The SU(3) symmetry of IBA-I is not strictly obeyed by the nuclei in which T(E2; I_i − I_f) transitions are observed, i.e., the symmetry SU(3) is broken. The percentage sum coincidence corrections are applied to marginalise contributions from crossover transitions and the intensities of affected transitions are found to agree fairly well with earlier sum peak method applications to the decay of ¹⁹²Ir.     

Fatigue and fracture emanating from notch; the use of the notch stress intensity factor

The analysis of the stress distribution at notch tip shows a pseudo-stress singularity characterised by the notch stress intensity factor (NSIF) K_ρ. The critical value of this parameter K_ρ^ccan be used to determine the fracture toughness of very brittle materials from notched specimens. The range of the notch stress intensity factor ΔK_ρ plays an important role in initiation of fatigue emanating from notches and in the notch fatigue sensitivity index.     

An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes

From a theoretical assessment of extensive critical heat flux (CHF) data under low pressure and low velocity (LPLV) conditions, it was found out that lots of CHF data would not be well predicted by a normal annular film dryout (AFD) mechanism, although their flow patterns were identified as annular–mist flow. To predict these CHF data, a liquid sublayer dryout (LSD) mechanism has been newly utilized in developing the mechanistic CHF model based on each identified CHF mechanism. This mechanism postulates that the CHF occurrence is caused by dryout of the thin liquid sublayer resulting from the annular film separation or breaking down due to nucleate boiling in annular film or hydrodynamic fluctuation. In principle, this mechanism well supports the experimental evidence of residual film flow rate at the CHF location, which can not be explained by the AFD mechanism. For a comparative assessment of each mechanism, the CHF model based on the LSD mechanism is developed together with that based on the AFD mechanism. The validation of these models is performed on the 1406 CHF data points ranging over P=0.1–2 MPa, G=4–499 kg m⁻² s⁻¹, L/D=4–402. This model validation shows that 1055 and 231 CHF data are predicted within ±30 error bound by the LSD mechanism and the AFD mechanism, respectively. However, some CHF data whose critical qualities are <0.4 or whose tube length-to-diameter ratios are <70 are considerably overestimated by the CHF model based on the LSD mechanism. These overestimations seem to be caused by an inadequate CHF mechanism classification and an insufficient consideration of the flow instability effect on CHF. Further studies for a new classification criterion screening the CHF data affected by flow instabilities as well as a new bubble detachment model for LPLV conditions, are needed to improve the model accuracy.     

Some problems for bundle CHF prediction based on CHF measurements in simple flow geometries

A comparison of critical heat flux (CHF) fuel bundles data with CHF data obtained in simple flow geometries was made. The base for the comparison was primary experimental data obtained in annular, circular, rectangular, triangular, and dumb-bell shaped channels cooled with water and R-134a. The investigated range of flow parameters (pressure, mass flux, and critical quality) in R-134a was chosen to be equivalent to modern nuclear reactor water flow conditions (p=7 and 10 MPa, G=350–5000 kg (m² s)⁻¹, x_cr=−0.1–1). The proper scaling laws were applied to convert the data from water to R-134a equivalent conditions and vise versa. The effects of flow parameters (p, G, x_cr) and the effects of geometric parameters (D, L) were evaluated during comparison. The comparison showed that no one simple flow geometry can be used for accurate and reliable bundle CHF prediction in wide range of flow parameters based on local (critical) conditions approach. The comparison also showed that the limiting critical quality phenomenon is unique characteristic for each flow geometry which depends on many factors: flow conditions (pressure and mass flux), geometrical parameters (diameter or surface curvature, gap size, etc.), flow obstructions (spacers, appendages, turbulizers, etc.) and others.     

Single and multiple discharge from a stratified two-phase region through small branches

Experimental data are presented for the mass flow rate and quality during single, dual and triple discharge from a stratified air–water region through small side branches (d=6.35 mm) installed on a semicircular wall. Dimensions of the semicircular wall and branches were chosen such that interaction among the branches is possible under certain flow conditions. All the branches were adjusted to have the same hydraulic resistance (R=1000 (kg m)^−1/2) and for the cases of dual and triple discharge, the same pressure drop ΔP was imposed across all active branches. Tests were conducted at two system pressures P₀=316 and 517 kPa and the pressure drop was varied within the range 40≤ΔP≤235 kPa. Data analysis is presented with emphasis on the effect of wall curvature and also the effect of additional discharges on the flow from a certain branch. The present data can serve as benchmark data for testing numerical safety codes and they should guide future research on the flow from two-phase headers.     

CHF and dryout point in vertical narrow annuli

Experimental study associated with CHF and dryout point in narrow annuli is conducted with 1.5 mm and 1.0 mm gap, respectively. Distilled water is used as work fluid. The parameters examined were: pressure from 2.0 MPa to 4.0 MPa; mass flux from 26.0 kg/(m² s) to 69.0 kg/(m² s); heat flux from 10 kW/m² to 70 kW/m²; exit equilibrium mass quality from 0.52 to 1.08.It is found that CHF monotonously increases with mass flux in internally heated annuli and bilaterally heated annuli. However, the observed trends are not similar to that in externally heated annuli. The CHF is not affected significantly by mass flux.Critical qualities of dryout point (X_DO) decreases with mass flux and increases with inlet qualities. Under the same conditions X_DO in outer tube are always larger than that in inner tube. According to experimental data, a criterion for the appearance of dryout point for bilaterally heated has been presented.The comparison with the correlations [КУТАТЕЛАДЗЕ, C.C., 1979. Тедплоэнергетика, No. 6] and experimental data indicates that the existing correlations applied to tube cannot predict X_DO in narrow annuli well. Based on experimental data, a new correlation is developed.     

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.     

Simplified method to evaluate upper limit stress intensity factor range of an inner-surface circumferential crack under steady state thermal striping

Simplified method to evaluate the upper limit stress intensity factor (SIF) range of an inner-surface circumferential crack in a thin- to thick-walled cylinder under steady state thermal striping was considered in this paper. The edges of the cylinder were rotation-restrained and the outer surface was adiabatically insulated. The inner surface of the cylinder was heated by a fluid with constant heat transfer coefficient whose temperature fluctuated sinusoidally at constant amplitude ΔT. By combining our analytical temperature solution for the problem and our semi-analytical-numerical SIF evaluation method for the crack, we showed that the desired maximum steady state SIF range can be evaluated with an engineering accuracy after ΔT, the mean radius to wall thickness ratio r_m/W of the cylinder, the thermal expansion coefficient and Poisson's ratio are specified. By applying our method, no transient SIF analysis nor sensitivity analysis of the striping frequency on the SIF range is necessary. Numerical results showed that our method is valid for cylinders in a range of r_m/W = 10–1.     

Non-stationary outflow and rarefaction waves in flashing liquid

The outflow of high pressure liquid (in particular, water) to the atmosphere from a closed tube (of length a few metres and diameter more than a few centimetres) because of sudden destruction of one bottom is theoretically investigated. Evaporation takes places on the nucleus bubbles. The number of nuclei depends on the quality of the liquid or its purification. The process involves flashing evaporation of the liquid.There are two rarefaction waves at the initial stage. The velocity of the first wave (elastic forerunner) is sound speed in the one phase liquid and equals about 1000 m s⁻¹. After the elastic forerunner the liquid becomes superheated because the pressure drops and evaporation begins.The velocity of the second rarefaction wave is about 1–10 ms s⁻¹. There is intensive bubbly evaporation on and after the second wave. Intensity of the outflow is determined by the intensity of evaporation on the interface of the bubbles and by intensity of fragmentation of the bubbles because of their relative slip velocity in the liquid (0.1–1 m s⁻¹). The fragmentation of the bubbles significantly intensifies the evaporation because of augmentation of the bubbly interface.The degree of non-equilibrium or superheating behind the forerunner in water grows with the increasing initial temperature T₀. For T₀<530−540 K this superheating is negligible and the process may be described by an equilibrium scheme. For T₀ above 0.95T_cr≈605 K homogeneous nucleation is possible.After forerunner reflection from the closed bottom, intense evaporation is initiated near the bottom. Then the equalization of the pressure along the tube occurs (quasi-static homobaric stage).There is good correlation with experimental data.     

Critical heat flux at high velocity channel flow with high subcooling

A quantitative analysis of critical heat flux (CHF) in heated channels under high mass flux with high subcooling was successfully carried out by applying a new flow model to the existing CHF model of a macro-water-sublayer on the heated wall and steam blankets over it. The CHF correlation proposed could correctly predict the existing experimental data for circular tubes of 0.33–4 mm in diameter with mass flux of 124–90 000 kg (m² s)⁻¹ and inlet water subcooling of 35–210 K at 0.1–7.1 MPa, resulting in CHF of 4.2–224 MW m⁻², and for rectangular channels of 3–20 mm gap with a mass flux of 940–27 000 kg (m² s)⁻¹ and inlet water subcooling of 13–166 K at 0.1–3.0 MPa, resulting in CHF of 2.0–62 MW m⁻². An error of the CHF correlation has also been estimated.     

Development of the detecting method of helium gas leak from canister

In the concrete cask storage system, spent fuel is installed and weld-sealed in a cylindrical container called a canister. The canister is filled with helium gas and its containment shall be maintained and inspected during storage. The helium gas enhances heat removal from spent fuel. When the helium gas leaks, the effect of helium gas convection is weakened in the canister. Thereof, the temperature on the canister surface changes.In present tests, it was found that temperatures of the center of the top and the bottom on the canister surface change remarkably during the helium gas leak. Therefore, we defined the temperature difference as ΔT_BT. And one can detect helium gas leak using the change of ΔT_BT. ΔT_BT increases monotonously toward a constant value during helium gas leak, even if the inlet air temperature drops. The helium gas leak can be detected at the early stage of the leak by observing both ΔT_BT and inlet air temperature.     

Fluid-to-fluid modeling of critical heat flux in 4 × 4 rod bundles

Fluid-to-fluid modeling of critical heat flux (CHF) is to simulate the CHF behaviors for water by employing low cost modeling fluid, and the flow scaling factor is the key to apply the technique to fuel bundles. The CHF experiments in 4×4 rod bundles have been carried out in Freon-12 loop in equivalent nuclear reactor water conditions (P=10.0–16.0 MPa, G=488.0–2100.0 kg/m² s, X_cr=−0.20–0.30). The models in fluid-to-fluid modeling of CHF is verified by the CHF data for Freon-12 obtained in the experiment and the CHF correlation for water obtained by Nuclear Power Institute of China (NPIC) in the same 4×4 rod bundles. It has been found that the S.Y. Ahmad Compensation Distortion model, the Lu Zhongqi model, the Groeneveld model and Stevens–Kirby model overpredict the bundles CHF values for water. Then an empirical correlation of flow scaling factor is proposed. Comparison of the CHF data in two kinds of test sections for Freon-12, in which the distance of the last grid away the end of heated length is different, shows that the spacer grid, which is located at 20 mm away from the end of the heated length, has evidently influenced on the CHF value in the 4×4 rod bundles for Freon-12. This is different from that for water, and the need for further work is required.     

Temperature distribution in nuclear fuel rod and variation of the neutronic performance parameters in (D–T) driven hybrid reactor system

Temperature distribution in nuclear fuel rod and variation of the neutronic performance parameters are investigated for different coolants under various first wall loads (P_w=2, 5, 7, 8, 9, and 10 MW m⁻²) in (D, T) (deuterium and tritium) driven and fueled with UO₂ hybrid reactors. Plasma chamber dimension, DR, with a line fusion neutron source is 300 cm. The fissile fuel zone is considered to be cooled with four different coolants with various volume fractions, the volumetric ratio of coolant-to-fuel [(Vm/V_f) = 1:2, 1:1, and 2:1], gas (He, CO₂), flibe (Li₂BeF₄), natural lithium (Li), and eutectic lithium (Li₁₇Pb₈₃). Calculation in the fuel rods and the behavior of the fissile fuel have been observed during 4 years for discrete time intervals of Δt=15 days and by a plant factor (PF) of 75%. As a result of the calculation, cumulative fissile fuel enrichment (CFFE) value indicating rejuvenation performance has increased by increasing P_w for all coolants and . Although CFFE and neutronic performance parameter values increase to the higher values by increasing P_w, the maximum temperature in the centerline of the fuel roads has exceeded the melting point (T_m>2830°C) of the fuel material during the operation periods. However, the best CFFE (11.154%) is obtained in gas coolant blanket for =1:2 (29.462% coolant, 58.924% fuel, 11.614% clad), under 10 MW m⁻² first wall load, followed by flibe with CFFE=11.081% for =2:1 (62.557% coolant, 31.278% fuel, 6.165% clad), under 7 MW m⁻², and flibe with CFFE=9.995% for =1:1 (45.515% coolant, 45.515% fuel, 8.971% clad), under 7 MW m⁻² during operation period without reaching the melting point of the fuel material. While maximum CFFE value has been obtained in fuel rod row#10 in gas, natural lithium, and eutectic lithium coolant blankets, it has been obtained in fuel rod row#1 in flibe coolant blanket for all and P_w. At the same condition, the best neutronic performance parameter values, tritium breeding ratio (TBR)= 1.4454, energy multiplication factor (M)= 9.2018, and neutron leakage (L)= 0.0872, have been obtained in eutectic lithium coolant blankets for the =1:2, followed by gas, natural lithium, and flibe coolant blankets. The isotopic percentage of ²⁴⁰Pu is higher than 5% in all blankets for P_w 7 MW m⁻², so that plutonium component in all blankets can be never reach a nuclear weapon grade quality during the operation period.     

Time dependence of J-integral

Tests performed within the framework of earlier RWTÜV projects together with results obtained elsewhere with regard to the time dependence of fracture mechanics data show that time effects reduced the toughness of materials, according to the nature of the test (extremely slow load rate or hold times with sustained load).

Reduction in toughness has an effect on the following:

&#x02022; - decrease in critical material data (J₀, δ_i)

&#x02022; - levelling off of the crack resistance curve J = J(Δa) and in consequence a decrease of tearing modulus.

This tendency is confirmed quantitatively by recent test results. These tests were performed with the material 15 Mn Ni 63 at room temperature with hold times under sustained load and according to the appropriate standards (without hold times). The tests show that hold times cause additional stable crack growth. The resulting J − Δa curve is lower and less sloping than the curve obtained in a standardized test. The time effect should be taken into account in a safety analysis.