The solid solubility of Fe in α-Zr: A secondary ion mass spectrometry study

Secondary ion mass spectrometry techniques have been used to determine the terminal solid solubility (TSS) of Fe in α-Zr. Single crystals of nominally pure and Fe-doped α-Zr were annealed in the temperature range 770–1100 K to promote equilibration of Fe between surface Zr₃Fe precipitates, or β-Zr(Fe), and α-Zr. The results are fair in overall agreement with a recent investigation, based on thermoelectric power measurements, but they differ in detail. In particular this work indicates two regions of temperature dependence: above 930 K the TSS (ppma) is given by C_Fe = 1.56 × 10¹⁰exp(−1.70 ± 0.05 eV/kT), at lower temperatures a weaker temperature dependence is associated with extrinsic effects. In addition, the eutectoid temperature is shown to lie between 1063 and 1068 K.     

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.     

Study on the characteristic points of boiling curve by using wavelet analysis and genetic neural network

Local singularity of a signal includes a lot of important information. Wavelet transform can overcome the shortages of Fourier analysis, i.e., the weak localization in the local time- and frequency-domains. It has the capacity to detect the characteristic points of boiling curves. Based on the wavelet analysis theory of signal singularity detection, Critical Heat Flux (CHF) and Minimum Film Boiling Starting Point (q_min) of boiling curves can be detected by using the wavelet modulus maxima detection. Moreover, a genetic neural network (GNN) model for predicting CHF is set up in this paper. The database used in the analysis is from the 1960s, including 2365 data points which cover a range of pressure (P), from 100 to 1000 kPa, mass flow rate (G) from 40 to 500 kg m⁻² s⁻¹, inlet sub-cooling (ΔT_sub) from 0 to 35 K, wall superheat (ΔT_sat) from 10 to 500 K and heat flux (Q) from 20 to 8000 kW m⁻². GNN mode has some advantages of its global optimal searching, quick convergence speed and solving non-linear problem. The methods of establishing the model and training of GNN are discussed particularly. The characteristic point predictions of boiling curve are investigated in detail by GNN. The results predicted by GNN have a good agreement with experimental data. At last, the main parametric trends of the CHF are analyzed by applying GNN. Simulation and analysis results show that the network model can effectively predict CHF.     

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.     

Turbulent heat mixing of a heavy liquid metal flow in the MEGAPIE target geometry—The heated jet experiment

The MEGAPIE target installed at the Paul–Scherrer Institute is an example of a spallation target using eutectic liquid lead–bismuth (Pb⁴⁵Bi⁵⁵) both as coolant and neutron source. An adequate cooling of the target requires a conditioning of the flow, which is realized by a main flow transported in an annular gap downwards, u-turned at a hemispherical shell into a cylindrical riser tube. In order to avoid a stagnation point close to the lowest part of the shell a jet flow is superimposed to the main flow, which is directed towards to the stagnation point and flows tangentially along the shell.The heated jet experiment conducted in the THEADES loop of the KALLA laboratory is nearly 1:1 representation of the lower part of the MEGAPIE target. It is aimed to study the cooling capability of this specific geometry in dependence on the flow rate ratio (Q_main/Q_jet) of the main flow (Q_main) to the jet flow (Q_jet). Here, a heated jet is injected into a cold main flow at MEGAPIE relevant flow rate ratios. The liquid metal experiment is accompanied by a water experiment in almost the same geometry to study the momentum field as well as a three-dimensional turbulent numerical fluid dynamic simulation (CFD). Besides a detailed study of the envisaged nominal operation of the MEGAPIE target with Q_main/Q_jet = 15 deviations from this mode are investigated in the range from 7.5 ≤ Q_main/Q_jet ≤ 20 in order to give an estimate on the safe operational threshold of the target.The experiment shows that, the flow pattern establishing in this specific design and the turbulence intensity distribution essentially depends on the flow rate ratio (Q_main/Q_jet). All Q_main/Q_jet-ratios investigated exhibit an unstable time dependent behavior. The MEGAPIE design is highly sensitive against changes of this ratio.Mainly three completely different flow patterns were identified. A sufficient cooling of the lower target shell, however, is only ensured if Q_main/Q_jet ≤ 12.5. In this case the jet flow covers the whole lower shell. Although for Q_main/Q_jet ≤ 12.5 the flow is more unstable compared to the other patterns most of the fluctuations close to the centerline are in the high frequency range (>1 Hz), so that they will not lead to severe temperature fluctuations in the lower shell material. In this case the thermal mixing occurs on large scales and is excellent.For flow rate ratios Q_main/Q_jet > 12.5 complex flow patterns consisting of several fluid streaks and vortices were identified. Since in these cases the jet flow does not fully cover the lower shell an adequate cooling of the MEGAPIE target cannot be guaranteed and thus temperatures may appear exceeding material acceptable limits.All conducted experiments show a high sensitivity to asymmetries even far upstream. A comparison of the numerical simulation, which assumed a symmetric flow, with the experimental data was due to the experimentally found asymmetry only partially possible.     

Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow

Double sensor probe and hotfilm anemometry methods were developed for measuring local flow characteristics in bubbly flow. The formulation for the interfacial area concentration measurement was obtained by improving the formulation derived by Kataoka and Ishii. The assumptions used in the derivation of the equation were verified experimentally. The interfacial area concentration measured by the double sensor probe agreed well with one by the photographic method. The filter to validate the hotfilm anemometry for measuring the liquid velocity and turbulent intensity in bubbly flow was developed based on removing the signal due to the passing bubbles. The local void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter, liquid velocity, and turbulent intensity of vertical upward air–water flow in a round tube with an inner diameter of 50.8 mm were measured by using these methods. A total of 54 data sets were acquired consisting of three superficial gas flow rates, 0.015–0.076 m s⁻¹, and three superficial liquid flow rates, 0.600, 1.00, and 1.30 m s⁻¹. The measurements were performed at the three locations: L/D=2, 32, and 62. This data is expected to be used for the development of reliable constitutive relations which reflect the true transfer mechanisms in two-phase flow.     

JR curves of the low alloy steel 20 MnMoNi 5 5 with two different sulphur contents in oxygen-containing high temperature water at 240°C

J_R curves of the low alloy steel 20 MnMoNi 5 5 with two different sulphur contents (0.003 and 0.011 wt.%) were determined at 240°C in oxygen-containing high temperature water as well as in air. The tests were performed by the single-specimen unloading compliance technique at load line displacement rates from 1 × 10⁻⁴ down to 1 × 10⁻⁶ mm s⁻¹ on 20% side-grooved 2T CT specimens in an autoclave testing facility at an oxygen content of 8 ppm and a pressure of 7 MPa under quasi-stagnant flow conditions.In the case of testing in high temperature water, remarkably lower J_R curves than in air at the same load line displacement rate (1 × 10⁻⁴ mm s⁻¹) were obtained. A decrease in the load line displacement rate as well as an increase in the sulphur content of the steel caused a reduction of the J_R curves. At the fastest load line displacement rate a stretch zone could be detected fractographically on the specimens tested in air and in high temperature water and consequently J_i could be determined. When testing in high temperature water, the J_i value of the higher sulphur material type decreases from 45 N mm⁻¹ in air to 3 N mm⁻¹, much more than that of the optimized material type from 51 N mm⁻¹ in air to 20 N mm⁻¹ at 1 × 10⁻⁴ mm s⁻¹.     

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.     

Prediction of the single-phase turbulent mixing rate between two parallel subchannels using a subchannel geometry factor

This paper presents a simple method for predicting the single-phase turbulent mixing rate between adjacent subchannels in nuclear fuel bundles. In this method, the mixing rate is computed as the sum of the two components of turbulent diffusion and convective transfer. Of these, the turbulent diffusion component is calculated using a newly defined subchannel geometry factor F^* and the mean turbulent diffusivity for each subchannel which is computed from Elder's equation. The convective transfer component is evaluated from a mixing Stanton number correlation obtained empirically in this study. In order to confirm the validity of the proposed method, experimental data on turbulent mixing rate were obtained using a tracer technique under adiabatic conditions with three test channels, each consisting of two subchannels. The range of Reynolds number covered was 5000–66 000. From comparisons of the predicted turbulent mixing rates with the experimental data of other investigators as well as the authors, it has been confirmed that the proposed method can predict the data in a range of gap clearance to rod diameter ratio of 0.02–0.4 within about ±25% for square array bundles and about ±35% for triangular array bundles.     

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.     

MHD flow past a semi-infinite flat plate with heat transfer

Exact numerical solutions to the boundary layer similarity equations of MHD flow and heat transfer past a semi-infinite flat plate of an incompressible viscous fluid have been presented. The velocity of the fluid U and the magnetic field H₀ at a distance from the plate are both assumed to be uniform and parallel to the plate which is considered as isothermal. Velocity, magnetic and temperature fields have been shown graphically whereas the numerical values of ƒ′(0) and {−θ′(0)} are entered in tables. We observe that both ƒ′(0) and {−θ′(0)} decrease with increasing S (magnetic field parameter) and increase with increasing λ (ratio of magnetic diffusivity and viscous diffusivity).     

Release behavior of bred tritium from LiAlO2

The release behavior of bred tritium to the blanket purge gas is mainly controlled by such bulk phenomena as tritium forming reaction, diffusion of tritium in grain, interaction of tritium with irradiation defects, and absorption together with such surface phenomena as adsorption, isotope exchange reaction between molecular form hydrogen in purge gas and tritium on grain surface (isotope exchange reaction 1), isotope exchange reaction between water vapor and tritium on grain surface (isotope exchange reaction 2), and water formation reaction at addition of hydrogen. Following the observation of the present authors that the isotope exchange reaction 2 is much faster than the isotope exchange reaction 1, the release curve of bred tritium obtained at purge with humidified gas was used for estimation of the effective diffusivity of bred tritium in LiAlO₂. Then, the effective diffusivity of tritium in grain of LiAlO₂ is obtained as D_T = 2.5 × 10⁻⁷exp(−110 [kJ]/RT) [m²/s]. This equation gives the larger diffusivity than any other diffusivity presented so far because the mass transfer resistance at the grain surface is expected to be eliminated in the estimation procedure of this study.     

An experimental investigation on thermal striping: Mixing phenomena of a vertical non-buoyant jet with two adjacent buoyant jets as measured by ultrasound Doppler velocimetry

An experimental investigation on the thermal mixing phenomena of three quasi-planar vertical jets, with the central jet at a lower relative temperature than the two adjacent jets, was conducted. The central jet was unheated (‘cold’), while the two adjacent jets were heated (‘hot’). The temperature difference and velocity ratio between the heated (h) and unheated (c) jets were, ΔT_hc=5°C, 10°C and r=V_cold,exit/V_hot,exit=1.0 (isovelocity), 0.7, 0.5 (non-isovelocity) respectively. The typical Reynolds number was Re_D=1.8×10⁴, where D is the hydraulic diameter of the exit nozzle. Velocity measurement of a reference single-jet and triple-jet arrangement were taken by ultrasound Doppler velocimetry (UDV) while temperature data were taken by a vertically traversed thermocouple array. Our UDV data revealed that, beyond the exit region, our single-jet data behaved in the classic manner. In contrast, the triple-jet exhibited, for example, up to 20 times the root-mean-square velocity values of the single-jet, especially in the regions in-between the cold and hot jets. In particular, for the isovelocity case (V_exit=0.5 m/s) with ΔT_hc=5°C, we found that the convective mixing predominantly takes place at axial distances, z/D=2.0–4.5, over a spanwise width, x/D|2.25|, centered about the cold jet. An estimate of the turbulent heat flux distribution semi-quantitatively substantiated our results. As for the non-isovelocity case, temperature data showed a localized asymmetry that subsequently delayed the onset of mixing. Convective mixing however, did occur and yielded higher post-mixing temperatures in comparison to the isovelocity case.     

Two fluid model for two-phase turbulent jets

Eulerian two-fluid models are widely used in nuclear reactor safety and CFD. In these models turbulent diffusion of a dispersed phase must be formulated in terms of the fluctuating interfacial force and the Reynolds stresses. The interfacial force is obtained using the probability distribution function approach by Reeks (1992). This paper is the first application of this force to a case of engineering interest outside homogeneous turbulence. An Eulerian multidimensional two-fluid model for a cylindrical two-phase dispersed particle jet is proposed and compared with experimental data. The averaged conservation equations of mass and momentum are solved for each phase and the turbulent kinetic energy equation is solved for the continuous phase. The turbulent diffusion force and the Reynolds stresses are constituted within the context of the k- model of turbulence. A dissipation term has been added to the k- model for the turbulence modulation by the particles. Once the constitutive relations have been defined, the two-fluid model is implemented in a computational fluid dynamics code. It is shown that when the particles are very small the model is consistent with a convection-diffusion equation for particle transport where the diffusivity is defined according to Taylor's model (Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math. Society, A20, pp. 196–211). The two-fluid model is also compared against two experimental data sets. Good agreement between the model and the data is obtained. The sensitivity of the results to various turbulent mechanisms is discussed.     

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.     

Diffusion of uranium in molybdenum,niobium, zirconium,and titanium

The diffusion of uranium was studied in molybdenum, niobium, zirconium, and titanium. The diffusion coefficients were determined by measuring the over-all activity of the residue of the sample, using the a-radiation of uranium enriched with the U²³⁵ isotope to 90% at temperatures 1500 to 2000° C (molybdenum, niobium) and 915 to 1200° C (zirconium, titanium). The temperature dependence of the diffusion coefficients was given by the equationsD _Mo ^U=7.60.10³ exp (–76 400/RT) cm²/sec;D _Nb ^U=8.90.10^–2 exp (–76 800/RT) cm²/sec;D _Zr ^U=7.77,10^–5 exp (–25 800/RT) cm²/sec;D _Ti ^U=4.90. t0^–4 exp (–29 300/RT) cm²/sec.The considerable differences between the diffusion mobilities and activation energies of molybdenum and niobium on the one hand and zirconium and titanium on the other were probably due to the effects of lattice defects, for example, excess vacancies arising in zirconium and titanium during polymorphic transformations.Translated from Atomnaya Énergiya, Vol. 19, No. 6, pp. 521–523, December, 1965Report read by G. I. Budker at the International Conference on High-Energy Accelerators (Frascati, Italy).     

Quasi 3-D measurements of turbulence structure in horizontal air–water bubbly flow

Quasi 3-D measurements of the turbulence structure of air–water bubbly flow in a horizontal tube with 35 mm i.d. are undertaken with two TSI “X”-type hot-film probes. The turbulent fluctuations, u_f,v_f,w_f, in axial, radial and circumferential directions, respectively, and Reynolds stresses and are obtained. It is found that in the lower portion of the tube, the profiles of turbulent fluctuation and Reynolds stress resemble those of single phase flow; whereas in the upper portion of the tube, where the bubble population is high, the turbulence, especially the circumferential fluctuation w_f, is substantially enhanced, and the radial turbulence assumes highest value in the radial position −0.7<r/R<0.5. The magnitudes of Reynolds stresses and in our measurements are in the same level except in the lower portion of the tube where assumes a value close to zero as is the case in single phase flow and vertical air–water bubbly flow.     

Novel porous media formulation for multiphase flow conservation equations

Multiphase flows consist of interacting phases that are dispersed randomly in space and in time. An additional complication arises from the fact that the flow region of interest often contains irregularly shaped structures. While, in principle, the intraphase conservation equations for mass, momentum, and energy, and their initial and boundary conditions can be written, the cost of detailed fluid flow and heat transfer analysis with explicit treatment of these internal structures with complex geometry and irregular shape often is prohibitive, if not impossible. In most engineering applications, all that is required is to capture the essential features of the system and to express the flow and temperature field in terms of local volume-averaged quantities while sacrificing some of the details. The present study is an attempt to achieve this goal by applying time averaging after local volume averaging.Local volume averaging of conservation equations of mass, momentum, and energy for a multiphase system yields equations in terms of local volume-averaged products of density, velocity, energy, stresses, and field forces, together with interface transfer integrals. These averaging relations are subject to the following length scale restrictions:

dℓL,