Measurements of frequencies and spatial correlations of coherent structures in rod bundle flows

Cross-wire anemometry was used to identify and characterize coherent flow pulsations in isothermal air flow near the gap regions of a five-rod bundle with a design pitch-to-diameter ratio of 1.149 and contained in a quasi-trapezoidal duct. It was confirmed that such pulsations are quasi-periodic and contribute significantly to the velocity fluctuations across the gap. The frequency of pulsations was found to decrease with diminishing rod–wall gap size in the range between 0.015D and 0.250D, where D is the rod diameter. The pulsations in a rod–wall gap and an adjacent rod–rod gap were strongly coupled and occurred at the same frequency as one rod was displaced towards the duct wall.     

CFD investigation of vertical rod bundles of supercritical water-cooled nuclear reactor

The commercial CFD code STAR-CD v4.02 is used as the numerical simulation tool for the supercritical water-cooled nuclear reactor (SCWR). The numerical simulation is based on the real full 3D rod bundles’ geometry of the nuclear reactors. For satisfying the near-wall resolution of y⁺ ≤ 1, the structure mesh with the stretched fine mesh near wall is employed. The validation of the numerical simulation for mesh generation strategy and the turbulence model for the heat transfer of supercritical water is carried out to compare with 3D tube experiments. After the validation, the same mesh generation strategy and the turbulence model are employed to study three types of the geometry frame of the real rod bundles. Through the numerical investigations, it is found that the different arrangement of the rod bundles will induce the different temperature distribution at the rods’ walls. The wall temperature distributions are non-uniform along the wall and the values depend on the geometry frame. At the same flow conditions, downward flow gets higher wall temperature than upward flow. The hexagon geometry frame has the smallest wall temperature difference comparing with the others. The heat transfer is controlled by P/D ratio of the bundles.     

Stress waves in elastic rods induced by radiation heating

Consider a stress-free, thin, elastic rod, freely suspended. At time t = 0, the rod is rapidly exposed to a high temperature tube field inside, uniform over the cross-section T(x, t), t 0. Such a case arises in an external target when bombarded with a fast extracted proton beam of high energy and high intensity. In contrast to the quasi-static solution σ_x ≡ 0, stress waves are created at both free end-faces, at time t = 0, which propagate into the rod. Closed-form solutions are presented for a fast rise of a homogeneous temperature, during rise time t₀ to the final value T₀. Maximum compressive and tensile stresses will occur which may easily lead to failure of the rod. In particular, for an extremely fast rise t₀ < t_m, t_m being the characteristic mechanical time, |σ_x|max = EαT₀, which is the absolute value of a compressive stress in a rod fixed at the ends. For t₀ > t_m, |σ_x|max = EαT₀t_m/t₀, i.e. the maximum stresses are proportional to the length of the rod and inversely proportional to the rise time.     

Effect of thermal radiation on rewetting of top spray emergency coolant

A general physical model for top spray rewetting during an emrgency core cooling (ECC) transient is proposed which takes into account thermal radiation in the dry region. The model is employed to study the effect of thermal radiation on rewetting a single rod and a 3 × 3 rod bundle up to 2100°F. The results show that rewetting in a bundle is slower than for an isolated rod, due to reduced thermal radiation heat transfer in the dry region. Also, there is a definite correlation between the decreased radiation heat flux Δq_R and the corresponding decrease in rewetting velocity Δu. Values of Δu are not significant unless Δq_R is larger than 6000 Btu/hr ft², where Δq_R cannot exceed a value of 6000 Btu/hr ft² below a temperature of 1100°F, even in the most adverse conditions. Hence, it is concluded that radiant heat transfer does not significantly affect rewetting velocities up to an initial rod temperature of 1100°F. Beyond this temperature, the rewetting velocities change by more than 1.5% and hence radiation must be included in the model for top spray rewetting.     

Measurement of large negative reactivity in WWER-440. Sources of uncertainty

The sources of uncertainty in measurement of large negative reactivity in WWER-440 by the inverse point kinetics method, are evaluated quantitatively on the example of measurement of the reactivity worth of the shutdown control rod system of WWER-440 at zero power. Considering the specific features of the control rod system of WWER-440, it is demonstrated that using an appropriate formulation of the inverse solution of the equations of point kinetics, the uncertainty of measured reactivity ρ/β introduced by the assumption of constancy of the parameters of kinetics can be reduced to <3–5% for the case of the discussed rod-drop test at zero power. Based on an analysis of both numerically simulated and actual rod-drop transients, it is shown that the uncertainty of measured reactivity ρ/β can be quite considerable due to the underlying delayed neutron data set—the values of ρ/β obtained using different data sets can differ by 15%. Inexact accounting of the share of ²³⁹Pu in the fission neutron source is estimated to contribute to the total uncertainty of measured ρ/β of 1%, whereas possible spatial effects are expected to result in a relative error in ρ/β of 5%.     

Analytical prediction of friction factors and Nusselt numbers of turbulent forced convection in rod bundles with smooth and rough surfaces

A simple analytical method was developed for the prediction of the friction factor, f, of fully developed turbulent flow and the Nusselt number, Nu, of fully developed turbulent forced convection in rod bundles arranged in square or hexagonal arrays. The friction factor equation for smooth rod bundles was presented in a form similar to the friction factor equation for turbulent flow in a circular pipe. An explicit equation for the Nusselt number of turbulent forced convection in rod bundles with smooth surface was developed. In addition, we extended the analysis to rod bundles with rough surface and provided a method for the prediction of the friction factor and the Nusselt number. The method was based on the law of the wall for velocity and the law of the wall for the temperature, which were integrated over the entire flow area to yield algebraic equations for the prediction of f and Nu. The present method is applicable to infinite rod bundles in square and hexagonal arrays with low pitch to rod diameter ratio, P/D<1.2.     

Luminescence from low-energy impact of and ions (n = 1,2,3) on a Tore Supra carbon tile

The hydrogen Balmer series was observed when beams of H⁺, , and D⁺, , ions impinged at 100–1000 eV on a carbon fiber composite tile (Tore Supra). The excitation functions of the H_β (D_β) lines demonstrate the validity of the independent particle model. The logarithmic plot of the H_β (D_β) line intensity versus the reciprocal projectile ion velocity can be well reproduced by a model in which the hydrogen ion projectiles are neutralized in the entrance phase and subsequently electronically excited in collisions with carbon atoms. Finally, the excited hydrogen atoms leave the solid and emit the observed photons, unless they are quenched in non-radiative processes.     

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.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

Experimental study of the characteristics of the flow in the first rows of tube banks

This paper presents the experimental study of the flow instabilities in the first rows of tube banks. The study is performed using hot wire anemometry technique in an aerodynamic channel as well as flow visualizations in a water channel. In the wind channel three tube banks with square arrangement and pitch to diameter ratios P/D = 1.26, 1.4 and 1.6 were studied. The Reynolds number range for the velocities measurements, computed with the tube diameter and the flow velocity in the narrow gap between tubes was 7 × 10⁴–8 × 10⁴. Continuous and discrete wavelets were applied to decompose the velocity results, thus allowing the analysis of phenomena in time–frequency domain. Visualizations in a water channel complemented the analysis of the hot wire results. For this purpose, dye was injected in the flow in the water channel with a tube bank with P/D = 1.26. The range of the Reynolds number of the experiments was 3 × 10⁴–4 × 10⁴. The main results show the presence of instabilities, generated after the second row of the tube bank, which propagates to the interior of the bank. In the resulting flow, the three orthogonal components are equally significant. The three-dimensional behavior of the flow is responsible for a mass redistribution inside the bank that leads to velocity values not expected for the studied geometry, according to the known literature. The resulting flow process can be interpreted as a secondary flow which is characteristic of tube banks.     

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.     

High-energy γ-irradiation effect on physical ageing in Ge–Se glasses

Effect of Co⁶⁰ γ-irradiation on physical ageing in binary Ge_xSe_100–x glasses (5  x  27) is studied using conventional differential scanning calorimetry method. It is shown, that high-energy irradiation leads to additional increase in the glass transition temperature and endothermic peak area near the glass transition region over the one induced by isochronal storage of these glasses at normal conditions. This γ-induced physical ageing is shown to be well-pronounced in Se-rich glasses (x < 20), while only negligible changes are recorded for glasses of 20  x  27 compositions. The effect under consideration is supposed to be associated with γ-activated structural relaxation of the glass network towards thermodynamic equilibrium of supercooled liquid.     

Quantitative study of creep cavity area of HP40 furnace tubes

Ethylene cracking tubes of HP40 grade (25Cr–35Ni–0.4C) creep-resistant austenitic steel which failed after 80,000 h service were investigated for quantitative cavity evaluation. The results show that the creep cavity area fractions (Ω) present little difference from outer surface to inner surface through the thickness, and larger difference on different tube outer surfaces. The Ω obtained from the outer surface can stand for creep damage state for ethylene cracking tubes. The relationship between creep cavity area fraction and continuum damage mechanics is discussed. At failure, the critical value of damage variable D = 1 is corresponding to Ω = 2.8% measured on the tube outer surface.     

New analysis of prompt supercritical process with temperature feedback

The prompt supercritical process of a nuclear reactor with temperature feedback and initial power while inserting large step reactivity (ρ₀ > β) is analyzed. The new analytic expressions of reactivity and output power as well as reactor's temperature increase during the course of the prompt supercritical are derived. The maximal power and the related reactivity and time are obtained. The effects of the inserted step reactivity and initial power on the prompt supercritical process are analyzed and discussed. It is found that for considering only the effect of prompt neutron the reactivity, power and temperature vary much more quickly and the power peak value and the increase values of temperature are larger than those for considering the effect of both prompt neutron and delayed neutron.     

Stresses at the intersection of two cylindrical shells

The stress analysis based on the theory of a thin shell is carried out for two normally intersecting cylindrical shells with a large diameter ratio. Instead of the Donnell shallow shell equation, the modified Morley equation, which is applicable to ₀(R/T)^1/2 1, is used for the analysis of the shell with cut-out. The solution in terms of displacement function for the nozzle with a non-planar end is based on the Love equation. The boundary forces and displacements at the interaction are all transformed from Gaussian coordinates (α, β) on the shell, or Gaussian coordinates (ξ, θ) on the nozzle into three-dimensional cylindrical coordinates (π, θ, z). Their expressions on the intersecting curve are periodic functions of θ and expanded in Fourier series. Every harmonics of Fourier coefficients of boundary forces and displacements are obtained by numerical quadrature.The results obtained are in agreement with those from the finite element method and experiments for d/D 0.8.     

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.     

Monte Carlo simulation of the NaI(Tl) detector response to measure gold activated foils

This work deals with the implementation of a NaI(Tl) detector for the assessment of the specific saturation activities of pure gold foils after neutron irradiation. These gold foils can be placed in the centre of a set of polyethylene spheres with different diameters. This configuration, known as a passive Bonner sphere system, is suitable to measure neutron spectra normally extended over a wide energy range containing up to 11 decades (from thermal to a few MeV), at places where the neutron field is very intense, high frequency pulsed or where it is mixed with an important high-energy photon component. The MCNPX code was used to evaluate the NaI(Tl) responses to different incident photon energies in terms of pulse-height distributions. An experimental validation of the calculated NaI(Tl) responses, using certified standard sources at a given measurement arrangement, indicates that MCNPX is a valid tool for routine calibration and benchmarking studies of this detector. A good agreement is found between the measured pulse-height distributions of the certified standard sources and those obtained from MCNPX simulations. As a preliminary application, a bare disc Au foil was directly exposed to a Bremsstrahlung photon beam at the isocentre of an 18 MV medical LINAC, in order to test the suitability of this activation material to measure the photo-neutrons generated in such facility. Two differentiated main photo-peaks, arising from ¹⁹⁶Au and ¹⁹⁸Au predominant γ-ray emissions, were observed. The two isotopes are produced mainly by the photonuclear, ¹⁹⁷Au(γ, n)¹⁹⁶Au, and radiative capture, ¹⁹⁷Au(n, γ)¹⁹⁸Au, reactions of, respectively, high-energy photons and thermal neutrons on the gold foil. From the measured ¹⁹⁸Au saturation activity, a rough estimation of (378 ± 68) × 10⁴ cm⁻² Gy⁻¹ was derived for the thermal neutron flux within the LINAC treatment room. This value, although being very approximate, is comparable to those reported by other authors for similar LINAC facilities but with different treatment room configurations, nominal acceleration potentials and Bremsstrahlung photon irradiation areas.     

Molecular-sieving effect of zeolite 3A on adsorption of H2, HD and D2

Synthetic zeolite 3A has the molecular-sieving windows of nominal diameter 0.3 nm in its crystal lattice framework, which obstruct the crystalline adsorption of molecules of diameter larger than 0.3 nm, except water, hydrogen and helium. The window's diameter slightly varies with temperature, however, that is endorsed in experimental results that hydrogen cannot be adsorbed at the liquid-nitrogen temperature. Authors measured the range of temperature where zeolite 3A permits hydrogen adsorption, and revealed the temperature difference of several degrees in appearance of molecular sieving for H₂ and D₂. This difference is important because from a H₂–D₂ mixture one isotope could be isolated by adsorption if operated at a temperature regulated between the molecular-sieving appearance temperatures. We have reported large values of D₂/H₂ separation factor obtained from molecular-sieving experiments. In this study, the effect of sieving for the hybrid-atomic isotope HD is examined using a H₂–HD–D₂ mixture. We here report the experimental HD/H₂ separation factor evaluated between the D₂/H₂ factor and unity. This result is significant because where the effective molecular diameter concerning the sieving mechanism is suggested. From this knowledge, the isotopic effect of sieving for HT and DT can be predicted.     

Effect of irradiation by 140 Mev Ag ions on the optical and electrical properties of polypropylene/TiO2 composite

Changes in the optical, structural, dielectric properties and surface morphology of a polypropylene/TiO₂ composite due to swift heavy ion irradiation were studied by means of UV–visible spectroscopy, X-ray diffraction, impedance gain phase analyzer and atomic force microscopy. Samples were irradiated with 140 MeV Ag¹¹⁺ ions at fluences of 1 × 10¹¹ and 5 × 10¹² ions/cm². UV–visible absorption analysis reveals a decrease in optical direct band gap from 2.62 to 2.42 eV after a fluence of 5 × 10¹² ions/cm². X-ray diffractograms show an increase in crystallinity of the composite due to irradiation. The dielectric constants obey the Universal law given by ε α f ⁿ⁻¹, where n varies from 0.38 to 0.91. The dielectric constant and loss are observed to change significantly due to irradiation. Cole–cole diagrams have shown the frequency dependence of the complex impedance at different fluences. The average surface roughness of the composite decreases upon irradiation.     

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.