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.     

A numerical prediction on the turbulent flow in closely spaced bare rod arrays by a nonlinear k−? model

Fully developed turbulent flows in closely spaced bare rod arrays have been studied numerically by using a nonlinear κ−ε model. This model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in non-circular ducts. Results of the calculation are compared with experimental data. The present computations yield reasonable agreement with experiments. However, the modeling of the transport effect by large scale cross gap eddy motion is required.     

Metal location and thickness in a multilayered sheet by measuring Kα/Kβ, Lα/Lβ and Lα/Lγ X-ray ratios

When a multilayered material is analyzed by means of energy-dispersive X-ray fluorescence analysis, then the X-ray ratios of Kα/Kβ, or Lα/Lβ and Lα/Lγ, for an element in the multilayered material, depend on the composition and thickness of the layer in which the element is situated, and on the composition and thickness of the superimposed layer (or layers).Multilayered samples are common in archaeometry, for example, in the case of pigment layers in paintings, or in the case of gilded or silvered alloys. The latter situation is examined in detail in the present paper, with a specific reference to pre-Columbian alloys from various museums in the north of Peru.     

CASSPERR: A γ–γ cascade detector for resonant nuclear reaction analysis

Resonant nuclear reaction analysis (RNRA) is sometimes the only technique able to quantify elements in a matrix containing other elements. Background due to cosmic rays and natural radioactivity has limited traditional RNRA to samples with relatively high concentrations of the measured element, or to facilities with large amounts of passive shielding. Many nuclear reactions of interest in RNRA produce excited states in the resulting nuclei that then de-excite by product-specific sequences of photon emissions. The CAScade SPEctrometer for Resonant Reactions (CASSPERR) selects only events that match the desired combination of photon emissions. Rejection of other events greatly reduces the background, thus improving the signal to noise ratio (SNR). Since it is constructed from available commercial components, CASSPERR opens RNRA to typical ion beam analysis facilities. The design, operation and evaluation of CASSPERR with applications to materials science are currently under investigation.     

Deviations of the Kβ/Kα intensity ratio of Ti upon impact with low velocity ions

Deviations of the branching ratio of the decay of K-vacancies in Ti have been observed during bombardment with low velocity ions of H, He and N. Beams of these ions have been used for various applications in which resonant nuclear reactions were used as the main analytical technique, whereas the X-ray signal could conveniently be used for monitoring the accumulated charge. During the evaluation of this monitoring signal, it was observed that the commonly made assumption that the K_β/K_α intensity ratio is a constant can easily be off by 30% or more. Also a few data of L-shell ionisation cross sections has been measured on Au to establish if the onset of deviations in the branching ratio parallels the onset of deviations from the ECPSSR theory for inner shell ionisation.     

Development and validation of a transition boiling model for RELAP5/MOD3 reflood simulation

The current version of the RELAP5/MOD3.1 code significantly underpredicts the transition boiling heat transfer during reflooding of hot fuel rods. In order to extend the code’s range of application for LOCA and degraded core analyses, a new transition boiling model has been developed, assessed and implemented. The model is based entirely on local state variables calculated by the code (wall and fluid temperatures, pressure, void fraction, mass flux and static quality) and does not rely on other history parameters, such as quench position or CHF and minimum film boiling temperatures. A number of separate-effect and bundle experiments are analyzed with the modified version of the code, and the predictions are compared with the ones obtained by the current version and with available experimental data. In all cases, the predictions of the improved model better fit the measured data. The shape of the new temperature curves is more physically and conceptually sound than the one calculated by the current version of the code.     

Numerical analysis of turbulent mixed convection air flow in inclined plane channel with k-ε type turbulence model

Numerical study on turbulent mixed convection in inclined plane channels, from 15° to 90° (vertical), was carried out to examine the effect of inclination on fluid flow and heat transfer distributions. The turbulent air flows upward or downward into the duct with one wall heated from bottom. Calculation results with several kinds of k-εtype turbulence models were used to compare the experimental data with those in literatures to determine suitable model. The dependents of Nusselt number on the inclination angle of both the buoyancy-aided and buoyancy-opposed flow are discussed.     

Ion-beam induced effects in α-Al2O3 at 15 K

In order to study the primary effects of ion-beam induced damage formation in sapphire, implantation and subsequent damage analysis by Rutherford backscattering spectrometry (RBS) in channelling configuration were performed at 15 K without change of the sample temperature. We used 80 keV Na, 150 keV K and 150 keV Ar to investigate the damage accumulation with increasing ion fluence. During the RBS measurement with 1.4 MeV He ions at 15 K, defect annealing was observed. From the measured channelling spectra, defect profiles were calculated using the computer code DICADA. These profiles are narrower and distinctly lower than those calculated by SRIM2003, especially below the surface. This suggests an enhanced recombination of defects within this area. The damage concentration at the peak maximum is analysed as a function of ion fluence or rather displacements per atom. The model that was applied contains two different types of defects, namely point defects and clusters and takes into account the defect annealing under the He beam. For both defect profiles and damage accumulation, no significant influence of the implanted ion species was observed.     

A model for predicting static instability in two-phase flow systems

An analytical model for predicting the onset of Ledinegg instability in vertical channel under both downflow and upflow conditions has been developed and evaluated. The model divides the flow field into two regions based upon the fluid temperature. The pressure drop is then found by solving an appropriate set of equations for each region. The theoretical results are compared to an existing set of experimental data covering a range of channel diameters and operating conditions. A very good agreement is obtained with the available experimental data from the literature for water systems. A parameter, the ratio between the surface heat flux and the heat flux required to achieve saturation at the channel exit for a given flow rate, is found to be a very accurate indicator of the minimum point velocity in the demand curve.     

Studies of Na-segregation at Ni/α-quartz interfaces

Ni/α-quartz bilayers were irradiated at 77 K with 200 keV Na⁺ ions at a fluence of 5 × 10¹⁶ ions/cm² and annealed in hydrogen up to 883 K. The Na-migration at the Ni/α-quartz interface and towards the Ni-surface, the hydrogen storage in the irradiated region, and the Ni/α-quartz interface broadening due to Na implantation and decoration were investigated via Rutherford Backscattering Spectrometry (RBS) and Resonant Nuclear Reaction Analysis (RNRA). We demonstrate that after a one hour-annealing at 833 K a large fraction of the implanted Na has been trapped at the Ni/α-quartz interface from where it is released at 883 K. The results are discussed and compared with our findings in Na-irradiated metals and silicon compounds.     

A faster procedure for the calculation of the J(ξ, β) function

One of the biggest difficulties in obtaining an analytical expression for the J(ξ, β) function is its explicit dependence on the Doppler broadening function ψ(x,ξ). The objective of this paper is to present a method for the fast and accurate calculation for the J(ξ, β) function based on the recent advances in the calculation of the Doppler broadening function and on a systematic analysis of its integrand. The methodology proposed uses an analytical formulation for the calculation of ψ(x, ξ) and a representation in series for error functions with complex argument. The results were satisfactory from the accuracy and processing time standpoint and are an option to other calculation methods found in the literature.     

Isotope effects in thermal neutron transmission and backscattering processes for ε-phase zirconium hydrides and deuterides

Distributions of hydrogen isotope concentrations in ε-phase zirconium hydrides and deuterides (ε-ZrH_x and ε-ZrD_x: 1.8 < x < 2.0) were investigated by neutron radiography (NRG). The NRG images of the thermal neutron transmission and backscattering revealed hydrogen concentration dependence and isotope differences. The thermal neutron mass attenuation coefficients in relation to the hydrogen isotope concentrations were determined from the transmission NRG images. The results showed the isotope effects of the thermal neutron mass attenuation coefficients for ε-ZrH_x to be about 6–9 times higher than those for ε-ZrD_x. The neutron scattering processes for transmission and backscattering NRG images of ε-ZrH_x and ε-ZrD_x were also analyzed using a general Monte Carlo neutron-particle transport (MCNP) code.     

Comparisons of the RALIZA-2/02 two-phase flow model with experimental data

The RALIZA-2 computer program was designed for thermal-hydraulic analysis of flow channel and fuel element of PWR/BWR at steady-state and transient conditions. A nonhomogeneous, nonequilibrium model of a two-phase flow and a two-dimensional heat conduction model of fuel pin are used in the program. A fully implicit integration scheme for both models is used. The steady-state constitutive correlations set is used. The void fraction, pre- and post-DNB heat transfer mechanism are compared with data. Also a loss of flow experiment was calculated and compared with nuclear heated rod bundle experimental data for typical PWRs. A very good agreement was obtained.     

Evaluations of the Irwin βIc adjustment for small specimen fracture toughness data

Thickness size effects and large amounts of data scatter often occur in the cleavage fracture toughness testing of steel. It is shown that the Irwin β_Ic equation provides an effective adjustment for thickness size effects as well as reduces data scatter. Examples of applying the Irwin β_Ic adjustment to both static and dynamic toughness data are given. The significance of cleavage microcracking in the initiation of fast fracture is discussed and it is reasoned that this phenomenon is closely related to the sensitivity of the cleavage fracture toughness to triaxiality and strain rate.     

Strain aging in α-zirconium and α-zircaloy at 1000 K

Tensile deformation of fine grain-size zirconium and zircaloy-2 and -4 sheet specimens was investigated near 1000 K at strain rates between 10⁻⁴ and 10⁻² s⁻¹. Manifestations of dynamic strain aging, e.g., yield-point effect and rate-dependent work-hardening behavior, were evident in the materials. Also, the uniform strain versus temperature curve exhibited a minimum. Yield-point type transients following extension-rate change, serrated stress-strain curves, and flow-stress peaks were recorded for both zircaloys. A microstructure with a smaller volume fraction of second-phase particles is more conducive to the yield-point effect. An analysis of the composition of second-phase particles implies that iron atoms in solution are responsible for strain aging in zirconium and the zircaloys at 1000 K.     

A self-standing two-fluid CFD model for vertical upward two-phase annular flow

In this paper, a new two-fluid CFD (computational fluid dynamics) model is proposed to simulate the vertical upward two-phase annular flow. This model solves the basic mass and momentum equations for the gas core region flow and the liquid film flow, where the basic governing equations are accounted for by the commercial CFD package Fluent6.3.26^®. The liquid droplet flow and the interfacial inter-phase effects are accounted for by the programmable interface of Fluent, UDF (user defined function). Unlike previous models, the present model includes the effect of liquid roll waves directly determined from the CFD code. It is able to provide more detailed and, the most important, self-standing information for both the gas core flow and the film flow as well as the inner tube wall situations.     

An improved mixing-length model for annular two-phase flow with liquid entrainment

A differential model for adiabatic, fully developed, annular two-phase flow with liquid entrainment has been developed. The model is based on a modified form of the single-phase mixing length function to account for turbulence intensity attenuation due to the presence of entrained liquid droplets in the gas core. Simultaneous predictions of pressure drop and average film thickness for given flow rates show good agreement with a wide range of experimental results for various fluids at several pressures in a range of tube diameters for both horizontal and vertical (upwards and downwards) flows.