The measurement of void waves in bubbly two-phase flows

The propagation of void fraction disturbances (i.e. void waves) in bubbly two-phase air-oil flow was investigated experimentally.The void wave data often showed two simultaneous void wave propagations; in particular, the classical kinematic void wave and a faster void wave propagation associated with bubble clusters. Significantly, the bubbly-to-slug flow regime transition was found to be associated with amplification of the void waves associated with the propagating bubble clusters.These data should be valuable for the assessment of the closure laws used in two-fluid models and for the development of mechanistic models for the bubbly-slug flow regime transition.     

Derivation of new mass,momentum, and energy conservation equations for two-phase flows

System codes are used to analyze nuclear reactor systems during steady state and transient operations. These codes are able to predict pressure drop, void fraction distributions and temperature distributions for various coolants, heated flow geometries, and heat configurations. They also include models for various two-phase flow regimes, but extreme flow conditions that involve significant phase change can tax the current code capabilities. Current system codes have mass, momentum, and energy conservation equations for two fields (liquid and vapor), resulting in a model with six conservation equations. Recent developments in limited applications of a few of these codes have added a separate droplet field from the continuous liquid. This is part of a trend toward the inclusion of more fields (and requisite conservation equations) in system codes. The representation of two phase flow phenomena is improved by increasing the number of fields. Conservation equations based on six fields (liquid, vapor, small bubble, large bubble, small droplet and large droplet) are derived in this work.     

The dependence of wall lubrication force on liquid velocity in turbulent bubbly two-phase flows

Based on the significance of a computational fluid dynamics (CFD) simulation of dispersed two-phase flow systems in many engineering fields, especially in nuclear energy systems, extensive analytical and numerical studies of wall lubrication force for vertical upward turbulent bubbly two-phase flow are presented. An analytical expression of the wall lubrication force considering the effect of liquid velocity is developed and analyzed. A numerical methodology for evaluating the wall lubrication force coefficients is proposed, which is based on the assumption that the balance of the forces acting on a bubble perpendicularly to the flow direction determines the establishment of radial void fraction profiles. Wall lubrication force coefficients are determined based on a reasonable agreement in radial void fraction profiles between numerical results predicted by the CFD EAGLE (elaborated analysis of gas–liquid flows evolution) code and extensive experimental database in the open literature as well as experiments performed at the Korea Atomic Energy Research Institute-vertical air–water loop test facility. Liquid velocity dependence of wall lubrication force is clearly shown in both analytical and numerical ways in the present study, and new correlations are then proposed for the wall lubrication force coefficients.     

基于离散纵标输运计算方法的三维燃耗程序发展研究

为了精确描述和分析具有强烈各向异性中子注量率空间分布的反应堆燃耗过程,本文实现了三维SN 输运计算与燃耗计算的耦合,发展了相应的三维输运燃耗耦合计算程序.该程序系统采用接口程序自动耦合三维SN输运计算程序和同位素燃耗计算程序的方法实现对三维中子学计算模型的精细燃耗计算,获得燃料同位素成分、燃耗反应性、中子注量率空间分布等参数随燃耗时间的变化量.采用IAEA 基准校核例题对程序系统进行了校核,计算结果初步证明了所开发的三维燃耗程序系统的正确性.     

The 232Th(n, f) cross-section for thermal and 2.44 MeV neutrons

The thermal neutron induced fission cross-section of ²³²Th was measured at an intense and very pure thermal neutron beam of the Grenoble High Flux Reactor, yielding a value of (3 ± 1) μbarn. For control purposes, the same targets were used at the VandeGraaff accelerator of the CBNM (Geel), where a ²³²Th (n, f) cross-section value of (0.12 ± 0.02) barn was obtained with 2.44 MeV neutrons, in agreement with other published data.     

Non-linear dynamics of a two phase flow system in an evaporator: The effects of (i) a time varying pressure drop (ii) an axially varying heat flux

In this paper we study the phenomena of density wave oscillations (DWO) in a vertical heated channel. The homogeneous equilibrium model is used to simulate the flow in the two-phase region. The equations are solved numerically using a ‘shooting-method' technique. This in its turn employs an implicit backward finite difference scheme. The scheme can incorporate the movement of the interface. It is very elegant and does not involve storage of variables in large N×N matrices. This scheme is sufficiently general and can be used to simulate the dynamic behaviour when: (i) the heat flux imposed at the surface is non-constant, i.e. exhibits an axial variation; and (ii) the imposed pressure drop is varied periodically at a fixed frequency. A possible explanation for the conflicting reports of the effect of a periodic variation in heat flux is provided using a linear stability analysis and the D-partition method. The interaction of the natural frequency of the DWO and the fixed forcing frequency of the imposed pressure drop gives rise to various phenomena viz relaxation oscillations, sub-harmonic oscillations, quasi-periodic and chaotic solutions. To aid the experimentalist describe this infinite-dimensional system on the basis of his experimental results we discuss the characterisation using only the velocity time series data. This is done employing the method of delay coordinate embedding. The phase portraits, stroboscopic map and correlation dimension of the actual attractor are compared with that of the reconstructed attractor from the velocity time series.     

A measurement of the Li(n,α) cross-section

The relative shape of the ⁶Li(n,α)/²³⁵U(n,f) cross-section ratio has been determined in the range of incident neutron energy from 2 to 800 keV. The measurements were made by the time-of-flight method using the Harwell 45 MeV linac to provide the pulsed source of neutrons. A thin ⁶Li-glass scintillator was used to register the (n,α) events, and the (n,f) events (in a metallic sample of ²³⁵U) were registered with fission neutron detectors. The shape of the ⁶Li(n,α) cross-section was obtained by combining the measured ⁶Li(n,α)/²³⁵U(tn,f) cross-section ratio with an evaluation of the ²³⁵U(n,f) cross-section. The cross-section so derived was placed on an absolute scale by normalization in the neutron energy interval 2–10 keV, where the ⁶Li(n,α) cross-section is accurately known. The cross-section at the peak of the prominent p-wave resonance near 240 keV is found to be 3.29 ± 0.12 b. The results are compared with other measurements and also with a recent theoretical calculation of the cross-section.     

Simulation of a neutron scattering method for measuring void fraction in two-phase flow

Experiments have indicated that fast/epithermal neutron scattering techniques are attractive for void fraction measurement in two-phase flow. Some of these experiments have been simulated by Monte Carlo neutron transport calculations. The simulations predict results in agreement with the measurements. This suggests that the experimental technique has a sound theoretical basis, and that numerical simulations may be used to design experimental setups for different applications.     

The infinite medium Green's function method for multigroup discrete ordinates transport problems in multi-layered slab geometry

Analytic solutions of the multigroup discrete ordinates transport equation with linearly anisotropic scattering and arbitrarily distributed source for multi-layered slab problems are obtained by using the infinite medium Green's function (IMGF) and Placzek's lemma. In this approach, the infinite medium Green's function is derived analytically by using the spectral analysis for the multigroup discrete ordinates transport equation and its transposed equation, and this infinite medium solution is related to the finite medium solution by Placzek's lemma. The resulting equation leads to an exact relation that represents the outgoing angular fluxes in terms of the incoming angular fluxes and the interior inhomogeneous source for each slab. For heterogeneous problems having multi-layered slabs, the slabs are coupled through the interface angular fluxes. Since all derivations are performed analytically, the method gives exact solution with no truncation error. After the interface angular fluxes are calculated by using an iterative method, the continuous spatial distribution of the angular flux (i.e. analytic solution) in each slab is given straightforwardly in terms of the IMGF and the boundary angular fluxes.     

Transient behavior of natural circulation for boiling two-phase flow (flow after pump trip)

The idea of a flow diode has been proposed to improve the pump coastdown characteristics of the internal recirculation pumps adopted by the ABWR. In this paper, the transient behavior from forced to natural circulation was experimentally investigated by simulating a pump coastdown condition for the purpose of providing an available source of information that is necessary for designing the flow diode. The results of the study showed that the transient behavior after pump coastdown was influenced by the coastdown period, the trigger velocity and the initial driving force of natural circulation. The potential of each driving factor was governed by the delay time for boiling, which is a very important parameter in natural circulation of boiling two-phase flow. In consequence, a guide for the designing of a flow diode was proposed.     

Programming and modelling environment for studies of gas flows in micro- and nanostructures based on solving the Boltzmann equation

A set of programs has been developed for modelling gas flows in micro-and nanostructures. The programs are based on a method for solving the kinetic equation by a finite-difference technique on a fixed space-velocity grid. A projection method is used for calculating the Boltzmann collision integral which ensures that the conservation of mass, momentum, and energy is rigorously satisfied and that the collision integral goes to zero under thermodynamic equilibrium conditions. An explicit flux conservative scheme is used for approximating the differential part. The solution of the resulting system of difference equations is found by splitting into stages of collisional relaxation and free molecular flow. The computational algorithm is realized on a multiprocessor system using MPI technology. A graphical shell has been developed for visualizing the results during the computations and for convenient variation of the physical parameters of the flow under study. Some calculations of flows through a periodic system of square holes and a periodic system of slots whose transverse dimension is on the order of the mean free path of the gas molecules, as well as some model calculations of a micropump design, are given as examples. Translated from Atomnaya énergiya, Vol. 105, No. 4, pp. 211–217, October, 2008.     

Diffusion form of the transport equation and the method of kinetic diffusion (application to one-dimensional planar geometry)

A form of the transport equation with the same structure as the elementary diffusion equation is proposed. It is distinguished by the fact that the diffusion coefficient depends not only on the properties of the medium but also on certain angular moments of the differential flux. The existence of a reciprocal relation between the angular moments and the spatial distribution of the scalar flux makes it possible to obtain an exact numerical solution of the transport equation, expressed in diffusion form, by means of a simple iteration pocedure (the method of kinetic diffusion). The relation between the transport equation in the diffusion form and the elementary theory of diffusion is examined, the results of calculations of certain variants of the the Milne problem are presented, and the inherent properties of the method, which make it effective in many practical applications, are noted. 3 Tables, 5 references. Federal Science Center of the Russian Federation—Institute of Theoretical and Experimental Physics. Translated from Atomnaya Energiya, Vol. 86, No. 1, pp. 16–27, January, 1999.     

Assessment of the correlation method for determining the parameters of two-phase coolant in a vk-50 core

Measurements of the propagation velocity of small perturbations of the neutron flux along the height of the core of a VK-50 boiling water vessel reactor are presented. The method of measurement is based on the evaluation of the delay time of a signal between the axially positioned sensitive elements of a moving double direct-charge detector. The measurements are compared with calculations for the parameters of two-phase coolant in the measurement channels. It is shown that the agreement between the measurements and the calculations is best for the velocity of an interphase surface.     

Measurement of time varying thickness of liquid film flowing with high speed gas flow by a constant electric current method (CECM)

A constant-electric-current method (CECM) developed by the present author is a kind of conductance method. The characteristics of the CECM are (1) a constant-current power source is used for supplying the electric power and (2) two kinds of electrodes are installed. One is used for supplying electric power and the other is for detecting the information of hold-up or film thickness. The main merits of the CECM are (1) the output from the sensor electrode is independent of the location of gas phase, for example radial location in a tube cross-section, (2) the sensitivity of detecting the change in the hold-up is higher in the case of the thinner film thickness, and (3) the interaction among the electrodes is negligible. The basic idea, calibration and examples of the application of the CECM will be discussed in the present paper.     

Differential cross-section measurements for the C(d, p0)C reaction and applications to surface analysis of materials

This work involves surface analysis by nuclear techniques, which are non-destructive, and computer simulation. The “energy analysis” method for nuclear reaction analysis is used. Energy spectra are computer simulated and compared to experimental data, giving target composition and concentration profile information. Measured values are presented for the differential cross-section of the ¹²C(d, p₀)¹³C reaction in the deuteron energy range 0.81-2.07 MeV for laboratory detection angles of 165° and 135°, using self-supported two-layered targets consisting of high purity thin films of typically 13 μg/cm² natural carbon and 65 μg/cm² gold. The error in the absolute differential cross-section values is generally ∼6%. The method, using these values, is successfully applied to determination of uniform concentration profiles of ¹²C, along considerable depths, for a thick flat target of high purity pyrolitic graphite. It is characterised a thin surface film of carbon on a thick flat quartz target. Uniform concentration profiles of ¹⁶O are also obtained from (d, p) and (d, α) reactions.     

The spherical harmonics method for the multigroup transport equation in x−y geometry

A spherical harmonics equation in the form of a second-order differential equation is derived for the 2-D x−y geometry, including higher-order scattering within a group. Using this equation, a multigroup transport code for the spherical harmonics method of a general order of approximation is developed. Some numerical examples, including typical problems for the ray effect, are presented and compared with those obtained by the discrete-ordinates method. It is shown that the present method gives more accurate results than the discrete-ordinates method, although this spherical harmonics code requires more computer memory than the discrete-ordinates code.