Computational analysis of two-phase flow in horizontal bundles

Phase distribution during boiling flow in horizontal channels and fuel bundles tends to be asymmetric, particularly at low flows, due to gravity induced separation of the phases. Standard models and computational techniques developed for flow on vertical rod bundles cannot adequately simulate this tendency in horizontal flows, so more advanced techniques involving thermal and mechanical disequilibrium between phases are required.The paper describes the development and application of a drift flux code ASSERT (Advanced Solution of Subchannel Equations in Reactor Thermalhydraulics) which models departure from mechanical and thermal equilibrium between phases. Details of the model and computational technique are given, and parametric studies are shown to illustrate the capability of the code to simulate two-phase flow in horizontal bundles.Fundamental to the successful application of such a code are phenomenological studies aimed at the quantification of the empirical relationships selected for use. The paper concludes with a detailed study of mechanisms governing two-phase flow between neighbouring horizontal channels, isolating the driving effects of pressure gradient, gravity head and turbulent interchange by means of comparison with available experimental data.     

State of development of the computer programme BACCHUS-3D/TP for the description of transient two-phase flow conditions in LMFBR fuel pin bundles

The three-dimensional transient two-phase flow version of the computer programme BACCHUS-3D/TP (Two Phase) relies upon the basis supplied by the single phase flow version of the code. The bundle geometry typical of LMFBRs is modeled by means of the porous body approach based on the concepts of volume porosities, surface permeabilities, distributed resistances and heat sources. Two phase flow is described by means of two physical models available in two distinct versions of the code. One of these two-phase models is a three-equations Slip Model (SM) which provides as a subcase the Homogeneous Equilibrium Model (HEM) if no slip between the phases is assumed. The second is a six equation model referred to as Separated Phases Model (SPM) in which two coupled systems of governing equations are solved for the vapour and liquid phases.

A fully implicit treatment of the conservation equations for the coolant flow is followed in the SM and a half-implicit approach in the SPM. The article outlines the present state of the code development and future activities aiming at unifying both variants in a comprehensive code version describing the transition between different two-phase flow regimes from bubbly flow to dispersed annular flow. An assessment of the present capabilities of the code has been made with the theoretical interpretation of out-of-pile sodium boiling experiments in a 7- and 37-pin bundle. Numerical results are discussed and compared with experimental data.     

Three-dimensional deflection analyses of wire-spaced fuel pin bundles under temperature and hydrodynamic force fields with irradiation effects

An analytical method of evaluating the effects of non-uniform thermal expansion, hydrodynamic force acting on the periphery of a fuel pin and thermal and irradiation-induced creep and swelling on the three-dimensional deflection modes of a fuel pin bundle, as well as the deviation in engineering hot channel factor, are presented.The analysis consists mainly of deriving an expression for a flexibility matrix in terms of the general solution of a beam deflection equation with an arbitrary number of loads under either fuel pin to fuel pin or fuel pin to wrapper tube contact condition. The resulting matrix equation is solved for loads corresponding to all contact points, in terms of which the deflection modes are given.The drag coefficient for a wire-wrapped fuel pin in flowing fluid was investigated experimentally. Several cases of sample calculation show that for a prototype LMFBR fuel subassembly consisting of 169 fuel pins, the engineering hot channel factor accounting for the three-dimensional fuel pin bundle deflection is around 1.023–1.035 at zero irradiation and further increases to 1.045 after 500 day irradiation. The maximum load due to pin contact and the order of pin bundle deflection increase according to the irradiation level.     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.     

垂直上升矩形流道内气液两相流流型图的数值模拟

两相流流型在分析换热、流动不稳定性以及临界热流密度方面具有基础性作用.本文基于VOF(Volume of Fluid)多相流模型,对垂直上升矩形流道内气液两相流动进行数值模拟,表观气速0.1～110 m/s,表观液速0.1～3.2 m/s.得到了流道内气液两相流的主要流型:泡状流、弹状流、搅混流和环状流,分析了流道内截面含气率分布与流型的对应关系,以及截面含气率与气液两相流容积含气率的关系;分析了各种流型下的压降分布特性,并绘制了基于气液表观动能通量的不同流量下气液两相流的流型图,直观的表示出各种流型的分布区域及各流型间的流型转换边界,与已发表文献的实验结果对比符合较好.     

A domain decomposition methodology for pin by pin coupled neutronic and thermal-hydraulic analyses in COBAYA3

Nowadays, coupled 3D neutron-kinetics and thermal-hydraulic core calculations are performed by applying a radial average channel approach using a meshing of one quarter of assembly in the best case. This approach does not take into account the subchannels effects due to the averaging of the physical fields and the loose of heterogeneity in the thermal-hydraulic modelization. Therefore the models do not have enough resolution to predict those subchannels effects which are important for the fuel design safety margins, because it is in the local scale, where we can search the hottest pellet or the maximum heat flux. The aim of this paper is to present a domain decomposition methodology as our choice to asses this multi-scale issue in order to correct the results at the core scale with the ones from the subchannel scale.The UPM advanced multi-scale neutron-kinetics and thermal-hydraulics methodologies being implemented in COBAYA3 include domain decomposition by alternate core dissections for the local 3D fine-mesh scale problems (pin cells/subchannels) and an analytical nodal diffusion solver for the coarse mesh scale coupled with the thermal-hydraulic using a modelization of one channel per assembly or per quarter of assembly.The multi-scale domain decomposition is optimal for the thermal-hydraulic calculations, where the neutronic nodes (assemblies or quarters) can be mapped one-to-one to average channels and fuel rods and the pin cells to the detailed fuel pins and subchannels. For both levels we use the same channel code and, in order to facilitate the multi-scale mesh definition for the TH modules, the development of an input pre-processor has been a relevant part of this work.     

Numerical analyses on liquid-metal magnetohydrodynamic flow in sudden channel contraction

Three-dimensional numerical calculations have been performed on the magnetohydrodynamic (MHD) flows through a rectangular channel with sudden contraction, particularly in order to estimate the pressure drop through the sudden contraction. The sudden contraction is in the directions both perpendicular and parallel to the applied magnetic field. The Hartmann number, the Reynolds number, and the magnetic Reynolds number were set to ～100, ～1000, and ～0.001, respectively, in simulating laboratory conditions. The continuity equation, the momentum equation, and the induction equation were solved numerically. In the sudden contraction in the direction perpendicular to applied magnetic field, the loss coefficient takes a positive value in all the cases performed in this study, contrary to the expectation. This result is in contrast to that in the sudden expansion in the direction perpendicular to applied magnetic field, where the loss coefficient generally takes a negative value due to the MHD effect. In the sudden contraction in the direction of applied magnetic field, the loss coefficient takes a positive and large value in all the cases performed in this study. The loss coefficient generally becomes larger than that in the case of corresponding channel expansion in the direction of applied magnetic field.     

Numerical analyses on liquid-metal magnetohydrodynamic flow in sudden channel expansion

Three-dimensional numerical calculations have been performed on the magnetohydrodynamic (MHD) flows through a rectangular channel with sudden expansion, particularly in order to estimate the pressure drop through the sudden expansion. The sudden expansion is in the directions both perpendicular and parallel to the applied magnetic field. The Hartmann number, the Reynolds number and the magnetic Reynolds number are set to ～100, ～1000 and ～0.001, respectively, in simulating laboratory conditions. The continuity equation, the momentum equation and the induction equation were solved numerically by the finite difference method as discretization following the MAC method as solution procedure. On the whole, in the sudden expansion in the direction perpendicular to applied magnetic field, the loss coefficient is estimated to be nearly zero or small. In particular, the loss coefficient becomes negative for small aspect ratios. The reason of negative loss coefficient is attributable to decrease in the induced current just upstream of the expansion. On the other hand, in the sudden expansion in the direction of applied magnetic field, all the cases give positive and large loss coefficients, meaning that the pressure drop through the expansion becomes large. In particular, the loss coefficient becomes considerably large when the Hartmann number increases.     

Numerical research on oscillation of two-phase flow in multichannels under rolling motion

Two-phase flow instability and dynamics of a parallel multichannels system has been theoretically studied under periodic excitation induced by rolling motion in the present research. Based on the homogeneous flow model considering the rolling motion, the parallel multichannels model and system control equations are established by using the control volume integrating method. Gear method is used to solve the system control equations. The influences of the inlet, upward sections, heating power and rolling amplitudes on the flow instability under rolling motion have been analyzed. The marginal stability boundary (MSB) under the rolling motion condition is obtained. The unstable regions occur in both low and high equilibrium quality and inlet subcooling regions. The multiplied period phenomenon occurs in the high equilibrium quality region and the chaos phenomenon appears on the right of MSB. The concept of stability space is presented.     

Numerical simulation of multi-dimensional two-phase flow based on flux vector splitting

This paper describes a new approach to the numerical simulation of transient, multidimensional two-phase flow. The development is based on a fully hyperbolic two fluid model of two-phase flow using separated conservation equations for the two phases. Features of the new model include the existence of real eigenvalues, and a complete set of independent eigenvectors which can be expressed algebraically in terms of the major dependent flow parameters. This facilitates the application of numerical techniques specifically developed for high speed single-phase gas flows which combine signal propagation along characteristic lines with the conservation property with respect to mass, momentum and energy. Advantages of the new model for the numerical simulation of 1- and 2-dimensional two-phase flow are discussed.     

Numerical simulation of hyperbolic two-phase flow models using a Roe-type solver

The application of the generalized Roe scheme to the numerical simulation of two-phase flow models requires a fast and robust computation of the absolute value of the system matrix. In several models such as the two-fluid model or a general multifield model, this matrix has a non-trivial eigenstructure and the eigendecomposition is often ill conditioned. We give a general algorithm avoiding the diagonalization process. It is based on an iterative approach, but turns out to be an exact computation when the eigenvalues are real. The knowledge of the characteristic polynomial gives us an easy access to the eigenvalues but however, the iterative scheme can be used with only estimates of the eigenvalues, using for example Gershgorin’s disk localization. We finally show some numerical results of two-fluid model simulations involving interfacial pressure and a virtual mass force model.     

蒸汽发生器二次侧两相流传热特性数值研究

以AP1000核电站蒸汽发生器为原型,建立蒸汽发生器二次侧"平均通道"模型,利用计算流体动力学软件ANSYS CFX,基于相界面模型对蒸汽发生器二次侧两相流流动和沸腾换热过程进行研究。结果表明:数值模拟计算方法能准确模拟蒸汽发生器二次侧汽液两相流沸腾和传热过程;满负荷运行时,流体由预热区经过泡核沸腾区过渡到稳定沸腾区,含汽率和传热系数沿流动方向逐渐增大,出口含汽率与该型号蒸汽发生器设计值符合较好,平均传热系数的模拟结果和JensLottes经验关联式的预测值基本一致。     

Multi-dimensional modeling of two-phase flow in rod bundles and interpretation of velocities measured in BWRs by the cross-correlation technique

Two-phase flow in rod bundles is of the atmost importance in nuclear technology since it is a naturally occurring phenomenon in BWRs under normal operational conditions, or in PWRs undergoing a severe transient.It has recently been shown that by neutron noise analysis (cross-correlation) techniques, in the upper half of a normally operating BWR, one measures two or even three two-phase flow velocities (two or three peaks in the cross-correlation function); this was also found to be the case in measurements performed in simple air-water loops with different stationary and adiabatic two-phase flows, the direct consequence of these findings being that no cross-sectionally averaged two-phase flow models can be successfully employed for interpreting this kind of non-intrusive velocity measurements.It is the aim of this work to present an as precise as possible interpretation of velocity measurements in BWRs by the cross-correlation technique, which is based on the radially non-uniform quality and velocity distribution in BWR type bundles, as well as on our knowledge about the spatial ‘field of view’ of the in-core neutron detectors. After formulating the three-dimensional two-fluid model volume/time averaged equations and pointing out some problems associated with averaging, we expound a little on the turbulence mixing and void drift effects, as well as on the way they are modilled in advanced subchannel analysis codes like THERMIT or COBRA-TF. Subsequently, some comparisons are made between axial velocities measured in a commercial BWR by neutron noise analysis, and the steam velocities of the four subchannels nearest to the instrument tube of one of the four bundles as predicted by COBRA-III and by THERMIT. Although as expected, for well-known reasons, COBRA-III predicts subchannel steam velocities which are close to each other, THERMIT correctly predicts in the upper half of the core three largely different steam velocities in the three different types of BWR subchannels (corner, edge and interior).In the upper part of the core where a pronounced radial steam velocity and quality profile exists in the bundles, we associate the main peak of the cross-correlation function with the steam velocities in the edge subchannels, the second peak with the steam velocities in the corner subchannel, and the third small peak with the steam velocities in the interior subchannels. This interpretation is verified by a computer simulation with synthetic signals as well as by a simple phenomenological analytical model, and it opens the way for utilizing this kind of measurements (to a certain degree and within certain error bounds) for verification of advanced subchannel analysis codes like THERMIT-2 or COBRA-TF and in particular, for improving the two-phase mixing correlations employed in these codes.     

Advances in two-phase flow modeling for LMFBR applications

This paper summarizes the development of numerical models for analysis of sodium boiling phenomena in LMFBR which has been carried out at M.I.T. over the last five years.With regard to the degree of spatial averaging, our models use the porous body approach, in two and three-dimensional configurations. One important advantage of this model is the ability to accommodate homogenization of arbitrary-sized regions of interest.From a numerical point of view our basic approach is a semi-implicit method in which pressure pulse propagation and local effects characterized by short time constraints are treated implicitly, while convective transport and diffusion heat transfer phenomena, associated with longer time constants, are handled explicitly. This method remains tractable and efficient in multi-dimensional applications.Both a six-equation (“two-fluid”) model and a four-equation (“mixture”) model have been pursued. A considerable effort has been devoted to the development of constitutive relations. Our current package provides an adequate simulation capability for a wide range of applications.This paper will present the general physical formulation of the codes, the constitutive relations, the general numerical approach, applications, and finally some concluding remarks based on our experience with these codes.     

COBRA-3M: A modified version of COBRA for analyzing thermal-hydraulics in small pin bundles

COBRA-3M, a modified version of COBRA computer code, is most suitable for the analysis of thermal-hydraulics in small pin bundles commonly used in in-reactor or out-of-reactor experiments. It includes detailed thermal models for the fuel pins and duct walls. It can handle nonuniform power distribution across the bundle and/or within a fuel pin. Temperature dependence of material properties and fuel-cladding gap conductance can be treated. Heat generation in the duct walls and the effect of heat loss to the surroundings can also be simulated. COBRA-3M has been used extensively in the design and analysis of TREAT and SLSF experiments.     

Lattice Boltzmann methods for two-phase flow modeling

In this paper the most important properties of the lattice Boltzmann methods are reviewed with focus on two-phase flow modeling. The lattice methods are compared with the conventional computational fluid dynamics methods, their advantages and disadvantages are highlighted. Necessary improvements for practical applications are summarized.     

Macroscopic balance equations for two-phase flow models

The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analyzed. The equations obtained in this report supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. The flow-field model equations required by the balance equations are not discussed nor have applications and numerical solution techniques been considered.     

Choking flow modeling with mechanical non-equilibrium for two-phase two-component flow

A mechanistic model which considers the mechanical non-equilibrium is described for two-phase choking flow. The choking mass flux is obtained from the momentum equation with the definition of choking. The key parameter for the mechanical non-equilibrium is a slip ratio. The dependent parameters for the slip ratio are identified. In this research, the slip ratio which is defined in the drift flux model is used to identify the impact parameters on the slip ratio. Because the slip ratio in the drift flux model is related to the distribution parameter and drift velocity, the adequate correlations depending on the flow regime are introduced in this study. In this mechanistic modeling approach, the choking mass flow rate is expressed by the function of pressure, quality and slip ratio. The developed model is evaluated by comparing with the air–water experimental data to eliminate the thermal effect. The comparison of predicted choking model for mechanical non-equilibrium with other experimental data in high quality region (up to 80%) is quite reasonable with a small error.