Steady state and transient sodium boiling experiments in a 37-pin bundle

As part of the fast breeder reactor safety analysis steady state and transient sodium boiling tests were performed out-of-pile in an electrically heated 37-pin bundle. The steady state boiling experiments served for investigations of the two-phase flow physics and to support the analysis of the transient experiments. The experimental work concentrated on the transient sodium boiling tests which simulated the unprotected loss of flow accident (ULOF) from the start of the flow run down via boiling inception to the onset of dryout. Special emphasis was laid upon the analysis of the transition from the spatial to the mainly one-dimensional growth of the boiling region during the flow transient. The experimental results from both types of tests serve as data basis for computer code validations. A reference test (L22) of the transient experiments was satisfactorily recalculated with a one-dimensional and with a three-dimensional computer programme.     

Sodium boiling experiments in a 19-pin bundle under loss-of-flow conditions

An experimental study was conducted on transient sodium boiling in a 19-pin electrically heated LMFBR fuel subassembly mockup under loss-of-flow conditions. In each run the inlet flow was reduced or stopped at constant heater power. There was no strong effect of temperature ramp rate on incipient-boiling (IB) wall superheat. The observed coolant voiding was initially limited to the center subchannel because of steep temperature gradient in the bundle. The bulk pressure rise registered upon initial vaporization was markedly lower than the vapor pressure corresponding to the IB wall superheat. The pressure pulse generated at vapor bubble collapse correlated reasonably well with the re-entrant liquid velocity, but the measured value was very much smaller than the calculation by sodium hammer analysis.     

Loss-of-flow experiment in a 37-pin bundle LMFBR fuel assembly simulator

An experimental study was conducted on transient sodium boiling in an LMFBR fuel subassembly mockup under loss-of-flow conditions. In the test section, an electrically heated 37-pin bundle was centered in a hexagonal tube. The measured maximum IB wall superheat was 36°C, and the effects of heat flux, temperature rise rate, and system pressure were unclear. Boiling was initiated at the end of the heated section, the bubble expanded mainly to the upstream central subchannels and to the downstream unheated section according to the expansion of the saturated temperature region. When the voided zone covered the whole flow cross-section, the void pattern changed to the one-dimensional slug ejection-type and the inlet flow decreased rapidly. Dryout occurred after the inception of flow reversal in the wide region of the bundle.     

Steam generator transient studies using a simplified two-fluid computer code

A simplified two-fluid computer code has been used to simulate reactor-side (or primary-side) transients in a PWR steam generator. The disturbances are modelled as ramp inputs for pressure, internal energy and mass flow-rate for the primary fluid. The CPU time for a transient duration of 4 s is approx. 10 min on a DEC-1090 computer system. The results are thermodynamically consistent and encouraging for further studies.     

Sodium boiling experiments in a 7-pin bundle: Investigations into some safety aspects of the KNK II driver zone

A series of sodium boiling experiments, in which the thermohydraulic characteristics of KNK II driver subassemblies were simulated, has been carried out for the purpose of studying the effects of two types of cooling disturbances: rapid flow interruption and those flow reductions which develop rather gradually. Information about the spatial and temporal development of boiling, voidage and dryout was obtained. Furthermore the feasibility of individual subassembly temperature monitoring has been investigated as well as that of two integral boiling detection methods based on acoustic noise and reactivity measurements.     

Sodium boiling: one-dimensional two-liquid modeling using the SOKRAT-BN computer code

The results of testing the thermohydraulic module of the SOKRAT-BN computing code for analyzing accidents with boiling of sodium coolant in fast reactors are presented. The computational results are compared with experimental data. It is shown that the thermohydraulic module of the SOKRAT-BN code models stationary sodium boiling well. Using as a basis the results obtained by modeling sodium boiling in a vertical heated channel, a system of closure relations for calculating two-phase sodium flow regimes, including the interphase velocity, was modified and checked. Modeling sodium boiling in a vertical annular channel also showed that the closure relations incorporated in the thermohydraulic module of the SOKRAT-BN code are suitable for calculating heat-exchange with a wall.     

An improved numerical scheme with the fully-implicit two-fluid model for a fast-running system code

A new computational method is implemented in the FISA-2 (Fully-Implicit Safety Analysis-2) code to simulate the thermal-hydraulic response to hypothetical accidents in nuclear power plants. The basic field equations of FISA-2 consist of the mixture continuity equation, void propagation equation, two phasic momentum equations, and two phasic energy equations. The fully-implicit scheme is used to eliminate a time step limitation and the computation time per time step is minimized as much as possible by reducing the matrix size to be solved. The phasic energy equations written in the nonconservation form are solved after they are set up to be decoupled from other field equations. The void propagation equation is solved to obtain the void fraction. Spatial acceleration terms in the phasic momentum equations are manipulated with the phasic continuity equations so that pseudo-phasic mass flux may be expressed in terms of pressure only. Putting the pseudo-phasic mass flux into the mixture continuity equation, we obtain linear equations with pressure variables only as unknowns. By solving the linear equations, pressures at all the nodes are obtained and in turn other variables are obtained by back-substitution. The above procedure is performed until the convergence criterion is satisfied. Reasonable accuracy and no stability limitation with fast-running are confirmed by comparing results from FISA-2 with experimental data and results from other codes.     

TRACE simulation of sodium boiling in pin bundle experiments under loss-of-flow conditions

In the framework of PSI's FAST code system, the thermal–hydraulic code TRACE is being extended for representation of sodium two-phase flow. As the currently available version (v.5) is limited to the simulation of only single-phase sodium flow, its applicability range is not enough to study the behavior of a Generation IV sodium-cooled fast reactor (SFR) during transients in which boiling is anticipated. The work reported here concerns the extension of the non-homogeneous, non-equilibrium two-fluid models, which are available in TRACE for steam-water, to sodium two-phase flow simulation. The conventional correlations for ordinary gas–liquid flows are used as basis, with optional correlations specific to liquid metal where necessary. A number of new models for representation of the constitutive equations specific to sodium, with a particular emphasis on the interfacial transfer mechanisms, have been implemented and compared with the original closure models.A first assessment of the extended TRACE version has been carried out, by using the code to model experiments that simulate a loss-of-flow (LOF) accident in a SFR. One- and two-dimensional representations of the test section have been considered. Comparison of the 1D model predictions, with both experiment and SIMMER-III code predictions, confirm the ability of the extended TRACE code to predict the principal sodium boiling phenomena. Two-dimensional representation of the test section, however, has been found necessary for providing more detailed comparisons with the experimental data and thereby studying, in greater detail, the influence of the physical models on the calculated results.The paper thus presents a first-of-its-kind application of TRACE to two-phase sodium flow. It shows the capability of the extended code to predict sodium boiling onset, flow regimes, pressure evolution, dryout, etc. Although the numerical results are in good agreement with the experimental data, the physical models should be further improved. Other integral experiments are planned to be simulated, in order to further develop and validate the two-phase sodium flow modeling.     

Phenomenological investigation of sodium boiling in a SFR core during a postulated ULOF transient with CATHARE 2 system code: a stabilized boiling case

In the framework of the research and development on GEN IV sodium fast reactors (SFRs), the phenomenology of sodium boiling during a postulated unprotected loss of flow (ULOF) transient has been investigated with the CATHARE 2 system code. This study focuses on a stabilized boiling case: in such a regime, no flow redistribution occurs from the subassemblies which have reached the saturation temperature to those that are still single-phase. In this paper, for a subassembly design featuring no restrictive structures above the fuel bundle, a quasi-static approach is first developed to get an upper bound of the reactor core power at boiling onset that would be compatible with the well-known Ledinegg criteria for diphasic flow static equilibrium. Then, dynamics results achieved through simulation with the CATHARE 2 code for a postulated ULOF are presented: boiling is shown to remain stable during the transient for such a core power at boiling onset. Another important outcome of the simulation is the calculation of a dynamic instability, in the form of a two-phase hydrodynamic chugging phenomenon. The predicted phenomenology of this stabilized boiling case should be studied further in order to consider its dependency on the underlying closure laws and to eliminate the possibility of a numerical instability.     

CFD investigation of helical wire-wrapped 7-pin fuel bundle and the challenges in modeling full scale 217 pin bundle

Flow and temperature distributions of sodium in a heat generating fuel pin bundle with helically wound spacer wire have been predicted from basic principles by solving the three-dimensional conservation equations of mass, momentum and energy, for a wide range of Reynolds number. Turbulence has been modeled using the k– turbulence model. The geometry details of the bundle and heat flux from the fuel pin are similar to that of the Indian Prototype Fast Breeder Reactor (PFBR) that is currently under construction. The focus of the study is to assess the effect of transverse flow in promoting flow and temperature uniformity. It is seen that the ratio of maximum transverse velocity to the maximum axial velocity is nearly equal to the tangent of the rolling up angle of the spacer wire. Due to the wire wrap, the difference in bulk sodium temperature between the peripheral and central sub-channels is reduced to by a factor of 4 when compared to that without spacer wire. The film drop at the junction between wire and the pin is found to be only 70 °C. The predicted results are found to be in close agreement with that of the experimental results reported in literature. The present study considers a 7-pin bundle assembly of one helical pitch. The computational time and memory required for a 217 pin with 15 pitches assembly is ascertained to be 500 times that required for the current study. Hence, research activities have been directed towards developing a parallel CFD code and structural mesh generation software.     

Analysis of the primary containment response using a hydrodynamic-elastic-plastic computer code

The dynamic response of the primary reactor containment system to a hypothetical core disruptive accident (HCDA) is determined from the basic equations of mass, momentum, and energy, and the equations of state of the medium. These equations are first expressed in material coordinates and then set into finite difference form solved numerically on the computer using a hydrodynamic-elastic-plastic computer code, REXCO-HEP developed at ANL. Propagation of pressure waves, loads imposed on different parts of the reactor components, and the resulting deformations are determined at every time step throughout the sequence of the calculation. As a sample calculation, the code was applied to analyze the response of the FFTF reactor to a 150 MWsec HCDA. The mathematical model is described in detail, particularly in the areas of modeling reactor internals and extending the time range to cover the entire excursion phenomenon. Finally, the results obtained from the computer analysis are discussed in detail.     

On the stability of a one-dimensional two-fluid model

An analysis on the stability of the governing differential equations for area averaged one-dimensional two-fluid model is presented. The momentum flux parameters for gas and liquid are introduced to incorporate the effect of void fraction profiles and velocity profiles. The stability of the governing differential equations is determined in terms of gas and liquid momentum flux parameters. It is shown that the two-fluid model is well posed with certain restrictions on the liquid and gas momentum flux parameters. Simplified flow configurations for bubbly flow, slug flow, and annular flow are constructed to test the validity of proposed stability criteria. The momentum flux parameters are calculated for these flow configurations by assuming a power-law profile for both velocity and void fraction. Existing correlation for volumetric distribution parameter C_o is used. By employing simplified velocity profiles, the void fraction profile is determined from C_o correlation. It is found that the void fraction is wall-peaked at low void fraction and it becomes center-peaked as the void fraction increases. A simplified annular flow is also constructed. With these flow configurations, the momentum flux parameters are determined. It is shown that the calculated momentum flux parameters are located in the stable region above the analytically determined stability boundary. The analyses results indicate that the use of momentum flux parameter is promising, since they reflect flow structure and help to stabilize the governing differential equations.     

Numerical simulation of turbulent flow in a 37-rod bundle

The unsteady Reynolds averaged Navier–Stokes equations, combined with a Reynolds stress model, were solved numerically to determine fully developed isothermal turbulent flow in a 60° sector of a 37-rod bundle. It was found that this flow contained large-scale coherent structures, which affected strongly the local velocity fluctuations, especially near the gaps between rods or between rods and the surrounding wall. The time-averaged mean velocity and Reynolds stresses were in good agreement with experimental results in a similar channel. Coherent velocity fluctuations at different locations throughout the entire rod bundle were strongly correlated with each other.     

Analysis of PHWR lattice experiments with organic coolant by the computer code club

An efficient computer code club, based on the combination of a small-scale collision probability and a large-scale interface current method, was developed for the analysis of pressurized heavy-water reactor (PHWR) lattice cells. A large number of experiments with different fuel clusters and D₂O and air coolants were analysed using this code. The results were found to be very encouraging. However, when club was used for analysing experiments with organic coolants, the results were found not to be in good agreement with the experiments. This paper discusses the reasons for this and proposes a remedy. Finally, it gives the results of the analysis of these experiments with the modified computer code club.     

Simulation of nucleate boiling under ANSYS-FLUENT code by using RPI model coupling with artificial neural networks

The present study is to develop a new user-defined function using artificial neural networks intent Computational Fluid Dynamics(CFD)simulation for the prediction of water-vapor multiphase flows through fuel assemblies of nuclear reactor.Indeed,the provision of accurate material data especially for water and steam over a wider range of temperatures and pressures is an essential requirement for conducting CFD simulations in nuclear engineering thermal hydraulics.Contrary to the commercial CFD solver ANSYS-CFX,where the industrial standard IAPWS-IF97(International Association for the Properties of Water and Steam-Industrial Formulation 1997)is implemented in the ANSYS-CFX internal material database,the solver ANSYS-FLUENT provides only the possibility to use equation of state(EOS),like ideal gas law,Redlich-Kwong EOS and piecewise polynomial interpolations.For that purpose,new approach is used to implement the thermophysical properties of water and steam for subcooled water in CFD solver ANSYS-FLUENT.The technique is based on artificial neural networks of multi-layer type to accurately predict 10 thermodynamic and transport properties of the density,specific heat,dynamic viscosity,thermal conductivity and speed of sound on saturated liquid and saturated vapor.Temperature is used as single input parameter,the maximum absolute error predicted by the artificial neural networks ANNs,was around 3%.Thus,the numerical investigation under CFD solver ANSYSFLUENT becomes competitive with other CFD codes of which ANSYS-CFX in this area.In fact,the coupling of the Rensselaer Polytechnical Institute(RPI)wall boiling model and the developed Neural-UDF(User Defined Function)was found to be useful in predicting the vapor volume fraction in subcooled boiling flow.     

Cold-neutron tomography of annular flow and functional spacer performance in a model of a boiling water reactor fuel rod bundle

Dryout of the coolant liquid film at the upper part of the fuel pins of a boiling water reactor (BWR) core constitutes the type of heat transfer crisis relevant for the conditions of high void fractions. It is both a safety concern and a limiting factor in the thermal power and thus for the economy of BWRs. We have investigated adiabatic, air-water annular flows in a scaled-up model of two neighboring subchannels as found in BWR fuel assemblies using cold-neutron tomography. The imaging of the double suchannel has been performed at the ICON beamline at the neutron spallation source SINQ at the Paul Scherrer Institute, Switzerland. Cold-neutron tomography is shown here to be an excellent tool for investigating air-water annular flows and the influence of functional spacers of different geometries on such flows. The high-resolution, high-contrast measurements provide the spatial distributions of the coolant liquid film thickness on the fuel pin surfaces as well as on the surfaces of the spacer vanes. The axial variations of the cross-section averaged liquid hold-up and its fraction in the gas core shows the effect of the spacers on the redistribution of the two phases.     

Separate effects study on sodium boiling and dryout under forced-and natural-convection conditions performed with a one-dimensional LOOP code

A comprehensive separate effects study has been performed with the one-dimensional code LOOP-1 on powers and times for sodium boiling initiation and dryout in a closed loop system. Two different kinds of transients were considered: loss-of-flow and loss-of-heat-sink. Loss-of-flow transients were studied under both forced- and natural-convection conditions. Loss-of-heat-sink transients were studied under natural-convection conditions. The results for loss-of-flow transients indicate that the boiling initiation time was reduced by a small amount, and the dryout time was reduced very significantly by increasing either the input power or the inlet temperature, or by decreasing the test section pressure for both forced- and natural-convection conditions. Under forced-convection conditions, a stabilizing effect occured by either increasing the test section valve setting or by decreasing the bypass ratio with a pump head adjusted to provide the same steady state and initial transient flows; thus, longer boiling times could be maintained before dryout occurred. For natural-convection loss-of-flow conditions, increasing the test section valve setting or decreasing the bypass ratio reduced the test section inlet flow, which resulted in boiling inception and dryout occurring more rapidly. A larger flow before the loss of flow transient starts yielded longer boiling initiation and dryout times. Under loss-of-heat-sink conditions, the higher the inlet temperature, the lower the boiling and the dryout powers. The margin between boiling and dryout powers increases with increasing inlet temperature. Results have been verified with experimental data. These results indicate that a margin between several seconds and several hours (depending on the type of transient) is available before core damage may occur in an actual reactor.     

A two-fluid code for the thermohydraulic transient analysis of CICC superconducting magnets

We present here a finite element computer model (Mithrandir) for the transient thermohydraulics of compressible helium in a Cable-In-Conduit Conductor (CICC) with central cooling hole, as presently envisaged for superconducting magnets of the International Thermonuclear Experimental Reactor (ITER). In the model the He in the hole and that in the cable bundle are treated as separate fluids, each characterized by its own flow and thermodynamic properties, coupled by exchanges of mass, momentum and energy. Results for the simulation of a quench both with and without a wall delimiting the central cooling hole are discussed. Time and space convergence of the code are demonstrated numerically.     

CONTAIN-LMR程序中池式钠火事故分析计算模型的验证

CONTAIN-LMR是针对以液态钠为冷却剂的反应堆而开发的安全壳事故一体化分析程序。我国目前的CONTAIN-LMR程序版本为2000年左右从法国引进,还未进行过面向工程设计的系统性地程序开发和验证。本文主要针对CONTAIN-LMR程序中模拟池式钠火事故的分析模型进行详细分析,并采用国际上的池式钠火实验进行验证,实验验证结果表明CONTAIN-LMR程序可以较准确地模拟池式钠火事故造成的钠工艺间内的温度、压力升高及放射性钠气溶胶行为。本文的研究结果初步表明CONTAIN-LMR程序可用于钠冷快堆的钠火事故分析。