Analysis of low-heat-flux sodium boiling test in a 37-pin bundle by the two-fluid model computer code SABENA

This paper summarizes the development of a new detailed multi-dimensional multi-field computer code SABENA and its application to an out-of-pile low-heat-flux sodium boiling test in a 37-pin bundle. The semi-implicit numerical method employed in the two-fluid six-equation two-phase flow model has proved in solving a wide spectrum of sodium boiling transients in a rod bundle under low pressure conditions. The code is capable of predicting the spatial incoherency of the boiling, dryout on fuel cladding surfaces and fuel pin heat transfer. Essential to the successful application of such a mechanistic model computer code are validational efforts aimed at the LMFBR accident phenomenology analyses. Through the simulation of the natural circulation boiling conditions, this study provides a consistent analytical interpretation of the experimental data. The important influences of such parameters as the inlet flow restriction and bundle geometry have been examined through interpretations of two-phase flow analysis including considerations of the flow instability induced dryout mechanism.     

Sodium boiling experiments in the THORS facility

Experiments have been performed with 19- and 61-pin test assemblies in the Thermal-Hydraulic Out-of-Reactor Safety (THORS) Facility at the Oak Ridge National Laboratory (ORNL) since 1971. The THORS Facility is a high-temperature sodium system operated for the US Liquid-Metal Fast Breeder Reactor (LMFBR) Safety Program. The facility is used primarily for testing simulated LMFBR fuel subassemblies (pin (bundles). High-performance, electrically heated fuel pin simulators (FPSs) duplicate the heat generating capabilities and the dimensional characteristics of the nuclear fuel pins. A number of test bundles have been built and operated to obtain base thermal-hydraulic data, inlet and heated zone blockage data, and transient boiling data. Five of these bundles have been operated under two-phase conditions. Sodium boiling for periods up to twelve minutes were sustained in one bundle. (The lengths of the periods were limited only by automatic data recording capability). Clad dryout occurred in several tests. Tests were run at widely varying conditions of flow and power density. Testing with nonuniform power distribution across the bundle was also a part of the program.A 19-pin bundle with 12 peripheral guard heaters and a 6-subchannel blockage around the center pin in the heated zone was tested. The test program for this bundle was designed to determine if local boiling in the wake of the blockage propagates radially or axially during quasi-steady-state conditions. Post-test inspection revealed that significant helical distortion of the FPSs occurred in the vicinity of the blockage plate. This distortion probably influenced the boiling behavior. In the more severe tests, boiling initiated at the outlet of the heated zone and propagated radially into the unblocked subchannels after it had progressed upstream to the blockage. The subchannel analysis codes, SABRE and COBRA, accurately predict the extent of the boiling region.Experimental and analytical studies of sodium boiling behavior in unblocked 19- and 61-pin bundles indicate that cooling can be maintained for a significant period of time beyond boiling inception in a flow-power transient. Quasi-steady-state boiling occurred under natural-convection conditions.Investigations of the temperature data indicate that the thermal-hydraulic behavior during boiling transients is determined by two-dimensional effects, and that one-dimensional models cannot accurately predict the important phenomena associated with sodium boiling in test bundles. The subchannel code SABRE-2P (with a simple two-phase multiplier boiling model) and the two-region equilibrium mixture code THORAX (developed at ORNL) accurately predict the two-dimensional behavior between boiling inception and dryout.Extrapolation of the data from the smaller bundle tests to full-size fuel assemblies shows that the time between boiling inception and dryout would be lower for a 217-pin bundle than for a 61-pin bundle for a comparable transient. However, the time delay would still be significant, especially in a heterogeneous reactor core.     

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.     

Modifications to COBRA-TF to model dispersed flow film boiling with two flow,four field Eulerian–Eulerian approach – Part 1

In the case of a postulated loss of coolant accident (LOCA) in a nuclear reactor, an accurate prediction of clad temperature is needed to determine the safety margins. During the reflood phase of the LOCA, when the local void fraction is greater than 80% with the wall temperature above minimum film boiling temperature (T_min), the heat transfer process is dispersed flow film boiling (DFFB). This study has been performed to model DFFB in the reflood phase of a LOCA in a pressurized water reactor (PWR) rod bundle. The COBRA-TF computer code is utilized, since it has a detailed reflood package which takes into account the effect of spacer grids on the local heat transfer. The COBRA-TF code has also been improved to include a four field Eulerian–Eulerian modeling for the two-phase dispersed flow film boiling heat transfer regime. The modifications include adding a small droplet field to COBRA-TF as the fourth field. In addition, the spacer grid models of COBRA-TF have been revised and modified. In the first part of the paper, the results of the code predictions are presented by comparing the experimental data from rod bundle heat transfer (RBHT) experiments with the results of code simulations performed with original and modified code. Measurements and calculations for the heater rod, vapor temperatures and quench front progression have been compared and the results are described in detail. The results of the analysis performed with the modified code indicate the improvement in code predictions for the rod surface temperature, vapor temperature and quench front behavior. The results also indicate the need for improvement in the entrainment and interfacial drag models for the drop fields. The effects of spacer grids on the heat transfer, the models improved and developed for spacer grids and the results of the code calculations with these models are described in the part 2 of the paper.     

Impact of Pseudocolloid Formation on Migration of Nuclides within Fractures

Numerical simulation of boiling of Na-K eutectic alloy (22% Na; 78% K) in a parallel channel system under natural circulation conditions is presented in this work. The calculations pertain to an experimental analysis conducted at the AR-1 facility of IPPE (Russia), analyzing the reactor core coolabilty under severe thermal conditions. The geometrical and operational characteristics reproduce those typical of Russian FBRs. A thermohydraulic code system based on a subchannel analysis code has been developed and adopted for the simulation. Comparisons show that the adopted numerical procedure is capable of reproducing the boiling phenomena inside the parallel bundle test section, correctly predicting the heat transfer conditions prior to and during the boiling. Experimental as well as computational results show the marked influence of the parallel channel interaction, evidenced by the appearance of severe flow oscillations. The results confirm that stable heat removal is provided throughout the entire transient.     

Nonlinear effects in two-phase flow dynamics

Thermally induced two-phase flow oscillations in uniformly heated boiling channels have been analyzed numerically using a one-dimensional model of two-phase flow. Two different approaches to modeling of subcooled boiling have been considered: a mechanistic model and a profile-fit model. The overall model has been numerically implemented as a computer code, DYNOBOSS, which has been validated against a linear stability analysis code and experimental data.The effects of both modeling assumptions and numerical methods of solution have been studied. It has been shown that the calculated transient response of the boiling channel may be very sensitive to the numerical scheme and spatial discretization, especially for operating conditions in the linearly unstable region. For the range of operating parameters studied, phasic slip has shown a significant stabilizing effect on the system, whereas subcooled boiling has indicated smaller influence. Furthermore, it has been shown that the rate of increase of limit cycle amplitude with channel exit quality is higher for low than high inlet subcoolings.     

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.     

Validation of CFD-BWR, a new two-phase computational fluid dynamics model for boiling water reactor analysis

To allow the detailed analysis of the two-phase coolant flow and heat transfer phenomena in a boiling water reactor fuel bundle the CFD-BWR model is being developed for use with the commercial code STAR-CD which provides general two-phase flow modeling capabilities. The paper reviews the key boiling phenomenological models, describes the overall strategy adopted for the combined CFD-BWR and STAR-CD boiling models validation and presents results of a set of experiment analyses focused on the validation of specific models implemented in the code. The location of vapor generation onset, axial temperature profile and axial and radial void distributions were calculated and compared with experimental data. Good agreement between computed and measured results was obtained for a large number of test cases.     

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.     

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.     

Two-phase thermal-hydraulic simulations with COMMIX-2

The COMMIX-2 computer code has been developed for steady/unsteady, three-dimensional thermal-hydraulic analysis of reactor components under normal and off-normal operating conditions. To permit analysis of a wide spectrum of flow conditions, i.e., from homogeneous and equilibrium to nonhomogeneous and nonequilibrium conditions, we have provided two alternative models. One is the two-fluid model, and the other is the homogeneous equilibrium model. The new concept of volume porosity, surface permeability, distributed resistance, and distributed heat source is implemented in the code to permit modeling of a flow domain with stationary solid objects.The present paper briefly describes the unique features of the COMMIX-2 computer code and presents the results of two two-phase numerical simulations with COMMIX-2. One simulation is the transient-boiling experiment in a seven-pin hexagonal fuel assembly. The other is boiling due to blockage in a square fuel assembly. The converged results of numerical simulation and comparison with measurement demonstrate the two phase simulation capability of the COMMIX-2 computer code.     

Study of startup transients and power ramping of natural circulation boiling systems

Numerical models of a natural circulation test facility and its prototype have been developed with RELAP5/MOD3.4 code and verified for their grid independence by nodal sensitivity studies. The model of the test facility has been validated for its steady state as well as transient predictions with the help of experimental observations. The transient predictions and parametric trends obtained by the numerical model of the prototype have been compared with those of the numerical model of the test facility. Thus, the ability of RELAP5 code to predict the transients during startup of a natural circulation boiling water reactor is verified. A powering procedure for the test facility has been conceptualized with the help of its RELAP5 model and demonstrated experimentally. Based on this, a similar powering procedure for the prototype has been proposed and simulated numerically with its RELAP5 model.     

Detection of local boiling in an LMFBR subassembly by temperature fluctuations analysis at the outlet

The aim of the experiments is to detect boiling in a sodium cooled subassembly by measuring fluctuations behind the bundle outlet. The measurements were carried out on an electrically heated 28-rod bundle with a partially blocked section. Fast responding thermocouples were installed downstream of the bundle outlet and downstream of a flow mixing system. Statistical parameters were investigated such as root mean square (RMS) and power spectrum density (PSD). The boiling conditions were generated by reducing the system pressure or flow velocity reduction. The experiments have shown that statistical analysis of temperature fluctuations can produce significant results in the detection of boiling behavior at both the outlet of a subassembly, and behind a flow mixing system.     

Results of acoustic and temperature noise measurements on sodium cooled electrically heated 7 rod bundle

Assembly cooling deficiency in a LMFBR is one of the most important safety problems for reactor design and operation.

Studies on early detection and diagnosis of local accident by means of noise analysis techniques have been initiated at CNEN. Acoustic and temperature noise measurements have been carried out on a 7 rod bundle during slow power transients up to boiling conditions. The test section, simulating the italian PEC reactor fuel element, was mounted on ENA-2 sodium loop located at the CSN Casaccia.

Acoustic noise spectral analysis up to 32 kHz shows the appearance, in presence of boiling, of power increase at certain frequencies. Power spectra and rms values are updated and recorded every 0.3 sec and show large variations going from single phase to boiling.

Temperature noise spectral analysis shows that the power, between 1 and 50 Hz, increases, in presence of boiling, by a factor bigger than 30. It has been tested the sensitivity of other indicators of the temperature fluctuations, like skewness and flatness, to reveal boiling.     

Incipient Sodium Boiling Superheats in Bundle Geometry under Loss-of-Flow Conditions

Transient sodium boiling experiments were conducted using electrically heated pins arranged in 7-, 19- and 37-pin bundles to reproduce loss-of-flow conditions. The average degrees of superheat attained before inception of sodium boiling amounted to 47, 45 and 16°C respectively with the 7-, 19- and 37-pin bundles.

The experimental results indicated that the degree of superheat decreased with increasing number of heating pins in the bundle. This tendency can be explained from the fact that a larger bundle has a radially wider region of sodium saturation temperature at boiling inception comparatively—with the smaller cooling effect exerted by the peripheral subchannels—and consequently a larger number of active nuclei to trigger boiling and terminate the superheating phenomenon. No meaningful correlation was discerned between the degree of superheat and other factors like sodium velocity, rate of sodium temperature rise and intensity of applied heatflux.     

Using Anemometer for Particle Size Measurement of Sodium Mist

A code “ACTFCI” has been developed for analyses of Fuel Coolant Thermal Interaction in a coolant channel. The code can deal with the dynamic behavior of coolant in r-z geometry, but does not take into account the dynamics of fuel particle two-dimensional movement, the fuel being considered only as heat source for the coolant. The ICED-ALE method was used for the numerical analyses of the three conservation equations and two equations of state for single and two-phase sodium. A sample calculation is given concerning the period up to initiation of sodium boiling, for a geometry representing a wrapper tube of reduced size. Despite this difference of the model from actual size, the calculated results suffice for demonstrating the utility of this method in obtaining stable solutions on single-phase pressure wave propagation in both r and z directions, and on sodium boiling initiation triggered by the rarefaction wave returning to the interaction region from channel extremity.     

Molecular Approach to Sodium Vapour Condensation,Rewetting and Vaporization in LMFBR Bundle under Hypothetical Accident Conditions

In the frame of safety analysis of Liquid Metal Fast Breeder Reactors (LMFBRs) under hypothetical Unprotected Loss-of-Flow (ULOF) conditions, two phase flow of sodium is simulated in a reactor core. Traditional approaches used in safety analysis codes to simulate sodium vapour condensation and vaporization rely upon application of macroscopic semi-empirical correlations for heat transfer and vapour condensation or evaporation rates. As an alternative to this macroscopic approach, we developed a microscopic methodology based upon the application of the basic laws of the kinetic theory for the determination of the evaporation and condensation rates of vapour in a reactor bundle. This microscopic approach is based upon a Monte Carlo simulation of the molecular trajectories, collision rates between vapour molecules and of the molecules with the surfaces of the claddings of the pins of a reactor bundle. The pins surfaces are treated in the Monte Carlo simulation as diffusely reflecting surfaces. Scattering of sodium particles is simulated with the “hard sphere” collision model. The “step splitting” technique is applied, which consists in separating the collisions dynamic calculation from collisionsless paths of the molecules. Vapour particles are assumed to condense on the surfaces of the pins when, after diffuse reflection, their velocity would be less than one third of the most probable velocity corresponding to the wall temperature. Rewetting of dried out regions of the cladding surfaces is simulated with a dynamic film model which computes the velocity distribution of the liquid across the film thickness and then the mean liquid film velocity. Evaporation of sodium molecules from the film yields a source of molecules which re-enter into the Monte Carlo calculation of the molecular dynamic approach. The coupling of the micro- and macroscopic models has been applied to the numerical simulation of an out-of pile sodium boiling experiment run at the Nuclear Research Center of Karlsruhe, Germany.     

Numerical simulation and artificial neural network modeling of natural circulation boiling water reactor

Numerical simulation of natural circulation boiling water reactor is important in order to study its performance for different designs and under various off-design conditions. Numerical simulations can be performed by using thermal-hydraulic codes. Very fast numerical simulations, useful for extensive parametric studies and for solving design optimization problems, can be achieved by using an artificial neural network (ANN) model of the system. In the present work, numerical simulations of natural circulation boiling water reactor have been performed with RELAP5 code for different values of design parameters and operational conditions. Parametric trends observed have been discussed. The data obtained from these simulations have been used to train artificial neural networks, which in turn have been used for further parametric studies and design optimization. The ANN models showed error within ±5% for all the simulated data. Two most popular methods, multilayer perceptron (MLP) and radial basis function (RBF) networks, have been used for the training of ANN model. Sequential quadratic programming (SQP) has been used for optimization.