Application of Quick Subchannel Analysis Method for Three-Dimensional Pin-by-Pin BWR Core Calculations

Three-dimensional pin-by-pin core analysis is considered to be a candidate for the next-generation BWR core calculation method. In our previous study, the applicability of the transport and burnup calculations for a three-dimensional pin-by-pin BWR core analysis was investigated. However, the thermal-hydraulics calculation has not yet been studied in this framework. In the conventional core analysis code, the bundlewise thermal-hydraulics calculation is adopted. In the actual core analysis, the power distribution inside a fuel assembly is tilted at the region adjacent to a control blade or the core peripheral region. In these regions, the consideration of the subchannel-wise void distribution has an impact on the fission rate distribution. Therefore, an evaluation of the detailed void distribution inside an assembly, i.e., the incorporation of the subchannel wise void distribution, is desirable for the pin-by-pin BWR core analysis. Although several subchannel analysis codes have been developed, these subchannel analysis codes generally require a large computational effort to estimate the subchannel-wise void distribution in a whole BWR core. Therefore, to analyze a whole BWR core within a reasonable computation time, it was necessary to apply a fast subchannel analysis code. In this paper, a quick subchannel analysis code dedicated to pin-by-pin BWR core analysis is newly developed, and the void distribution of the present subchannel analysis code is compared with the prevailing subchannel analysis code NASCA using three-dimensional single-assembly geometries. Since the present subchannel analysis code is used for a coupled neutronics/thermal-hydraulics analysis, the results of the coupling calculation are also compared with those of NASCA. The calculation result indicates that the void distribution difference between NASCA and the present subchannel analysis code is slightly less than 10%. This result indicates that the prediction accuracy of the present subchannel analysis code will be reasonably appropriate for a pin-by-pin BWR core analysis. Furthermore, the results show that the calculation time of the present subchannel analysis code is only 10 min for a hypothetical three-dimensional ABWR quarter-core geometry using a single CPU. This calculation time is sufficient for a pin-by-pin BWR core analysis.     

Multi-dimensional analysis of two-phase flow inside subchannels of nuclear fuel assembly

In subchannel analysis, the conservation equations are solved for each channel in a complex fuel bundle, where the effects of fluid exchange between each subchannel are considered. The fluid exchange is commonly referred to as that caused by cross flow. Void drift is considered to be phenomenon resulting from attaining a hydrodynamic equilibrium state. Its mechanism has not been clarified, and the transport due to void drift is therefore estimated through empirical models in conventional subchannel analyses. Therefore, mechanistic model for the void drift phenomenon is required to apply the subchannel analysis to a variety of fuel bundle geometry. In this study, multi-dimensional analysis using two-fluid model was applied to two-phase flow inside a geometry simulating fuel bundle subchannels, for the purpose of clarifying the void drift mechanism. The comparison between the results of the numerical analysis and the experiment confirmed that the reliability of the numerical method used in this study. In this paper, a mechanistic model based on the Stanton number, which expresses the void diffusion coefficient based on the Lahey's proposal, was proposed.     

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.     

A subchannel analysis of DUPIC fuel bundle for the CANDU reactor

Thermal characteristics of the reference DUPIC fuel has been studied for its feasibility of loading in the CANDU reactor. Half of the DUPIC fuel bundle has been modeled for a subchannel analysis of the ASSERT-IV Code which was developed by AECL. From the calculated mixture enthalpy, equilibrium quality and void fraction distributions in subchannels of the fuel bundle, it is found that the gravity effect may be pronounced in the DUPIC fuel bundle when compared with the standard CANDU fuel bundle. The asymmetric distribution of the coolant in the fuel bundle is known to be undesirable since the minimum critical heat flux ratio can be reduced for a given value of the channel flow rate. On the other hand, the central region of the DUPIC fuel bundle has been found to be cooled more efficiently than that of the standard fuel bundle in the subcooled and the local boiling regimes due to the fuel geometry and the fuel element power changes. Based upon the subchannel modeling used in this study, the location of minimum critical heat flux ratio in the DUPIC fuel bundle turned out to be very similar to that of the standard fuel when the equivalent values of channel power and channel flow rate are used. From the calculated mixture enthalpy distribution at the exit of the fuel channel, it is found that the subchannel-wise mixture enthalpy and void fraction peaks are located in the peripheral region of the DUPIC fuel bundle while those are located in the central region of the standard CANDU fuel bundle. Reduced values of the channel flow rates were used to study the effect of channel flow rate variation. The effect of the channel flow reduction on different thermal-hydraulic parameters have been discussed. This study shows that the subchannel analysis for the horizontal flow is very informative in developing new fuel for the CANDU reactor.     

燃料组件精细化定位格架模型开发及评价

为提高燃料组件子通道内两相局部参数预测的准确性,本文基于分布式阻力方法建立精细化定位格架模型,选用合适的摩擦阻力表达式,对格架上的交混翼进行精细化建模,采用Carlucci湍流交混模型计算湍流交混速率,引入阻塞因子计算由定位格架引起的湍流交混效应,并将建立的精细化定位格架模型植入子通道分析程序（ATHAS）,对压水堆子通道和棒束实验（PSBT）基准题进行计算分析。结果表明,本文开发的精细化定位格架模型能够提高燃料组件子通道内空泡份额和温度分布的预测准确性,为棒束通道流场、焓场计算和临界热流密度（CHF）预测奠定了基础。      

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.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part I: Experiments

Lack of local void fraction data in a rod bundle makes it difficult to validate a numerical method for predicting gas–liquid two-phase flow in the bundle. Distributions of local void fraction and bubble velocity in each subchannel in a 4×4 rod bundle were, therefore, measured using a double-sensor conductivity probe. Liquid velocity in the subchannel was also measured using laser Doppler velocimetry (LDV) to obtain relative velocity between bubbles and the liquid phase. The size and pitch of rods were 10 and 12.5 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. The volume fluxes of gas and liquid phases ranged from 0.06 to 0.15 m/s and from 0.9 to 1.5 m/s, respectively. Experimental results showed that the distributions of void fraction in inner and side subchannels depend not only on lift force acting on bubbles but also on geometrical constraints on bubble dynamics, i.e. the effects of rod walls on bubble shape and rise velocity. The relative velocity between bubbles and the liquid phase in the subchannel forms a non-uniform distribution over the cross-section, and the relative velocity becomes smaller as bubbles approach the wall due to the wall effects.     

Development of one-dimensional two-fluid model with consideration of void fraction covariance effect

Accurate evaluation of gas-liquid two-phase flow behavior within rod bundle geometry is crucial for the safety assessment of the nuclear power plants. In safety assessment codes, two-phase flow in rod bundle geometry has been treated as a one-dimensional flow. In order to obtain the reliable one-dimensional two-fluid model, it is essential to utilize proper area-averaged models for governing equations and constitutive relations. The area-averaged interfacial drag term utilized to evaluate two-phase interfacial drag force is typically given by the drift-flux parameters which consider the velocity profile in two-phase flow fields. However, in a rigorous sense, the covariance due to void fraction profile is ignored in traditional formulations. In this paper, the rigorous formulation of one-dimensional momentum equation was derived by taking consideration of void fraction covariance, and a new set of one-dimensional momentum equation and constitutive relations for interfacial drag was proposed. The newly obtained set of formulations was embedded into TRAC-BF1 code and numerical simulation was performed to compare against the traditional model without covariance. It was found that effect of covariance was almost negligible for steady-state adiabatic conditions, but for high void fraction condition with added perturbation, the traditional model underpredicted the damping ratio at around 8%.     

Prediction of Transient Boiling Transition in BWR Fuel Rod Bundles by Subchannel Analysis Program MENUETT

Transient CHF (critical heat flux) tests of a 4 X 4 rod bundle were analyzed by the subchannel analysis program MENUETT. MENUETT is based on a non-equilibrium, five equation, two-phase flow model and is available both for steady state and transient analyses. Turbulent mixing and void drift effects are taken into account to calculate cross flows in fuel rod bundles. The tendency of calculated subchannel mass fluxes and qualities agreed with experimental data. By using a critical quality correlation obtained from steady state CHF data, the position of the earliest boiling transition could be predicted regardless of non-uniform axial heat flux distributions. This transition occurrence time was predicted within a difference of 0.1～0.3 s from the experimental time. MENUETT applicability was confirmed for transient calculations predicting thermalhydraulic behavior in bundles.     

Void fraction estimation within rod bundles based on three-fluid model and comparison with x-ray CT void data

An interfacial shear stress equation in the dispersed-annular two-phase flow regime has been developed, which is based on a three-fluid model consisting of a liquid film on a rod, vapor and entrained liquid associated with a vapor flow. It is an extension of J.G.M. Andersen's procedure that provides a two-fluid interfacial shear stress equation using the drift flux parameters C₀ and V_gj. This interfacial shear stress equation can take into account a phase and velocity distribution through an equivalence between the drift flux parameters and the interfacial shear stress.

Using the three-fluid subchannel analysis code TEMPO with the three-fluid interfacial shear stress model, the capability of a three-fluid calculation using the drift flux parameters C₀ and V_gj that reproduce a measured void fraction is demonstrated. A comparison was made with advanced X-ray computed tomography (CT) void fraction data within a 4×4 rod bundle in diabatic 1 MPa pressure conditions. The three-fluid velocity field was estimated to be in good agreement with the experimental result of a void fraction.     

Parallel Two-Phase-Flow-Induced Vibrations in Fuel Pin Model

This paper reports the experimental results of vibrations of a fuel pin model —herein meaning the essential form of a fuel pin from the standpoint of vibration— in a parallel air-and-water two-phase flow.

The essential part of the experimental apparatus consisted of a flat elastic strip made of stainless steel, both ends of which were firmly supported in a circular channel conveying the two-phase fluid. Vibrational strain of the fuel pin model, pressure fluctuation of the two-phase flow and two-phase-flow void signals were measured. Statistical measures such as power spectral density, variance and correlation function were calculated.

The authors obtained (1) the relation between variance of vibrational strain and two-phase-flow velocity, (2) the relation between variance of vibrational strain and two-phase-flow pressure fluctuation, (3) frequency characteristics of variance of vibrational strain against the dominant frequency of the two-phase-flow pressure fluctuation, and (4) frequency characteristics of variance of vibrational strain against the dominant frequency of two-phase-flow void signals.

The authors conclude that there exist two kinds of excitation mechanisms in vibrations of a fuel pin model inserted in a parallel air-and-water two-phase flow; namely, (1) parametric excitation, which occurs when the fundamental natural frequency of the fuel pin model is related to the dominant travelling frequency of water slugs in the two-phase flow by the ratio 1/2, 1/1, 3/2 and so on; and (2) vibrational resonance, which occurs when the fundamental frequency coincides with the dominant frequency of the two-phase-flow pressure fluctuation.     

基于丝网传感器的5×5棒束通道空泡分布测量研究

为研究压水反应堆燃料组件棒束通道内的两相分布规律,设计并制造了适用于棒束通道的丝网传感器模块,开展了5×5棒束通道内空气-水泡状流的空泡分布测量实验,分析了棒束通道内空泡份额的分布规律及气泡尺寸对空泡分布的影响。实验结果表明,发生横升力方向反转的小气泡在壁面附近聚集、大尺寸气泡则聚集在子通道中心;常温常压下发生横升力方向反转的临界气泡直径在4~6 mm之间,证明了横升力模型在棒束通道中的适用性。      

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.     

Three-dimensional time-averaged void fraction distribution measurement technique for BWR thermal hydraulic conditions using an X-ray CT system

We have developed a void fraction distribution measurement technique using the three-dimensional (3D) time-averaged X-ray computed tomography (CT) system to understand two-phase flow behavior inside a fuel bundle for boiling water reactor (BWR) thermal hydraulic conditions of 7.2 MPa and 288 °C. As a first step, we measured the 3D void fraction distribution in a vertical square (5?×?5) rod array that simulated a BWR fuel bundle in the air–water test. A comparison of the volume-averaged void fractions evaluated by the developed X-ray CT system with those evaluated by a differential pressure transducer showed satisfactory agreement within a difference of 0.03. Thus, we confirmed that the developed system could be used to get 3D imaging of the vertical square rod array used in the test under the BWR operating pressure condition. In the next step, we did a verification test using the vertical pipe (11.3 mm ID) for BWR thermal hydraulic conditions. A comparison of the cross-sectional-averaged void fractions evaluated by the X-ray CT system with those evaluated by the drift-flux model showed good agreement within a difference of 0.05. We confirmed that the evaluated void fraction distribution forms in the horizontal cross section changed with the quality in response to the flow regime transition.     

Deformation analysis of fuel pins within the wire-wrap assembly of an LMFBR

Deformation of fuel pins within the wire-wrap fuel assembly of a fast breeder reactor is analyzed by two computational codes, the subchannel deformation analysis code SHADOW and the thermal-hydraulic analysis code DIANA. Coupling these codes makes it possible to analyze percisely the mechanical interactions between all fuel pins in an assembly, and the deviation of coolant temperature distribution in deformed flow channels from the nominal distribution.In this paper, particular attention is paid to the effect on fuel pin deformation of the following factors: dimensional changes in the fuel assembly components, displacement of wrapper tube walls and changes in the radial power gradients.     

Analytical study on effects of BWR fuel spacer on droplet deposition

In a boiling water nuclear reactor (BWR), liquid film dryout may occur on a fuel rod surface when the fuel assembly power exceeds the critical power. The spacers supporting fuel rods affect on the thermal-hydraulic performance of the fuel assembly. The spacer is designed to enhance critical power significantly. If spacer effects for two-phase flow could be estimated analytically, the cost and time for the development of the advanced BWR fuel would be certainly decreased. The final goal of this study is to be able to analytically predict the critical power of a new BWR fuel assembly without any thermal-hydraulic tests. Initially, we developed the finite element code to estimate spacer effects on the droplet deposition. Then, using the developed code, the spacer effects were estimated for various spacer geometries in a plane channel and one subchannel of BWR fuel bundle. The estimated results of the spacer effects showed a possibility to analytically predict the critical power of a BWR fuel assembly.     

Channel deformation analysis for fast reactor fuel assemblies undergoing swelling and thermal bowing

Differential thermal expansion and swelling of fuel pins, hexagonal flow ducts and fuel spin spacers, fuel pin bowing between the spacers due to subchannel temperature differentials, and fuel pin bundle bowing due to the cambered hexagonal wrapper tube were analyzed for sodium-cooled fast reactor fuel assemblies.     

Development of a Numerical Analysis Method for Cross-sectional Void Fraction Distribution in Subchannels of Nuclear Fuel Assemblies

Detailed information about the void fraction distribution in fuel assemblies is increasingly important with the development of high burn-up fuels. A numerical method has been developed for the steady cross-sectional void fraction profile in fuel assemblies using a marching method in the axial direction, considering cross-flows due to lift forces, void diffusion and momentum balance. Uniform pressure in a cross section was assumed under the dominant vertical flow and the secondary lateral flow condition in each subchannel. The merit of this simplified method is its high-performance computation using many BFC meshes for expression of complex void fraction and velocity distributions inside the subchannels. The calculated results were compared with the observed void distributions obtained with X-ray computed tomography in the NUPEC tests of full-scale advanced BWR fuels. The comparison showed the capability of this method for predictions of overall void fraction distributions inside the subchannels. This method will provide a good tool for void fraction profile prediction in high burn-up fuels, while future studies for reliable correlations of lift forces are required over a wide range of flow conditions.     

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.     

The effect of a CANDU fuel bundle geometry variation on thermalhydraulic performance

The effect of fuel bundle geometry has been evaluated using the subchannel code ASSERT to enhance the thermalhydraulic performance. Based on the configuration of a standard 37-element fuel bundle, the element diameter in each ring has been changed while those of other rings are kept as the original size. The dryout power of each element in a fuel bundle has been obtained for the modified fuel bundle and compared with that of a standard fuel bundle. The results obtained show that the modification of element diameter largely affects the thermal characteristics of the subchannel on the upper region of a modified element due to the buoyancy drift effect. The explicit effect of the element size on the dryout power of a fuel bundle is investigated by acquiring comprehensive numerical solutions. It is found that the dryout power of a fuel bundle has a tendency to increase as the element size decreases, except for the case where the outer ring is modified. The dependency of the transverse interchange model on the present results has been assessed by examining the dryout power of a bundle for different mixing coefficients and buoyancy drift models.