Systematic and exact scaling analysis of the single-phase natural circulation flow: The hydraulic similarity

For the study of the hydraulic similarity in a single-phase natural circulation loop, the integral momentum equation is non-dimensionalized with respect to the initial flow kinematic energy of reference section, without intuitively specifying any reference parameters. By this mean, a unique hydraulic time scale, characterizing the system hydraulic response, is identified along with two dimensionless physical numbers: the dimensionless flow resistance number and the dimensionless gravitational force number. From the integral momentum equation, the mass flow rate at steady state is also obtained. The identified dimensionless parameters are then applied to derive a set of scaling criteria for the design of a full-pressure reduced-size similar model for a PWR (Pressurized Water Reactor). For exact hydraulic similarity, it was found for the first time that the cross sectional area scaling ratio should be related to the axial length scaling ratio. In addition, it is also found out that the relative cross-sectional area ratio should be preserved in order to preserve the flow resistances. Moreover, the scaling ratio for the number of the U-tubes was found to be unity if exact hydraulic similarity is pursued for the whole system. Three sets of scaling criteria for the design of a full-pressure model for a PWR are summarized in a table for different application. The accuracy and applicability of this proposed scaling method is demonstrated by proposing a simple loop and a PWR-like system, by scaling down the systems to get two corresponding models with this proposed scaling methodology, and by comparing the model results with their corresponding prototype results. Furthermore, the method for the evaluation of both system-level and local hydraulic scaling distortions are addressed.     

Steady-state performances and scaling analyses for an open flashing-driven natural circulation system

Simulating investigations are carried out to study the steady-state performances, the pressure resistance distributions and the scaling methods of the single-phase and flashing-induced two-phase flow in the open natural circulation system, which is designed for the passive containment cooling system. The results show that the steady-state mass flow rate changes with the heat transfer regularly both in the single-phase and flashing-induced two-phase flow under a certain inlet subcooling. From the sensitivity analysis, it can be found that the riser height only has impact on the single-phase flow but has little influence on the flashing-driven two-phase flow. Both increasing the diameters of the riser and downcomer can enhance the flow and heat transfer in sing-phase and two-phase flow when keeping the structure of the heat exchanger unchanged, but the influence degree for each flow type is different. The flow resistance distributions of the loops under different flow modes have been studied to provide the foundation for improving the heat transfer capacity by choosing the structural parameters reasonably. The pressure resistance distribution of the steady single-phase flow only relates to the geometrical, but the pressure resistance distribution of the two-phase flow relates both to the pipe diameters and to the external conditions. The acceleration pressure resistance in the riser section is the main resistance under the higher-quality two-phase conditions. Therefore, the influence of the riser diameter on the flashing-induced two-phase flow is far greater than that of downcomer diameter and the most effective method to improve the two-phase flow and heat transfer is to increase the diameter of the riser. Finally, the scaling analysis is performed for the penetration and economy considerations after selecting the optimal dimensions. The scaling of the cold and hot sections is considered separately to insure the driven force of the system unchanged, and different scaling criterions are given for the single-phase and flashing-induced two-phase flow according to the analyses of the pressure resistance distributions. The results show that the scaling criterion of the two-phase flow can deal with the scaling problem accurately both in the single-phase and two-phase flow. However, the scaling criterion of the single-phase flow only can solve the single-phase scaling problem, but it will overestimate the operating results in the scaling model.     

一维自然循环比例分析的结果与讨论

根据一维自然循环比例分析理论模型推导的试验装置与实际电站热工水力特性的相似准则,对整体性能试验装置主要参数的确定方法进行了深入讨论。结果表明:采用小尺度、等压力、同工质的实验装置模拟实际系统自然循环现象更为准确实际,单相和两相自然循环比例准则可同时满足,不存在复杂比例变化带来的失真,不利因素是试验成本偏高。同工质非等物性(不等压)模拟能够降低试验成本,但比例参数不能满足从单相自然循环到两相自然循环的平滑过渡。如保持功率连续,其速度比和特征时间比会有所差异。     

一维自然循环比例分析的理论模型

整体性能试验研究是验证先进非能动压水堆核电站堆芯冷却系统设计有效性的核心技术,一回路系统两相自然循环热工水力特性比例分析是确定整体性能试验装置尺度的主要理论依据。以一维漂移流模型为基础,对整个一回路两相自然循环系统控制方程积分,并求得稳态解,由此获得了系统的流动条件。应用初始流动条件与边界条件,对两相自然循环系统控制方程直接无量纲化,最终得到了整体性能试验装置与实际非能动电站热工水力特性的相似准则。     

SENHOR-IV: A computer code for small pipe-break analysis of pressure-tube type reactors

A computer program SENHOR-IV was developed which describes blowdown phenomena associated with a small pipe-break accident in pressure-tube type reactors. Thermal-hydraulic transients of single-phase and two-phase flow in a primary cooling system, which is composed of the pressure tubes, a steam drum, downcomers, a lower header and pipings connecting these components, were calculated from the conservation equations of mass, momentum and energy by assuming pressure propagation and flow rate distribution to be quasi-steady and by applying the method of characteristics to enthalpy transport. The void propagation velocity in two-phase flow was given from Smith's equation for void-quality relationship to the program. Calculation of a flow transient, which has an exact solution, with use of this program showed small deviations from the exact solution. Predicted transients of pressure and water level in the steam drum indicated a good agreement with those observed in a full scale test facility at O-arai Engineering Center.     

Scale modelling in LMFBR safety

This paper reviews scale modelling techniques used in studying the structural response of LMFBR vessels to HCDA loads. The geometric, material, and dynamic similarity parameters are presented and identified using the methods of dimensional analysis. Complete similarity of the structural response requires that each similarity parameter be the same in the model as in the prototype. The paper then focuses on the methods, limitations, and problems of duplicating these parameters in scale models and mentions an experimental technique for verifying the scaling.Geometric similarity requires that all linear dimensions of the prototype be reduced in proportion to the ratio of a characteristic dimension of the model to that of the prototype. The overall size of the model depends on the structural detail required, the size of instrumentation, and the costs of machining and assemblying the model.Material similarity requires that the ratio of the density, bulk modulus, and constitutive relations for the structure and fluid be the same in the model as in the prototype. A practical choice of a material for the model is one with the same density and stress-strain relationship as the operating temperature. Ni-200 and water are good simulant materials for the 304 SS vessel and the liquid sodium coolant, respectively. Scaling of the strain rate sensitivity and fracture toughness of materials is very difficult, but may not be required if these effects do not influence the structural response of the reactor components.Dynamic similarity requires that the characteristic pressure of a simulant loading source equal that of the prototype HCDA for geometrically similar volume changes. The energy source is calibrated in the geometry and environment in which it will be used to assure that heat transfer between high temperature loading sources and the coolant simulant and that non-equilibrium effects in two-phase sources are accounted for. For the geometry and flow conditions of interest, the viscous and gravity forces are usually negligible compared with pressure forces and, therefore, are not scaled.     

Determination of a test section parameters for IRIS nuclear reactor pressurizer

An integral, modular and medium size nuclear reactor, known as IRIS, is being developed by Westinghouse and by research centers. IRIS is characterized by having most of its components inside the pressure vessel, eliminating the probability of accidents. Due to its integral configuration, there is no spray system for boron homogenization, which may cause power transients. Thus, boron mixing must be investigated. The aim of this paper is to establish the conditions under which a test section has to be built for boron dispersion analysis inside IRIS reactor pressurizer. Through Fractional Scaling Analysis, which is a new methodology of similarity, the main parameters for a test section are obtained. By combining Fractional Scaling Analysis with local scaling for the densimetric Froude number and a previously established volumetric scale factor, the values of recirculation orifices, inlet water temperature, time scale factor and recirculation flow for the test section (model) are determined so that boron distribution is well represented in IRIS reactor pressurizer (prototype). Analytical solutions were used to validate the adopted methodology and when the results simulated in the model are compared to those that characterize the prototype, the agreement for both systems is absolute. The thermal power also influences boron distribution inside the test section. This power is determined by condensation laws in the vapor region and by suitable correlations for free convection. The fractions for rising inlet recirculation water enthalpy and vapor formation are also considered.     

Determination of a test section parameters for IRIS nuclear reactor pressurizer

An integral, modular and medium size nuclear reactor, known as IRIS, is being developed by Westinghouse and by research centers. IRIS is characterized by having most of its components inside the pressure vessel, eliminating the probability of accidents. Due to its integral configuration, there is no spray system for boron homogenization, which may cause power transients. Thus, boron mixing must be investigated. The aim of this paper is to establish the conditions under which a test section has to be built for boron dispersion analysis inside IRIS reactor pressurizer. Through Fractional Scaling Analysis, which is a new methodology of similarity, the main parameters for a test section are obtained. By combining Fractional Scaling Analysis with local scaling for the densimetric Froude number and a previously established volumetric scale factor, the values of recirculation orifices, inlet water temperature, time scale factor and recirculation flow for the test section (model) are determined so that boron distribution is well represented in IRIS reactor pressurizer (prototype). Analytical solutions were used to validate the adopted methodology and when the results simulated in the model are compared to those that characterize the prototype, the agreement for both systems is absolute. The thermal power also influences boron distribution inside the test section. This power is determined by condensation laws in the vapor region and by suitable correlations for free convection. The fractions for rising inlet recirculation water enthalpy and vapor formation are also considered.     

A new method to derive one set of scaling criteria for reactor natural circulation at single and two-phase conditions

Natural circulation is one of the most important thermal-hydraulic phenomena that makes the fluid flow along a closed loop without any external driving force. With this merit, it is adopted by the passive heat removal system to bring the residual heat out of the core at accidents, and by the primary system of some new conceptual reactors instead of pumps to drive the coolant in the loop at operation. To investigate the reactor natural circulation and verify system thermal-hydraulic codes, it is a way to construct an integrated effect test facility and perform experiments on it with the scaling criteria. With one-dimensional assumption, the natural circulation system was simplified as the heat source, heat sink and pipes, and described by two groups of equations independently for the single-phase and two-phase flow conditions. Based on these equations, a set of non-dimensional equations were derived and the criteria were obtained both applicable for single-phase and two-phase natural circulation. According to these criteria, the practical application was analyzed and discussed. In the paper, the property similarity was strongly suggested in most cases. Though equal height simulation was widely used in the past, the reduced height simulation is a good way to reproduce three-dimensional (3D) phenomena that are of concern in the investigation. The CHF simulation is not suggested. The mass of metal and its distribution is of concern instead of heat transfer at transient simulation.     

Scaling methodology for a reduced-height reduced-pressure integral test facility to investigate direct vessel injection line break SBLOCA

A scaling methodology for a small-scale integral test facility was investigated in order to analyze thermal-hydraulic phenomena during a DVI (direct vessel injection) line SBLOCA (small break loss-of-coolant accident) in an APR1400 (advanced power reactor 1400 MWe) pressurized water reactor. The test facility SNUF (Seoul National University Facility) was utilized as a reduced-height and reduced-pressure integral test loop. To determine suitable test conditions for simulating the prototype in the SNUF experiment, the energy scaling methodology was propose to scale the coolant mass inventory and the thermal power for a reduced-pressure condition. The energy scaling methodology was validated with a system code (MARS) analysis for an ideally scaled-down SNUF model and that predicted a reasonable transient of pressure and coolant inventory when compared to the prototype model. For the actually constructed SNUF, the effect of scaling distortions in the test facility's thermal power and the loop geometry was analytically investigated. To overcome the limitation of the thermal power supply in the facility, the convective heat transfer between primary and secondary systems at the steam generator U-tubes was excluded and a modified power curve was applied for simulating the core decay heat. From the code analysis results for the actual SNUF model, the application of the modified power curve did not affect the major events occurring during the transient condition. The results revealed that the scaling distortion in the actual SNUF geometry also did not strongly disturb significant thermal-hydraulic phenomena such as the downcomer seal clearing. Thus, with an adoption of the energy scaling methodology, the thermal-hydraulic phenomena observed in the SNUF experiment can be properly utilized in a safety analysis for a DVI line break SBLOCA in the APR1400.     

Author index to volume 79

Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.     

Scaling laws for thermal-hydraulic system under single phase and two-phase natural circulation

Scaling criteria for a natural circulation loop under single phase and two-phase flow conditions have been derived. For a single phase case the continuity, integral momentum, and energy equations in one-dimensional area average forms have been used. From this, the geometrical similarity groups, friction number, Richardson number, characteristic time constant ratio, Biot number, and heat source number are obtained. The Biot number involves the heat transfer coefficient which may cause some difficulties in simulating the turbulent flow regime. For a two-phase flow case, the similarity groups obtained from a perturbation analysis based on the one-dimensional drift-flux model have been used. The physical significance of the phase change number, subcooling number, drift-flux number, friction number are discussed and conditions imposed by these groups are evaluated. In the two-phase flow case, the critical heat flux is one of the most important transients which should be simulated in a scale model. The above results are applied to the LOFT facility in case of a natural circulation simulation. Some preliminary conclusions on the feasibility of the facility have been obtained.     

Analysis of startup oscillations in natural circulation boiling systems

The aim of the present work is to get an insight of the phenomena behind the low-pressure low-power transients that occur during startup of a natural circulation boiling system. A RELAP5 model developed for a test facility and its prototype is used to record additional system parameters that were not included in the data obtained from experiments. The flow oscillations observed during experimental and numerical studies are analyzed and classified. It is inferred that the low amplitude oscillations are not condensation induced geysering instabilities, but a density wave instability supported by flashing. The similarity between the nature of startup transients observed in the test facility and the prototype is also examined. The effect of flashing is more pronounced in the prototype due to the strong variation of saturation temperature as the length scale is 4 times that of the model. The time series data obtained from experimental observations and numerical simulations are analyzed to identify the structural nature of flow oscillations. The power spectral density estimated using fast Fourier transform (FFT) algorithm illustrates the chaotic nature of the signals. The nonlinear time series analysis (TISEAN) package has been used for the estimation of Lyapunov exponent and the Poincaré section. The Poincaré section and the Lyapunov exponent confirm the chaotic nature of the flow oscillations.     

Scaling single-state variable catastrophe functions: an application to two-phase natural circulation

In this paper I present transformation laws to scale physical processes governed by polynomial equations. Of particular importance is the class of polynomials which describe catastrophe functions. Many important, stability-related, thermal hydraulic phenomena are described by these catastrophe functions, including flooding, two-phase natural circulation, and critical heat flux. Catastrophe functions can be used to define the boundaries of stable system behavior. If a process evolves such that one of these boundaries are crossed, it will undergo a discontinuity which radically alters its evolution (i.e. morphogenesis). By scaling these catastrophe functions, processes exhibiting discontinuous behavior can be studied in scaled test models rather than experimenting with a full-scale, and typically very expensive, prototype. To illustrate their usefulness, the catastrophe function transformation laws are applied to the practical problem of scaling two-phase fluid natural circulation. In addition, the catastrophe manifold for two-phase fluid natural circulation is developed and evaluated to obtain a criterion for the onset of flow instability.     

Validation of the sub-channel code F-COBRA-TF: Part I. Recalculation of single-phase and two-phase pressure loss measurements

The present paper deals with recalculations of single-phase and two-phase pressure loss measurements with the advanced two-phase, three-field sub-channel code F-COBRA-TF. Thereby, experimental data of both the OECD/NRC BFBT benchmark and in-house tests in AREVA NP's KATHY loop are used. The main goal of this paper is not to focus on a special new model or correlation but to give an overview how a complete pressure loss calculation for practical purposes can be carried out being based on a simplified and straightforward method to estimate sub-channel spacer pressure loss coefficients on the one hand and an advanced sub-channel code on the other hand.The pressure loss coefficients are calculated analytically and calibrated at available measurements of total single-phase bundle pressure loss. Thus, they are not adapted to any two-phase measurement and also do not depend on the sub-channel code they are used in.The results of the recalculations of the measurements especially demonstrate the capability of a three-field code to predict both single-phase and two-phase pressure losses with high accuracy, whereas the code is not based on conventional pressure loss correlations using two-phase multipliers but rather on interfacial friction correlations for each flow regime. Thereby, the F-COBRA-TF standard models - which are usually applied for all sorts of calculations (pressure loss, void distribution, lateral mixing, critical heat flux, etc.) - were used. It was not necessary to do special code tuning with respect to certain experiments.     

Evaluation of analytically scaled models of a pressurized water reactor using the RELAP5/MOD3 computer code

This paper performs analytical evaluations for the potential distortions caused by the scaled models using RELAP5/MOD3 computer codes. By use of scaling analysis, two scaled models with the same volumetric ratio are constructed for the Korean next generation reactor (KNGR), which is an advanced light water reactor. The scaling methodology adopted in this paper preserves the two-phase natural circulation similarities between prototype and scaled models. One scaled model is at full height with reduced flow area. The other model is at reduced height with reduced flow area. By using appropriate scale factors the RELAP5/MOD3 input models are developed. Then, the transient responses of the two ideal scaled models are simulated for small break loss of coolant accidents (SBLOCAs) by using the RELAP5/MOD3 computer code. The transient responses of the two scaled models are compared with those of the prototype. The results indicate that qualitative and quantitative similarities are well preserved for both models during SBLOCA with different break sizes.     

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.     

Modeling of thermal hydraulic instabilities in single heated channel loop during startup transients

A thermal hydraulics computer code was developed to simulate the geysering instability in a natural circulation system starting from subcooled conditions and to assess the impact of the system pressure and channel inlet subcooling on the inception of instability. The formulation of thermal hydraulics is inherently general and accounts for both single-phase liquid flow and nonhomogeneous, nonequilibrium two-phase flow. The computer code is based on momentum integral method where the current practice of basing fluid properties on the system averaged pressure has been relaxed and the local properties are based on local pressures estimated using the shape of steady-state pressure distribution, thereby, improving the predictions while preserving the computation speed, one of the important strength of the integral methods. This is an important modeling feature since the local vapor generation rate depends on local saturation temperature The methodology has been validated with the experiments conducted to investigate the instabilities in a low pressure natural circulation loop at low powers and high inlet subcoolings. The numerical simulations predicted periodic channel flow reversal, which is one of the feature of condensation-induced geysering. Basing local properties on local pressures instead of system average pressure led to decrease in the discrepancy in the prediction of the positive side amplitude from 40% to 6% and in the frequency from −15% to 5%. In addition, it was observed that the start-up instability can be avoided by increasing system pressure or by decreasing channel inlet subcooling. This study showed that the integral method coupled with local pressure variation for the vapor generation model is suitable to predict startup or geysering transients.     

Assessment of the CATHARE 1D pump model

The development of an advanced model to determine the dynamic pump performance under two-phase flow conditions is presented. This model is included in CATHARE 2, version V1.3. It is based on the two-fluid six-equation CATHARE model which describes the mechanical and thermal non-equilibria.In a previous review (P. Van den Hove and G. Geffraye, The CATHARE code— one-dimension pump model, Fifth Int. Topical Meet. on Nuclear Reactor Thermal Hydraulics (NURETH-5), Salt Lake City, USA, September, 1992), various calculations were presented concerning Eva single-phase and two-phase steam–water test results in the first three quadrants. Here, the range of assessment of the first quadrant is enlarged with Eva air–water tests and Bethsy pump steam–water tests. Both pumps are mixed flow pumps, the Bethsy one being radial at the impeller outlet.Some improvements suggested in the above cited paper are tested against all single-phase liquid, single-phase vapor, two-phase steam–water, and two-phase air–water data in the first quadrant. They concern a new deviation model and head losses model, and the model of mechanical interaction between phases.     

Effect of depressurization on reactor vessel inventory in the absence of ECCS injection

A series of tests were performed to evaluate inventory depletion as a reactor vessel undergoes depressurization in the absence of any emergency core coolant system injection (ECCS). These tests were carried out in a scaled representation of a reactor vessel which was initially filled with saturated water up to the elevation of the hot legs. Depressurization valves installed on take-off lines from the hot legs were opened and level swell ensued in the reactor vessel initiating a two-phase blowdown. This was followed by subsequent single-phase discharge transient which in some cases led to core uncovery. A combined model encompassing the two-phase and single-phase discharge portions of the transient is proposed. The inventory-versus-pressure traces obtained from the model compare well with the experimental results. These traces are discussed as bounding trajectories for a large class of small break loss of coolant accident (LOCA) transients which otherwise must be considered individually.