Semi-implicit modeling of condensation in the presence of non-condensables in the relap5/mod3 computer code

A methodology is developed for modeling condensation in the presence of non-condensables based on the stagnant film (couette flow) model. The methodology, which is fully compatible with the mathematical representation and numerical solution scheme for the two-fluid conservation equations in the relap5/mod3 computer code, rigorously treats the coupling between the heat and mass transfer processes and allows for implicit treatment of the interphase mass and momentum exchange terms without iterations and without adversely affecting the stability of the code's solution scheme. The relap5/mod3 computer code is accordingly modified and is successfully validated against published 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.     

Validation of the MCNP5 computer code

The MCNP5 computer code with the ENDF/B6 neutron data library is validated for problems which are of current importance at the Russian Federal Nuclear Center — All-Russia Research Institute of Technical Physics. Comparative calculations performed with the MCNP5 code and its preceding version MCNP4c are identical within the limits of computational error. This confirms that the MCNP5 code can be used instead of the previous versions. __________ Translated from Atomnaya énergiya, Vol. 101, No. 2, pp. 112–116, August, 2006.     

Numerical computation of thermally controlled steam bubble condensation using Moving Particle Semi-implicit (MPS) method

In the present study, single steam bubble condensation behaviors in subcooled water have been simulated using Moving Particle Semi-implicit (MPS) method. The liquid phase was modeled using moving particles and the two phase interface was set to be a movable boundary which can be tracked by the topological position of the interfacial particles. The interfacial heat transfer was determined according to the heat conduction through the interfacial liquid layer and the coupling between momentum and energy was specially treated. Computational results showed that the bubble experiences various deformations at lower degrees of liquid subcooling while it remains nearly spherical at higher degrees of liquid subcooling. The bubble lifetime is nearly proportional to bubble size and is prolonged at higher system pressures. Bubble lifetime obtained from the MPS method agrees well with the experiments of 10 and 11, however it is lower than the predictions of Sudhoff et al. (1982). The underestimation is caused by severe bubble deformation at lower degrees of subcooling. The present study exhibits some fundamental characteristics of single steam bubble condensation and is expected to be instructive for further applications of the MPS method to evaluate more complicated bubble dynamics problems.     

Development of multicomponent vaporization/condensation model for a reactor safety analysis code SIMMER-III: Theoretical modeling and basic verification

It is believed that the numerical simulation of thermal-hydraulic phenomena of multiphase, multicomponent flows in a reactor core is essential to investigate core disruptive accidents (CDAs) of liquid-metal fast reactors. A new multicomponent vaporization/condensation (V/C) model was developed to provide a generalized model for a fast reactor safety analysis code SIMMER-III, which analyzes relatively short-time-scale phenomena relevant to accident sequences of CDAs. The model characterizes the V/C process associated with phase transition through heat-transfer and mass-diffusion limited models to follow the time evolution of the reactor core under CDA conditions. The heat-transfer limited model describes the nonequilibrium phase-transition processes occurring at interfaces, while the mass-diffusion limited model is employed to represent effects of noncondensable gases and multicomponent mixture on V/C processes. Verification of the model and method employed in the multicomponent V/C model of SIMMER-III was performed successfully by analyzing a series of multicomponent phase-transition experiments.     

Numerical treatment of the cladding mechanics in the fuel rod computer code IAMBUS

IAMBUS (INTERATOM Model for Burn-Up Studies on Fuel Rods) is a digital computer code for the thermal and mechanical design, in-pile performance prediction and post-irradiation analysis of fuel rods. The mechanical analysis of the cladding is approximated by a state of generalized plane strain. The analysis includes routines for plasticity, creep and swelling due to void nucleation and growth. The numerical integration of these equations is described in detail and the accuracy of the results is discussed.     

The development of a transient version of the HOTROD computer code

The full length fuel rod steady state performance code HOTROD has been developed to predict fuel performance during a transient. This paper explains the theory used to calculate the transient fuel temperatures using the Crank-Nicolson method. Transient HOTROD predictions of SGHWR and PWR axial clad temperatures during a loss-of-coolant accident are given and are compared with those predicted by other codes. The code is being further developed to model Zircaloy clad ballooning and the creep equations coupled to the heat transfer equation derived in this paper.     

Simulation of basic gas mixing tests with condensation in the PANDA facility using the GOTHIC code

The paper reports the results of the assessment of the GOTHIC code using the data of four basic tests with condensation performed in the PANDA large-scale facility. Three of these experiments featured vertical injection, and in one the transient response due to a high-momentum horizontal injection (jet) was investigated. The injected fluid was either saturated steam or a superheated mixture of steam and helium, and the fluid initially present in the vessels was pure air. The simulations were carried out using a detailed three-dimensional representation of the vessels. In general, the results of the simulations, which used a relatively coarse mesh, were in good agreement with the data. Limitations in modelling local phenomena controlled by complex flow patterns (e.g. heat transfer in the region of an impinging jet) and the need for refined meshes to reproduce certain aspects of the transients (e.g. erosion of the interface between layers of different gas composition) were also identified. Finally, the analyses indicated that in two tests the role played by re-vaporisation of the condensate film was unexpectedly large, and this effect should be more carefully considered in the containment analyses and future model developments.     

A three-dimensional finite-element computer code for the analysis of complex structures

General computational procedures are described with emphasis on FORTRAN based ‘dynamic’ storage allocation and adaptability of specialized input routines for the analysis of complex structures, including pump casings and pipe tees and elbows. A brief discussion is given on the algorithms used in this code for the formation and solution of banded linear equatons. The basic finite element building blocks, including isoparametric tetrahedra, pentahedra, and hexahedra are described. The results of a complex structural analysis, along with sample computer output, is presented.     

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.     

蒙特卡罗程序TRIPOLI自动建模方法研究

TRIPOLI是法国原子能署(CEA)开发的三维蒙特卡罗粒子输运计算程序,在反应堆物理分析、辐射防护设计、核安全评估等领域得到广泛应用。但是手工描述其输入文件耗时,容易出错,质量得不到保证。本文研究了TRIPOLI自动建模方法,实现了CAD工程模型与TRIPOLI模型的相互转换。通过对基准例题的计算分析,证明了其转换结果正确、可靠。     

Theoretical modeling of condensation of steam outside different vertical geometries (tube, flat plates) in the presence of noncondensable gases like air and helium

Condensation of steam coming out from the coolant pipe during a loss of coolant accident (LOCA) plays a key role in removing heat from the primary containment of the advanced nuclear reactor (ANR). The presence of large mass fractions of air (W_air = 0.25-0.9) and a small mass fraction of helium (W_He = 0.017-0.083) reduces the overall heat transfer coefficient (HTC) substantially. The present work emphasizes on the issue that modeling the diffusion of water-vapor through the gas-liquid interface is the key to give good predictions in HTC. In this, condensation conductivity and effective diffusivity plays a key role. Therefore, modifications have been made in the derivation for calculation of condensation conductivity in the case of steam-air mixture and effective diffusivity (in the case of multicomponent mixture). The model validation has been done with the experimental data of Dehbi et al. [Dehbi, A.A., Golay, M.W., Kazimi, M.S., 1991. National Conference of Heat Transfer AIChE Symposium Series, pp. 19-28] and Anderson et al. [Anderson, M.H., Herranz, L.E., Corradini, M.L., 1998. Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. 185, 153-172] and other analytical models available in the literature [Herranz, L.E., Anderson, M.H., Corradini, M.H., 1998a. The effect of light gases in noncondensable mixtures on condensation heat transfer. Nucl. Eng. Des. 183, 133-150; Herranz, L.E., Anderson, M.H., Corradini, M.L., 1998b. A diffusion layer model for steam condensation within the AP600 containment. Nucl. Eng. Des. 185, 153-172; Peterson, P.F., Schrock, Y.E., Kageyama, T., 1993. Diffusion layer theory for turbulent vapor condensation with noncondensable gases. J. Heat Transf., 115; Dehbi, A.A., Golay, M.W., Kazimi, M.S., 1991. National Conference of Heat Transfer AIChE Symposium Series, pp. 19-28]. Since the validations of the results were found satisfactory, the datasets [Dehbi, A.A., Golay, M.W., Kazimi, M.S., 1991. National Conference of Heat Transfer AIChE Symposium Series, pp. 19-28; Anderson, M.H., Herranz, L.E., Corradini, M.L., 1998. Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. 185, 153-172] have been compared with a wide range of subcooling and the operating pressures. An extensive comparison has been reported and the results predicted by the present model were found to be satisfactory.     

Diffusion layer modeling for condensation in vertical tubes with noncondensable gases

Noncondensable gases significantly modify the mechanism of condensation for cocurrent downward flow in vertical tubes. Two-dimensional experimental measurements presented here show similarity between gas concentration distributions and the temperature distributions encountered in laminar and turbulent heat transfer. Thus the analogy between heat and mass transfer, coupled with a reasonable condensate film model, can provide predictions of the local condensation rate. This work presents a simple 9-step iterative calculation procedure for calculating the local heat flux. The empirical model, based on a modified Dittus-Boelter formulation and utilizing an effective condensation thermal conductivity, converges with 2 to 10 iterations at each axial location. Experimental results from several investigators are compared with the predictions of the model, with good agreement.     

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.     

Verification study of the FORE-2M nuclear/thermal-hydraulic analysis computer code

The verification of the LMFBR core transient performance code, FORE-2M, was performed in two steps. Different components of the computation (individual models) were verified by comparing with analytical solutions and with results obtained from other conventionally accepted computer codes (e.g., TRUMP, LIFE, etc.). For verification of the integral computation method of the code, experimental data in TREAT, SEFOR and natural circulation experiments in EBR-II were compared with the code calculations. Good agreement was obtained for both of these steps. Confirmation of the code verification for undercooling transients is provided by comparisons with the recent FFTF natural circulation experiments.     

Analytical thermal hydraulic model for oscillatory condensation of steam in presence of air

An analytical thermal hydraulic model has been developed from fundamental conservation laws, for the process of oscillatory condensation of steam in a pool of water, in presence of non-condensable gas (air). The oscillatory condensation phenomena addressed here is steam chugging, with an emphasis laid on studying the effect of small amount of air present in steam, on the phenomena. The objective of developing the model is to present an approximation of the real phenomena and to obtain an analytical solution. At the outset, a parametric study was conducted by using the developed model to capture and identify the salient features of steam chugging and compare the wave shapes obtained with those available in open literature. Subsequently, the effect of presence of air in steam was studied in detail using the non-condensable gas model. An attempt has been made to show numerically that the presence of a small amount of air in steam would effectively stabilize condensation and prevent inception of chugging. Typical results are presented in this paper to bring out the difference in oscillatory behavior due to presence and absence of non-condensable gas.     

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.     

Modeling condensation heat transfer on a horizontal finned tube in the presence of noncondensable gases

European designs for the next generation of nuclear reactors incorporate innovative passive systems in their containments to enhance heat removal by condensation under postulated accident conditions. These systems consist of several units of cross-flow finned tube bundles internally cooled with water. So far most of the studies that have been addressed to the issue of heat transfer onto finned surfaces under condensing conditions have involved refrigerants and pure vapor conditions. This study presents a model (HTCFIN) capable of predicting condensation of a cross-flow air–steam mixture onto a single horizontal finned tube. The comparison of HTCFIN predictions to the available databases shows its acceptable accuracy in a wide range of conditions and allows an interpretation of the influence of major variables acting on the scenario. As a consequence, HTCFIN model represents a step forward in the present theoretical capability to estimate heat transfer within containments of next generation of European reactors in the case of a hypothetical accident.     

Experimental verification of the fast reactor safety analysis code SIMMER-III for transient bubble behavior with condensation

Experimental verification of a reactor safety analysis code, SIMMER-III, was undertaken for transient behaviors of large-scale bubbles with condensation. The present study aimed to verify the code for numerical simulations of relatively short-time-scale multi-phase, multi-component hydraulic problems. Among these, vaporization and condensation, or simultaneous heat and mass transfer, play important roles. In this study, a series of transient bubble behavior experiments dedicated to condensation phenomena with noncondensable gases was carried out. In the experiments, a pressurized mixture of noncondensable gas and steam was discharged as a large-scale single bubble into a cylindrical pool filled with stagnant subcooled water. The concentration of noncondensable gas was taken as an experimental parameter as was the species of noncondensable gas. The characteristics of transient behavior of large-scale bubbles with condensation observed in the experiments were estimated through experimental analyses using SIMMER-III. In the experiments with steam condensation, dispersion of the gas mixture discharged into the liquid pool was accompanied by vapor condensation at the bubble surface. SIMMER-III simulations suggested that the noncondensable gas had a less inhibiting effect on the condensation of large-scale bubbles. This is a different characteristic to that of the quasi-steady condensation of small-scale bubbles observed in our previous experiments.