Research on the steam–gas pressurizer model with Relap5 code

Steam–gas pressurizers are self-pressurizing, and since steam and noncondensable gas are used to sustain their pressure, they experience very complicated thermal–hydraulic phenomena owing to the presence of the latter. A steam–gas pressurizer model was developed using Relap5 code to investigate such a pressurizer's thermal–hydraulic characteristics.The important thermal–hydraulic processes occurring in the pressurizer model include bulk flashing, rainout, wall condensation with noncondensable gas, and interfacial heat and mass transfer. The pressurizer model was verified using results from insurge experiments performed at the Massachusetts Institute of Technology. It was found that noncondensable gas was one of the important factors governing the pressure response, and the accuracy of the developed model would change with different mass fractions and types of noncondensable gas.     

Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube

An experimental study was performed to investigate local condensation heat transfer coefficients in the presence of a noncondensable gas inside a vertical tube. The data obtained from pure steam and steam/nitrogen mixture condensation experiments were compared to study the effects of noncondensable nitrogen gas on the annular film condensation phenomena. The condenser tube had a relatively small inner diameter of 13 mm (about 1/2-in.). The experimental results demonstrated that the local heat transfer coefficients increased as the inlet steam flow rate increased and the inlet nitrogen gas mass fraction decreased. The results obtained using pure steam and a steam/nitrogen mixture with a low inlet nitrogen gas mass fraction were similar. Therefore, the effects of noncondensable gas on steam condensation were weak in small-diameter condenser tubes.A new correlation was developed to evaluate the condensation heat transfer coefficient inside a vertical tube with noncondensable gas, irrespective of the condenser tube diameter. The new correlation proposed herein is capable of predicting heat transfer rates for tube diameters between 1/2- and 2-in. because of the unique approach of accounting for the heat transfer enhancement via an interfacial shear stress factor.     

Evaporation and condensation heat transfer with a noncondensable gas present

To evaluate the system pressure of an external water wall type containment vessel, which is one of the passive systems for containment cooling, the evaporation and condensation behavior under a noncondensable gas presence has been experimentally examined. In the system, steam evaporated from the suppression pool surface into the wetwell, filled with noncondensable gas, and condensed on the containment vessel wall. The system pressure was the sum of the noncondensable gas pressure and saturated steam pressure in the wetwell. The wetwell temperature was, however, lower than the supression pool temperature and depended on the thermal resistance on the suppression pool surface. The evaporation and condensation heat transfer coefficients in the presence of air as noncondensable gas were measured and expressed by functions of steam/air mass ratio. The evaporation heat transfer coefficients were one order higher than the condensation heat transfer coefficients because the local noncondensable gas pressure was much lower on the evaporating pool surface than on the condensing liquid surface. Using logal properties of the heat transfer surfaces, there was a similar trend between evaporation and condensation even with a noncondensable gas present.     

Forced convection condensation in the presence of noncondensable gas in a horizontal tube; experimental and theoretical study

To have a better understanding on forced convection condensation with noncondensable gas inside a horizontal tube, an experimental research and theoretical investigation were conducted under annular and wavy flow. The effects of noncondensable gas mass concentration, mixture gases velocity, pressure and inner wall sub-cooling on the condensation heat transfer have been analyzed. The results indicate that the local heat transfer coefficient increases with the increase of the mixture inlet velocity and pressure while decreases with the increase of the noncondensable mass fraction and wall sub-cooling. Based on the above conclusions, an empirical correlation for predicting the local heat transfer coefficient was proposed which showed a good agreement with the experimental data with an error of ±20%. Furthermore, a theoretical model using the heat and mass transfer (HMT) analogy method was developed including the suction effect. The heat transfer capacity for the film, gaseous boundary and convective heat transfer of the bulk gases were compared along the tube. Besides, the axial distribution of the bulk gases and liquid–gas interface temperatures inside the tube were analyzed. The present theoretical model fits better with the experimental data compared with Lee's and Caruso's models for stratified flow.     

A model for the performance of a vertical tube condenser in the presence of noncondensable gases

Some proposed vertical tube condensers are designed to operate at high noncondensable fractions, which warrants a simple model to predict their performance. Models developed thus far are usually not self-contained as they require the specification of the wall temperature to predict the local condensation rate. The present model attempts to fill this gap by addressing the secondary side heat transfer as well. Starting with a momentum balance which includes the effect of interfacial shear stress, a Nusselt-type algebraic equation is derived for the film thickness as a function of flow and geometry parameters. The heat and mass transfer analogy relations are then invoked to deduce the condensation rate of steam onto the tube wall. Lastly, the heat transfer to the secondary side is modelled to include cooling by forced, free or mixed convection flows. The model is used for parametric simulations to determine the impact on the condenser performance of important factors such as the inlet gas fraction, the mixture inlet flowrate, the total pressure, and the molecular weight of the noncondensable gas. The model performed simulations of some experiments with pure steam and air-steam mixtures flowing down a vertical tube. The model predicts the data quite well. The model described also provides a basis under which the presence of aerosol particles in the gas stream could be analyzed.     

Modeling of condensation heat transfer for a PRHRS heat exchanger in a SMART-P plant

A theoretical model using a heat and mass transfer analogy and a simple model using Lee and Kim's [Lee, K.-Y., Kim, M.H., 2008a. Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube. Nucl. Eng. Des. 238, 207-216] correlation were developed to investigate steam condensation in the presence of a noncondensable gas inside a vertical tube submerged in pool water. Rohsenow's correlation was used to consider the secondary pool-boiling heat transfer. Both models were assessed with the experimental data of Oh and Revankar [Oh, S., Revankar, S.T., 2005a. Investigation of the noncondensable effect and the operational modes of the passive condenser system. Nucl. Technol. 152, 71-86; Oh, S., Revankar, S.T., 2005b. Effect of noncondensable gas in a vertical tube condenser. Nucl. Eng. Des. 235, 1699-1712; Oh, S., Revankar, S.T., 2005c. Complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 593-602; Oh, S., Revankar, S.T., 2005d. Analysis of the complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 716-727; Oh, S., Revankar, S.T., 2006. Experimental and theoretical investigation of film condensation with noncondensable gas. Int. J. Heat Mass Trans. 49, 2523-2534; Oh, S., Gao, H., Revankar, S.T., 2007. Investigation of a passive condenser system of an advanced boiling water reactor. Nucl. Technol. 158, 208-218] for low pressure and Kim [Kim, S.J., 2000. Turbulent film condensation of high pressure steam in a vertical tube of passive secondary condensation system. Ph.D. dissertation, Korea Advanced Institute of Science and Technology] for high pressure, which were obtained from in-tube steam condensation with air in the pool water. These models predicted the data of Oh and Revankar well, but they slightly underestimated the data of Kim. The design of the Passive Residual Heat Removal System (PRHRS) condensation heat exchanger was evaluated with the theoretical model at real operating conditions (e.g., secondary pool-boiling, high system pressure). The PRHRS condensation heat exchanger designed was estimated to remove sufficiently the remaining heat in a reactor during a major accident.     

Investigation on condensation in presence of a noncondensable gas for a wide range of Reynolds number

A theoretical model has been developed to study the local heat transfer coefficient of a condensing vapour in the presence of a noncondensable gas, where the gas/vapour mixture is flowing downward inside a vertical tube. The two-phase heat transfer is analysed using an annular flow pattern with a liquid film at the tube wall and a turbulent gas/vapour core. The gas/vapour core is modeled using the analogy between heat and mass transfer. The model incorporates Nusselt equation with McAdams modifier and Blangetti model for calculating the film heat transfer coefficient, Moody and Wallis correlations to account for film waviness effect on gas/vapour boundary layer. The suction effect due to condensation, developing flow and property variation of the gas phase is also considered. A comparative study of heat transfer coefficient and vapour mass flow rate has been made with various models to account for condensate film resistance and condensate film roughness. Results show that for very high Reynolds number, the condensation heat transfer coefficient is higher than the film heat transfer coefficient.     

非凝性气体于竖直壁面处冷凝传热压力特性影响机理研究

非凝性气体于竖直壁面处冷凝传热的研究对一体化压水堆汽-气稳压器的瞬态调节以及紧凑型安全壳余热排出进程具有重要影响,当前对含有非凝性气体的蒸汽竖直壁面冷凝传热中压力的影响特性研究较少。基于传热传质比拟方法,采用适用于高压的改进扩散层模型对汽-气竖直壁面冷凝传热的压力影响进行研究。研究发现,基于传热传质比拟方法改进的扩散层模型与已有的实验结果基本一致,适用于较高压力汽-气竖直壁面冷凝传热系数的预测;总压的增加对存在非凝性气体的冷凝传热具有促进作用,这种促进作用随总压的增加逐渐减弱;在一定压力范围内(0.1~7.0 MPa),存在压力分界点pc,在压力影响分界点以下的低压力区域(0.1 MPa~pc)为压力影响敏感区,在压力影响分界点以上的高压力区(pc~7.0 MPa)为非敏感区。同时,本文还对非凝性气体的种类和含量对蒸汽在竖直壁面处冷凝传热过程的影响进行了分析,从气体扩散系数方面进一步分析了造成影响差异的原因。     

Numerical Analysis of the PHEBUS Containment Thermal Hydraulics

This paper describes numerical analysis of the PHEBUS FP containment thermal-hydraulics. PHEBUS FP is an international project undertaken with the aim of evaluating the behavior of radioactive fission products released from a LWR pressure vessel into the containment vessel during a hypothetical severe accident. Six integral in-pile tests have been planned and are being carried out at Cadarache, France. The European Union, the United States, Canada, Korea and Japan are participating in this project. From Japan, the Nuclear Power Engineering Corporation and the Japan Atomic Energy Research Institute are collaborating the other parties involved in the project.

Since the behavior of fission products is strongly dependent on the surrounding environmental conditions, accurate prediction of the thermal-hydraulics in the containment vessel is essential to accurately evaluate the behavior. Characteristics of condensation heat transfer in the presence of noncondensable gases play a key role in the PHEBUS thermal-hydraulics, especially under the condition of high noncondensable gas mass fraction. Many models for condensation heat transfer in the presence of noncondensable gases have been proposed. However, these models were not found suitable for PHEBUS analysis, because they were focused on the low noncondensable gas mass fraction condition.

In this study, a single-phase multi-component code, TFLOW-FP has been newly developed to predict thermal-hydraulics in the PHEBUS FP containment. Moreover, a new degradation factor correlation for the condensation heat transfer coefficient due to the presence of noncondensable gases has also been developed and incorporated into the code. This code was applied for analysis of the thermal-hydraulic benchmark tests and the first in-pile test, FPTO. The results show that the code can predict the total pressure, gas temperature distributions, the relative humidity in the containment vessel and steam condensation rate on the surface of condenser rods very well.     

PWR pressurizer modeling

A series of experiments have been performed which help to provide fundamental understanding of the phenomena which are important to the analysis of a PWR pressurizer. The transients considered include insurges to a partially-full tank, outsurges, insurges to a tank with hot walls, empty tank insurges, and combined insurges and outsurges. The experiments include the effects of noncondensable gases, and free surface heat transfer. These experiments provide a data base from which recommendations are made for calculating such phenomena, as: (i) stratification of the hot water and incoming cold water, (ii) wall condensation, (iii) flashing, (iv) rainout, (v) suppression of flashing, (vi) wall conduction, (vii) the effect of noncondensable gases on wall heat transfer, and (viii) free surface heat transfer. From these experiments a general model of a PWR pressurizer has been developed. It will predict the pressure-time behavior of a PWR pressurizer during a variety of transients. The model has been benchmarked against the low pressure experiments of this study and a single full scale pressurizer transient experiment. The most significant finding is the pool in the pressurizer remains stratified during an insurge transient so that practically no heat transfer to the cold insurge liquid occurs. Wall heat transfer can be significant for insurge transients, however.     

Experimental Study on Heat Removal Characteristics for Water Wall Type Passive Containment Cooling System

To evaluate the heat removal capability of a water wall type cooling system, which is one passive containment cooling system (PCCS), the thermal hydraulic behavior in the suppression pool (S/P) and the outer pool (O/P, flat plate water wall) have been investigated experimentally. The following results were obtained. (1) A thermal stratification boundary, which separates the pools into the upper high temperature and lower low temperature regions, was formed just below the vent tube outlet. (2) Convection heat transfer characteristics in the S/P and O/P along the primary containment vessel (PCV) wall had no significant differences and were those of natural convection. Correlation of the natural convection heat transfer up to the Ra number of 2×10¹⁴ was obtained. (3) Vertical variations of local condensation heat transfer coefficients under a noncondensable gas presence were within ±10% of the average value for the 4.7 m heat transfer length. An experimental correlation for the average condensation heat transfer coefficients was obtained as a function of steam and noncondensable gas mass ratio. (4) An analytical model to evaluate the system performance of the water wall type PCCS was verified. (5) A baffle plate concept to mitigate thermal stratification at the vent outlet and to enlarge the high temperature region in the S/P was considered as a means to improve heat release capability. Thermal hydraulics with a baffle plate were examined, and effectiveness of the baffle plate to improve the heat release capability was confirmed.     

Effect of noncondensable gas in a vertical tube condenser

An experimental study is performed to investigate the effects of noncondensable (NC) gas in the steam condensing system. A vertical condenser tube is submerged in a water pool where the heat from the condenser tube is removed by boiling heat transfer. The design of the test section is based on the passive condenser system in an advanced boiling water nuclear power reactor. Data are obtained for various process parameters, such as inlet steam flow rate, noncondensable gas concentration, and system pressure. Degradation of the condensing performance with increasing noncondensable gas is investigated. The condensation heat transfer coefficient and heat transfer rate decrease with noncondensable gas. The condensation heat transfer rate is enhanced by increasing the inlet steam flow rate and the pressure. The condensation heat transfer coefficient increases with the inlet steam flow rate, however, decreases with the system pressure. For the condenser submerged in a water pool with saturated condition, the strong primary pressure dependency is observed.     

Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions

The new AP600 reactor designed by Westinghouse uses a passive safety system relying on heat removal by condensation to keep the containment within the design limits of pressure and temperature. Even though some research has been done so far in this regard, there are some uncertainties concerning the behavior of the system under postulated accident conditions. In this paper, steam condensation onto the internal surfaces of the AP600 containment walls has been investigated in two scaled vessels with similar aspect ratios to the actual AP600. The heat transfer degradation in the presence of noncondensable gas has been analyzed for different noncondensable mixtures of air and helium (hydrogen simulant). Molar fractions of noncondensables/steam ranged from (0.4–4.0) and helium concentrations in the noncondensable mixture were 0–50% by volume. In addition, the effects of the bulk temperatures, the mass fraction of noncondensable/steam, the cold wall surface temperature, the pressure, noncondensable composition, and the inclination of the condensing surface were studied. It was found that the heat transfer coefficients ranged from 50 to 800 J s⁻¹ K⁻¹ m⁻² with the highest for high wall temperatures at high pressure and low noncondensable molar fractions. The effect of a light gas (helium) in the noncondensable mixture were found to be negligible for concentrations less than approximately 35 molar percent but could result in stratification at higher concentrations. The complete study gives a large and relatively complete data base on condensation within a scaled AP600 containment structure, providing an invaluable set of data against which to validate models. In addition, specific areas requiring further investigation are summarized.     

A diffusion layer model for steam condensation within the AP600 containment

Steam condensation plays a key role in removing heat from the atmosphere of the Westinghouse AP600 containment in case of a postulated accident. A model of steam condensation on containment surfaces under anticipated accident conditions is presented and validated against an extensive and sound database. Based on the diffusion layer theory and on the use of the heat/mass transfer analogy, one can deal with large temperature gradients across the gaseous boundary layer under high mass flux circumstances. The thermal resistance of the condensate film, as well as its wavy structure, have also been considered in this model. As compared to Anderson et al. (1998) (Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions. Nucl. Eng. Des. (submitted)) experimental database, an average error lower than 15%, within the experimental confidence range, has demonstrated its remarkable accuracy. In particular, the model has shown a good response to the influence of primary variables in steam condensation (i.e. subcooling, noncondensable concentration and pressure), providing a mechanistic explanation for effects such as the presence of light noncondensable gas (i.e. helium as a simulant for hydrogen) in the gaseous mixture. In addition, the model has been contrasted against correlations used in safety analysis (i.e. Uchida, Tagami, Kataoka, etc.) and occasionally to Dehbi’s database. This cross-comparison has pointed out several shortcomings in the use of these correlations and has extended the model validation to other databases.     

高压条件下含有非凝结性气体的水蒸气凝结传热模型研究

研究高压条件下含有非凝结性气体的水蒸气凝结传热过程对于小型堆的安全非常重要。当前对这一物理过程的研究集中于压力较低的工况,高压条件下的研究尚不成熟。本文建立了一种适用于高压条件下含有非凝结性气体的水蒸气自然对流凝结传热理论模型,使用真实气体状态方程求解扩散方程中摩尔浓度梯度和分压梯度之间的关系,取代了前人方法中的理想气体假设。计算结果与已有的实验数据吻合较好,证明本方法可用于小型堆紧凑型安全壳和汽 气稳压器等安全级设备的热工分析。     

An experimental investigation of a passive cooling unit for nuclear plant containment

A set of condensation experiments in the presence of noncondensables (e.g. air, helium) was conducted to evaluate the heat removal capacity of a passive cooling unit in a post-accident containment. Condensation heat transfer coefficients on a vertically mounted smooth tube have been obtained for total pressure ranging from 2.48×10⁵ Pa(abs) to 4.55×10⁵ Pa(abs) and air mass fraction ranging from 0.30 to 0.65. An empirical correlation for heat transfer coefficient (h), has been developed in terms of a parameter group made up of steam mole fraction (Xs), total pressure (P_t), temperature difference between bulk gas and wall surface (dT). This correlation covers all data points within 20%. All data points are also in good agreement with the prediction of the diffusion layer model (DLM) with suction and are approximately 2.2 times the Uchida heat transfer correlation. Experiments with an axial shroud around the test tube to model the restriction on radial flow experienced within a tube bundle demonstrated a reduction of the heat transfer coefficient by a factor of about 0.6. The effect of helium (simulating hydrogen) on the heat transfer coefficient was investigated for helium mole fraction in noncondensable gases (X_He/X_nc) at 15, 30 and 60%. It was found that the condensation heat transfer coefficients are generally lower when introducing helium into noncondensable gas. The difference is within 20% of air-only cases when X_He/X_nc is less than 30% and total pressure is less than 4.55×10⁵ Pa(abs). A gas stratification phenomenon was clearly observed for helium mole fraction in excess of 60%.     

Computational analysis for prediction of pressure of PWR presurizer under transient conditions

A computer model has been developed for prediction of the pressure in the pressurizer under transient conditions.In the model three separate thermodynamic regions which are not required to be in thermal equilibrium have been considered.The mathematical model derived from the general conservation equations includes all of the important thermal-hydraulics phenomena occurring in the pressurizer,i.e.,stratification of the hot water and incoming cold water,bulk flashing and condensation ,wall condensation,and interfacial heat and mass transfer,etc.The bubble rising and rain-out models are developed to describe bulk flashing and condensation.respectively.To obtain the wall condensation rate,a one-dimensional heat conduction equation is solved by the pivoting method.The presented model will predict the pressure-time behavior of a PWR pressurzer during a variety of transients.The results obtained from the propesed mathematical model are in good agreement with available data on the CHASHMA nuclear power plant‘s pressurizer performance.     

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.     

Development of nonequilibrium pressurizer model with noncondensable gas

To investigate thermal–hydraulic characteristics of a steam–gas pressurizer in the integral type reactor, the steam–gas pressurizer model based on the two-region nonequilibrium concept was developed and introduced into RETRAN-3D/INT code. The model includes an explicit solution method for the one-dimensional governing equations and the equation of the state solution method to determine the thermal–hydraulic state of the steam–gas pressurizer volume. In addition, the wall condensation model based on the diffusion layer modeling was included to consider the effect of the noncondensable gas. The developed model was verified with the results from the pressurizer insurge experiment conducted at Massachusetts Institute of Technology. From the verification results, it was concluded that the developed steam–gas pressurizer model can sufficiently predict the pressurizer transient and it can be used as a component model of the one-dimensional system code based on the homogeneous equilibrium model.     

Implementation of a generalized diffusion layer model for condensation into MELCOR

Condensation of co-current steam-noncondensable gas mixtures in vertical tubes is an important, yet difficult to model, component of many passive nuclear reactor cooling systems. The stagnant film model, which is used by the severe accident code MELCOR, gains its name by assuming that the gas-vapor film formed along the condensation surface is stagnant. Liao developed a generalized diffusion layer model that removes limitations of the stagnant film model and considers additional phenomena to improve predictive capabilities for condensation heat transfer with noncondensable gases. Similarities between the formulations of the stagnant film model and generalized diffusion layer model allow for the generalized diffusion layer model to be implemented into MELCOR. Input decks representing experimental facilities that produced co-current condensation data have been created to analyze and validate the generalized diffusion layer model implemented in MELCOR. The experimental data span a wide range of noncondensable gas mass fractions and include condensation mass transfer both on a vertical flat plate and in vertical tubes. MELCOR predictions of the condensation mass flux are seen to improve when using the generalized diffusion layer model instead of the stagnant film model.