Modeling of high pressure steam condensation in inclined horizontal tubes of PAFS in APR+

A Single-tube COndensation exPeriment (SCOP) was performed at Korea Advanced Institute of Science and Technology (KAIST) to simulate the condensation phenomena of Passive Auxiliary Feedwater System (PAFS), which is introduced in Advanced Power Reactor Plus. SCOP tests were conducted for two pipes of different diameters [22.6 and 44.8 mm inside diameter] with 8.2 m length and 2.5–4 degrees of the inclined angles of the upper and lower section of each tube. The experiment were performed at 1.5–6.5 MPa of steam pressure and 0.12–0.45 kg/s of steam flow. Based on the Kim and No correlation (KAIST, 2000), we developed a new turbulent–condensation correlation for the turbulent region of the liquid film in the inclined tube. We introduced the factors to account for the different inclined angle effect, different diameter effect. The Nusselt correlation is adopted for condensation near the tube inlet where the laminar region of the liquid film is dominant due to the small amount of condensed water. The present correlation was compared with the Shah and RELAP5 condensation model using the SCOP data. The root mean square errors of the present correlation, Shah model, and RELAP5 model are 17.41%, 57.88%, and 43.07%, respectively: the present correlation can predict well the condensation characteristics in comparison with other correlations in PAFS.     

Modeling of bubble shape in horizontal and inclined tubes

An experimental and theoretical study on the bubble shape of intermittent flow in the horizontal and inclined pipes has been carried out. The experiment results show that the bubble shape depends on the Froude number, bubble length and pipe inclination. The bubble with staircase pattern tail is observed at low Froude numbers, which is corresponding to plug flow. A model for the prediction of the bubble shape in horizontal and inclined pipes is proposed. The model is able to predict the bubble shape, flow pattern transition between plug and slug flow regimes as well as nose-tail inversion phenomenon observed in the downwardly inclined pipe. Validation shows the model can well predict the bubble shapes in horizontal and inclined pipes. The model discloses that the transition between plug and slug flow regimes occurs within a region. The Froude number range for plug flow regime in the downwardly inclined pipe is much wider than that in the horizontal or upwardly inclined pipe. The assumption of fully developed liquid film under the long bubbles tends to under-estimate the liquid fraction in this part of the slug structure, especially, for the intermittent flow in the upwardly inclined pipe with high Froude numbers.     

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.     

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.     

Effect of steam condensation on countercurrent flow limiting in nearly horizontal two-phase flow

An analytical model that includes the steam condensation effect has been derived and a parametric study has been performed. In addition, a series of experiments were performed and a total of 34 experimental data for the onset of countercurrent flow limiting (CCFL) in nearly horizontal countercurrent two-phase flow have been obtained for various flow rates of water. Comparisons of the present CCFL data with slug formation models show that the agreement between the present as well as the existing model and the data is about the same. However, the deviation between Taitel and Dukler’s model predictions and the data is the largest when j_f<0.04 m s⁻¹. A parametric study of the effect of condensation using the present model shows that, when all local conditions are similar, the model predicted local gas velocities that cause the onset of flooding are slightly lower when condensation occurred. Based on the visual observation and the evaluation of the present work, it has been concluded that the criterion derived for the onset of slug flow can be directly used to predict the onset of inner flooding in nearly horizontal two-phase flow within the experimental ranges of the present work.     

One-dimensional three-field model of condensation in horizontal countercurrent flow with supercritical liquid velocity

A one-dimensional three-field model was developed to predict the flow of liquid and vapor that results from countercurrent flow of water injected into the hot leg of a PWR and the oncoming steam flowing from the upper plenum. The model solves the conservation equations for mass, momentum, and energy in a continuous-vapor field, a continuous-liquid field, and a dispersed-liquid (entrained-droplet) field. Single-effect experiments performed in the upper plenum test facility (UPTF) of the former SIEMENS KWU (now AREVA) at Mannheim, Germany, were used to validate the countercurrent flow limitation (CCFL) model in case of emergency core cooling water injection into the hot legs. Subcooled water and saturated steam flowed countercurrent in a horizontal pipe with an inside diameter of 0.75 m. The flow of injected water was varied from 150 kg/s to 400 kg/s, and the flow of steam varied from 13 kg/s to 178 kg/s. The subcooling of the liquid ranged from 0 K to 104 K. The velocity of the water at the injection point was supercritical (greater than the celerity of a gravity wave) for all the experiments. The three-field model was successfully used to predict the experimental data, and the results from the model provide insight into the mechanisms that influence the flows of liquid and vapor during countercurrent flow in a hot leg. When the injected water was saturated and the flow of steam was small, all or most of the injected water flowed to the upper plenum. Because the velocity of the liquid remained supercritical, entrainment of droplets was suppressed. When the injected water was saturated and the flow of steam was large, the interfacial shear stress on the continuous liquid caused the velocity in the liquid to become subcritical, resulting in a hydraulic jump. Entrainment ensued, and the flow of liquid to the end of the hot leg was greatly reduced.The influence of condensation on the transition from supercritical to subcritical flow as observed in the experimental data is also predicted with the three-field model. When the injected water was subcooled, condensation on the flow of continuous liquid caused a reduction in the flow of vapor and, consequently, a reduction in the interfacial shear stress. Therefore, the flow of liquid remained supercritical to the end of the hot leg at the upper plenum. The entire flow of injected water flowed to the end of the hot leg at higher flows of steam when the injected water was subcooled than when it was saturated. When the flow of vapor was large enough to cause a hydraulic jump in the subcooled liquid, the rate of entrained droplets was greatly increased. The interfacial surface area of the droplets was several orders of magnitude greater than for the continuous-liquid field, and condensation rate on the droplet field was also several orders of magnitude greater. When the flow of vapor from the upper plenum was at its greatest, most of the flow in the continuous liquid was entrained before reaching the upper plenum. The large flow of subcooled droplets caused three-quarters of the steam to condense.     

Fluid-to-fluid modeling of two-phase flow critical heat flux in horizontal helically coiled tubes

The new similarity laws for fluid-to-fluid modeling of two-phase flow critical heat flux (CHF) in horizontal helically coiled tubes were derived based on the dimensional analysis and similarity theory considering the effect of the geometrical parameters on CHF. A generalized factor D_n was introduced to the new similarity laws, and all the new dimensionless numbers were derived from the classical theorem of Buckingham π for dimensional analysis. The obtained dimensionless parameter sets were a reasonable extension to Ahmad's compensated distortion model, which may be considered as a special case of the new dimensionless parameter sets when the variable n is equal to unity. Based on the experimental data, the specific similarity numbers were determined for CHF phenomena in horizontal helically coiled tubes. A new equivalent characteristic parameter D_e-helix was developed, which could reflect the influence of complex flow channels on the occurrence of CHF. The equivalent characteristic parameter consists of the essential geometrical parameters of tubes and the fluid thermophysical properties. The new fluid-to-fluid modeling methods were proposed for CHF of R134a-water in horizontal helically coiled tubes, which could be used readily to derive the CHF data of water through the CHF data of R134a at the corresponding experimental conditions.     

Modeling of eddy current probe response for steam generator tubes

Sample calculations were performed with a three-dimensional (3D) finite-element model to describe the response of an eddy current (EC) probe to defects in steam generator (SG) tubing. Such calculations could be very helpful in understanding and interpreting EC probe response to complex tube/defect geometries associated with the inservice inspection (ISI) of SG tubes. The governing field equations are in terms of coupled magnetic vector and electric scalar potentials in conducting media and of total or reduced scalar potentials in nonconducting regions. To establish the validity of the model, comparisons of the theoretical and experimental responses of an absolute bobbin probe are given for two types of calibration standard defects. Simulation results are also presented on the effect of ligament size in axial cracks on bobbin probe response.     

Non-iterative model for condensation heat transfer in presence of non-condensable gases inside passive containment cooling vertical tubes

Some contributions have been stated in order to improve the modeling of concurrent downflow condensation in presence of non-condensables inside vertical tubes. In particular, the influence of non-condensables over the liquid side heat transfer has been considered. The new proposed mechanistic models solve explicitly the real interface temperature by means of a cubic or a fourth order equation. As these models have a non-iterative nature, they can avoid the weakest point of the traditional mechanistic models, which is the slowdown computation if the model had to be implemented in a code. Moreover, as the main non-condensables effects can be accounted for in the heat and mass transfer processes, the new models will be more realistic. The models have been validated with the Vierow experimental data, obtaining a total average relative error, for the fourth order equation method model, of 21% for 268 points.     

Modeling of turbulent condensation heat transfer in the boiling water reactor primary containment

A condensation heat transfer model is developed for the purpose of predicting the atmosphere temperature response within the primary containment of a boiling water reactor during the initial forced convection heat transfer period following a postulated loss-of-coolant accident. The model utilizes simultaneous heat and mass transfer for the process of condensation in the presence of a non-condensible gas. The gas-vapor diffusion layer formed is in the mode of turbulent, forced convection. The predicted heat transfer is determined to be diffusion controlled with negligible resistance being contributed by the condensate film. The model is qualified through the analysis of the response of a containment test facility; the results compare favorably with experimental observations made by the General Electric Co. Predicted temperature responses for a typical containment are also shown and compared with those obtained through use of the Uchida heat transfer correlations.     

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.     

Effect of non-condensable gas and wavy interface on the condensation heat transfer in a nearly horizontal plate

An experimental study was conducted to investigate the effect of non-condensable gas and wavy water film on condensation heat transfer. The experiment was performed in a nearly horizontal (4.1°) square duct of 0.1 m height, 0.15 m width and 1.52 m length at atmospheric pressure. A water film in a steady thermal condition was injected to simulate the effect of a wavy interface on the condensation. The experimental data for the heat transfer coefficient and the interfacial structure of the wavy condensate were obtained along with the three parameters: air mass fraction, mixture velocity and film flow rate. When the interface is smooth, the heat transfer coefficients with or without non-condensable gas agree reasonably with the previous theories. The waviness of condensate film increases the heat transfer up to several tenths of a per cent.     

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.     

Laminar combined convection heat transfer of liquid sodium flowing through a single horizontal row of cooling tubes in the direction of gravity

The laminar combined convection heat transfer of the liquid sodium which flows through a single horizontal row of cooling tubes in the direction of gravity are studied using numerical analysis. The heat transfer characteristics at large Reynolds numbers are improved when Richardson numbers (= GR/Re²) are increased and the improvement rate is enlarged with an increase in value. The temperature field at small Reynolds numbers does not exhibit much change even when the Richardson number reaches a high value. Consequently the Nusselt numbers do not differ from those of forced convection. In other words, in a decay heat removal system at a low velocity, there is a possibility that an improvement in the heat transfer characteristics by combined convection cannot be expected even in a system with a large Richardson number.     

Steam condensation on finned tubes,in the presence of non-condensable gases and aerosols: Influence of impaction,diffusiophoresis and settling on aerosol deposition

This paper presents a mechanistic model to predict the steam condensation on containment finned tube heat exchangers in the presence of non-condensable gases (NC) and aerosols. The total thermal resistance from the bulk gas to the coolant is formulated as a parallel combination of the convective and condensation gas resistances coupled in series to those of condensate layer, the aerosol fouling layer, the wall, and the coolant. The condensate layer thermal resistance is calculated by means of an Adamek-based condensation model. The aerosol fouling layer is computed based on diffusiophoresis, settling and impaction mechanisms. The gas mixture (steam plus NC) thermal resistance is formulated based on a diffusion layer modeling. Finally, this paper presents a Montecarlo method implemented in the FORTRAN code TAEROSOL that is able to compute the amount of aerosol mass that is deposited by impaction on the top of the finned tubes. The model results are compared with the available experimental data of the CONGA European project.     

Free convective condensation in a vertical enclosure

Free convective condensation in a vertical enclosure was studied numerically and the results were compared with experiments. In both the numerical and experimental investigations, mist formation was observed to occur near the cooling wall, with significant droplet concentrations in the bulk. Large recirculation cells near the end of the condensing section were generated as the heavy noncondensing gas collecting near the cooling wall was accelerated downward. Near the top of the enclosure the recirculation cells became weaker and smaller than those below, ultimately disappearing near the top of the condenser. In the experiment the mist density was seen to be highest near the wall and at the bottom of the condensing section, whereas the numerical model predicted a much more uniform distribution. The model used to describe the formation of mist was based on a modified critical saturation model (MCSM), which allows mist to be generated once the vapor pressure exceeds a critical value. Equilibrium, nonequilibrium, and MCSM calculations were performed, showing the experimental results to lie somewhere in between the equilibrium and nonequilibrium predictions of the numerical model. A single adjustable constant (indicating the degree to which equilibrium is achieved) is used in the model in order to match the experimental results.