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.     

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.     

Diameter effect on critical heat flux

The critical heat flux look-up table (CHF LUT) is widely used to predict CHF for various applications, including design and safety analysis of nuclear reactors. Using the CHF LUT for round tubes having inside diameters different from the reference 8 mm involves conversion of CHF to 8 mm. Different authors [Becker, K.M., 1965. An Analytical and Experimental Study of Burnout Conditions in Vertical Round Ducts, Aktiebolaget Atomenergie Report AE 177, Sweden; Boltenko, E.A., et al., 1989. Effect of tube diameter on CHF at various two phase flow regimes, Report IPE-1989; Biasi, L., Clerici, G.C., Garriba, S., Sala, R., Tozzi, A., 1967. Studies on Burnout, Part 3, Energia Nucleare, vol. 14, pp. 530-536; Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. AECL-UO critical heat flux look-up table. Heat Transfer Eng., 7, 46-62; Groeneveld et al., 1996; Hall, D.D., Mudawar, I., 2000. Critical heat flux for water flow in tubes - II subcooled CHF correlations. Int. J. Heat Mass Transfer, 43, 2605-2640; Wong, W.C., 1996. Effect of tube diameter on critical heat flux, MaSC dissertation, Ottawa Carleton Institute for Mechanical and Aeronautical Engineering, University of Ottawa] have proposed several types of correlations or factors to describe the diameter effect on CHF. The present work describes the derivation of new diameter correction factor and compares it with several existing prediction methods.     

Thermal–hydraulic modeling of the onset of flow instability in MTR reactors

Prediction of the onset of the flow instability (OFI) in steady and transient sub-cooled flow boiling is an important consideration in the design and operation of nuclear reactors, in particular for materials testing reactors (MTR). In this study, a predictive model for OFI in the MTR has been developed. The model is based on both the heat balance during the bubble generation and condensation processes, and the force balance for the detached bubbles at the onset of significant void (OSV). The only adjustable coefficient involved in the proposed model is quantified by comparison with the experimental data of Whittle and Forgan [Whittle, R.H., Forgan, R., 1967. A correlation for the minima in the pressure drop versus flow-rate curves for sub-cooled water flowing in narrow heated channels. Nucl. Eng. Des. 6, 89–99], which covers the wide range of MTR operating conditions. The model predictions are compared with predictions of some previous models, and it is shown that the present model results in smaller deviation from the experimental data. A correlation for the heat flux at OFI is also developed based on the present model. The developed correlation gives lower deviation from the experimental data than the well-known correlation of Whittle and Forgan. The model is also used to predict the OFI locus during a transient, where it shows good agreement with the short transient data of Lee and Bankoff [Lee, S.C., Bankoff, S.G., 1993. Prediction of the onset of flow instability in transient sub-cooled flow boiling. J. Nucl. Eng. Des. 139, 149–159] as well.     

Preliminary analysis of compatibility with low activation martensitic steel blanket for the fusion experimental breeder: Impact of ferromagnetic behavior on plasma burning cycle

The reduced activation ferritic martensitic steels is considered a candidate for the first wall (FW) blanket structural material because of its safety environmental advantages [R.L. Klueh, D.S. Geiles, et al., Ferritic/martensitic steels overview of recent results, J. Nucl. Mater. 307-312 (2002) 455-465; T. Muroga, M. Gasparotto, S.J. Zinkle, Overview of materials research for fusion reactors, Fusion Eng. Des. 61-62 (2002) 3-25]. An engineering design analysis concerning the electromagnetic issues is performed. Preliminary analysis results show that design effort of the fusion reactor can cope with the effect of the ferromagnetic FW blanket on the electromagnetic forces, which increases by 28-38% during a major plasma disruption and overcome the influence of the poloidal field, which reduces by 10-20%, comparing with the austenitic steel blanket. Both the effect and influence depend on the saturation magnetic susceptibility and blanket configurations.     

An independent assessment of Groeneveld et al.'s 1995 CHF look-up table

The prediction capability of the 1995 CHF look-up table (Groeneveld D.C., et al., Nucl. Eng. Des. 163 (1996) 1–23) is independently assessed based on the KAIST data base consisting of 10?822 data for uniformly-heated, vertical, round tubes. This confirms the error statistics for the heat balance method reported by Groeneveld et al. and shows overall average and RMS errors of 4.2 and 36.7%, respectively, for the direct substitution method. The new 1995 table shows better prediction capability than the 1986 AECL-UO table (Groeneveld et al., 1986), especially for the low-pressure, low-flow region. The error analysis indicates the length effect even for significantly long tubes.     

Critical heat flux under choking flow conditions: Part II – Maximum values of flow parameters attained under choking flow conditions

Under conditions of forced convective boiling at low pressures and high mass fluxes, beyond a certain quality, choking flow may occur at the exit of a heated channel. An experimental investigation carried out by Olekhnovitch et al. (Olekhnovitch, A., Teyssedou, A., Tye, P., Champagne, P., 2000. Critical heat flux under choking flow conditions. Part I — Outlet pressure fluctuations. Nucl. Eng. Des., this issue) has shown that the occurrence of choking flow does not radically influence the values of the critical heat flux (CHF). However, once the choking flow conditions have occurred, for a given mass flux and quality, the outlet pressure cannot be lowered below a certain value that is fixed by the flow itself. A model that allows this pressure to be determined and which must be used in conjuction with correlations for the prediction of the CHF is presented.     

Transient analysis of blowdown thrust force under PWR LOCA

The analytical results of blowdown characteristics and thrust forces were compared with the experiments, which were performed as pipe whip and jet discharge tests under the PWR LOCA conditions. The blowdown thrust forces were obtained by Navier-Stokes momentum equation for a single-phase, homogeneous and separated two-phase flow, assuming critical pressure at the exit if a crifical flow condition was satisfied.The following results are obtained:

1. (1) The node-junction method is useful for both the analyses of the blowdown thrust force and of the water hammer phenomena.

2. (2) The Henry-Fauske model for subcooled critical flow is effective for the analysis of the maximum thrust force under the PWR LOCA conditions. The jet thrust parameter of the analysis and experiment is equal to 1.08.

3. (3) The thrust parameter of saturated blowdown has the same one with the value under pressurized condition when the stagnant pressure is chosen as the saturated one.

4. (4) The dominant terms of the blowdown thrust force in the momentum equation are the pressure and momentum terms except that the acceleration term has large contribution only just after the break.

Heat transfer from a totally blocked fuel subassembly of a liquid metal fast breeder reactor: II. Numerical simulation

Fast breeder nuclear reactors used for power generation, have fuel subassemblies in the form of rod bundles enclosed inside tall hexagonal cavities. Each subassembly can be considered as a porous medium with internal heat generation. A three-dimensional analysis is carried out here to estimate the heat transfer due to natural convection, in such an anisotropic, partially heat generating porous medium, which corresponds to the typical case of blocked flow in a fuel subassembly inside the reactor core. Using the finite volume technique, the temperatures at various locations inside hexagonal cavity are obtained. The simulations by the three-dimensional code developed are compared with the results of experiments [Suresh, Ch.S.Y., Sateesh, G., Das, Sarit K., Venkateshan, S.P., Rajan, M., 2004. Heat transfer from a totally blocked fuel subassembly of a liquid metalfast breeder reactor. Part 1: Experimental investigation. Nucl. Eng. Design, present issue] conducted using liquid sodium as the heat transfer fluid. Further, the code is used to predict the maximum temperature in typical liquid metal fast breeder reactors to find the power level where the liquid sodium starts boiling. It helps to decide the power level for initiation of monitoring the temperature for the purpose of reactor control.     

Critical heat flux data in a vertical tube at low and medium pressures

AECL Research and École Polytechnique have been cooperating on the validation of the critical heat flux (CHF) look-up table (D.C. Groeneveld et al., Heat Transfer Eng. 7(1–2) (1986) 46–62). For low and medium pressures the values in the table have been obtained by extrapolation and curve fitting; therefore, errors could be expected. To reduce these possible extrapolation errors, CHF experiments are being carried out in water cooled 8 mm internal diameter (ID) tubes, at conditions where the data are scarce. This paper presents some of the experimental CHF data obtained for vertical up flow in an 8 mm ID test section, for a wide range of exit qualities (5–70%) and the exit pressure ranging from 5 to 30 bar. The experiments were carried out for heated lengths of 0.75, 1, 1.4 and 1.8 m. In general, the collected data show parametric trends similar to those described in the open literature. However, it was observed that for low pressure conditions CHF depends on the heated length; this dependence begins to disappear for exit pressure of about 30 bar. The CHF data have also been compared with predictions of well-known correlations (L. Biasi et al., Energia Nucl. 14(9) (1967) 530–536; R. Bowring, Br. Report AEEW-R789, Winfrith, UK, 1972; Y. Khatto and H. Ohno, Int. J. Heat Mass Transfer 27 (1984) 1641–1648) and those of the look-up table given by Groeneveld et al. For low pressures and low mass fluxes the look-up table seems to yield better predictions of the CHF than the correlations. However, for medium pressures and mass fluxes the correlations perform better than the look-up table; among those tested, Katto and Ohno's correlation gives the best results.     

A critical heat flux approach for square rod bundles using the 1995 Groeneveld CHF table and bundle data of heat transfer research facility

The critical heat flux (CHF) approach using CHF look-up tables has become a widely accepted CHF prediction technique. In these approaches, the CHF tables are developed based mostly on the data bank for flow in circular tubes. A set of correction factors was proposed by Groeneveld et al. [Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. 1986 AECL-UO Critical Heat Flux lookup table. Heat Transf. Eng. 7(1–2), 46] to extend the application of the CHF table to other flow situations including flow in rod bundles. The proposed correction factors are based on a limited amount of data not specified in the original paper. The CHF approach of Groeneveld and co-workers is extensively used in the thermal hydraulic analysis of nuclear reactors. In 1996, Groeneveld et al. proposed a new CHF table to predict CHF in circular tubes [Groeneveld, D.C., et al., 1996. The 1995 look-up table for Critical Heat Flux. Nucl. Eng. Des. 163(1), 23]. In the present study, a set of correction factors is developed to extend the applicability of the new CHF table to flow in rod bundles of square array. The correction factors are developed by minimizing the statistical parameters of the ratio of the measured and predicted bundle CHF data from the Heat Transfer Research Facility. The proposed correction factors include: the hydraulic diameter factor (K_hy), the bundle factor (K_bf), the heated length factor (K_hl), the grid spacer factor (K_sp), the axial flux distribution factors (K_nu), the cold wall factor (K_cw) and the radial power distribution factor (K_rp). The value of constants in these correction factors is different when the heat balance method (HBM) and direct substitution method (DSM) are adopted to predict the experimental results of HTRF. With the 1995 Groeneveld CHF Table and the proposed correction factors, the average relative error is 0.1 and 0.0% for HBM and DSM, respectively, and the root mean square (RMS) error is 31.7% in DSM and 17.7% in HBM for 9852 square array data points of HTRF.     

Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions

A literature review of critical heat flux (CHF) experimental visualizations under subcooled flow boiling conditions was performed and systematically analyzed. Three major types of CHF flow regimes were identified (bubbly, vapor clot and slug flow regime) and a CHF flow regime map was developed, based on a dimensional analysis of the phenomena and available experimental information. It was found that for similar geometric characteristics and pressure, a Weber number (We)/thermodynamic quality (x) map can be used to predict the CHF flow regime.Based on the experimental observations and the review of the available CHF mechanistic models under subcooled flow boiling conditions, hypothetical CHF mechanisms were selected for each CHF flow regime, all based on a concept of wall dry spot overheating, rewetting prevention and subsequent dry spot spreading. Even though the selected concept has not received much attention (in term or theoretical developments and applications) as compared to other more popular DNB models, its basis have often been cited by experimental investigators and is considered by the authors as the “most-likely” mechanism based on the literature review and analysis performed in this work. The selected modeling concept has the potential to span the CHF conditions from highly subcooled bubbly flow to early stage of annular flow and has been numerically implemented and validated in bubbly flow and coupled with one- and three-dimensional (CFD) two-phase flow codes, in a companion paper. [Le Corre, J.M., Yao, S.C., Amon, C.H., in this issue. A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one and three-dimensional computer codes. Nucl. Eng. Des.].     

Large eddy simulation of subchannels using the lattice Boltzmann method

Large eddy simulation results of a subchannel of a rod bundle with triangular rod arrangement are presented. The simulations have been carried out using the lattice Boltzmann method. The simulation results are compared with the measurements of (Trupp and Azad, 1975) [Trupp, A.C., Azad, R.S., 1975. The structure of turbulent flow in triangular array rod bundles. Nucl. Eng. Des. 32, 47]. The mean axial velocity profile shows good agreement with the measurement data. Secondary flow has been deduced from the measurements and it has been observed directly in the simulation results. Reasonable agreement has been achieved for most Reynolds stresses. Nevertheless, the calculated normal stresses show small, but systematic deviation from the measurement data.     

Analysis of large-scale tests for AP-600 passive containment cooling system

All next-generation light water reactors utilize passive systems to remove heat via natural circulation and are significantly different from past and current nuclear plant designs. One unique feature of the AP-600 is its passive containment cooling system (PCCS), which is designed to maintain containment pressure below the design limit for 72 h without action by the reactor operator. During a design-basis accident (DBA), i.e., either a loss-of-coolant or a main-steam-line break accident, steam escapes and comes in contact with the much cooler containment vessel wall. Heat is transferred to the inside surface of the steel containment wall by convection and condensation of steam and through the containment steel wall by conduction. Heat is then transferred from the outside of the containment surface by heating and evaporation of a thin liquid film that is formed by applying water at the top of the containment vessel dome. Air in the annular space is heated by both convection and injection of steam from the evaporating liquid film. The heated air and vapor rise as a result of natural circulation and exit the shield building through the outlets above the containment shell. All of the analytical models that are developed for and used in the COMMIX-1D code for predicting performance of the PCCS will be described. These models cover governing conservation equations for multicomponents single-phase flow, transport equations for the k − two-equation turbulence model, auxiliary equations, liquid-film tracking model for both inside (condensate) and outside (evaporating liquid film) surfaces of the containment vessel wall, thermal coupling between flow domains inside and outside the containment vessel, and heat and mass transfer models. Various key parameters of the COMMIX-1D results and corresponding AP-600 PCCS experimental data are compared and the agreement is good. Significant findings from this study are summarized.     

A study of the effects of the location of flashing inception on maximum and minimum critical two-phase flow rates:: Part II: analysis and modelling

A general unified model is developed to predict one-component critical two-phase pipe flow. An extension of the Henry [Henry, R.E., 1970. The Two-Phase Critical Discharge of Initially Saturated or Subcooled Liquid. Nucl. Sci. Eng. 41, 336-342.] and Henry and Fauske [Henry, R.E., Fauske, H.K., 1970. The two-Phase critical Flow of One-Component Mixtures in Nozzles; Orifices and Short Tubes, ASME J. Heat Transfer, May 1970.] models to incorporate the effects of wall friction and the location of flashing inception is proposed. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the experimental study of critical two-phase flow rates of saturated and subcooled water through long tubes given in Part I of this work. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass fluxes occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. The results of the present study, as well as available data since 1970 are compared with the model predictions. These data cover a wide range of conditions and include test section L/D ratios from 25 to 302 and a temperature and pressure range of 110-280°C and 0.16-6.9 Mpa, respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data.     

Dynamic analysis of multiple nuclear-coupled boiling channels based on a multi-point reactor model

This work investigates the non-linear dynamics and stabilities of a multiple nuclear-coupled boiling channel system based on a multi-point reactor model using the Galerkin nodal approximation method. The nodal approximation method for the multiple boiling channels developed by Lee and Pan [Lee, J.D., Pan, C., 1999. Dynamics of multiple parallel boiling channel systems with forced flows. Nucl. Eng. Des. 192, 31–44] is extended to address the two-phase flow dynamics in the present study. The multi-point reactor model, modified from Uehiro et al. [Uehiro, M., Rao, Y.F., Fukuda, K., 1996. Linear stability analysis on instabilities of in-phase and out-of-phase modes in boiling water reactors. J. Nucl. Sci. Technol. 33, 628–635], is employed to study a multiple-channel system with unequal steady-state neutron density distribution. Stability maps, non-linear dynamics and effects of major parameters on the multiple nuclear-coupled boiling channel system subject to a constant total flow rate are examined. This study finds that the void-reactivity feedback and neutron interactions among subcores are coupled and their competing effects may influence the system stability under different operating conditions. For those cases with strong neutron interaction conditions, by strengthening the void-reactivity feedback, the nuclear-coupled effect on the non-linear dynamics may induce two unstable oscillation modes, the supercritical Hopf bifurcation and the subcritical Hopf bifurcation. Moreover, for those cases with weak neutron interactions, by quadrupling the void-reactivity feedback coefficient, period-doubling and complex chaotic oscillations may appear in a three-channel system under some specific operating conditions. A unique type of complex chaotic attractor may evolve from the Rossler attractor because of the coupled channel-to-channel thermal-hydraulic and subcore-to-subcore neutron interactions. Such a complex chaotic attractor has the imbedding dimension of 5 and the fractal dimension ranging from 1.26 to 1.35.     

A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one- and three-dimensional computer codes

Based on a review of visual observations at or near critical heat flux (CHF) under subcooled flow boiling conditions and consideration of CHF triggering mechanisms, presented in a companion paper [Le Corre, J.M., Yao, S.C., Amon, C.H., 2010. Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions. Nucl. Eng. Des.], a model using a two-dimensional transient thermal analysis of the heater undergoing nucleation was developed to mechanistically predict CHF in the case of a bubbly flow regime. The model simulates the spatial and temporal heater temperature variations during nucleation at the wall, accounting for the stochastic nature of the boiling phenomena. It is postulated that a high local wall superheat occurring underneath a nucleating bubble at the time of bubble departure can prevent wall rewetting at CHF (Leidenfrost effect). The model has also the potential to evaluate the post-DNB heater temperature up to the point of heater melting.Validation of the proposed model was performed using detailed measured wall boiling parameters near CHF, thereby bypassing most needed constitutive relations. It was found that under limiting nucleation conditions; a peak wall temperature at the time of bubble departure can be reached at CHF preventing wall cooling by quenching. The simulations show that the resulting dry patch can survive the surrounding quenching events, preventing further nucleation and leading to a fast heater temperature increase. The model was applied at CHF conditions in simple geometry coupled with one-dimensional and three-dimensional (CFD) codes. It was found that, within the range where CHF occurs under bubbly flow conditions (as defined in Le Corre et al., 2010), the local wall superheat underneath nucleating bubbles is predicted to reach the Leidenfrost temperature. However, a better knowledge of statistical variations in wall boiling parameters would be necessary to correctly capture the CHF trends with mass flux (or Weber number).     

安全壳模型装置内氢气分布特性及影响因素分析

采用计算流体力学方法,首先利用THAI HM-2实验对CFX分析模型的适用性进行验证,通过与实验数据的比对,表明计算结果与实验数据基本吻合,从而验证选用的模型适合对安全壳模拟装置氢气分布特性的分析。之后,建立待研究中等规模安全壳模型实验装置的三维几何模型和网格模型,采用基准工况+单因素对比的方式,分别模拟湍流浮力射流中心喷射和近壁面喷射工况以及考虑蒸汽壁面冷凝情况下安全壳模型内的氦气(氢气替代工质)流动扩散分布,讨论喷射位置因素、壁面蒸汽凝结效应对氦气分布的影响。分析结果表明,喷射位置对氦气分布的影响主要体现在壁面引流现象上,即氦气流更倾向于沿着安全壳壁面进行流动和扩散;而与安全壳壁面的换热和蒸汽的冷凝会进一步促进大空间自然对流的建立,从而较为显著地提高氦气在安全壳内的扩散和混合效果。