Modelling of low-pressure subcooled flow boiling using the RELAP5 code

A new model for upward vertical subcooled flow boiling at low pressure has been proposed. The model considers the most relevant closure relationships of one-dimensional thermal-hydraulic codes that are important for accurate prediction of vapour contents in the channel: wall evaporation model, condensation model, flow regime transition criterion and drift-flux model. The new model was incorporated in the current version of the RELAP5 code, MOD3.2.2 Gamma. The modified code was validated against a number of published low-pressure subcooled boiling experiments, and in contrast to the current code, shows good agreement with experimental data. The presented analysis also leads to a better understanding of the basic mechanisms of subcooled flow boiling at low pressure.     

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).     

Modeling of low-pressure subcooled boiling flow of water via the homogeneous MUSIG approach

Applying a three-dimensional two-fluid model coupled with homogeneous multiple size group (MUSIG) approach, numerical simulations of upward subcooled boiling flow of water at low pressure were performed on the computational fluid dynamics (CFD) code CFX-10 with user defined FORTRAN program. A modified bubble departure diameter correlation based on the Unal's semi-mechanistic model and the empirical correlation of Tolubinski and Kostanchuk was developed. The water boiling flow experiments at low pressure in a vertical concentric annulus from reference were used to validate the models. Moreover, the influences of the non-drag force on the radial void fraction distribution were investigated, including lift force, turbulent dispersion force and wall lubrication force. Good quantitative agreement with the experimental data is obtained, including the local distribution of bubble diameter, void fraction, and axial liquid velocity. The results indicate that the local bubble diameter first increases and then decreases due to the effect of bubble breakup and coalescence, and has the maximum bubble diameter along the radial direction. Especially, the peak void fraction phenomenon in the vicinity of the heated wall is predicted at low pressure, which is developed from the wall repulsive force between vapor bubbles and heated wall. Nevertheless, there is a high discrepancy for the prediction of the local axial vapor velocity.     

Some challenges to the thermal-hydraulic codes

The thermal-hydraulic codes were developed with the data and correlations obtained from separate effect tests. As such. There are some system-related phenomena which cannot be depicted properly by the codes. In this paper we discuss the difficulties encountered by code modeling for the following systems: feedback loop, multichannel system, multidimensional flow and multiloop circulation. The discussion shows that codes can only give probable answers; the difficulties encountered are due to maldistribution of heat and flow, primary-secondary interaction, feedback effect, instrumentation-control interaction and other unknown factors.     

A subcooled boiling heat transfer predictive model for ITER EHF FW designs

Recent experimental data from the ITER critical heat flux (CHF) mock-ups was used to benchmark a 3D CFD code concerning subcooled boiling heat transfer for high heat flux removal. The predicted temperatures show good agreement with experimental measurements for a range of operating parameters and of cooling configurations. Specifically, it applies to a hypervapotron channel exposed to a 5 MW/m² surface heat load and cooled by velocity of 2 m/s. Such flow geometry and operating condition seem necessary for ITER-enhanced heat flux first wall modules if an adequate design margin in CHF is needed. A detailed CFD and heat transfer analysis performed on a prototyped CAD model provided a higher confidence on the design and is deemed a desirable feature for continued design exploration and optimization processes. This is particularly crucial in regard to flow distribution among the FW fingers.     

Interfacial area measurements in subcooled flow boiling

The purpose of the present study was to measure two-phase parameters in subcooled flow boiling. These parameters include void fraction distribution, interfacial area concentration distribution, Sauter mean diameter, and the interfacial velocity. A literature review was conducted and the results show that only three researchers have made local measurements in the subcooled boiling region. None of the previous have included results for interfacial area concentration distribution. To make these measurements an experimental facility was constructed that allows insertion of advanced local two-phase flow instrumentation. Experiments were performed for a number of conditions at atmospheric pressure.     

An investigation of transition boiling mechanisms of subcooled water under forced convective conditions

A mechanistic model for forced convective transition boiling has been developed to investigate transition boiling mechanisms and to predict transition boiling heat flux realistically. This model is based on a postulated multi-stage boiling process occurring during the passage time of the elongated vapor blanket specified at a critical heat flux (CHF) condition. Between the departure from nucleate boiling (DNB) and the departure from film boiling (DFB) points, the boiling heat transfer is established through three boiling stages, namely, the macrolayer evaporation and dryout governed by nucleate boiling in a thin liquid film and the unstable film boiling characterized by the frequent touches of the interface and the heated wall. The total heat transfer rates after the DNB is weighted by the time fractions of each stage, which are defined as the ratio of each stage duration to the vapor blanket passage time. The model predictions are compared with some available experimental transition boiling data. The parametric effects of pressure, mass flux, inlet subcooling on the transition boiling heat transfer are also investigated. From these comparisons, it can be seen that this model can identify the crucial mechanisms of forced convective transition boiling, and that the transition boiling heat fluxes including the maximum heat flux and the minimum film boiling heat flux are well predicted at low qualities/high pressures near 10 bar. In future, this model will be improved in the unstable film boiling stage and generalized for high quality and low pressure situations.     

Vapour void fraction in subcooled flow boiling

Experimental data on steam void fraction and axial temperature distribution in an annular boiling channel for low mass-flux forced and natural circulation flow of water with inlet subcooling have been obtained. The ranges of variables covered are: mass flux = 1.4 × 10⁴−1.0 × 10⁵ kg/hr m²; heat flux = 4.5 × 10³−7.5 × 10⁴ kcal/hr m²; and inlet subcooling = 10–70°C. The present and literature data match well with the theoretical void predictions using a four-step method similar to that suggested by Zuber and co-workers.     

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.].     

An integral equation model for critical heat flux at subcooled and low quality flow boiling

A new theoretical model of critical heat flux (CHF) is developed for the flow boiling condition from bubble-detached to low quality range. The CHF condition is postulated to occur when the superheated liquid layer on the heated wall, which is formed under the bubbly layer from the point of the onset of significant void generation, is depleted due to the evaporation along the heated length. The model shows a very promising agreement with the uniformly heated round tube data for both water and refrigerants by simply applying well-known constitutive relationships without any tuning constant for the CHF data. The significance of the proposed model in unifying the existing models is also discussed.     

Void fraction distribution in low flow rate subcooled boiling

Experimental data are presented for the void fraction distribution in low flow rate forced convection subcooled boiling of water in a heated vertical tube at steady-state conditions. The measurements are based on gamma attenuation and X-ray radiography techniques. The measured local equilibrium quality at the point of net vapor generation and the void fraction profiles are compared with theoretical and empirical models of subcooled boiling. A close fit to the experimental results is obtained by the Levy model and by the Saha and Zuber correlation.     

A mechanistic critical heat flux model for wide range of subcooled and low quality flow boiling

A mechanistic model to predict a critical heat flux (CHF) over a wide operating range in the subcooled and low quality flow boiling has been proposed based on a concept of the bubble coalescence in the wall bubbly layer. The conservation equations of mass, energy and momentum, together with appropriate constitutive relations, are solved analytically to derive the CHF formula. The model is characterized by an introduction of the drag force due to wall-attached bubbles roughness in the momentum balance, which determines the limiting transverse interchange of mass flux crossing the interface of the wall bubbly layer and core. Comparison between the predictions by the proposed model and the experimental CHF data shows good agreement over a wide range of parameters for both light water and fusion reactors operating conditions. The model correctly accounts for the effects of flow variables such as pressure, mass flux and inlet subcooling as well as geometry parameters.     

CSNI validation matrix for PWR and BWR thermal-hydraulic system codes

An internationally agreed validation matrix for PWR and BWR thermal-hydraulic system codes has been established by the CSNI-PWG-2 Task Group on Status and Assessment of Codes for Transients and ECCS. The matrix will be a guide for independent code assessment, will be a basis for the comparisons of code predictions performed with different system codes, and may contribute to the quantification of the uncertainty range of code predictions.     

Dependence of bubble behavior in subcooled boiling on surface wettability

This paper presents the results of visualization experiments that were carried out to investigate the dynamics of vapor bubbles generated in water pool boiling. In the experiments, vapor bubbles were generated on a vertical circular surface of a copper block containing nine cartridge heaters, and the contact angle of the heated surface was used as a main experimental parameter. The experiments were performed under subcooled as well as nearly saturated conditions. To enable clear observation of individual bubbles with a high speed camera, the heat flux was kept low enough to eliminate significant overlapping of bubbles. When the contact angle was small, the bubbles were lifted-off the vertical heated surface within a short period of time after the nucleation. On the other hand, when the contact angle was large, they slid up the vertical surface for a long distance. When bubbles were lifted-off the heated surface in subcooled liquid, bubble life-time was significantly shortened since bubbles collapsed rapidly due to condensation. It was shown that this distinct difference in bubble dynamics could be attributed to the effects of surface tension force.     

Vapour bubble growth and recondensation in subcooled boiling flow

A physical model for the dynamics of vapour bubbles is presented, which is applicable to bubbles generated at the heated wall of channels with boiling flow. By comparing the theory with experimental data from various sources, it is shown that simultaneous agreement can be obtained with regard to bubble size, bubble lifetime and recondensation rate within the error band of experimental data by the proper choice of one fitting parameter only. The proposed model is then compared with some previously published approaches. Correlations for the dependence of bubble lifetime and bubble size on local fluid conditions are derived which are suitable for the prediction of vapour contents in heated channels with subcooled inlet flow.     

Prediction of the onset of flow instability in transient subcooled flow boiling

A new model to predict the onset of flow instability (OFI) in transient subcooled flow boiling has been developed. The model is based upon the influence on vapor bubble departure of the single-phase temperature profile. The steady-state result of the present model was compared to the experimental data of Whittle and Forgan [1] and Dougherty et al. [2], showing an excellent agreement. The model was then employed in a transient analysis of OFI for vertical downwards turbulent flow to predict whether OFI takes place. The condition for OFI to occur in transient flow situations was also predicted by this model. Two modes for pressure gradient change inside the channel are considered in the present study: step change and ramp change. The calculations were made for various combinations of the flow operating condition and the mode of pressure drop change.     

Analytical benchmarks for verification of thermal-hydraulic codes based on sub-channel approach

Over the last year (2007), preliminary tests have been performed on the Moroccan TRIGA MARK II research reactor to show that, under all operating conditions, the coolant parameters fall within the ranges allowing the safe working conditions of the reactor core. In parallel, a sub-channel thermal-hydraulic code, named SACATRI (Sub-channel Analysis Code for Application to TRIGA reactors), was developed to satisfy the needs of numerical simulation tools, able to predict the coolant flow parameters. The thermal-hydraulic model of SACATRI code is based on four partial differential equations that describe the conservation of mass, energy, axial and transversal momentum. However, to achieve the full task of any numerical code, verification is a highly recommended activity for assessing the accuracy of computational simulations. This paper presents a new procedure which can be used during code and solution verification activities of thermal-hydraulic tools based on sub-channel approach. The technique of verification proposed is based mainly on the combination of the method of manufactured solution and the order of accuracy test. The verification of SACATRI code allowed the elaboration of exact analytical benchmarks that can be used to assess the mathematical correctness of the numerical solution to the elaborated model.     

Experimental study of onset of subcooled annular flow boiling

An experimental study on the onset of nucleate boiling (ONB) is performed for water annular flow to provide a systematic database for low pressure and velocity conditions. A parametric study has been conducted to investigate the effect of pressure, inlet subcooling, heat and mass flux on flow boiling. The test section includes a Pyrex tube with 21 mm inner diameter and a stainless steel (SS-304) rod with outer diameter of 6 mm. Pressure, heat and mass flux are in the range of 1.73 < P < 3.82 bar, 40 < q < 450 kW/m² and 70 < G < 620 kg/m² s, respectively. The results illustrate that inception heat flux is extremely dependent on pressure, inlet subcooling temperature and mass flux; for example in pressure, velocity and inlet subcooling as 3.27 bar, 230 kg/m² s and 41.3 °C; consequently q_w,ONB is 177.3 kW/m². In other case with higher inlet temperature of 71.5 °C and with P, 3.13 bar and G, 232 kg/m² s the inception heat flux reached to 101.6 kW/m². The data of ONB heat flux are over estimated from the existing correlation, and maximum deviation of wall superheat (ΔT_w,ONB) from correlations is 30%. Experimental data of inception heat flux are within 22% of that predicted from the correlation.