A theoretically based critical heat flux prediction for rod bundles at PWR conditions

A theoretically based procedure developed for round tubes has been applied to the prediction of DNB heat fluxes in rod bundles at PWR conditions. State-of-the-art subchannel analysis procedures were used to determine local flows and enthalpies. Very good comparison between DNB predictions and experimental observations are found for rod bundles which both uniform and non-uniform axial heat fluxes.     

An utilization of liquid sublayer dryout mechanism in predicting critical heat flux under low pressure and low velocity conditions in round tubes

From a theoretical assessment of extensive critical heat flux (CHF) data under low pressure and low velocity (LPLV) conditions, it was found out that lots of CHF data would not be well predicted by a normal annular film dryout (AFD) mechanism, although their flow patterns were identified as annular–mist flow. To predict these CHF data, a liquid sublayer dryout (LSD) mechanism has been newly utilized in developing the mechanistic CHF model based on each identified CHF mechanism. This mechanism postulates that the CHF occurrence is caused by dryout of the thin liquid sublayer resulting from the annular film separation or breaking down due to nucleate boiling in annular film or hydrodynamic fluctuation. In principle, this mechanism well supports the experimental evidence of residual film flow rate at the CHF location, which can not be explained by the AFD mechanism. For a comparative assessment of each mechanism, the CHF model based on the LSD mechanism is developed together with that based on the AFD mechanism. The validation of these models is performed on the 1406 CHF data points ranging over P=0.1–2 MPa, G=4–499 kg m⁻² s⁻¹, L/D=4–402. This model validation shows that 1055 and 231 CHF data are predicted within ±30 error bound by the LSD mechanism and the AFD mechanism, respectively. However, some CHF data whose critical qualities are <0.4 or whose tube length-to-diameter ratios are <70 are considerably overestimated by the CHF model based on the LSD mechanism. These overestimations seem to be caused by an inadequate CHF mechanism classification and an insufficient consideration of the flow instability effect on CHF. Further studies for a new classification criterion screening the CHF data affected by flow instabilities as well as a new bubble detachment model for LPLV conditions, are needed to improve the model accuracy.     

Development of a critical heat flux mapping method for fin-structured surfaces

In this study, we performed critical heat flux (CHF) experiments using structured surfaces to validate the parameter effects and understand their physical meanings. Experimental results showed that the CHF has a peak value as the fin geometry changes. Fins with height of 0.5 mm produced the largest CHF, 1.7 MW/m², and fins longer than 2 mm reduced the CHF values. To explain the results, a CHF mapping method was developed describing the liquid supply-side and demand-side limits. The liquid demand-side limit is governed by the heat removal capability, mainly the nucleate boiling, calculated using the hot spot model. We consider three liquid supply-side limits restricting the liquid supply to the heating surface: capillary limit and counter-current flow limitations (CCFLs). The capillary limit is determined by balancing the capillary pressure and viscous dissipation in the liquid film on the fin side. The CCFL in the structure is calculated using the Wallis correlation and the CCFL in the free volume limits the liquid downward flow by the vapor jetting from the heating surface. The CHF map for our experimental results successfully describes the CHF trend of the structured surfaces. As a result, we concluded that CHF mapping method is an effective means of explaining CHF in pool boiling.     

Development of critical heat flux correlation for In-vessel retention

ABSTRACT

In-vessel retention (IVR) is a strategy for severe accident management in which the lower head of the reactor vessel is submerged in a water-flooded reactor cavity. Critical heat flux (CHF) data for IVR are important for estimating cooling capacity of the reactor vessel. The existing CHF data for IVR which were obtained for the specific geometries and thermal-hydraulic conditions of actual plants are difficult to be applied to plants with other specifications. Hence, the purpose of this study is to develop CHF correlations applicable to various pressurized water reactor plants in a wide range of thermal outputs based on newly obtained CHF data. A rectangular test section with a cross-section of 150 mm × 150 mm and length of 600 mm was used for simulating a cooling channel. The thermal-hydraulic conditions expected in actual plants were studied, and the results were used in the experiment. The effects of parameters such as pressure, mass flux, thermodynamic quality, and angle on CHF were investigated . Based on these results, we developed a CHF correlation formula that can be applied to a wider range than previously, up to a maximum heat flux of 3000 kW/m², and that predicts CHF with an error of ± 10%.     

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).     

An improved mechanistic critical heat flux model and its application to motion conditions

The motion of the flow channel will create a new acceleration field other than gravitational acceleration field for the fluid flow in the heated channel. And the new acceleration field will create new forces acting on bubbles, which will make the intermittent vapor blankets and bubbles in the near-wall region behave in a different way. In order to investigate the influence of this new arisen acceleration field on the occurrence of critical heat flux (CHF), an improved model based on microscopic mechanism of bubble dynamics is developed with the liquid sublayer dryout mechanism which has been well investigated by the previous researchers. Forces exerted on the vapor blankets have been taken into account to determine the liquid sublayer thicknesses and relative velocities of the vapor blankets through force balances in the radial direction and axial direction, respectively. At the same time, the proposed liquid sublayer dryout model presents pretty good prediction ability for saturated flow boiling CHF. The parametric trends of CHF in terms of mass flow rate, inlet subcooling and pressure for both the subcooled and saturated flow boiling are studied qualitatively and quantitatively. The effects of accelerations induced by channel motions in both the flow direction and the normal direction to the heated wall are investigated. Comparisons between the prediction results and the experimental data show good precision and accuracy.     

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.].     

The mechanism and prediction of critical heat flux in inverted geometries

Recent interest in a severe accident management scheme known as ‘In-Yessel Retention’ has created the need to establish the coolability limits of large, inverted geometries. In this paper, full-scale simulations conducted at UCSB's ULPU facility are examined at the microscopic level. Because of the peculiar geometry, it has become possible to directly visualize the boiling transition phenomenon, and with the help of microthermocouples to quantitatively identify the mechanism of dryout. Altogether, a new boiling transition regime was identified, with a significant coupling between overall systems dynamics and the microphenomena. This leads the way to the a priori prediction of critical heat flux and factors that may influence it.     

Effect of pressure on critical heat flux in uniformly heated vertical annulus under low flow conditions

Critical heat flux (CHF) experiments have been carried out in a wide range of pressure for an internally heated vertical annulus. The experimental conditions covered a range of pressure from 0.57 to 15.01 MPa, mass fluxes of 0 kg m⁻² s⁻¹ and from 200 to 650 kg m⁻² s⁻¹, and inlet subcoolings from 85 to 413 kJ kg⁻¹. Most of the CHFs were identified to the dryout of the liquid film in the annular-mist flow. For the mass fluxes of 550 and 650 kg m⁻² s⁻¹, the CHFs had a maximum value at a pressure of 2–3 MPa, and the pressure at the maximum CHF values had a trend moving toward the pressure at the peak value of pool boiling CHF as the mass flux decreased. The CHF data under a zero mass flux condition indicate that both the effects of pressure and inlet subcooling on the CHF were smaller, compared with those for the CHF with a net water upflow. The Doerffer correlation using the 1995 CHF look-up table and the Bowring correlation show a good prediction capability for the present CHF data.     

Critical heat flux prediction in rod bundles under upward low mass flux densities

The analysis of experimental data and results of calculations for heat transfer crisis in heated channels under low upward coolant mass flux densities is presented. This analysis allows the determination of the basic features of the boiling crisis phenomenon. It is shown that the methods currently used for critical heat flux (CHF) prediction have insufficient accuracy in the given range of parameters. A new relationship for the CHF calculation is presented. It should be used for the water–water energy reactor (WWER) and uran–graphite channel reactor—Chernobyl-type (RBMK) rod bundles, and is verified by the test data. The comparison of results obtained by a new CHF correlation and the relationship used in RELAP5/MOD3.1 Code is presented. It is shown that the latter overpredicts the CHF values at atmospheric pressure and for x_cr>0.4 and does not provide conservative estimations for the RBMK fuel bundles.     

Development of the critical film thickness correlation for an advanced annular film mechanistic dryout model applicable to MARS code

It is generally assumed in the mechanistic film dryout model that the critical heat flux (CHF) arises when liquid film calculated from evaporation, droplet entrainment and deposition gets dryout. The dryout of film is usually assumed when film thickness becomes zero. However, it was indicated that the complete dryout assumption can estimate CHF well for uniform heating case but cannot simulate accurately for non-uniform heating case. The critical film thickness concept may be an appropriate approach physically because there is a possibility of instantaneous disappearance of liquid film when it gets very thin. Therefore, a critical dryout film thickness correlation was developed to properly model dryout phenomenon together with MARS code based on experimental data. The modified version of MARS implementing a newly developed critical dryout film thickness correlation was assessed using various dryout data including those of non-uniform heating case and flow reduction transient test. The prediction results showed improved agreement with the experimental data.     

Classification and prediction of the critical heat flux using fuzzy theory and artificial neural networks

A new method to predict the critical heat flux (CHF) is proposed, based on the fuzzy clustering and artificial neural network. The fuzzy clustering classifies the experimental CHF data into a few data clusters (data groups) according to the data characteristics. After classification of the experimental data, the characteristics of the resulting clusters are discussed with emphasis on the distribution of the experimental conditions and physical mechanism. The CHF data in each group are trained in an artificial neural network to predict the CHF. The artificial neural network adjusts the weight so as to minimize the prediction error within the corresponding cluster. Application of the proposed method to the KAIST CHF data bank shows good prediction capability of the CHF, better than other existing methods.     

On the definition of critical heat flux margin

This paper reviews the current definition of critical heat flux (CHF) margins and discusses their differences.     

Assessment of a DNB-type theoretical critical heat flux model for rod bundles with non-uniform axial power shapes

A general critical heat flux (CHF) prediction method with a wide applicable range and reasonable accuracy is essential to the thermal-hydraulic design and safety analysis at the conceptual design stage for a new pressurized water reactor (PWR). In this study, the Korea Advanced Institute of Science and Technology (KAIST) liquid sub-layer dryout CHF prediction model for Departure from Nucleate Boiling (DNB) region has been implemented in a sub-channel analysis code, and investigated for the method's possible use in a rod bundle environment with various non-uniform axial power shapes. The KAIST model showed comparable prediction capability to Lin's method for bottom-, center-, and top-peaked heat flux shapes. The KAIST model, without any correction factors or empirical constants, turned out to be suitable to fulfill the needs for a basis of a general CHF prediction method as compared to Lin's method and Westinghouse-3 (W-3) correlation.     

Prediction of critical heat flux using ANFIS

The prediction of Critical Heat Flux (CHF) is essential for water cooled nuclear reactors since it is an important parameter for the economic efficiency and safety of nuclear power plants. Therefore, in this study using Adaptive Neuro-Fuzzy Inference System (ANFIS), a new flexible tool is developed to predict CHF. The process of training and testing in this model is done by using a set of available published field data. The CHF values predicted by the ANFIS model are acceptable compared with the other prediction methods. We improve the ANN model that is proposed by Vaziri et al. (2007) to avoid overfitting. The obtained new ANN test errors are compared with ANFIS model test errors, subsequently. It is found that the ANFIS model with root mean square (RMS) test errors of 4.79%, 5.04% and 11.39%, in fixed inlet conditions and local conditions and fixed outlet conditions, respectively, has superior performance in predicting the CHF than the test error obtained from MLP Neural Network in fixed inlet and outlet conditions, however, ANFIS also has acceptable result to predict CHF in fixed local conditions.     

The critical heat flux for boiling water in tubes

An analysis of the experimental results obtained by various authors on critical heat flux is carried out by using nondimensional criteria. Recommendations are given for the numerical methods of determining values of the critical heat flux in the case of a steam-water mixture, underheated to saturation in tubes and in ring-shaped and plane slotted channels.     

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.     

A new model for predicting the critical heat flux based on nucleation site density in downward-face boiling

ABSTRACT

Due to the important role critical heat flux (CHF) plays in the boiling field, it is of great significance to study CHF, especially the mechanism of CHF in the nucleate boiling. In this study, a new model to predict CHF both in pool boiling and flow boiling of downward-face was proposed and the relationship between CHF and nucleation site density (NSD) was studied. The model was based on the bubble interaction theory, which assumed that CHF happened due to the coalescing of the bubbles generated on the heating surface and prevented liquid to be supplied. The relationship between NSD and CHF was derived from previous observations in the experiments and simulations. To validate the relationship between NSD and CHF, several experiments with CHF and NSD were chosen and they all showed good agreement with our assumptions. Due to the rarity of experimental data on NSD and CHF, the numerical method was also used to validate. The results also showed an inverse relationship between CHF and NSD.     

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.     

Analysis of the critical heat flux in round vertical tubes under low pressure and flow oscillation conditions. Applications of artificial neural network

Artificial neural networks (ANNs) for predicting critical heat flux (CHF) under low pressure and oscillation conditions have been trained successfully for either natural circulation or forced circulation (FC) in the present study. The input parameters of the ANN are pressure, mean mass flow rate, relative amplitude, inlet subcooling, oscillation period and the ratio of the heated length to the diameter of the tube, L/D. The output is a nondimensionalized factor F, which expresses the relative CHF under oscillation conditions. Based on the trained ANN, the influences of principal parameters on F for FC were analyzed. The parametric trends of the CHF under oscillation obtained by the trained ANN are as follows: the effects of pressure below 500 kPa are complex due to the influence of other parameters. F will increase with increasing mean mass flow rate under any conditions, and will decrease generally with an increase in relative amplitude. F will decrease initially and then increase with increasing inlet subcooling. The influence curves of mean mass flow rate on F will be almost the same when the period is shorter than 5.0 s or longer than 15 s. The influence of L/D will be negligible if L/D>200. It is found that the minimum number of neurons in the hidden layer is a product of the number of neurons in the input layer and in the output layer.