Critical heat flux of water in vertical round tubes at low pressure and low flow conditions

An experimental study on critical heat flux (CHF) has been performed for water flow in vertical round tubes under low pressure and low flow (LPLF) conditions to provide a systematic data base and to investigate parametric trends. Totally 513 experimental data have been obtained with Inconel-625 tube test sections in the following conditions: diameter of 6, 8, 10 and 12 mm; heated length of 0.31.77 m; pressure of 106951 kPa; mass flux of 20277 kg m⁻² s⁻¹; and inlet subcooling of 50654 kJ kg⁻¹, thermodynamic equilibrium critical quality of 0.3231.251 and CHF of 1081598 kW m⁻². Flow regime analysis based on Mishima & Ishii’s flow regime map indicates that most of the CHF occurred due to liquid film dryout in annular-mist and annular flow regimes. Parametric trends are examined from two different points of view: fixed inlet conditions and fixed exit conditions. The parametric trends are generally consistent with previous understandings except for the complex effects of system pressure and tube diameter. Finally, several prediction models are assessed with the measured data; the typical mechanistic liquid film dryout model and empirical correlations of (Shah, M.M., 1987. Heat Fluid Flow 8 (4), 326–335; Baek, W.P., Kim, H.G., Chang, S.H., 1997. KAIST critical heat flux correlation for water flow in vertical round tubes, NUTHOS-5, Paper No. AA5) show good predictions. The measured CHF data are listed in Appendix B for future reference.     

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.     

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.     

Prediction of critical heat flux for water flow in vertical round tubes using support vector regression model

This paper deals with ν-support vector regression (ν-SVR) based prediction model of critical heat flux (CHF) for water flow in vertical round tubes. The dataset used in this paper is obtained from available published literature. The dataset is partitioned into two independent sets, a training data set and a test data set, to avoid overfitting problem. To train the ν-SVR models with more informative data, the training data is selected using a subtractive clustering (SC) scheme, and then the remaining data is used as test data to evaluate the performance of the ν-SVR models. Next, the parametric trends of CHF are investigated using the ν-SVR models. The results obtained from the ν-SVR models are compared with those obtained from the radial basis function (RBF) network, which is a kind of artificial neural networks (ANNs). It is found that the results of the ν-SVR models are not only in better agreement with the experimental data than those of the RBF network, but also follow the general understanding. The analysis results indicate that the ν-SVR models can be successfully applied to CHF prediction.     

An investigation of flow characteristics and critical heat flux in vertical upward round tube

Prediction of critical heat flux （CHF） in annular flow is important for the safety of once - through steam generator and the reactor core under accident conditions. The dryout in annular flow occurs at the point where the film is depleted due to entrainment, deposition, and evaporation. The film thickness, film mass flow rate along axial distribution, and CHF are calculated in vertical upward round tube on the basis of a separated flow modcl of annular flow. The theoretical CHF values are higher than those derived from experimental data, with error being within 30%.     

Critical heat flux for finned and unfinned geometries under low flow and low pressure conditions

This paper presents the experiment and analysis for the critical heat flux (CHF) in a vertical annulus with finned and unfinned geometries under low flow and low pressure conditions. To consider the fin effect on CHF, the tests were performed on both finned heater and unfinned heater having same dimension as finned heater without fins. An analytical model was applied to estimate the heat flux and temperature distributions along the periphery of the finned geometry. The physical phenomena observed during the experiments are discussed and the parametric trends of the obtained data are examined to investigate the CHF characteristics for the finned geometry. A new correlation is proposed to predict the CHF for both finned and unfinned geometries at low flow and low pressure conditions. The developed correlation predicts the experimental data with an RMS error of 13.7%.     

Comparison of correlations for predicting critical heat flux for uniformly heated vertical porous coated tubes at low pressure

The paper includes comparison of correlations for predicting critical heat flux for uniformly heated vertical porous coated tubes at pressure between 0.1 and 0.7 MPa. In this study, a total of 1120 data points of CHF (Critical heat flux) in uniformly heated vertical porous coated tubes were used. Accuracy of correlations was estimated by calculating average and RMS error with available experimental data, and a new correlation is presented. The new correlation predicts that the CHF data are significantly better than those currently available correlations, with average error 0.69% and RMS error 10.9%.     

Prediction of critical heat flux in vertical pipe flow

A previously developed semi-empirical model for adiabatic two-phase annular flow is extended to predict the critical heat flux (CHF) in a vertical pipe. The model exhibits a sharply declining curve of CHF versus steam quality (X) at low X, and is relatively independent of the heat flux distribution. In this region, vaporization of the liquid film controls. At high X, net deposition upon the liquid film becomes important and CHF versus X flattens considerably. In this zone, CHF is dependent upon the heat flux distribution. Model predictions are compared to test data and an empirical correlation. The agreement is generally good if one employs previously reported mass transfer coefficients.     

Critical heat flux under flow oscillation of water at low-pressure, low-flow conditions

In this work, the effect of flow oscillations on critical heat flux (CHF) is investigated for water flow in vertical round tubes at low-pressure, low-flow (LPLF) conditions. An experimental study has been conducted to investigate the difference in CHF between forced and natural circulations, and between stable and oscillating flow conditions with three vertical round tube test sections (5.0 mm ID×0.6 m in length, 6.6 mm ID×0.5 m in length, and 9.8 mm ID×0.6 m in length) for mass fluxes below 400 kg m⁻² s⁻¹ under near atmospheric pressure. It is found that flow oscillations can drastically reduce the CHF, in particular for natural-circulation conditions. In addition to the experiments, CHF correction factors for flow oscillation effects are developed for forced and natural circulations, respectively, based on the experimental data of the present work and others.     

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 experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions

An experimental study of the critical heat flux (CHF) has been performed for a water flow in a non-uniformly heated vertical 3 × 3 rod bundle under low flow and a wide range of pressure conditions. The experiment was especially focused on the parametric trends of the CHF and the applicability of the conventional CHF correlations to a return-to-power conditions of a main steam line break accident whose conditions might be a low mass flux, intermediate pressure, and a high inlet subcooling. The effects of the mass flux and pressure on the CHF are relatively large and complicated in the low pressure conditions. At a high mass flux or a low critical quality, the local heat flux at the CHF location sharply decreases with an increasing local critical quality. However, at a low mass flux or a high critical quality, the local heat flux at the CHF location shows a nearly constant value regardless of the increase of the critical quality. The CHF data at the very low mass flux conditions are correlated well by the churn-to-annular flow transition criterion or the flow reversal phenomena. Several conventional CHF correlations predict the present return-to-power CHF data with reasonable accuracies. However, the prediction capabilities become worse in a very low mass flux of below about 100 kg/(m² s).     

Critical heat flux under zero flow conditions in vertical annulus with uniformly and non-uniformly heated sections

The experimental study of water CHF (critical heat flux) under zero flow conditions has been carried out in an annulus flow channel with uniformly and non-uniformly heated sections over a pressure range of 0.52–14.96 MPa. In the present boiling system, the CHFs occur in the upper region of the heated section, in contrast to the results in the experiments for boiling tubes conducted by several investigators. The general trend of the CHF with pressure is that the CHF increases up to a medium pressure of about 6–8 MPa and decreases as the pressure is further increased. A comparison of the present data with the existing flooding CHF correlations shows that the correlations depend greatly on the effect of the heat flux distribution. When the correction terms with the density ratio and the effect of the heat flux distribution proposed in the present work are used with the CHF correlation based on the Wallis flooding correlation, it predicts the measured flooding CHF within an RMS error of 9.0%.     

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.     

An experimental investigation on the critical heat flux enhancement by mechanical vibration in vertical round tube

In order to gain an understanding of the relationship between critical heat flux (CHF) and flow-induced vibration (FIV), an experimental investigation was carried out with vertical round tube at the atmosphere. In the both condition of departure from nucleate boiling (DNB) and the liquid film dryout (LFD), CHF increases up to 12.6% with vibration intensity, represented by vibrational Reynolds number (Re_v). CHF enhancement by tube vibration seems to come from the reinforced flow turbulent mixing and the increment of deposition of droplet into the liquid film. Based on the experimental results, an empirical correlation is proposed for the prediction of CHF enhancement ratio. The correlation predicts the CHF enhancement ratio (E_n) with reasonable accuracy, with an average error rate of 4.5 and 26.5% for RMS. Vibration is an effective method for heat transfer enhancement as well as CHF. Nonetheless, the risk of system failure by FIV has made it very difficult to take advantage of vibration in heat transfer facilities. Therefore, it is necessary to find out optimal fuel design enhancing the CHF but preventing FIV damage in an acceptable vibration range.     

Parametric trends analysis of the critical heat flux based on artificial neural networks

Parametric trends of the critical heat flux (CHF) are analyzed by applying artificial neural networks (ANNs) to a CHF data base for upward flow of water in uniformly heated vertical round tubes. The analyses are performed from three viewpoints, i.e., for fixed inlet conditions, for fixed exit conditions, and based on local conditions hypothesis. Katto's and Groeneveld et al. dimensionless parameters are used to train the ANNs with the experimental CHF data. The trained ANNs predict the CHF better than any other conventional correlations, showing RMS errors of 8.9%, 13.1% and 19.3% for fixed inlet conditions, for fixed exit conditions, and for local conditions hypothesis, respectively. The parametric trends of the CHF obtained from those trained ANNs show a general agreement with previous understanding. In addition, this study provides more comprehensive information and indicates interesting points for the effects of the tube diameter, the heated length, and the mass flux. It is expected that better understanding of the parametric trends is feasible with an extended data base.     

Experimental investigation on critical heat flux in horizontal channel for low pressure low flow (LPLF) condition

Studies reported in the past on critical heat flux (CHF) are mostly limited to vertical flow, large channel diameter, high pressure and high mass flux. Only few investigations are reported in the literature for horizontal flow CHF especially under low pressure and low flow conditions. Hence, predictive methods of CHF for horizontal flow are scarce. There is a need for understanding CHF in horizontal flow under low pressure and low flow conditions because they are commonly encountered in nuclear reactor fuel channels of pressurized heavy water reactor (PHWR) under loss of coolant accidental (LOCA) conditions. The present work investigates CHF of horizontal flow for low flow rates (mass flux of 100–400 kg/m² s) at nearly atmospheric pressure conditions. Parameters covered in this study are diameter (5.5 mm, 7.5 mm and 9.5 mm), length (0.45 m and 0.8 m) and a inlet temperature of 32 °C. The first occurrence of ‘red hot’ spot on the test section is considered as the onset of critical heat flux condition in the present work. Experimental results obtained are compared with Groeneveld et al. (2007) look up table data for vertical flow after applying correction factor given by Wong et al. (1990). The deviation of experimental CHF data from those predicted using Groeneveld et al. (2007) look up table and Wong et al. (1990) correction factor is more than 50%.     

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.     

An experimental and analytical investigation of uncovered core heat transfer under high pressure, low heat flux conditions

Experimental and analytical results are reported from two series of high pressure core uncovering experiments. It was determined that the uncovered core is cooled primarily by convection and radiation to dry steam and that droplets are confined to the immediate vicinity of the mixture level. Spacer grids substantially increased heat transfer at and downstream of the grid. A simple heat transfer model is presented which accurately predicts uncovered core heat transfer at modified wall Reynolds numbers greater than 2000. Results are expected to be use in modelling small break loss of coolant accidents.     

Type of flow, pressure drop, and critical heat flux of a two-phase sodium flow

Little is known about the two-phase pressure loss, the flow pattern, and the critical heat flux conditions for boiling sodium under forced convection. The specific thermohydraulic properties of sodium prohibit extrapolation to sodium of experimental data obtained for other liquids. Therefore, some new test series were carried out in a sodium loop with an induction heated test section of 9 mm inner diameter and 200 mm heated length. The two-phase pressure loss and the film thickness were measured up to the critical cooling conditions. The experimental results are compared with values predicted by known models on annular flow and annular mist flow, respectively. Satisfactory predictions of the flow pattern and the critical heat flux conditions could only be obtained using the measured two-phase pressure losses.