An experimental and analytical study of the effect of axial power profile on CHF

The effect of axial heat flux distribution (AFD) on the critical heat flux (CHF) was investigated. CHF measurements were obtained with HFC-134a cooled vertical tubes having four non-uniform and one uniform AFD profiles. The HFC-134a test conditions covered a pressure range from 1.6 to 2.4 MPa, a mass-flux range from 2.8 to 4.7 Mg m⁻² s⁻¹, and an inlet-quality range from −0.9 to 0. The water-equivalent pressure and mass-flux ranges are 10–14 MPa and 4–6.5 Mg m⁻² s⁻¹, respectively.In general, the observed AFD effect on critical power is small at high inlet subcoolings. At low inlet subcoolings, the critical power for the inlet-peak profile is up to 15% higher than that for the outlet-peak profile. A local conditions analysis showed that the AFD has the strongest effect on CHF at high dryout qualities. CHF values for non-uniform AFDs could be 50% lower than those for the uniform AFD. The AFD effect on CHF becomes diminished with decreasing dryout quality.Four different approaches to account for the effect of AFD on CHF were assessed against the experimental values from the current experiment. The boiling-length-average heat-flux approach with the boiling-length starting point at the onset of annular flow (OAF) provided the best prediction of the critical power and the CHF location.     

Fluid-to-fluid modeling of critical heat flux in 4 × 4 rod bundles

Fluid-to-fluid modeling of critical heat flux (CHF) is to simulate the CHF behaviors for water by employing low cost modeling fluid, and the flow scaling factor is the key to apply the technique to fuel bundles. The CHF experiments in 4×4 rod bundles have been carried out in Freon-12 loop in equivalent nuclear reactor water conditions (P=10.0–16.0 MPa, G=488.0–2100.0 kg/m² s, X_cr=−0.20–0.30). The models in fluid-to-fluid modeling of CHF is verified by the CHF data for Freon-12 obtained in the experiment and the CHF correlation for water obtained by Nuclear Power Institute of China (NPIC) in the same 4×4 rod bundles. It has been found that the S.Y. Ahmad Compensation Distortion model, the Lu Zhongqi model, the Groeneveld model and Stevens–Kirby model overpredict the bundles CHF values for water. Then an empirical correlation of flow scaling factor is proposed. Comparison of the CHF data in two kinds of test sections for Freon-12, in which the distance of the last grid away the end of heated length is different, shows that the spacer grid, which is located at 20 mm away from the end of the heated length, has evidently influenced on the CHF value in the 4×4 rod bundles for Freon-12. This is different from that for water, and the need for further work is required.     

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.     

氟利昂CHF数据对压水堆工况下LUT-2006过冷CHF预测能力的评估

以R-134a为模化工质,在内径为8 mm的圆管中进行了临界热流密度（CHF）实验研究。讨论了R-134a的CHF参数变化趋势,评价了Katto的流体模化方法。结果表明,CHF仅受局部参数影响,长径比的影响可以忽略。R-134a的CHF参数趋势与典型水的CHF参数趋势相似。Katto的模化方法在低临界含气率甚至是负临界含气率下都有很高的精度。将R-134a的CHF实验数据通过模化方法转换成等效水数据,并与CHF查询表（LUT）-2006进行了比较。评价结果表明,即使在几乎没有过冷CHF数据的压水堆工况,LUT-2006仍具有很高的预测精度。      

CHF and dryout point in vertical narrow annuli

Experimental study associated with CHF and dryout point in narrow annuli is conducted with 1.5 mm and 1.0 mm gap, respectively. Distilled water is used as work fluid. The parameters examined were: pressure from 2.0 MPa to 4.0 MPa; mass flux from 26.0 kg/(m² s) to 69.0 kg/(m² s); heat flux from 10 kW/m² to 70 kW/m²; exit equilibrium mass quality from 0.52 to 1.08.It is found that CHF monotonously increases with mass flux in internally heated annuli and bilaterally heated annuli. However, the observed trends are not similar to that in externally heated annuli. The CHF is not affected significantly by mass flux.Critical qualities of dryout point (X_DO) decreases with mass flux and increases with inlet qualities. Under the same conditions X_DO in outer tube are always larger than that in inner tube. According to experimental data, a criterion for the appearance of dryout point for bilaterally heated has been presented.The comparison with the correlations [КУТАТЕЛАДЗЕ, C.C., 1979. Тедплоэнергетика, No. 6] and experimental data indicates that the existing correlations applied to tube cannot predict X_DO in narrow annuli well. Based on experimental data, a new correlation is developed.     

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.     

Critical heat flux at high velocity channel flow with high subcooling

A quantitative analysis of critical heat flux (CHF) in heated channels under high mass flux with high subcooling was successfully carried out by applying a new flow model to the existing CHF model of a macro-water-sublayer on the heated wall and steam blankets over it. The CHF correlation proposed could correctly predict the existing experimental data for circular tubes of 0.33–4 mm in diameter with mass flux of 124–90 000 kg (m² s)⁻¹ and inlet water subcooling of 35–210 K at 0.1–7.1 MPa, resulting in CHF of 4.2–224 MW m⁻², and for rectangular channels of 3–20 mm gap with a mass flux of 940–27 000 kg (m² s)⁻¹ and inlet water subcooling of 13–166 K at 0.1–3.0 MPa, resulting in CHF of 2.0–62 MW m⁻². An error of the CHF correlation has also been estimated.     

Critical heat flux in a vertical tube at low and medium pressures. Part II — new data representation

An analysis of the physical processes taking place in a dispersed-annular flow which govern dry-out type CHFs has been carried out. The analysis has shown that the number of variables required to describe the critical phenomena can be reduced by the introduction of a new parameter: the length over which dispersed-annular flow takes place, L_dan. In this case only, for a given tube diameter, pressure and mass flux, the critical heat flux may be expressed in terms of a single variable: L_dan. A correlation which may be used to determine this length has also been developed. The representation of the CHF data obtained at low pressures in terms of the coordinate system (L_dan, q″_cr) has shown that the dispersion of the data about the regression curves is considerably reduced as compared with the traditional presentation of the critical heat flux as a function of the thermodynamic quality at the end of the heated length.     

CHF experiment and CFD analysis in a 2 × 3 rod bundle with mixing vane

In this study, the CHF enhancement using various mixing vanes is evaluated and the flow characteristics are investigated through the CHF experiments and CFD analysis.CHF tests were performed using 2 × 2 and 2 × 3 rod bundles and with R-134a as the working fluid. The test section geometry was identical to that of commercial PWR fuel assembly not including the heated length (1.125 m) and number of fuel rods. From the CHF tests, it was found that the CHF enhancement using mixing vanes under higher mass flux (1400 kg/m² s) and lower pressure (15 bar) conditions is larger than the CHF enhancements under other conditions. Among the mixing vanes used in this study, the swirl vane showed the best performance under relatively low pressure (15 bar) and mass flux (300-1000 kg/m² s) conditions and the hybrid vane performed best near the PWR operating conditions.The detailed flow characteristics were also investigated by CFD analysis using the same conditions as the CHF tests. To calculate the subcooled boiling flow, the wall partitioning model was applied to the wall boundary and various two-phase parameters were also considered. The reliability of the CFD analysis in the boiling analysis was confirmed by comparing the average void fractions of the analysis and the experiments: the results agreed well. From the CFD analysis, the void fraction flattening as a result of the lateral velocity induced by the mixing vane was observed. By the lateral motion of the liquid, the void fraction in the near wall was decreased and that of the core region was increased resulting in the void fraction flattening. The decrease of the void fraction in the near wall region promoted liquid supply to the wall and consequently the CHF increased. For the quantification of the void flatness, an index was developed and the applicability of the index in the CHF assessment was confirmed.     

Study on the characteristic points of boiling curve by using wavelet analysis and genetic neural network

Local singularity of a signal includes a lot of important information. Wavelet transform can overcome the shortages of Fourier analysis, i.e., the weak localization in the local time- and frequency-domains. It has the capacity to detect the characteristic points of boiling curves. Based on the wavelet analysis theory of signal singularity detection, Critical Heat Flux (CHF) and Minimum Film Boiling Starting Point (q_min) of boiling curves can be detected by using the wavelet modulus maxima detection. Moreover, a genetic neural network (GNN) model for predicting CHF is set up in this paper. The database used in the analysis is from the 1960s, including 2365 data points which cover a range of pressure (P), from 100 to 1000 kPa, mass flow rate (G) from 40 to 500 kg m⁻² s⁻¹, inlet sub-cooling (ΔT_sub) from 0 to 35 K, wall superheat (ΔT_sat) from 10 to 500 K and heat flux (Q) from 20 to 8000 kW m⁻². GNN mode has some advantages of its global optimal searching, quick convergence speed and solving non-linear problem. The methods of establishing the model and training of GNN are discussed particularly. The characteristic point predictions of boiling curve are investigated in detail by GNN. The results predicted by GNN have a good agreement with experimental data. At last, the main parametric trends of the CHF are analyzed by applying GNN. Simulation and analysis results show that the network model can effectively predict CHF.     

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.     

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.     

Critical Heat Flux in a Heater Rod Bundle Cooled by R-134a Fluid near the Critical Pressure

In the development of supercritical pressure water cooled reactors, it is important to understand the characteristics of a heat transfer near the thermodynamic critical point. An experimental study on the critical heat flux near the critical pressure has been performed with a 5 × 5 square array heater rod bundle cooled by R-134a fluid (P _c = 4:059MPa, T _c = 101°C). The critical power has been accurately measured up to the reduced pressure of 0.99 (4.03 MPa). The critical power decreases sharply at a pressure of about 3.8–3.9 MPa as the pressure approaches the critical pressure. For the low mass fluxes of 50 to 250kg/m², a sharp decrease in the critical power is not observed near the critical pressure. The CHF phenomenon near the critical pressure no longer leads to an inordinate increase in the heated wall temperature such as the case of DNB at normal pressure conditions. In the pressure region close to the critical pressure, there is a threshold pressure at which the CHF phenomenon disappears. When the pressure exceeds the threshold pressure, the wall temperature increases monotonously without a CHF occurrence according to the power level applied to the heater rods. The threshold pressure moves toward the lower pressure region gradually with an increasing mass flux.     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

The 2006 CHF look-up table

CHF look-up tables are used widely for the prediction of the critical heat flux (CHF). The CHF look-up table is basically a normalized data bank for a vertical 8 mm water-cooled tube. The 2006 CHF look-up table is based on a database containing more than 30,000 data points and provides CHF values at 24 pressures, 20 mass fluxes, and 23 qualities, covering the full range of conditions of practical interest. In addition, the 2006 CHF look-up table addresses several concerns with respect to previous CHF look-up tables raised in the literature. The major improvements of the 2006 CHF look-up table are:

• An enhanced quality of the database (improved screening procedures, removal of clearly identified outliers and duplicate data).

• An increased number of data in the database (an addition of 33 recent data sets).

• A significantly improved prediction of CHF in the subcooled region and the limiting quality region.

• An increased number of pressure and mass flux intervals (thus increasing the CHF entries by 20% compared to the 1995 CHF look-up table).

• An improved smoothness of the look-up table (the smoothness was quantified by a smoothness index).

A discussion of the impact of these changes on the prediction accuracy and table smoothness is presented. The 2006 CHF look-up table is characterized by a significant improvement in accuracy and smoothness.     

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.     

Experimental study on the effect of angles and positions of mixing vanes on CHF in a 2 × 2 rod bundle with working fluid R-134a

In this paper, the CHF experiment on the effect of angles and position of mixing vanes was performed in a 2 × 2 rod bundle. The test section had rectangular geometry in which four rod, each with a diameter of 9.5 mm, were inserted. The rod-to-rod gap was 3.15 mm, and the rod-to-wall gap was 1.575 mm. It was vertically installed in the test loop and was uniformly heated by electricity. The heating length was 1.125 m. The working fluid was R-134a. The mass flux ranged from 1000 to 1800 kg/m². The test pressure ranged from 14.67 to 25.67 bar. CHF data in the 2 × 2 rod bundle without a mixing vane were compared to the Bowring correlation and a CHF look-up table at equivalent hydraulic diameter. For this comparison, Katto's fluid-to-fluid model is applied. The results had a good agreement with error rates of 16 and 20%. In the CHF experiment with the mixing vanes with various angles, the angles of the mixing vanes were 20–40°. The CHF enhancement ratio (CER) was largest at 30°. CHF was enhanced up to 19%. A CHF experiment on the position of the mixing vane was also performed. In the experiment on the position of mixing vane, CER was reduced with increasing distance between grid and CHF location because swirl flow decayed. We also performed the CHF experiment on mixing vane developed by KAIST.     

Critical heat flux of forced convection boiling in an oscillating acceleration field — III. Reduction mechanism of CHF in subcooled flow boiling

To investigate the effect of variation in acceleration on the critical heat flux (CHF) in subcooled flow boiling, a photographic study was made. The test section was an internally heated vertical annulus with a glass shroud, in which Freon-113 flowed upwardly. The observation was made at a pressure of 3 bar, a mass flux of 920 kg/m²s, an inlet subcooling 45 K and a slightly lower heat flux level than steady CHF. The vertical acceleration was oscillated with amplitude of 0.3g_e and a period of 6 s.At low apparent gravitational acceleration, bubbles generated on the heated surface moved longer along the surface without detachment and coalesced with other bubbles to form large vapor slugs. This causes early CHF, the mechanism of which is dry-out of the liquid film existing between the heated surface and vapor slugs.     

Experimental evaluation of the limiting critical quality values in circular and non-circular flow geometries

An experimental evaluation of the limiting critical quality (or limiting quality in short) values in different flow geometries (circular, rectangular, triangular, and dumb-bell shaped) was performed using R-134a as a coolant. The limiting quality characterized by a sharp drop of critical heat flux (CHF) is affected by the following geometric parameters: hydraulic-equivalent diameter, channel shape, and gap size. The effect of flow geometry on limiting quality is influenced by flow parameters (pressure and mass flux). The effects of these parameters on limiting quality and CHF were examined, and recommendations for predicting the limiting quality in circular and non-circular geometries have been made.