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.     

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.     

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.     

The Effect of Vibration on Critical Heat Flux in a Vertical Round Tube

This paper deals with the results of experimental investigations on the effects of tube vibration on critical heat flux (CHF) in order to gain an understanding of the relationship between CHF and flow-induced vibration (FIV). The experiment was carried out in the following range of parameters: diameter (D)=0.008 m; heated length (L)=0.2, 0.4 m; pressure (P)=101 kPa; mass flux (G)=403–2,551 kg/m².s; quality (x)=-0.045–0.289; amplitude (a)=0.0001–0.001 m; frequency (f)=0–70Hz. The CHF generally increases with vibration intensity, which is represented by vibrational Reynolds number (Re _v ); the CHF enhancement is more dependent on amplitude than on frequency. CHF enhancement seems to come from the reinforced flow turbulent mixing effect by vibration in the vicinity of heat transfer surface. Based on the experimental results, an empirical correlation is proposed for the prediction of CHF enhancement by tube vibration. The correlation predicts the CHF enhancement ratio (En) with reasonable accuracy, with an average error rate of -2.18% and 27.75% for RMS.     

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.     

A flow boiling burnout correlation for water and Freon-12

An empirical correlation has been developed for calculating critical heat flux (CHF) for vertical upflow in uniformly heated tubes. The correlation is based on parameter groups derived from a dimensional analysis and has been compared with experimental CHF data for Freon-12 and for water. Except for coolant conditions in which (i) mass fluxes are less than 300 kg s⁻¹ m⁻², (ii) dryout qualities are below 10%, or (iii) water pressures are outside the range 3.5 to 12 MPa, the correlation agrees very favourably with the experimental data. The overall mean ratio of calculated to experimental CHF values for 1760 sets of Freon-12 data is 0.992 and the r.m.s. error 3.3%; the corresponding values for 2063 sets of water data are 0.982 and 5.8%. This provides a basis for predicting CHF levels over a wide range of coolant conditions, as required in the analysis of hypothetical loss-of-coolant accidents in water-cooled nuclear reactors.     

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.     

Some problems for bundle CHF prediction based on CHF measurements in simple flow geometries

A comparison of critical heat flux (CHF) fuel bundles data with CHF data obtained in simple flow geometries was made. The base for the comparison was primary experimental data obtained in annular, circular, rectangular, triangular, and dumb-bell shaped channels cooled with water and R-134a. The investigated range of flow parameters (pressure, mass flux, and critical quality) in R-134a was chosen to be equivalent to modern nuclear reactor water flow conditions (p=7 and 10 MPa, G=350–5000 kg (m² s)⁻¹, x_cr=−0.1–1). The proper scaling laws were applied to convert the data from water to R-134a equivalent conditions and vise versa. The effects of flow parameters (p, G, x_cr) and the effects of geometric parameters (D, L) were evaluated during comparison. The comparison showed that no one simple flow geometry can be used for accurate and reliable bundle CHF prediction in wide range of flow parameters based on local (critical) conditions approach. The comparison also showed that the limiting critical quality phenomenon is unique characteristic for each flow geometry which depends on many factors: flow conditions (pressure and mass flux), geometrical parameters (diameter or surface curvature, gap size, etc.), flow obstructions (spacers, appendages, turbulizers, etc.) and others.     

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.     

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.     

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.     

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.     

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.     

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.     

HFE-7100工质稳态临界沸腾传热实验研究

池沸腾临界热通量是沸腾相变传热的重要参数,决定了相变换热器件的推广应用。表面粗糙度和饱和压力对沸腾传热边界层分布、表面铺展润湿及工质动力学特性具有重要影响,进而对临界热通量作用显著。本文对HFE-7100工质在4种不同粗糙度的铜基表面（0.019、0.205、0.311和0.587 μm）条件及在不同饱和压力（0.07、0.10、0.15及0.20 MPa）工况下的池沸腾稳态临界状态下的传热及可视化实验进行了研究。对表面粗糙度及饱和压力对稳态临界沸腾的影响机制进行了分析,并考察了临界热通量预测模型对临界热通量的预测准确性。可视化研究表明,临界状态下的沸腾气液两相工质由小气泡、大气泡、气柱及蘑菇状气团组成,而在过渡状态下,沸腾表面会形成非平滑气膜,并不断分离出气泡。同时传热数据表明,表面粗糙度及饱和压力的增加能使表面临界热通量得到提升。相比而言,Bailey等建立的临界热通量预测模型能相对准确地预测HFE-7100工质沸腾临界热通量数据。为进一步提升预测准确度,建立了临界热通量无因次参数K预测经验关联式,其预测值与本实验及文献实验数据吻合较好。     

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.     

Corrosion of Type 304L Stainless Steel in Concentrated Plutonium Nitrate Solution

Dryout experiments of water have been conducted in an annulus with inside heating (heat flux from inner wall only) under high-pressure, low-flow and mixed inlet conditions which are of importance in the core thermal-hydraulic behavior during a loss-of-coolant accident (LOCA) and also partially during an anticipated transient without scram (ATWS) of a nuclear reactor. The experimental conditions have covered ranges of pressure of 3 MPa, mass flux from 105 to 320 kg/m²·s and inlet quality from 0.15 to 0.90. The dryout data have been compared with several existing empirical critical heat flux (CHF) correlations and a new correlation. The Katto correlation predicts best the CHF among the existing correlations examined. However, even the Katto correlation overpredicts the CHF by factors up to 2 at about 1/6 data points of the present dryout data. The present dryout data are divided into two groups (regions) according to the value of a non-dimensional number l _bo/d _he, where l _bo is the assumed boiling length and dh, the heated equivalent diameter. A new correlation covering both the regions has been developed by correlating the present dryout data in terms of two non-dimensional numbers. The new correlation performs best among the correlations examined in predicting the present dryout data.     

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.     

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.