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.     

Critical heat flux prediction in vertical bottom-closed rod bundles

This paper presents the analysis of experimental data and calculational relationships for heat the transfer crisis in LWR rod bundle with closed bottom. A new relationship for critical heat flux prediction in the rod bundle with closed bottom based on the improved drift model is described. The comparison of critical heat flux values given by different correlations (including Groeneveld's algorithm used in RELAP5/MOD3.1 Code) and those obtained from the tests in the wide range of regime and geometric parameters is presented.     

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.     

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%.     

Experimental research progress on critical heat flux of Chinese PWR

One of the most important requirements in the design of pressurized water reactor (PWR) is to avoid the occurrence of critical heat flux (CHF). The design criteria for PWR specify that they must be operated at a certain percentage below CHF at all times and locations so as to the cladding temperature of fuel element at safe values. So in the process of safety assessment, CHF is one of important thermal-hydraulic parameters limiting the available power, whose size directly affects safety and economy of PWR nuclear power plant. This paper deals with a summary of experimental research progress on CHF of Chinese PWR. It mainly presents CHF experimental researches of Φ10 fuel assembly, CHF experimental researches of standard fuel assembly, and CHF experimental progress of non-uniform heated rod bundles. It should be emphasized that it also presents experimental research programs on CHF of Chinese advanced fuel assembly with self-reliance copyright. All CHF data obtained will be used for design improvement of Chinese PWR and R&D program of New Generation 1000 MWe PWR.     

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.     

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 and heat transfer above mixture level under high-pressure boil-off conditions in PWR type and tight-lattice type fuel bundles

Heat transfer tests were conducted in PWR 17 × 17 type and tight-lattice type fuel bundles under high-pressure boil-off (very-low flow, mass fluxes lower than 100 kg/m²s) conditions. There is almost no significant difference in both critical heat flux (CHF) (or dryout point) data and convective heat transfer data above the mixture level between the PWR type and tight-lattice type bundles. The “complete vaporization equation” predicts well the CHF data, i.e. the dryout occurs nearly at the elevation where the thermal-equilibrium quality reaches 1.0. The Groeneveld CHF table used in the RELAP5/MOD3 code should be improved in the region of mass flux between 10 and 100 kg/m²s. The radiative heat transfer has an important contribution to total heat transfer above the mixture level. The Dittus-Boelter correlation, with use of the film temperature in evaluating steam properties, predicts well the convective heat transfer above the mixture level.     

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%.     

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.     

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.     

A flow boiling critical heat flux correlation for water and Freon-12 at low mass fluxes

An empirical correlation has been developed for calculating critical heat flux (CHF) at low mass fluxes for vertical upflow in uniformly heated tubes. The correlation is based upon dimensionless groups. It compares favourably with experimental CHF data for both Freon-12 and pressurized water. When solved iteratively in conjunction with the heat balance equation, an overall mean ratio of predicted to experimental CHF of 0.986 was obtained with a root means square (r.m.s.) error of 7.0%, for the 233 low flow rate data sets examined.The boundary between the high flow rate correlation developed in earlier work and the proposed low flow rate correlation can be specified by a dimensionless factor δ₁. For values of δ₁ greater than 0.07, the low flow correlation is valid whereas for values less than 0.07 the high flow correlation applies.Development of this correlation and a means of defining its range of validity enables the prediction of CHF levels to be made over an increased range of coolant flow conditions. This is important in the analysis of postulated loss-of-coolant accidents in water-cooled nuclear reactors.     

Critical heat flux in a vertical tube at low and medium pressures: Part I. Experimental results

This paper presents experimental CHF data obtained for vertical up flow in an 8 mm I.D. test section, for a wide range of exit qualities (5–75%) and exit pressures ranging from 5 to 40 bar. The experiments were carried out for heated lengths of 0.75, 1, 1.4, 1.8, 2.5 and 3.5 m. A number of different coordinate systems are used to present the experimental results, these include CHF as a function of the inlet subcooling, as a function of the outlet thermodynamic quality, and as a function of the boiling length. An analysis of these commonly used representations of the CHF, has shown, that for all of the cases studied, the critical heat flux is dependent in some manner on the heated length. This dependence greatly complicates the possibility of obtaining a universal correlation for the critical heat flux at low and medium pressures.     

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%.     

Mass velocity and cold-wall effects on critical heat flux in an advanced light water reactor

The characteristics of Critical Heat Flux (CHF) were investigated for a square array of rod bundles which could possibly be loaded into an integral-type advanced light water reactor. The parametric effects of the mass velocity and the unheated rod were examined by conducting CHF experiments with 5 × 5 test bundles in a Freon-loop. The influence of a cold wall on the CHF was interpreted by introducing a simple phenomenological model which accounts for the influence of a thermal mixing inside the boiling channel. A local parameter CHF correlation applicable to an integral-type reactor was developed from the CHF data base for square-arrayed rod bundles. The local thermal–hydraulic conditions calculated by the subchannel analysis code MATRA were used for the optimization of the correlation coefficients. Correction factors for the low mass velocity, spacer grids, and the non-uniform axial power shapes have been devised which reflected the results of the data assessment and the experimental observations. As a result of the thermal margin evaluation at steady state conditions, it was revealed that the integral-type reactor core has a greater DNBR margin than a typical 1000 MW_e PWR core.     

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.].     

Reactivity Behavior During RBMK Startup

During startup of an RBMK reactor, the reactivity varies from –(4–7)_eff to 0–0.1_eff. Positive reactivity is introduced locally – by extracting control rods. Since the physical dimensions of an RBMK reactor are large, a local change in the properties can produce a large change in the spatial distribution of the neutron flux in the core. The possible range of variation of the reactivity of a subcritical and a critical reactor with one control rod extracted is analyzed for the actual states of the power-generating units of a nuclear power plant with RBMK reactors. It is shown that the extraction of some rods in an RBMK reactor in subcritical and critical states can increase the reactivity by 1_eff or more.     

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.     

Development of a bundle correction method and its application to predicting CHF in rod bundles

A bundle correction method, based on the conservation laws of mass, energy, and momentum in an open subchannel, is proposed for the prediction of the critical heat flux (CHF) in rod bundles from round tube CHF correlations without detailed subchannel analysis. It takes into account the effects of the enthalpy and mass velocity distributions at subchannel level using the first derivatives of CHF with respect to the independent parameters. Three different CHF correlations for tubes (Groeneveld's CHF table, Katto correlation, and Biasi correlation) have been examined with uniformly heated bundle CHF data collected from various sources. A limited number of CHF data from a non-uniformly heated rod bundle are also evaluated with the aid of Tong's F-factor. The proposed method shows satisfactory CHF predictions for rod bundles both uniform and non-uniform power distributions.