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

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

A compilation of rod array critical heat flux data sources and information

The geometric characteristics of rod array test sections employed in critical heat flux (CHF) tests with water coolant, and the ranges of the operating parameters for the tests, are presented for 126 test sections. The corresponding 4277 CHF data points have been stored on a magnetic tape for ease of reference and analysis. A versatile computer program associated with the data library has been used to determine the distributions of the data with respect to geometric and operating parameters. The dependence of CHF on operating parameters and the importance of subchannel conditions are shown through the use of some of the data. Tables are given for CHF data with a Freon coolant, for CHF data from test sections which only simulate a rod array, and for CHF data for transient situations.     

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.     

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.     

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

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

Analysis of data and recommendations on heat transfer by liquid metals in rod bundles

Translated from Atomnaya Énergiya, Vol. 65, No. 6, pp. 423–426, December, 1988.     

Numerical study on flow and heat transfer characteristics in the rod bundle channels under super critical pressure condition

In this study, the 3D flow and heat transfer characteristics in rod bundle channels of the super critical water-cooled reactor were numerically investigated using CFX codes. Different turbulent models were evaluated and the flow and heat transfer characteristics in different typical channels were obtained. The effect of pitch-to-diameter ratio (P/D) on the distributions of surface temperature and heat transfer coefficient (HTC) was analysed. For typical quadrilateral channel, it was found that HTC increases with P/D first and then decreases significantly when P/D is <1.4. There exists a “flat region” at the maximum value when P/D is 1.4. If P/D is larger than 1.4, heat transfer deterioration (HTD) occurs as main stream enthalpy is quite small. Furthermore, the HTD under low mass flow rate and the non-uniformity of circumferential temperature were also discussed.     

Check of the 2005-look up table for prediction of CHF in bundles

The check whether it is possible to use the 2005-look up table primary designed for heated pipes also for heated rod bundles gives the surprising result that the bundle critical power for five data sets of three different bundles and different power distributions are predicted by a simple method described above using the 2005-look up table within the accuracy reported by the authors of this table.     

Letter to the editor on the paper by D.C. Groeneveld and L.K.H. Leung, “The 1995 look-up table for critical heat flux in tubes”

This letter gives a brief critique of the new 1995 Look-Up-Table for critical heat flux (CHF). Issues on Look-Up-Table statistics, table usage and CHF values for critical flow are highlighted.     

Tabular method of calculating the critical heat flux in water-cooled triangular rod assemblies

A new method of calculating the critical heat flux in fuel-rod assemblies is presented. The method is based on a generalization of the experimental data in tabular form. The table for the critical heat fluxes is constructed for the correct macrocells of triangular bundles with relative rod spacing s/d=1/4 and a 9.36 mm heat diameter of a microcell for the following conditions: no effect due to peripheral zones and unheated rods; turbulizing influence of the entrance conditions and spacers; and, the heating along the length and across assemblies is uniform. To use the table for other, quite wide regions of the determining parameters, relations are presented for calculating the effect of the important parameters: heating diameter, relative rod spacing in the assembly, distance to the entrance (heated length), turbulizing influence of the spacers, and others. 1 figure, 1 table, 9 references. State Science Center of the Russian Federation—A. I. Leipunskii Physics and Power-Engineering Institute. Translated from Atomnaya énergiya, Vol. 87, No. 1, pp. 17–24, July, 1991.     

Investigation of pre- and post-dryout heat transfer of steam-water two-phase flow in a rod bundle

Pre- and post-dryout heat transfer experiments were performed for steam-water two-phase flow in a 5 × 5 rod bundle under conditions of total mass fluxes from 80 to 320 kg/m²s, inlet qualities from 0.1 to 0.8, heat fluxes from 3 to 26 W/cm² and a pressure of 3 MPa. Heater rod surface temperatures or heat transfer coefficients predicted by several correlations were compared with experimental data with emphasis on the applicability of the correlations to the present experimental conditions which were pertinent to thermal-hydraulic conditions during a LOCA in a nuclear reactor. The Chen and Biorge et al. correlations underestimated heat transfer coefficients in the pre-dryout region. The Varone-Rohsenow prediction which accounted for the thermal nonequilibrium effect, calculated heater rod surface temperatures relatively well in the post-dryout region over the whole region of the present experimental conditions. The Dittus-Boelter and Groeneveld correlations predicted heater rod surface temperatures relatively well in the post-dryout region under high total mass flux conditions, but underestimated considerably under low total mass flux conditions.     

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).     

An analytical method of evaluating the effect of rod displacement on circumferential temperature and heat flux distributions in turbulent flow through unbaffled rod bundles

An analytical method of evaluating the circumferential variations of temperature and heat flux fields inside and around a displaced fuel rod in triangular rod bundles in turbulent flow is presented with illustrative examples. The analysis consists mainly of the derivation of the simultaneous solutions of a set of heat conduction equations for fuel, cladding and coolant under the assumption of fully developed flow and heat transfer conditions. The local coolant velocity distribution, which is necessary for deriving the temperature field in coolant, is determined by solving the Navier-Stokes equation and the turbulent mixing of coolant is taken into consideration. The results show how the circumferential variations in the temperature and heat flux fields on the outer surface of the cladding increase the lower the ratio and the larger the fuel rod displacement due to thermal conduction and peripheral coolant flow velocity distribution.     

The flow and heat transfer characteristics of turbulent flow in typical rod bundles in ocean environment

The flow and heat transfer characteristic of turbulent flow in typical 4 and 7 rod bundles in ocean environment is investigated theoretically. In ocean environment, the periodic variation of secondary flow in 7 rod bundles is not obvious. Because of the velocity oscillation, there is a periodic heat accumulation on the tube wall. And the restriction of the channel wall on the rolling motion is considerable. In 7 rod bundles, because of the restriction of the channel wall, the effect of the additional force perpendicular to flowing direction is limited, and the turbulent flowing and heat transfer is mainly determined by the axial turbulent intensity and inlet velocity. However, in the 4 rod bundles, the restriction of the channel wall is small. The effect of the additional force perpendicular to flowing direction on the flowing and heat transfer is significant. And the additional force perpendicular to flowing direction can also affect the Reynolds stress.     

A study of the effect of rod-bowing on critical heat flux

An experimental study was carried out to determine the effect of rod-bowing on critical heat flux, using an electrically-heated rod cluster. In this experiment, rod-bow was set to occur in the severest subchannel and axially at the middle between the last two spacers, with uniform axial heat flux. The minimum gap between the outer and inner rods was reduced variously to 1.6 mm, 1.0 mm and zero from the nominal value of 2.1 mm. Other experimental conditions were as follows: pressure 7 MPa; mass velocity 640–2600 kg/m² sec; inlet subcooling 40–560 kJ/kg.Experimental results show only a slight rod-bowing effect, if any, compared with normal spacing, as confirmed by analysis of three-dimensional heat conduction around the rod-bowing area and by the local steam quality deviations calculated by subchannel analyses.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

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.