Local Thermal-hydraulic Conditions Research Articles

Development of a dimensionless rod-bundle CHF correlation based on stepwise regression method, Part I: determination of the basic form with CHF data obtained with uniform axial heat flux profile

Accurate prediction of rod-bundle critical heat flux (CHF) is a main challenge in thermal-hydraulic design and safety assessment of Pressurized Water Reactor (PWR). The most widely applied approach is empirical correlation developed based on rod-bundle experiments carefully tested with geometry and power distribution representative to PWR working conditions. The standard procedure is to correlate the experimentally obtained CHF values as empirical functions of local thermal-hydraulic conditions obtained with subchannel analysis. However, up-to-date empirical correlations developed according to this manner are in general quite complicated with a number of dimensional coefficients and correction factors with less or non-physical meanings. In this study, stepwise regression method was used to develop a novel, dimensionless rod-bundle CHF correlation covering typical PWR working conditions. First, various dimensionless parameters affecting CHF were selected as candidate independent variables. With stepwise regression, the form and coefficients of the proposed CHF correlation were dynamically optimized and determined.

Revision of a CHF correlation for PWR under low pressure conditions with only dimensionless parameters as independent variables

Abstract Accurate prediction of the critical heat flux (CHF) is one of the key tasks of PWR core design and safety assessment, for the maximal allowable heat flux in the reactor core is limited by CHF. Since CHF in rod bundle cannot be predicted analytically, up-to-date predictive approach is based on empirical correlations related to the local thermal-hydraulic conditions, geometry and power distribution. However, development of CHF correlation for PWR fuel assemblies under low pressure conditions (2–10 MPa) is constrained by limited amount of experimental data points, which builds up in statistics a typical problem of small sample amounts, but requiring simultaneously high prediction accuracy. In our previous study, stepwise regression method was applied to develop a dimensional, empirical CHF correlation for PWR under low pressure conditions, termed as the advanced low pressure CHF correlation (ALPC), which successfully solves the challenge of small sample problem. However, the ALPC correlation still uses dimensional independent variables with less physical meanings, which limits its physical interpretability. In the current study, stepwise regression method was used to develop a revised, dimensionless version of the ALPC CHF correlation. First, various dimensionless, two-phase thermal-hydraulic parameters that might influence CHF were selected as candidate independent variables. With stepwise regression, the form and coefficients of the revised CHF correlation were optimized in a dynamic manner. Compared to the current ALPC correlation, the revised version developed in this study possesses a similar simple form but a much higher prediction accuracy. Revision of the ALPC correlation demonstrates clearly the advantages of utilizing dimensionless parameters as independent variables in CHF correlation, which points out a new direction of developing rod-bundle CHF correlations for engineering purpose.

Measurement uncertainty and quenching phenomena in uniform heating rod bundle CHF tests

The uniform heated rod bundle Critical Heating Flux (CHF) tests have been often conducted as a part of mixing vane performance evaluation processes. Presently, several commercial CHF correlations were developed based on a large amount of rod bundle CHF data using axial uniformly heated rod bundles. With a uniformly heated test section, majority of CHF events are dominated by dry-out mechanism under high quality, high void fraction local conditions. Considering the inverse proportional relationship between the quality and CHF, for an axially uniformly heated test section, the CHF events should occur near the end of heating length (EOHL) where the void fraction/quality is the highest. However, the upstream shift of CHF location is often observed in the uniform heating tests, sometime as much as 250 mm or higher upstream from the EOHL.In the past, without any sufficient convincing proof, long dryout areas as well as “unknown” “mysteries” mixing effects from the mixing vane grid were often considered as the contributing factors for this type of upstream shift. Based on further and detailed examination, this paper offer analysis and evidence to demonstrate another most plausible explanation, exit quenching effect, which ultimately concludes that rod bundle CHF using uniform heated rods could have data with huge measurement uncertainty and as much as over 30% of non-conservatism due to heat lose and quenching effects at the exit of the heated length. The quenching effect at the exit of heater length is mainly due to reflood phenomena generated between the high void/low flow test section exit region and the relatively cold single phase coolant immediately above in the top plenum resulting from either excessive heat loss or operating transient condition.In this paper, system code and CFD modeling were utilized to simulate the quenching phenomena in both steady state and transient conditions. The significant void fraction drop near the exit of the test section due to quenching were clearly observed in these simulations and also evidenced by the various degrees of coloration of the heaters surface in the experiment. This exit reflood quenching phenomena may change the CHF location, suppress boiling, cool down the heated surface, and eventually lead to non-conservative high CHF values. Based on this analysis and experimental observation, it is concluded that the CHF correlations developed based on these type of data are potentially non-conservative in various degrees pending on local thermal-hydraulic conditions, which should be taken into consideration for their applications, especially for safety analysis in nuclear reactor.

Numerical study on the effect of grid mixing span in 2 × 1 spacer grid

Abstract Spacer grid or Mixing Vane Grid (MVG) is recognized as an important component that could greatly improve Critical Heat Flux (CHF) performance in the fuel assembly. The temperature around the rod would be more uniform, bubbles around the rod wall would be broken off or driven to the center of the subchannel by the mixing effects produced by spacer grids. This would potentially result in a higher CHF value. However, as the grid span increases, the mixing effects will decay as the coolant travels further away from the mixing vane grid. The local thermal hydraulic conditions become severe as the heated length increases. As a result, from the decay of the mixing function, CHF usually occurs at immediate upstream of spacer grid, or the furthest distance from the MVG upstream. On the other hand, with the narrowing of grid span, the pressure drop increases with increasing hydraulic resistance. Therefore, a proper grid span is quite important in the fuel assembly design. In this paper, the effects of grid span were studied by applying Computational Fluid Dynamics (CFD) simulation. The flow field with 2 × 1 spacer grids were simulated instead of prototype full scale spacer grid. CFD was validated by the experimental data from XJTU-ANFR low pressure and low temperature test loop. Flow field with different length of grid span were modeled to investigate the fundamental mechanism on how key factors, such as “mixing performance”, are impacted by the length of grid span. In order to evaluate the mixing performance, several popular mixing indexes, including Secondary Flow (SF), and thermal non-uniformity, were introduced to evaluate the effects of grid span on the mixing performance. Effective Mixing Length (EML) was defined by considering the effect of mixing and temperature distributions. Grid Span (GS) function was proposed to take various thermal hydraulic indexes into consideration in order to address the issue of local condition dependency and to obtain proper grid span. Different grid design thermal hydraulic indexes have different weighting factors, in such, the optimal grid span functions may not be the same for different fuel assemblies.

Critical heat flux experiments and a post-CHF heat transfer analysis using 2D inverse heat transfer

Abstract The critical heat flux (CHF) is one of the main thermal-hydraulics safety limits in water-cooled reactors. At CHF, a film of vapor is formed on the heated wall and the wall temperature can sharply increase in a short period of time, which may lead to damage of the heater surface. In spite of many studies, the CHF mechanisms are still not well understood due to the complexity of this two-phase phenomenon and its dependence on local thermal-hydraulic conditions. Two-phase boiling experiments have been conducted to observe CHF and post-CHF behavior in prototypical conditions for small modular reactors (mass flux: 560–1570 kg/m2.s, pressure: 7.6–16.4 MPa, inlet subcooling: 160–440 kJ/kg) in a 2 × 2 square rod bundle geometry with a chopped-cosine power profile at the University of Wisconsin-Madison. The fuel rods temperature history during and following CHF were used in the solution of the two-dimension inverse heat transfer problem to estimate the wall temperatures and wall heat fluxes. This analysis showed different transient boiling curves for different flow regimes that differ qualitatively and quantitatively from the typical boiling curve considered in steady-state two-phase heat transfer analysis. The experiments suggest that the inverse heat transfer analysis approach can be used to estimate the post-CHF heat transfer and to better understand the CHF mechanisms at high pressure typical of water-cooled reactors.

Numerical Study of Integral Inherently Safe Light Water Reactor in Case of Inadvertent DHR Operation Based on the Multiscale Method

In detailed previous work by the authors, an innovative decay heat removal (DHR) system has been proposed and designed for the Integral Inherently Safe Light Water Reactor (I2S-LWR). The current paper studies the inadvertent actuation of one DHR system train during I2S-LWR normal operation due to a false signal or operator action. The RELAP5 code is used to perform a one-dimensional study, and important thermal-hydraulic characteristics, including primary loop coolant flow rate, pressure, temperature, DHR primary-side flow rate, and coolant temperature, are achieved during this transient. Then, a detailed computational fluid dynamics simulation utilizing STARCCM+ is carried out to investigate the coolant mixing characteristics in the downcomer and lower plenum and obtain the local thermal-hydraulic conditions at the reactor core inlet. It is found that as a consequence of inadvertent DHR actuation, the maximum overcooling at the reactor core inlet is about 3 K, which would not result in significant reactivity insertion. Furthermore, a more severe transient of inadvertent DHR operation with intermediate loop break is studied, and the results show that this would not lead to more significant overcooling to the I2S-LWR core compared with inadvertent DHR operation without intermediate loop break. This work is an indispensable supplement for DHR system comprehensive assessment in the I2S-LWR project.

Critical Heat Flux in Square- and Nonsquare-Array Rod Bundles for Advanced Light Water Reactors

Critical heat flux (CHF) in rod bundles is a parameter of great importance for the thermal-hydraulic design and safety analysis of advanced light water reactors. An experimental investigation has been conducted for the 19-rod hexagonal test bundles with a tightly spaced nonsquare arrangement of heater rods. The parametric effects on the CHF were examined for the heated length, the unheated rod, and the nonuniform axial power shape. As a result, a pertinent CHF correlation has been developed on the basis of the bundle cross-sectional averaged conditions. The available CHF database for rod bundles with square and nonsquare rod pitches was employed for the assessment of representative CHF correlations that were applicable to the round tubes and rod bundles. The database covered a wide range of operating conditions and test bundle geometries that are applicable to advanced light water reactors. The prediction accuracy of the CHF correlations was evaluated on the basis of the local thermal-hydraulic conditions calculated by a subchannel analysis code.

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.

Critical Heat Flux during Reflood Transients in Small-Hydraulic-Diameter Geometries

Critical heat flux (CHF) at a low-flow condition in a small-hydraulic-diameter duct is an important phenomenon for a Materials Test Reactor/Advanced Test Reactor (MTR/ATR) design under a number of accident conditions, including reflood transients. Current CHF models in the literature, such as the Mishima/Nishihara and Oh/Englert CHF models, are based on macroscopic system parameters and not local thermal-hydraulic conditions. These macroscopic parameter–based models cannot be readily used for analysis in transient best-estimate thermal-hydraulic codes. The present work focuses on developing a low-flow-rate CHF correlation, based on local conditions, that is amenable to implementation into a best-estimate transient thermal-hydraulic code for a small-hydraulic-diameter duct. The model development proceeds with a means of correlating CHF data to local conditions parameters and then applying a correction factor to the resulting correlation, subsequently permitting accurate predictions over a range of pressures. An evaluation of the proposed local conditions-based CHF model is conducted by predicting independent sets of CHF experimental results over a range of flow rate, pressure, and subcooling conditions. Conclusions on the viability of the proposed CHF model and suggestions for future efforts in improving the reflood heat transfer CHF models for small-hydraulic-diameter ducts are provided with an evaluation of the model results.