A new model for predicting the critical heat flux based on nucleation site density in downward-face boiling

ABSTRACT

Due to the important role critical heat flux (CHF) plays in the boiling field, it is of great significance to study CHF, especially the mechanism of CHF in the nucleate boiling. In this study, a new model to predict CHF both in pool boiling and flow boiling of downward-face was proposed and the relationship between CHF and nucleation site density (NSD) was studied. The model was based on the bubble interaction theory, which assumed that CHF happened due to the coalescing of the bubbles generated on the heating surface and prevented liquid to be supplied. The relationship between NSD and CHF was derived from previous observations in the experiments and simulations. To validate the relationship between NSD and CHF, several experiments with CHF and NSD were chosen and they all showed good agreement with our assumptions. Due to the rarity of experimental data on NSD and CHF, the numerical method was also used to validate. The results also showed an inverse relationship between CHF and NSD.     

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.     

基于汽泡壅塞流模型的竖直圆管临界热流密度理论研究

为研究单管壅塞流的临界热流密度（CHF）现象,建立了基于近壁处汽泡壅塞机理的CHF计算模型。模型通过求解相应的质量、动量和能量方程,再结合汽泡直径脱离模型、壁面临界空泡份额等模型,从而计算得到CHF。将模型计算结果同实验值比较,吻合良好,验证了模型的正确性。在此基础上,以建立的CHF模型为基础,研究了进口焓差、质量流速、管径和加热长度对CHF的影响,为预测壅塞流CHF提供依据。      

池沸腾下朝向SA508钢表面临界热流密度特性试验研究

反应堆压力容器外部冷却（ERVC）是实现熔融物堆内滞留（IVR）的重要方案之一,而反应堆压力容器（RPV）外壁面的临界热流密度（CHF）决定了ERVC冷却能力的限值。为此建立小型CHF试验装置,并采用RPV用SA508钢制作试验块加热表面。以去离子水为试验工质,开展池沸腾下朝向CHF试验,研究真实RPV表面材料在不同倾角和过冷度条件下的CHF特性,及其老化效应对CHF的影响。结果表明：SA508钢表面极易氧化生锈,其CHF较不易生锈的铜和不锈钢表面要高;SA508钢表面CHF随倾角的增大而增加,但在30°附近存在转折,转折角以下范围内的CHF随倾角增加趋势不明显;CHF随过冷度的增加而增加,且基本呈线性变化。本试验有助于进一步认识RPV外壁面的CHF行为,为后续开展CHF增强方法研究奠定基础。     

Experimental Research on Critical Heat Flux for Downward-facing Pool Boiling with SA508 Steel Plate

The external reactor vessel cooling (ERVC) is one of the important methods to achieve the in-vessel retention (IVR), while the critical heat flux (CHF) on the outside wall of the reactor pressure vessel (RPV) decides the maximum heat removal capacity of ERVC. In present work, a small CHF test facility was established. The test surface was made of SA508 steel which was the same surface material of prototype RPV. The deionized water was used as coolant in downward-facing CHF test under pool boiling condition. The influence of the real RPV material surface at different inclination angles and sub-cooling conditions on the CHF characteristics was studied. The influence of aging on CHF was also studied. The results show that the SA508 steel surface is easily oxidized, so its CHF is higher than that of copper and stainless steel surfaces. The CHF of SA508 steel surface increases with inclination angle, but there is a turning point near 30° and the CHF below the turning angle has no obvious trend with the increase of inclination angle. The CHF increases with the sub-cooling, and it shows linear growth characteristics. The test results provide a further understanding of the CHF behavior on the RPV outside wall and lay the foundation for future research work on CHF enhancement methods.     

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.     

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%.     

A comparative study of correlations of critical heat flux of pool boiling

Nucleate pool boiling is desirable for many engineering systems. One challenge task for designing a system with nucleate pool boiling is to estimate the critical heat flux (CHF), which needs an accurate pool boiling CHF correlation. A few evaluations of pool boiling CHF correlations were reported, which used limited experimental data or covered limited correlations, resulting in inconsistent results. Therefore, it is difficult to determine which one is more appropriate for a given application. In this paper, a database containing 600 data points of pool boiling CHF of 12 pure liquids on plain surfaces having orientation angles of 0°?180° is compiled from 40 published papers. The reduced pressure is from 0.0001 to 0.98, and the 13 fluids are water, helium, nitrogen, hydrogen, R113, FC-72, FC-87, HFE-7100, ethanol, benzene, hexane, pentane, and methanol. With the database, 21 pool boiling CHF correlations are assessed. The most accurate one has a mean absolute deviation of 27.1%, indicating a need for developing more accurate correlations for engineering applications. Besides, the factors affecting the accuracy of correlations are analyzed and some valuable conclusions are obtained. The work lays a valuable foundation for the further study of pool boiling CHF correlations and provides a guide for choosing proper correlations for given applications. Several topics worthy of attention for future studies are suggested.     

Systematic process to determine DNBR limit of CHF correlation with repetitive cross-validation technique

The concerns have been raised about the potential for overfitting, which means that the correlation can predict the data used to develop the correlation well, but lacks in predictive capability on other data not used in the development of the correlation. In developing the CHF correlations to avoid overfitting problem when validation data are not enough or has a meaningless range, currently, it has been suggested that the database for a CHF correlation should be divided into a training data-set and a validation data-set. The systematic process to develop CHF correlation with cross-validation technique and to yield 95/95 DNBR values was developed to estimate quantitatively the risk of its overfitting on the resulting DNBR limit of CHF correlation. The repeated hold-out method out of cross-validation techniques was applied to the example CHF correlation (KCE-1M) by running 1000 random-sampling trials of CHF database with training (75%) and validation (25%) data-set. The effect of cross-validation technique on determination of the DNBR limit was estimated less than 3% at 95% probability with 95% confidence. Also, it was verified that DNBR limit of CHF correlation with cross-validation was more conservative to be applicable to the thermal-hydraulic design than that without cross-validation.     

Studies on cooling by two-dimensional confined jet flow of high heat heat flux surface in fusion reactor

Divertor surface of a magnetic confinement fusion reactor is exposed to strong radiative heating. According to standard design of the ITER, maximum heat flux on the divertor surface becomes locally near 30 MW m⁻². To cool such high heat flux surface by water flow, it is necessary to establish a cooling method which enhanced the critical heat flux (CHF). We proposed a cooling by a planar impinging jet with free surface in the previous report. In the jet cooling on flat surface, high CHF was obtained in the limited region where the jet flow hits directly. As apart from the region, the CHF decreases abruptly with the distance from the center. To overcome this difficulty, it was proposed that the planar jet is applied to cool concave surface where the centrifugal force is efficiently used to enhance the CHF. In this study, the CHFs were investigated in the confined jet flow which was guarded by a wall on the other side of the heated wall, because the guard wall works to protect splash of water from liquid film by violent boiling and expects further enhancement of the CHF. In this study, the CHFs were investigated in the confined flow of two-dimensional jet on flat and concave surfaces in the various flow conditions and got a correlation for the CHF. Applicability of this cooling for divertor surface was assessed by using the experimental results.     

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.     

环形通道内棒偏心和弯曲工况临界热流密度机理研究

本文分别从两种不同类型的临界热流密度（CHF）的触发机理出发,分析了内棒偏心和弯曲对CHF的影响。以氟利昂（R-134a）作为流动工质,在竖直向上流动的环形通道内开展了仅内棒加热的CHF实验研究。实验段包含3种形式：同心、偏心和弯曲。偏心实验结果表明：在高过冷工况下,内棒偏心将对CHF造成惩罚,且偏心率为0783的实验段对CHF惩罚更严重;在低过冷工况下,偏心效应减弱。高压高质量流速工况,空泡漂移效应会导致偏心率为0783的CHF大于偏心率为0435的CHF。弯曲实验结果表明：小闭合度的弯曲对CHF几乎没有影响。大闭合度的弯曲对于低质量流速的Dryout型CHF,弯曲棒会破坏液膜的稳定性;对于低质量流速的DNB型CHF,空泡漂移效应远小于偏心通道,弯曲的CHF小于相同最小间隙下偏心的CHF。     

Investigation on the characteristic of CHF in various flow pattern regimes based on look-up table data

The critical heat flux (CHF) is one of the important phenomena limiting the maximum rate of heat transfer and hence power rating of nuclear reactors. The thermal hydraulic phenomena like pressure drop, heat transfer, stability, etc. depends upon the flow pattern in the system. The CHF phenomenon is also closely related to the two-phase flow patterns. It is important to investigate the dependence of CHF on the flow pattern regimes to understand the underlying mechanisms. The present investigation reveals that CHF generally increases with mass flux in the churn/slug region. However, in the annular region the CHF decreases with increase in mass flux. Considering the dependency of the CHF trend on the flow pattern regime, it will be useful to develop CHF models, which are specific to the flow pattern regime. The data of CHF look-up table has been considered in this investigation since this approach is one of the most reliable methods for the prediction of CHF and is being used in several best-estimate thermal-hydraulic system codes, such as RELAP5, CATHARE and CATHENA. The pressure, mass flux and quality have been considered as important thermal hydraulic parameters to characterize the flow pattern during CHF under various operating condition.     

Critical heat flux during natural convective boiling in inclined tubes submerged in saturated liquids

An experimental study was carried out to improve and expand understanding of boiling phenomena and the critical heat flux (CHF) during natural convective boiling in uniformly heated inclined tubes submerged in a pool of saturated liquids under atmospheric pressure. The test conditions were as follows: inter diameters of the test tubes ranged from 0.9 to 8.0 mm; heated lengths ranged from 100 to 400 mm, and inclination angles varied from 30° to vertical position. The test fluids were water and R-11. The experimental results showed that the CHF decreases with the increasing ratio of the tube length to the tube diameter, and with the reducing of the inclination angle. A semi-theoretical correlation, which originally used for the CHF during natural convective boiling in vertical tubes, was modified to predict the CHF occurs in the inclined tubes. The modified correlation agreed reasonably well with the present experimental data and other CHF data for narrow inclined annular tubes.     

Analysis of critical heat flux during subcooled boiling for finned fuel elements

Experimental and analytical studies were performed to determine the critical heat flux (CHF) during subcooled boiling on finned fuel elements. Tests were conducted in a vertical, concentric-annulus test section consisting of a glass tube containing a finned heater element with either six, eight, or ten longitudinal fins. The phenomena leading to CHF are described and the parametric trends are discussed.A two-dimensional finite-element heat transfer model using the Galerkin method was used to analyse the experimental data to obtain CHF values. A dimensionless correlation was derived to predict the CHF values during subcooled boiling. Over 90% of the predicted CHF values agreed with those obtained from the two-dimensional analysis within ±30%.     

氧化铝纳米流体增强球形下封头IVR能力边际研究

为评价氧化铝纳米流体相对于纯水工质对球形下封头熔融物滞留（IVR）能力边际的拓展程度,采用基于气泡力平衡的氧化铝纳米流体临界热流密度（CHF）机理模型和壁面热通量拆分CHF模型计算球形下封头外表面纳米流体CHF。利用熔融物堆内滞留分析软件CISER开展衰变热分布抽样计算,得到下封头壁面CHF随倾角变化的随机分布,并将其与纳米流体CHF模型的理论值相比,以CHF比值小于1作为IVR成功准则,研判纳米流体对IVR能力边际拓展的影响程度。研究结果表明,若不对下封头内外传热构成采取任何优化措施,仅采用纳米流体替代纯水工质,压水堆核电厂的IVR能力边际能够拓展至1300 MW额定电功率水平。      

棒束子通道CHF机理模型开发及初步验证

目前棒束通道中临界热流密度的预测多基于实验关系式,受限于特定的适用范围,无法有效外推或外推后预测精度下降。为满足不同轻水堆中临界热流密度的预测要求,有必要开发适用于不同几何尺寸及热工边界的宽范围临界热流密度预测方式。本文以子通道分析方法为基础,考虑偏离泡核沸腾和干涸两类临界现象,通过耦合子通道分析程序与临界热流密度机理模型,实现对棒束通道中临界热流密度的计算。通过与临界热流密度实验数据的对比,初步证明了耦合程序对棒束通道中临界热流密度具有较好的预测精度。     

Application of artificial neural networks in analysis of CHF experimental data in round tubes

Artificial neural networks (ANNs) are applied successfully to analyze the critical heat flux (CHF) experimental data from some round tubes in this paper. A set of software adopting artificial neural network method for predicting CHF in round tube and a set of CHF database are gotten. Comparing with common CHF correlations and CHF look-up table, ANN method has stronger ability of allow-wrong and nice robustness. The CHF predicting software adopting artificial neural network technology can improve the predicting accuracy in a wider parameter range, and is easier to update and to use. The artificial neural nefwork method used in this paper can be applied to some similar physical problems.     

基于液膜蒸干模型的低压低流量环状流CHF理论研究

为对低压低流量下的环状流临界热流密度（CHF）进行预测,建立了考虑液膜蒸发、液滴沉积和夹带的液膜蒸干模型,并用已有的实验数据对其进行验证。计算结果表明：在实验参数范围内,CHF计算值与实验值相对偏差在25%以内,两者符合较好。以建立的环状流CHF模型为基础,研究了进口焓差、质量流速、管径和加热长度对CHF的影响。该模型能够有效地计算低压低流量环状流CHF和分析CHF随不同参数的变化趋势。     

成核密度模型对弧形表面CHF的影响

反应堆发生严重事故时,必须及时对反应堆压力容器（RPV）下封头进行外部冷却以降低下封头损毁可能性,事故期间下封头具有很高的热流分布,在实施外部冷却时可能出现由于过冷沸腾导致的气泡聚集而产生换热恶化从而烧毁。本研究利用ANSYS Fluent软件进行RPV外部冷却的临界热流密度（CHF）数值计算,并通过实验对比发现Basu Warrier和Dhir研究的成核密度模型可以很好地应用于球形表面CHF计算。通过对比球形和椭球形下封头CHF,认为椭球形下封头的CHF特性与球形结构完全不同,并不能用球形结构的实验和计算结果去推测椭球形结构的数值和变化规律。