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.     

极限干度现象区CHF评估

在圆形管内,对极限干度区的临界热流密度(CHF)进行了理论研究.通过对Whalley模型进行数值求解,并分析其在极限干度流动条件下的适应性,得到了适用于圆形管内环状流临界热流密度的本构方程.数值预测结果通过与几个主要的CHF预测模型相比较表明该本构方程对极限干度区CHF的预测精度较高.     

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.].     

Diameter effect on critical heat flux

The critical heat flux look-up table (CHF LUT) is widely used to predict CHF for various applications, including design and safety analysis of nuclear reactors. Using the CHF LUT for round tubes having inside diameters different from the reference 8 mm involves conversion of CHF to 8 mm. Different authors [Becker, K.M., 1965. An Analytical and Experimental Study of Burnout Conditions in Vertical Round Ducts, Aktiebolaget Atomenergie Report AE 177, Sweden; Boltenko, E.A., et al., 1989. Effect of tube diameter on CHF at various two phase flow regimes, Report IPE-1989; Biasi, L., Clerici, G.C., Garriba, S., Sala, R., Tozzi, A., 1967. Studies on Burnout, Part 3, Energia Nucleare, vol. 14, pp. 530-536; Groeneveld, D.C., Cheng, S.C., Doan, T., 1986. AECL-UO critical heat flux look-up table. Heat Transfer Eng., 7, 46-62; Groeneveld et al., 1996; Hall, D.D., Mudawar, I., 2000. Critical heat flux for water flow in tubes - II subcooled CHF correlations. Int. J. Heat Mass Transfer, 43, 2605-2640; Wong, W.C., 1996. Effect of tube diameter on critical heat flux, MaSC dissertation, Ottawa Carleton Institute for Mechanical and Aeronautical Engineering, University of Ottawa] have proposed several types of correlations or factors to describe the diameter effect on CHF. The present work describes the derivation of new diameter correction factor and compares it with several existing prediction 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.     

Type of flow, pressure drop, and critical heat flux of a two-phase sodium flow

Little is known about the two-phase pressure loss, the flow pattern, and the critical heat flux conditions for boiling sodium under forced convection. The specific thermohydraulic properties of sodium prohibit extrapolation to sodium of experimental data obtained for other liquids. Therefore, some new test series were carried out in a sodium loop with an induction heated test section of 9 mm inner diameter and 200 mm heated length. The two-phase pressure loss and the film thickness were measured up to the critical cooling conditions. The experimental results are compared with values predicted by known models on annular flow and annular mist flow, respectively. Satisfactory predictions of the flow pattern and the critical heat flux conditions could only be obtained using the measured two-phase pressure losses.     

A study of the critical flow models used in reactor blowdown analysis

Two-phase critical flow models widely used in safety calculations are compared with extensive published experimental measurements of the choked flowrates of steam-water mixtures. Comments are made on the applicability of the models in their supposed regions of validity and a mathematical upper limit to discharge flowrate is derived. The data fall below this limit and generally above a homogeneous isentropic flow model in thermal equilibrium. Suitable measurements of critical flowrates in pipes of diamater in the range of direct relevance to reactor blowdown calculations are still unavailable.     

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%.     

Prediction of critical heat flux using ANFIS

The prediction of Critical Heat Flux (CHF) is essential for water cooled nuclear reactors since it is an important parameter for the economic efficiency and safety of nuclear power plants. Therefore, in this study using Adaptive Neuro-Fuzzy Inference System (ANFIS), a new flexible tool is developed to predict CHF. The process of training and testing in this model is done by using a set of available published field data. The CHF values predicted by the ANFIS model are acceptable compared with the other prediction methods. We improve the ANN model that is proposed by Vaziri et al. (2007) to avoid overfitting. The obtained new ANN test errors are compared with ANFIS model test errors, subsequently. It is found that the ANFIS model with root mean square (RMS) test errors of 4.79%, 5.04% and 11.39%, in fixed inlet conditions and local conditions and fixed outlet conditions, respectively, has superior performance in predicting the CHF than the test error obtained from MLP Neural Network in fixed inlet and outlet conditions, however, ANFIS also has acceptable result to predict CHF in fixed local conditions.     

Experimental study of the effect of non-circular flow geometry on the critical heat flux

An experimental study of the effect of flow geometry (circular, rectangular, triangular, and dumb-bell shaped) on the critical heat flux (CHF) was performed using R-134a as a coolant. The CHF is affected by the following geometric parameters: hydraulic-equivalent diameter, heated length, gap size, channel shape, and curvature. It may also be affected by the thermal conductivity of the wall material and wall thickness. The effect of flow geometry on CHF is influenced by flow parameters. The effect of these parameters on CHF was examined, and recommendations for predicting the CHF in non-circular geometries have been made.     

An investigation of flow characteristics and critical heat flux in vertical upward round tube

Prediction of critical heat flux （CHF） in annular flow is important for the safety of once - through steam generator and the reactor core under accident conditions. The dryout in annular flow occurs at the point where the film is depleted due to entrainment, deposition, and evaporation. The film thickness, film mass flow rate along axial distribution, and CHF are calculated in vertical upward round tube on the basis of a separated flow modcl of annular flow. The theoretical CHF values are higher than those derived from experimental data, with error being within 30%.     

窄矩形通道自然循环流动停滞与临界热流密度研究

在华北电力大学自然循环实验室进行了自然循环条件下窄矩形通道内的临界热流密度(CHF)实验,对实验中出现的流动停滞及传热恶化现象进行了观察。提出自然循环饱和沸腾条件下,窄矩形通道内的流动停滞-传热恶化发生机理。即自然循环流量漂移发生后会产生流型变迁不稳定,继而造成流量的持续波动,并导致停滞现象,从而使出口附近的液膜层在一定的热流密度下被完全蒸发并引起CHF现象。而窄矩形通道内,由于受间隙尺寸的限制,蒸汽流对加热面上的液膜层产生挤压作用,加热面上液膜层厚度因此会变得较薄,在较小的加热量下便能发生传热恶化。基于机理分析,给出了相应的计算模型。引入了考虑窄通道间隙尺寸效应的无量纲约束数Nconf和反映自然循环流动特点的特征因子C,分别对模型进行了修正。根据实验结果,对计算模型进行了多元回归拟合,并对其准确性进行了验证。通过对实验结果与模型计算值的比较发现,随着通道入口流速和系统压力的增大,CHF均增大;而随着出口干度的增大,CHF会减小。     

On the definition of critical heat flux margin

This paper reviews the current definition of critical heat flux (CHF) margins and discusses their differences.     

An integral equation model for critical heat flux at subcooled and low quality flow boiling

A new theoretical model of critical heat flux (CHF) is developed for the flow boiling condition from bubble-detached to low quality range. The CHF condition is postulated to occur when the superheated liquid layer on the heated wall, which is formed under the bubbly layer from the point of the onset of significant void generation, is depleted due to the evaporation along the heated length. The model shows a very promising agreement with the uniformly heated round tube data for both water and refrigerants by simply applying well-known constitutive relationships without any tuning constant for the CHF data. The significance of the proposed model in unifying the existing models is also discussed.     

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 mechanistic critical heat flux model for wide range of subcooled and low quality flow boiling

A mechanistic model to predict a critical heat flux (CHF) over a wide operating range in the subcooled and low quality flow boiling has been proposed based on a concept of the bubble coalescence in the wall bubbly layer. The conservation equations of mass, energy and momentum, together with appropriate constitutive relations, are solved analytically to derive the CHF formula. The model is characterized by an introduction of the drag force due to wall-attached bubbles roughness in the momentum balance, which determines the limiting transverse interchange of mass flux crossing the interface of the wall bubbly layer and core. Comparison between the predictions by the proposed model and the experimental CHF data shows good agreement over a wide range of parameters for both light water and fusion reactors operating conditions. The model correctly accounts for the effects of flow variables such as pressure, mass flux and inlet subcooling as well as geometry parameters.     

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%.