A new correlation for the prediction of critical quality in tubes

https://doi.org/10.1016/j.anucene.2020.107796Get rights and content

Highlights

  • A high applicability and accuracy correlation for predicting critical quality is proposed.

  • The influence of multiple factors are fully considered.

  • The applicable range and accuracy of different correlations are compared.

  • Suggestions on selecting the correlations for predicting critical quality under different working conditions are given.

Abstract

In this paper, dryout phenomenon of steam-liquid two-phase flow in vertical tube is studied. Based on Becker’s experimental data, 393 points of dryout data with pressure ranging from 2.9 to 20.1 MPa, mass flow rate ranging from 496 to 3120 kg/(m2 s), heat flux less than 1268 kW/m2 and pipe diameter ranging from 10 to 24.7 mm are re-fitted, and a new correlation for predicting the critical quality is proposed. The MAE of the new correlation is 7.2% when predicting the Becker's data. It also positively correlated with other databases of steam-liquid critical quality. However, the prediction accuracy of the new correlation is relatively low for refrigerant and deformation channel, which will be further revised in future work.

Introduction

Straight tube once-through steam generator is widely used in the integrated reactor because of its high efficiency and superheated steam generated at the outlet of the heat transfer tube bundle. However, the secondary side heat transfer process is relatively complex, including single-phase liquid convection zone, bubble nucleation boiling zone, liquid film forced convection evaporation zone, liquid deficiency zone and single-phase vapor convection zone. The boiling crisis may occur in the process of flow boiling, i.e. deterioration of heat transfer. The second type of heat transfer deterioration, dryout (Wang et al., 2014); occurs in the forced convective evaporation zone of the liquid film with high vapor quality. When the evaporation rate and entrainment rate are larger than the deposition rate of droplets, the liquid film on the wall becomes thinner gradually, and eventually torn and disappeared, making the wall directly contact with the vapor with low heat transfer coefficient. As a result, the wall temperature rises sharply, the heat transfer performance decreases greatly, and the tube bundles are prone to stress concentration near the dryout position, which leads to rupture. In practical engineering applications, accurate prediction of critical quality is very important for the safe and economical operation of heat exchangers.

At present, scholars at home and abroad have done a lot of useful research on three methods to predict the occurrence of dryout. The first one is to judge the occurrence of dryout by the critical heat flux corresponding to the sharp rise of wall temperature when the heat flux and quality are high. As early as 1980, Levy et al. (1981) extended the existing adiabatic two-phase annular flow model to predict the critical heat flux with mass flow rate, pressure and pipe diameter. It is found that CHF decreased slowly with the increase of critical quality, and droplet deposition played an important role in this process. In 1995, a look-up table for critical heat flux based on an extensive database of CHF values was jointly developed by the Canadian AECL Research and the Russian IPPE Institute. Meanwhile, Groeneveld et al. (1996) evaluated several empirical correlations based on the database. El Nakla et al. (2013) have established two look-up tables for critical heat flux prediction of large-diameter vertical and horizontal boiler tubes, which are equally applicable to accident scenarios and flow oscillation. Kim et al. (2000) carried out an experimental study on steam-water two-phase flow in a vertical smooth tube under low pressure and low flow rate (LPLF) in 2000, which acquired 513 experimental data of critical heat flux. The variation trend of critical heat flux with pressure and mass flow rate was obtained, and the CHF values were compared with the prediction results. It is found that the prediction results of Shah correlation are more accurate.

The second method is based on the mechanism of dryout to analyze the breakdown of the liquid film. With the process of flow and heat transfer, film evaporation, droplet splash and droplet entrainment in the forced convection evaporation zone of the liquid film will cause film breakdown, and dryout occurs when the film disappears completely. That is to say, when the liquid film thickness or flow rate is zero, dryout occurs. The study of liquid film rupture characteristics can be divided into theoretical and experimental studies. In theoretical research, firstly, Hatley and Murgatroyd (1964) proposed the force balance model and the minimum energy model for the breakdown of the isothermal liquid film and gave the formula for calculating the critical liquid film thickness. After that, David G et al. (Penn et al., 2001) proposed a new CFD method for calculating the surface interaction force of liquid film on the heated wall of vapor–liquid two-phase flow. However, most experimental studies consider that the non-uniform temperature distribution is the main cause of the tearing of liquid film. Fujita and Ueda (1978) proposed a formula for calculating the liquid film deformation coefficient K and observed the whole process of the tearing in the experiment. Budiman et al. (1996) studied the relationship between the breakdown of the liquid film and the surface tension of mixed refrigerant by the experimental method. It was observed that when the liquid film flowed over the heated surface, it would cause local thinning, instability, rupture, and dry spots. If the surface tension of the mixture increased with the evaporation, the liquid film would be stable. On the contrary, it is unstable.

The third method is to predict the location of dryout by calculating the critical quality in different working conditions through empirical correlation. Chung et al. (2014) studied the boiling heat transfer and dryout conditions of helical tubes under high pressure by changing the pressure and mass flow rate. According to the experimental results, the dryout position of helical tubes was analyzed, and the applicability of various empirical correlations was obtained. Based on a large number of experimental data, Sameer S et al. (Marathe and Webb, 2008) took the steam generator as the research background and analyzed various methods for predicting the forced convection evaporation zone of the liquid film in a vertical tube on high mass flow rate conditions. The working medium included water and refrigerant. Kim and Mudawar (2013) obtained a correlation for predicting boiling heat transfer and evaporation of two-phase flow in a microchannel in 2013 by using 997 dryout data points of water, CO2 and refrigerant from 26 microchannels of different sources. The correlation is composed of Weber number, pressure, boiling number, capillary number and density ratio. According to the prediction accuracy preference, the errors were within (+50%). Mastrullo et al. (2012) monitored and analyzed visually the flow patterns of CO2 and R410a in horizontal smooth tubes during the boiling process in 2012. 1420 experimental data were collected, and a new correlation formula for predicting the critical quality of two-phase flow boiling heat transfer with CO2 and R410a as working mediums was proposed. In terms of numerical simulation, Hoyer (1998) proposed a method of predicting heat transfer in tubes based on the three-flow field model according to the disappearance of liquid film on the wall in 1998. It was applied to the MONA code framework of a general simulator for the one-component two-phase flow system, and the experimental results of pressure drop, the position of dryout, critical quality and inner wall temperature were used to verify. The results show that the method is accurate and the root mean square error is less than 5%. Jayanti and Valette (2005) studied the wall temperature rise range and the position of dryout point in vertical upward rod bundle by numerical simulation and proposed a new one-dimensional three-flow field model for predicting critical quality and critical heat flux. The model also includes interphase momentum equation, thermal phase transformation equation, entrainment deposition equation of droplets and so on. The simulation results were compared with the experimental results. The results show that the model is more accurate when the pressure range is 0.3–13.0 MPa and the mass flow rate range is 50–800 kg/(m2 s).

In summary, the experimental process of the first prediction method, namely critical heat flux method, is to obtain critical heat flux by continuously increasing the heat flux on the outer wall of the pipeline until the wall temperature rises rapidly. The experimental operation is simple comparatively. Scholars have proposed many empirical models that can accurately predict CHF, but for a particular working condition of the study, in general, the heat flux is usually constant (e.g. electric heating). By comparing the CFH calculated by this method with the given heat flux, we can judge whether the dryout occurs or not, but we cannot predict the general location of the dryout under specific conditions. The second prediction method based on the mechanism of dryout is put forward according to the sufficient theoretical basis. This method is the most accurate method to judge the occurrence of dryout, but it is very difficult to monitor the thickness and flow rate of the liquid film in heat transfer tubes in engineering practice, so this method cannot be widely used. Compared with the previous two methods, the third method fits empirical correlations based on a large number of experimental data which can be used to predict the critical quality under specific conditions. Although it is not as accurate as the prediction method based on the dryout mechanism, its calculation process is simple and the prediction results meet the engineering requirements so that it is popularized. At the same time, for the critical quality under high pressure and high mass flow rate, the prediction accuracy of the empirical correlation is low and the error is large.

Therefore, the purpose of this study is to give a new empirical correlation for predicting the critical quality of large-scale steam-liquid two-phase flow accurately to provide some technical support for the safe operation of heat exchangers.

Section snippets

Different correlations of dryout quality

There are many correlations for calculating critical quality, and the predicted results are quite different. The common formula correlations are given below in Table 1.

Most of the existing formula correlations for predicting critical quality are fitted by physical parameters such as density, viscosity, surface tension and operating parameters such as mass flow rate, pressure. A lot of experiments show that the diameter of the heat transfer tube, mass flow rate, operating pressure, working fluid

Results analysis

The comparison of predicted and experimental values of critical quality in Becker experiment by correlation (8) is shown in Fig. 3. The (a)–(f) in the figure corresponds to six regions in Eq. (8) respectively. It can be seen that when the operating pressure ranges from 2.9 MPa to 8.5 MPa, the error between the predicted value and the experimental value of the correlation (8) is within (±20%), and the maximum error is 15.1%. When the operating pressure is greater than 8.5 MPa, only a few data

Conclusions

A new correlation for predicting the critical quality is proposed, which can be used to accurately predict the critical quality of steam-liquid two-phase flow in vertical pipes with water as the working medium, with pressure ranging from 2.9 to 20.1 MPa, mass flow rate ranging from 496 to 3120 kg/(m2 s), heat flux less than 1268 kW/m2 and pipe diameter ranging from 10 to 24.7 mm.

In engineering practice, the selection of empirical correlations needs to be based on the actual situation. For the

CRediT authorship contribution statement

Wanze Wu: Conceptualization, Methodology, Validation, Visualization Preparation, Software, Investigation, Data collection, Writing - Original Draft. Baozhi Sun: Resources, Visualization Preparation, Formal analysis, Review & Editing. Jianxin Shi: Validation, Formal analysis, Review & Editing. Xiang Yu: Review & Editing, Supervision. Zhirui Zhao: Review & Editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was sponsored by the National Natural Science Foundation of China (No. 51579048) and the Fundamental Research Funds for the Central Universities (No. 3072019CFJ0303) which we gratefully acknowledge.

References (29)

Cited by (1)

View full text