A new correlation of two-phase frictional pressure drop for evaporating flow in pipesNouvelle corrélation pour la chute de pression due au frottement lors de l'écoulement diphasique évaporatif àl'intérieur de canaux

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Abstract

The calculation of two-phase frictional pressure drop for evaporating flow in pipes is required in many fields. Although plenty of studies associated with this issue have been carried out, an accurate correlation is still needed. In this paper, a comprehensive survey of correlations and experimental investigations of two-phase frictional pressure drop is conducted. The 2622 experimental data points of 15 refrigerants are obtained, with hydraulic diameter from 0.81 to 19.1 mm, mass flux from 25.4 to 1150 kg m−2 s−1, and heat flux from 0.6 to 150 kW m−2. There are 29 existing correlations evaluated against the experimental database. It is found that the best correlation has a mean absolute relative deviation (MARD) of 28.5%. Based on the experimental database, a new correlation is proposed, which has an MARD of 25.2%, improving remarkably the prediction of two-phase frictional pressure drop for pipe evaporating flow, especially for micro-channels.

Highlights

► Correlations of two-phase frictional pressure drop (THFPD) are reviewed. ► Survey of THFPD experimental data of evaporating flow is conducted. ► Applicability of the existing THFPD correlations to evaporating flow is assessed. ► A new THFPD correlation for evaporating flow in pipes is proposed.

Introduction

Frictional pressure drop of two-phase flow in pipes has been a research subject for several decades. It is an important parameter in the design of many industrial devices and systems, such as pipes, heat exchangers, refrigeration systems, air conditioning systems, and spacecraft thermal control systems. Evaporating flow is an important branch of two-phase flow, which has been widely deployed in numerous applications.

In order to calculate two-phase frictional pressure drop, extensive theoretical and experimental studies have been conducted. Since the mechanisms occurring in two-phase flow have not been effectively understood, lots of empirical correlations have been proposed instead. In order to assess which correlations could predict two-phase frictional pressure drop more accurately, some researchers have compared certain correlations with different experimental data sets (Tribbe and Muller-Steinhagen, 2000, Choi et al., 2008, Sun and Mishima, 2009, Zhang et al., 2010, Li and Wu, 2010, Fang et al., 2012).

The characteristic of two-phase frictional pressure drop of evaporating flow is different from that of other flows (Zhang et al., 2010), thus, understanding the two-phase frictional pressure drop characteristic of evaporating flow is of considerable necessity. Many investigations associated with evaporating flow have been conducted, while attempts to evaluate two-phase frictional pressure drop correlations applied to evaporating flow are limited, among which some conclusions are inconsistent, even controversial. Some investigations which are closely connected to two-phase frictional pressure drop for evaporating flow in pipes are briefly reviewed in the following.

Ould Didi et al. (2002) evaluated 7 correlations (Lockhart and Martinelli, 1949, Chisholm, 1973, Bankoff, 1960, Chawla, 1967, Friedel, 1979, Gronnerud, 1979, Muller-Steinhagen and Heck, 1986) according to the experimental data of 5 fluids evaporating in two pipes of 10.92 and 12.0 mm ID with mass flux from 100 to 500 kg m−2 s−1 and vapor quality from 0.04 to 1.0. It was found that the methods of Muller-Steinhagen and Heck (1986) and Gronnerud (1979) provided the most accurate predictions and that the widely quoted method of Friedel (1979) gave the third-best results. They also categorized the experimental data according to the flow pattern map proposed by Kattan et al. (1998), and found that the method of Muller-Steinhagen and Heck (1986) was the best for annular flow and the Gronnerud (1979) method predict best for intermittent flow and stratified-wavy flow.

Yun and Kim (2004) investigated the two-phase frictional pressure drop of CO2 during evaporation in micro-channels of 1.08–1.54 ID with mass flux from 100 to 400 kg m−2 s−1 and heat flux in the range of 5–20 kW m−2. They evaluated 5 correlations (Chisholm, 1967, Friedel, 1979, Chen, 1982, Mishima and Hibiki, 1996, Tran et al., 2000) with their own experimental data and found that all of them showed large deviations. Although Pettersen et al. (2000) and Bredesen et al. (1997) reported that the Friedel correlation (1979) showed good estimation for CO2 in both macro- and micro-channels, it still failed to predict two-phase frictional pressure drop.

Thome and Ribatski (2005) conducted a review of two-phase frictional pressure drop of CO2 in both macro- and micro-channels. There were 5 correlations (Chisholm, 1973, Friedel, 1979, Gronnerud, 1979, Muller-Steinhagen and Heck, 1986, Yoon et al., 2004) evaluated with Brendsen et al.’s (1997) 325 experimental data of CO2 evaporating flow in a 7 mm ID tube with mass flux from 200 to 400 kg m−2 s−1 and heat flux from 3 to 9 kW m−2. Their comparisons depicted that the Friedel (1979) correlation gave the best overall results and the Muller-Steinhagen and Heck (1986) correlation followed closely. Meanwhile, they pointed out that owing to the insufficient experimental data, the reliability of Friedel (1979) correlation should be verified by a broader database.

Ribatski et al. (2006) compared 12 two-phase frictional pressure drop correlations (Lockhart and Martinelli, 1949, Chisholm, 1973, Cicchitti et al., 1960, Friedel, 1979, Gronnerud, 1979, Muller-Steinhagen and Heck, 1986, Mishima and Hibiki, 1996, Yan and Lin, 1998, Tran et al., 2000, Zhang and Webb, 2001, Chen et al., 2001) against 913 experimental data with 8 fluids flowing in micro-scale channels with mass flux in the range of 23–6000 kg m−2 s−1 and vapor quality up to 1. It was found that the correlations by Muller-Steinhagen and Heck, 1986, Mishima and Hibiki, 1996, and Cicchitti et al. (1960) could provide the most accurate predictions. They further noted that none of the evaluated correlations could be regarded as a general design correlation since even the best ones were only able to capture about one half of the data within ±30%.

Mauro et al. (2007) verified 5 methods (Moreno Quiben and Thome, 2007, Friedel, 1979, Gronnerud, 1979, Muller-Steinhagen and Heck, 1986, Jung and Radermacher, 1989) using 1110 experimental data of 7 fluids in a test section of 6.0 mm ID with mass flux in the range of 190–1150 kg m−2 s−1 and heat flux between 5 and 40 kW m−2. Their comparisons showed that the methods by Gronnerud (1979) and Moreno Quiben and Thome (2007) were equally the best. The same conclusions were gained by Revellin and Haberschill (2009) when they compared the same 5 methods with another 485 data points covering both diabatic and adiabatic experimental results. Moreover, considering different flow patterns, Mauro et al. (2007) found that in the intermittent flow the methods by Muller-Steinhagen and Heck (1986) and Moreno Quiben and Thome (2007) could give more reliable predictions and the method by Moreno Quiben and Thome (2007) was the best in annular and dryout flow.

Copetti et al. (2011) performed an experimental study of R134a evaporating flow in a horizontal tube of 2.66 mm ID with mass flux from 240 to 930 kg m−2 s−1 and heat flux between 10 and 100 kW m−2. Based on their own experimental data of two-phase frictional pressure drop, 3 correlations (Friedel, 1979, Muller-Steinhagen and Heck, 1986, Tran et al., 2000) were assessed. The correlation of Tran et al. (2000) was found to be the best satisfied one while the correlations of Friedel (1979) and Muller-Steinhagen and Heck (1986) exhibited larger errors. Besides, Wongsa-ngam et al. (2004) found that the correlation of Friedel (1979) under-predicted their experimental data of R134a flowing in a tube of 8.12 mm ID within 40% and might be not appropriate to predict the frictional pressure drop. In addition, Copetti et al. (2011) reminded that the deviations of the best correlation still remained quite large in relation to the accuracy desired for reliable thermal designs.

The above literature review clearly indicates that the correlation of two-phase frictional pressure drop for evaporating flow is still an issue needing to be solved. The present paper aims to develop a new correlation which can offer a better prediction of the two-phase frictional pressure drop for evaporating flow, for which a comprehensive survey of the experimental data of the two-phase frictional pressure drop for evaporating flow and the existing correlations for two-phase frictional pressure drop is performed. Based on the available experimental data, the evaluation of the existing correlations is conducted and a new correlation for two-phase frictional pressure drop of evaporating flow is developed.

Section snippets

The available experimental data of two-phase frictional pressure drop for evaporating flow

A comprehensive search of experimental studies on two-phase frictional pressure drop for evaporating flow is conducted and 19 available data sources are selected, as listed in Table 1. The experimental database contains 2622 data points of 15 refrigerants flowing in a wide scope of test geometries and operation conditions.

The Kandlikar (2002) classification of channel size, the Lockhart and Martinelli (1949) classification of flow regimes and the Wojtan et al. (2005) criteria of flow patterns

Existing correlations of two-phase frictional pressure drop

The correlations in each of the existing evaluations are relatively few, no more than 12. In this paper, eleven ϕl2 and ϕg2 based correlations, ten ϕlo2 and ϕgo2 based correlations, and eight homogeneous correlations are evaluated with the 2622 experimental data of evaporating flow. The eleven ϕl2 and ϕg2 based correlations include those of Lockhart and Martinelli, 1949, Chisholm, 1967, Mishima and Hibiki, 1996, Wang et al., 1997, Lee and Lee, 2001, Yu et al., 2002, Lee and Mudawar, 2005, Hwang

New correlation of two-phase frictional pressure drop for evaporating flow

Since the Muller-Steinhagen and Heck (1986) equation is the best for evaporating flow in pipes among the existing two-phase frictional pressure drop correlations, a new correlation based on the Muller-Steinhagen and Heck (1986) equation is developed by applying the least square method to the 2622 experimental data points of evaporating flow. The new correlation of two-phase frictional pressure drop for evaporating flow in pipes is of the formϕlo2={Y2x3+(1x)1/3[1+2x(Y21)]}[1+1.54(1x)0.5La1.47]

Conclusions

The 2622 experimental data points of two-phase frictional pressure drop for evaporating flow in pipes with hydraulic diameter from 0.81 to 19.1 mm, mass flux between 25.4 and 1150 kg m−2 s−1, and heat flux in the range of 0.6–150 kW m−2 are collected through a comprehensive literature survey. The 29 existing correlations for two-phase frictional pressure drop are reviewed. A new equation of two-phase frictional pressure drop for evaporating flow in pipes is proposed.

All the correlations are

Acknowledgments

This study is supported by National Natural Science Foundation of China (51176074), Funding of Jiangsu Innovation Program for Graduate Education (CXZZ12_0172), Funding for Outstanding Doctoral Dissertation in NUAA (BCXJ12-01), and the Fundamental Research Funds for the Central Universities.

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