Numerical study of enhanced and deteriorated heat transfer phenomenon in supercritical pipe flow

https://doi.org/10.1016/j.anucene.2019.106966Get rights and content

Highlights

  • Heat transfer to supercritical water flowing in a vertical pipe was numerically studied.

  • The behavior of heat transfer in supercritical fluid with different heat flux to mass flux ratio and flow direction is studied.

  • Mechanism of heat transfer enhancement and heat transfer deterioration are explained.

Abstract

The mechanism of heat transfer enhancement and heat transfer deterioration for supercritical water flowing in vertical pipe is numerically studied using in-house 2D axi-symmetric CFD code, named NAFA. The numerical results obtained by the NAFA code for Yamagamata’s experiments, agree with their experimental results, thus validating the code. Simulations are carried out for low as well as high mass fluxes keeping the same heat flux to mass flux ratio. The study of effect of flow direction is also performed. The major contribution of this work is explanation of mechanism of heat transfer enhancement and deterioration in various conditions and various factors assisting or resisting the two. This explanation is given on the basis of radial variation of thermo-physical properties of the working fluid and turbulence parameters, plotted at selected axial locations where heat transfer coefficient ratio is high or low indicating enhancement/deterioration.

Introduction

Supercritical water cooled reactor (SCWR) is one of the six next generation designs of nuclear reactor proposed by Generation-IV International Forum (U.S. DOE, 2002). SCWR has competitive advantage of higher thermal efficiency (up to 44%) (Cheng et al., 2003), which is most important reason for its consideration. The unique property of the coolant in SCWR is that no phase change from liquid to gas occurs. Hence boiling crisis gets avoided. Also, steam separator, steam drier, steam drum, etc. are not required. The coolant which enters the core in liquid like state gets heated in the core to steam like state and hence can be sent directly to the turbine. This results in simple plant design compared to conventional pressurized water reactor (PWR) and boiling water reactor (BWR). Hence SCWR is expected to achieve much low capital and operational cost compared to the conventional reactors. All these factors lead to significant economic benefits. Knowledge of Supercritical Heat Transfer (SCHT) is important for design of SCWR. Due to this, SCHT research is getting a lot of attention of researchers.

Though boiling crisis is not present at supercritical conditions, heat transfer at supercritical pressures is more complicated than that at atmospheric pressure. The SCHT gets affected by the significant changes in thermo-physical properties with temperature at such a high pressure. The most significant thermo-physical property variation occurs near the pseudo-critical point. For a given pressure, pseudo-critical point is defined as the temperature at which, specific heat has maximum value. Fig. 1 shows the isobaric variation of thermo-physical properties of water with temperature at pressure of 245 bar (Lemmon et al., 2007). From the figure, it is clear that all thermo-physical properties undergo significant change near pseudo-critical temperature (Tpc).

Such a property variation leads to complex heat transfer characteristics. The property variation affects turbulent parameters of the flow, thermal and hydrodynamic boundary layers etc., which eventually results into complex heat transfer and pressure drop characteristics at supercritical conditions compared to that at near ambient pressures where properties are nearly constant over a wide temperature range.

Supercritical flow and heat transfer has been a topic of discussion for many reviews (Cheng and Schulenberg, 2001, Pioro et al., 2004, Pioro and Duffey, 2005, Rahman et al., 2016, Wang et al., 2018). The reported reviews have discussed use of supercritical water for nuclear reactor applications which includes experimental and numerical studies. Among all the studies, most of the authors have focused on flow in vertical pipes (Shiralkar and Griffith, 1969, Zhao et al., 2014) as well as horizontal (Yu et al., 2013) whereas others have focused on flow through rod bundle (Wang et al., 2014, Gu et al., 2015a). Based on experiments performed by various authors, the heat transfer in supercritical fluids has three different characteristics, ‘normal’, ‘enhanced’ and ‘deteriorated’. The ‘normal’ SCHT characteristics refer to those in which the heat transfer rates are similar to those at atmospheric pressures (wherein fluid properties are constant). The heat transfer coefficient (HTC) can be reasonably accurately estimated by Dittus-Boelter correlation (or similar correlation e.g. Sieder-Tete correlation). The normal heat transfer phenomenon usually occurs if the bulk fluid temperature is far away from pseudo-critical point. In ‘enhanced’ heat transfer regime, HTC is significantly higher than that obtained in ‘normal’ heat transfer regime. This phenomenon is observed when bulk temperature is near pseudo-critical temperature and heat flux to mass flux ratio q/G is small. In ‘deteriorated’ heat transfer regime, heat transfer rate from wall to fluid decreases which leads to higher wall temperature. This deteriorated heat transfer phenomenon is generally observed for high q/G ratio condition. The three characteristics of heat transfer (normal, enhanced and deteriorated) in supercritical fluids are usually defined by the heat transfer coefficient ratio (HTCR). It is the ratio of actual HTC to the same computed by Dittus-Boelter correlation for the given operating and design conditions. For supercritical fluids, it is generally accepted that, normal heat transfer occurs when HTCR is close to unity. HTCR higher than unity is indicative of heat transfer enhancement (HTE), whereas the value below 0.3 indicates heat transfer deterioration (HTD) (Koshizuka et al., 1995).

In HTD regime, wall temperature increases abruptly due to insufficient heat transfer from wall to fluid. From SCWR point of view, this may increase the fuel cladding temperature. So, it is very important to understand the mechanism of HTD. In order to do so, researchers have performed experiments under various conditions of heat and mass fluxes and with various working fluids e.g. water (Yamagata et al., 1972), carbon dioxide (Adebiyi and Hall, 1976), Freon (Zhang et al., 2014), all at their respective supercritical conditions. Shiralkar and Griffith (1969) performed experiments in pipe using carbon dioxide as working fluid at supercritical pressure and they observed HTD at high heat flux for upward as well downward flow. Yamagata et al. (1972) performed experiments in vertical as well as horizontal tubes using water as working fluid. They proposed a correlation which can predict HTC at normal and enhanced heat transfer regime. For vertically upward flow, they have developed a correlation for determining the critical heat flux qc above which HTD takes place for a given mass flux (G). Zhao et al. (2014) studied the heat transfer behavior of supercritical water in vertically downward flow. On the basis of experimental data, a new correlation based on buoyancy parameter has been developed which can determine the HTC for vertically downward flow. Parametric studies, for example effect of pressure, mass flux etc. on heat transfer were performed as well. Similar types of parametric studies were also performed by Gu et al. (2015b) for vertically upward flow.

Apart from experimental studies, several numerical analyses also have been carried out by researchers. Koshizuka et al. (1995) had numerically studied the HTD in supercritical water flowing vertically upward in pipe. Two dimensional axi-symmetric solver based on k-ε turbulence model was used for numerical simulations. They proposed two different mechanisms to explain HTD depending on high or low flow rates. Wen and Gu (2010) and Zhang et al. (2011) evaluated the accuracy of different turbulence models for numerical analysis of heat transfer to supercritical fluid. Similarly, Kao et al. (2010) studied the HTD in upward pipe flow using Reynolds stress turbulence model and RNG k-ε turbulence model. They showed the importance of buoyancy, which originates from large property variation. They found that HTD can be diminished by increasing inlet temperature and operating pressure. Jaromin and Anglart (2013) studied the normal and HTD phenomenon at high and low mass fluxes in upward flow condition. They concluded that for HTD, buoyancy is mainly responsible in low mass flux cases whereas property variation is the main cause in high mass flux cases.

Some authors have proposed SCWR core design concepts (Schulenberg et al., 2008, Yamaji et al., 2005, Cheng et al., 2008). As shown in Fig. 2, in a concept proposed by Schulenberg et al. (2008), the reactor core is divided into three zones namely evaporator, superheater-1 and superheater-2, with each zone containing 52 assembly clusters. The flow path has a three-pass concept. The coolant enters reactor core in evaporator zone and flows upwards. Then it enters upper mixing chamber after which it turns downward and flows downwards in the superheater-1 zone. Finally, it flows upwards in superheater-2 zone. Similarly, the design concepts proposed by other authors (Cheng et al., 2008, Yamaji et al., 2005) are also based on multiple flow passes. Hence, the supercritical coolant flows in upward as well as downward directions and receives heat from bundles. Hence it is important to understand the effect of upward/downward flow direction on supercritical heat transfer characteristics. Further, in each pass, it encounters different heat fluxes as well as cross sectional flow areas. Hence heat flux to mass flux ratios are different in each zone.

Hence in present work, the focus is on studying the effect of flow direction with respect to gravity and q/G ratio on supercritical heat transfer characteristics.

Another important objective of this work is explanation of mechanism of heat transfer enhancement and deterioration in various conditions and understanding various factors affecting the two phenomena. This is done by simulating various cases and analyzing in the detail the flow field data obtained from the CFD simulations.

This study is carried out using an in-house axi-symmetric CFD code (NAFA) which is especially developed for this purpose. The methodology of numerical simulation implemented in NAFA code is explained in next section and in later sections, various results are discussed.

Section snippets

Geometrical model

NAFA is based on axi-symmetric formulation. For vertically upward or downward pipe flows axi-symmetric assumption is valid. Fig. 3 shows the actual geometry which is a circular cross-section pipe. The corresponding axi-symmetric model is also shown in the figure. The governing equations are axi-symmetric forms of (i) Reynolds averaged continuity equation; (ii) Reynolds averaged radial and axial momentum equations; (iii) Reynolds averaged thermal energy conservation equation and (iv) turbulence

Results and discussion

Since the objective of current work is to study the mechanisms behind HTE and HTD, the simulations are performed for various cases. The supercritical flow in pipe is computed under various conditions. The computational geometry is a vertical circular pipe with dimensions same as that of Yamagata in all cases. Operating pressure is 245 bar in all the cases.

Summary and conclusions

The flow and heat transfer behavior of supercritical water in vertical pipe has been studied using in-house CFD code (NAFA). The code results are validated against experimental data reported by Yamagata et al. (1972). Simulations are performed for various cases (low/high q/G ratio, upward/downward flow and low/high mass flux) to understand the mechanisms of HTE and HTD. The main conclusions are as follows.

  • For low q/G, the effect of flow direction is not significant. In this case HTE has been

References (27)

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