Review of the nuclear reactor thermal hydraulic research in ocean motions

Nuclear Engineering and Design 313 (2017) 370–385

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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Review of the nuclear reactor thermal hydraulic research in ocean motions B.H. Yan Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Tangjiawan, Zhuhai, Guangdong, China

a r t i c l e

i n f o

Article history: Received 17 October 2016 Received in revised form 29 December 2016 Accepted 31 December 2016

Keywords: Ocean motion Thermal hydraulic Critical heat flux Flow and heat transfer

a b s t r a c t The research and development of small modular reactor in floating platform has been strongly supported by Chinese government and enterprises. Due to the effect of ocean waves, the thermal hydraulic behavior and safety characteristics of floating reactor are different from that of land-based reactor. Many scholars including the author have published their research and results in open literatures. Much of these literatures are valuable but there are also some contradictory conclusions. In this wok, the nuclear reactor thermal hydraulic research in ocean motions was systematically summarized. Valuable results and experimental data were analyzed and classified. Inherent mechanism for controversial issues in different experiments was explained. Necessary work needed in the future was suggested. Through this work, we attempt to find as many valuable results as possible for the designing and subsequent research. Ó 2017 Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

4.

5. 6.

7.

Description of ocean motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Single phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Two phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Single phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Circular tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Rectangular channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Two phase flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Frictional pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Flow pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3. Bubble behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CFD analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Single channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Complex channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Code analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Instability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Forced circulation and natural circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1. Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2. Numerical research. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Critical heat flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Application of empirical correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E-mail address: [email protected] http://dx.doi.org/10.1016/j.nucengdes.2016.12.041 0029-5493/Ó 2017 Elsevier B.V. All rights reserved.

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In 20th century, many countries have accelerated the development of advanced small modular reactor (SMR). According to the classification adopted by the IAEA, ‘‘‘SMRs’ are reactors with equivalent electric power less than 300 MW (IAEA-TECDOC-1451, 2005)”. Compared with the third generation nuclear power plant, the SMR of modular design is more flexible and of higher passive safety According to the report (IAEA-TECDOC-1451, 2005), several countries have launched their development program of SMRs, including America (SMR, mPower, and NuScale), Russia (KLT-40S, ABV, VK-300 and VBER-300), India (AHWR), Argentina (CAREM), Korea (SMART), France (NP-300), Japan (MRX and HTTR), China (HTR-PM, ACP100 and ACPR50S), etc. Until now, there are 26 SMRs under operation in the world. Besides that, there are also 4 SMRs under construction (Li et al., 2013a1). SMRs are of particular interest for both near-term, e.g. seawater desalination, and advanced future non-electrical applications, such as hydrogen production and coal liquefaction. In China, the resources of oil and natural gas are in rich deposits in coastal region. The existing energy supply method is of high cost and pollution, resulting in a large emission reduction pressure. The SMR is an effective way to solve this problem and could fulfill the requirement of electrical energy supplying in oceans. The SMR could be built on land or on a floating platform. Lee et al. (2013) presented a new concept for offshore nuclear power plants (ONPP) with enhanced safety features. The design concept of a nuclear power plant was mounted on gravity-based structures. A new emergency passive containment cooling system and emergency passive reactor-vessel cooling system were proposed. The seawater was used as coolant against earthquakes, Tsunamis, storms, and marine collisions. Buongiorno and his team proposed a new offshore floating nuclear plant (OFNP) concept with high potential for attractive economics and an unprecedented level of safety (Jurewicz, 2015). OFNP creatively combined state-of-theart light water reactors and floating platforms similar to those used in offshore oil/gas operations. It eliminated earthquakes and tsunamis as accident precursors; its ocean-based passive safety systems eliminate the loss of ultimate heat sink accident by design. The OFNP crews operated in monthly or semimonthly shifts with onboard living quarters, like on oil/gas platforms. OFNP was a reactor for the global market which can be constructed in one country and exported internationally. In China, several SMRs built on a floating platform are being designed (Li et al., 2013a). In ocean motions, the designing and operation of nuclear reactor is not exactly the same with that on land. Due to the action of waves, the coolant flow in primary loop and secondary loop is affected by additional forces. The gravitational pressure drop might also be changed due to the height variation between the reactor core and steam generator. The earliest open literature about the designing floating nuclear reactor was published by Isshiki (1966), Hiroshi and Kazuo (1969). They suggested that the guarantee of safety in nuclear ship is a dominant design criterion. From then on, more and more scholars have participated in the designing of nuclear reactor in ocean motions. Most of them were devoted in nuclear reactor thermal hydraulic analysis. In recent years, the SMRs ACP100 and ACPR50S are being designed and are going to be built in China. Until now, much work including mathematical models for single phase and two phase flow and heat transfer in ocean motions, developing of thermal

1 In order to distinguish the references from different authors with the same first name and the same publication year, the abbreviation of their second names is added in the citation. For example, the reference authored by Li et al. in 2013 is cited as Li et al. (2013a), rather Li et al. (2013). The reference authored by Li et al. in 2013 is cited as Li et al. (2013d), rather Li et al. (2013). This kind of citation is introduced in the subsequent section.

Heaving Rolling Yawing Surging

Axis Pitching Swaying Fig. 1. Ship motions.

hydraulic code and sub-channel analysis code in ocean motions have been carried out. Although many analysis results and theoretical models have been published in open literatures, there are still plenty of numerical and experimental researches need to be finished. In this work, the investigation about nuclear reactor thermal hydraulic is systematically summarized. From mathematical models to the sub-channel analysis code and two phase flow experiments, most papers published in open literatures in this field are classified and evaluated. Through this work, we wish to find as many valuable results as possible for future work. 1. Description of ocean motions The ocean motions that contributing to the nuclear reactor thermal hydraulic characteristics are usually caused by the ocean surface waves that occur in the upper layer of the ocean. They usually result from wind or geologic effects and range in size from small ripples to huge waves. Then the ocean motions affect on the ships or floating platforms and then result in difficult ship motions, as shown in Fig. 1. The ship motions are determined by ocean motions and ship parameters, like weight, length, height, etc. The law of ocean waves is complex, which one sees on an ocean beach usually result from winds. The wind usually changes with space and time. Therefore, the ocean motions and ship motions change with space and time, just like the wind waves. Due to the complexity of ocean motions, the real time simulation with high accuracy of nuclear power system on a floating platform is unrealizable. The research of seakeeping theory reveals that the complex ship motions are equivalent to the superposition of several single sinusoidal motions, approximately (Lewis, 1967). Ishida et al. (1990) investigated the thermal hydraulic behavior of a reactor with RETRAN code by assuming the ship motions to be a sinusoidal function. This method has been followed by nearly all scholars. The ship motions mainly include heeling, heaving, rolling, pitching, yawing, swaying and surging motions (Ishida et al., 1990). In heeling or inclination motion, there is only height difference change but no additional force, which is different form the other six motions. The amplitudes of yawing, surging and swaying motions are usually very small, since the ship and floating platforms are long and narrow designed. Compared with these three motions, the heeling, heaving, rolling and pitching motions are more frequent. In heeling motion, neither additional acceleration nor inertial force exists. Only the relative height difference between reactor core and steam generator is changed. That is the simplest motion and closest to the stationary state. In heaving motion, contrast to the heeling motion, there is no spatial distance variation, only an additional gravitational acceleration affects on the coolant flow. It was expressed by Ishida et al. (1990) as:

gðtÞ ¼ g 0 þ g a sinðntÞ

ð1Þ

where g 0 is gravitational acceleration in stationary state, g a and n are the amplitude and frequency of the heaving motion, respectively. t is time.

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B.H. Yan / Nuclear Engineering and Design 313 (2017) 370–385

Ft '

Z

Fn'

u

Fc'

r

Y

O X Fig. 2. Additional force.

In rolling and pitching motions, the coolant flow in nuclear systems is affected by an additional force in a non-inertial coordinate (Zhou et al., 2015). The additional force consists of three parts, tangential force, normal force and the Coriolis force, as shown in Fig. 2. It can be expressed as: !

!

!

!

!

!

!

F ¼ F 0n þ F 0t þ F 0c ¼ q  ½b  r þ x ðx  r Þ þ 2 x  u  where F,

F 0n ,

F 0t ,

and

F 0c

ð2Þ

are additional force, tangential force, normal !

!

force and the Coriolis force, respectively. q is fluid density. x and b !

stand for rolling angle velocity and acceleration, respectively. r is !

the vector radius and u denotes velocity. The comparison of heeling, heaving, rolling and pitching motions are shown in Table 1. It shows that the heeling motion is the simplest, followed by the heaving motion. The rolling motion and pitching motion are the most complex. 2. Theoretical models 2.1. Single phase flow As for the flow in a tube or a channel, ocean motion might result in two additional forces, one is parallel to the flowing direction and the other is vertical to the flowing direction. The former one might induce an oscillating velocity while the latter one might result in a change of boundary layer, and the flowing resistance and heat transfer coefficient changes finally. The developing of theoretical models for the single phase flow and heat transfer should be based on the momentum and energy equation in ocean motions. The models for the laminar flow and turbulent flow should be established separately. Huang et al. (2010) developed the flowing model in a tube in rolling motion by assuming that the pressure gradient variation caused by rolling motion is in a cosine function. Then they obtained the velocity profile with the segregation variable method and complex function method. Liu (2011) applied this method and developed the flowing model in a rectangular channel in rolling motion. He obtained the velocity profile in rectangular channels and analyzed the effects of period, amplitude and channel size on the velocity field. Yan et al. (2011a) expanded their researches and developed the flow and heat transfer models of laminar flow

in heaving and rolling motions. Then they derived the correlations for frictional resistance coefficient and the Nusselt number. Their results indicated that the time averaged frictional resistance coefficient and Nusselt number were equivalent to that in stationary state. This conclusion was verified by Xing (2013). Zhou et al. (2015) established mathematical model for adiabatic laminar flow in narrow rectangular channel in heaving motion. They derived the analytical solution of the frictional resistance coefficient based on some reasonable assumptions. Yan et al. (2010) obtained the flow and heat transfer models of turbulent flow in tubes and rectangular channels in rolling motion. They got the correlations for the frictional resistance coefficient and the Nusselt number of turbulent flow in rolling motion. Wang (2013) carried out similar works and developed the mathematical models of pulsating flow in tubes. His results revealed that there was a phase difference between flowing velocity and pressure difference. It seems that the theoretical models for laminar flow and heat transfer could be established if the ocean motions are equivalent to pressure oscillations. But the models for the turbulent flow need more assumptions. The transition from laminar to turbulent flow is a complex process. In ocean motions, whether the critical Reynolds number will be increased or decreased is not clear. Yan (2011) tried to analyze the transition in ocean motions with energy gradient method. His research revealed that the effect of ocean motions on transition process depended on the oscillating amplitude and period. This work was conducted by Yuan et al. (2014) subsequently. Their results indicated that the critical Reynolds number of accelerated flow was smaller than that of steady flow. While that of decelerated flow was larger than that of steady flow. These results were in agreement with experimental data. Zhang (2013a) investigated the transition process of pulsating flow in narrow rectangular channel. His results revealed that the laminar flow transit to turbulent flow in advance with positive acceleration, which was consistent with the result of Yuan et al. (2014). They also analyzed the flow and heat transfer in laminar-turbulent transitional flow regime in rolling motion. It was found that the average friction factor and Nusselt number were higher than that of the corresponding steady flow as the flow rate fluctuates in transition regime (Yuan et al., 2016). Until now, the experiments about the transition were mainly conducted for the accelerated flow and decelerated flow. The effects of pressure oscillation on the transition process should be analyzed. 2.2. Two phase flow The two phase flow and heat transfer is more complex than the single phase flow and heat transfer. The available quantitative results and their application ranges in steady state are usually attributed to plenty of experimental data. Qin and Gao (2008) compared the forces acting on bubbles in rolling motion with that in stationary state. Their results indicated that rolling motion may contribute significantly to the bubble departure position and finally affect on the boiling heat transfer. Hong et al. (2011) analyzed the forces on bubbles in heaving motion. Their work revealed that the effect of heaving motion on bubbles in natural circulation was more significant than that in forced circulation. In natural

Table 1 Comparison of different motions. Ocean motions

Height variation

Heeling Heaving Rolling Pitching

Yes

Gravitational acceleration

Tangential force

Normal force

Coriolis force

Yes Yes

Yes Yes

Yes Yes

Yes Yes Yes

B.H. Yan / Nuclear Engineering and Design 313 (2017) 370–385

circulation, the effect of heaving motion depended on the flow rate fluctuation. But in forced circulation, the effect of heaving motion was dominated by the buoyancy force. Their work also showed that ocean motions may change the position of vapor bubble departure, which was in agreement with the results of Qin and Gao (2008). Yan et al. (2013) developed the mathematical model describing the effect of periodical inertial forces on bubbles in rolling motion. In their derivation, the rotation of bubbles was neglected. Their research indicated that the effect of centrifugal and Coriolis forces on bubbles could be ignored, while the tangential force contribute significantly to the bubble behavior, and reaching to its maximum when the rolling motion was at maximum rolling angle. Cao (2006) tried to establish the slug flow unit model for further analyzing the slug flow in tubes in rolling motion. She derived the correlation of average void fraction with less than 40% error compared with experimental data. Yan et al. (2015) expanded her research and established the pressure model for slug flow in rectangular channels in rolling motion. They obtained the correlation of frictional pressure drop with about 20% error compared with experimental results. Wang et al. (2013b) analyzed the high quality flow in natural circulation in rolling motion and found that the relative stable flow was mainly caused by the increasing of driving head and frictional resistance. In the analysis of two phase flow, it is important to identify the magnitudes of various forces. If the magnitude of additional force is two or three orders less than the other forces, the effect of ocean motions could be neglected. Otherwise, the effect of ocean motions should be analyzed. The two phase flow could be divided into bubbly flow, slug flow, annular flow, mist flow, and so on. The theoretical models published in open literatures are mainly about the slug flow and bubbly flow. The models for the other flow pattern with high accuracy are also needed in the subsequent investigation.

3. Experiments 3.1. Single phase flow 3.1.1. Circular tube The experimental research about the single phase flow and heat transfer in ocean motions is mainly focused on the circular tube and rectangular channel. Tan (2006) conducted the flow and heat transfer experiments of single phase natural circulation in a vertical tube in rolling motion. His results revealed that rolling motion could generate periodical pulsating flow. In ocean motions, the natural circulation flow rate decreases due to the increasing of flowing resistance. The experiments of Cao (2006) revealed that the frictional resistance coefficient oscillates with rolling motion, which is in agreement with the experiments of Zhang (2009). But its oscillating amplitude decreases with the Reynolds number increasing. The effect of rolling amplitude on the frictional resistance coefficient is not as significant as that of rolling period. Jia et al. (2011) investigated the flowing resistance of pulsating flow experimentally. Their results showed that there is a phase difference between frictional pressure drop oscillation and flow oscillation. The effect of acceleration could not be neglected. Pendyala et al. (2008a) measured the flow rate and pressure drop in a vertical tube subjected to low frequency oscillations. They found that the induced flow rate fluctuations were dependent on the Reynolds number with stronger fluctuations at lower Reynolds numbers. The effective friction factor, based on the mean pressure drop and the mean flow rate, was also found higher than to be expected. This conclusion was consistent with the experiments of Tan (2006). Pendyala et al. (2008b) examined the effect of the oscillations on the heat transfer coefficient. They found that the heat transfer

373

coefficient increased with oscillations in laminar regime. But the effect of oscillations was invisible in turbulent flow regime (Re > 2100). Tan et al. (2009b) found that the heat transfer of natural circulation was enhanced in rolling motion. The heat transfer coefficient increased with the rolling amplitude and frequency increasing. Jia et al. (2010) investigated the single phase natural circulation heat transfer in rolling motion experimentally. Their results showed that the flow oscillation caused by rolling motion enhance the heat transfer. The effect of heat capacity of channel wall could not be neglected. Du et al. (2011) conducted the heat transfer experiment of single phase natural circulation in heeling and rolling motions. Their experiments indicated that the heat transfer coefficient increased at tube downside and decreased at tube upside in heeling motion. The heat transfer coefficient in forced circulation fluctuated in rolling motion. Wang et al. (2013a) conducted the single phase heat transfer experiments in a circular tube in rolling motion. Their results showed that rolling motion could contribute to the instantaneous heat transfer but had slight effect on the time averaged heat transfer. The experiments in circular tubes showed that the variation of time averaged parameters were different. But the oscillation of parameters increased with the increasing of amplitude and frequency of ocean motions. The detailed experimental parameters and contents of single phase flow in tubes are shown in Table 2. In Table 2, P, Tin, Q and Qw denote pressure, inlet temperature of the test section, flow rate and heat flux, respectively. 3.1.2. Rectangular channel The flowing channel between plate type fuel elements is one kind of rectangular channel. This design is widely used in research reactors because of its compact structure and huge heat transfer surface. Liu (2011) investigated the phase difference between velocity and pressure drop of pulsating laminar flow in rectangular channel. His results revealed that the imposed flow pulsation could cause a phase difference between velocity and pressure drop. The phase difference was determined by the channel size, fluctuation period and fluid properties. This conclusion was consistent with the experimental result of Jia et al. (2011), who found that there was a phase difference between frictional pressure drop oscillation and flow oscillation. Xie et al. (2012) carried out experiments of single phase pressure drop in a narrow rectangular channel in rolling motion. Their results showed that the frictional factor oscillates periodically in rolling motion. The mean frictional factor and its amplitude decreased with the Reynolds number increasing. The experiments of Xing (2013) indicated that the frictional pressure drop in rolling motion fluctuates periodically, with its amplitude decaying as the Reynolds number increasing and the rolling amplitude decreasing. However, they found that the effect of rolling period on the oscillating amplitude of frictional pressure drop is invisible. The results of Xing (2013) also indicated that rolling motion result in an increase of time averaged frictional resistance coefficient. This conclusion needs further test in the future. Zhuang et al. (2014) carried out flowing resistance experiments of pulsating laminar flow in rectangular channels with four different sizes. Their experiments showed that the period and amplitude of Reynolds number had no influence on the average pressure drops. Lan and Tan (2013) investigated the heat transfer in a narrow rectangular channel in rolling motion. Their experimental data indicated that rolling motion could induce the oscillation of flow rate and outlet temperature. The heat transfer coefficient in rolling motion was equivalent to that in stationary state in turbulent flow region (Re > 5000). Yu et al. (2015) investigated the temperature fluctuation in a rectangular mini-channel in rolling motion. Their results are similar with that of Lan and Tan (2013). They also observed that the temperature fluctuations were changed in different flow regions. Obviously, the oscillation of thermal hydraulic

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Table 2 Experiments of single phase flow in tubes. References

Inner diameter

Cao (2006) Du et al. (2011) Jia et al. (2011) Jia et al. (2010) Pendyala et al. (2008a) Pendyala et al. (2008b) Tan (2006) Tan et al. (2009b) Wang et al. (2013a) Zhang (2009)

15, 25, 34.5 mm 10 mm 16.1 mm 16 mm 16 mm 16 mm 14 mm 14 mm 12 mm 34.5 mm

Direction

Vertical Vertical Horizontal Horizontal Vertical Vertical Vertical Vertical Vertical Horizontal

Ocean motion

Parameters

Contents 2

Amplitude

Period (s)

P (MPa)

Tin (°C)

Q

Qw (kw/m )

10–20° 30° – 10–20° – – 10–20° 10–20° 10–20° 10–20°

5–15 – 10–20 7.5–12.5 2–8 2–8 7.5–12.5 7.5–12.5 10–20 10–20

0.1 10 – 0.1–0.4 – – 0.1–0.4 0.1–0.4 – 0.1

– 57–60 18–20 40–80 – – 40–90 40–100 – 25

0–10 m3/h 1061–1414 kg/(m2 s) 1.1–3.8 m/s – Re = 500–6500 Re = 500–6500 – – Re = 5000–16,000 0.15–2.4 m/s

– 265–531 – – – 3.4–10.8 – – Heat transfer –

Flow Heat transfer Flow Heat transfer Flow Heat transfer Flow Heat transfer Heat transfer Flow

Notes: ‘‘–” means the data is unavailable in this reference.

(a) Fanning factor from Ma J et al 2013

(b) Frictional resistance coefficient from Xie et al 2012

Fig. 3. Comparison of frictional resistance coefficients in rolling motion.

parameters in rectangular channel is similar to that in circular tube. Liu et al. (2011) conducted single phase isothermal flow experiments in heaving motion. Their results indicated that the heaving motion had no effects on isothermal flow. The formula for friction resistance calculation obtained in stationary state is also available in heaving motion. Their experiments in rolling motion also showed that the correlations of frictional resistance coefficient in stationary state were applicable in rolling motion (Liu et al., 2012). Ma et al. (2013a) carried out laminar flow experiments in a rectangular duct in rolling motion. Their results showed that the friction factor of laminar flow (900 < Re < 2600) were not affected by rolling motion, which were in satisfactory agreement with the experimental results of Liu et al. (2011, 2012). Obviously, the results of Liu et al. (2011, 2012) and Ma et al. (2013a) are not in satisfactory agreement with the results of Liu (2011), Jia et al. (2011), Xie et al. (2012), Xing (2013) and Lan and Tan (2013), even in laminar flow region. We compare the experimental results of Ma et al. (2013a) and Xie et al. (2012) in Fig. 3. The experimental parameters in Fig. 3a from Ma et al. (2013a) are of Re = 918 and 15° and 10 s, while that in Fig. 3b from Xie et al. (2012) are of Re = 902 and 10° and 8 s. The thermal hydraulic parameters and rolling motion are very similar. The frictional resistance coefficient shown in Fig. 3b is four times of the Fanning factor shown in Fig. 3a, with the formula as followings:

f ¼ 4C f

ð3Þ

Fig. 3 indicates that the relative oscillating amplitude of the Fanning factor is next to zero while that of the frictional resistance coefficient is more than 5%. This discrepancy is caused by the fact

Fig. 4. Effect of pressure head on mass flow rate (Xing (2013)).

that the flowing velocity in the experiment of Ma et al. (2013a) is constant while that in the experiment of Xie et al. (2012) oscillates periodically. Although the rolling amplitude in the experiments of Ma et al. (2013a) was higher than that in the experiment of Xie et al. (2012), the velocity oscillation in the former was less than that in the latter. This phenomenon is caused by the discrepancy

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B.H. Yan / Nuclear Engineering and Design 313 (2017) 370–385 Table 3 Experiments of single phase flow in rectangular channels. References

Channel size (mm)

Direction

Lan and Tan (2013) Liu (2011) Liu et al. (2011) Liu et al. (2012) Ma et al. (2013a) Xie et al. (2012) Xing (2013) Yu et al. (2015) Zhuang et al. (2014)

40  2 40.38  3.1 40  2 40  2 40  2 – 40  2, 43  1.53 40  2 39.87  1.95 39.86  2.82 20.0  4.15 10.0  4.15

Vertical – Vertical Vertical Vertical Vertical Vertical Vertical Horizontal

Ocean motion

Parameters

Contents

Amplitude

Period (s)

P (MPa)

Tin (°C)

Re

Qw

10–20° – 0.8 m 25° – 10–30° 10–30° 10–20° Relative amplitude: 0.047–0.92

10–20 5–120 6–10 8 – 8–16 8–16 10–20 6–600

0.3 0.1 3 3 3 0.1 0.1 0.4 0.1

50 14–15 30 30 24–37.5 20 20 30 7.8–24

1000–20,000 0–4000 1000–12,000 1000–12,000 1000–2550 551–46,995 200–25,000 1500–10,000 142–10,678 230–11,025 304–4013 520–6850

– – – – – – – 2–18 kw –

Heat transfer Flow Flow Flow Flow Flow Flow Temperature Flow

Notes: ‘‘–” means the data is unavailable in this reference.

of different loop configurations. For example, assuming there are two loops, a complex loop and a simple loop. The flowing velocity in one loop is equivalent to the other one. The driving and drag pressure drop in the complex loop is 1000 Pa, while that in the simple loop is 100 Pa. If the additional pressure drop caused by ocean motion is 10 Pa. The variation of ocean motion on the pressure drop in the complex loop is 1%, while that in the simple loop is 10%. Finally, the velocity oscillation in the complex loop is much weaker than that in the simple loop. The detailed theoretical formula is shown in Eq. (4).

L dW ¼ DP d  DP f þ DP a A dt

ð4Þ

where L is channel length, A is flow area, W is mass flow rate, t is time, DPd , DPf and DPa are the driving pressure drop, resistance pressure drop and additional pressure drop, respectively. It can be found that the velocity oscillation is determined by the ratio of DP a and DP d . The amplitude of velocity oscillation increases with the ratio increasing. This is in agreement with the experiments of Xing (2013). His experiments revealed that the oscillating amplitude of mass flow rate decreased with the pressure head increasing. The relative oscillating amplitude decreases from 10% to 1% as the pressure head increases from 4.0 mH2O to 48 mH2O, as shown in Fig. 4. The detailed experimental parameters and contents of single phase flow in rectangular channels are shown in Table 3. Therefore, it could be concluded that the effect of ocean motions on the single phase flow and heat transfer is dominated by the ratio of additional pressure drop and drive pressure drop. If the ratio is very small (<1%), the effect of ocean motions could be neglected. However, if the ratio is big enough, the single phase flow and heat transfer are affected by the ocean motions. The oscillating amplitudes of parameters increase with the amplitude and frequency of ocean motions increasing. 3.2. Two phase flow 3.2.1. Frictional pressure drop Cao (2006) analyzed the two phase frictional pressure drop of bubble flow in rolling tubes. She compared the theoretical correlations with the experimental data and obtained a relative error of ±25%. Li et al. (2013b) conducted the experiments of two phase frictional pressure drop in rolling motion. They found that the effect of rolling period on the oscillating amplitude of frictional pressure drop was invisible. The correlations of two phase frictional pressure drop in stationary state are applicable in rolling motion. Jin et al. (2012, 2013) carried out two phase flow

experiments in narrow channels in rolling motion. Their experiments showed that the frictional pressure drop oscillate periodically in rolling motion. The oscillating amplitude of frictional resistance coefficient increases with the increasing of rolling amplitude, frequency and mass quality. Jin and his group continued to investigate the frictional resistance of bubbly flow in rectangular ducts with different sizes (Jin et al., 2014a). Their subsequent experiments revealed that the restriction of channel wall on flowing resistance was significant. Liu (2012) investigated the frictional pressure drop of two phase flow in a tube and a rectangular channel. His experiments revealed that rolling motion resulted in the oscillation of flowing parameters. But the time averaged values remain constant, which are consistent with the experiments of Li et al. (2013b). The results of Liu (2012) are also in agreement with the research of Xing (2013) and Chen et al. (2015). The experimental researches of two phase frictional pressure drop revealed that ocean motions induce the oscillation of flowing parameters, but have no effect on the time averaged parameters of two phase flow. This unified conclusion might be caused by the fact that the two phase frictional pressure drop is usually about 2–3 orders higher than the additional pressure drop. According to Eq. (4), the additional pressure drop is so small that could be neglected. This conclusion is encouraging but we still need more experiments in much wider ranges to approve it. The detailed experimental parameters of two phase frictional pressure drop are shown in Table 4. 3.2.2. Flow pattern Yan et al. (2008) carried out experiments for upward gas-liquid two phase flow in rolling motions. Their results revealed that rolling motion might change the flow pattern. The churn flow region was extended since the bubble flow was transferred to slug flow earlier. The void fraction in slug flow region was smaller in rolling motion than that in stationary state. Fan et al. (2006) analyzed the two phase flow pattern and pressure fluctuation in rolling motion and found that periodical pressure fluctuation could not be found in churn flow. Luan (2009) investigated the flow pattern of gaswater flow in horizontal and vertical tubes. He summarized the flow pattern picture and found that the rolling motion contributed significantly to the transition boundary of flow pattern. These results are in agreement with that of Zhang (2009). Comparing the flow pattern pictures in the same case obtained by Luan (2009) and Zhang (2009) separately, it is found that the transition boundaries are not identical, as shown in Fig. 5. These discrepancies were possibly caused by the experimental error and limited data. Therefore, more experimental data are needed in the

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Table 4 Experiments of two phase frictional pressure drop. References

Channel size

Direction

Ocean motion

Parameters

Amplitude

Period (s)

P (MPa)

Mass quality

Q (kg/(m2 s))

Qw

Ql = 0–10 m3/h, Qg = 0.16–1.0 m3/h 535–1525 kg/(m2 s) – Re = 2000–6000 – – 420–1500 kg/(m2 s) 0.1–0.35 m3/h Rel = 543–13,250 Reg = 221–8310

–

Cao (2006)

Di = 15, 25, 34.5 mm

Vertical

10–20°

5–15

0.1

–

Chen et al. (2015) Jin et al. (2012) Jin et al. (2013) Jin et al. (2014a) Li et al. (2013b) Liu (2012)

40  2 mm 40  10 mm 40  1.6 mm 40  1.41 (3.25, 9.96) mm 42  1.6 mm Di = 3.8 mm 45  2 mm 43  1.41 mm

Vertical Vertical Vertical Vertical Vertical Vertical Vertical Vertical

10–20° 5–15° 10–30° 5–15° 10° 10–15° 10–20° 10–30°

10–20 8–16 8–16 8–16 8–16 8–16 10–20 8–16

0.6–1.5 0.1 0.1 – 0.1 0.1 0.1–1.2 0.2

x = 0–0.1 – x = 0.02–0.1 – – x = 0–0.1 x = 0–0.6 –

Xing (2013)

184–337 kw/m2 – – – – – 150–550 kw/m2 –

Notes: ‘‘–” means the data is unavailable in this reference.

bubble flow

bubble flow slug flow quasi slug flow

quasi slug flow annular flow

annular flow

intermittent flow

(a) from Luan (2009)

(b) from Zhang (2009)

Fig. 5. Flow pattern picture in a tube of 25 mm in rolling motion of 15° and 10 s.

Table 5 Experiments of two phase flow pattern. References

Channel size

Direction

Ocean motion

Parameters

Amplitude

Period (s)

P (MPa)

Mass quality

Q (kg/(m2 s)) Ql = 0–10 m3/h, Qg = 0.16–44 m3/h Ql = 0–10 m3/h, Qg = 0.1–40 m3/h Ql = 19–903 kg/h, Qg = 0.03–12.5 kg/h Ql = 0.2–1.4 m3/h, Qg = 0.28–2.0 m3/h ul = 0.03–3.3 m/s, ug = 0.06–30 m/s

Fan et al. (2006)

Di = 15, 25, 34.5 mm

Vertical

10–20°

5–10

–

–

Luan (2009)

Di = 25, 34.5 mm

10°–20°

5–15

0.1

–

Wang et al. (2011)

40  1.6 mm

Vertical, Horizontal Vertical

–

–

–

–

Yan et al. (2008)

Di = 25 mm

Vertical

10°

5

0.1

–

Zhang (2009)

Di = 25 mm

Horizontal

10°–20°

5–15

0.1

–

Notes: ‘‘–” means the data is unavailable in this reference.

developing of flow pattern picture in ocean motions. Wang et al. (2011) investigated the flow pattern in a rectangular channel. They found that the flow pattern in rolling motion was similar to that in stationary state. Finally, they attributed this phenomenon to the restriction of channel wall in the narrow duct. The experiments revealed that the flow pattern in ocean motions is different from that in stationary state. The transition boundaries are changed in different motions and different

channels. The determination of flow pattern picture is very important for both thermal hydraulic analysis and nuclear designing. In stationary state, the drawing of flow pattern needs plenty of experimental data in wide ranges. Therefore, the experimental cases should be organized systematically in order to get a complete flow pattern picture in ocean motions. Detailed experimental parameters of two phase flow pattern are shown in Table 5.

B.H. Yan / Nuclear Engineering and Design 313 (2017) 370–385

3.2.3. Bubble behavior Bubble behavior is very important for flow boiling. The bubble growth, departure, sliding, reattaching and condensation play important roles in the two phase flow and heat transfer. The experiments for the bubble behavior are usually conducted by visual observation and measurement. Wen et al. (2016) carried out experiments to study the bubble velocity under sway motion. They found that the bubble velocity and its flowing path are significantly affected by sway motion. Compared with the inertial force, the sloshing of free surface has a greater impact on the horizontal velocity. Xu (2010) investigated the bubble density variation in a narrow channel in heeling and rolling motions. He found that the bubble density oscillated periodically in rolling motion. However, the oscillating form in different motions remains unchanged. Xie et al. (2014) analyzed the effect of rolling motion on bubble departure diameter in a narrow rectangular channel. Their experiments revealed that the bubble growth was unstable and the bubble departure diameter oscillated in a certain range in rolling motion. The bubble departure diameter had a trend to be the smallest when the angular displacement of rolling motion was zero. Hong et al. (2012) carried out visual experiments of bubble departure size in forced convective subcooled boiling flow in heaving motion. Their experiments indicated that the bubble departure size was affected by heaving acceleration and flow rate oscillation. Then they developed a theoretical model to predict the departure diameter with an average deviation of ±17.5%. Jin et al. (2014b) investigated the void fraction of dispersed bubbly flow in a narrow channel in rolling motion. They found that rolling motion could result in a reduction of the time averaged void fraction, which was in agreement with the experiments of Yan et al. (2008). Li et al. (2013d) analyzed bubble sliding in subcooled boiling flow in a vertical narrow rectangular channel. They found two kind of typical bubbles. One with rapid vaporizing and condensing while the other with a long lifetime. Due to the difference between these two kinds of bubbles, the range of bubble sliding velocity and bubble diameter is very wide. The bubble density and bubble diameter fluctuated with the same period as that of rolling motion (Li et al. (2015a)). This is in agreement with the experiments of Xu (2010). The experiments of Li et al. (2015a) also revealed that the variation of wall superheat was the main reason accounting for the fluctuation of bubble parameters. Yan et al. (2014a) analyzed the effects of heeling and rolling motions on the lateral distribution of interfacial parameters for bubbly flow in a narrow rectangular channel. In their experiments, no obvious differences were observed among interfacial parameters in lateral distribution at the same position in heeling and rolling motions. They attribute this phenomenon to the reason that the lateral buoyancy caused by ocean motions was less than the lateral buoyancy induced by gravity. Then they investigated the slug behavior and pressure drop of air-water slug flow in the same channel in heeling motion (Yan et al., 2014b). It is found that both the slug velocity and the slug length increase with the heeling angle increasing in laminar flow region. But this phenomenon could not be observed in turbulent flow region. The existed empirical correlations could be used to predict the slug flow in heeling motion. They also conducted experiments of bubble velocity in a 3  3 rod bundle in rolling motion (Yan et al. (2014c)). It was found that there were one or two peaks in a rolling period. The fluctuation of bubble velocity is caused by the axial resultant acceleration. Besides, their experiments indicated that the effect of rolling amplitude on bubble velocity was more significant than that of rolling period. The experiments of bubble behavior in rolling motion were mainly carried out in vertical rectangular channels. It was found that rolling motion could affect bubble velocity, density, size, and

377

void fraction. In stationary state, both the channel size and inclination angle may change the bubble behavior. Therefore, the experiments of bubble behavior in different kinds of channels with several inclination angles are needed. The experimental cases should also be extended to other kinds of flow patterns, like annular flow, mist flow, etc. The detailed experimental parameters of bubble behavior are shown in Table 6.

4. CFD analysis 4.1. Single channel The application of CFD software in nuclear reactor thermal hydraulic analysis started from about twenty years ago. Researchers could obtain more quantitative information through CFD simulation. After a strict verification and validation process, scholars and engineers tend to trust the CFD results. The CFD analysis of the nuclear reactor thermal hydraulic analysis in ocean motions started from several years ago. Du and Zhang (2010) investigated the flowing resistance in a tube in ocean motions with commercial software CFX. Their results revealed that translational inertial force did not contribute to the velocity profile and flowing resistance. The contribution of Coriolis force on the frictional pressure drop was less than 1%. The single phase heat transfer around the tube in heeling motion was unsymmetrical due to buoyancy effect (Du and Zhang, 2012). The effect of heeling motion on the two phase heat transfer is so weak that could be neglected. Li et al. (2013c) investigated the flow and heat transfer in a narrow rectangular channel in rolling motion with CFD methods. Their results indicated that the time averaged Nusselt number and frictional resistance coefficient were slightly higher than that in stationary state. The Nusselt number and frictional pressure drop oscillate periodically with relative amplitude of less than 5%. Yan et al. (2011a) investigated the effects of several parameters on the flow and heat transfer in ocean motions. It was found that the effect of rolling radius and rolling axis was slight. The Nusselt number and frictional resistance coefficient oscillate periodically with relative amplitudes less than 10% in ocean motions, which is similar with that of Li et al. (2013c). Their subsequent research showed that the restriction of channel wall on the flow and heat transfer was significant in narrow channels (Yan et al., 2012a). This conclusion is consistent with that of Jin et al. (2014a) and Wang et al. (2011). Yan et al. (2012b) investigated the local loss coefficient in a 90° bend in rolling motion with CFD code FLUENT. It was found that the effect of spanwise and transverse additional forces on the bend loss was significant. The oscillation of bend loss in rolling motion was irregular. Yan and Gu (2013) analyzed the sudden expansion and sudden contraction loss coefficients in rolling motion. Their numerical results indicated that the effects of spanwise and transverse additional forces on the expansion and contraction loss coefficients are different. The effect of velocity oscillation on the contraction loss coefficient is more significant than that on the expansion loss coefficient. Song et al. (2014) simulated the rising bubble behavior in sloshing motion with VOF (Volume of Fluid) model. They found that the violent sloshing motion could affect the bubble departure size and the aggregation phenomena. The bubbles oscillate in horizontal direction due to the effect of sloshing motion. Wei et al. (2011) simulated the bubble behavior in subcooled boiling flow in swing motion. Their results indicated that the fluctuation of mass flow rate caused by swing motion contribute to the bubble behavior significantly. The swing motion increased the pressure drop of subcooled boiling flow. Zeng and Cai (2014) simulated bubble rising

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Table 6 Experiments of bubble behavior. References

Channel size

Direction

Ocean motion Amplitude

Parameters Period (s)

P (MPa)

Tsub

Qw (kw/m2)

Q (kg/(m2 s)) 300–710 kg/(m2 s) ul = 1.12–2.59 m/s ug = 0.071–0.16 m/s 304.1–760.2 kg/(m2 s) 300–800 kg/(m2 s) Ql = 0, Qg = 40 ml/min 300–700 kg/(m2 s) Ql = 100 kg/h ul = 1.601–2.001 m/s ug = 0.069–0.111 m/s Rel = 1115–22,015 Reg = 55–2042 Qg = 0.079–0.2 m3/h

Hong et al. (2012) Jin et al. (2014b)

40  2 mm 40  3 mm

Vertical Vertical

Heaving motion 5–15° 8–16

0.15 0.1

20–40 20

65–298 –

Li et al. (2013d) Li et al. (2015a) Wen et al. (2016)

40  2 mm 40  2 mm 200  400  500 mm

Vertical Vertical Vertical

– 10–15° –

– 8–16 2.6–4.8

– 0.2–0.56 0.1

13.4–43.6 5.7–24.8 –

– 92.4–255.3 –

Xie et al. (2014) Xu (2010) Yan et al. (2014a)

40  2 mm 40  2 mm 43  3.25 mm

Vertical Vertical Vertical

10–30° 10–15° 10–30°

3–10 8–16 8–16

0.15 0.1 0.1

40 24.6 –

– 103 –

Yan et al. (2014b)

43  3.25 mm

Vertical

Heaving motion (0–30°)

0.1

–

–

Yan et al. (2014c)

3  3 bundle P = 11 mm, D = 8 mm

Vertical

5–15°

–

–

–

8–16

Notes: ‘‘–” means the data is unavailable in this reference.

under non-linear oscillation with ALE method. They found that the oscillating frequency of container contributed both to the frequency and amplitude of the bubble velocity. The bubble breakup phenomenon was observed in cases with large horizontal velocity. The research about two phase flow and heat transfer in ocean motions with CFD simulation is very limited, because of the unsatisfactory accuracy and high computational resources. This is a long and hard work. As far as concerned, the CFD simulation for the two phase flow in ocean motions should be used to the quantitative analysis. 4.2. Complex channel The effect of ocean motions in complex channel might be different from that in single channel. The spanwise and transverse additional forces might contribute more significant in complex channels. Yan et al. (2011b) simulated the turbulent flow and heat transfer in a 4 rod bundles in ocean motions with Large Eddy Simulation (LES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) methods. Their results indicated that the effect of ocean motions on the flow and heat transfer in rod bundles should not be neglected. The effect of ocean motions decreased with the decreasing of channel size (Yan and Gu, 2012). The numerical simulation on the hydraulic behavior in reactor pressure vessel in ocean motions is limited because of its complex structure and huge computational resources needed. Yan et al. (2012c,d) analyzed the effect of rolling motion on fluid mixing and flow distribution at the core inlet with commercial software CFX 12.0. Their results revealed that the effect of rolling motion on fluid mixing and flow distribution was not regular. The minimum flow distribution factor was decreased. The rolling motion contributed more significantly to the flow distribution in case of single loop operation than that in case of double loops operation. The effect of ocean motions should be considered since the demand for the non-uniform flow distribution was very high. The CFD analysis for the thermal hydraulic behavior in rolling motion is mainly about the tube, rectangular channel, rod bundle and reactor pressure vessel. It was found that the effect of ocean motions on the frictional resistance coefficient and Nusselt number was limited, with relative variation of less than 10% (Li et al., 2013c). The hydraulic behavior in complex channel in ocean motions is irregular due to its complex structure. Therefore, it is necessary to evaluate the effect of ocean motions on the hydraulic behavior in important and complex equipment in engineering application.

Fig. 6. Variation of pressure drop with the Reynolds number (Yan et al., 2012a).

Until now, many numerical and experimental results revealed that the effect of ocean motions decayed with the Reynolds number increasing. This physical phenomenon was explained by Yan et al. (2012a). The drive pressure drop is in a quadratic relation with the Reynolds number while the additional pressure drop is in a linear relation with the Reynolds number. The profiles of these two pressure drop and the Reynolds number are shown in Fig. 6. Where pdriv e and pa are drive and additional pressure drop, respectively. In high Reynolds number, the drive pressure drop is much higher than the additional pressure drop, which means the effect of ocean motions is weak. The difference between drive and additional pressure drops decreases as the Reynolds number decreasing, which means the effect of ocean motions increases.

5. Code analysis The code analysis is important for the nuclear designing and safety analysis. The accidental analysis with code is indispensable in the designing of a nuclear reactor. The development of specific codes for the reactor system in floating platform is necessary. Kim and Park (1996) modified the RETRAN03 code to analyze the thermal hydraulic transients in ocean motions. With the modified code, they analyzed the MUTSU reactor under various ship motions with the results showing good agreement with the JAERI analysis.

B.H. Yan / Nuclear Engineering and Design 313 (2017) 370–385

Their research indicated that the reactor system could maintain stable thermal hydraulic conditions for both normal operation and natural circulation states in various ship motions. Su et al. (1996) developed a code MISAP-02 to analyze the natural circulation of a passive residual heat removal system in ship motions. They found that ship motions could change the natural circulation flow and the ability of heat transfer. Kim et al. (2001) investigated the thermal hydraulic characteristics during natural circulation in a system-integrated modular advanced reactor (SMART) with RETRAN-03/INT. It was found that feed water isolation did not enhance the asymmetric temperature distribution at the outlets of the steam generator cassettes. Flow rates in ascending steam generator cassettes increased with the increasing of thermal driving head. The code RETRAN-03/INT was capable of analyzing threedimensional phenomena in SMART. Tan et al. (2009a) modified the RELAP5 code to analyze a simple natural circulation system in ocean motions. Their simulation results were consistent with physical phenomenon. Yan and Yu (2011) and Yan et al. (2009) developed an advanced code to simulate the thermal hydraulic behavior of nuclear systems on the basis of RELAP5 code. The advanced flow and heat transfer models were introduced. Comparing with the experimental parameters of a natural circulation system, it was found that the advanced code could be used to simulate the thermal hydraulic system in ocean motions. The RELAP5-3D code is typically used to model stationary, landbased, thermal-hydraulic systems. It can also model thermalhydraulic systems in other inertial and accelerating frames of reference. By changing the magnitude of the gravitational vector through user input, RELAP5-3D can model thermal-hydraulic systems on planets, moons, and space stations (Mesina et al., 2016). They modified the field equations to model thermal-hydraulic systems in a non-inertial frame, such as occur onboard moving craft or during earthquakes for land-based systems. The equations for three-dimensional fluid motion in a non-inertial frame of reference were also developed. Li et al. (2015b) investigated the effect of ocean motions on the MUTSU reactor with advanced COBRA code. They found that the core parameters oscillated periodically in ocean motions. The pressure drop in sub-channels was greatly affected by heaving motion, while the coolant flow and temperature were affected in swing motion. Wu et al. (2016) developed an upgraded version of ATHAS code to simulate the reactor core in ocean motions. Their results revealed that the outlet mass flux, outlet temperature, outlet flow equilibrium quality and MDNBR of the reactor oscillated periodically. The rolling amplitude contributed significantly to the oscillation of these parameters. The MDNBR in heaving motion was reduced. It is feasible to develop a thermal hydraulic code in ocean motions by modifying existed code. The modifying process includes two parts, the theoretical models and field equations. In the new code, the conventional models should be replaced with the models applicable in ocean motions. The validation process with integral test loop is also necessary. Until now, the mathematical models applicable in ocean motions and experimental data of integral test loop are urgently needed.

6. Discussion 6.1. Instability Two phase flow oscillation is a common thermal hydraulic phenomenon in nuclear system, which could cause mechanical vibration, reduce critical heat flux (CHF) and bring some control problems to the safety of nuclear reactor. The coupling of two

379

phase flow instability with ocean motions will result in complex nonlinear oscillation. The rolling motion might cause the onset of natural circulation flow instability in advance. The flow oscillation is caused by rolling motion overlapped with the density wave oscillation. An unstable region was found between two stable regions in rolling motion (Tan, 2006). The marginal stability boundary (MSB) of regular complex flow oscillation was similar to that of density wave oscillation without rolling motion. The influence of rolling parameters on the MSB was slight (Tan et al., 2009c). Yu et al. (2016) conducted experiments on the flow instability of forced circulation in a mini-rectangular channel in rolling motion. Their results are similar to that of Tan et al. (2009c). Tang et al. (2014) found that the flow oscillation in ocean motions was the superposition of thermal-induced oscillation and motion-induced oscillation, which was in agreement with the experiments of Tan (2006). Through the comparison of experiments in stationary and ocean motions, it was found that the difference of boundary heat flux induced by ocean motions was no more than ±5%. The instability is mainly affected by thermal parameters rather than ocean motions. They also summarized an empirical formula which was capable of predicting the instability boundary under both static and motion conditions. Guo et al. (2008) developed the models of two-phase flow instability between multi-channels (FIBM) in ocean motions. They obtained the instability oscillating trajectories of the multichannel system and found that some of the trajectories showed chaotic characteristics. The instability zone of a nine-channel system in rolling motion was also obtained. Then they analyzed the complex curve of mass flow with Fast Fourier Transformation (FFT) method and analyzed the onset of inherent parallel-channel instability (Guo et al., 2010). Based on the research of Guo et al. (2008, 2010), Zhang et al. (2011) established a parallel nine channel model in rolling motion based on the homogeneous flow model. They obtained the marginal stability boundary in rolling motion and found that the unstable regions occurred in both low and high equilibrium quality regions. In high equilibrium quality region, the multiplied period phenomenon was found and the chaotic phenomenon appeared on the right of marginal stability boundary. Ma et al. (2013b) studied the effect of additional acceleration on the flow oscillation. Their code analysis results indicated that the coupled motions had no effect on the flow instability boundary in parallel channels under forced circulation, which were in agreement with the experiments of Tang et al. (2014). Zhou et al. (2013) investigated the coupled neutronic and thermodynamic instabilities in a double parallel channel natural circulation system in rolling motion by coupling thermal-hydraulic analysis code RELAP5/ MC and 3D neutron transport code TDOT-T. Both the in-phase oscillation caused by rolling motion and the out-of-phase oscillation caused by density wave oscillation (DWO) were observed. The neutronic feedback stabilized the system in type 1 DWO region and suppressed the in-phase oscillation in two-phase region, but had little effect on the type 2 DWO and the in-phase oscillation in single-phase region. It was found that the nonlinear characteristic of system was enhanced with nuclear feedback. Since the flow oscillation caused by rolling motion superimposed with DWO, the synchronization and chaotic phenomena in the thermal and physical coupling. Shen et al. (2015) developed a lumped model of flow instability in parallel-rectangular channels in heaving motion. Their results indicated that heaving amplitude contribute slightly to the flow instability, which was in agreement with the results of Tan et al. (2009c), Ma et al. (2013b) and Tang et al. (2014). It was also found that the threshold power was decreased when the heaving frequency was next to the system inherent frequency.

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The above investigation revealed that the flow instability in ocean motions was the superposition of thermal-induced instability and motion-induced instability. The instability boundary was mainly affected by thermal parameters, rather than the parameters of ocean motions. The difference of boundary heat flux induced by ocean motions was no more than ±5% in the pressure range of 3– 8 MPa. In order to meet the requirement of engineering application, flowing instability experiments in higher pressure are needed in the future. The research for flowing instability in ocean motions was mainly based on the homogeneous flow model and linear analysis method. Both the phasic slip and truncation error were neglected. It can be expected that the flowing instability analysis with unhomogeneous flow model and nonlinear analysis method will produce much better results. 6.2. Forced circulation and natural circulation In forced circulation, the drive pressure head is very high due to the rotation of coolant pump. But the drive pressure head in natural circulation is much lower because of the small buoyancy force. Since the effect of ocean motions is greatly dominated by the ratio of additional pressure drop and drive pressure drop, the effects of ocean motions in forced circulation and natural circulation are different. 6.2.1. Experiments Iyori et al. (1987) performed a steady state single phase natural circulation test using a model facility of an integrated type marine reactor. It was found that several types of flow pattern occurred in the natural circulation loop corresponding to inclination angle. The temperature distribution in steam generator at inclined attitude depended essentially only on the elevation. One dimensional analysis failed in predicting the angle at which the cold leg flow reversed. Murata et al. (1990) performed a series of single phase natural circulations in a model reactor with rolling motion to investigate the natural circulation characteristics of a marine reactor in a stormy weather. In their tests, the loop flow rate in each leg oscillated periodically in rolling motion, while the core flow rate did not oscillate. The flow rate oscillation in hot leg and cold leg attenuated as the rolling frequency decreasing and the thermal driving head increasing. The coolant flow pattern in the core and steam generator changed with rolling angle due to the effect of rolling motion and the temperature gradient in the effective core. Kim et al. (2001) conducted single phase natural circulation experiments to investigate the thermal hydraulic characteristics during natural circulation in an integral type marine reactor using scaled test facilities of the System-integrated Modular Advanced Reactor (SMART). They found that feed water isolation did not enhance the asymmetric temperature distribution at the outlets of the steam generator cassettes. Typical flow characteristics according to the inclination angles were observed in inclined conditions. Murata et al. (2002) carried out a series of single-phase natural circulation tests in a model reactor in rolling motion to investigate the effects of rolling motion on its thermal hydraulic behavior. It was found that the phase lag between rolling angle and loop flow rate oscillations increased as the rolling period decreasing. The variation of core flow rate correlated well with both the rolling Reynolds number and the pressure loss through the loop. Heat transfer in the core was enhanced which was thought to be caused by the internal flow due to the rolling motion. Yan et al. (2009) carried out experiments to analyze the effect of rolling motion on a passive residual heat removal system. They found that the decreasing of flow rate was caused by the decreasing of gravity pressure drop and the increasing of flowing resistance. As for their test facility, the contribution of gravity

pressure drop on the decreasing of flow rate is less than 20%. The other is due to the increasing of flowing resistance. Gong et al. (2013) performed a series experiments without heating to investigate the flowing characteristics of an integral reactor in rolling motion. They observed that no water flow into heat exchangers from heating channel through rise section, which means the natural circulation flow was not established in this kind of experiments. Yang et al. (2013) conducted experiments to simulate the natural circulation of an integrated natural circulation reactor on a test loop with a symmetric two-circuit configuration. It was found that the density difference between the up plenum and down plenum caused an additional driven force perpendicular to the original one and introduced an outer circulation. Under the co-action of inner and outer circulation, one branch circulation was enhanced and the other was depressed. This unbalance could be alleviated by shortening the distance between heat exchangers and enlarging the distance between the heat exchanger and heating section. Zhu et al. (2015) investigated the natural circulation characteristics in symmetrical loops under rolling condition experimentally. The rolling experiments with a zero power load showed that angular acceleration caused the fluctuation in branch flow channels, but had no influence on the middle channel. Besides that, the flow rate and temperature oscillations were observed in each branch of the flow channel in full power experiments. Tan (2006) found that rolling motion resulted in an oscillation of natural circulation flow. The effect of rolling motion includes two parts, the first is the variation of drive head and the other one is the additional pressure drop. The experiments of Liu et al. (2010) showed that rolling motion result in a decrease of natural circulation flow rate and an increase of heat exchanged. Wang et al. (2014) found that the relative pulsation amplitude of flow rate increased with the driving head increasing and the frictional resistance decreasing. The effect of additional inertial force could be neglected if the driving force was 10 times higher than the additional inertial force. The pulsation of flow rate depended on the relative quantity of driving head, frictional resistance and additional inertial acceleration. Xing et al. (2012) also got the similar experimental results. Their subsequent research indicated that the influence of rolling motion on transient flow rate and frictional resistance largely depended on the pump head (Xing et al., 2013). The flow rate in rolling motion oscillated periodically with its amplitude decreasing rapidly in case of pump head increasing, and finally, tended to be steady as the pump head further increased to a high level. They also observed that rolling motion has no influence on time averaged flow resistance. 6.2.2. Numerical research Kim et al. (2001) developed the RETRAN-03/INT code to investigate the natural circulation characteristics of SMART, with the simulation results validated with experiments. It was concluded that RETRAN-03/INT was capable of analyzing three dimensional phenomena in SMART. They also suggested that the comparison with the experimental results and three dimensional analysis using CFD software should be made for the verification and validation of the three dimensional analysis of RETRAN-03/INT. Ishida and Yoritsune (2002) simulated the effects of heeling and heaving motions on the thermal hydraulic behavior of a small integral type PWR (DRX) with RETRAN-02/GRAV code. The analysis showed that ship inclination induced the core flow to decrease but reactor power recovered to the initial level without the help of reactor automatic control system. The heaving results in oscillations of core flow rate and reactor power. These oscillations were different from the density wave oscillation. The density wave oscillation occured when the reactor power increases over the rated power. The boundary of its occurrence was also analytically revealed. They suggested that an effective measure to suppress the oscillations

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due to heaving was to pressurize the primary loop by filling noncondensable gas. Yan and Yu (2009) analyzed the natural circulation operating characteristics and the transitions between forced circulation and natural circulation of a nuclear machinery in ocean motions. It was found that the effect of pitching motion on natural circulation was greater than that of rolling motion. Violent flow oscillation may cause the control rods to respond so frequently that the system could not realize the transition from forced circulation to natural circulation smoothly. However, the effect of ocean motion on the transition from natural circulation to forced circulation was limited. Xi et al. (2015) simulated the thermal hydraulic behavior of a passive residual heat removal system in ocean motions and found that the effect of rolling motion was different from that of pitching motion due to the configuration of the system, which was consistent with the result of Yan and Yu (2009). Yang et al. (2015) analyzed the effect of inclination and swing on natural circulation of floating nuclear power plant under site black out (SBO) accident with RELAP5/MC code. It was found that the effect of ocean motions on the direct passive reactor heat removal (PRHR) system was different from the secondary PRHR. The flow exchange between the loop and the pressurizer had major effect on cooling capacity for the left side loop. They suggested that the configuration of steam generator and PRHR condenser and the effect of ocean motions on the control and protection system should be considered. Besides that, many scholars established theoretical models for natural circulation flow in ocean motions to simulate the thermal hydraulic behaviors of simplified nuclear systems. Pang et al. (1995) established the mathematical models of primary loop natural circulation to analyze the natural circulation ability in heaving and rolling motions. Gao et al. (1999) analyzed the effect of heaving motion upon forced circulation and natural circulation with mathematical models. They found that the effect of heaving motion on natural circulation was more significant than that on forced circulation. Yang et al. (2002) developed mathematical simulation models to analyze the natural circulation ability of a coolant system in ocean motions. The decreasing of core mass flow and power proved that natural circulation ability was greatly impacted by ocean motions. Tan (2006) analyzed the effect of rolling motion on natural circulation with mathematical models and found that the increase of flowing resistance was the main factor resulted in the decreasing of flow rate. Jiang et al. (2009) analyzed the effect of heaving motion on the natural circulation of an integrated type reactor. They found that heaving motion was likely to lead more serious consequence than rolling motion under some certain conditions. Zhang (2013c) investigated the nonlinear behavior of natural circulation flow in rolling motion. He thought that the nonlinear characteristics of natural circulation system were caused by the mutual feedback and coupling of thermal driving force, flowing resistance and additional force in rolling motion. The irregular complex flow oscillation in rolling motion was the typical chaotic oscillation. Zhang (2013b) carried out a nuclear thermal coupling simulation for the natural circulation in rolling motion. It was found that nuclear thermal coupling resulted in a decreasing of flow rate and heating power. The temperature oscillation was suppressed due to this coupling effect. Zhang et al. (2015) analyzed the effect of rolling motion on trough fluctuation in natural circulation. They found that the additional pressure drop play a major role in the trough fluctuation. The research about the forced circulation and natural circulation in ocean motions revealed that the oscillation of total flow rate was weaker than that of the loop flow rate due to the mutual offset between each loop in symmetrical system. The effects of ocean motions were different for every system and facility. Therefore,

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the integral experiments were necessary for each nuclear system in ocean motions. The effect of ocean motions was more significant in natural circulation due to its low thermal driving head (Xing et al., 2013; Wang et al., 2014). In forced circulation, the coolant flow was usually driven by a pump, which resulted in a high driving head. However, if the pump head decreased to a low level in the forced circulation, the effect of ocean motions increased and the phenomenon was similar with that in natural circulation. Therefore, the ocean motions contributed slightly to the forced circulation. The natural circulation in ocean motions should be focused on. 6.3. Critical heat flux Critical heat flux (CHF) is a parameter of vital importance in nuclear designing and thermal hydraulic analysis. The accurate prediction of CHF characteristics is an important factor to reactor safety and designing. Otsuji and Kurosawa (1983) found that the deterioration of CHF in the high exit quality region could almost wholly be attributed to the variation of inlet flow rate. Then they conducted a photographic study to investigate the effect of variation in acceleration on the critical heat flux (CHF) in subcooled flow boiling (Otsuji and Kurosawa, 1984). Their experiments were made at a pressure of 3 bar, a mass flux of 920 kg/m2 s, an inlet subcooling 45 K and a slightly lower heat flux level than steady CHF. They found that the bubbles generated on heated surface moved longer along the surface without detachment and coalesced with other bubbles to form large vapor slugs at low apparent gravitational acceleration. This phenomenon caused early CHF. The experiments of Isshiki (1966) revealed that the CHF decreased linearly with the heaving amplitude increasing. A semi-empirical correlation was summarized. It was also found that the CHF cease to be uniform in heeling motion. Therefore, the effect of heeling motion on CHF should not be neglected. Pang et al. (1997) investigated the CHF of water at atmospheric pressure in a vertical tube. They found that the CHF oscillate in rolling motion, with the time averaged value decreased. Due to the limit of experimental cases, their results were only applicable within their specific experiments range. Gao et al. (1998) carried out experiments on CHF of natural circulation upward water flow at atmospheric pressure. They found that the low flow rate and flow oscillation could result in the decreasing of CHF. Ishida et al. (1990) computed the temporal change of CHF in oscillating gravity oscillation field and obtained the CHFR values higher than 1.8 in the sub-channel analysis of Mutsu. They suggested that the examining of cross flow in rod bundles was necessary for a precise evaluation of CHF. Hwang et al. (2011) assessed the CHF under heaving conditions using the MARS code with CHF experimental data. Their research indicated that the variation of acceleration affected the flow conditions, such as the mass flow rate and the void fraction. The MARS code had an ability to predict the CHF in heaving motion by simulating inlet flow rate oscillation. Hwang et al. (2012) conducted CHF experiments for the boiling of R-134a in vertical tube under rolling motion, with mass flux ranged from 285 kg/m2 s to 1300 kg/m2 s, inlet subcooling from 3 to 38 °C and outlet pressures from 1.3 to 2.4 bar, respectively. Fluid to fluid scaling was applied to convert the test from water to R134a equivalent conditions. Their experiments revealed that CHF ratios (ratio of the CHF in rolling motion to the stationary CHF) as mass flux and pressure in rolling motion were quite different from those in stationary experiments. The CHF ratios was smaller than unit in region of relative low mass flux at 13 and 16 bar but increased in region of relatively high mass flux. Moreover, rolling CHFs tended to enhance compared with stationary CHFs in the entire mass flux region at 24 bar.

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Table 7 Experiments of CHF. References

Test section

Fluid

Direction

Ocean motion Amplitude

Gao et al. (1998) Hwang et al. (2012) Isshiki (1966)

Di = 25 mm Di = 9.5 mm Di = 8 mm

Water R-134a Water

Upward Upward Upward

Otsuji and Kurosawa (1983, 1984) Pang et al. (1997)

– Di = 25 mm

Freon-113 Water

Upward Upward

Parameters

Empirical correlation 2

Period (s)

P (MPa)

Tsub (°C)

Q (kg/(m s))

5–15° 5–10 15–40° 6–12 Heaving: 0–1.0 g, 3–6 s Heeling: 30° 0.3 g 6 5–15° 5–10

0.12 1.2–2.4 0.1

26–42 3–38 0.4

20–165 285–1300 0–1 m/s

No No Yes

0.3 0.12

45 9–43

920 933–2104

Yes Yes

Simple loop

Pressure drop

Complex loop

Time Fig. 7. Effect of additional pressure drop in different loops.

Most of the experiments of CHF in ocean motions were carried out in a not high pressure (<3.0 MPa) due to the difficulty of experiments with high temperature and high pressure. These existed experimental results revealed that the CHF in ocean motions is quite different from that in stationary state. Most results indicated that the rolling CHF is lower than the stationary CHF. But the experiments of Hwang et al. (2012) showed that the rolling CHF increase in region of relative high mass flux at 13 and 16 bar. Due to the difficult mechanism of CHF, more systematic experiments are required. The detailed experimental parameters of CHF are shown in Table 7. 6.4. Application of empirical correlations The theoretical models for the flow and heat transfer are important for the analysis code. In order to develop a commonly used thermal hydraulic code in ocean motions, accurate models that are applicable for wide conditions are necessary. Due to the high cost and difficulty of experiments, there is only limited empirical correlation for two phase flow, bubble behavior and critical heat flux. These correlations are only applicable in specific cases. There are more correlations for single phase flow and heat transfer. However, a basic contradiction exists in these results. Some experiments indicate that the flow and heat transfer oscillate periodically which could not be predicted by the existed relations (Liu (2011), Jia et al. (2011), Xie et al. (2012), Xing (2013), Lan and Tan (2013), etc). The other scholars insisted that the oscillation of flow and heat transfer in ocean motions was too weak to be neglected (Liu et al. (2011, 2012), Ma et al. (2013a), etc). This discrepancy originates from the different ratios of the additional pressure drop and driving pressure drop (pump head), as shown in Fig. 7. As for a simple loop, the driving pressure drop is low, the additional pressure drop would be superimposed on it and results

in a flow oscillation (Xing et al. (2013) and Wang et al. (2014)). However, if the loop is complex, the driving pressure drop is much higher compared with the additional pressure drop. The effect of ocean motions could be neglected and the existed correlations could be used to predict the flow and heat transfer. Therefore, whether the existed empirical relations could be used in ocean motions is determined by the ratio of additional pressure drop and driving pressure drop. Due to the different configurations of experimental loops, the obtained empirical correlations were advised to be used in specified cases. Eq. (2) shows that the additional force is in a function of rolling radius. Theoretically, the flow and heat transfer in each location are different due to the variation of rolling radius. There will be a discrepancy between the frictional resistance coefficient and heat transfer coefficient in different locations. Therefore, the effect of rolling radius on the flow and heat transfer is difficult to be captured in experimental and theoretical investigations. However, the research of Yan and Gu (2011) and Yan et al. (2012a) revealed that the relative oscillating amplitude of frictional resistance coefficient and heat transfer coefficient was no more than 10% in a tube with rolling radius of 5 m in acute rolling motion. 10% is next to the margin of experimental error for single phase flow and heat transfer. The additional force in ocean motions could be divided into an additional force parallel to the flowing direction and an additional force vertical to the flowing direction. The former one is equivalent to a pressure oscillation which results in a velocity oscillation finally. The ocean motion is one kind of low frequency movement with a frequency lower than 1 Hz. The velocity oscillation with low frequency did not contribute significantly to single phase flow and heat transfer (Yan et al., 2011a). The additional force vertical to the flowing direction may result in an irregular oscillation of the flow and heat transfer. The simulation of Yan et al. (2011a) revealed that the relative oscillating amplitude of the flowing resistance and the Nusselt number were less than 10% even in ocean motion with high amplitude and frequency (amplitude of 25° and period of 3 s). Therefore, the author would like to believe that we could estimate the flow and transfer in ocean motions with the empirical correlations in stationary state before we get the flow and heat transfer models validated with plenty of experimental data. This is in agreement with the results of Liu et al. (2011, 2012), Ma et al. (2013a) and Li et al. (2013c). 7. Conclusions The nuclear reactor thermal hydraulic research in ocean motions was summarized and evaluated. Valuable results and conclusions are collected for the subsequent research. The conclusions are listed as follows: 1. The phenomenon that the effect of ocean motions decays with the Reynolds number increasing is caused by the functions of pressure drop and the Reynolds number. The drive pressure drop is in a quadratic relation while the additional pressure drop is in a linear relation with the Reynolds number.

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2. Since the two phase frictional pressure drop is usually about 2– 3 orders higher than the additional pressure drop, the ocean motions could induce the oscillation of flowing parameters, but have slight effect on the time averaged parameters of two phase flow. 3. The contradictory issue that whether ocean motions change the frictional resistance coefficient and heat transfer coefficient or not is determined by the ratio of additional pressure drop and driving pressure drop. If the additional pressure drop is very small compared with the driving pressure drop, the effect of ocean motions is weak. If the additional pressure drop is close to the driving pressure drop, the effect of ocean motions is considerable and the existed correlations could not predict the oscillations in ocean motions. However, since this ratio is difficult to be obtained in complex thermal conditions and configurations, the existed empirical correlations are still suggested before the flow and heat transfer models in ocean motions are available. 4. The ocean motions may contribute to the flow distribution and fluid mixing at the core inlet. Since the demand for the nonuniform flow distribution is very high, the effect of ocean motions should be considered. 5. The restriction of channel wall is an effective way to depress the effect of ocean motions in both single phase flow and two phase flow. 6. The modified thermal hydraulic codes in ocean motions could be used to simulate a specific system. Their application in other experimental conditions needs to be testified. 7. The flow instability in ocean motions is the superposition of thermal-induced instability and motion-induced instability. The instability boundary is mainly affected by thermal parameters, rather than the parameters of ocean motions. 8. The effect of ocean motions is more significant in natural circulation due to the small thermal driving head. The integral experiments in ocean motions are necessary because of the different configurations of facilities. 9. The CHF in ocean motions is quite different from that in stationary state. Many results indicated that the rolling CHF is lower than the stationary CHF. But some experiments showed that the rolling CHF increased in some thermal conditions. More CHF experiments in ocean motions are required, especially in high temperature and high pressure. In the future, the following works in ocean motions are suggested. a) Theoretical models for the two phase flow. b) Experimental results for the two phase flow pattern and bubble behavior. c) CFD simulation in complex channels and facilities. d) Validation of thermal hydraulic code. e) Flowing instability experiments in high temperature and high pressure. f) CHF experiments in high temperature and high pressure.

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