Experimental study on distribution parameter characteristics in vertical rod bundles

International Journal of Heat and Mass Transfer 132 (2019) 593–605

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Experimental study on distribution parameter characteristics in vertical rod bundles Ting-pu Ye a, Liang-ming Pan a,⇑, Quan-yao Ren a,b, Wen-xiong Zhou a,⇑, Tao Zhong a a b

Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400044, China Science and Technology on Reactor System Design Technology Laboratory, Chengdu 610041, China

a r t i c l e

i n f o

Article history: Received 23 June 2018 Received in revised form 1 December 2018 Accepted 2 December 2018

Keywords: Drift-flux model Rod bundles Two-phase flow Distribution parameter Flow recirculation

a b s t r a c t The drift-flux model is important for rod bundle two-phase flow analysis. A 5
5 rod bundles experiment has been performed under air-water two-phase flow conditions. The superficial liquid velocity ranges from 0.00 to 1.50 m/s while the superficial gas velocity ranges from 0.02 to 6.00 m/s. The void fraction has been measured by the impedance meter. Four typical drift-flux models developed for rod bundles have been compared with present data. By analyzing the experimental data and visualization, the distribution parameter may be influenced by the flow recirculation and turbulence significantly. In order to consider these two effects, a critical liquid velocity has been defined to determine which effect is dominant as the increase of liquid velocity, and a new critical void fraction correlation related to the flowregime transition from cap-bubbly to cap-turbulent flow is incorporated to determine the distribution parameter. The new drift-flux model developed from existing models shows a good prediction capability. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Nuclear safety is the most critical part of nuclear reactor systems. The safety analysis codes are widely used in the design of nuclear reactor systems, as well as to predict thermal-hydraulic parameters in the mid-loop operations or under accidents like the loss of coolant accidents (LOCA). In particular, complex twophase flow should be inevitably considered in the PWRs and BWRs, two-phase prediction models are vital for system analysis programs. Currently, two-fluid model and drift-flux model have been extensively used for predicting two-phase flow parameters. As regards to two-fluid model, six equations of liquid and gas for mass, momentum, and energy transport need to be solved separately in two-phase systems [1]. As a simple one, the drift-flux model can provide satisfactory accuracy and sufficient system details, which is more practical and convenient. Moreover, the drift-flux terms known as the distribution parameter and drift velocity are required in both of the two models for solving their associated field equations. Hence the drift-flux model is of great significance to the analysis of two-phase flow in rod bundles. Several researchers have conducted a lot of meaningful studies on the one-dimensional drift-flux model for different channel

⇑ Corresponding authors. E-mail addresses: [email protected] (L.-m. Pan), [email protected] (W.-x. Zhou). https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.008 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

geometries such as small round tube and rectangular channel [2–4], large diameter pipe [5,6], annulus channel [7], and rod bundle [8–11]. Although many convincing conclusions have been drawn, some views are still controversial. It is essential to obtain more data to verify and modify the drift-flux models to improve the ability of predicting thermal-hydraulic parameters in rod bundles. For rod bundle channel, there are two important length scales: the sub-channel scale and the outer casing scale [12], which make rod bundle channel different from the conventional ones. On the one hand, the bubble size may be partially confined by the subchannel scale, which makes sub-channel void fraction characteristics and flow regimes different from those in global channel. Julia et al. [13] experimentally studied the sub-channel drift velocity and distribution parameter by utilizing conductivity probe. Ren et al. [14,15] acquired the sub-channel flow regimes objectively based on random forest algorithm, and demonstrated that the rods have a significant effect on the phase distribution in the subchannel. On the other hand, the outer casing with large diameter, to some extent, may make the hydrodynamic mechanisms analogous to that of large diameter pipes. For instance, Hibiki and Ishii [6] pointed out that the slug bubbles cannot be sustained due to the surface instability when the channel diameter is larger than pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 40 r=gDq corresponding to 0.1 m for air-water at atmosphere pressure, otherwise the slug bubbles would disintegrate into multiple cap bubbles and distorted bubbles. Similarly, Chen et al. [12] proposed that the outer casing length scale in rod bundle channel

594

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

Nomenclature C0 C1 D DH g P0 j jf jg Nl f Vgj

distribution parameter asymmetric value of distribution parameter rod diameter (m) hydraulic diameter (m) gravitational acceleration (m/s2) rod pitch (m) mixture volumetric flux (m/s) superficial liquid velocity (m/s) superficial gas velocity (m/s) viscosity number drift velocity (m/s)

Greek symbols a void fraction Dq density difference (qf  qg) (kg/m3) q density (kg/m3) r surface tension (N/m) l viscosity (Pas) m kinematic viscosity (m2/s)

is the limit size for the slug bubble. In addition, according to the experiments conducted by Yoshitaka et al. [16] and Zhou et al. [17], the slug flow has not been observed in rod bundles although outer casing size was lower than 0.1 m. This may be attributed to the strong secondary flow and mixing rate in rod bundles, which will cause the large bubble to disintegrate. Flow regimes for rod bundles have been researched by Paranjape et al. [18], Chen et al. [12], and Liu et al. [19]. Moreover, the flow recirculation has been observed in rod bundles under low flow conditions due to the effect of outer casing scale [12]. This phenomenon has also been demonstrated to have a great effect on void fraction characteristics in large diameter pipe, resulting in an increase of the distribution parameter and drift velocity [5,6]. Chen et al. [8] and Clark et al. [10] focused on the effects of recirculation on the distribution parameter to develop drift-flux models for rod bundle channel under low flow and low pressure conditions. However, Hibiki and Ishii [6] argued that the turbulence would diminish the flow recirculation in a large diameter pipe when flow velocity is high enough, and this means the turbulence would have a negative effect on distribution parameter. According to the above analysis, the channel size of sub-channel and outer casing plays a key role in the two-phase characteristics of rod bundles. Meanwhile, the effects of flow recirculation and turbulence on the distribution parameter should be considered in drift-flux model of rod bundles. Therefore, further experiments are needed to confirm these effects on the distribution parameter. This work focuses on the distribution parameter based on measured void fraction data in 5
5 rod bundles. A performance analysis is conducted on four typical drift-flux models by using present data. The effects of flow recirculation and turbulence are discussed through the characteristics of distribution parameters and flow visualization, and a drift-flux model that appropriately considers these effects is developed. 2. Existing drift-flux correlations 2.1. Drift-flux approach The one-dimensional drift-flux model can be used to calculate void fraction in two-phase flow systems. This drift-flux correlation

Subscripts cal. calculated value crit. critical value exp. experimental value max maximum value g gas phase f liquid phase B bubbly flow P pool flow Superscripts + and ⁄ non-dimensional Mathematical symbol hi area-averaged parameter hh ii void weighted mean parameter Acronyms BWR boiling water reactor PWR pressurized water reactor

takes account of the effects of non-uniform distribution in flow velocity and void fraction across the flow channel, as well as the local relative velocity between phases, primarily through two adjustable parameters, which was given by Zuber and Findlay [2] as



vg



    jg ¼ C 0 hji þ V gj ¼ hai

ð1Þ

where mg , jg , a, C 0 , j, and V gj are the gas velocity, superficial gas velocity, void fraction, distribution parameter, mixture volumetric flux, and drift velocity, respectively. The hi and hhii notations indicate area-average and void-weighted mean values, respectively. Here, the distribution parameter is a measure of global interphase slip resulting from flow-area-averaging. The drift velocity represents the local slip between the dispersed phase and the local volumetric flux. They are respectively defined by

C0 ¼

haji haihji





V gj

 ¼

ð2Þ

aV gj hai

 ð3Þ

and a common approach for evaluating the two parameters is to plot hjg i=hai versus hji by using experimental data [2]. Here, the ordinate intercept of the data trend is regarded as the drift velocity while the slope represents the distribution parameter. However, this approach is appropriate to the fully developed flow condition. For the developing flow condition, the two parameters should be researched independently, otherwise a parameter would be affected by the other and transfer compensating errors to the other [10]. 2.2. Existing drift velocity correlations for rod bundles As mentioned above, the drift velocity and distribution parameter should be studied independently. In this section, the existing drift velocity correlations for rod bundles are summarized in Table 1, and discussed separately as follows. Ishii [3] discussed the force balance of multi-bubble between buoyancy and drag in vertical two-phase bubbly flow, and proposed a drift velocity correlation as

595

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605 Table 1 Drift velocity correlations for rod bundles. Model

Drift velocity DD EE pffiffiffi Vþ ¼ 2ð1  haiÞ1:75 gj qffiffiffiffiffiffiffiffiffiffiffi   V gj ¼ 0:188 gDqqDH

Ishii [3] Bestion [20]

Details Bubbly flow Whole flow range

g

when N lf 6 2:25
103 DD EE  0:157 qg N 0:562 for Dþ Vþ ¼ 0:0019Dþ0:809 H H 6 30 lf gj qf DD EE  0:157 qg þ 0:562 þ V gj N lf for DH > 30 ¼ 0:030 q

Kataoka and Ishii [5]

Stagnant liquid flow lf

N lf ¼

qf r

1=2 pffiffiffiffiffi r g Dq

f

Hibiki and Ishii [6]

DD

V þgj

EE

¼

pffiffiffi 2ð1  haiÞ1:75

ð4Þ

where V þ gj is the non-dimensional drift velocity and it is given by

DD

V þgj

EE



¼

 V gj 1=4

ð5Þ

r g Dq q2f

where r, g, and Dq are surface tension, gravitational acceleration, and density difference ðqf  qg Þ, respectively. The denominator in the non-dimensional drift velocity expression represents the bubble rise velocity. In addition,  mg , hjg i, hjf i and hji can be made in non-dimensional form as

DD

v

þ g

EE



¼

vg

  D E jg þ jg ¼  1=4



1=4

rg Dq q2f

  D E jf þ jf ¼  1=4 r g Dq q2f

rg Dq q2f

 þ hji j ¼ 1=4

ð6Þ

r g Dq q2f

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   g DqDH V gj ¼ 0:188

ð7Þ

qg

where DH is the hydraulic diameter. The correlation has been used to determine the drift velocity for rod bundles in the TRAC-BF1/ MOD1 [21] and TRACE/V5.0 [22] safety analysis codes. It should be noted that the drift velocity in this correlation would increase to an unphysical value as the hydraulic diameter increases. Kataoka and Ishii [5] demonstrated that the drift velocity is independent of hydraulic diameter once the flow channel becomes pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sufficiently large (DH > 30 r=gDq). They utilized the viscosity number Nlf and the non-dimensional hydraulic diameter Dþ H to develop a drift velocity correlation for pool conditions in large diameter pipe. Hibiki and Ishii [6] considered the effect of liquid recirculation and formulated a drift velocity correlation for large diameter pipes by combining Eq. (4) and Kataoka-Ishii drift velocity correlation [5] as

V þgj

EE

¼

DD

V þgj;B

EE

e1:39hjg i þ þ

DD

g Dq

whole flow range DD EE Vþ = Ishii (1977) gj;B DD EE þ = Kataoka and Ishii (1987) V gj;P

As for rod bundles, the phenomenon of recirculation flow has also been found in close wall region [12]. In addition, Chen et al. [8] have analyzed that the drift velocity for rod bundles should depend on the two types of channel size. Hence the two-phase flow characteristics in rod bundles would be analogous to the characteristics in small and large diameter pipes. Exactly, the effects of these characteristics were considered on the drift velocity in Hibiki and Ishii correlation [6]. Therefore, Eq. (8) has been adopted in rod bundle drift-flux model for calculating drift velocity by Chen et al. [8], Clark et al. [10], Ozaki et al. [9] and Ozaki and Hibiki [11]. 2.3. Typical distribution parameter correlations for rod bundles In this section, the distribution parameter correlations have been discussed based on the typical drift-flux models for rod bundles and large diameter pipe. And the models were summarized in Table 2. In 1977, Ishii [3] modeled the distribution parameter as the following simple form,

sffiffiffiffiffiffi

Based on experimental data, Bestion [20] proposed a rod bundle drift velocity correlation considering the influences of hydraulic diameter and gas density. It is given by

DD

H pDffiffiffiffiffi Dþ r H ¼

when N lf > 2:25
103 DD EE  0:157 q Vþ ¼ 0:92 qg for Dþ gj H P 30 f  DD EE DD EE DD EE þ þ þ 1:39hjþ g i þ V gj Vþ ¼ V gj;B e 1  e1:39hjg i gj;P

V þgj;P

 EE þ 1  e1:39hjg i

ð8Þ

C 0 ¼ C 1  ð C 1  1Þ

qg qf

ð9Þ

where C 1 represents the asymptotic value of distribution parameter. Eq. (9) is based on the limit that the distribution parameter should approach unity as the density ratio approaches unity. This condition of thermodynamics is very important to extend the drift-flux models developed in low pressure systems to high pressure systems. With regard to fully developed upward vertical two-phase flow, the values of C 1 for small round, rectangular and annulus channel approximately are 1.2, 1.35 and 1.1, respectively [3,7]. However, due to the complex geometry of rod bundle channel, the value of C 1 may be different from that of the traditional channels. The TRACE/V5.0 [22] safety analysis code recommended C 1 ¼ 1:2, but utilizing this value would markedly lead to underpredicting the void fraction for values above about 0.4 according to the assessment of TRACE/V5.0 [22]. This correlation is given by

sffiffiffiffiffiffi

C 0 ¼ 1:2  0:2

qg qf

ð10Þ

Ozaki et al. [9] obtained the value of C 1 approximately was 1.1 based on experimental data from NUPEC test facility. In addition, they pointed out that C 1 ¼ 1:1 was valid for void fraction higher than 0.2 conditions, and the distribution parameter correlation is given by

596

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

Table 2 Typical drift-flux models for rod bundles and large diameter pipe. Model

Drift velocity

Parameter distribution

Hibiki and Ishii [6]

Hibiki-Ishii model

When inlet condition: hai 6 0:3 ( 8  þ 1:69 )  qffiffiffiffi D E   qffiffiffiffi > q q hjg i þ > > 6 0:9 1  qg þ qg 0 6 jþ < C 0 ¼ exp 0:475 hjþ i g = j f f   þ    D E ffiffiffiffi q q ffiffiffiffi >  > q q hj i þ > : C 0 ¼ 2:88 jgþ þ 4:08 1  qg þ qg 0:9 6 jþ 61 g = j f f h i When inlet condition: hai P 0:3   qffiffiffiffi qffiffiffiffi 8     < C 0 ¼ 1:2 exp 0:110 jþ 2:22 1  qg þ qg 0 6 jþ 6 1:8 qf qf   ffiffiffiffi q q ffiffiffiffi : C 0 ¼ 0:6 exp 1:2 jþ   1:8  þ 1:2 1  qg þ qg jþ  P 1:8 qf qf qffiffiffiffi q C 0 ¼ 1:2  0:2 qg

Kataoka-Ishii model

TRACE/V5.0 [22]

Bestion model

Chen et al. [8]

Hibiki-Ishii model

Ozaki et al. [9]

Hibiki-Ishii model

Clark et al. [10]

Hibiki-Ishii model

f

For pool condition  qffiffiffiffi  D E  D E 8 qffiffiffiffi qg qg þ > jþ 6 0:5 < C 0 ¼ 4:79 jg þ 1:00 1  qf þ qf g      qffiffiffiffi D E D E0:51 qffiffiffiffi q q þ g g > : C 0 ¼ 3:45 exp 0:52 jþ þ j þ 1:00 1  > 0:5 g g qf qf 8 hai < 0:1 < C 0;l C 0 ¼ C 0;l x þ C 0;h ð1  xÞ 0:1 6 hai 6 0 :2 : C 0;h hai > 0:2    qffiffiffiffi 8 qg 0:780 > D=P ¼ 0:3 > 1:03  0:03 qf 1  exp 26:3hai > <   qqffiffiffiffi D=P ¼ 0:5 1:04  0:04 qg 1  exp 21:2hai0:762 C 0;l ¼ f >   qqffiffiffiffi > > : D=P ¼ 0:7 1:05  0:05 qg 1  exp 34:1hai0:925 f qffiffiffiffi q C 0;h ¼ 1:10  0:10 qg f qqffiffiffiffi C 0 ¼ C 1  ðC 1  1Þ qg f (  þ  þ C 1L j 6 j  þ   þ C 1 max C1 ¼ C 1H j > j C 1 max  3 2  C 1H hjþ iC1 max 1 D E 4 5 jþ þ 1 C 1L ¼ g hjþ iC1 max hjþf i  

C 1H ¼ 1:1 þ 1:84 exp 0:1 jþ

sffiffiffiffiffiffi C 0 ¼ 1:1  0:1

qg qf

ð11Þ

Ozaki and Hibiki [11] adopted different C 1 values for different rod bundle channel geometries, such as utilizing C 1 ¼ 1:08 for Type II bundle and C 1 ¼ 1:03 for FRIGG test bundle. For heating conditions, the wall-peaked void distribution would significantly affect the two-phase flow. Ishii [3] modified Eq. (9) to boiling flow by adding a weighting factor that takes into account the wall bubble nucleation and makes C 1 ! 0 when hai ! 0. The distribution parameter is given by

qffiffiffiffiffiffiffiffiffiffiffiffiffi  C 0 ¼ 1:2  0:2 qg =qf ½1  exp ð18haiÞ

ð12Þ

Julia et al. [13] derived similarly distribution parameter correlations for subcooled boiling flow in rod bundle sub-channel based on the bubbly-layer thickness model which was proposed by Hibiki et al. [23]. Here, it is important to note that the Eq. (13) should be applied under void fraction lower than 0.1 conditions.

  qqffiffiffiffi 8 > D=P ¼ 0:3 1:03  0:03 qg 1  exp 26:3hai0:780 > f > > <   qqffiffiffiffi 0:762 1:04  0:04 qg 1  exp 21:2hai D=P ¼ 0:5 C0 ¼ f > >       ffiffiffiffi q > > : 1:05  0:05 qg 1  exp 34:1hai0:925 D=P ¼ 0:7 q f

ð13Þ Then, Ozaki et al. [9] proposed a distribution parameter correlation for rod bundles by incorporating Eqs. (11) and (13). Since the Eq. (13) is derived from rod bundle sub-channel, it is unreasonable to apply it to the global channel. Previously, Hibiki and Ishii [6] found that the distribution parameter in large diameter pipes is quite different from that of small diameter pipes under low mixture volumetric flux because

of the liquid recirculation. The proposed distribution parameter correlations were relevant to mixture volumetric flux based on numerous experimental data. Similarly, due to the flow recirculation in rod bundles, Chen et al. [8] demonstrated the distribution parameter initially increases before exponentially decreasing as the superficial gas increases under pool condition, and the maximum C 0 is located þ at hjg i  0:5. They considered the conditions: C 1 ! 1 when þ

þ

hjg i ! 0 or hjg i ! 1 and proposed an empirical distribution parameter correlation as

D E D E 8 þ þ > jg 6 0:5 < C 1 ¼ 4:79 jg þ 1:00   D E0:51 D E þ > : C 1 ¼ 3:45 exp 0:52 jþg þ 1:00 jg > 0:5

ð14Þ

Clark et al. [10] appropriately considered the effect of flow recirculation on the distribution parameter in rod bundles under low liquid flow and low pressure conditions. And a critical void fraction was utilized to correlate the maximum C 0 . They also considered þ þ C 1 ! 1 as hjg i ! 0, but C 1 ! 1:1 as hjg i ! 1. New correlations of the distribution parameter in ascending and descending parts were proposed based on new experimental data [24]. However, the effect of turbulence was not taken into account in Clark et al. [10] model. Hence more experimental data are needed to validate it.

3. Experimental facility and method 3.1. Experimental facility The schematic of the air-water two-phase flow experimental facility is shown in Fig. 1. The facility contains the water supply

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

597

Fig. 1. Schematic diagram of the experimental facility.

system, air supply system, mixer and test section. Liquid flow is provided by the pump and measured by two HONEYWELL electromagnetic flow meters with an accuracy of ±0.5%. The air flow rate is measured by two OMEGA gas mass flow meters with an accuracy of ± (0.8%RDG + 0.2%FS). Water and air meet in a mixer, which can produce even-distributed small bubbles. The mixer contains four air-water injector units, and the even-distributed small bubbles with the size of 1–3 mm from the mixer have been validated by Ren at al. [15] using the four-sensor conductivity probe. Then the air-water mixture flows through the 5
5 rod bundles test section, and the void fraction is measured by an impedance meter. More detailed information of the system can refer to Ren at al. [14,15]. The casing of rod bundle channel is made of transparent acrylic plates in a 66.1
66.1 mm square duct. The 5
5 acrylic rods have the diameter of 9.5 mm and the pitch of 12.6 mm, the axial view and cross-section view of test section are shown in Fig. 2. The height of test section is 1.5 m. There are five spacer grids (as shown in Fig. 3) located along the length of the test section to limit vibration and keep rod pitch. The spacer grids are installed at L/DH = 0, 27.2, 57.4, 83.7 and 121.6, respectively. Moreover, the spacer grids do not contain dimples, springs, and mixing vanes, etc., which are much more simplified than typical spacers used in PWRs and BWRs. Since the typical spacer grid can cause a strong disturbance in pressure distribution and create a downstream wake region, which affects the interfacial structure and void distribution [18]. The simplified spacer grid is used to avoid these effects and better focus on the effects of rod bundle geometry on two-phase flow, and the impedance meter is located at L/DH = 110 below the fifth spacer grid where are far enough downstream from the fourth one so that the impacts of the above part can be negligible.

3.2. Impedance meter The impedance meter has been used to measure the areaaverage void fraction in rod bundles by some researchers [12,18,24,25]. It is made of two stainless steel electrodes with the width of 10 mm in axial direction, which are flush mounted on opposite side of the flow channel as shown in Fig. 2. Theoretically, the impedance meter method is based on the different conductivities of air and water. It can obtain different voltages for varied two-phase flow when one of electrodes is fed into current while the other receives inductive potentials. Then the voltage signals can be acquired using NI-9220 with a frequency of 10 kHz for at least 30 s. The measured voltages can be made non-dimensional as

V ¼ 1 

V  V Air V Water  V Air

ð15Þ

where V is the measured voltage and related to the area-averaged void fraction. V Air and V Water are measured voltages in full air and full water flow, respectively. Eq. (15) has been assumed V ¼ 0 as hai ¼ 0 and V ¼ 1 as hai ¼ 1. There are five differential pressure measurements along the axial length of test section. Each pressure drop is obtained from a pressure differential transmitter (Yokogawa, EJA-110A) with an error of 0.065%. Generally, the area-averaged void fraction can be calculated from measured pressure drop under stagnant or low liquid flow conditions, under which the acceleration and frictional pressure drops can be negligible compared with the gravitational pressure drop in air-water two-phase flow [26]. Hence, the void fraction can be calculated by the following relation:

598

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

Fig. 2. Rod bundles test section: axial view and cross-section view (mm).

1.0

Stagnant liquid flow Low liquid flow Fitting curve

Void Fraction, < > [-]

0.8

0.6

0.4

0.2

5

4

3

2

< > = 0.9996V* - 5.1123V* + 7.6923V* - 4.4028V* + 1.8213V*

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Non-D Impedance, V* [-] Fig. 4. The calibration of impedance meter. Fig. 3. Structure of the simplified spacer grid.

Dp hai ¼ Dqgh

ð16Þ

The V obtained simultaneously from the impedance meter can be plotted against the calculated void fraction in Fig. 4. A fifth order polynomial expression is used to fit the experimental data as the calibration curve. Then, the void fraction can be calculated by the impedance meter in two-phase flow. Clark et al. [24] have analyzed that the void measurement error of the impedance meter consists of three parts, which can be expressed as:

Ehai ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðEDP Þ2 þ ðEV Þ2 þ Efit

ð17Þ

where EDP , EV and Efit represent the errors of the differential pressure calculated void fraction, the non-dimensional voltage, and the calibration curve fit, respectively. These errors are obtained from uncertainty analysis process as 2.08%, 2.00% and 1.64%, respec-

tively. Finally, the error Ehai of void fraction measured from meter is about 3.32%.

3.3. Flow conditions The experiment has been carried out at room temperature and atmospheric pressure conditions. The superficial liquid velocity ranges from 0.00 to 1.50 m/s while the superficial gas velocity from 0.02 to 6.00 m/s. Fig. 5 shows the comparison of experimental data with the flow-regime map proposed by Liu and Hibiki [19]. According to the summarization by Liu and Hibiki [19] based on existing experiment, there are about six flow regimes in rod bundles. These flow regimes are bubbly (B), finely dispersed bubbly (F), capbubbly (CB), cap-turbulent (CT), churn (C) and annular (A) flow. Liu and Hibiki [19] proposed a new flow regime transition criteria for vertical rod bundles, which has shown fairly good agreement with existing data. As shown in Fig. 5, current flow conditions mainly cover bubbly, cap-bubbly, and cap-turbulent flow. It should

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

599

be noted here that the data at the bottom of the figure represent the stagnant liquid condition. In order to reflect the void characteristics in the prototypic reactor as far as possible, the same sizes of diameter and pitch of rods of PWR have been adopted in this experiment. Moreover, this 5
5 structure contains three types of sub-channel: corner, side and center ones, and it remains the similar scale as the fuel assembly of PWR to model the two-phase characteristics in the prototypic reactor. Although the experimental data might not be applied to the situation of reactor directly, it would help to better understand the two-phase flow behavior in rod bundles and supplement the rod bundle experimental database as a benchmark for CFD validation.

distribution parameter correlation. Hence the model tends to overestimate the void fraction compared with present data in Fig. 6(b). It is interesting that the prediction error decreases with the increase of liquid velocity. This may be the fact that the model was developed based on the NUPEC data close to the prototypic BWR conditions [9], thereby it is applicable to high flow conditions in strong turbulence. Chen et al. [8] considered the effect of flow recirculation in their correlations under stagnant liquid condition in 8
8 and 4
4 rod bundles. Therefore, the model shows good agreement with present data under stagnant liquid condition in Fig. 6(c). But for other conditions, the prediction errors are relatively high. Clark model [10] was proposed based on 8
8 rod bundles experimental data at low pressure and low liquid flow. The model was an improvement of Chen model and focused on the effect of flow recirculation on the distribution parameter. As can be seen from Fig. 6(d), Clark model has a good prediction to the present data. However, it should be noted that the prediction error is relatively large in the void fraction approximately from 0.2 to 0.5, which may be attributed to the effect of the channel size on distribution parameters. Moreover, the TRACE/V5.0 model [22] and Ozaki model [9] are more concerned with the prototypic reactor of high pressure, high flow, and diabatic conditions. Consequently, the two models may not be applicable for air-water two-phase flow. In general, the effect of flow recirculation should be considered in the drift velocity and the distribution parameter in rod bundle channel. Thus the Hibiki-Ishii correlation [6] considered this effect on the drift velocity has a better performance than the Bestion correlation [20]. Chen et al. [8] and Clark et al. [10] considered the flow recirculation by associating the distribution parameter to the mixture volumetric flux. Furthermore, the influences of turbulence and channel size on the distribution parameter need further discussion.

4. Results and discussion

4.2. Influencing factors on distribution parameter for rod bundles

4.1. Drift-flux correlation comparison

In view of the fact that the Hibiki-Ishii correlation [6] is appropriate for calculating the drift velocity in rod bundle channel, this work utilizes this correlation, and the distribution parameters are obtained from experimental data. For subcooled boiling flow, the wall-peaked void distribution is obvious in round tubes, thus the distribution parameter depends on the void fraction [3]. Julia et al. [13] obtained a same conclusion in the sub-channel of rod bundles under subcooled boiling as well. However, for air-water two-phase flow, Yang et al. [26] found there is a distinct center-peaked phase distribution at low void fraction in rod bundles. Besides, Fig. 7 shows the distribution parameters have not converged at their asymptotic values over all the void fraction. It seems inapplicable to correlate the distribution parameter with the void fraction for all conditions in air-water two-phase flow. As shown in Fig. 8, with the increase of mixture volumetric flux, the distribution parameter initially increases to reach the maximum, then decreases exponentially. In addition, these distribution parameter data are compared with Hibiki-Ishii model [6] and Clark model [10]. From the results, the Hibiki-Ishii model proposed for large diameter pipes that differs far from present data, and on the whole, the Clark model is in good agreement with the data, but there are obvious errors in the ascending part of distribution parameters under conditions of hjfi = 0.24 and 0.49 m/s. For the initial rising section of distribution parameter, which previously has been found in the large diameter pipe by Hibiki and Ishii [6], and they attributed this phenomenon to the liquid recirculation. Then Chen et al. [8] and Clark et al. [10] considered the recirculation as an important effect on the distribution parameter in rod bundles as well. For the flow recirculation, as shown in

Superficial Liquid Velocity, [m/s]

100

10

Liu and Hibiki Bubbly to Cap-Bubbly Bubbly to Dispersed Bubbly Cap-Bubbly to Cap-Turbulent Dispersed Bubbly to Cap-Turbulent Cap-Turbulent to Churn Churn to Annular

F 1

B

0.1

CB 0.01 0.01

0.1

CT

C

1

10

Superficial Gas Velocity, [m/s] Fig. 5. Experimental matrix presented on flow-regime maps.

Fig. 6 shows the comparisons between present data and four typical drift-flux models for rod bundles as TRACE/V5.0 [22], Ozaki et al. [9], Chen et al. [8], and Clark et al. [10] model. The average absolute relative errors of these models are 43.69%, 30.81%, 25.82%, and 10.80%, respectively. Here, the relative error, g, and average absolute relative error, MRE, are defined by

g¼

  hacal: i  aexp :  
100%

MRE ¼

aexp :

! N 1X jgj
100% N i¼1

ð18Þ

ð19Þ

where N, hacal: i and haexp: i are the number of sample, calculated void fraction, and measured void fraction, respectively. In the TRACE/V5.0 [22] code, the Bestion drift velocity correlation Eq. (7) was implemented, and the distribution parameter qffiffiffiffiffiffiffiffiffiffiffiffiffi was calculated by C 0 ¼ 1:2  0:2 qg =qf . Since the Bestion drift velocity correlation depends on the gas density, which would lead to unrealistically high value for drift velocity under low pressure conditions. Thus it may not be appropriate for current conditions, and the drift-flux model tends to underestimate the present data as shown in Fig. 6(a). Ozaki model [9] considered the effect of void fraction distribution for heating conditions in rod bundle channel. The drift velocity correlation of Hibiki-Ishii [6] was adopted to consider the effect of flow recirculation, although this effect was not considered in the

600

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605 1.00 0.75

(a)

= 0.73 m/s

= 0.10 m/s

= 0.97 m/s

1.75

= 0.24 m/s

= 1.21 m/s

1.50

= 0.49 m/s

= 1.47 m/s

1.25

Relative Error, [-]

Relative Error, [-]

0.50

2.00

= 0.00 m/s

0.25 0.00 -0.25 -0.50

TRACE/V5.0 model MRE = 43.69% ±25% Relative Error

-0.75 -1.00 0.2

0.4

0.6

Void Fraction, <

0.8

Ozaki et al. model MRE = 30.81% ±25% Relative Error

1.00 0.75 0.50 0.25 0.00 -0.25

= 0.00 m/s

= 0.73 m/s

-0.50

= 0.10 m/s

= 0.97 m/s

-0.75

= 0.24 m/s

= 1.21 m/s

= 0.49 m/s

= 1.47 m/s

-1.00

0.0

1.0

0.0

0.2

> [-] exp.

0.4

0.6

Void Fraction, <

1.00

0.8

1.0

> [-] exp.

1.00

(c) 0.75

= 0.00 m/s

= 0.73 m/s

= 0.10 m/s

= 0.97 m/s

= 0.24 m/s

= 1.21 m/s

= 0.49 m/s

= 1.47 m/s

0.75

0.25 0.00 -0.25 -0.50

Chen et al. model MRE = 25.82% ±25% Relative Error

-0.75

(d)

0.50

Relative Error, [-]

0.50

Relative Error, [-]

(b)

= 0.00 m/s

= 0.73 m/s

= 0.10 m/s

= 0.97 m/s

= 0.24 m/s

= 1.21 m/s

= 0.49 m/s

= 1.47 m/s

0.25 0.00 -0.25 -0.50

Clark et al. model MRE = 10.80% ±25% Relative Error

-0.75

-1.00

-1.00

0.0

0.2

0.4

0.6

Void Fraction, <

exp.

0.8

1.0

0.0

0.2

0.4

Void Fraction, <

> [-]

0.6 exp.

0.8

1.0

> [-]

Fig. 6. Comparisons of drift-flux models with experimental data.

3.5 = 0.00 m/s = 0.10 m/s

Distribution Parameter, C0 [-]

3.0

= 0.24 m/s = 0.49 m/s = 0.73 m/s

2.5

= 0.97 m/s = 1.21 m/s

2.0

= 1.47 m/s Ozaki model

1.5

1.0

0.5

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Void Fraction, < > [-] Fig. 7. Relationship between distribution parameter and void fraction.

Fig. 9, the large cap bubbles (e.g. bubble A) gather in the subchannel and move faster than the small bubbles, while driving the liquid to a higher velocity than that in the near-wall region, finally it would lead to a slow flow or even occasional recirculation near the wall area. Such phenomenon would further bring a higher void peak in the center region, resulting in an increase in the drift velocity and the distribution parameter.

However, with the further increase of gas velocity, the cap bubbles may expand to the maximum size allowed by sub-channel size, which would cause distortion at the cap bubbles surface. As a result, the resulting bubble would become unstable and immediately breakup into smaller bubbles. Schlegel et al. [27] pointed out that the rapid creation and destruction of cap bubbles would result in greater turbulence. This turbulence would diminish the recirculation as to reduce the distribution parameter. It can be seen from the Fig. 8 that the distribution parameter reaches the maximum value at the transition from cap-bubbly to cap-turbulent flow, and then begin to decrease. In addition, the maximum distribution parameters may be affected by the channel size, so there are obvious errors between the experimental data and the Clark model in the ascending part of distribution parameters under low liquid velocity conditions. For the high liquid velocity conditions, the bubbles would be mainly influenced by the liquid shear-induced turbulence instead of the channel size, although the distribution parameter still increases initially due to the bubbles gathering in the center of channel. However, for the turbulence, whether induced by the bubbles or the liquid phase, its effect on the distribution parameter seems to be independent of the channel size. Thus the Clark model agrees well with the experimental data in the turbulent region. To sum up, on the one hand, the distribution parameter under low flow conditions is mainly determined by the flow recirculation that would be affected by the channel size and the bubble-induced turbulence. On the other hand, the characteristics of distribution

601

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

2.2

= 0.49 m/s

= 0.24 m/s Bubbly flow Cap bubbly flow Cap turbulent flow Churn flow Clark model Hibiki-Ishii model ( < 0.3) Hibiki-Ishii model ( > 0.3)

2.5

2.0

1.5

1.0 0

10

20

30

Bubbly flow Cap bubbly flow Cap turbulent flow Clark model Hibiki-Ishii model ( < 0.3) Hibiki-Ishii model ( > 0.3)

2.0

Distribution Parameter, C0 [-]

Distribution Parameter, C0 [-]

3.0

1.8

1.6

1.4

1.2

1.0

40

0

+

Non-D. Mixture Volumetric Flux, [-]

30

40

Non-D. Mixture Volumetric Flux, [-] 1.6

= 0.97 m/s Bubbly flow Cap bubbly flow Cap turbulent flow Clark model Hibiki-Ishii model ( < 0.3) Hibiki-Ishii model ( > 0.3)

1.6

20

+

Distribution Parameter, C0 [-]

Distribution Parameter, C0 [-]

1.8

10

1.4

1.2

1.0

= 1.21 m/s Bubbly flow Dispersed bubbly flow Cap turbulent flow Clark model Hibiki-Ishii model ( < 0.3) Hibiki-Ishii model ( > 0.3)

1.4

1.2

1.0 5

10

15

20

25

30 +

Non-D. Mixture Volumetric Flux, [-]

35

8

12

16

20

24

28

32

+

Non-D. Mixture Volumetric Flux, [-]

Fig. 8. Dependence of distribution parameter on mixture volumetric flux.

Fig. 9. The observation of flow recirculation (hjf i = 0.1 m/s, hjgi = 0.09 m/s).

parameter would be governed by the shear-induced turbulence under high flow conditions.

4.3. Development of drift-flux model for rod bundles As mentioned above, the drift velocity for rod bundles is calculated by the Hibiki-Ishii correlation [6]. As for the distribution parameter, there are two parts of correlations that need to be built.

For the ascending part, Chen et al. [8] and Clark et al. [10] proposed the distribution parameter linearly increases from 1 to the maximum with the increase of superficial gas velocity. Moreover, Clark et al. [10] utilized a simple interpolation scheme to determine the distribution parameter as:    1 20 3 sffiffiffiffiffiffi! sffiffiffiffiffiffi þ C 1H j C 1 max  1 D E qg qg þ D E A jg þ 15 1  ð20Þ C 0L ¼ 4@   þ þ þ qf qf j C 1 max  jf

602

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605 þ

D E DD EE þ D E jf C 0 þ V þgj  þ þ j C 1 max ¼ jf þ 1  C0 hai

ð21Þ

crit:

where haicrit: is the critical void fraction to associate the maximum distribution parameter for a given superficial liquid velocity. Clark et al. [10] demonstrated the maximum distribution parameter would occur at the flow-regime transition from bubbly to capbubbly flow, and proposed a critical void fraction correlation as:

haicrit:



D E  þ ¼ min 0:0284 jf þ 0:125; 0:52

ð22Þ

However, as shown in Fig. 10, the transition data are compared with the flow-regime maps of Liu-Hibiki [19] and Mishima-Ishii [28]. Here, the Mishima-Ishii [28] flow-regime maps was proposed for vertical small diameter round tubes. The results show current maximum distribution parameters tend to occur at the transition from cap-bubbly to cap-turbulent flow, and the data of Kamei et al. [29] show the same conclusion. It is because that the increasing trend of distribution parameter will last until the turbulence begins to diminish the flow recirculation. It should be noted that the data at the bottom of Fig. 10 represent the stagnant liquid condition. Moreover, Liu and Hibiki [19] proposed the transition void fraction at bubbly to cap-bubbly for rod bundles is:

sffiffiffiffiffiffi

qg hai ¼ 0:234 þ 0:066 qf

ð23Þ

Therefore, the critical void fraction for the transition from capbubbly to cap-turbulent flow should be higher than 0.234, which agrees well with present data as shown in Fig. 11. As above analysis, the distribution parameter in ascending part would be mainly affected by flow recirculation under low liquid flow conditions. Meanwhile, it would gradually be governed by the turbulence effect with the increase of liquid velocity. There is a certain liquid velocity that can determine which effect is dominant. The liquid velocity may be related to when turbulent forces begin to induce dispersion of the gas phase, which can be estimated from the transition criterion between bubbly and finely-dispersed bubbly flow proposed by Taitel et al. [30].

1.0

Critical Void Fraction, < >crit. [-]

where hj iC 1 max represents the non-dimensional mixture volumetric flux at the maximum distribution parameter, and C 0L is the disþ tribution parameter in ascending part. The hj iC1 max can be derived from Eq. (1) as:

Present data Clark et al. Kamei et al. Clark's correlation Present correlation

0.8

+

crit.

0.6

0.4

0.2

Eq. (27)

Eq. (22)

0.0 0

2

4

6

8

Non-D. Superficial Liquid Velocity, [-] Fig. 11. Dependence of critical void fraction on superficial liquid velocity.

2 3  0:089 !0:446 0:429 r D     H q g Dq 6 7 f jf þ jg ¼ 44 5 0:072

vf

qf

Superficial Liquid Velocity, [m/s]

Liu and Hibiki Mishima and Ishii

  j   g   ¼ 0:52 jf þ jg

ð25Þ

Combining Eqs. (24) and (25), an equation about the hjf i is obtained by eliminating the hjg i. Here, the hjf icrit: is defined as critical superficial liquid velocity:

2  0:089 0:429 r   qf 6DH jf crit: ¼ 1:924 0:072

mf

3 !0:446 g Dq 7 5

qf

Therefore, when the superficial liquid velocity is lower than hjf icrit: , the void fraction characteristics will be governed by the recirculation. As shown in Fig. 11, current data on the left of hjf icrit: show a linear relationship between critical void fraction and superficial liquid velocity. This relationship is approximately by

haicrit:

0.1

0.1

1

ð26Þ

ð27Þ

When the superficial liquid velocity is higher than the hjf icrit: , the shear-induced turbulence will be the dominant part in determining the characteristics of void fraction, which seems to be independent of the channel size. Hence the relationship on the right side of critical liquid velocity is same as Eq. (22) in Fig. 11. Combining Eqs. (22) and (27), the new critical void fraction correlation is obtained as,

Present data Kamei et al. Clark et al.

1

0.01 0.01

ð24Þ

where mf is the kinematic viscosity of liquid phase. According to Taitel et al. [30], the upper limit of Eq. (24) approximately is

D E þ hacrit: i ¼ 0:0463 jf þ 0:253

10

10

+

10

Superficial Gas Velocity, [m/s] Fig. 10. Dependence of maximum distribution parameter on flow-regime maps.

8 D E     > < 0:0463 jþf þ 0:253 jf < jf crit:  D E    ¼   þ > : min 0:0284 jf þ 0:125; 0:52 jf P jf crit:

ð28Þ

Finally, the distribution parameter in the ascending part can be calculated by Eqs. (20), (21), (26), and (28). Moreover, the relationship between critical void fraction and superficial liquid velocity may have some enlightenment to the flow-regime transition of rod bundles. For the descending part, the bubble-induced turbulence would play a significant role in the distribution parameter according to

603

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605 Table 3 Details of experimental data for stagnant condition. Researchers

jf (m/s)

P (MPa)

D/P0 (mm)

DH (mm)

Others

Anklam and Miller [31] Kumamaru et al. [32] Kamei et al. [29]

0.00 0.00 0.00

3.9–8.1 3–17 0.1

0.00 0.00

0.1 0.1

10.8 10.1 9.0 12.7 14.8 10.3

8
8 (steam-water) 32 (steam-water) 4
4 (air–water)

Clark et al. [24] Present

9.5/12.7 9.5/12.6 A:10.0/12.3 B:12.0/16.0 12.7/16.7 9.5/12.6

Distribution Parameter,C [-]

5

 þ   C 0 ¼ 1:1 þ 1:84 exp 0:1 j 1

Clark data (air-water) Anklam & Miller data (steam-water) Kumamaru data (steam-water) Kamei A-RB data (air-water) Kamei B-RB data (air-water) Present data (air-water) Chen correlation Clark correlation

4

3

2

1

0 0

10

20

30

40

50

60

70

+

Non-D. Mixture Volumetric Flux, < j > [-] Fig. 12. Distribution parameter exponential descending trend.



8
8 (air–water) 5
5 (air–water)

sffiffiffiffiffiffi!

qg þ qf

sffiffiffiffiffiffi

qg qf

ð30Þ

Through analyzing the influence of flow recirculation and turbulence on distribution parameters, a drift-flux model as detailed in Table 4 is developed based on the existing rod bundle experimental data. The Hibiki-Ishii correlation [6] is adopted to calculate the drift velocity. A new distribution parameter correlation is developed based on the Clark model [10], as can be seen from Fig. 13, the new correlation is in good agreement with the current distribution parameters. In addition, the model has been compared with current data and Yang et al. data [25] in Fig. 14, the results show that the present model has a good prediction accuracy. It should be noted that the present model fits to the void fraction under air-water twophase flow conditions. However, Clark et al. [11] have demonstrated that it is practicable to apply the drift-flux model developed from air-water two-phase flow to the prototypic conditions. Furthermore, it is necessary to validate the model with more data over wide ranges of condition. 5. Conclusion

Table 4 Present drift-flux model. hV gj i

C0

Hibiki-Ishii correlation

C0 ¼

(

 þ  þ C 0L j 6 j  þ   þ C 1 max C 0H j > j C 1 max  1 20  3  qffiffiffiffi qffiffiffiffi C 0H hjþ iC1 max 1 D E þ A 5 1  qg þ qg C 0L ¼ 4@ jþ þ 1 j g qf qf h iC1 max hjþf i  qffiffiffiffi h  i qffiffiffiffi  þ 0:51  qg q þ 1:00 1  q þ qg C 0H ¼ 3:45 exp 0:52 j f f     D E  þ hjþf iC 0 þ V þgj j C 1 max ¼ jþ þ 1 f C 0 haicrit: D E D E D E 8 þ < 0:0463 jf þ 0:253 jf < jf  D E  D E D Ecrit haicrit: ¼ : min 0:0284 jþ þ 0:125; 0:52 j P jf f f crit 2 3  0:089 r D E  0:446 D0:429 H q 6 7 f g Dq ¼ 1:924 jf 5 qf m0:072 crit:

f

above analysis. The distribution parameter data of this part acquired from existing experiments (detailed in Table 3) are presented in Fig. 12. It is interesting that these distribution parameters almost have the same downward trend for different rod bundle channel, and this would imply the effect of turbulence is independent of channel size. By comparing with Chen correlation [8] (Eq. (29)) and Clark correlation [10] (Eq. (30)), the results show the Chen correlation has a better agreement. Moreover, when þ hjg i ! 1 for a given liquid velocity, the void fraction hai and the C 0 should tend to be 1, which is a bounding condition considered in Eq. (29).

h  i  þ 0:51  C 0 ¼ 3:45 exp 0:52 j þ 1:00 1 

sffiffiffiffiffiffi!

qg þ qf

sffiffiffiffiffiffi

qg qf

ð29Þ

In this study, an air-water two-phase flow experiment in 5
5 rod bundles has been performed. The impedance meter has been used to measure area-averaged void fraction. The ranges of superficial liquid velocity and gas velocity are from 0.00 to 1.50 m/s and 0.02 to 6.00 m/s, respectively. Current flow regimes cover bubbly, cap-bubbly, and cap-turbulent flow. Several conclusions can be obtained from data analysis: (1) Four typical drift-flux models for rod bundles were compared with present data. The average relative prediction errors are 43.69%, 30.81%, 25.82% and 10.80% for TRACE/V5.0 [22], Ozaki et al. [9], Chen et al. [8] and Clark et al. [10] model, respectively. (2) The experimental data and visualization show that the flow recirculation and turbulence have significant effects on the distribution parameter. The recirculation would increase the distribution parameter at low liquid flow conditions, which might be influenced by the channel size and the bubble-induced turbulence. At the same time, the shearinduced turbulence would decrease the distribution parameter under high flow conditions, which seems to be independent of the channel size. A critical liquid velocity is defined to determine which effect is dominant on the distribution parameter. (3) With the increase of mixture volumetric flux, the distribution parameter initially increases to reach a maximum value, then decreases exponentially. Due to bubble-induced turbulence diminishing flow recirculating, the maximum distribution parameter is related to a critical void fraction during the flow-regime transition from cap-bubbly to cap-turbulent flow, and a new critical void fraction correlation has been

604

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605 2.2

= 0.49 m/s

= 0.24 m/s Experimental data Clark model Present model

2.5

Experimental data Clark model Present model

2.0

Distribution Parameter, C0 [-]

Distribution Parameter, C0 [-]

3.0

2.0

1.5

1.8

1.6

1.4

1.2

1.0

1.0 0

10

20

30

0

40

10

1.6

= 0.97 m/s Experimental data Clark model Present model

1.6

30

40

Non-D. Mixture Volumetric Flux, [-]

Distribution Parameter, C0 [-]

Distribution Parameter, C0 [-]

1.8

20

+

+

Non-D. Mixture Volumetric Flux, [-]

1.4

1.2

1.0

= 1.21 m/s Experimental data Clark model Present model

1.4

1.2

1.0 5

10

15

20

25

30

35

8

+

12

16

20

24

28

32

+

Non-D. Mixture Volumetric Flux, [-]

Non-D. Mixture Volumetric Flux, [-]

Fig. 13. Comparison of present data with distribution parameter correlations.

1.0

1.0

Presnet data Clark et al. model (MRE = 10.80%) Present model (MRE = 6.81%) ± 25%

0.8

cal.

0.6

Void Fraction, <

Void Fraction, <

cal.

> [-]

> [-]

0.8

Yang et al. data Clark et al. model (MRE = 20.83%) Present model (MRE = 13.90%) ± 25%

0.4

0.2

0.6

0.4

0.2

0.0

0.0 0.0

0.2

0.4

0.6

Void Fraction, <

exp.

0.8

> [-]

1.0

0.0

0.2

0.4

Void Fraction, <

Fig. 14. Comparison of experimental data with present drift-flux model.

0.6

> [-] exp.

0.8

1.0

T.-p. Ye et al. / International Journal of Heat and Mass Transfer 132 (2019) 593–605

proposed to determine the distribution parameter in ascending part. Based on the comparison of the correlations with existing experimental data, the Chen correlation [8] was recommended for descending part of the distribution parameter. (4) The Hibiki-Ishii correlation [6] is implemented to calculate the drift velocity, and the new drift-flux model based on the form of Clark model [10] shows good prediction capability for present data and Yang et al. data [25]. Conflicts of interest The authors declared that there is no conflict of interest. Acknowledgments The authors would like to express their thanks to Hang Liu, Song-song Li, Bin Yu, Jie Wan, Yang Liu, and Ding Fu in performing the experiment and manuscript preparing. In addition, the authors also would like to express their grateful appreciation for the financial support of the Natural Science Foundation of China (Grant Nos.: 51676020, 51706026, 11805027) and Natural Science Foundation of Chongqing (Grant No. cstc2018jszx-cyzdx0100). References [1] M. Ishii, T. Hibiki, Thermo-fluid Dynamics of Two-Phase Flow, Springer Science & Business Media, 2010. [2] N. Zuber, J. Findlay, Average volumetric concentration in two-phase flow systems, J. Heat Transf. 87 (4) (1965) 453–468. [3] M. Ishii, One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes, ANL-7747, USA, 1977. [4] T. Hibiki, M. Ishii, One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes, Int. J. Heat Mass Transf. 46 (25) (2003) 4935–4948. [5] K. Isao, I. Mamoru, Drift flux model for large diameter pipe and new correlation for pool void fraction, Int. J. Heat Mass Transf. 30 (9) (1987) 1927–1939. [6] T. Hibiki, M. Ishii, One-dimensional drift–flux model for two-phase flow in a large diameter pipe, Int. J. Heat Mass Transf. 46 (10) (2003) 1773–1790. [7] B. Ozar, J. Jeong, A. Dixit, J. Juliá, T. Hibiki, M. Ishii, Flow structure of gas–liquid two-phase flow in an annulus, Chem. Eng. Sci. 63 (15) (2008) 3998–4011. [8] S.-W. Chen, Y. Liu, T. Hibiki, M. Ishii, Y. Yoshida, I. Kinoshita, M. Murase, K. Mishima, One-dimensional drift-flux model for two-phase flow in pool rod bundle systems, Int. J. Multiph. Flow 40 (2012) 166–177. [9] T. Ozaki, R. Suzuki, H. Mashiko, T. Hibiki, Development of drift-flux model based on 8
8 BWR rod bundle geometry experiments under prototypic temperature and pressure conditions, J. Nucl. Sci. Technol. 50 (6) (2013) 563– 580. [10] C. Clark, M. Griffiths, S.-W. Chen, T. Hibiki, M. Ishii, T. Ozaki, I. Kinoshita, Y. Yoshida, Drift-flux correlation for rod bundle geometries, Int. J. Heat Fluid Flow 48 (2014) 1–14. [11] T. Ozaki, T. Hibiki, Drift-flux model for rod bundle geometry, Prog. Nucl. Energy 83 (2015) 229–247.

605

[12] S.-W. Chen, Y. Liu, T. Hibiki, M. Ishii, Y. Yoshida, I. Kinoshita, M. Murase, K. Mishima, Experimental study of air–water two-phase flow in an 8
8 rod bundle under pool condition for one-dimensional drift-flux analysis, Int. J. Heat Fluid Flow 33 (1) (2012) 168–181. [13] J.E. Julia, T. Hibiki, M. Ishii, B.-J. Yun, G.-C. Park, Drift-flux model in a subchannel of rod bundle geometry, Int. J. Heat Mass Transf. 52 (13–14) (2009) 3032–3041. [14] Q.-Y. Ren, W.-X. Zhou, S.-J. Du, Z.-C. Li, L.-M. Pan, Sub-channel flow regime maps in vertical rod bundles with spacer grids, Int. J. Heat Mass Transf. 122 (2018) 1138–1152. [15] Q.-Y. Ren, L.-M. Pan, W.-X. Zhou, S.-J. Du, Z.-C. Li, Phase distribution characteristics of bubbly flow in 5
5 vertical rod bundles with mixing vane spacer grids, Exp. Therm. Fluid Sci. 96 (2018) 451–459. [16] Y. Mizutani, A. Tomiyama, S. Hosokawa, A. Sou, Y. Kudo, K. Mishima, Twophase flow patterns in a four by four rod bundle, J. Nucl. Sci. Technol. 44 (6) (2007) 894–901. [17] Y. Zhou, Y. Hou, H. Li, B. Sun, D. Yang, Flow pattern map and multi-scale entropy analysis in 3
3 rod bundle channel, Ann. Nucl. Energy 80 (2015) 144–150. [18] S. Paranjape, D. Stefanczyk, Y. Liang, T. Hibiki, M. Ishii, Global flow regime identification in a rod bundle geometry, in: 16th International Conference on Nuclear Engineering, American Society of Mechanical Engineers, 2008, pp. 421–429. [19] H. Liu, T. Hibiki, Flow regime transition criteria for upward two-phase flow in vertical rod bundles, Int. J. Heat Mass Transf. 108 (2017) 423–433. [20] D. Bestion, Interfacial friction determination for the 1-D, 6 equation, 2 fluid model used in the Cathare code, European Two Phase Flow Group Meeting. Marchwood, UK, 1985 (sn). [21] J.A. Borkowski, N.L. Wade, S. Rouhani, R. Shumway, W. Weaver, W. Rettig, C. Kullberg, TRAC-BF1/MOD1 models and correlations, Nuclear Regulatory Commission, Washington, DC (United States), Div. of Systems Research; EG and G Idaho Inc, Idaho Falls, ID (United States), 1992. [22] S. Bajorek, TRACE V5. 0 Theory manual, field equations, solution methods and physical models, United States Nuclear Regulatory Commission, 2008. [23] T. Hibiki, R. Situ, Y. Mi, M. Ishii, Modeling of bubble-layer thickness for formulation of one-dimensional interfacial area transport equation in subcooled boiling two-phase flow, Int. J. Heat Mass Transf. 46 (8) (2003) 1409–1423. [24] C. Clark, M. Griffiths, S.-W. Chen, T. Hibiki, M. Ishii, I. Kinoshita, Y. Yoshida, Experimental study of void fraction in an 8
8 rod bundle at low pressure and low liquid flow conditions, Int. J. Multiph Flow 62 (2014) 87–100. [25] X. Yang, J.P. Schlegel, Y. Liu, S. Paranjape, T. Hibiki, M. Ishii, Measurement and modeling of two-phase flow parameters in scaled 8
8 BWR rod bundle, Int. J. Heat Fluid Flow 34 (2012) 85–97. [26] X. Yang, J.P. Schlegel, Y. Liu, S. Paranjape, T. Hibiki, M. Ishii, Experimental study of interfacial area transport in air–water two phase flow in a scaled 8
8 BWR rod bundle, Int. J. Multiph. Flow 50 (2013) 16–32. [27] J.P. Schlegel, P. Sawant, S. Paranjape, B. Ozar, T. Hibiki, M. Ishii, Void fraction and flow regime in adiabatic upward two-phase flow in large diameter vertical pipes, Nucl. Eng. Des. 239 (12) (2009) 2864–2874. [28] M. Kaichiro, M. Ishii, Flow regime transition criteria for upward two-phase flow in vertical tubes, Int. J. Heat Mass Transf. 27 (5) (1984) 723–737. [29] A. Kamei, S. Hosokawa, A. Tomiyama, I. Kinoshita, M. Murase, Void fraction in a four by four rod bundle under a stagnant condition, J. Power Energy Syst. 4 (2) (2010) 315–326. [30] Y. Taitel, D. Bornea, A. Dukler, Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes, AIChE J. 26 (3) (1980) 345–354. [31] T. Anklam, R. Miller, Void fraction under high pressure, low flow conditions in rod bundle geometry, Nucl. Eng. Des. 75 (1) (1983) 99–108. [32] H. Kumamaru, M. Kondo, H. Murata, Y. Kukita, Void-fraction distribution under high-pressure boil-off conditions in rod bundle geometry, Nucl. Eng. Des. 150 (1) (1994) 95–105.