Study on flow characteristics of high-Pr heat transfer fluid near the wall in a rectangular natural circulation loop

International Journal of Heat and Mass Transfer 121 (2018) 1350–1363

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Study on flow characteristics of high-Pr heat transfer fluid near the wall in a rectangular natural circulation loop Yukyung Shin, Seok Bin Seo, In Cheol Bang ⇑ Department of Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea

a r t i c l e

i n f o

Article history: Received 30 September 2017 Received in revised form 13 January 2018 Accepted 14 January 2018 Available online 7 March 2018 Keywords: Natural circulation High-Prandtl number (Pr) Flow characteristics Boundary layer PIV visualization CFD simulation

a b s t r a c t Among the promising advanced nuclear reactors, molten salt reactor employs various types of passive heat transfer system using the single-phase natural circulation of molten salts. The unique feature of molten salt, which has high Prandtl number, gives distinct heat transfer characteristics compared to other candidate fluids. To understand the heat transfer characteristics of molten salts, the similarity technique with a new simulant fluid was introduced based on the match of Prandtl number, in the previous studies. Extended from the previous studies, the present study investigated the unique thermal-hydraulic characteristics of high Prandtl number fluid in the natural circulation through the rectangular loop. Especially, the distinct flow phenomena of high Prandtl number fluid near the wall around the heating section were analyzed through both experimental and numerical approaches. The experimental approach employed direct observation of flow pattern at the upper part of the heating section using particle image velocimetry (PIV) technique. The visualized velocity profiles and gradients gave the clear evidence of unique flow development. Furthermore, a computational fluid dynamics (CFD) simulation using the ANSYS-CFX commercial CFD code verified the unique flow pattern of high Prandtl number fluid. With the aid of theoretical development based on the boundary layer theory, the unique flow phenomena was attributed to the enhanced local natural convection induced by high Prandtl number. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction After the Fukushima accident in 2011, the concepts of inherent and passive safety became the more important factors for nuclear reactor development. Then various working fluids as a coolant have been introduced and studied for the improved nuclear reactor systems. Among them, molten salts, which are based on fluoride or chloride salts, are the most extensively studied because of their superior properties in terms of both inherent and passive safety, which can prevent expanded or secondary disasters following nuclear accidents. This research trend even refocused attention on the molten salt reactor (MSR). As an effort to apply molten salts in the nuclear industry, many studies on the heat transfer characteristics of molten salts have been performed [1–3]. In particular, the fluoride molten salts, which were introduced as the most promising molten salt coolant or fuel in the original MSR, are characterized by high-Prandtl (Pr) number compared to other candidate coolants, as shown in Table 1. The heat transfer of high Pr number fluid is dominated by the convective heat transfer, which is different from that of low Pr number fluid such as liquid metal. ⇑ Corresponding author. E-mail address: [email protected] (I.C. Bang). https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.064 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.

Therefore, the understanding of heat transfer characteristics of high Pr number fluid in natural circulation is required to retain the reliability of diverse passive heat removal systems of nuclear reactors. The previous study in UNIST presented the heat transfer capability and characteristics of high-Pr number fluid using simulant [5]. The similarity technique was used because it is difficult to experiment with molten salt, owing to its characteristics such as high operating temperature, high temperature corrosion, and toxicity. The simulant fluids based on the similarity technique could reproduce the thermal behavior and fluid dynamics of molten salts, at a reduced temperature, pressure, dimension, and power scale [6]. The targeted molten salt was FLiBe (2LiF-BeF2) in the study. The matched Pr number and Grashof (Gr) number with those of target molten salt, ensured the similarity in the heat transfer characteristics in natural circulation. Fig. 1 shows that both DOWTHERM A and DOWTHERM RP heat transfer oil can cover Pr number range of major molten salt coolants including FLiBe. The previous study in UNIST [5] employed DOWTHERM RP as a simulant fluid, because it can treat the upper range of Pr and also is non-toxic fluid compared to the other candidates. Using the simulant fluid, a set of natural circulation experiments through rectangular loop was conducted. As a result, a laminar heat transfer correlation for the natural circulation of high Pr number fluid

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Nomenclature Cp g k L T Tavg Tb Tw

t w

specific heat [J/kg K] gravitational acceleration [m/s2] thermal conductivity [W/mK] characteristic length scale [m] temperature [K] average temperature [K] bulk temperature [K] wall temperature [K]

thermal wall

Abbreviations B.L. Boundary Layer CCD camera Charge-Coupled Device camera CFD Computational Fluid Dynamics FHR Fluoride-salt-cooled High temperature Reactor FLiBe a mixture of lithium fluoride (LiF) and beryllium fluoride (BeF2) Gr Grashof number MCR Molten Chloride Reactor MSR Molten Salt Reactor Nu Nusselt number PIV Particle Image Velocimetry Pr Prandtl number Ra Rayleigh number Re Reynolds number

Greek symbols a thermal diffusivity [m2/s] b thermal expansion coefficient [1/K] d boundary layer thickness [m] l dynamic viscosity [kg/m sec] m kinematic viscosity [m2/s ⁄ 106] q density [kg/m3] Subscript avg average b bulk

Table 1 Thermophysical properties of the major coolants of nuclear reactors [4]. Coolant

Temperature (°C)

Volumetric heat capacity Cp (kJ/m3-K)

Viscosity m (m2/s * 106)

Thermal conductivity k (W/m-K)

Pr (Prandtl number)

Water (7.5 MPa, saturated) Na (atm) He (7.5 MPa) Molten salts 2LiF-BeF2 LiF-ThF4 LiF-BeF2-NaF

300 550 700 700 700 700

4130 1040 19 4690 6576 4522

0.13 0.28 12.4 2.9 2.5 3.8

0.54 62.0 0.36 1 1.01 0.83

0.97 0.004 0.66 13.5 16 21

phenomena of high Prandtl number fluid near the wall around the heating section were analyzed through both experimental and numerical approaches. The experimental approach employed direct observation of flow pattern at the upper part of the heating section using particle image velocimetry (PIV) technique. Furthermore, a computational fluid dynamics (CFD) simulation using the ANSYS-CFX commercial CFD code verified the unique flow pattern of high Prandtl number fluid. With the aid of theoretical development based on the boundary layer theory, the unique flow phenomena were analyzed.

2. Flow characteristics of high-Pr natural circulation

Fig. 1. Comparison of Pr range between molten salts and simulant oils [4,7–9].

was developed based on Nu-Ra relationship, which gave the feasibility of similarity technique to the natural circulation capability for molten salt applications, especially for the passive safety systems [5]. Extended from the previous studies, the present study revealed the unique flow patterns and flow characteristics of high Pr number fluid in the natural circulation. Especially, the distinct flow

Single-phase natural circulation is driven by the buoyancy force, which is induced by local temperature gradients and resulting density differences in working fluids. While various parameters give the effects on the natural circulation characteristics, thermalhydraulic parameters including wall thermal conductivity, fluid viscosity, power and loop inclinations, geometry, or the orientation of the heating and cooling sections determine the intensity and stability of the natural circulation [10]. The assessment of thermal-hydraulic performance in natural circulation can tested in two different aspects: heat transfer correlation and flow patterns. Heat transfer correlations of natural circulation are the fundamental concepts of the heat transfer intensity based on two dimensionless numbers, Pr and Gr, as seen in Eqs. (1) and (2). Pr number

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Table 2 Convective heat transfer correlations including molten salt application [11–14]. Options

Correlation

Range Condition

0:7 6 Pr 6 160

Nu ¼ 0:023Re Pr ðn ¼ 0:4 for heating; n ¼ 0:3 for coolingÞ

Re P 10; 000 L=D P 10

Dittus-Boelter

0:7 6 Pr 6 16; 700

Nu ¼ 0:0242Re0:81 Pr0:333 ðlb =lw Þ0:14

Re P 10; 000 L=D P 10

Sieder-Tate

0:5 6 Pr 6 1000ðmolten saltsÞ

Nu ¼ 0:037ðRe0:75  180ÞPr 0:42 ð1 þ ðd=lÞ

Þðlb =lw Þ0:14

2300 6 Re 6 106

Hausen

0:11

2300 6 Re 6 106

Gnielinski

3500 6 Re 6 12; 000 Re P 12; 000

ORNL

0:8

5

0:6 6 Pr 6 10 ðmolten saltsÞ Nu ¼ 0:023Re 4 6 Pr 6 14

0:8

Pr

n

2=3

0:87

Nu ¼ 0:012ðRe

 280ÞPr

0:4

ð1 þ ðd=lÞ

2=3

ÞðPr b =Pr w Þ

1=3

Nu ¼ 0:107ðRe2=3  135ÞPr1=3 ðlb =lw Þ0:14 Nu ¼ 0:0234Re0:8 Pr 1=3 ðlb =lw Þ0:14

8 6 Pr 6 36

l

3400 6 Re 6 14; 0001:4 6 l b 6 3:1

Nu ¼ 0:015ðRe0:85 þ 138ÞPr 1=3 ðlb =lw Þ0:11

0:5 6 Pr 6 2000

Nu ¼ ½ðf =8ÞRePr=½1:07 þ 12:7ðf =8Þ

0:5 6 Pr 6 2000

Nu ¼ ½ðf =8ÞðRe  1000ÞPr=½1 þ 12:7ðf =8Þ

1=2

ðPr

2=3 1=2

UCB-HT2

w

4

6

 1Þ

10 6 Re 6 5  10

ðPr 2=3  1Þ

3000 6 Re 6 5  106

Petukhov Gnielinski

Fig. 2. Natural convection near the wall by the buoyancy effect: no buoyancy, (b) medium buoyancy, (c) strong buoyancy [22].

is the ratio between momentum diffusivity and thermal diffusivity; thus, it only comprises the thermophysical properties of a fluid. Gr number is the ratio between buoyancy force and viscous force; thus, it comprises thermophysical properties and a geometric scale. The Rayleigh (Ra) number, which is a function of Pr and Gr as shown in Eq. (3), is also the relevant one and it represents the heat transfer capability in natural circulation. Table 2 presents various experimental correlations for natural circulation using numerous fluids [11–14]. Wang et al. [15] studied the effect of the viscous dissipation according to the change of Ra in molten salt natural circulation and concluded that as Ra number increases, the effect of viscous dissipation decreased.

Pr ¼

Gr ¼

Ra ¼ Re ¼

lC p

ð1Þ

k gbðT w  T b ÞD3

ð2Þ

m2 gbðT w  T b ÞD3

ma qVD l

¼ Gr  Pr

ð3Þ ð4Þ

where l is a dynamic viscosity, Cp is a specific heat capacity, k is a thermal conductivity, b is a thermal expansion coefficient, Tw is a wall temperature, Tb is a bulk fluid temperature, D is a characteristic length, m is a kinetic viscosity, a is a thermal diffusivity, q is a fluid density, V is a fluid velocity. The flow pattern is another major characteristic to assess the thermal-hydraulic performance in natural circulation. Generally, the natural circulation loops employed rectangular, toroidal, or

Fig. 3. UNIST’s single-phase natural circulation loop.

annular geometries. Previous studies numerically analyzed the flow patterns in natural circulation to observe the distinct phenomena induced by the transition between flow regimes. Desrayaud and Fichera [16] presented various flow regimes referred as ‘‘route to chaos” numerically using the natural circulation of water with Pr = 5 in a 2D-annular loop. They also found that the

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Table 3 Dimensions of the experimental single-phase natural circulation loop. (m)

Values

Loop height Loop width Inner/Outer diameter Heating section length Cooling section length

0.80 1.54 0.023/0.0254 0.22 1.14

Fig. 6. PIV visualizing facilities.

Fig. 4. Visualizing section of the UNIST’s single-phase natural circulation loop.

Fig. 5. Flow of DOWTHERM RP natural circulation in visualizing section at 300 W.

complexity of the dynamic properties including the flow reversal was met in both toroidal and rectangular loops experimentally. Ridouane et al. [17] observed the locally recirculation and helical motion with secondary flow in the toroidal natural circulation loop using 3-D numerical simulations. Wang et al. [18] studied on the natural circulation in a rectangular loop using FLUENT code simulation. As a result, the flow patterns such as a thermal stratification

around the heater section and secondary flow pattern near the elbow, were observed. Chouhan et al. [19] studied on the natural circulation of a molten fluoride salt, LiF-ThF4, using the OpenFOAM CFD code, and observed the temperature and velocity distribution and gradient on each section. On the contrary, few studies directly observed distinct flow patterns experimentally. Mil’man and Fetisov [20] presented the effect of the inclination on the intensity of heat transfer under natural circulation in a heated pipe. They explained the presence of a maximum heat transfer in a certain inclination using the visualized images about the pattern changes by the eddy-like motion. In addition, different flow patterns were analyzed with respect to the driving pressure. The present study seeks to consider the distinct flow patterns using the boundary layer concepts based on Pr number. Theoretically, the natural convection phenomenon is vulnerable to the environmental parameters due to its low flow rate and resulting low inertia. In a flat plate or in a pipe with sufficiently developed length, the buoyancy forces are largely affected by the flow laminarization near the wall. The previous studies done by Aicher and Martin [21] investigated the laminarization of the flow in natural convection by the observation of buoyancy effect. As the fluid near the wall became hotter, the difference between the boundary layer velocity and the average velocity decreased because of the reduction of shear stress between the bulk flow and perimeter. As a result, the series of process led to laminarization of flow. As shown in Fig. 2(c), turbulence reappeared in case of strong buoyancy, which might give significant effect on thermal-hydraulic characteristics of high Pr number fluids due to their high viscosity. By the definition of Pr, it determines the dominant heat transfer mode on a basis of unity, which comes from the boundary layer theory. Two concepts of the boundary layers, thermal boundary

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Fig. 7. Mesh convergence for temperature (upper) and velocity (lower) distribution on the cross-section of the upper vertical part of the heating section.

Table 4 Main parameters in comparison of the mesh convergence at 300 W. Number of nodes Bulk temperature (°C) Bulk velocity (m/s)

517,774 56.28 0.018

1,636,283 59.28 0.021

1,894,064 60.96 0.021

Fig. 8. Meshing of DOWTHERM RP natural circulation model in CFD simulation.

2,026,456 61.27 0.021

2,246,420 61.42 0.021

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Y. Shin et al. / International Journal of Heat and Mass Transfer 121 (2018) 1350–1363 Table 5 Representative values of DOWTHERM RP thermophysical properties.

Dowtherm RP

T (K)

q (kg/m3)

m (m2/s * 106)

Cp (kJ/kgK)

k (W/mK)

b (1/K)

Pr

423 473 623

937.3 901.0 768.1

1.408 0.888 0.398

2.007 2.156 2.602

0.115 0.108 0.089

0.0009 0.0009 0.0011

23 16 9

layer and velocity boundary layer, determine the heat transfer mode. In a fluid with Pr higher than 1, the velocity boundary layer becomes thicker than the thermal boundary layer. In addition, the difference between two boundary layer thicknesses becomes larger as Pr increases. Since thermal and velocity boundary layers imply thermal and momentum diffusivity, respectively, the convective heat transfer mode dominates the overall heat transfer characteristics in case of Pr over the unity. The previous study [22] using analytical method identified the significance of the flow development near the wall, and the governing equations of natural convection are in combined form with elliptic partial differential equations. The concepts of boundary layers and Pr come from the simplification of the equations. In addition, various correlations for the relationship between boundary layers and Pr were developed based on the boundary layer theory. It was revealed theoretically that the Pr dominated the ratio of velocity and thermal boundary layer thicknesses [23]. One of the relationships is shown in Eq. (5), and it was approximated within 0.6  Pr  50 as shown in Eq. (6).

dt 1 1 ’ ¼ d 1:025Pr 1=3 ½1  ðd2 =14d2 Þ1=3 1:025Pr 1=3 t

ð5Þ

Fig. 10. Velocity distribution of DOWTHERM RP natural circulation at 300 W: (a) constant property condition (b) temperature dependent property condition.

d ffi Pr1=3 dt

ð6Þ

where d is a velocity boundary layer thickness, and dt is a thermal boundary layer thickness. Several studies investigated the relationship between heat transfer capability and boundary layer development. Lu et al. [24] studied the velocity and temperature boundary distribution in the laminar natural convection of molten salt around a horizontal cylinder by simulation with the FLUENT commercial CFD software. As the diameter increased from 0.1 mm to 10 mm, the thickness of the thermal boundary layer and thermal resistance increased in such manner that the heat transfer coefficient decreased. In the study, the boundary layer thickness was calculated based on the definition coming from the boundary layer theory, as shown in Eq. (7).

ðT  T s Þ=ðT s  T b Þ ¼ 0:99

Fig. 9. Temperature distribution of DOWTHERM RP natural circulation at 300 W: (a) constant property condition (b) temperature dependent property condition.

ð7Þ

Most of the previous correlations for the relationship between the velocity and thermal boundary layer thicknesses adopted dimensionless numbers, Pr, and Gr, with different constant coefficients and exponents. These become the foundation of the flow characteristics of high-Pr natural circulation near the boundary layer with a specific criterion. The present study focused on the

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Fig. 11. Observation points on the horizontal cross-section of natural circulation loop in a radial direction in CFD simulation.

Table 6 Local velocities at different locations on the upper part of heating section at 300 W.

300 W

PIV (m/s) CFD (m/s)

A

B

C

D

E

0.02  0.07 0.069

0.0205

0.009

0.0256

0.069

Fig. 12. Average velocity profile of DOWTHERM RP natural circulation (left: 100 W, right: 300 W).

approximated analysis of natural convection using the modified boundary-layer approximations, which dealt with the natural circulation of the high Pr number fluid where the boundary layer development near the wall was important. 3. Performance evaluation of high-Pr natural circulation 3.1. Natural circulation model with high-Pr heat transfer fluid The natural circulation experiments with visualization technique were conducted using DOWTHERM RP to observe the flow

characteristics of the high Pr number fluid. Particle image velocimetry (PIV) technique was employed for the visualization of velocity profiles and gradients. Fig. 3 and Table 3 show the experimental facilities of the rectangular natural circulation loop with their specifications. The experimental facility consists of three main parts: vertical heating section, heat exchangers, and the remaining piping sections. The coil heater was installed at the lower part of the left side of the loops, and the power was supplied by the indirect heating method. Concentric heat exchangers were used as the cooling section. The water circulated the annulus path from the bottom in counter direction to the main flow, with con-

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Fig. 13. Instantaneous velocity profile of DOWTHERM RP natural circulation (left: 100 W, right: 300 W).

(a) 2D concept flow

(b) 3D concept flow

Fig. 14. Prediction of the development of the thermal and momentum boundary layers.

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composed of an Nd-YAG double-cavity laser and a chargecoupled device (CCD) camera, which were perpendicular to each other. For the observation of the velocity field at the crosssection of the visualizing part, the laser beam illuminated and reacted with the PIV tracer particles, which were silver-coated glass hollow spheres with a mean diameter of 20 lm, mixed in the DOWTHERM RP working fluid. The CCD camera traced the movement of the tracer particles that reflected the flow patterns of DOWTHERM RP natural circulation. The PIV visualization filmed the velocity distribution on the cross-section of the center part of the visualizing section. The filming was conducted at three stages of power, 100, 200, and 300 W.

3.3. CFD analysis in natural circulation of high-Pr heat transfer fluid

Fig. 15. Temperature and velocity distribution on the whole sections of DOWTHERM RP natural circulation at 300 W.

stant inlet temperature (10 °C) and flow rate (2.42 kg/s). The remaining piping section were assumed to be adiabatic due to the surrounding insulator. The power range was restricted by the boiling point (353 °C) of the working fluid, DOWTHERM RP, to satisfy the single-phase condition. At the upper part of heating section, the visualizing section was installed with transparent quartz glass to identify the natural circulation phenomena and development of flow, as shown in Fig. 4. The natural flow rate was measured by a turbine flowmeter. The visualized flow patterns are shown in Fig. 5. The flow patterns showed that the intensity of the fluctuation increased as the power increased. 3.2. PIV visualization in natural circulation of high-Pr heat transfer fluid Fig. 6 showed the visualized images by PIV in the cross section with more detail. The experimental equipment for PIV was

The distinct flow patterns of DOWTHERM RP were also observed by PIV visualization technique. For the verification and validation of experimental results, a set of CFD simulations, in which a more detailed analysis can be conducted, was performed using the ANSYS-CFX commercial CFD code. Same geometry and specifications of experimental facility were adopted in the simulation model. Denser grid near the wall was generated to evaluate the relationship between the boundary layer development and Pr number. Then, a mesh convergence study was conducted for mesh optimization, as seen in Fig. 7. Table 4 and Fig. 7 show the results of the mesh convergence study. The temperature and velocity distribution of the radial cross-section of the heating section were converged when the total number of nodes exceeded approximately 2,000,000. The overall mesh convergence study showed that the results for temperature and velocity were converged well, within a deviation of 0.4%. Fig. 8 shows the entire mesh of the natural circulation model in the CFD simulation. The initial and the boundary conditions from the experimental data were applied to the model. The initial velocity and temperature were set based on the experimental data, while a constant temperature of 10 °C was applied to the cooling section. The turbulent model was set to the laminar model, since Reynolds number in the experiment was less than 200. For the comparison of temperature and velocity distribution on each specific section, several monitoring points were set at the inlet and outlet locations of the heating and cooling sections, in both axial and radial directions. DOWTHERM RP, which was used in the PIV visualization, was also used as the working fluid in the CFD simulation. Because the thermophysical properties of DOWTHERM RP were not included in the basic code, they were inserted as a form of fitting equation data from the reference data sheet [8]. Table 5 shows the thermophysical properties of DOWTHERM RP. Prior to the main simulation, the effect of the thermophysical property changes was tested by comparison of the natural circulation with constant bulk temperature and with temperature-dependent properties. Figs. 9 and 10 show the comparison of natural circulation performance, according to the different property conditions. The constant properties resulted in lower temperature and thermal stratification in a vertical direction on the upper horizontal part, while the overall temperature distribution was similar More clear difference was shown in the case of velocity distribution using constant property model. Finally, the temperature-dependent properties in the form of variables were inserted into the model.

Table 7 Bulk values of temperature and velocity in DOWTHERM RP natural circulation according to each power. Power (W) Tbulk (°C) Velbulk (m/s)

100 34.26 0.0109

200 49.19 0.0170

300 61.35 0.0213

400 72.05 0.0236

500 84.42 0.0262

600 89.58 0.0276

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Fig. 16. Radial velocity development of DOWTHERM RP natural circulation at 300 W.

4. Results and discussion Before the analysis of the flow characteristics of high-Pr natural circulation, the velocity distributions in both the experiment data and the CFD simulation were compared to identify the reliable results. Fig. 11 and Table 6 show the velocity distribution at the upper part, where the visualizing section was located. From the comparison, the CFD results was validated.

4.1. Prediction of the flow characteristics of high-Pr natural circulation from PIV visualization The average and the instantaneous velocity profiles were evaluated as shown in Figs. 12 and 13. At all power conditions, large zigzag-shape velocity patterns appeared, while the thickness of the velocity boundary layer near the wall became thinner as the power increased. In addition, the velocity decreased, but it became

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Fig. 19. Comparison of the velocity on each observation point on the heating section according to the change of Pr.

Fig. 17. Velocity distribution on the whole section of DOWTHERM RP natural circulation (enlarged figure; flow pattern in the upper part of the heating section).

more normalized as the power decreased. The instantaneous velocity profiles shown in Fig. 13 revealed the irregular and locally rotating flows. Considering the visualization of cross-section along the centerline of the test region, the irregular velocity distribution with winding patterns implied the rotating-rising upstream, considered as the irregular movement in the radial direction in 3D. The stream line shown in the left-side of Fig. 13 also displayed several local vortices near the wall. In the PIV visualization, the zigzag up-flow was observed at the visualizing section located in the upper part of the heating section. Based on the literature survey and the PIV visualization experiment, the expected temperature and velocity distribution and the characteristic flow patterns of the high-Pr natural circulation were proposed. First, near the wall where the boundary layers developed and the gradient in the temperature and velocity were generated, the increase of Pr number gave significant effect of the viscous shearing forces. Then, the velocity difference between the boundary region and the core region was generated. In the core region,

the frictional effect became negligible compared to the boundary region, and an essentially constant velocity remained near the core in the radial direction. Finally, extended to 3D as shown in Fig. 14, the hot fluid flowed from the wall to the centerline and cold fluid flowed from the centerline to the wall, while the vertical forces of the gravity and viscous force also worked. The series of process lead to a helix up-flow near the wall and a lower velocity on the center part. 4.2. Prediction of the flow characteristics of high-Pr natural circulation from CFD simulation CFD simulation results presented temperature and velocity distribution in each section of the entire natural circulation loop. As shown in Fig. 15, different temperature and velocity profiles near the heating section were formed. The main flow was observed near the wall with a large velocity gradient, while the temperature profile didn’t, as seen in the expanded figure. The simulations were conducted on the power range from 100 W to 600 W to investigate the development of the flow patterns. Table 7 shows the results of the bulk temperature and velocity values in DOWTHERM RP natural circulation at each power level. As the power increased, the bulk velocities increased, while the difference in bulk velocity was small within 0.01–0.02 m/s. The detailed observation of the flow patterns in the heating section was conducted using both steady-state and transient condition. From the results of the steady-state simulation, the development of flow over the entire section was observed using

Fig. 18. Velocity distribution of DOWTHERM RP natural circulation on the horizontal cross-section in the upper part of the heating section at 600 W (vertical height increases with the interval of 0.1 m).

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Fig. 20. Comparison of the heater and H.X. outlet temperature profile in a radial direction in DOWTHERM RP natural circulation.

Fig. 21. Comparison of the heater and H.X. outlet velocity profile in a radial direction in DOWTHERM RP natural circulation.

Fig. 22. Comparison of the heater outlet velocity profile in a radial direction in DOWTHERM RP natural circulation.

Fig. 23. Comparison between modified boundary layer thicknesses and Pr in CFD simulation.

the Vector function in the CFX-Post processing. The considerable velocity gradients appeared near the wall as shown in Fig. 16. The simulation results well agreed with the proposed flow patterns

in 2D. The additional transient simulations were conducted to present distinct flow patterns. The simulation results revealed that the development of flow patterns near the centerline accompanied circulating flow, as seen in Fig. 17. As shown in the enlarged figure, similar flow patterns as those obtained from the experimental results, zigzag up-flows, were observed over 400 W of power. The helix-like up-flow became more stable with a balanced velocity distribution along the flow direction as shown in Fig. 18. In addition, the temperature and velocity at the inlet and outlet of both the heating and cooling sections were compared. First, the five velocities along the radial direction were compared. The result showed the clear difference in velocity gradient along the radial direction, as shown in Fig. 19. In addition, macroscopic changes in the dominant velocity and the gradient of the boundary layers are shown in Figs. 20–22. Fig. 20 shows that as power increased and the resulting Pr decreased, the gradient of the temperature near the wall increased at the outlet of the heating and cooling sections. In addition, the main value of the temperature formed in the core region increased as power increased. On the contrary, the velocity was nearly same at the core region of the heating section, as shown in Fig. 21. However, as Pr decreased, the velocity distribution in the core region

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Table 8 Comparison of the correlation between the ratio of the boundary layer thicknesses and Pr in CFD simulation. Power (w)

Free Stream Velocity (m/s)

Ratio of Velocity B.L. per Thermal B.L. (Thickness)

Pr1/3

1.025*Pr1/3

200 300 400 500 600

0.0436 0.0560 0.0681 0.0800 0.0941

4.27 4. 4.00 3.75 3.30

5.13 4.53 4.06 3.74 3.46

5.26 4.65 4.17 3.83 3.54

became more normalized. In addition, as shown in Fig. 22, the velocity profile became developed as Pr increased. That is, the thickness of developing layer in a radial direction increased as Pr increased. 4.3. Theoretical evaluation of the flow characteristics of high-Pr natural circulation In this section, the theoretical discussion on the unique flow characteristics was presented. The analysis of the radial distribution according to Pr number was conducted based on the theory of natural circulation and the boundary layer. During the analysis, the following assumptions were made: – The velocity of free stream flow is assumed to have the average value of the DOWTHERM RP velocity along the centerline of the entire loop. – The boundary layer thickness is calculated as the distance from the wall to the location where 99% of the free stream flow developed. – The DOWTHERM RP properties are inserted as the correlations of fitting, except for the specific heat capacity. Since the change in specific heat capacity is within 7% in the operating temperature, we assume that taking constant specific heat capacity with the average value gives negligible effect on the evaluation of heat transfer of DOWTHERM RP. Using the simplified thermal energy conservation from Eq. (6), the influence of Pr on the ratio of both thermal and velocity boundary layer thicknesses was evaluated. Fig. 23 and Table 8 show the relationship between the ratio of boundary layer thicknesses and Pr number [23]. The ratio of boundary layer thicknesses increased as Pr increased, and it was attributed to the decrease of thermal boundary layer thickness. The thin thermal boundary layer implied the large temperature gradient near the wall. As a result, the local natural convection induced by temperature gradient was enhanced, and also flow laminarization occurred with the strong buoyancy effect resulting in the reappearance of turbulence. Finally, the radial flow with upward inertia produced the distinct helix up-flow pattern in high Pr number fluid. 5. Conclusions In this study, the unique thermal-hydraulic characteristics of high Prandtl number fluid in the natural circulation through the rectangular loop were investigated. Especially, the distinct flow phenomena of high Prandtl number fluid near the wall around the heating section were analyzed through both experimental and numerical approaches. In the experiments with PIV visualization, the zigzag up-flow was observed at the visualizing section located in the upper part of the heating section. Based on the literature survey and the PIV visualization experiment, the expected temperature and velocity

distribution and the characteristic flow patterns of the high-Pr natural circulation were proposed. The generated gradient in the temperature and velocity in high Pr number produced helix up-flow near the wall and a lower velocity on the center part. The detailed observation of the flow patterns in the heating section was conducted using both steady-state and transient condition using CFD simulation using the ANSYS-CFX commercial CFD code. The considerable velocity gradients appeared near the wall which agreed with the proposed flow patterns in 2D. The additional transient simulations revealed that the development of flow patterns near the centerline accompanied circulating flow which was similar flow patterns as those obtained from the experimental results, zigzag up-flows. Finally, with the aid of theoretical development based on the boundary layer theory, the proposed flow pattern concept was verified. Thinner thermal boundary layer accompanied by the increase of Pr implied the large temperature gradient near the wall, which resulted in the enhancement of local natural convection. The flow laminarization with the strong buoyancy effect resulted in the reappearance of turbulence, and then produced the distinct helical-upward flow pattern in high Pr number fluid. Acknowledgements This work was supported by ‘‘Human Resources Program in Energy Technology” of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20174030201430), ‘‘Nuclear Energy Research Program” through the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (2016M2A8A6900481), and ‘‘Basic Science Research Program” through the National Research Foundation of Korea (NRF) funded by the Korea government (MSIT) (No. 2017R1A2B2008031). References [1] A. Pini, A. Cammi, L. Luzzi, Linear and nonlinear analysis of the dynamic behavior of natural circulation with internally heated fluids, in: NUTHOS-10, Okinawa, Japan, 14–18 December, 2014. [2] J.E. Bickel et al., Design, Fabrication and Startup Testing in the Compact Integral Effects Test (CIET 1.0) Facility in Support of Fluoride-Salt-Cooled, High-Temperature Reactor Technology, UCBTH-14-009, UC Berkeley, December, 2014. [3] S. Kang, I.C. Bang, Numerical analyses of a single-phase natural convection system for Molten Flibe using MARS-FLIBE code, in: Korean Nuclear Society Autumn Meeting (KNS-2014); Pyeongchang, Korea, 30–31 October, 2014. [4] M.S. Sohal, M.A. Ebner, Piyush Sabharwall and Phil Sharpe, Engineering Database of Liquid Salt Thermophysical and Thermochemical Properties, INL (INL/EXT-10-18297), Idaho, 2010. [5] Y. Shin, S.B. Seo, I.G. Kim, I.C. Bang, Single-phase natural circulation of high-Pr heat transfer simulant oil, in: Korean Nuclear Society Spring Meeting (KNS2016); Jeju, Korea, 12–13 May, 2016. [6] P.M. Bardet, P.F. Peterson, Options for scaled experiments for high temperature liquid salt and helium fluid mechanics and convective heat transfer, Therm. Hydraul. 163 (2008) 344–357. [7] DOWTHERM A Heat Transfer Fluid: in DOW Chemical Company. [8] DOWTHERM RP Heat Transfer Fluid: in DOW Chemical Company. [9] DOWTHERM SR-1 Heat Transfer Fluid: in DOW Chemical Company. [10] M. Misale, Overview on single-phase natural circulation loops, in: Int. Conf. on Advances in Mechanical and Automation Engineering (MAE 2014), Rome, Italy, 7–8 June, 2014. [11] Frank P. Incropera, David P. DeWitt, Fundamentals of Heat and Mass Transfer, fourth ed., 2000. [12] E.N. Sieder, G.E. Tate, Heat transfer and pressure drop of liquids in tubes, Ind. Eng. Chem. 28 (1936) 1429–1435. [13] V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. J. Chem. Eng. 16 (1976) 359–367. [14] J.W. Cooke, B. Cox, Forced Convection Heat Transfer Measurements with a Molten Fluoride Salt Mixture Flowing in a Smooth Tube, ORNL-TM-4079, ORNL, March, 1973. [15] J.Y. Wang, T.J. Chuang, Y.M. Ferng, Laminar natural convection heat transfer characteristics of molten salt around horizontal cylinder, Ann. Nucl. Energy 58 (2013) 65–71.

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