Experimental study on single-phase heat transfer of natural circulation in circular pipe under rolling motion condition

Nuclear Engineering and Design 273 (2014) 497–504

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Experimental study on single-phase heat transfer of natural circulation in circular pipe under rolling motion condition Chang Wang a,∗ , Xiaohui Li a , Hao Wang a , Puzhen Gao b a b

China Ship Development and Design Center, Hubei 430064, PR China Key Discipline Laboratory of Nuclear Safety and Simulation Technology, Harbin Engineering University, Heilongjiang 150001, PR China

h i g h l i g h t s • • • •

The effect of rolling motion on natural circulation flow pulsation is studied. The effect of flow pulsation on natural circulation cycle-averaged heat transfer is studied. The relationship between the cycle-averaged flow rate before and after rolling motion is studied. The instantaneous heat transfer coefficient of natural circulation pulsating flow is obtained.

a r t i c l e

i n f o

Article history: Received 24 August 2013 Received in revised form 8 March 2014 Accepted 17 March 2014

a b s t r a c t Experimental investigation of the single-phase natural circulation heat transfer characteristic in static and rolling motion conditions are conducted. The results show that rolling motion leads to the reduction of cycle-averaged flow rate compares to that in the static state with the same thermal–hydraulic parameters. And the flow rate changes cyclically with the same period of the rolling motion. In addition, the results also indicate that the flow pulsation enhances the cycle-averaged heat transfer characteristic. Furthermore, the relative pulsation amplitude of the Nusselt number increased linearly with the relative pulsation amplitude of Reynolds number. Based on the relationship between the cycle-averaged flow rate before and after rolling motion start, and the relationship between rolling motion parameters, the relative pulsation amplitude of Nusselt number and cycle-averaged Reynolds number, the instantaneous Nusselt number under rolling motion condition can be predicted using the thermal–hydraulic parameter in static condition. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Natural circulation is widely used in thermal equipment of many industries. As no pumping power can be used, natural convection is the only possible way to circulate fluids. Therefore, it is very important to determine correctly the heat transfer performance of the fluid in the heat transfer tube during design and safety analysis of the power system with natural circulation. In recent years, several investigations were conducted to analyze the heat transfer characteristic of natural circulation under rolling motion condition. Murata et al. (1990) conducted the singlephase natural circulation experiment in a model reactor under rolling motion, and they found that the flow rate in each leg changes

∗ Corresponding author. Tel.: +86 451 82569655; fax: +86 451 82569655. E-mail addresses: wangchang [email protected], [email protected] (C. Wang). http://dx.doi.org/10.1016/j.nucengdes.2014.03.045 0029-5493/© 2014 Elsevier B.V. All rights reserved.

cyclically due to the inertial force of the rolling motion. The amplitude of the flow rate oscillations decreases with the increase of thermal driving head, and the change is more noticeable in the hot legs than that in the cold legs and at small angular velocities. Thereafter, Murata et al. (2000, 2002) conducted a series of more detailed studies about the natural circulation heat transfer characteristic under rolling motion condition. They found the flow rates in both the hot legs and the cold legs change periodically with the rolling motion, while the core flow rate does not oscillate. However, the heat transfer in the core is enhanced by the rolling motion and the enhancement is thought to be caused by the internal flow due to the rolling motion. The heat transfer coefficient in the core is well correlated with the Richardson number for rolling motion and is classified into three regimes namely: (1) 0.05 < RiR ≤ 0.3 where heat transfer is dominated by the inertial force due to the rolling motion; (2) 0.3 < RiR ≤ 2 where heat transfer is affected by the combined effect of inertial force and natural convection; and (3) RiR < 2 where heat transfer is affected only by natural convection.

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C. Wang et al. / Nuclear Engineering and Design 273 (2014) 497–504

Nomenclature c Cp D g Gr h H k L Nu P Pr q Q r Ra Re Ri T t tR u V

capacity specific heat, kJ/(kg ◦ C) diameter, m gravity acceleration, m/s2 Grashof number heat transfer coefficient, kW/m2 heated length, m thermal conductivity, kW/(m ◦ C) length, m Nusselt number pressure, Pa Prandtl number heat flux, W/m2 heat power, W radius, m Rayleigh number Reynolds number Richardson number temperature, ◦ C time, s rolling period, s velocity, m/s volume, m3

Subscript calculated value cal in inlet d driver experimental data exp f frictional liquid l max maximum value min minimum value out outlet R rolling condition tangential ta w wall wi inner wall outer wall wo Greek symbol thermal expansion coefficient ˛  heat conductivity, W/(m2 ◦ C) ˚ heat generation, W/m3  density, kg/m3  rolling angle,◦  dimensionless rolling amplitude angular acceleration, rad/s2 ˇ ω angular velocity, rad/s dimensionless rolling period ˝ ave average centripetal ce  kinematic viscosity coefficient, Pa s ı thickness of the wall, m

Tan et al. (2009a,b) carried out a series of experimental researches about the single-phase natural circulation heat transfer in a circular pipe both in static and rolling motion conditions. They also found that the rolling motion leads to the flow rate pulsations periodically and the heat transfer in enhanced. The heat transfer coefficient of natural circulation flow increases with the increase of maximum rolling angle and decreases with the increase of rolling

period. Based on the force analyze of the fluid element, they developed a mathematical model to calculate the natural circulation flow rate and heat transfer under rolling motion condition. Yan and Yu (2009) and Yan et al. (2009) experimentally and theoretically studied the operation characteristics of passive residual heat removal system under different rolling motion conditions. They found the pulsation amplitude of the condensate flow rate increases with the increase of rolling amplitude. However, when the power becomes larger for the same rolling motion condition, the pulsation amplitude of condensate flow rate also will become larger. In addition, the pulsating flow will significantly enhance the flow resistance. As in small amplitude rolling motion, the heat transfer coefficient increases due to the increasing alternating flow. However, as in a large amplitude rolling motion, the heat transfer coefficient reduces due to the decreasing flow velocity. More recently, Yan and Gu (2011), Yan and Yu (2012), and Yan et al. (2012) conducted a series of theoretical and numerical studies about the heat transfer of pulsating flow induced by the rolling motion. The particular descriptions of the velocity distribution, friction resistance factor and heat transfer characteristic indicated that the flow pulsation significantly influenced the thermal–hydraulic characteristic. It can be found from the above discussions that all of the investigators focused their research interests on the local heat transfer characteristic in the test section as the rolling motion started. It also can be concluded that the rolling motion will lead the natural circulation flow rate pulsations periodically, and thus the heat transfer is changed as compared from that in steady flow. However, as in the view of engineering design, the flow rate pulsation behavior and heat transfer characteristic of the pulsation flow under any rolling motion condition should be able to be predicted from the thermal hydraulic parameters in a static condition, and none of previous investigations can satisfy the demand. It is the original motivation to conduct the present experimental study. In the present study, the relationship between the natural circulation cycle-averaged flow rate before and after rolling motion start, the relationship between the natural circulation cycle-averaged heat transfer characteristic before and after rolling motion start, and the relationship between the relative pulsation amplitude of Nusselt number, cycle-averaged Reynolds number and rolling motion parameters are obtained. Thus the instantaneous heat transfer characteristic for any rolling motion condition in the present experimental parameter extent can be acquired as the thermal–hydraulic condition in static condition is presented.

2. Experimental apparatus The experimental apparatus is composed of an experimental loop and a rolling motion driving mechanism. The experimental loop shown in Fig. 1 consists of a test section, a cooler and tower for condensing the hot water, a pump for circulating the water as in forced circulation, however, the pump is not used in the present study, a pressurizer for controlling the system pressure, a electromagnetic flowmeter for measuring the circulate flow rate and a preheater for inlet fluid temperature control. The test section electrically insulated from the rest by using Teflon washers is a vertical stainless steel pipe with an inner diameter of 12 mm, wall thickness of 2 mm and a length of 1760 mm. A section of 1370 mm of the pipe is heated electrically by using a DC power supply from a rectifier with copper cables clamped at both ends. Another 110 mm section in the inlet is left for flow full development. Moreover, the pipe is wrapped with several asbestos wool insulation layers to assure perfect adiabatic. As shown in Fig. 1, the temperatures and pressures are measured at various locations. The distribution of thermocouples along the

C. Wang et al. / Nuclear Engineering and Design 273 (2014) 497–504

499

condition was preceded by a static state test at the same heat power and inlet water temperature. 3. Experimental phenomena and discussion 3.1. Heat transfer characteristic in static condition From the measured outer wall temperatures of the test section, the local inner wall temperatures can be obtained through solving the heat conduction equation of the tube wall. Twi,x =

test section is relatively concentrated near the entrance to measure the dramatic change of the temperature in this region. In addition, the locations of these thermocouples from the inlet are 217, 300, 420, 540, 780, 895, 1135 and 1495 mm. At each position, two thermocouples are welded symmetrically along the circumference to measure the temperature of the external surface and then the average values will be taken. The bulk fluid temperatures at the inlet and outlet of the test section are measured simultaneously. In addition, the water temperature at the outlet of the cooler is also measured to analysis the natural circulation driving head. The pressures are measured at the inlet of the test section and pressurizer using the capacitive manometer, respectively. In addition, in the present study, the instruments and data acquiring system response time is less than 0.001 s, and data acquiring frequency is 0.05. The whole experimental loop is placed on a platform which can be rolled periodic around a fixed axis. The rolling driven device comprised of a gearbox, a crank and rocker mechanism, and a motor connect to a frequency transducer. The maximum rolling amplitude can be adjusted through changing the length of the rocker and linkage, and the rolling period can be controlled by regulating the speed of electromotor. The instantaneous rolling angle of the experimental loop is measured by an angular transducer. In the present study the experimental loop rolls in harmonic displacement motion, which can be approximated by,

ω = max ˇ = max

 2t 

 2  tR

tR cos

 2 2 tR

sin

 2t  tR

 2t  tR

1 2

2 + rwi

Q 2L

 ln

r  wi

rwo

+ Two,x

(4)

In which, rwo and rwi is the outer and inner wall diameter, Two and Twi is the outer and inner wall temperature, respectively. Q is the heat power, Q = UI, U and I are the electrical voltage and current. L is the length of the heated section.  is the thermal conductivity of the wall, the relationship between the temperature and the thermal conductivity can be approximately expressed as  = 14.6106 + 0.01505T. is the heat generation per unit volume (Holman, 1986),

Fig. 1. Experimental loop.

(t) = max sin

1 2 2 )+ (r − rwi 4  wo

Q

=

(5)

2 − r 2 )L (rwo wi

The Reynolds number of water flow is calculated by, Re =

uD

(6)

The local and average heat transfer coefficient are determined respectively by, hx = h=

Q DL(Twi,x − Tl,x )

(7)

Q DL(Twi − Tl )

In which, Twi

L

(8) is the average inner wall temperature,

Twi = 1L 0 Twi,x dx. Tl is the average water temperature, Tl = 0.5(Tl,in − Tl,out ). Thus the average Nusselt number can be calculated by Nu =

hD 

(9)

(1)

To verify the dependability of the experimental data, the singlephase natural circulation heat transfer experimental data in static state are compared with the correlation suggested by Yang et al. (2006)

(2)

Nus = Nu0 Ra−0.11 Ra = GrPr

(3)

In which,  is the instantaneous rolling angle,  max is the maximum rolling angle, tR is the rolling period, ω is the rolling angular velocity, ˇ is the angular acceleration. In the present study, the system pressure varies from 0.3 to 0.4 MPa, the water temperature at the inlet of the test section from 40 to 50 ◦ C, the heat power from 0.3 to 11 kW, flow rate from 0.05 to 0.3 m3 /h. In addition, the maximum rolling angles are 10◦ , 15◦ and 20◦ , and the rolling periods are 7.5 s, 10 s, 12.5 s, 15 s and 20 s. The present experiments include a total of 126 tests for different cases of cycle-averaged Reynolds number, rolling angles and periods. Each set of experimental data under rolling motion

Gr = 2 ˛gd3 (Twi − Tl )

(10)



Cp,l

k



(11) (12)

In which, Nus is the average Nusselt number in static state, Nu0 is the Nusselt number calculated by the Gnielinski equation. Ra is the Rayleigh number, Gr is the Grashof number, Pr is the Prandtl number, d is the inner diameter, , ˛, Cp,l , and k is the water density, thermal expansion coefficient, specific heat, dynamic viscosity and thermal conductivity. As seen in Fig. 3, the single-phase natural circulation heat transfer characteristic in the thermal fully developed region is in agreement well with the predicted values.

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Fig. 2. Rolling motion driving mechanism. 60

carried by the water in rolling motion condition should be recalculated by the following equation.

Experimental data Gnielinski correlation Yang correlation

50

QR = Q − w Cp,w Vw

(13)

In which, w , Cp,w and Vw is the is the density, the specific heat and the volume of the test section, respectively. t is the time.

40

Nu

dTwo dt

30

3.3. Cycle-averaged heat transfer characteristic in rolling motion

20

To analyze the effect of rolling motion on cycle-averaged heat transfer characteristics, the cycle-averaged Nusselt number and the cycle-averaged Reynolds number can be defined as follows,

10

0 2000

1 tR

Nu = 4000

6000

8000

10000

12000

Re

Re =

1 tR





Fig. 3. Natural circulation heat transfer characteristic.

3.2. Experimental phenomena in rolling motion It can be seen in Fig. 4 that the flow rate, wall temperatures and water temperature at the outlet of the test section both varies periodically as the experimental apparatus keeps in rolling motion condition. In addition, due to the heat capacity of the test section, the water temperature does not vary in-phase with the wall temperatures and flow rate. Thus the instantaneous heat power QR

tR

Nu(t)dt

(14)

Re(t)dt

(15)

0 tR

0

As seen in Fig. 5, the cycle-averaged Nusselt number in rolling motion condition is larger than that in the static state at the same thermal–hydraulic condition. The discrepancy of heat transfer characteristic between rolling motion and static state increases with the increasing maximum rolling amplitude as in the same rolling period and cycle-averaged Reynolds number, however, it decreases with the increase of rolling period and cycle-averaged Reynolds number. The results indicate that the pulsating flow

Tw / ºC

60 150 140 130 120 110 100

50

Static state 40

Tout

100

Nu

Tl / ºC

110

45

Tin

40

30

20

u / m·s

-1

0.4 0.3

10

0.2 0.1

0

10

20

t/s Fig. 4. Natural circulation experimental phenomena in rolling motion.

30

0 2000

4000

6000

8000

10000

Re Fig. 5. Cycle-average heat transfer characteristic of pulsating flow in rolling motion.

C. Wang et al. / Nuclear Engineering and Design 273 (2014) 497–504

501

1.2

1.0

0.6

*

Reamp

0.8

0.4

0.2

0.0 2000

4000

6000

8000

10000

12000

ReR Fig. 7. Influencing factors of flow pulsation relative amplitude.

of angular velocity and decreases with the flow velocity, it also in accordance with the experimental phenomena in Fig. 5. To simplify the analysis, dimensionless rolling amplitude ˝max and dimensionless rolling period R are defined as follows, Fig. 6. Force analyze.

˝max =

induced by rolling motion can lead to the heat transfer enhancement. Yang et al. (2006) point out that the flow laminarization in the layer induced by co-current bulk natural circulation and free convection will lead to the Nusselt number in the upward natural circulation flow lower than that in the forced circulation flow. In addition, the experimental and numerical investigations (Armellini et al., 2011; Chang et al., 2010; Qin and Pletcher, 2006) both find the Coriolis force due to the rotating of test section will change the secondary flow and lead to the variation of heat transfer. Furthermore, the researchers also find the effect of the Coriolis force on the heat transfer can be evaluated by the Rotation number, Ro =

ωd u

(16)

In which, ω is the rotational angular speed of the test section. In the present study, the force analysis of the fluid element in an upright pipe under rolling motion condition can be seen in Fig. 2. There are three inertial accelerations imposed on the fluid, namely, centripetal acceleration, tangential acceleration, Coriolis acceleration. Accordingly, the expression of the inertial accelerations can be written as follows, respectively, ៝ × (ω ៝ × r)  ce = ω a a៝ ta

៝ × r =ˇ

  co = 2ω  ×u a

R =

(19)

In which, ace is the centripetal acceleration. ata is the tangential acceleration. aco is the Coriolis acceleration. r is the distance between fluid element and rolling axis (Fig. 6). Obviously, the inertial force perpendicular to the flow direction introduced by the rolling motion will lead the secondary flow various periodically and demolish the laminarization effect, thus the heat transfer enhancement will exist through the whole rolling period and lead the cycle-averaged Nusselt number larger than that in static condition. In addition, Eq. (16) indicates that the effect of the Coriolis force on the heat transfer increases with the increase

(20)

tR 20

(21)

Therefore, based on the experimental data, the cycle-averaged Nusselt number in rolling motion condition can be calculated by the following correlation, 0.334

NuR = 0.07Nus ReR

0.332 −0.685 ˝max R

(22)

In which, NuR and Nus is the cycle-averaged Nusselt number in rolling motion and static condition at the same thermal–hydraulic condition. 3.4. Instantaneous heat transfer characteristic in rolling motion The relative pulsation amplitude of the Reynolds number and Nusselt number is defined to evaluate the influencing degree of rolling motion, ∗ Reamp =

Nu∗amp =

(17) (18)

max  180

Reamp ReR Nuamp NuR

(23)

(24)

In which, Reamp and Nuamp is the pulsation amplitude of the Reynolds number and Nusselt number, respectively. As seen in Fig. 7, the flow pulsation characteristic is similar to that in forced circulation flow mentioned by Xing et al. (2012). The relative pulsation amplitude increases with the increase of rolling amplitude, decreases with the increase of rolling period and flow rate. As mentioned by Tan et al. (2009a,b), the momentum conservation equation in rolling motion condition can be expressed as follows,



i

   dui = pd + pf + padd dt

pd = gH cos  + gL sin 

(25) (26)

C. Wang et al. / Nuclear Engineering and Design 273 (2014) 497–504

padd = ˇ



i yi Li + ω2



(xi i dx + yi i dy)

In which, pd , pf and padd is the instantaneous driving head, the total frictional and local pressure drop and additional pressure drop, respectively.  is the density difference between cold and hot water. H and L is the height and width of the rectangular loop, respectively. In addition, Tan et al. (2009a) also point out that the flow rate pulsation leads to the increase of frictional resistance factors, thus the pressure drop should be modified using the following equations. pf,R = CR pf,s CR = 1 +

12000

(27)

10000

8000

ReR

502

6000

4000

(28)



180˝max 0.2678 −0.085 +  R

(29)

As seen in Eq. (26), the variation of the rolling period will not change the pulsation amplitude of the driving head as in the same thermal–hydraulic condition. However, as in the same water temperature at the inlet of the test section and rolling motion parameters condition, the larger the density difference, the bigger the flow rate. Therefore, the pulsation amplitude of the natural circulation driving head will increase with the increasing flow rate as the driving head is the main reason of the flow rate pulsation. However, as seen in Fig. 7, the experimental phenomena are different from the situation that the variation of driving head leads to the periodically pulsation of flow rate, and the similar experimental phenomena also were reported by Murata et al. (1990). As referred by Xing et al. (2013), the relative pulsation amplitude of flow rate in rolling motion condition depends on the relative magnitude of driving head, friction resistance and additional inertial force. The relative pulsation amplitude of flow rate decreases with the increase of driving head and frictional resistance as in the same additional inertial force condition. In addition, the variation of the water temperature distribution from the outlet of the cooler to the inlet of the preheater is very small in the present experimental study due to the accommodating of the coolant flow rate of the cooler. However, the density difference  will increase with the increasing flow rate as referred in above and lead the total additional inertial force decrease with the increasing flow rate. Therefore, the combined action of increased driving head and decreases additional inertial force leads to the decreases of the relative pulsation amplitude of flow rate, and the additional inertial force introduced by the rolling motion is the dominant factor that leads to the flow rate pulsation. As seen in Fig. 8, the rolling motion leads the cycle-averaged flow rate less than that in static condition in the same thermal–hydraulic condition. The more drastic of the rolling motion, the more prominence of the cycle-averaged flow rate reduction. On the basis of the experimental data, the relationship between the rolling motion parameters and the cycle-averaged flow rate before and after rolling motion condition can be expressed as 1.1467

ReR = 0.2484Res

−0.05324 0.1738 ˝max R

2000 2000

4000

6000

8000

10000

12000

Res Fig. 8. Effect of rolling motion on average flow rate. ∗ of the relative pulsation amplitude of Reynolds number Reamp , and ∗ as Reamp less than 0.25, ∗ Nu∗amp = 1.76Reamp

However, as Nu∗amp

(32)

∗ Reamp ≥0.25,

∗ = 0.88Reamp + 0.22

(33)

Therefore, substitute Eq. (30) into Eq. (31), the relationship between the relative pulsation amplitude of Reynolds number, rolling motion parameters and the flow rate before the rolling motion start is obtained and can be expressed as −1.189

∗ Reamp = 26589.1Res

−0.2148 0.29 ˝max R

(34)

Substitute Eq. (30) into Eq. (22), 0.56

NuR = 0.628Nus Res

0.3142 −0.625 ˝max R

(35)

Thus the single-phase natural circulation instantaneous Nusselt number under rolling motion condition can be calculated by the following correlation, NuR = NuR + Nu∗amp sin

 2t  tR

(36)

(30)

In addition, based on the experimental data in Figs. 7 and 8, the relationship between the relative pulsation amplitude of flow rate, the cycle-averaged flow rate in rolling motion and the rolling motion parameters can be calculated through the following correlation, −1.037

∗ Reamp = 6273ReR

−0.27 0.47 ˝max R

(31)

Furthermore, it can be seen in Fig. 9 that the relative pulsation amplitude of the Nusselt number Nu∗amp increases with the increase

Fig. 9. Relationship between flow and heat transfer relative pulsating amplitude.

C. Wang et al. / Nuclear Engineering and Design 273 (2014) 497–504 80

503

50

Nuexp

Nupred,s

Nupred,R

Nuexp

Nus

Nupred

60 40

Nu

Nu

40 30

20

20

0

-20

0

5

10

10

15

0

10

20

t/s

t/s

a.

Reave,s=4438

30

θmax=10° tR=7.5s

b.

Reave,s=5227 θmax=10° tR=15s

60

80

Nuexp

Nus

Nuexp

Nupred

Nus

Nupred

50 60

40

Nu

Nu

40

30

20

20

0

0

5

10

15

20

10

0

10

t/s

c.

Reave,s=6830

20

30

40

t/s

θmax=15° tR=10s

d.

Reave,s=7550 θmax=20°

tR=20s

Fig. 10. Comparisons between experimental and predicted values.

Substitute Eqs. (32), (33) and (35) into Eq. (36), it can be found that the variation of the flow rate and heat transfer characteristic under rolling motion condition can be obtained as the thermal hydraulic parameters in static condition is given. As seen in Fig. 10, Eq. (36) has a better prediction ability to calculate the instantaneous Nusselt number of natural circulation pulsating flow induced by rolling motion as compared to the Yang equation.

pulsation as compared to that in steady flow. In addition, the relative pulsation amplitude of the Nusselt number increased linearly with the relative pulsation amplitude of the Reynolds number. Furthermore, based on the relationship between the cycle-averaged flow rate before and after rolling motion start, and the relationship between rolling motion parameters, the relative pulsation amplitude of Nusselt number and cycle-averaged Reynolds number, the instantaneous Nusselt number under rolling motion condition can be predicted using the thermal–hydraulic parameter in static condition.

4. Conclusion Heat transfer characteristic of natural circulation pulsating flow induced by rolling motion is experimentally investigated in the present study. The results show that significant flow rate pulsation occurs in the experimental loop in rolling motion condition. The periodic variation of driving head under rolling motion condition is not the predominant factor that leads to the flow rate pulsation, and the additional force introduced by the rolling motion is the main reason that leads to the flow pulsation of natural circulation. The cycle-averaged heat transfer characteristic is enhanced by the flow

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