Three-dimensional study on steady thermohydraulics characteristics in secondary side of steam generator

Progress in Nuclear Energy 70 (2014) 188e198

Contents lists available at ScienceDirect

Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene

Three-dimensional study on steady thermohydraulics characteristics in secondary side of steam generator Tenglong Cong a, Wenxi Tian a, Guanghui Su a, *, Suizheng Qiu a, Yongcheng Xie b, Yangui Yao b a b

School of Nuclear Science and Technology, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China Shanghai Nuclear Engineering Research and Design Institute, Shanghai 200233, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 March 2013 Received in revised form 29 August 2013 Accepted 30 August 2013

Steam generator (SG), as the primary-to-secondary heat exchanger and pressure boundary of primary loop, should be integrated and perform well in heat transfer ability. Flow characteristics of the secondary side fluid of SG are essential to analyze U-tube wastage caused by the flow-induced vibration and thermal stress. In this paper, secondary side two-phase flow was simulated based on the porous media model. Additional momentum and energy source terms were appended to the momentum and energy equations for porous media region, respectively. The additional momentum source contained the resistances of downcomer, tube bundle, support plate and separator. The additional energy source included the heat transfer from primary side to secondary side fluid. Solving the governing equations by ANSYS FLUENT solver yielded the distributions of velocity, temperature, pressure, density and quality, which can be used in the analysis of flow-induced vibration and separators. The thermal-hydraulic characteristics of hot side differed from these of cold side considerably. The minimum flow quality of cold side was 0.07, while the maximum one of hot side was 0.71; the average flow quality of outlet was 0.272. The flow rate in the gap of the hot side was 1.02 times of that of the cold side. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Steam generator Secondary side flow Porous media

1. Introduction Steam generator (SG) plays a key role in the operation of pressurized water reactor (PWR). Primary side fluid, heated in the core, passes through SG, where it transfers energy to secondary side fluid to evaporate the liquid water to vapor. Besides, SG also acts as the pressure boundary of the primary side and secondary side fluids, preventing radioactive primary coolant releasing to secondary side fluid. The tube wastage will reduce the heat transfer performance as well as release the radionuclide to surroundings. Characteristics of secondary side fluid flow of SG are essential to the analysis of Utube damage caused by the flow-induced vibration and thermal stress. In general, secondary side flow features are analyzed by the general system codes such as RELAP and RETRAN, or some other system codes for specific reactor systems (Wu et al., 2012) or steam generators (Wang et al., 2012). These codes can provide just the lumped or one-dimensional parameters for SG. Since these codes

* Corresponding author. Tel./fax: þ86 29 82663401. E-mail address: [email protected] (G. Su). 0149-1970/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pnucene.2013.08.011

were programmed based on the lumped, one-dimensional or simplified pseudo-muti-dimensional models, they could not be utilized to estimate the localized three-dimensional (3D) parameters of SG, which should be calculated by the 3D computational fluid dynamics (CFD) technique. Given the complexity of SG secondary side and the computer capacity, 3D simulation on SG secondary side flow based on microscopic meshes, which present the detailed geometries of SG (such as U-tubes and support plates) is out of the question, since hundreds billion meshes will be needed for this simulation. A simplified method on the bases of porous media method was first presented by (Patankar and Spalding, 1974), who employed the porous media theory to calculate the shell side flow of heat exchanger. (Sha et al., 1982) simulated the flow field of SG and the reactor core based on porous media model. (Stosic and Stevanovic, 2001) proposed an advanced porous media method to forecast the transient flow characteristics among tube bundle. (Ferng et al., 2001) performed a steady calculation for the secondary side flow distribution of SG. (Ferng and Chang, 2008) simulated the thermal-hydraulic phenomena for the steady abnormal operation conditions, including increasing the inlet flow rate and decreasing the inlet temperature of secondary side fluid. (Ferng, 2007) also studied the released nuclide distribution in SG

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

Nomenclature d E f ! F ! g G k l p Re S t T v ! v w x

diameter total energy flow fraction factor body force acceleration of gravity mass flux conductivity length of flow path/characteristic dimension pressure Reynolds number source term time temperature velocity in x or y direction velocity velocity in z direction mass quality of vapor phase

Greek symbols a void fraction b porosity

secondary side. (Rämä et al., 2010) investigated the flow phenomena of the VVER-440 SG secondary side based on porous media method with Euler two-phase model. The 3D CFD simulations on the thermal-hydraulic characteristics of SG secondary side need improvement, though many studies have been performed on multi-dimensional calculation of SG. In Ferng’s publications (Ferng, 2007; Ferng and Chang, 2008; Ferng et al., 2001), 1) the inlet and outlet boundary conditions were not set appropriately; 2) the two-phase flow model, turbulence model and the resistance model were not accurate enough; 3) the support plates were ignored. Rämä et al. (2010) employed the Euler model for two-phase flow, however, they calculated the tube bundle resistance for each phase with a simplified method that resistance of each phase was equal to the total resistance for mixture multiplied by the void fraction of the corresponding phase. This method was also employed by Zhang and Bokil (1997), but it was quite unreasonable. In this paper, we proposed a porous media based simulation on the thermal-hydraulic characteristics of secondary side of AP1000 SG. In this simulation, downcomer, tube support plates, separator were all taken into account. Drift flux model coupled with a verified zero-equation turbulent model was employed. 2. Mathematical and physical models There are three common methods to simulate two-phase flow in CFD, i.e., the homogenous flow, drift flux flow and two-fluid flow. In the early investigations (Ferng, 2007; Ferng and Chang, 2008; Ferng et al., 2001), the homogenous flow model was employed to simplify the calculation. This model treats the two-phase flow as a quasisingle-phase flow and cannot model the interactions between phases. The two-fluid model, theoretically, should be the most exact model in the above three models, since it models each phase respectively. Nevertheless, for lack of closure models for the phase interactions, lots assumptions should be introduced to model the interactions, which would reduce the accuracy of two-fluid model. The drift flux model treats two-phase fluid as a mixture and introduced the drift velocity to represent the interphase slip as well

r m

189

density viscosity two-phase multiplier

42

Subscripts a axial flow c cross flow dr drift E energy source term e equivalent eff effective g vapor phase gs saturated vapor k phase k l liquid phase ls saturated liquid m mixture max maximum ! v momentum source term Superscript T turbulent

as the interphase drag force. Although the drift flux model might be coarse compared to the two-fluid model, it needs less hypothesis and the calculated results for SG are satisfactory (Keeton et al., 1986). Thus, in this paper, we employed the drift flux model. The governing equations are listed below. Mass equation:


v ðbrm Þ þ V$ brm ! vm ¼ 0 vt

(1)

Momentum equation:



  v
brm ! vm þ V$ brm ! vm ! vm vm ¼ bVp þ V$ bmm;eff V ! vt ! ! þ brm g þ F   bag rg !  rm v! þ bV$  v dr;g dr;g 1  ag rl þ S! v (2) Energy equation:

 X2
v Xn ! ba r ba r ð ð E Þ þ V$ v E þ pÞ k k k k k k k k¼1 k¼1 vt 
¼ V$ bkeff VT þ SE

(3)

Void fraction equation:



 v
bag rg þ V$ bag rg ! vm ¼ V$ bag rg v! dr;g þ Sg vt

(4)

where, b is the porosity, i.e., the ratio of fluid occupied volume and total volume in a control volume, which is calculated by the geometry calculation; rg is the vapor phase density; rm is the mixture density, defined by





rm ¼ rl 1  ag þ rg ag

(5)

190

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

Fig. 1. Node diagram for RELAP5 calculation.

! vm is the mixture velocity; mm, eff is the mixture effective viscosity, equaling to the sum of laminar viscosity and turbulent one; p ! is the pressure; F is the sum of body forces except the forces introduced by components such as tube bundle and support plates; keff is the effective conductivity; v! dr;k is the drift velocity of phase k. Sv is the additional momentum source term proposed to consider the effects of downcomer, tube bundle, separators and support plates. The effects caused by the former three are taken into account as the distribution resistances added into the cells in the regions of downcomer, tube bundle and separators, respectively; while effects caused by the last one are regarded as the concentration resistances put on the cell faces where support plates situated. Since the tube bundle resistance is anisotropic, we project the total force along the three directions of rectangular coordinate system. The resistances are classified as the axial flow resistance and the cross flow one. The axial flow resistance is calculated by (MacAdams, 1954)

Dpa l

¼ 4fa

G2 1 2 $ $f 2r l de

(6)

where G is the mass flux; rl is the density of liquid phase; de is the equivalent hydraulic diameter; fa is the axial flow friction factor, which is calculated by the MacAdams equation (MacAdams, 1954)

where rm is the density of mixture and mm is the laminar viscosity of mixture. 42 is the two-phase multiplier estimated by Thom correlation (Thom, 1964)

f2 ¼ 1:0 þ BxC

where x is the mass quality of vapor phase; B and C are constants given as follows.

B ¼ 1:0531

C ¼

fa ¼ 0:048Re

rm jwm jde mm

8 r < 0:0048 rgsls þ 1:10755 : 0:0016 rls þ 1:0492 rgs

(10)

x  0:01 x > 0:01

(11)

Dpc

¼ 4fc

rm v2max 1 2

pV

f2

(12)

(7) where vmax is the maximum cross flow velocity through tubes; pV is the pitch of tube bundle; fc is the cross flow friction factor (Grimison, 1937)

where Re is the Reynolds number

Re ¼

rls þ 1:05455 rgs

where rls and rgs are the densities of saturated liquid and vapor, respectively. The cross flow resistance is computed by the following correlation (Kays and London, 1984)

l 0:2

(9)

(8)

fC ¼ 0:864Re0:205

(13)

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198 Table 1 Spatial discretization methods. Terms Gradient Pressure Momentum Volume fraction Energy

First 3000 iterations Least squares cell based Body forced weighted First order upwind First order upwind First order upwind

Dpm ¼ C$ After first 3000 iterations Least squares cell based Body forced weighted QUICK QUICK QUICK

G2 2 $f 2rl

191

(17)

where fd is the resistance factor to consider the friction resistance and the local resistance caused by the structures in downcomer; dd is the gap dimension in downcomer. The resistance caused by primary separators is given by

where C is the resistance factor. SE is the energy source representing the heat transfer from primary side coolant to secondary side mixture. To simplify the calculation, this 3D energy source is reduced to 1D along the tube bundle. It is evaluated by the system code RELAP5 and compiled into FLUENT solver by user defined functions (UDFs). A total number of 24 control volumes are divided in the heat source calculation. The node diagram for RELAP5 calculation is shown in Fig. 1. Sg is the mass source for vapor phase. The mass transfer process is complex since it depends very much on the flow conditions, such as flow rate, flow properties of both phases, bubble size and its distribution, flow geometry, gravity and wall surface conditions (Liu et al., 2012; Son and Dhir, 1998; Wu et al., 2009). Investigators (Krepper et al., 2013; Lifante et al., 2012b, a; Lucas et al., 2011; Pellacani et al., 2010) model this process under subcooled boiling condition accurately with RPI wall boiling model, however, this model is suitable only if the void fraction of vapor phase is less than 0.3 (Inc., 2009). Other researchers (Ferng, 2007; Ferng et al., 1990, 2003, 2003, 2001; 1991, 2001) simulate the boiling process with reduced models by ignoring the transient bubble evaporation and condensation processes. In this work, a simplified mass transfer model is employed, as

Dps

Sg ¼

where Re is the Reynolds number

Re ¼

rm jvmax jde mm

(14)

The resistances introduced by support plates, downcomer and separator are figured up based on correlations given in literature (ANSYS, 2011; Keeton et al., 1986). The pressure drop in downcomer is calculated by

Dpd l

l

¼ fd

¼ fs

G2 1 2rl dd

G2 1 2 $ $f 2rl ds

(15)

(16)

where fs is the equivalent resistance factor of separators and ds is the inner diameter of separators. The effect of steam-water separation is not taken into consideration. Given the thickness of tube plates is much less than the mesh dimension, porous jump boundaries are introduced at the positions where tube plates situated to consider the resistance of plates. Pressure drop caused by the tube plate is estimated by

SE Hfg þ 4182e8DTsub þ2  DTsub

(18)

where Hfg is the latent heat of vaporization; SE is the volumetric heat source, i.e., heat transferred from primary to secondary side per second per unit volume; and DTsub is the subcooled temperature equaling to the difference between fluid temperature and saturation temperature. In the steady simulation, the vapor condensation is not taken into account because of the ignorance of transient bubble actions.

Fig. 2. Calculated domain and grid scheme.

192

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198 0.268

111099

outlet flow vapor quality

0.266

138348

0.264

53421

0.262

outlet flow vapor quality 0.260

38433 0.258 40000

60000

80000

100000

120000

140000

grid number Fig. 3. Grid independence check.

The drift velocity is calculated by the Manninen drift flux model (Manninen et al., 1996).






!


 rg  rm r v ! vm ! v! $ $ m $ g  ! vm $V ! vm  dr;g ¼ rg rl al vt fdrag

sp

(19)

where sp is the particle relaxation time; fdrag is the drag function defined by

fdrag ¼

1 þ 0:15Re0:687 Re  1000 0:0183Re Re > 1000

(20)

As to the turbulence model, the most general turbulence models are developed for the microscopic simulation on the pure single phase fluid domain, such as keε (Launder and Spalding, 1972), keu (Wilcox, 1998) and SST (Menter et al., 2004) turbulence models. Many researchers integrate the microscopic turbulent equations in the macroscopic control volume of porous media, yielding some modified equations for turbulence in porous media (Antohe and Lage, 1997; Chandesris et al., 2006; De Lemos, 2012; Getachew et al., 2000; Kuwahara et al., 2006). However, these models are

Fig. 4. Temperature distribution on the symmetry plane.

Fig. 5. Temperature distribution on the support plates.

only suitable for single phase flow and are much too complex. In this paper, we employed a validated zero-equation turbulence model to calculate the effective viscosity for flow in tube bundle (Hopkins, 1988; Launder and Spalding, 1972; Schlichting, 1979).

meff ¼ 0:047rm wm l

(21)

where l is the characteristic dimension, which is defined as, 1) l ¼ the hydraulic diameter of the flow passage through the tube bundle in the tube bundle region; 2) l ¼ shell inner diameter when above the tube bundle; 3) l ¼ gap dimension in downcomer; 4) l ¼ channel diameter in separator.

Fig. 6. Enthalpy distribution on the symmetry plane.

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

193

2600000.0

2000000.0 1800000.0

0.8

void fraction

2200000.0

enthaply (J/kg)

1.0

axial height(m) 0.2 1.0 3.0 6.0 8.0 10.0

2400000.0

1600000.0 1400000.0

axial height(m) 0.2 1.0 3.0 6.0 8.0 10.0

0.6

0.4

0.2

1200000.0

0.0 1000000.0 -3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

-3.0

-2.0

-1.0

0.0

x (m)

1.0

2.0

3.0

x (m)

Fig. 7. Enthalpy distribution along the horizontal curves at symmetry plane.

Fig. 9. Void fraction along the horizontal lines located at the symmetry plane.

The aforementioned equations are partial differential equations. These coupled equations are solved by the COUPLED algorithm in ANSYS FLUENT solver (ANSYS, 2011). The spatial discretization methods are listed in Table 1. The convergence criteria employed are 1) the residual of every control volume for every governing equation is less than 1.0E-6 and 2) the average vapor fraction at the outlet surface and the pressure at the inlet surface does not change.

inlet boundary is set as the velocity-inlet boundary, with an inlet velocity calculated by the inlet mass flow rate, the cross section area and the density. The outlets of separators are connected with the plenum. Thus, the pressure on separator outlets should be uniform. We set the outlet boundary as pressure-out boundary with an identical pressure equaling to the plenum pressure. Since the frictional resistance is added in the control cell adjacent to the walls, we set the wall boundary as a slip wall boundary. The heat transferred from primary coolant to shell side fluid is added as the volumetric heat source by UDFs. The grid scheme is shown in Fig. 2(b). All meshes are hexahedral. The quality is larger than 0.5. To ensure the results are grid independent, we perform the calculations on four sets of grid, which contain 38433, 53421, 111099 and 138348 meshes, respectively. The independence grid is determined by comparing the outlet flow vapor quality. The results of grid independence test are shown in Fig. 3. As can be seen, The grid scheme with 111099 meshes is the independence one.

3. Grid strategy and boundary conditions We put the support plates, downcomer and separators into the calculated domain. The inlet boundary is put on the top of downcomer and the outlet boundary on the top of separators. Calculated domain is shown in Fig. 2(a). The separator channels are changed into rectangular channels for the sake of simplifying grid, though they are cylindrical actually, as shown in Fig. 2(a). The center lines and flow areas of separator channels are remained unchanged. The

4. Calculation results Carrying out the thermal-hydraulic simulation on the SG secondary side flow with ANSYS FLUENT generates the local velocity,

1.0

void fraction

0.8

0.6

separator No. 18 21 30 31

0.4

0.2

0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

z (m) Fig. 8. Void fraction distribution on the symmetry plane.

Fig. 10. Void fraction along the vertical lines located at the center of separators.

194

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

relative pressure (Pa)

100000.0

seperator No. 18 21 30 31

80000.0

60000.0

40000.0

20000.0

0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

z Fig. 13. Pressure along the vertical lines located at the center of separators. Fig. 11. Void fraction distribution on the separator outlets.

temperature, pressure, density and quality distributions, which are discussed in detail below. The temperature nephogram on the symmetry plane is shown in Fig. 4, where the left side (x > 0) is the hot side (primary coolant flowing upwards in U-tube) and the right side is cold side (primary coolant flowing downwards in U-tube). It can be seen that the shell side fluid temperature reaches saturation rapidly after it turns into tube bundle region in hot side; while the cold side fluid reaches the saturation point after a long flow path (about four meters) over tube bundle. The mixture temperature keep constant after being saturated. The saturated temperature is 544.7 K, which is determined by the plenum pressure, 5.64 MPa. Fig. 5 presents the temperature distribution on the planes where the support plates locate. It can be noted that the temperatures distribute symmetrically with the y ¼ 0 plane. Fig. 6 presents the enthalpy distribution on the symmetry plane. The mixture enthalpy of hot side differs significantly from that of cold side. The difference between hot and cold side enthalpies

increases with increasing the height, as shown in Fig. 7, where the enthalpy along the horizontal lines at the symmetry plane is given. The horizontal lines are illuminated in Fig. 2(a). Enthalpy reaches a largest value at the top of U-tube bundle. Fig. 8 demonstrates the void fraction distribution on the center plane. The void fraction of hot side is larger than that of cold side. The region where void fraction less than 0.1 is rather small in hot side; while in cold side, this region is far larger than that in hot side. The peak of void fraction appears in the hot side at the bottom of tube bundle. This position moves towards the center of SG with fluid flowing upwards, as shown in Fig. 9. It also can be seen from Fig. 9 that the difference in the void fraction of hot and cold sides diminishes with the height increasing, which is because of the diffusion of vapor phase. Fig. 10 illuminates the void fraction along the vertical lines located at the center of separators No. 18, 21, 30 and 31. These four vertical lines are also shown in Fig. 2(a). Fig. 11 gives the numbering scheme of separators and the void fraction

Fig. 12. Pressure distribution on the symmetry plane.

Fig. 14. Velocity distribution on the symmetry plane.

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

195

Fig. 15. Velocity of U-tube region on the symmetry plane.

nephogram at the outlet of separators. It can be noted that the void fraction distribution varied significantly. Void fraction of the inside separators in hot side is the highest; while void fraction of the outside separators in cold side is the lowest. The highest and lowest void fraction values at the separator inlets are 0.98 and 0.63, respectively. The flow vapor quality in each separator also can be obtained from the calculation. The flow quality in No. 01 and 16 separators are the lowest, with values of about 0.07; while flow quality in No. 30 and 32 separators are the highest, with values of about 0.71. The highest value is about ten times of the lowest one, i.e., the flow quality distribution varies markedly in separators. The given inlet mass flow rate is 3496.80 kg/s, while the calculated outlet mass flow rate is 3496.85 kg/s. The resultant relative error of mass flow rate is 1.4e-5. The calculated vapor flow rate is 953.4 kg/s, with a relative of about 1.03% when compared to the designed value of 943.7 kg/s. Pressure distribution at the symmetry plane is shown in Fig. 12. The reference pressure location is set at separator outlet with a

value of the plenum pressure. Thus, the relative pressure is zero at the outlet boundary. It can be seen from Fig. 12 that pressure increases with decreasing the height in downcomer owing to the effects of gravitational, acceleration and friction pressure drops. Pressure decreases with the increase in height in flow-upwards region. In addition, the pressure of hot side is slightly higher than that of cold side at the same height. Fig. 13 presents the pressure along the four vertical lines defined in Fig. 2(a). Pressure decreases steply with increasing the height, which is due to the concentration resistance introduced by support plates. It also can be seen that the pressure drop due to support plate increases with height. It is because the void fraction as well as the two-phase multiplication factor increases with increasing height. Fig. 14 shows the velocity vectors on the symmetry plane. Fig. 15 describes the velocity vectors in the elbow region. Fig. 16 and Fig. 17 present the velocity magnitude along the vertical lines and horizontal lines, respectively. Fig. 18 and Fig. 19 give the axial velocity and radial velocity along the vertical lines, respectively. It can be

8.0

6.0 5.0

5.0 4.5 4.0

axial velocity (m/s)

7.0

velocity magnitude (m/s)

5.5

seperator No. 18 21 30 31

4.0 3.0 2.0 1.0

3.5 3.0

axial height(m) 0.2 1.0 3.0 6.0 8.0 10.0

2.5 2.0 1.5 1.0 0.5 0.0

0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

z (m) Fig. 16. Velocity magnitude along the vertical lines located at the center of separators.

-0.5 -3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

x (m) Fig. 17. Velocity magnitude along the horizontal lines located at the symmetry plane.

196

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

seperator No. 18 21 30 31

8.0

axial velocity (m/s)

6.0

4.0

2.0

0.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

z (m) Fig. 18. Axial velocity along the vertical lines located at the center of separators. Fig. 20. X-velocity at the interface between hot and cold sides.

seen from these figures that the fluid velocity of hot side is significantly larger than that of cold side. Velocity magnitude increases rapidly in the hot side by reason of the evaporation; while liquid fluid velocity magnitude decreases slightly in the cold side because of the homogenization of cold side velocity. The velocity magnitude as well as the axial velocity decreases after flowing out of tube bundle region and then increases after flowing into the separators owing to the variations of flow area. The radial velocity is less than 0.3 m/s in the straight tube region except in the bottom, which is considerably smaller than axial velocity in this region. The radial velocity increases sharply in the U-bend region and the fluid domain above U-tube bundle due to the effects of elbows and separators. The x-direction crossflow velocity (flow from cold side to hot side) on the interface between hot and cold sides is shown in Fig. 20. The interface is illuminated in Fig. 11. It can be noted from Fig. 20 that the cross flow velocity in the downcomer at the interface of hot and cold sides is quite small, with values within the range of 0.02 m/s. In most regions within the shroud, the x-direction velocity is negative, which meant that fluid went from hot side to cold side. In the region nearby the inlets of No. 30 and No. 32

separators, the cross flow from cold to hot side changes into positive rapidly, which is because that the centers of No. 30 and No. 32 separators are in the hot side. The tangential velocity distribution in the downcomer is given in Fig. 21. The circumferential velocity in downcomer is less than 0.05 m/s, except in the region near the cone and the bottom of shroud. In the region dominated by the cone and gap between the shroud and tubesheet, the maximum circumferential speed is about 0.17 m/s, which is still fairly small. In the SGs of generation two PWRs (such as M310 and CNP650), the ratio of feedwater flow rate supplied by the feedwater ring of hot side and that of cold side was 4:1, which was corresponding to the general understanding that the excepted flow rate of hot side was much larger than that of cold side in downcomer. However, in AP1000 SG, feedwater enters the downcomer through the feedwater nozzle uniformity in the tangential direction and then mixes with the recirculating water, i.e., the mass flux distribution at the inlet boundary of downcomer is uniform. The mass flux is autoregulated on the basis of flow resistance distribution from downcomer inlet to separator outlets. The mass flux flowing into the gap

0.8

radial velocity (m/s)

0.4 0.2

seperator No. 18 21 30 31

14.0 12.0

conical section

10.0

axial-coordinate

0.6

0.0 -0.2 -0.4

tangential velocity(m/s)

8.0

-0.16 -0.12

6.0

-0.08 -0.04

4.0

0.00

-0.6

0.04

-0.8 -2.0

0.08

2.0

0.12

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

z (m) Fig. 19. Radial velocity along the vertical lines located at the center of separators.

0.16

0.0 0

0.5π

π

angular-coordinate

1.5π

2.0π

Fig. 21. Tangential velocity distribution in the downcomer.

lower edge of sleeve

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

References

1020.0

hot side

hot side

cold side

1000.0 980.0

mass flux (kg/(m2·s))

197

960.0 940.0 920.0 900.0 880.0 860.0

mass flux 840.0

0.5π

0

π

θ (ραδ)

1.5π

2.0π

Fig. 22. Mass flux distribution in the gap.

between shroud and tubesheet is illuminated in Fig. 22. The mass flux varies considerably with circumferential direction with a maximum and a minimum fluxes of about 1000 kg/m2/s and 850 kg/m2/s. The mass fluxes of hot side are slightly larger than these of cold side. The ratio of total mass flow rate of hot side and that of cold side is 1.02:1, in detail, the total mass flow rates of hot and cold sides are 1763.9 kg/s and 1732.9 kg/s, respectively. 5. Conclusions In this paper, porous media model was employed to calculate the steady localized thermal-hydraulic characteristics of steam generator (SG) secondary side fluid, yielding the following conclusions. 1) Macroscopic simulation on SG shell side fluid based on porous media model can economize computation meshes and cost compared to microscopic simulation. The results were satisfactory. 2) The thermal-hydraulic features of hot side differed from these of cold side significantly owing to the difference in heat source. The diffusion of vapor phase, which cannot be represented in the simulation based on homogenous flow model, can reduce this distinction between hot side and cold side. 3) The flow qualities in separators were varied from each other, with values from 0.07 to 0.71, which were of great importance for the design of separators. 4) The cross flow in downcomer was quite small. 5) The mass flux in the gap varied significantly along the circumference of the shroud, while the ratio of hot and cold sides flow rate was rather small, with value of 1.02:1. 6) The simulation generated the localized velocity distribution of shell side, which can be used for the flow-induced vibration of U-tubes. Acknowledgment This work was supported by the Shanghai Nuclear Engineering Research and Design Institute of China and the National Science Fund for Distinguished Young Scholars in China (No. 11125522).

ANSYS, 2011. ANSYS FLUENT Theory Guide. Canonsburg, PA, USA. Antohe, B., Lage, J., 1997. A general two-equation macroscopic turbulence model for incompressible flow in porous media. Int. J. Heat Mass Transfer 40, 3013e3024. Chandesris, M., Serre, G., Sagaut, P., 2006. A macroscopic turbulence model for flow in porous media suited for channel, pipe and rod bundle flows. Int. J. Heat Mass Transfer 49, 2739e2750. De Lemos, M.J.S., 2012. Turbulence in Porous Media: Modeling and Applications. Elsevier. Ferng, Y., 2007. Investigating the distribution characteristics of boiling flow and released nuclide in the steam generator secondary side using CFD methodology. Ann. Nucl. Energy 34, 724e731. Ferng, Y., Chieng, C., Pan, C., 1990. Two-phase and Heat Transfer Characteristics of Rewetting Process. Ferng, Y., Chieng, C., Pan, C., 1991. Predictions of rewetting process for a nuclear fuel rod using first-principles equations. Nucl. Eng. Des. 126, 189e205. Ferng, Y., Sun, C., Su, A., 2003. Numerical simulation of thermalehydraulic characteristics in a proton exchange membrane fuel cell. Int. J. Energy Res. 27, 495e 511. Ferng, Y.M., Chang, H.J., 2008. CFD investigating the impacts of changing operating conditions on the thermal-hydraulic characteristics in a steam generator. Appl. Therm. Eng. 28, 414e422. Ferng, Y.M., Yinpang, M., Kang, J.C., 2001. Thermal-hydraulic simulation of localized flow characteristics in a steam generator. Nucl. Technol. 136, 186e196. Getachew, D., Minkowycz, W., Lage, J., 2000. A modified form of the keε model for turbulent flows of an incompressible fluid in porous media. Int. J. Heat Mass Transfer 43, 2909e2915. Grimison, E., 1937. Correlation and utilization of new data on flow resistance and heat transfer for cross flow of gases over tube banks. Trans. ASME 59, 583e594. Hopkins, G., 1988. Verification of the ATHOS3 Code Against Feedring and Preheat Steam Generator Test Data. Electric Power Research Institute, Palo Alto, CA, US. Inc., A., 2009. ANSYS CFX Multiphase 12.0 Workshop 7-Wall Boiling Model. Kays, W.M., London, A.L., 1984. Compact Heat Exchangers. Keeton, L., Singhal, A., Srikantiah, G., 1986. ATHOS3: a Computer Program for Thermal-hydraulic Analysis of Steam Generators. Electric Power Research Institute, Palo Alto, CA, US. Krepper, E., Rzehak, R., Lifante, C., Frank, T., 2013. CFD for subcooled flow boiling: coupling wall boiling and population balance models. Nucl. Eng. Des. 255, 330e 346. Kuwahara, F., Yamane, T., Nakayama, A., 2006. Large eddy simulation of turbulent flow in porous media. Int. Commun. Heat Mass Transf. 33, 411e418. Launder, B.E., Spalding, D.B., 1972. Lectures in Mathematical Models of Turbulence. Academic Press, London, France. Lifante, C., Reiterer, F., Frank, T., Burns, A., 2012a. Coupling of Wall Boiling with Discrete Population Balance Model, third ed. Multi-Science Publishing Co. Ltd, 5 Wates Way, Brentwood, Essex, CM15 9TB, United Kingdom, pp. 287e298. Lifante, C., Reiterer, F., Frank, T., Burns, A., 2012b. Coupling of wall boiling with discrete population balance model. J. Comput. Multiph. Flows 4, 287e298. Liu, X., Chen, Y., Shi, M., 2012. Influence of gravity on gaseliquid two-phase flow in horizontal pipes. Int. J. Multiphase Flow 41, 23e35. Lucas, D., Frank, T., Lifante, C., Zwart, P., Burns, A., 2011. Extension of the Inhomogeneous MUSIG Model for Bubble Condensation, eleventh ed. Elsevier Ltd, Langford Lane, Kidlington, Oxford, OX5 1GB, United Kingdom, pp. 4359e4367. MacAdams, W.H., 1954. Heat Transmission. McGraw Hill, New York, US. Manninen, M., Taivassalo, V., Kallio, S., 1996. On the Mixture Model for Multiphase Flow. VTT Publ., Finland. Menter, F., Langtry, R., Likki, S., Suzen, Y., Huang, P., Völker, S., 2004. A Correlationbased Transition Model Using Local Variables: Part IdModel Formulation. ASME. Patankar, S., Spalding, D., 1974. A calculation procedure for transient and steady state behavior of shell-and-tube heat exchangers. In: Afgan, N.H., Schlunder, E.U. (Eds.), Heat Exchanger Design Theory Source Book, first ed. McGraw-Hill, New York, US. Pellacani, F., Mestre, S.M., Vicent, S.C., Juan, R.M., 2010. CFD modeling of subcooled boiling in vertical bubbly flow condition using ansys CFX 12. Parts A and B. In: 18th International Conference on Nuclear Engineering, ICONE18, May 17, 2010May 21, 2010. American Society of Mechanical Engineers, Xi’an, China, pp. 1153e1162. Rämä, T., Toppila, T., Pättikangas, T., Niemi, J., Hovi, V., 2010. CFD-simulation of the vver-440 steam generator with porous media model. In: The 8th Int. Semin. on Horizontal Steam Generators, Podolsk, Russia. Schlichting, H., 1979. Boundary-layer Theory, seventh ed. Springer, Germany. Sha, W., Yang, C., Kao, T., Cho, S., 1982. Multidimensional numerical modeling of heat exchangers. J. Heat Transfer 104, 417e425. Son, G., Dhir, V., 1998. Numerical simulation of film boiling near critical pressures with a level set method. J. Heat Transfer 120, 183e192. Stosic, Z.V., Stevanovic, V.D., 2001. An advance porous media method for transient multidimensional two-phase flow thermal-hydraulics in complex geometries with rod or tube bundles. ICHMT Digit. Libr. Online 4, 945e952. Thom, J., 1964. Prediction of pressure drop during forced circulation boiling of water. Int. J. Heat Mass Transfer 7, 709e724. Wang, Z., Tian, W., Wu, Y., Qiu, S., Su, G., 2012. Numerical study on annular tube once-through steam generator using compressible flow model. Ann. Nucl. Energy 39, 49e55.

198

T. Cong et al. / Progress in Nuclear Energy 70 (2014) 188e198

Wilcox, D.C., 1998. Turbulence Modeling for CFD. DCW industries, La Canada, California. Wu, J., Chen, Y., Shi, M., Fu, P., Peterson, G., 2009. Three-dimensional numerical simulation for annular condensation in rectangular microchannels. Nanoscale Microscale Thermophys. Eng. 13, 13e29.

Wu, Y., Su, G., Qiu, S., Tian, W., 2012. Development of a thermalehydraulic analysis software for a passive residual heat removal system. Ann. Nucl. Energy 48, 25e39. Zhang, C., Bokil, A., 1997. A quasi-three-dimensional approach to simulate the twophase fluid flow and heat transfer in condensers. Int. J. Heat Mass Transfer 40, 3537e3546.