Numerical studies of a helical coil once-through steam generator

Annals of Nuclear Energy 109 (2017) 52–60

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Numerical studies of a helical coil once-through steam generator Genglei Xia a,b, Yuan Yuan c, Minjun Peng a,⇑, Xing Lv a, Lin Sun a a

Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin, China School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an City 710049, China c China Nuclear Power Simulation Technology Co., Ltd., Shenzhen, China b

a r t i c l e

i n f o

Article history: Received 21 July 2016 Received in revised form 8 October 2016 Accepted 9 May 2017

Keywords: HCSG Four-equation drift-flux model Fixed boundary Thermal-hydraulic dynamic model

a b s t r a c t A Thermal Hydraulic analysis code for Helical Coil once-through Steam Generator (TH-HCSG) is developed in the present study in order to predict the heat transfer process and thermal hydraulic characteristics in vertical helical coil steam generators. The numerical model is programmed using a one-dimensional four-equation drift-flux model and evaluated according to the data on HCSG published by the International Reactor Innovative and Secure (IRIS). The results achieved under full load conditions are, then, compared with the RELAP5 codes, with the results of this comparison showing that this model is both correct and reliable and can be used to investigate the instantaneous characteristics of helical coil steam generators. This model is also used to evaluate the influence of the main representative HCSG boundary parameters on HCSG operation characteristics. It was subsequently found that, when there was a ±10% step change in the boundary parameters, the length of the single-phase water region in the secondary side of the HCSG changed considerably, so that the steam flow oscillated obviously, lagging the feedwater flow at an early stage and rapidly reaching a steady state as the water capacity of the secondary side of the HCSG was changed. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Due to its compact structure, high heat transfer coefficient and good compensation for thermal expansion, helical coil tube-type once-through steam generators (HCSG) have been utilized in various reactors, especially in integral type reactors such as the CAREM-25 (Fukami and Santecchia, 2000), MRX (Kusunoki et al., 2000), IRIS (Carelli et al., 2004), MASLWR (Mascari et al., 2011), SMART (Chung et al., 2013). In the heat transfer tubes of HCSGs, single-phase primary coolant passes outside down the tube of the helical coil through the space of helical coil tube. The cold water is heated, becoming superheated steam by using primary coolant. The thermalhydraulic phenomena of the secondary side of the HCSG are very complex, as the flow direction is constantly changing because of their very particular spiral geometry. The centrifugal forces acting on the fluid inside the helical ducts tend to laminarize the flow, enhance the heat transfer coefficient and increase the frictional pressure drop. In HCSGs, the geometric parameters, such as the diameters of the pipes, spiral radius and coil pitch (curvature and torsion) affect

⇑ Corresponding author. E-mail address: [email protected] (M. Peng). http://dx.doi.org/10.1016/j.anucene.2017.05.025 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

the heat transfer coefficient and pressure drop (Hardik et al., 2015). Many researchers have investigated the thermal performance of helical coil heat exchangers experimentally. Naphon (2007) reported that the temperature of the cold water outlet, the effectiveness of the heat exchanger and the average heat transfer rate increased with an increase in the mass flow rate of hot water. Ghorbani et al. (2010) found that the convection heat transfer coefficient of the shell-side increased when the coil pitch was increased, and the overall heat transfer coefficient of the heat exchanger increased with an increase in the heat transfer rate. Hardik et al. (2015) researched the influence of curvature and Reynolds number on the local heat transfer coefficient in helical coils, suggesting correlations for the overall averaged and local circumferentially averaged Nusselt number for their inner side, outer side and total surface. Saffari et al. (2014) reported a correlational equation to predict the length of the hydrodynamic entrance as a function of various helical coil parameters. The development of simulation models suited to HCSGs is more complex than for straight tube once-through steam generators. In recent years, numerous studies have been carried out on the single-phase and two-phase pressure drop and heat transfer characteristics of HCSGs. A large number of empirical relationships have been able to provide strong support for the preparation of simulation program. In order to calculate the steady state of

G. Xia et al. / Annals of Nuclear Energy 109 (2017) 52–60

53

Nomenclature A cp d Dc fvis g Gm h hfg hp hs k Nu p Pr q Q Re Rf t T z 4Tsat

heat transfer area (m2) constant pressure specific heat (J/kg/°C) inner diameter of spiral pipe (m) curvature radius (m) pressure drop gradient by wall friction gravitational acceleration (m/s2) mass flux (kg/m2/s) enthalpy (J/kg) latent heat of vaporization (J/kg) primary heat transfer coefficient (W/m2/K) secondary heat transfer coefficient (W/m2/K) thermal conductivity (W/m/°C) Nusselt number pressure (Pa) Prandtl number heat flux (W/m2) heating power (W) Reynolds number foul resistance coefficient (m2K/W) calculation time (s) fluid temperature (K) length (m) subcooling degree (K)

HCSGs, Yoon et al. (2000) wrote an ONCESG program based on the movable boundary method. Yang et al. (2008) validated the HCSG model using the system transient analysis program TASS/SMR developed by Chung et al. (2012). Lee and Park (2013a–c), Lee et al. (2012) developed the TAPINS thermal hydraulic analysis program, which was based on four drift flow models for the integration of natural circulation in PWR, validating the model developed for HCSG by comparing the simulation results with experimental data. By taking the HCSG of HTR-10 as their research objectives, Li et al. (2008) established a lumped-parameter dynamic mathematical model based on the movable boundary method. Abdalla (1994) suggested a dynamic mathematical model for advanced liquid metal reactors, their method consisted in adopting the four-region model and the movable boundary method and the drift flow model method of calculation. RELAP5 codes were utilized to build their system model (2006, 2011, 2012), and the operating characteristics of HCSGs can be analyzed in the whole system. By examining the relevant literature, we can see that research has achieved a detailed analysis of the steady state and two-phase flow within HCSG, but that it has failed to take the overall characteristics of HCSGs and their transient operating process into account. In this paper, a mathematical model for HCSGs is established. Utilizing the established model, the operating characteristics of HCSGs under a steady state and transient conditions are investigated, and the calculated results are compared with the RELAP5 codes. Finally, the step changes of the representative boundary parameters of HCSGs are studied. It is hoped that the results of our research can be used to improve the design and operation of HCSGs. 2. Mathematical models Based on the characteristics of HCSG, the following assumptions are made to simplify the mathematical model. 1) HCSG is configured as one flow channel. 2) Each side is treated as a single flow channel according to the heat transfer area and equivalent diameter.

Greek letters 4 difference operator a vapor volume fraction q density (kg/m3) vr relative velocity (m/s) h spiral pipe rotation angle (°) lf viscosity coefficient (Pas) k thermal conductivity (W/m/K) Subscripts f liquid g vapor i inner m mixture o outer p primary side s secondary side sat saturation w wall

3) One-dimensional approach is used and neglecting axial heat conduction. 4) Ignoring fluid expansion works and works force by wall friction and fluid viscous force. 5) Ignoring interphase kinetic energy exchange and the work done by gravity. 6) Assuming uniform pressure distribution in the same cross section. 7) Thermal equilibrium model for two phase flow. The basic conservation equations of mass, energy, and momentum according to the abovementioned basic assumptions can be given as follows. 2.1. Basic mathematical models Conservation equations for mass, energy and momentum are utilized for the primary and secondary sides. Two phase mixture continuity conservative equation:

@ @ q þ ðq vm Þ ¼ 0 @t m @z m

ð1Þ

Single phase gas conservative equation:


 @ @ @ að1  aÞqg qf ðaqg Þ þ ðaqg vm Þ þ vr ¼ C @t @z @z qm

ð2Þ

Two phase mixture momentum conservative equation:


 @ @ @ að1  aÞqg qf 2 ðqm vm Þ þ ðqm v2m Þ þ vr @t @z @z qm @p  f vis  qm gsinh ¼ @z

ð3Þ

Two phase mixture energy conservative equation:


 @ @ @ að1  aÞqg qf ðhg  hf Þ ðqm hm Þ þ ðqm vm hm Þ þ vr @t @z @z qm ¼

Q @p þ ADz @t

ð4Þ

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G. Xia et al. / Annals of Nuclear Energy 109 (2017) 52–60

The equations of qm, vm, hm and vr are given respectively by Eqs. (5)-(8).

qm ¼ aqg þ ð1  aÞqf 1

vm ¼

qm

hm ¼

qm

1

ð5Þ

½qg av g þ qf ð1  aÞvf 

ð6Þ

½qg ahg þ qf ð1  aÞhf 

ð7Þ

vr ¼ vg  vf

ð8Þ

The stationary and convective term in mixture momentum equation are transformed into non-conservative form, and simultaneous mass conservative equation, the momentum equation can be expressed as follows:






@vm @vm 1 @ að1  aÞqg qf 2 1 @p f vis  vr ¼   gsinh þ vm þ @t @z qm @z qm qm @z qm ð9Þ The phase change does not occur during the whole operation conditions for primary coolant, assuming the void fraction a = 0. Based on the two-phase conservation equations, and consider the direction of fluid flow and heat transfer, conservation equations are expressed as follows:

@ @ q þ ðq vm Þ ¼ 0 @t m @z m

ð10Þ

@ @ @p ðq vm Þ þ ðqm v2m Þ ¼   f vis þ qm gsinh @t m @z @z

ð11Þ

@ @ @p Q ðq hm Þ þ ðqm vm hm Þ  ¼ @t m @z @t ADz

ð12Þ

(2) Convection heat transfer coefficient of subcooled nucleate boiling Heat transfer characteristics of spiral in subcooled boiling and two-phase forced convection region are similar with straight tube, so the heat transfer coefficient are using the modified Chen formula. Eq. (17) is used to determine the starting position of the bubble out of wall. The subcooled boiling convection heat transfer coefficient of boiling region is calculated by Eq. (18). The use of correction factor M to compensate for the structure of helical tube, which is calculated in Eq. (19).

TFDB ¼

8 < Tsat  0:0022 qdi ; Pe 6 70000 k f

: Tsat  154 G qc ; m


hTP ¼ 0:023

Gm di

þ 0:00122S  "



M ¼ Re

di Dc

ð13Þ

Rec < Re < 4  104 ;

Pr  1

 Rec ¼ 2  104

di Dc

Pr > 1

r

ð14Þ 0:061 2:5

½Reðdi =Dc Þ 

9 = ; 1 6;

ð17Þ

! 0:75 DT 0:24 sat DP sat

l

q

ð18Þ " ¼

Gm di



lf

di Dc

2 #0:05 ð19Þ

(3) Convection heat transfer coefficient of saturated nucleate boiling The saturation boiling convection heat transfer coefficient of boiling region is calculated by Eq. (20), and the corresponding correction factor M is illustrated in Eq. (21).




Gm ð1  xÞdi

"



di M ¼ Rel Dc

0:8 ðPrf Þ0:4

lf

q

0:79 0:45 0:49 cpf f 0:5 h0:24 0:24 0:29 fg g f

kf

r

2 #0:05

q

kf M di ! 0:75 DT 0:24 sat DP sat

l

"  2 #0:05 Gm ð1  xÞdi di ¼ lf Dc

ð20Þ

ð21Þ

(4) Convection heat transfer coefficient of liquid deficient region Eq. (22), obtained by helical coils experimental data is used for the judgment of dry out point. Heat transfer coefficient in this region is calculated using empirical relationships, as shown in Eq. (23). 2

8 9  101 < = 4 1 Pr d 0:098 i  2  Re5 ; Nu ¼ 1þ 1 26:2 Pr3  0:074 Dc : 2 ; ½Reðdi =Dc Þ 5 8  121 < 5 1 d i Nu ¼ Re6 Pr0:4 1þ 41:0 Dc :

q

0:79 0:45 0:49 cpf f 0:5 h0:24 0:24 0:29 fg g f

xdryout ¼ 1  4  104 q  0:0109ð103 Gm Þ

 0:194 where a ¼ 0:5 þ 0:2903 Ddic

Rec < Re < 4  104 ;

kf M di

kf

2 #0:05

þ 0:00122S

" #  0:9 1 di Re < Rec Nu ¼ 3:65 þ 0:08 1 þ 0:08 Rea Pr3 Dc

ðPrf Þ0:4

Tw  Tsat Tw  Tf

2.2. Calculation of heat transfer coefficient

(1) Single phase convection heat transfer coefficient Based on the Reynolds number, the inner single phase convection heat transfer coefficient is determined from the inner Nusselt number, which calculates using Eq. (13) for the laminar flow regime, and Eqs. (14) and (15) for the turbulent flow condition (Kim et al., 2013). The critical Reynolds number is calculated in Eq. (16) is used to identify the transitional regime boundaries.

0:8

lf

hTP ¼ 0:023F

2.2.1. Inner convection heat transfer coefficient

Pe > 70000

pf

Nu ¼ 0:023y

Gd

lg

!0:8 " xþ

qf ð1  xÞ qg

 0:5 Dc di

ð22Þ

#0:8 Pr0:8 w

ð23Þ

where y ¼ 1  0:1ðqf =qg  1Þ0:4 ð1  xÞ0:4 Fig. 1 is a schematic diagram showing the logic to select the appropriate heat transfer mode. The program uses a fixed node length, each node select the appropriate heat transfer model depending on thermodynamic condition.

ð15Þ

0:32 ð16Þ

2.2.2. Outer convection heat transfer coefficient Primary coolant flow from top to bottom at the outside of spiral tubes, since the spiral inclination angle is small (typically less than 15°), the coolant flow pattern is similar to cross tube bundles. Zhu-

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G. Xia et al. / Annals of Nuclear Energy 109 (2017) 52–60

kauskas equation is widely used to describe the heat transfer of single-phase fluid swept outer tubes, as shown in Eq. (24).

 0:36 Nuf ¼ CRem f Prf

Prf Prw

0:25 ð24Þ

where C and m are listed in Table 1. According to bundle different arrangement, such as in-line or staggered, select the corresponding heat transfer coefficients. 2.2.3. Equations of tube wall Heat transfer process within HCSG contains convective heat transfer of fluid and wall on both sides of the pipe and thermal conductivity of the wall. Wall heat flux is calculated as follows:

q¼

1 do hp di

pdo ðTp  Ts Þ þ 2kdow ln ddoi þ Rf þ h1s

ð25Þ

2.3. Calculation of friction factor 2.3.1. Inner single-phase flow friction factor The inner flow friction factor includes laminar and turbulent are presented by Ito based on experimental and theoretical research. The accuracy of the formula is verified by Ricotti (2013) uses experimental data, the results show that, the average error between calculation results and experimental value is 4.03% in laminar flow region, 3.77% in transition region, and 3.75% in turbulence region. The laminar flow friction coefficient (fc) is calculated in Eq. (26), and the turbulent flow friction coefficient (fd) is calculated in Eq. (27).

; Re 6 Rec

ð26Þ

f d ¼ 0:304Re0:25 þ 0:029ðdi =Dc Þ ; Re > Rec

ð27Þ

f c =f s ¼ 21:5De=ð1:56 þ log10 DeÞ

5:73

0:5

2.3.2. Inner two-phase flow friction factor Using the Lockhart-Martinelli method, Ricotti (2013) obtained a new two-phase pressure drop calculation formula through fitting method according to the experimental data of Santini et al. (2008). The average error between calculation results and experi-

Table 1 C and m selection scheme. (Where a denotes transversal pitch; b indicates longitudinal pitch.) Re

C

10–100 100–1000 1000–2  105 – – >2  105

m

In-line

Staggered

0.8 0.51 0.27 – – 0.033

0.9 0.5 – 0.35(a/b)0.2, a/b  2 0.40, a/b > 2 0.031(a/b)0.2

0.4 0.5 0.63 0.60 0.60 0.8

Table 2 Data for IRIS steam generator design and full power operating. System parameters

Values

Rated power/MW Primary coolant flow/(kg/s) Primary inlet temperature/K Primary outlet temperature/K Primary pressure/MPa Feedwater flow/(kg/s) Feedwater temperature/K Steam temperature/K Steam pressure/MPa Number of tubes Tube material Tube internal diameter/mm Tube external diameter/mm External shell inner diameter/mm Tube bundle average length/m

125.0 589.0 601.55 565.1 15.5 62.85 497.05 590.1 5.8 655 Inconel-690 13.24 17.46 1640 32.0

Table 3 Comparison with the IRIS HCSG results under full load condition. HCSG operation parameters

Operation parameters

TH-OTSG calculated

Error/%

Heat flux/MW Primary coolant outlet temperature/K Primary coolant pressure drop/kPa Steam temperature/K Secondary side pressure drop/kPa

125.0 565.15 72.0 590.15 296.0

124.9 565.19 70.0 589.82 304.4

0.08 0.007 2.778 0.056 2.84

mental value of 5.15% shows that the prediction procedure can respond the request of prediction. The two-phase friction coefficient is calculated by Eq. (28).

    Dp Dp ¼ U2l L tp L l

ð28Þ

After considering spiral structure characteristic correction, fullliquid conversion coefficient is calculated as follows:



U2l ¼ 0:13U2lM De0:15 l

qm ql

0:37

where Del denotes the liquid Dean number, which is calculated as follows:

sffiffiffiffiffiffi sffiffiffiffiffiffi di Gm ð1  xÞdi di Del ¼ Rel ¼ Dc ll Dc

Fig. 1. Wall heat transfer flow chart.

2.3.3. Spiral pipe outside flow friction factor The HCSG primary side frictional resistance coefficient is estimated using a formula based on single-phase water flows through

56

G. Xia et al. / Annals of Nuclear Energy 109 (2017) 52–60

the spiral coiled tube bundle (Yin et al., 2006), which is calculated in Eq. (29).

DP ¼ ða=do  1Þ

0:5

Re0:2 HeðuÞqv 2 =b

ð29Þ

where H denotes the height of the spiral coiled tube; eð/Þ indicate scour angle correction factor. 2.4. Model implementation The governing equations are discretized by the fully conservative implicit finite difference and second-order upwind scheme on the staggered grid. For superheated steam regions, the nonlinear equations are simplified into nonlinear equation about density and solved by the secant method. For two-phase regions, the governing equations are simplified into nonlinear equations about pressure, void fraction and enthalpy, and solved by the modified Newton method. The dynamic simulation flow chart is shown in Fig. 2. 3. Results and discussion 3.1. Steady-state characteristics The IRIS HCSG is a helical coil heat exchanger, primary coolant flows on the heat transfer tube surface and secondary side feedwater flows in the helically coiled tubes. After a countercurrent heat transfer, the single-phase water is heated to superheated steam by using primary coolant. The major design parameters of an IRIS steam generator are shown in Table 2. The mathematical model of the IRIS HCSG was established using the TH-HCSG program. And the RELAP5 code was then utilized to verify the accuracy of the model in a steady as well as a transient state. The RELAP5/MOD3 code is a best-estimate system analysis code based on two-fluid model for two-phase flows (INEL, 1998). The RELAP5 nodalization of the HCSG is shown in Fig. 3. The secondary side of the HCSG is simplified as an inclined pipe, with the angle of its inclination being the same as that of the helical coil tube. The temperature of the secondary side inlet is determined by a time-dependent volume (210TDV), the steam pressure is

Start

imposed by a time-dependent volume (218TDV) and the inlet feedwater flow is indicated using a time-dependent junction (211TDJ). The primary coolant inlet temperature is fixed using a timedependent volume (108TDV), the outlet pressure is imposed by a time-dependent volume (118TDV), and the inlet coolant flow is specified using a time-dependent junction (109TDJ). The heat transfer between the primary side (114A) and the secondary side (214P) is realized through the heat structure (1214H). The results of the calculation under full load conditions are compared not only with the RELAP5 codes (RELAP5-HEU), but also with relevant literature (RELAP5-Italy) (Cioncolini et al., 2003). The temperature of the primary coolant decreases with the decreasing height of the heat transfer tube, and the temperature distribution calculated by three programs accords with it, as shown in Fig. 4a. The secondary side of heat transfer tube is suffering from a strong boiling and phase transition phenomenon. In the singlephase water region, the temperature of the fluid rises in the process of upward flow with the heat flux being reduced as the temperature difference between the heat transfer tubes decreases. When the system enters the subcooled boiling region, the heat transfer model converts to nucleate boiling and the heat flux increases as the intensity of the heat transfer increases. When the temperature of the fluid in the secondary side reaches the saturation state, the heat transfer model turns into the saturated boiling heat transfer region. In this region, the heat flux increases rapidly with the increasing void fraction, the temperature change of the primary coolant becomes more obvious, the secondary saturation temperature decreases slightly due to the drop in pressure and the temperature of the heat transfer tube wall increases slowly with the increasing tube height, as shown in Fig. 4b. After reaching its dry-out point, the heat transfer model changes to the liquid deficient heat transfer region. The temperature of the wall and the temperature distribution of the fluid in the secondary side calculated by the TH-HCSG differ from those in the RELAP5 codes, as shown in Fig. 4c. With respect to the calculation of the RELAP5 codes, the heat transfer of the liquid deficient region is divided into three parts: heat conduction, heat convection and radiation heat transfer, taking into consideration the effects of thermal imbalance in the heat transfer process. The TH-OTSG calculation in this area is based on the effects of thermal equilibrium derived from empirical formula involving heat transfer, which ignores the overheating of the steam. This means that the temperature of the fluid in this region is still in a state of saturation, but that the temperature of the wall and the heat flux will change

Input initial conditions and geometrical parameters

Program initionalization

Assume primary coolant temperature distribution Tp and heat transfer coefficient distribution h p

108TDV 109TDJ 110S

218TDV 217J

112B

216S 215J

Calculate the conservative equation of srcondary side nodes

1 1 4 A

Calculate the conservative equation of primary side nodes no

Accuracy requirement

Fig. 2. Dynamic simulation flow chart.

2 1 4

P

213J

115J

yes Next time step calculation

121 4H

Under relaxation treatment to Tp and hp

116S 117J 118TDV

212S 211TDJ 210TDV

Fig. 3. RELAP5 nodalization of HCSG.

G. Xia et al. / Annals of Nuclear Energy 109 (2017) 52–60

610

Temperature/ K

600 590 580 570 RELAP5-Italy TH-OTSG RELAP5-HEU

560 550 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

a. Primary side Temperature. 610 600

Temperature/ K

590 580 570 560 550

RELAP5-Italy TH-OTSG RELAP5-HEU

540 530 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

57

Under full load conditions, the steady-state results calculated by the TH-HCSG program accord well with the RELAP5-HEU results, and the nonlinear distribution characteristics of temperature, heat flux and other parameters along the tube height show that the development process is correct. The results calculated by the TH-HCSG accord well with operation parameters, as is shown in Table 3. The maximal deviation of the calculated value is 2.84% (secondary side pressure drop), whereas the minimum deviation is only 0.007% (primary coolant outlet temperature). The temperature distribution along the heat transfer tube height at 80%FP, 60%FP, 40%FP and 20%FP conditions are shown in Fig. 5a–d. From the figures, we can see that the lengths of the subcooled region and two-phase region are shortened, while the region containing the superheated steam is lengthened as the load is reduced. The temperature distribution through the heat transfer tube obtained by the TH-HCSG program accords with the RELAP5 results. Because the thermal equilibrium model is used and the temperature in the liquid deficient region is still in a state of saturation, there is no match in the superheated region between the developed TH-HCSG code and the existing RELPA5 code. However, this does not affect the temperature distribution of the primary coolant and the outlet temperature of the steam, which are the most important parameters. A comparison of the results shows that the TH-HCSG program is able to predict steady-state operating characteristics under different load conditions.

b. Heat transfer tube wall temperature. 3.2. Transient characteristics

600

The dynamic behavior of the system was thoroughly studied using a 10% step change in the main representative boundary parameters, such as the feedwater flow, primary coolant flow, feedwater enthalpy, primary coolant inlet enthalpy and steam pressure. These parameters changed rapidly by 10% after the occurrence of a time step. The corresponding simulation results were compared with the RELAP5 codes. It was found that the results of the TH-HCSG program accorded with these codes.

Temperature/ K

580 560 540 520 RELAP5-Italy TH-OTSG RELAP5-HEU

500 480 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

c. Secondary side temperature. 300

RELAP5-Italy TH-OTSG RELAP5-HEU

Heat flux/ (kW/m2)

250 200 150 100 50 0 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

d. Thermal flux through the tube wall. Fig. 4. A comparison of the system parameters of HCSG in nominal conditions.

rapidly as the heat transfer coefficient is significantly reduced in this region. In the superheated steam region, the temperature of the steam increases as the height of the heat transfer tube increases, whereas the heat flux decreases with the increase in the temperature of the steam, as is shown in Fig. 4d. If we compare the RELAP5-Italy and RELAP5-HEU, we can see that the system parameters predicted by the RELAP5-HEU code agree with the data in RELAP5-Italy, proving that the RELAP5-HEU can be used to analyze the characteristics of HCSG dynamics.

3.2.1. Step changes to feedwater flow The variation in the parameters of the main system when a step change in the feedwater flow was applied is shown in Fig. 6. The feedwater flow decreases abruptly to 90% (56.56 kg/s) and remains constant within 200 s, then returns abruptly to full load status (62.85 kg/s), as shown in Fig. 6a. When they run at a steady state, the feedwater flow and steam flow are exactly the same. But, when the feedwater flow decreases, the length of the superheated steam region in the secondary side of the HCSG is greatly increased and the water capacity in the secondary side of the HCSG decreases, so that the change in the steam flow lags the feedwater flow in order to release excess room in which to hold water. When the feedwater flow increases, the steam flow is less than the feedwater flow during the transient process. The abrupt decrease in the feedwater flow causes the temperature of the steam to increase, but the temperature of the primary coolant outlet increases as the heat transfer decreases, as shown in Fig. 6b. When the feedwater flow increases at 250 s, both the outlet temperature of the primary coolant and the temperature of the steam in the secondary side decrease, these parameters being gradually restored to a full load operational value after a 100 s adjustment time. 3.2.2. Step changes in primary coolant flow The primary coolant flow remains constant at 589.0 kg/s for 050 s. Up to 50 s, the primary coolant flow abruptly decreases to 530.1 kg/s and maintains this value. At 250 s the primary coolant flow is increased to 589.0 kg/s. A comparison of the main system parameters is shown in Fig. 7.

G. Xia et al. / Annals of Nuclear Energy 109 (2017) 52–60

620

64

600

62

580

60

Mass flow rate/ (kg/s)

Temperature/ K

58

560 540 TH-OTSG (primary side) TH-OTSG (secondary side) RELAP5-HEU (primary side) RELAP5-HEU (secondary side)

520 500 480 0

4

8 12 16 20 24 Tube position from inlet / m

28

Feedwater flow TH-HCSG RELAP5-HEU

58 56 64 62 60

Steam flow TH-HCSG RELAP5-HEU

32

58

a. 80% FP

56 0

620

600 595

540 TH-OTSG (primary side) TH-OTSG (secondary side) RELAP5-HEU (primary side) RELAP5-HEU (secondary side)

520

500

590

480 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

b. 60% FP

Temperature/ K

400

Steam temperature TH-HCSG RELAP5-HEU

560

500

585 570

Primary coolant outlet TH-HCSG RELAP5-HEU

568

620

566

600

564 0

580

100

200

300

400

500

Time/ s

560

b. Steam temperature and primary coolant outlet temperature.

540 TH-OTSG (primary side) TH-OTSG (secondary side) RELAP5-HEU (primary side) RELAP5-HEU (secondary side)

520 500 480 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

c. 40% FP 620 600

Temperature/ K

200 300 Time/ s

a. Feedwater flow and steam flow.

580

Temperature/ K

Temperature/ K

600

100

580 560

Fig. 6. Change in the main system parameters due to a 10% step change in feedwater flow.

so that both the convective heat transfer coefficient of the primary side and the average temperature of the primary coolant are reduced. Initially, the temperature of the steam increases slightly as the steam flow decreases, but an insufficient heat exchange causes a gradual reduction in the temperature of the steam to 561 K. At 250 s, the temperature of the primary coolant outlet and the temperature of the steam both increase as the primary coolant flow increases and the system parameters are gradually restored to full load value, as is shown in Fig. 7b.

540 TH-OTSG (primary side) TH-OTSG (secondary side) RELAP5-HEU (primary side) RELAP5-HEU (secondary side)

520 500 480 0

4

8 12 16 20 24 Tube position from inlet / m

28

32

d. 20% FP Fig. 5. Temperature distribution with respect to heat transfer tube height under different load conditions.

As shown in Fig. 7a, when the mass flow rate of the primary coolant is reduced, the steam production suddenly decreases, as some of the water is used to compensate for the increase in water capacity in the secondary side of the HCSG. When the primary coolant flow increases to 589.0 kg/s, the steam generator needs to create additional capacity for the water, resulting in a rapid rise in steam production at an early stage and then reaching a steady state within 50 s. The temperature in the primary coolant outlet decreases as the coolant flow decreases, while the feedwater flow remains constant,

3.2.3. Step changes in feedwater enthalpy A change of enthalpy is directly related to temperature. As is shown in Fig. 8a, the feedwater temperature increases suddenly from 497.0 K to 517.6 K to accord with a step increase in feedwater enthalpy. At 250 s, the feedwater temperature step decreases to 497.0 K. The single-phase water capacity in the secondary side of the HCSG is reduced as the feedwater temperature increases, so the steam flow increases rapidly, becoming stable after about 30 s. A sudden increase in steam flow causes the temperature of the steam to decrease suddenly, as shown in Fig. 8b. When the temperature of the feedwater decreases, the production of steam decreases rapidly as the water is used to compensate for the increase in water capacity. The temperature of the steam suddenly increases and is gradually restored to full load value. The initial step change in feedwater temperature causes a sudden increase in the temperature of the primary coolant outlet, and the fluctuation in steam flow leads to a slight shock in the temperature of the primary coolant outlet, but the parameters are gradually stabilized within 50 s. At 250 s, the primary coolant outlet temperature gradually returns to full load value with the increase

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3.2.5. Step changes in steam pressure As is shown in Fig. 10a, the steam pressure step increases from 5.8 MPa to 6.38 MPa and then remains constant. The heat transfer is reduced as the saturation temperature of the second loop increases. The temperature of the primary coolant outlet is thus increased and the temperature of the steam is decreased. Since

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3.2.4. Step changes in primary coolant inlet enthalpy Owing to the enthalpy variation, the temperature of the primary coolant inlet step decreases to 576.45 K and returns to full load conditions (601.55 K) after running for 200 s, as is shown in Fig. 9a. The temperature of the primary coolant outlet decreases rapidly as the temperature of the primary coolant inlet decreases, resulting in a decrease in the average temperature of the primary coolant. The difference in the average temperature with regard to the heat transfer between the heat transfer tubes is reduced. The temperature of the steam is reduced as the temperature of the primary coolant inlet decreases, as is shown in Fig. 9b. When the temperature of the primary coolant decreases, the water capacity in the secondary side of the steam generator is increased as the length of the single-phase water region increases. The steam flow thus decreases rapidly during the initial state. When the temperature of the primary coolant inlet increases, the steam flow increases rapidly and is able gradually to resume its stable state, as is shown in Fig. 9b.

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in the temperature of the feedwater, as shown in Fig. 8a. During this transient process, the change in the temperature of the primary coolant outlet calculated by the RELAP5 codes is faster than if the TH-HCSG program is used, although there is a better match as far as the secondary parameters are concerned.

Fig. 8. Main system parameter change due to a 10% step change in feedwater enthalpy.

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Fig. 7. Main system parameter changes due to a 10% step change in primary coolant flow.

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References

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(2) The system dynamic behavior was thoroughly studied with regard to a 10% step change in the main representative boundary parameters, with the results of the corresponding simulation agreeing with the RELAP5 codes. (3) When the feedwater flow decreased abruptly, the length of the single-phase water region in the secondary side of the HCSG was significantly reduced and the water capacity in the secondary side of the HCSG decreased so that the change to the steam flow lagged the feedwater flow in order to create excess room for water. When the feedwater flow increased, the steam flow was less than the feedwater flow during the transient process. (4) Step changes in the primary coolant flow, feedwater enthalpy, primary coolant inlet enthalpy, and the step increase in steam pressure changed the characteristics of the operation of the steam generator, so that, in the early stages, there was a profound shock to the steam production, which then ultimately reached a steady state.

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b. Steam temperature and primary coolant temperature. Fig. 10. Change in the main system parameters due to a 10% step change in the steam pressure.

the length of the single-phase water region in the secondary side of the HCSG is increased, the steam flow is rapidly reduced at the start so as to compensate for changes to the water capacity in the secondary side of the steam generator, as shown in Fig. 10b. At 250 s, the pressure step decreases to 5.8 MPa and remains constant. The steam flow increases rapidly and then resumes a steady state. The temperature of the primary coolant outlet decreases, while the temperature of the steam increases. However, the steam flow increases rapidly due to the decreasing steam pressure, with the two-phase fluid flowing from the steam generator in this transient process. 4. Conclusions A mathematical model relating to HCSG has been established in this paper and evaluated according to the data of the IRIS HCSG with regard both to steady and transient states. The influence of the main boundary parameters on the characteristics of an HCSG operation have also been studied. The results of our analyses and their conclusions can be briefly summarized as follows: (1) The numerical model was programmed based on a onedimensional four-equation drift-flux model, with the resulting comparison made in accordance with IRIS HCSG data in a steady state showing that the results of the TH-HCSG program accord well with both design parameters and literature references.

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