- Email: [email protected]
Flow instability analysis of natural circulation under ERVC condition for SMR
Progress in Nuclear Energy 117 (2019) 103063
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Flow instability analysis of natural circulation under ERVC condition for SMR
T
Nan Jiang, Minjun Peng, Tenglong Cong∗ Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin, 150001, China
A R T I C LE I N FO
A B S T R A C T
Keywords: IVR-ERVC Natural circulation Density wave instability RELAP5
In this work, the internal natural circulation flow of ERVC system in SMR is calculated by the thermal-hydraulic code RELAP5. Both the transient characteristics and the flow instability are analyzed in detail to reveal the flow mechanism. Firstly, to verify the applicability of RELAP5 models, multiple cases of steady-state natural circulation with low heating power are simulated by comparing with the REPEC experiment. Next, a sliced model of ERVC loop is built to obtain the transient phenomena of natural circulation. As the circulation loop has no cold source, the inlet temperature of the heating section will keep rising to transform the flow patterns into stableoscillating-stable in turns. During this transition, the flow is dominated by the subcooled boiling of heating section, and the mass flux is about 60–160 kg/m2·s. Based on the features of flow oscillation, the unstable flow patterns can be further divided into low-frequency and high-frequency oscillations. Both of them belong to the density wave oscillation, and their trajectory diagrams can present the attributes of the limit cycle. Finally, in the plane formed with the inlet subcooling (horizontal axis) and heating power (vertical axis), the boundaries of flow instability are divided. The instability domain change with the effects of heating power, back pressure, inlet resistance coefficient, and rising section height is discussed. The results indicate that increasing the back pressure will compress the instability domain. Reducing the inlet resistance coefficient will shift the instability boundaries towards the direction of power increase. When lengthening the height of the rising section, the flow can be gradually dominated by the flashing with the decrease of inlet subcooling, which may also introduce another instability.
1. Introduction The initial researches of In-Vessel melt Retention (IVR) mainly focus on the heat transfer characteristics of the molten pool, the external cooling of Reactor Pressure Vessel (RPV) is only considered as a boundary condition. However, the results of ULPU-IV&V (Theofanous et al., 2002; Dinh et al., 2003) experiment indicate that the natural circulation flow in RPV insulation will significantly influence the Critical Heat Flux (CHF) of an outside wall. And the driving force of natural circulation is very sensitive to the external conditions, such as the structure parameters of the flow channel or the internal heat of the molten pool. Thus, the natural circulation in External Reactor Vessel Cooling (ERVC) loop is gradually separated from the IVR to be studied separately. The current studies of ERVC flow can be divided into three aspects by the thermal-hydraulic mechanism: 1) Studies related to the CHF enhancement, including the observation of flow patterns under CHF (Lu et al., 2017), the prediction of mass flux for CHF (Yang and Cheung,
∗
2005) and the increase of convective heat transfer coefficient by surface structure (Chang et al., 2017). 2) Studies about the steady-state flow characteristics, such as the pressure drop distribution of circulation loop (Zhao et al., 2013), the calculation of vapor quality and drift velocity (Kim et al., 2008a), the effects of geometrical/thermal parameters on circulation ability (Kim et al., 2008b). 3) Studies for the flow instability, involving the dynamic instability of density wave caused by boiling or flashing (Zhang et al., 2018), and the static instability due to flow drift (Chu et al., 1997). However, compared with the two preceding aspects, existing studies that focus on the flow instability of natural circulation in ERVC system are fewer, especially for the dynamic instability. Flow instability refers to the dynamic instability (the flow oscillation with constant/variable amplitude caused by the changes in void fraction or buoyancy), or the static instability (flow excursion). All of the natural circulation systems should be designed to avoid any flow instability. However, the vapor-liquid phase transitions in natural circulation will often induce various unstable flows, since the ERVC
Corresponding author. E-mail address: [email protected] (T. Cong).
https://doi.org/10.1016/j.pnucene.2019.103063 Received 10 December 2018; Received in revised form 12 April 2019; Accepted 13 May 2019 Available online 20 May 2019 0149-1970/ © 2019 Elsevier Ltd. All rights reserved.
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
system operates in low-pressure. Besides, these flow instabilities will not only cause the mechanical shock on insulation structure, but also create the local heat transfer deterioration on lower head, and even reduce CHF to make boiling crisis happen in advance (Song et al., 2005). Song (Song et al., 2002) uses RELAP5 code to simulate the transient characteristics of two-phase natural circulation flow in ERVC loop. With the uniform heating of 600 kW/m2, the oscillation of density wave caused by the saturated boiling in the heating section is observed. Besides, the calculation results of multiple conditions all indicate that the thermal margin of CHF on the lower head will decline under the disturbance of flow instability. But, this flow oscillation can be restrained by increasing the inlet area of the heating section or decreasing the resistance coefficient at the inlet. This study assesses the trends of flow oscillation development, but the regularity of instability domain or the essential reason of unstable flow are not analyzed, and the quantitative results of calculation also lack experimental verification. Therefore, it can only provide a qualitative reference for the trend analysis of dynamic instability. Rouge (Rouge and Seiler, 1994) predicts the static instability domain of flow drift in ERVC loop with FLICA code. The flow characteristics of a vertical channel under the low pressure (1 bar) and large hydraulic diameter (15 cm) are calculated, then the characteristic curve of pressure drop - flow rate is obtained by adjusting various heating powers. The unstable flow domain of flow drift is finally separated from the negative slope zone of the characteristic curve, and the calculation results are verified with the SULTAN experiment (Rouge, 1997). However, to get the specified mass flow, the forced circulations are adopted both in the above calculation and analysis. Thus, the deviations will be introduced into the results comparing with the actual ERVC flow, since the driving force of forced circulation will be constant by the external settings, while the driving force of natural circulation will show mutability under the coupling of various factors. Therefore, this study is only preferable for the optimization design of loop resistance but is inadequate for the real instability mechanism of natural circulation. Ha (Ha et al., 2012) conducts a 1/2 scaled experiment (HERMESHALF) to evaluate the flow status of natural circulation in APR1400's ERVC. Considering the test section of the lower head has a large size with 3D-spherical shape, it will be challenging and dangerous to establish the natural circulation with a high void fraction by the direct heating of high heat flux. Hence, a non-heating method of air injection is adapted to generate the two-phase mixed flow. It is observed in the experiment that the bubbles will accumulate periodically at the narrowest part of insulation channel to cause a local reflow. When the void fraction in loop rises to a high level, this reflow can even result in a strong periodic flow oscillation at the inlet. But, the fluctuation does not be explicitly classified by the instability mechanism in this study, since the bubble annihilation in non-heating condition should be different from that in heating condition. The researchers only recommend installing a gas groove to increase the smoothness of gas-phase flow, and to avoid this instability. It can be summarized from the existing studies that various flow instabilities can occur in the natural circulation of ERVC system. The causes and behaviors of variability can also be various under the influences of loop structure and thermal condition. However, the instability mechanism of ERVC flow is still studied insufficiently by the limitation of experimental factors. Moreover, the current studies of ERVC flow mainly focus on high-power reactors, while the studies for small-power reactors (lower than 300 MW) are fewer. The flow characteristics of ERVC's natural circulation should be significantly different for the large and small reactors, and these differences can be embodied in the following aspects: 1) Different Thermal Conditions: With the heating of a high-power molten pool, the natural circulation will be dominant by the saturation boiling of the heating section. For this condition, the flow rate and vapor quality should be
both higher, so that the second type of dynamic instability can be easily induced into the loop by friction (Goswami and Paruya, 2011). Nevertheless, with the heating of a low-power molten pool, the natural circulation will be dominant by the subcooled boiling of heating section, or the flashing of the rising part. In this condition, the vapor quality should be low. The first type of dynamic instability can be potentially induced into the loop by gravity (Prasad et al., 2007). 2) Different Loop Structures: The design of a small reactor is usually required to be compact that the loop structure of ERVC will differ from that of a large reactor. Specifically, in terms of the rising section height of the circulation loop, and the setting mode of cold source, etc. That will also affect the pressure drop distribution and transient flow of ERVC. From the above, it can be considered that, the natural circulation characteristic of ERVC for a small-power reactor and its possible flow instability are both unique that should be considered independently, and to be studied further. Then, this work aims to solve the insufficiency, and will focus on the transient characteristics of ERVC flow and the mechanism of flow instability, under the IVR thermal load of SMR. Firstly, multiple cases of steady-state natural circulation with low heating power from the REPEC experiment are simulated by the thermal-hydraulic code RELAP5. The outlet temperature and circulation flow rate are selected as indexes to verify the model applicability for the natural circulation which dominated by subcooled boiling. And the ranges of mass flux and heat flux are also estimated. Next, a sliced model of ERVC system for SMR is established with RELAP5 by simplifying the loop into the heating section, rising section, and downcomer. The transient flow of natural circulation is calculated, and the high/low subcooling boundaries of flow instability are obtained. Based on the oscillating patterns of mass flux, exit temperature and void fraction, the mechanism of flow instability and the development of limit cycles are both explained. Finally, the effects of the thermal boundary (back pressure, heating power) and loop structure (inlet resistance coefficient, rising section height) on the flow instability are quantitatively discussed by parametric analysis. Specifically, in the plane where the inlet temperature is horizontal axis, the characteristic of transient flow and the shift of the instability domain are compared.
2
Nomenclature CHF ERVC IVR RPV SMR Nsub Npch
Critical heat flux External reactor vessel cooling In-vessel melt retention Reactor pressure vessel Small modular reactor Subcooling number Phase change number
Lh τi F S hmac hmic Re x e, B hf , in
Length of heating section Transit time Reynolds number factor Boiling correction factor Convection heat transfer coefficient for flow Convection heat transfer coefficient for boiling Reynolds number Thermodynamic vapor quality vapor starting point Saturated water enthalpy at the inlet
hin hfg, in
Fluid enthalpy at inlet Latent heat of vaporization at the inlet
Q G νg, in
Heating power Mass flow-rate of natural circulation Saturated steam's specific volume at the inlet
νf , in
Saturated water's specific volume at the inlet
Lr μave De xm χe Pe Pr α
Length of rising section Average velocity of natural circulation Characteristic diameter of the channel Real mass quality of vapor Thermodynamic vapor quality at outlet Peclet number Prandtl number Void fraction
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 1. aREPEC experiment facility.(b). RELAP5 nodalization of REPEC experiment.
2. Experiment validation
be seen from the comparison results (Fig. 2a–d) that, in all cases, the temperature errors are within 2% and the flow errors are within 20%. The fluctuation range of mass flux in the simulation is about 60–160 kg/m2·s, but the mass flux range in the validation only gets 95–132 kg/m2·s. A part of simulation conditions are out of the range validated in REPEC experiment. Besides, the actual flow in ERVC will also be affected by the geometrical or thermal factors. But the effects of backpressure or loop height in this simulation cannot be verified. Thus, some errors may exist in the quantitative calculation results of RELAP5. However, the point of this work is to given the development trend of flow instability under the influence of various parameters, which prefers to be a qualitative analysis. For this trend analysis, this validation analysis can still be useful.
In this section, the RELAP5 code is used to simulate multiple groups of steady-state natural circulation in the REPEC facility (Li et al., 2013; Li et al., 2012; LI et al., 2011). REPEC is an experiment for ERVC flow characteristics. The outlet temperature of heating section and the mass flux of circulation are selected as the indexes; then the simulation results are compared with the experimental data to verify the model applicability of RELAP5 for calculating ERVC flow. Furthermore, the rationality of calculation error is also evaluated. REPEC is a large-scaled slice experiment with direct heating, which takes the CPR1000 reactor as a prototype. The experiment facility and its RELAP5 (Ransom et al., 2001) model are shown in Fig. 1a and b. Under the IVR thermal load of SMR, the surface heat flux on the lower head should be low. Thus, in this work, only the experimental cases with low heating power are chosen for verifying the natural circulation, which dominated by subcooled boiling. The specific heat flux distribution in REPCE (low heating condition) is presented in Fig. 3c, and the heat flux of SMR's IVR is shown in Fig. 3d. With the contrastive analysis, although their distribution is not the same, the total heating power and the peak heat flux are similar. Considering there is no particular experiment for the natural circulation of SMR's ERVC, the present low-heating conditions can be a good choice. Besides, the flow patterns of these cases are consistent with that of SMR. Thus the verification can be reliable. The detail conditions of verification cases are presented in Table 1. The heating power, inlet area of the heating section and inlet water temperature, are adjusted respectively to change the flow status. It can
3. System and model 3.1. ERVC loop In this section, RELAP5 code is used to simulate the transient flow of natural circulation in ERVC system after the severe accident of SMR. (The design features of SMR (Zhao et al., 2018) are different from that of general large power plant (Wang et al., 2012)). Fig. 3a shows the structure of ERVC, which is mainly composed of containment pool, RPV insulation and inlet/outlet valves. The circulation loop connects with the containment atmosphere and operates at low pressure. Before the molten material collapses into the lower head, the containment water will enter into insulation channel from the bottom inlet, then be heated to form the two-phase mixture. The density difference can drive the
Table 1 Flow cases of REPEC experiment for validation. Cases
Parameter description
Heating Power/kW
Inlet area/m2
Inlet temperature/K
Simulation mass flux/kg/m2·s
Simulation outlet temperature/K
1–1 1–2 1–3 1–4 2–1 2–2 2–3 3–1 3–2 3–3 3–4
Adjusting heating power
20% 30% 40% 50% 30% 30% 30% 20% 20% 348.15 368.15
0.01767 0.01767 0.01767 0.01767 0.00530 (0.3) 0.00884 (0.5) 0.01767 (1.0) 0.01767 0.01767 105.7 102.4
338.15 338.15 338.15 338.15 328.15 328.15 328.15 328.15 338.15 352.8 373.0
102.8 110.0 118.2 126.1 90.0 102.9 109.9 97.3 102.8
343.5 344.4 345.1 346.2 336.6 335.7 334.8 334.4 343.6
Adjusting inlet area
20% 20%
Adjusting inlet temperature 0.01767 0.01767
3
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 2. Comparison of simulation and experiment. a. Adjusting heating power. b. Adjusting inlet area. c. Adjusting inlet temperature. d. Error analysis.
fluid to establish an upward flow of natural circulation. The vapor phase will be vented to the containment atmosphere, and the liquid phase will return to the containment pool to continue circulation. The inner heat of the molten pool can be transferred to the fluid in insulation channel, and finally released into the atmosphere as steam. The RELAP5 nodalization of ERVC's 2D-slice model is shown in Fig. 3b. The whole loop is simplified into the heating section, rising section, and downcomer. Especially, the effects of the complex structure will be discussed by parametric analyses. The main structure parameters are listed in Table 2. The heating of lower head is set as a constant heat flux boundary to the flow, and the angle distribution of heat flux (Fig. 3d) is adopted from the previous SMR's safety analysis (Jiang et al., 2019).
Then, the real mass quality of vapor ( x m ) and the void fraction (α ) can be calculated.
3.2. Constitutive models
xm =
For the constitutive models in RELAP5 (Ransom et al., 2001), the Chen model is used to calculate the heat transfer of flow-boiling convection, and the Saha-Zuber model is used to calculate the non-equilibrium void fraction for pressure drop. Chen model adopts the correction factors between flow and boiling, to define the total heat transfer coefficient of flow-boiling convection (htot ) .
α=
htot = Fhmac + Shmic
Saha-Zuber model introduces a concept of a vapor starting point to calculate the non-equilibrium void fraction (α). First, the thermodynamic vapor quality of vapor starting point ( x e, B ) is calculated.
x e, B = −0.0022
x e, B = −154
Pe > 70000
(4)
(5)
x e − x e, B exp(x e / x e, B − 1) 1 − x e, B exp (x e / x e, B − 1)
(6)
xm
⎢ ⎣
+
ρg
⎤ ⎥+
ρf ⎥
⎥ ⎦
ρg Wgm G
(7)
For the conservation equations, RELAP5 uses the one-dimensional two-fluid model with six equations, involving the mass, energy and momentum equations for the gas and liquid phases. The boundary conditions in ERVC model is simulated by 202Volmue (Fig. 3b), the backpressure is given by 0.101 MPa, and the temperature is provided by 340.0 K. For the flow rate calculation of natural circulation, firstly, the vapor mass quality can be determined by the governing equations of energy. Secondly, the pressure drop can be calculated to get the flow rate.
(1)
(2)
When calculating the convection heat transfer coefficient for boiling (hmic ) , 0.79 0.45 0.49 0.25 ⎛ k f cpf ρf g ⎞ hmic = 0.00122 ⎜ 0.25 0.29 0.24 0.24 ⎟ ΔTw0.24 ΔP 0.75 σ μf hfg ρg ⎝ ⎠
q′ ′ Gi fg
Pe ≤ 70000
kf i fg
⎡ xm ⎛⎜ρf − ρg ⎟⎞ ⎠ 1.13 ⎢ ⎝ ρ ⎢ f
When calculating the convection heat transfer coefficient for flow (hmac ) ,
hmac = 0.023Re 0.8Pr 0.4kf / De
cp, f q′ ′De
3.3. Nodalization analysis (3)
Considering the heating section and the rising section will play the 4
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 3. a. Structure of ERVC system in SMR. b. RELAP5 nodalization of ERVC loop. c. Heat flux distribution in REPEC experiment (Low heating conditions) d. Heat flux boundary of heating section (heat flux distribution on lower head) d.Nodalization analysis for stable and oscillating flow.
number is increased from N2 to N3, the change of flow oscillation is not apparent. Therefore, the present N2 nodalization (indicated in Fig. 3b) can be reasonable for the flow instability. Given that the REPEC experiment does not publish the data of flow instability, the oscillating flow in this simulation cannot be quantitatively verified. Some errors may exist in the dynamic results. But, the point of this work is to give the development trend of flow instability
main roles in this open natural circulation, their optimum node numbers are discussed here by sensitivity calculation. The mass flux of natural circulation (which is the most representative and sensitive parameter) is selected as the evaluation index. Four different nodalization cases are listed in Table 3. Their results of stable and oscillating flow are presented in Fig. 3d. In the steady state calculation, the effect of nodalization is slight. In the dynamic calculation, when the node 5
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
low pressure (0.10 MPa) and high heat flux (105W/m2 magnitude) provide the main density difference for the driving force of natural circulation, and the subcooled boiling in the heating section dominates the flow. With the rising of inlet temperature, the increase of average void fraction can also enhance the natural circulation driving force, then to make the flow rate presents a trend of continuous rise. The fluctuation range of mass flux is about 60–160 kg/m2·s, which is roughly consistent with the range of experimental verification. When the inlet temperature reaches about 354 K, the natural circulation cannot maintain a stable flow. The mass flux, void fraction, and outlet temperature of the heating section all changed into the regular oscillations. However, the inlet temperature of the heating section is not affected by the flow instability, since the outlet of the rising section directly connects with the containment atmosphere to reduce the pressure feedback from the outlet to inlet. That is a feature of ERVC flow in SMR. When the inlet temperature rises about 361 K, the oscillation becomes weak and gradually disappears, then the flow returns into a stable state. The dynamic flow instability in natural circulation can be considered as a mismatch between driving force and flow resistance. 1) In the initial condition, the driving force matches the flow resistance perfectly and maintains the flow stable. 2) When the vapor quality in the circulation loop is meager, a small increase of vapor quality will have little effect on the flow resistance, but can significantly raise the void fraction. Then, the fluid density will be changed to enhance the driving force. Hence, when the inlet temperature begins to increase, the void fraction will increase, and the growth of driving force will firstly exceed that of flow resistance. The flow cannot stay in a stable state and starts to oscillate. 3) Given the phase differences of oscillations exist among the void fraction, temperature and mass flux, the oscillations will occur repeatedly. 4) When the vapor quality continuously increases to a certain extent by heating, the effect of vapor quality on the driving force will become lighter, but its enhancement on the friction and acceleration pressure drop can become more apparent. Thus, raising the inlet temperature equals to accelerate the increase of flow resistance, and to rematch the flow resistance with the driving force. Then, the flow recovers stability. Considering there is a one-to-one correspondence between the inlet temperature and outlet vapor quality, it can be considered that the flow oscillation will occur within a certain range of inlet temperature.
Table 2 Structure parameters of ERVC system. Item
Parameter
Containment pressure Initial temperature of containment water Flow area of downcomer (slice) Flow area of insulation channel (slice) Height of rising section Height of rising section (lower head) Width of heating section Total heating power Peak heat flux
0.10–0.40 MPa 350.0 K 2.123 m2 0.018385 m2 0.90 m 0.738 m 0.1355 m 60.63–108.74 kW 0.1232–0.4630 MW/m2
Table 3 Nodalization cases for sensitivity analyses. Nodalization cases
Node number of heating section
Node number of rising section
N1 N2 N3 N4
7 14 21 28
5 10 15 20
under the influence of various parameters, which prefers to be a qualitative analysis. For this trend contrast analysis with multiple parameters, these validation and sensitivity analysis can be useful. 4. Transient simulation of ERVC system 4.1. Flow characteristics of natural circulation In this section, RELAP5 code is used to simulate the transient flow of natural circulation in ERVC system after the severe accident of SMR (the design features of SMR (Zhao et al., 2018) are different with that of general large power plant (Wang et al., 2012)). Under a constant power heating, the calculation results of natural circulation transient flow are shown in Fig. 4. Considering the ERVC loop has no cold source, the heat can only be absorbed by the store water in containment. Thus, the inlet temperature of the heating section will gradually rise. But, the temperature rise of the outlet is not apparent as that of the inlet, since the non-negligible vaporization occurs in the heating section. During the whole progression, the outlet temperature of the heating section is still below the local saturation temperature. Besides, the void fraction declines significantly after the fluid enters into the adiabatic rising section. It can be considered that the vapor-liquid phase transition under
4.2. Oscillation patterns After spreading out the oscillations of temperature, flow rate and void fraction in the time axis, it can be found that the oscillating
Fig. 4. Transient characteristics of natural circulation. 6
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 5. a. Low frequency oscillation b. High frequency oscillation c. Comparsion between transit time and oscillation period.
time in the circulation loop. Notably, the ERVC in this work is an open loop that will be different from the general closed natural circulation. Considering the outlet of the rising section is connected to the environment (a constant pressure boundary), the flow oscillation cannot transmit from the outlet of the rising section to the inlet of the heating section. Thus, the transit time (τi ) should only consider the rising and heating sections as follows (Hou et al., 2017):
frequency is gradually accelerated by the rise of inlet temperature, as well as the oscillating amplitude is increased. The unstable flow patterns can be roughly divided into low-frequency (Fig. 5a) and highfrequency (Fig. 5b). The cycle period of low-frequency oscillation is about 9.5s, and that of high-frequency oscillation is about 4.5s. The operating conditions in Fig. 5a are that heating power, backpressure, and inlet temperature are respectively set to 0.0967 MW, 0.101 MPa and 354.32 K. The heating power and backpressure in Fig. 5b are same as that in Fig. 5a, but its inlet temperature of the heating section gets from 359.74 K to 360.43 K. The following explanation can be made for the generation of unstable flows. In the first stage (Fig. 5a), the cold fluid will be heated up when it flows into the heating section, and the fluid temperature will be raised from trough to crest; thus the vaporization should also be intensified to increase the void fraction. Then, the gravity pressure drop of upward flow can be reduced by the decline of average density in the heating section, to improve the flow rate briefly. (For the flow with low void fraction, the gravity pressure drop - ρgh provides the main flow resistance.) But, in the next stage, the above flow improvement can drop the fluid temperature from crest to trough. Hence, the vaporization in the heating section will be weakened, and the void fraction will decline. After the average density is recovered, the gravity pressure drop of upward flow will be increased to raise the flow resistance, and finally to reduce the flow rate into the initial stage. The above two stages can repeatedly occur to form a self-sustained oscillation, and the constant phase differences will be maintained in the crests of temperature, void fraction and flow rate. Therefore, the essence of this instability can be considered as the variations of fluid density, which will be circularly propagated through the flow channel. And this flow phenomenon is caused by the delayed feedback of multiple parameters and is often called as density wave instability. Introducing a variable of transit time (τi ), to identify the density wave instability. This parameter indicates the oscillation transmission
τi = (Lh + Lr )/ uave
(8)
As presented in Fig. 5c, all of the flow states locate near to the double timeline. For the density wave instability (DWI), the oscillation period is approximate twice the transit time. That can prove the flow oscillations in Fig. 5a and b belong to the density wave instability. The period of density wave instability depends on the time that the fluid passes through the loop. Thus, the oscillation frequency should present an acceleration trend with the rise of inlet temperature, since the vaporization can also be intensified to increase the circulation flow velocity. As shown in Fig. 6a and b, the oscillating flow trajectories can be depicted by switching the low and high-frequency oscillations into another plane, which consist of pressure drop and mass flux. (The inlet pressure of the heating section can directly represent the pressure drop of upward flow since the outlet pressure is constant.) It can be seen that all of the trajectories can reveal an irregular structure with a closed ring. The development of limit cycle should be continuous. The six types of limit cycles are just a result of intentional segmentation, to make the cycle figure clearer. This regular phenomenon is a specific attribute of dynamic instability, often called a limit cycle. Its trajectories in phase plane can only demonstrate that the flow system has nonlinear characteristic. One oscillating flow pattern will only correspond to one shape of the limit cycle, as indicated in Fig. 6c. Besides, with the reduction of inlet subcooling, the oscillations can be intensified to expand the limit cycles gradually. 7
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 6. a. Low frequency limit cycles. b. High frequency limit cycles. c. The development of limit cycles.
stability domain, which is conducive to keep the stable flow. Conversely, if the flow condition stays on the low subcooling boundary, reducing heating power or increasing inlet subcooling will make the flow state enter into instability domain, and intensify the oscillation. In order to make the instability evaluation more universal, the instability boundaries are usually plotted in the dimensionless plane which consists of subcooling number (Nsub) and phase change number (Npch), and the mass vapor quality of heat section outlet (Xe line) is used to help demarcate the position of instability domain, as shown in Fig. 7c. Given the natural circulation is induced by subcooled boiling, all of the flow points are distributed below the saturation line, and on the side of negative vapor quality. For the quantitative results, the vapor quality span of instability domain is small, and the unstable flow points locate within the range of −0.00246 ∼ −0.0164. (It is generally recognized that the flow instability can only occur within a certain range of outlet vapor quality (Ruspini et al., 2014).)
5. Parametric analysis of instability In this section, the effects of the typical thermal and structural parameter on the flow instability of natural circulation in ERVC are discussed. Considering the inlet temperature of the heating section will rise after the circulation is started, and to maintain a single variable, the transient flow characteristics under different parameters are compared in the plane where the inlet temperature is set as a horizontal axis. The flow characteristics here involve the variation of mass flux, void fraction, pressure drop, and instability boundary. 5.1. Heating power The influence of heating power on the transient natural circulation flow is shown in Fig. 7a. The circulation ability will be enhanced by increasing the heating power, and this enhancement of mass flux will be more apparent when the inlet temperature of the heating section rises higher. Besides, even the heating power is changed; all of the flow patterns will still be transformed into stable-oscillating-stable in turns with the increase of inlet temperature. In the heating condition of 0.1002 MW, the flow changes from stable to oscillating when the inlet temperature reaches 354.2 K. Thus, this temperature can be regarded as the demarcation point of instability at high supercooling. Similarly, the flow changes from oscillating to stable when the inlet temperature reaches 360.8 K, then this temperature is regarded as the demarcation point of instability at low subcooling. If the demarcation points of variability under different heating power are linked together, the flow instability domain of natural circulation in ERVC system can be obtained, as indicated in Fig. 7b with black points. It can be concluded that the flow instability induced by subcooled boiling will only appear within a certain range of inlet supercooling and heating power. Moreover, with the decline of heating power, the temperature span of instability domain will become narrow and gradually shift towards the direction of lower subcooling. That means if the flow condition stays on the high subcooling boundary, reducing heating power or increasing inlet subcooling will maintain the flow state within the
Nsub =
hf , in − hin νfg, in • hfg, in νf , in
Npch =
νfg, in Q • G hfg, in•νf , in
χe =
hout − hf , out hfg, out
=
(9)
(10) Q G
+ hin − hf , out hfg, out
hfg, in•νf , in ⎡ νfg, in (hf , in − hf , out ) ⎤ = Npch − Nsub + ⎥ hfg, out •νfg, in ⎢ hfg, in•νf , in ⎦ ⎣
(11)
5.2. Containment pressure The containment pressure will determine the back pressure level of natural circulation since the outlet of ERVC loop is directly connected to the containment atmosphere. The influence of back pressure on the transient flow is shown in Fig. 8a. Considering the latent vaporization heat of inlet fluid will be increased by raising the back pressure, when 8
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 7. a. Effect of heating power on transient flow b. Instability domain of natural circulation c. Instability boundary in dimensionless plane.
the fluid at same inlet temperature is heated, the vapor quality at heating section outlet in high-pressure condition should be lower than that of low-pressure condition. Accordingly, the driving force of natural circulation should also be smaller, as well as the flow rate. Even, the mass flux disparity of two-phase flow caused by pressure can get more prominent in the higher inlet temperature. The above phenomena can indicate that, only at higher inlet temperature, the high-pressure flow can produce the same vapor quality or driving force as the low-pressure flow, which is equivalent to delaying the vaporization process. Therefore, the two-phase oscillation will also be postponed to higher inlet temperature. The effect of back pressure on the instability domain is shown in Fig. 8b. The instability domain will be overall compressed by increasing the back pressure. The low subcooling boundary will shift towards the higher subcooling direction, and the upper subcooling boundary will change towards the lower subcooling direction, to improve the flow stability of natural circulation.
5.3. Inlet resistance coefficient of heating section Considering inlet valve will be installed in the ERVC loop that may change the local flow resistance, and the pressure drop of the two-phase section can affect the density variation, the inlet resistance coefficient of heating section is selected as the common parameter for analysis. The influence of inlet resistance on the transient flow is shown in Fig. 9a. The pressure drop of the form loss at heating section inlet will be decreased after reducing the local resistance coefficient. With the same inlet subcooling, the two-phase flow rate in low resistance condition should be higher, since the total flow resistance is reduced. Then, the vaporization in the heating section will be restrained by a cold flow, and the average vapor quality will decline. But, this change in mass flux is not significant, given the form loss pressure drop at inlet only occupies a small part in the total pressure drop. The effect of inlet resistance on the instability domain is shown in Fig. 8b. Reducing the resistance coefficient can enhance flowing and weaken vaporization, which means the flow also needs higher heating power to reach the vapor quality point (Xe) on instability boundary. Thus, the instability boundaries of
Fig. 8. a. Effect of back pressure on transient flow. b. Effect of back pressure on instability domain. 9
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 9. a. Effect of inlet resistance on transient flow b. Effect of inlet resistance on instability domain.
flashing in the rising part. Increasing the height of rising section will increase the pressure difference of rising section to intensify the flashing vaporization. The simultaneous increase of density difference and height difference will significantly enhance the driving force. Thus, as indicated in point B, the flow rate in 1.6 m-case rises higher, G1 < G2.
high and low subcooling will require both shifts towards the direction of higher heating power. If the flow condition stays on the low subcooling boundary, reducing inlet resistance will make the flow state enter into instability domain to break the stable natural circulation. Conversely, if the flow condition stays on the high subcooling boundary, reducing inlet resistance will help the flow state away from instability boundary, and maintain within the stability domain.
6. Conclusion 5.4. Height of rising section
In this work, both the transient characteristics and the flow instability are analyzed in detail to reveal the flow mechanism of natural circulation in ERVC. The main conclusions are obtained as follows:
The influence of the rising section height on the transient flow is shown in Fig. 10. When the rising section height is low (0.8 m), only the flow instability caused by subcooled boiling will occur in the loop, and the oscillation of void fraction comes from the heating section. However, after lengthening the rising section height (1.6 m), the pressure difference between the heating section outlet and rising section outlet should become larger. Then, the vaporization in the rising section will be intensified, since the pressure drop of adiabatic upward flow is increased. Hence, an extra disturbance of void fraction caused by the intensified flashing can occur in the rising section, and a new flow instability will be introduced into the loop. Besides, it can be found by observing the mass flux state of 1.6 m that, the oscillation shapes caused by two different vaporization modes (subcooled boiling and flashing) are significantly different. This transition in vaporization modes can also determine the flow patterns of natural circulation, thereby to change the effects of rising section height on the circulation ability. When the inlet temperature is low, the flow is dominated by the subcooled boiling in the heating section. Increasing the height of the rising section means increasing the inlet pressure of the heating section, which is not conducive to vaporization. Thus, the driving force will be decreased to reduce the flow rate (as indicated in point A, G1 > G2). But, when the inlet temperature is high, the flow is dominated by the
1) Considering the ERVC loop of SMR has no cold source, the inlet temperature of the heating section will gradually rise during the transients. The subcooled boiling in the heating section under low pressure (0.10 MPa) and low heat flux (105W/m2 magnitude) provides the main density difference for the driving force of natural circulation, meanwhile to dominate the flow states. This phenomenon is different from the natural circulation in the high power reactor's ERVC, which is dominated by saturation boiling. 2) With the decline of inlet subcooling degree, the flow patterns of natural circulation will be transformed into stable-oscillating-stable in turns. Based on the features of mass flux, exit temperature and void fraction, the oscillating patterns can be roughly divided into low-frequency and high-frequency oscillations. Both of them belong to the density wave instability, and their trajectory diagrams will present the attributes of the limit cycle. 3) In the plane where the inlet temperature is along horizontal axis, and the heating power is along vertical axis, the instability domain with high/low subcooling boundaries can be demarcated. Besides, increasing the back pressure can reduce the flow rate and compress the instability domain. Decreasing the inlet flow resistance can enhance flow rate, and shift the instability boundaries towards the direction of power increase. When lengthening the height of the rising section, the flow can be gradually dominated by the flashing with the decline of inlet subcooling, which may also induce an extra instability. Some deficiencies can be improved in future work. A part of simulation conditions are out of the range validated in REPEC experiment. The fluctuation range of mass flux in the simulation is about 60–160 kg/m2·s, but the mass flux range in the validation only gets 95–132 kg/m2·s. A more complete model validation may be done by finding some other experiments if there are new experiments for SMR’ ERVC in the future. Acknowledgements
Fig. 10. Effect of rising section height on transient flow.
This work is supported by National Natural Science Foundation of 10
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
China (No. 11705035) and Natural Science Foundation of Heilongjiang (No. LH2019A009), which are gratefully acknowledged.
the non-heating experiment under the external reactor vessel cooling condition. J. Shanghai Jiaot. Univ. 3, 023. Li, F., Li, Y., Cheng, X., 2012. Simulation and analysis on REPEC heating experimental mechanism. Atomic Energy Sci. Technol. 46 (7), 815–820. Li, F., Jin, D., Liu, X.J., Cheng, X., 2013. July). Analysis of flow stability boundaries of ERVC system. In: 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers (pp. V004T09A051-V004T09A051). Lu, W., Cheung, F.B., Hu, T., Liu, H., Zhang, X., Chang, H., 2017. Experimental investigation of 3-D ERVC process for IVR strategy–CHF limits and visualization of boiling phenomena. Nucl. Eng. Des. 322, 240–255. Prasad, G.V.D., Pandey, M., Kalra, M.S., 2007. Review of research on flow instabilities in natural circulation boiling systems. Prog. Nucl. Energy 49 (6), 429–451. Ransom, V.H., Trapp, J., Wagner, R., 2001. RELAP5/MOD3. 3 Code Manual Volume IV: Models and Correlations. Information Systems Laboratories, IR, Maryland Idaho Falls. Idaho. Rouge, S., 1997. SULTAN test facility for large-scale vessel coolability in natural convection at low pressure. Nucl. Eng. Des. 169 (1–3), 185–195. Rouge, S., Seiler, J.M., 1994. Core Debris Cooling with Flooded Vessel or Core-Catcher. Heat Exchange Coefficients under Natural Convection (No. NEA-CSNI-R–1994-32). Organisation for Economic Co-Operation and Development-Nuclear Energy Agency. Ruspini, L.C., Marcel, C.P., Clausse, A., 2014. Two-phase flow instabilities: a review. Int. J. Heat Mass Transf. 71, 521–548. Song, J.H., Kim, S.B., Kim, H.D., 2002. Analysis of external cooling of the reactor vessel during severe accidents. Nucl. Technol. 138 (1), 79–89. Song, J.H., Kim, S.B., Kim, H., 2005. On some salient unresolved issues in severe accidents for advanced light water reactors. Nucl. Eng. Des. 235 (17–19), 2055–2069. Theofanous, T.G., Tu, J.P., Salmassi, T., Dinh, T.N., 2002. Quantification of limits to coolability in ULPU-2000 configuration IV. 05, 3 CRSS-02. Wang, M., Zhao, H., Zhang, Y., Su, G., Tian, W., Qiu, S., 2012. Research on the designed emergency passive residual heat removal system during the station blackout scenario for CPR1000. Ann. Nucl. Energy 45, 86–93. Yang, J., Cheung, F.B., 2005. A hydrodynamic CHF model for downward facing boiling on a coated vessel. Int. J. Heat Fluid Flow 26 (3), 474–484. Zhang, L., Wang, Y., Yu, Z., 2018. Experimental study of flow boiling instabilities in horizontal tubes under gas–liquid stratification condition: effects of heat flux and inlet subcooling degree. Int. J. Heat Mass Transf. 118, 1040–1045. Zhao, G., Cao, X., Shi, X., 2013. Study theoretically on two-phase circulation flow characteristics under ERVC condition in advanced PWR. Prog. Nucl. Energy 67, 104–113. Zhao, Y., Peng, M., Xia, G., Lv, L., 2018. Flashing-driven natural circulation characteristics analysis of a natural circulation integrated pressurized water reactor. Nucl. Eng. Des. 337, 236–244.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.pnucene.2019.103063. References Chang, H., Hu, T., Lu, W., Yang, S., Zhang, X., 2017. Experimental study on CHF using a full scale 2-D curved test section with additives and SA508 heater for IVR-ERVC strategy. Exp. Therm. Fluid Sci. 84, 1–9. Chu, T.Y., Bentz, J.H., Slezak, S.E., Pasedag, W.F., 1997. Ex-vessel boiling experiments: laboratory-and reactor-scale testing of the flooded cavity concept for in-vessel core retention Part II: reactor-scale boiling experiments of the flooded cavity concept for in-vessel core retention. Nucl. Eng. Des. 169 (1–3), 89–99. Dinh, T.N., Tu, J.P., Salmassi, T., Theofanous, T.G., 2003. June). Limits of coolability in the AP1000-related ULPU-2400 configuration V facility. In: 10th International Topical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-10), Seoul, South Korea, Oct, pp. 5–11. Goswami, N., Paruya, S., 2011. Advances on the research on nonlinear phenomena in boiling natural circulation loop. Prog. Nucl. Energy 53 (6), 673–697. Ha, K.S., Cheung, F.B., Park, R.J., Kim, S.B., 2012. Evaluations of two-phase natural circulation flow induced in the reactor vessel annular gap under ERVC conditions. Nucl. Eng. Des. 253, 114–124. Hou, X., Sun, Z., Fan, G., Wang, L., 2017. Experimental and analytical investigation on the flow characteristics in an open natural circulation system. Appl. Therm. Eng. 124, 673–687. Jiang, N., Cong, T., Peng, M., 2019. Margin evaluation of in-vessel melt retention for small IPWR. Prog. Nucl. Energy 110, 224–235. Kim, J.C., Ha, K.S., Park, R.J., Kim, S.B., Hong, S.W., 2008a. Loop analysis of a natural circulation two-phase flow under an external reactor vessel cooling. Int. Commun. Heat Mass Transf. 35 (8), 1001–1006. Kim, J.C., Ha, K.S., Park, R.J., Kim, S.B., Hong, S.W., 2008b. One-dimensional experiments of a natural circulation two-phase flow under an external reactor vessel cooling. Int. Commun. Heat Mass Transf. 35 (6), 716–722. LI, Y.C., ZHOU, W.H., YANG, Y.H., KUANG, B., CHENG, X., 2011. RELAP simulation on
11
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Flow instability analysis of natural circulation under ERVC condition for SMR
T
Nan Jiang, Minjun Peng, Tenglong Cong∗ Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin, 150001, China
A R T I C LE I N FO
A B S T R A C T
Keywords: IVR-ERVC Natural circulation Density wave instability RELAP5
In this work, the internal natural circulation flow of ERVC system in SMR is calculated by the thermal-hydraulic code RELAP5. Both the transient characteristics and the flow instability are analyzed in detail to reveal the flow mechanism. Firstly, to verify the applicability of RELAP5 models, multiple cases of steady-state natural circulation with low heating power are simulated by comparing with the REPEC experiment. Next, a sliced model of ERVC loop is built to obtain the transient phenomena of natural circulation. As the circulation loop has no cold source, the inlet temperature of the heating section will keep rising to transform the flow patterns into stableoscillating-stable in turns. During this transition, the flow is dominated by the subcooled boiling of heating section, and the mass flux is about 60–160 kg/m2·s. Based on the features of flow oscillation, the unstable flow patterns can be further divided into low-frequency and high-frequency oscillations. Both of them belong to the density wave oscillation, and their trajectory diagrams can present the attributes of the limit cycle. Finally, in the plane formed with the inlet subcooling (horizontal axis) and heating power (vertical axis), the boundaries of flow instability are divided. The instability domain change with the effects of heating power, back pressure, inlet resistance coefficient, and rising section height is discussed. The results indicate that increasing the back pressure will compress the instability domain. Reducing the inlet resistance coefficient will shift the instability boundaries towards the direction of power increase. When lengthening the height of the rising section, the flow can be gradually dominated by the flashing with the decrease of inlet subcooling, which may also introduce another instability.
1. Introduction The initial researches of In-Vessel melt Retention (IVR) mainly focus on the heat transfer characteristics of the molten pool, the external cooling of Reactor Pressure Vessel (RPV) is only considered as a boundary condition. However, the results of ULPU-IV&V (Theofanous et al., 2002; Dinh et al., 2003) experiment indicate that the natural circulation flow in RPV insulation will significantly influence the Critical Heat Flux (CHF) of an outside wall. And the driving force of natural circulation is very sensitive to the external conditions, such as the structure parameters of the flow channel or the internal heat of the molten pool. Thus, the natural circulation in External Reactor Vessel Cooling (ERVC) loop is gradually separated from the IVR to be studied separately. The current studies of ERVC flow can be divided into three aspects by the thermal-hydraulic mechanism: 1) Studies related to the CHF enhancement, including the observation of flow patterns under CHF (Lu et al., 2017), the prediction of mass flux for CHF (Yang and Cheung,
∗
2005) and the increase of convective heat transfer coefficient by surface structure (Chang et al., 2017). 2) Studies about the steady-state flow characteristics, such as the pressure drop distribution of circulation loop (Zhao et al., 2013), the calculation of vapor quality and drift velocity (Kim et al., 2008a), the effects of geometrical/thermal parameters on circulation ability (Kim et al., 2008b). 3) Studies for the flow instability, involving the dynamic instability of density wave caused by boiling or flashing (Zhang et al., 2018), and the static instability due to flow drift (Chu et al., 1997). However, compared with the two preceding aspects, existing studies that focus on the flow instability of natural circulation in ERVC system are fewer, especially for the dynamic instability. Flow instability refers to the dynamic instability (the flow oscillation with constant/variable amplitude caused by the changes in void fraction or buoyancy), or the static instability (flow excursion). All of the natural circulation systems should be designed to avoid any flow instability. However, the vapor-liquid phase transitions in natural circulation will often induce various unstable flows, since the ERVC
Corresponding author. E-mail address: [email protected] (T. Cong).
https://doi.org/10.1016/j.pnucene.2019.103063 Received 10 December 2018; Received in revised form 12 April 2019; Accepted 13 May 2019 Available online 20 May 2019 0149-1970/ © 2019 Elsevier Ltd. All rights reserved.
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
system operates in low-pressure. Besides, these flow instabilities will not only cause the mechanical shock on insulation structure, but also create the local heat transfer deterioration on lower head, and even reduce CHF to make boiling crisis happen in advance (Song et al., 2005). Song (Song et al., 2002) uses RELAP5 code to simulate the transient characteristics of two-phase natural circulation flow in ERVC loop. With the uniform heating of 600 kW/m2, the oscillation of density wave caused by the saturated boiling in the heating section is observed. Besides, the calculation results of multiple conditions all indicate that the thermal margin of CHF on the lower head will decline under the disturbance of flow instability. But, this flow oscillation can be restrained by increasing the inlet area of the heating section or decreasing the resistance coefficient at the inlet. This study assesses the trends of flow oscillation development, but the regularity of instability domain or the essential reason of unstable flow are not analyzed, and the quantitative results of calculation also lack experimental verification. Therefore, it can only provide a qualitative reference for the trend analysis of dynamic instability. Rouge (Rouge and Seiler, 1994) predicts the static instability domain of flow drift in ERVC loop with FLICA code. The flow characteristics of a vertical channel under the low pressure (1 bar) and large hydraulic diameter (15 cm) are calculated, then the characteristic curve of pressure drop - flow rate is obtained by adjusting various heating powers. The unstable flow domain of flow drift is finally separated from the negative slope zone of the characteristic curve, and the calculation results are verified with the SULTAN experiment (Rouge, 1997). However, to get the specified mass flow, the forced circulations are adopted both in the above calculation and analysis. Thus, the deviations will be introduced into the results comparing with the actual ERVC flow, since the driving force of forced circulation will be constant by the external settings, while the driving force of natural circulation will show mutability under the coupling of various factors. Therefore, this study is only preferable for the optimization design of loop resistance but is inadequate for the real instability mechanism of natural circulation. Ha (Ha et al., 2012) conducts a 1/2 scaled experiment (HERMESHALF) to evaluate the flow status of natural circulation in APR1400's ERVC. Considering the test section of the lower head has a large size with 3D-spherical shape, it will be challenging and dangerous to establish the natural circulation with a high void fraction by the direct heating of high heat flux. Hence, a non-heating method of air injection is adapted to generate the two-phase mixed flow. It is observed in the experiment that the bubbles will accumulate periodically at the narrowest part of insulation channel to cause a local reflow. When the void fraction in loop rises to a high level, this reflow can even result in a strong periodic flow oscillation at the inlet. But, the fluctuation does not be explicitly classified by the instability mechanism in this study, since the bubble annihilation in non-heating condition should be different from that in heating condition. The researchers only recommend installing a gas groove to increase the smoothness of gas-phase flow, and to avoid this instability. It can be summarized from the existing studies that various flow instabilities can occur in the natural circulation of ERVC system. The causes and behaviors of variability can also be various under the influences of loop structure and thermal condition. However, the instability mechanism of ERVC flow is still studied insufficiently by the limitation of experimental factors. Moreover, the current studies of ERVC flow mainly focus on high-power reactors, while the studies for small-power reactors (lower than 300 MW) are fewer. The flow characteristics of ERVC's natural circulation should be significantly different for the large and small reactors, and these differences can be embodied in the following aspects: 1) Different Thermal Conditions: With the heating of a high-power molten pool, the natural circulation will be dominant by the saturation boiling of the heating section. For this condition, the flow rate and vapor quality should be
both higher, so that the second type of dynamic instability can be easily induced into the loop by friction (Goswami and Paruya, 2011). Nevertheless, with the heating of a low-power molten pool, the natural circulation will be dominant by the subcooled boiling of heating section, or the flashing of the rising part. In this condition, the vapor quality should be low. The first type of dynamic instability can be potentially induced into the loop by gravity (Prasad et al., 2007). 2) Different Loop Structures: The design of a small reactor is usually required to be compact that the loop structure of ERVC will differ from that of a large reactor. Specifically, in terms of the rising section height of the circulation loop, and the setting mode of cold source, etc. That will also affect the pressure drop distribution and transient flow of ERVC. From the above, it can be considered that, the natural circulation characteristic of ERVC for a small-power reactor and its possible flow instability are both unique that should be considered independently, and to be studied further. Then, this work aims to solve the insufficiency, and will focus on the transient characteristics of ERVC flow and the mechanism of flow instability, under the IVR thermal load of SMR. Firstly, multiple cases of steady-state natural circulation with low heating power from the REPEC experiment are simulated by the thermal-hydraulic code RELAP5. The outlet temperature and circulation flow rate are selected as indexes to verify the model applicability for the natural circulation which dominated by subcooled boiling. And the ranges of mass flux and heat flux are also estimated. Next, a sliced model of ERVC system for SMR is established with RELAP5 by simplifying the loop into the heating section, rising section, and downcomer. The transient flow of natural circulation is calculated, and the high/low subcooling boundaries of flow instability are obtained. Based on the oscillating patterns of mass flux, exit temperature and void fraction, the mechanism of flow instability and the development of limit cycles are both explained. Finally, the effects of the thermal boundary (back pressure, heating power) and loop structure (inlet resistance coefficient, rising section height) on the flow instability are quantitatively discussed by parametric analysis. Specifically, in the plane where the inlet temperature is horizontal axis, the characteristic of transient flow and the shift of the instability domain are compared.
2
Nomenclature CHF ERVC IVR RPV SMR Nsub Npch
Critical heat flux External reactor vessel cooling In-vessel melt retention Reactor pressure vessel Small modular reactor Subcooling number Phase change number
Lh τi F S hmac hmic Re x e, B hf , in
Length of heating section Transit time Reynolds number factor Boiling correction factor Convection heat transfer coefficient for flow Convection heat transfer coefficient for boiling Reynolds number Thermodynamic vapor quality vapor starting point Saturated water enthalpy at the inlet
hin hfg, in
Fluid enthalpy at inlet Latent heat of vaporization at the inlet
Q G νg, in
Heating power Mass flow-rate of natural circulation Saturated steam's specific volume at the inlet
νf , in
Saturated water's specific volume at the inlet
Lr μave De xm χe Pe Pr α
Length of rising section Average velocity of natural circulation Characteristic diameter of the channel Real mass quality of vapor Thermodynamic vapor quality at outlet Peclet number Prandtl number Void fraction
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 1. aREPEC experiment facility.(b). RELAP5 nodalization of REPEC experiment.
2. Experiment validation
be seen from the comparison results (Fig. 2a–d) that, in all cases, the temperature errors are within 2% and the flow errors are within 20%. The fluctuation range of mass flux in the simulation is about 60–160 kg/m2·s, but the mass flux range in the validation only gets 95–132 kg/m2·s. A part of simulation conditions are out of the range validated in REPEC experiment. Besides, the actual flow in ERVC will also be affected by the geometrical or thermal factors. But the effects of backpressure or loop height in this simulation cannot be verified. Thus, some errors may exist in the quantitative calculation results of RELAP5. However, the point of this work is to given the development trend of flow instability under the influence of various parameters, which prefers to be a qualitative analysis. For this trend analysis, this validation analysis can still be useful.
In this section, the RELAP5 code is used to simulate multiple groups of steady-state natural circulation in the REPEC facility (Li et al., 2013; Li et al., 2012; LI et al., 2011). REPEC is an experiment for ERVC flow characteristics. The outlet temperature of heating section and the mass flux of circulation are selected as the indexes; then the simulation results are compared with the experimental data to verify the model applicability of RELAP5 for calculating ERVC flow. Furthermore, the rationality of calculation error is also evaluated. REPEC is a large-scaled slice experiment with direct heating, which takes the CPR1000 reactor as a prototype. The experiment facility and its RELAP5 (Ransom et al., 2001) model are shown in Fig. 1a and b. Under the IVR thermal load of SMR, the surface heat flux on the lower head should be low. Thus, in this work, only the experimental cases with low heating power are chosen for verifying the natural circulation, which dominated by subcooled boiling. The specific heat flux distribution in REPCE (low heating condition) is presented in Fig. 3c, and the heat flux of SMR's IVR is shown in Fig. 3d. With the contrastive analysis, although their distribution is not the same, the total heating power and the peak heat flux are similar. Considering there is no particular experiment for the natural circulation of SMR's ERVC, the present low-heating conditions can be a good choice. Besides, the flow patterns of these cases are consistent with that of SMR. Thus the verification can be reliable. The detail conditions of verification cases are presented in Table 1. The heating power, inlet area of the heating section and inlet water temperature, are adjusted respectively to change the flow status. It can
3. System and model 3.1. ERVC loop In this section, RELAP5 code is used to simulate the transient flow of natural circulation in ERVC system after the severe accident of SMR. (The design features of SMR (Zhao et al., 2018) are different from that of general large power plant (Wang et al., 2012)). Fig. 3a shows the structure of ERVC, which is mainly composed of containment pool, RPV insulation and inlet/outlet valves. The circulation loop connects with the containment atmosphere and operates at low pressure. Before the molten material collapses into the lower head, the containment water will enter into insulation channel from the bottom inlet, then be heated to form the two-phase mixture. The density difference can drive the
Table 1 Flow cases of REPEC experiment for validation. Cases
Parameter description
Heating Power/kW
Inlet area/m2
Inlet temperature/K
Simulation mass flux/kg/m2·s
Simulation outlet temperature/K
1–1 1–2 1–3 1–4 2–1 2–2 2–3 3–1 3–2 3–3 3–4
Adjusting heating power
20% 30% 40% 50% 30% 30% 30% 20% 20% 348.15 368.15
0.01767 0.01767 0.01767 0.01767 0.00530 (0.3) 0.00884 (0.5) 0.01767 (1.0) 0.01767 0.01767 105.7 102.4
338.15 338.15 338.15 338.15 328.15 328.15 328.15 328.15 338.15 352.8 373.0
102.8 110.0 118.2 126.1 90.0 102.9 109.9 97.3 102.8
343.5 344.4 345.1 346.2 336.6 335.7 334.8 334.4 343.6
Adjusting inlet area
20% 20%
Adjusting inlet temperature 0.01767 0.01767
3
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 2. Comparison of simulation and experiment. a. Adjusting heating power. b. Adjusting inlet area. c. Adjusting inlet temperature. d. Error analysis.
fluid to establish an upward flow of natural circulation. The vapor phase will be vented to the containment atmosphere, and the liquid phase will return to the containment pool to continue circulation. The inner heat of the molten pool can be transferred to the fluid in insulation channel, and finally released into the atmosphere as steam. The RELAP5 nodalization of ERVC's 2D-slice model is shown in Fig. 3b. The whole loop is simplified into the heating section, rising section, and downcomer. Especially, the effects of the complex structure will be discussed by parametric analyses. The main structure parameters are listed in Table 2. The heating of lower head is set as a constant heat flux boundary to the flow, and the angle distribution of heat flux (Fig. 3d) is adopted from the previous SMR's safety analysis (Jiang et al., 2019).
Then, the real mass quality of vapor ( x m ) and the void fraction (α ) can be calculated.
3.2. Constitutive models
xm =
For the constitutive models in RELAP5 (Ransom et al., 2001), the Chen model is used to calculate the heat transfer of flow-boiling convection, and the Saha-Zuber model is used to calculate the non-equilibrium void fraction for pressure drop. Chen model adopts the correction factors between flow and boiling, to define the total heat transfer coefficient of flow-boiling convection (htot ) .
α=
htot = Fhmac + Shmic
Saha-Zuber model introduces a concept of a vapor starting point to calculate the non-equilibrium void fraction (α). First, the thermodynamic vapor quality of vapor starting point ( x e, B ) is calculated.
x e, B = −0.0022
x e, B = −154
Pe > 70000
(4)
(5)
x e − x e, B exp(x e / x e, B − 1) 1 − x e, B exp (x e / x e, B − 1)
(6)
xm
⎢ ⎣
+
ρg
⎤ ⎥+
ρf ⎥
⎥ ⎦
ρg Wgm G
(7)
For the conservation equations, RELAP5 uses the one-dimensional two-fluid model with six equations, involving the mass, energy and momentum equations for the gas and liquid phases. The boundary conditions in ERVC model is simulated by 202Volmue (Fig. 3b), the backpressure is given by 0.101 MPa, and the temperature is provided by 340.0 K. For the flow rate calculation of natural circulation, firstly, the vapor mass quality can be determined by the governing equations of energy. Secondly, the pressure drop can be calculated to get the flow rate.
(1)
(2)
When calculating the convection heat transfer coefficient for boiling (hmic ) , 0.79 0.45 0.49 0.25 ⎛ k f cpf ρf g ⎞ hmic = 0.00122 ⎜ 0.25 0.29 0.24 0.24 ⎟ ΔTw0.24 ΔP 0.75 σ μf hfg ρg ⎝ ⎠
q′ ′ Gi fg
Pe ≤ 70000
kf i fg
⎡ xm ⎛⎜ρf − ρg ⎟⎞ ⎠ 1.13 ⎢ ⎝ ρ ⎢ f
When calculating the convection heat transfer coefficient for flow (hmac ) ,
hmac = 0.023Re 0.8Pr 0.4kf / De
cp, f q′ ′De
3.3. Nodalization analysis (3)
Considering the heating section and the rising section will play the 4
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 3. a. Structure of ERVC system in SMR. b. RELAP5 nodalization of ERVC loop. c. Heat flux distribution in REPEC experiment (Low heating conditions) d. Heat flux boundary of heating section (heat flux distribution on lower head) d.Nodalization analysis for stable and oscillating flow.
number is increased from N2 to N3, the change of flow oscillation is not apparent. Therefore, the present N2 nodalization (indicated in Fig. 3b) can be reasonable for the flow instability. Given that the REPEC experiment does not publish the data of flow instability, the oscillating flow in this simulation cannot be quantitatively verified. Some errors may exist in the dynamic results. But, the point of this work is to give the development trend of flow instability
main roles in this open natural circulation, their optimum node numbers are discussed here by sensitivity calculation. The mass flux of natural circulation (which is the most representative and sensitive parameter) is selected as the evaluation index. Four different nodalization cases are listed in Table 3. Their results of stable and oscillating flow are presented in Fig. 3d. In the steady state calculation, the effect of nodalization is slight. In the dynamic calculation, when the node 5
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
low pressure (0.10 MPa) and high heat flux (105W/m2 magnitude) provide the main density difference for the driving force of natural circulation, and the subcooled boiling in the heating section dominates the flow. With the rising of inlet temperature, the increase of average void fraction can also enhance the natural circulation driving force, then to make the flow rate presents a trend of continuous rise. The fluctuation range of mass flux is about 60–160 kg/m2·s, which is roughly consistent with the range of experimental verification. When the inlet temperature reaches about 354 K, the natural circulation cannot maintain a stable flow. The mass flux, void fraction, and outlet temperature of the heating section all changed into the regular oscillations. However, the inlet temperature of the heating section is not affected by the flow instability, since the outlet of the rising section directly connects with the containment atmosphere to reduce the pressure feedback from the outlet to inlet. That is a feature of ERVC flow in SMR. When the inlet temperature rises about 361 K, the oscillation becomes weak and gradually disappears, then the flow returns into a stable state. The dynamic flow instability in natural circulation can be considered as a mismatch between driving force and flow resistance. 1) In the initial condition, the driving force matches the flow resistance perfectly and maintains the flow stable. 2) When the vapor quality in the circulation loop is meager, a small increase of vapor quality will have little effect on the flow resistance, but can significantly raise the void fraction. Then, the fluid density will be changed to enhance the driving force. Hence, when the inlet temperature begins to increase, the void fraction will increase, and the growth of driving force will firstly exceed that of flow resistance. The flow cannot stay in a stable state and starts to oscillate. 3) Given the phase differences of oscillations exist among the void fraction, temperature and mass flux, the oscillations will occur repeatedly. 4) When the vapor quality continuously increases to a certain extent by heating, the effect of vapor quality on the driving force will become lighter, but its enhancement on the friction and acceleration pressure drop can become more apparent. Thus, raising the inlet temperature equals to accelerate the increase of flow resistance, and to rematch the flow resistance with the driving force. Then, the flow recovers stability. Considering there is a one-to-one correspondence between the inlet temperature and outlet vapor quality, it can be considered that the flow oscillation will occur within a certain range of inlet temperature.
Table 2 Structure parameters of ERVC system. Item
Parameter
Containment pressure Initial temperature of containment water Flow area of downcomer (slice) Flow area of insulation channel (slice) Height of rising section Height of rising section (lower head) Width of heating section Total heating power Peak heat flux
0.10–0.40 MPa 350.0 K 2.123 m2 0.018385 m2 0.90 m 0.738 m 0.1355 m 60.63–108.74 kW 0.1232–0.4630 MW/m2
Table 3 Nodalization cases for sensitivity analyses. Nodalization cases
Node number of heating section
Node number of rising section
N1 N2 N3 N4
7 14 21 28
5 10 15 20
under the influence of various parameters, which prefers to be a qualitative analysis. For this trend contrast analysis with multiple parameters, these validation and sensitivity analysis can be useful. 4. Transient simulation of ERVC system 4.1. Flow characteristics of natural circulation In this section, RELAP5 code is used to simulate the transient flow of natural circulation in ERVC system after the severe accident of SMR (the design features of SMR (Zhao et al., 2018) are different with that of general large power plant (Wang et al., 2012)). Under a constant power heating, the calculation results of natural circulation transient flow are shown in Fig. 4. Considering the ERVC loop has no cold source, the heat can only be absorbed by the store water in containment. Thus, the inlet temperature of the heating section will gradually rise. But, the temperature rise of the outlet is not apparent as that of the inlet, since the non-negligible vaporization occurs in the heating section. During the whole progression, the outlet temperature of the heating section is still below the local saturation temperature. Besides, the void fraction declines significantly after the fluid enters into the adiabatic rising section. It can be considered that the vapor-liquid phase transition under
4.2. Oscillation patterns After spreading out the oscillations of temperature, flow rate and void fraction in the time axis, it can be found that the oscillating
Fig. 4. Transient characteristics of natural circulation. 6
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 5. a. Low frequency oscillation b. High frequency oscillation c. Comparsion between transit time and oscillation period.
time in the circulation loop. Notably, the ERVC in this work is an open loop that will be different from the general closed natural circulation. Considering the outlet of the rising section is connected to the environment (a constant pressure boundary), the flow oscillation cannot transmit from the outlet of the rising section to the inlet of the heating section. Thus, the transit time (τi ) should only consider the rising and heating sections as follows (Hou et al., 2017):
frequency is gradually accelerated by the rise of inlet temperature, as well as the oscillating amplitude is increased. The unstable flow patterns can be roughly divided into low-frequency (Fig. 5a) and highfrequency (Fig. 5b). The cycle period of low-frequency oscillation is about 9.5s, and that of high-frequency oscillation is about 4.5s. The operating conditions in Fig. 5a are that heating power, backpressure, and inlet temperature are respectively set to 0.0967 MW, 0.101 MPa and 354.32 K. The heating power and backpressure in Fig. 5b are same as that in Fig. 5a, but its inlet temperature of the heating section gets from 359.74 K to 360.43 K. The following explanation can be made for the generation of unstable flows. In the first stage (Fig. 5a), the cold fluid will be heated up when it flows into the heating section, and the fluid temperature will be raised from trough to crest; thus the vaporization should also be intensified to increase the void fraction. Then, the gravity pressure drop of upward flow can be reduced by the decline of average density in the heating section, to improve the flow rate briefly. (For the flow with low void fraction, the gravity pressure drop - ρgh provides the main flow resistance.) But, in the next stage, the above flow improvement can drop the fluid temperature from crest to trough. Hence, the vaporization in the heating section will be weakened, and the void fraction will decline. After the average density is recovered, the gravity pressure drop of upward flow will be increased to raise the flow resistance, and finally to reduce the flow rate into the initial stage. The above two stages can repeatedly occur to form a self-sustained oscillation, and the constant phase differences will be maintained in the crests of temperature, void fraction and flow rate. Therefore, the essence of this instability can be considered as the variations of fluid density, which will be circularly propagated through the flow channel. And this flow phenomenon is caused by the delayed feedback of multiple parameters and is often called as density wave instability. Introducing a variable of transit time (τi ), to identify the density wave instability. This parameter indicates the oscillation transmission
τi = (Lh + Lr )/ uave
(8)
As presented in Fig. 5c, all of the flow states locate near to the double timeline. For the density wave instability (DWI), the oscillation period is approximate twice the transit time. That can prove the flow oscillations in Fig. 5a and b belong to the density wave instability. The period of density wave instability depends on the time that the fluid passes through the loop. Thus, the oscillation frequency should present an acceleration trend with the rise of inlet temperature, since the vaporization can also be intensified to increase the circulation flow velocity. As shown in Fig. 6a and b, the oscillating flow trajectories can be depicted by switching the low and high-frequency oscillations into another plane, which consist of pressure drop and mass flux. (The inlet pressure of the heating section can directly represent the pressure drop of upward flow since the outlet pressure is constant.) It can be seen that all of the trajectories can reveal an irregular structure with a closed ring. The development of limit cycle should be continuous. The six types of limit cycles are just a result of intentional segmentation, to make the cycle figure clearer. This regular phenomenon is a specific attribute of dynamic instability, often called a limit cycle. Its trajectories in phase plane can only demonstrate that the flow system has nonlinear characteristic. One oscillating flow pattern will only correspond to one shape of the limit cycle, as indicated in Fig. 6c. Besides, with the reduction of inlet subcooling, the oscillations can be intensified to expand the limit cycles gradually. 7
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 6. a. Low frequency limit cycles. b. High frequency limit cycles. c. The development of limit cycles.
stability domain, which is conducive to keep the stable flow. Conversely, if the flow condition stays on the low subcooling boundary, reducing heating power or increasing inlet subcooling will make the flow state enter into instability domain, and intensify the oscillation. In order to make the instability evaluation more universal, the instability boundaries are usually plotted in the dimensionless plane which consists of subcooling number (Nsub) and phase change number (Npch), and the mass vapor quality of heat section outlet (Xe line) is used to help demarcate the position of instability domain, as shown in Fig. 7c. Given the natural circulation is induced by subcooled boiling, all of the flow points are distributed below the saturation line, and on the side of negative vapor quality. For the quantitative results, the vapor quality span of instability domain is small, and the unstable flow points locate within the range of −0.00246 ∼ −0.0164. (It is generally recognized that the flow instability can only occur within a certain range of outlet vapor quality (Ruspini et al., 2014).)
5. Parametric analysis of instability In this section, the effects of the typical thermal and structural parameter on the flow instability of natural circulation in ERVC are discussed. Considering the inlet temperature of the heating section will rise after the circulation is started, and to maintain a single variable, the transient flow characteristics under different parameters are compared in the plane where the inlet temperature is set as a horizontal axis. The flow characteristics here involve the variation of mass flux, void fraction, pressure drop, and instability boundary. 5.1. Heating power The influence of heating power on the transient natural circulation flow is shown in Fig. 7a. The circulation ability will be enhanced by increasing the heating power, and this enhancement of mass flux will be more apparent when the inlet temperature of the heating section rises higher. Besides, even the heating power is changed; all of the flow patterns will still be transformed into stable-oscillating-stable in turns with the increase of inlet temperature. In the heating condition of 0.1002 MW, the flow changes from stable to oscillating when the inlet temperature reaches 354.2 K. Thus, this temperature can be regarded as the demarcation point of instability at high supercooling. Similarly, the flow changes from oscillating to stable when the inlet temperature reaches 360.8 K, then this temperature is regarded as the demarcation point of instability at low subcooling. If the demarcation points of variability under different heating power are linked together, the flow instability domain of natural circulation in ERVC system can be obtained, as indicated in Fig. 7b with black points. It can be concluded that the flow instability induced by subcooled boiling will only appear within a certain range of inlet supercooling and heating power. Moreover, with the decline of heating power, the temperature span of instability domain will become narrow and gradually shift towards the direction of lower subcooling. That means if the flow condition stays on the high subcooling boundary, reducing heating power or increasing inlet subcooling will maintain the flow state within the
Nsub =
hf , in − hin νfg, in • hfg, in νf , in
Npch =
νfg, in Q • G hfg, in•νf , in
χe =
hout − hf , out hfg, out
=
(9)
(10) Q G
+ hin − hf , out hfg, out
hfg, in•νf , in ⎡ νfg, in (hf , in − hf , out ) ⎤ = Npch − Nsub + ⎥ hfg, out •νfg, in ⎢ hfg, in•νf , in ⎦ ⎣
(11)
5.2. Containment pressure The containment pressure will determine the back pressure level of natural circulation since the outlet of ERVC loop is directly connected to the containment atmosphere. The influence of back pressure on the transient flow is shown in Fig. 8a. Considering the latent vaporization heat of inlet fluid will be increased by raising the back pressure, when 8
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 7. a. Effect of heating power on transient flow b. Instability domain of natural circulation c. Instability boundary in dimensionless plane.
the fluid at same inlet temperature is heated, the vapor quality at heating section outlet in high-pressure condition should be lower than that of low-pressure condition. Accordingly, the driving force of natural circulation should also be smaller, as well as the flow rate. Even, the mass flux disparity of two-phase flow caused by pressure can get more prominent in the higher inlet temperature. The above phenomena can indicate that, only at higher inlet temperature, the high-pressure flow can produce the same vapor quality or driving force as the low-pressure flow, which is equivalent to delaying the vaporization process. Therefore, the two-phase oscillation will also be postponed to higher inlet temperature. The effect of back pressure on the instability domain is shown in Fig. 8b. The instability domain will be overall compressed by increasing the back pressure. The low subcooling boundary will shift towards the higher subcooling direction, and the upper subcooling boundary will change towards the lower subcooling direction, to improve the flow stability of natural circulation.
5.3. Inlet resistance coefficient of heating section Considering inlet valve will be installed in the ERVC loop that may change the local flow resistance, and the pressure drop of the two-phase section can affect the density variation, the inlet resistance coefficient of heating section is selected as the common parameter for analysis. The influence of inlet resistance on the transient flow is shown in Fig. 9a. The pressure drop of the form loss at heating section inlet will be decreased after reducing the local resistance coefficient. With the same inlet subcooling, the two-phase flow rate in low resistance condition should be higher, since the total flow resistance is reduced. Then, the vaporization in the heating section will be restrained by a cold flow, and the average vapor quality will decline. But, this change in mass flux is not significant, given the form loss pressure drop at inlet only occupies a small part in the total pressure drop. The effect of inlet resistance on the instability domain is shown in Fig. 8b. Reducing the resistance coefficient can enhance flowing and weaken vaporization, which means the flow also needs higher heating power to reach the vapor quality point (Xe) on instability boundary. Thus, the instability boundaries of
Fig. 8. a. Effect of back pressure on transient flow. b. Effect of back pressure on instability domain. 9
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
Fig. 9. a. Effect of inlet resistance on transient flow b. Effect of inlet resistance on instability domain.
flashing in the rising part. Increasing the height of rising section will increase the pressure difference of rising section to intensify the flashing vaporization. The simultaneous increase of density difference and height difference will significantly enhance the driving force. Thus, as indicated in point B, the flow rate in 1.6 m-case rises higher, G1 < G2.
high and low subcooling will require both shifts towards the direction of higher heating power. If the flow condition stays on the low subcooling boundary, reducing inlet resistance will make the flow state enter into instability domain to break the stable natural circulation. Conversely, if the flow condition stays on the high subcooling boundary, reducing inlet resistance will help the flow state away from instability boundary, and maintain within the stability domain.
6. Conclusion 5.4. Height of rising section
In this work, both the transient characteristics and the flow instability are analyzed in detail to reveal the flow mechanism of natural circulation in ERVC. The main conclusions are obtained as follows:
The influence of the rising section height on the transient flow is shown in Fig. 10. When the rising section height is low (0.8 m), only the flow instability caused by subcooled boiling will occur in the loop, and the oscillation of void fraction comes from the heating section. However, after lengthening the rising section height (1.6 m), the pressure difference between the heating section outlet and rising section outlet should become larger. Then, the vaporization in the rising section will be intensified, since the pressure drop of adiabatic upward flow is increased. Hence, an extra disturbance of void fraction caused by the intensified flashing can occur in the rising section, and a new flow instability will be introduced into the loop. Besides, it can be found by observing the mass flux state of 1.6 m that, the oscillation shapes caused by two different vaporization modes (subcooled boiling and flashing) are significantly different. This transition in vaporization modes can also determine the flow patterns of natural circulation, thereby to change the effects of rising section height on the circulation ability. When the inlet temperature is low, the flow is dominated by the subcooled boiling in the heating section. Increasing the height of the rising section means increasing the inlet pressure of the heating section, which is not conducive to vaporization. Thus, the driving force will be decreased to reduce the flow rate (as indicated in point A, G1 > G2). But, when the inlet temperature is high, the flow is dominated by the
1) Considering the ERVC loop of SMR has no cold source, the inlet temperature of the heating section will gradually rise during the transients. The subcooled boiling in the heating section under low pressure (0.10 MPa) and low heat flux (105W/m2 magnitude) provides the main density difference for the driving force of natural circulation, meanwhile to dominate the flow states. This phenomenon is different from the natural circulation in the high power reactor's ERVC, which is dominated by saturation boiling. 2) With the decline of inlet subcooling degree, the flow patterns of natural circulation will be transformed into stable-oscillating-stable in turns. Based on the features of mass flux, exit temperature and void fraction, the oscillating patterns can be roughly divided into low-frequency and high-frequency oscillations. Both of them belong to the density wave instability, and their trajectory diagrams will present the attributes of the limit cycle. 3) In the plane where the inlet temperature is along horizontal axis, and the heating power is along vertical axis, the instability domain with high/low subcooling boundaries can be demarcated. Besides, increasing the back pressure can reduce the flow rate and compress the instability domain. Decreasing the inlet flow resistance can enhance flow rate, and shift the instability boundaries towards the direction of power increase. When lengthening the height of the rising section, the flow can be gradually dominated by the flashing with the decline of inlet subcooling, which may also induce an extra instability. Some deficiencies can be improved in future work. A part of simulation conditions are out of the range validated in REPEC experiment. The fluctuation range of mass flux in the simulation is about 60–160 kg/m2·s, but the mass flux range in the validation only gets 95–132 kg/m2·s. A more complete model validation may be done by finding some other experiments if there are new experiments for SMR’ ERVC in the future. Acknowledgements
Fig. 10. Effect of rising section height on transient flow.
This work is supported by National Natural Science Foundation of 10
Progress in Nuclear Energy 117 (2019) 103063
N. Jiang, et al.
China (No. 11705035) and Natural Science Foundation of Heilongjiang (No. LH2019A009), which are gratefully acknowledged.
the non-heating experiment under the external reactor vessel cooling condition. J. Shanghai Jiaot. Univ. 3, 023. Li, F., Li, Y., Cheng, X., 2012. Simulation and analysis on REPEC heating experimental mechanism. Atomic Energy Sci. Technol. 46 (7), 815–820. Li, F., Jin, D., Liu, X.J., Cheng, X., 2013. July). Analysis of flow stability boundaries of ERVC system. In: 2013 21st International Conference on Nuclear Engineering. American Society of Mechanical Engineers (pp. V004T09A051-V004T09A051). Lu, W., Cheung, F.B., Hu, T., Liu, H., Zhang, X., Chang, H., 2017. Experimental investigation of 3-D ERVC process for IVR strategy–CHF limits and visualization of boiling phenomena. Nucl. Eng. Des. 322, 240–255. Prasad, G.V.D., Pandey, M., Kalra, M.S., 2007. Review of research on flow instabilities in natural circulation boiling systems. Prog. Nucl. Energy 49 (6), 429–451. Ransom, V.H., Trapp, J., Wagner, R., 2001. RELAP5/MOD3. 3 Code Manual Volume IV: Models and Correlations. Information Systems Laboratories, IR, Maryland Idaho Falls. Idaho. Rouge, S., 1997. SULTAN test facility for large-scale vessel coolability in natural convection at low pressure. Nucl. Eng. Des. 169 (1–3), 185–195. Rouge, S., Seiler, J.M., 1994. Core Debris Cooling with Flooded Vessel or Core-Catcher. Heat Exchange Coefficients under Natural Convection (No. NEA-CSNI-R–1994-32). Organisation for Economic Co-Operation and Development-Nuclear Energy Agency. Ruspini, L.C., Marcel, C.P., Clausse, A., 2014. Two-phase flow instabilities: a review. Int. J. Heat Mass Transf. 71, 521–548. Song, J.H., Kim, S.B., Kim, H.D., 2002. Analysis of external cooling of the reactor vessel during severe accidents. Nucl. Technol. 138 (1), 79–89. Song, J.H., Kim, S.B., Kim, H., 2005. On some salient unresolved issues in severe accidents for advanced light water reactors. Nucl. Eng. Des. 235 (17–19), 2055–2069. Theofanous, T.G., Tu, J.P., Salmassi, T., Dinh, T.N., 2002. Quantification of limits to coolability in ULPU-2000 configuration IV. 05, 3 CRSS-02. Wang, M., Zhao, H., Zhang, Y., Su, G., Tian, W., Qiu, S., 2012. Research on the designed emergency passive residual heat removal system during the station blackout scenario for CPR1000. Ann. Nucl. Energy 45, 86–93. Yang, J., Cheung, F.B., 2005. A hydrodynamic CHF model for downward facing boiling on a coated vessel. Int. J. Heat Fluid Flow 26 (3), 474–484. Zhang, L., Wang, Y., Yu, Z., 2018. Experimental study of flow boiling instabilities in horizontal tubes under gas–liquid stratification condition: effects of heat flux and inlet subcooling degree. Int. J. Heat Mass Transf. 118, 1040–1045. Zhao, G., Cao, X., Shi, X., 2013. Study theoretically on two-phase circulation flow characteristics under ERVC condition in advanced PWR. Prog. Nucl. Energy 67, 104–113. Zhao, Y., Peng, M., Xia, G., Lv, L., 2018. Flashing-driven natural circulation characteristics analysis of a natural circulation integrated pressurized water reactor. Nucl. Eng. Des. 337, 236–244.
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.pnucene.2019.103063. References Chang, H., Hu, T., Lu, W., Yang, S., Zhang, X., 2017. Experimental study on CHF using a full scale 2-D curved test section with additives and SA508 heater for IVR-ERVC strategy. Exp. Therm. Fluid Sci. 84, 1–9. Chu, T.Y., Bentz, J.H., Slezak, S.E., Pasedag, W.F., 1997. Ex-vessel boiling experiments: laboratory-and reactor-scale testing of the flooded cavity concept for in-vessel core retention Part II: reactor-scale boiling experiments of the flooded cavity concept for in-vessel core retention. Nucl. Eng. Des. 169 (1–3), 89–99. Dinh, T.N., Tu, J.P., Salmassi, T., Theofanous, T.G., 2003. June). Limits of coolability in the AP1000-related ULPU-2400 configuration V facility. In: 10th International Topical Meeting on Nuclear Reactor Thermalhydraulics (NURETH-10), Seoul, South Korea, Oct, pp. 5–11. Goswami, N., Paruya, S., 2011. Advances on the research on nonlinear phenomena in boiling natural circulation loop. Prog. Nucl. Energy 53 (6), 673–697. Ha, K.S., Cheung, F.B., Park, R.J., Kim, S.B., 2012. Evaluations of two-phase natural circulation flow induced in the reactor vessel annular gap under ERVC conditions. Nucl. Eng. Des. 253, 114–124. Hou, X., Sun, Z., Fan, G., Wang, L., 2017. Experimental and analytical investigation on the flow characteristics in an open natural circulation system. Appl. Therm. Eng. 124, 673–687. Jiang, N., Cong, T., Peng, M., 2019. Margin evaluation of in-vessel melt retention for small IPWR. Prog. Nucl. Energy 110, 224–235. Kim, J.C., Ha, K.S., Park, R.J., Kim, S.B., Hong, S.W., 2008a. Loop analysis of a natural circulation two-phase flow under an external reactor vessel cooling. Int. Commun. Heat Mass Transf. 35 (8), 1001–1006. Kim, J.C., Ha, K.S., Park, R.J., Kim, S.B., Hong, S.W., 2008b. One-dimensional experiments of a natural circulation two-phase flow under an external reactor vessel cooling. Int. Commun. Heat Mass Transf. 35 (6), 716–722. LI, Y.C., ZHOU, W.H., YANG, Y.H., KUANG, B., CHENG, X., 2011. RELAP simulation on
11