- Email: [email protected]
Scaling analysis on LOFA for the test model of WCCB blanket in CFETR
Fusion Engineering and Design 146 (2019) 719–722
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Scaling analysis on LOFA for the test model of WCCB blanket in CFETR a
a
b
Zihan Liu , Yun Guo , Hui Bao , Changhong Peng a b
a,⁎
T
Department of Engineering and Applied Physics, University of Science and Technology of China, Hefei, China Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Scaling analysis WCCB blanket CFETR Loss of flow accident
The water Cooled Ceramic Breeder (WCCB) blanket, as a candidate for Chinese Fusion Engineering Test Reactor (CFETR), must demonstrate its safety before engineering application. Enough data are necessary and the test model should ensure that the data are convincing within reasonable expenses. In this paper, scaling criteria are identified for loss of flow accident (LOFA) in WCCB blanket coolant system, which guides the design scheme of test model that the length scaling factor of 1 and volume scaling factor of 1/120. Scaling analyses are performed to develop similarity criteria for pump coastdown and loop natural circulation in three temporal phases identified by LOFA simulation. The test model only preserves a branch at the sector level and sub-module level, which results in different volume scaling factors at levels. Typical heat-transferring cells, constituted by blanket components, are preserved for heat transfer similarity. By computational simulation of an ideal model, it is testified that the test model can reproduce thermal-hydraulic responses within acceptable range of the distortion.
1. Introduction
2. LOFA analysis for WCCB BCS
CFETR, proposed as a next step fusion facility, is a superconducting tokamak reactor. In CFETR, the blanket is a key component, responsible for producing tritium and removing nuclear heat. As one of three candidates, the WCCB blanket has developed profoundly [1]. Enough experimental data are required to demonstrate the safety of WCCB blanket coolant system (BCS). The expense of direct experiments is so great that it is inevitable to design a simplified and scaled-down model instead of the prototype for experiments with appropriate scaling techniques. Previously, scaling techniques [2,3] were well developed on the aspect of fission reactors. Scaling laws of kinds of thermal-hydraulic phenomena such as natural circulation (NC), heat transfer and flow regime transitions, were proposed. However, scaling criteria derived from fission reactors should be reexamined prudently because of obvious differences of system structure. The main objective for the present paper is to identify scaling criteria for postulated accident in WCCB BCS and to provide basic design scheme of the test model. The loss of flow accident, being a potential initiating accidents, is selected to be performed scaling analysis [4]. Based on the data of fission reactors and computational simulation, important phenomena for LOFA in WCCB BCS can be discerned. By scaling analysis for those phenomena, scaling criteria can be obtained, which can guide the model design.
2.1. WCCB BCS structure
⁎
A conceptual design of WCCB CS [1,4] is formed now. Fig. 1 shows the design for a WCCB sector. A typical sub-module contains the first wall (FW), cooling plates (CPs), side walls (SWs) and stiffening plates (SPs), and manifolds (1–6). In general, the WCCB BCS has the characteristic of multi-hierarchy and multi-branch. The system (S) can be divided downward into sectors (SE), N# module (M), N# sub-module (SM), blanket components (BC), and channels (CH). The upper level usually includes several components of the lower level, which forms the multi-branch structure. For example, a module (inboard or outboard) is linked to two or three submodules. Moreover, the structure and operation conditions of the branches at the same level are similar. 2.2. LOFA simulation The LOFA caused by pump failure in WCCB system is simulated by RELAP5 Mod3.4. Fig. 2 shows the mass flow rate and void fraction of the 3# sub-module outlet during LOFA. Three temporal phases of a prolonged LOFA transient, including pump coastdown, steam cavities formation and clearance, and longterm single phase natural circulation are identified from the scoping
Corresponding author. E-mail address: [email protected] (C. Peng).
https://doi.org/10.1016/j.fusengdes.2019.01.063 Received 7 October 2018; Received in revised form 3 December 2018; Accepted 10 January 2019 Available online 17 January 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 146 (2019) 719–722
Z. Liu et al.
Table 1 PPIRT for WCCB blanket system LOFA. Component Phenomena
Phase
Blanket Pressure drop Decay heat Wall stored heat NC flow Critical heat flux Flow regime transition Flow rate distributing SG NC flow heat transfer Secondary condition Pressurizer surge line Pressure drop - regime transition Piping NC flow HL-Flow regime transition Pump Pump performance
Fig. 1. Conceptual design of WCCB BCS. (a) Multi-pipe manifolds design for a typical sector (b) Sub-module structure.
1
2
3
H H L — — — L
H H P H P P P
H H P H — — L
— — —
H M M
H — —
—
P
—
— —
H H
H —
H
—
—
identification and ranking table (PPIRT) is made to identify the important phenomena in each phase, and showed in Table 1. The importance of phenomena is ranked high (H), plausible (P), moderate (M), low (L) or no impact (—) [3,5]. 3. Scaling laws 3.1. Rationale for scaling choices The working fluid, component materials (except heating material), and operating pressure in test model are the same as the prototype, so the properties of fluids and solids are the same as well. The full-height scaling is adopted to obtain accurate data. The integral scaling ratios of main parameters under the same-property and full-height scaling, can be derived with power-to-volume scaling method [2], and showed in Table 2. The volume scaling factor, kv, for the test model is designed to be 1/120 in consideration of the cost, design and accuracy of the model. 3.2. Pump coastdown scaling Fig. 2. The simulation of 3# sub-module during the LOFA.
When pump coastdown, the energy from the inertia of pump and coolant is consumed by the resistance in the loops [6]. That is:
analysis. During the phase-1, the mass flow rate decreases gradually and single phase NC in the system is still maintained because of the pump coastdown and inertia of the water. When the water velocity reduces to a certain value which the steam cannot be taken out of the inverted u-shaped channels in WCCB blanket, the steam gathers at the upper part of the channels gradually and further prevents water from flowing. When the steam is enough, the driving force, generated by the density variation of coolant in hot leg (HL) and cool leg (CL), makes steam discharge from WCCB blanket, so two phase NC occurs. This process is reduplicative during the phase-2. During the last phase, there is no condition of steam cavities formation, so long-term single phase natural circulation can be maintained.
d (Es + Ep ) dt
+ Pf = 0
(1)
Es = K1 Qm2
(2)
Ep = K2 ω2
(3)
Table 2 Integral scaling ratios of the main parameters. Parameter
ratios
Parameter
ratios
Length Area
1 kv
kv 1
Volume Time Velocity Temperature
kv 1 1 1
Power Power/ volume Pressure Flow rate Diameter of channels Number of channels
2.3. Plausible phenomena identification and ranking Scaling analysis should focus on the phenomena which are important for overall system performance during LOFA. Based on engineering judgments and simulations, the plausible phenomena 720
1 kv 1 kv
Fusion Engineering and Design 146 (2019) 719–722
Z. Liu et al.
Pf = K3 Qm3
(4)
Where Es, Ep, Pf, Qm and ω are the coolant kinetic energy, pump kinetic energy, resistance power, mass flow rate, and rotor angular velocity respectively. K1, K2 and K3 are constant. Introducing the assumption and initial condition that:
ω Q = m ω0 Qm0
(5)
Pf ,0 = Qm0 gH0
(6)
Fig. 3. The schematic of heat transfer in a typical cell.
Where subscript 0 denotes the initial value. Defining τ1/2 as the time during which the mass flow rate is halved. Substituting Eqs. (2–6) into Eq. (1) yields:
τ1/2 =
performed based on the assumption that the heat transfer occurs mainly along radial and toroidal direction, so simplify a cell into a plane, showed in Fig. 3. The following dimensionless partial differential equation and conditions for unique solution (only two) for a cell can be obtained:
2(Es,0 + Ep,0 ) Qm0 gHp,0
(7)
To preserve the similarity of mass flow rate, the following scaling criterion is required:
+
′′ ′′ ks Ts,0 ⎛ 2 ∂2Ts+ ∂Ts+ ∂ 2T + ⎛ q′ ⎞ ⎛ q′ ⎞ = x 0 +2 + y02 +s2 ⎞ + ⎜ s ⎟ ⎜ s ⎟ ∂t ρs cps ⎝ ∂x ∂y ⎠ ρc T ρc ⎝ s ps s ⎠0 ⎝ s ps ⎠
(12)
∂Ts+ ∂x +
⎜
τ1/2, R = t0, R
(8)
Where t0R refers to the time ratio. The subscript R denotes the ratio of the model and prototype. For detail scaling for the pump, three ratios of the dimensionless parameters including specific speed ratio (Ns,R), specific capacity ratio (Qs,R) and specific head ratio (Hs,R) can be identified as follows [7]:
Ns, R =
NR QR1/2 HR3/4
Qs, R =
QR NR dR3
(10)
H = 2R 2 NR dR
(11)
Hs, R
∂Ts+ ∂y+
The scaling criteria for loop natural circulation are well developed based on a one-dimensional formulation [2,3]. In FW, CPs, and SWs& SPs, the fluid has a characteristic of one-dimensional flow, so traditional scaling groups listed in Table 3 are accepted in the aspect of flow. These scaling groups are required to be set as unity in the prototype and model. Moreover, single phase and two phase natural circulation can be reproduced in a test facility for same-property scaling. However, the heat transfer, being an obvious multi-dimensional process, deserves a specialized scaling analysis. The zone of heat transfer is separated into many cells by the FW, CPs and SWs&SPs. A cell is approximately cuboid. Scaling analysis for heat transfer is
Length no. Area no. Zuber no.
Li = li / l 0 Ai = ai / a0
(12) (13) (14)
′
4q ′ l0 ⎞ ⎛ Δρ ⎞ ΠZu = ⎛⎜ 0 ⎟ du ρ i ρ ⎝ 0 f fg ⎠ ⎝ g ⎠ ⎜
Sub-cooling no.
i Δρ Πsub = ⎛ sub ⎞ ⎛ ⎞ ⎝ i fg ⎠ ⎝ ρg ⎠ ⎟⎜
⎜
Froude no.
2
u ΠFr = ⎛ 0 ⎞ gl α ⎝ 0 0⎠ ⎜
Drift-flux no. Heat flux no. Resistance no.
⎟
ρf Δρ
y+ = 0
= −⎛ ⎝
y0 q2 (x +, 0, t ) ⎞ + + q2 (x , 0, t ) ks Ts ⎠0
(14)
⎜
⎟
x 0, R = y0R = 1
(15)
qs′,′′R = ks, R = (ρs cps )R = [q1 (0, y+ , t )]R = [q2 (x +, 0, t )]R
(16)
(17)
Where acell, ucell and Ncell are the flow area, velocity, and number of channels in cell for a specific component, respectively. 4. Model design scheme and simulation 4.1. Model design scheme The model of WCCB BCS can be designed based on following simplifying assumptions: (1) the thermal-hydraulic phenomena at the ‘SE’ level and at the ‘SM’ level are the same, respectively; (2) the thermalhydraulic phenomena of channels at the ‘CH’ level are similar and can be reproduced in heat-transferring cells constituted by fewer channels; (3) the interactions of each sector and each sub-module are negligible for LOFA. The test model only preserves a sector at the ‘SE’ level and a sub-module at the ‘SM’ level, so the branches of sectors and sub-modules are merged into one branch. Ten modules are preserved because of obvious differences of the structure and heat transfer. The following relations among volume scaling factor of branches at different levels can be obtained:
⎟
(15)
⎟
( )
(13)
⎟
qs′,′′R = qcell, R = (ρf acell ucell ΔT )R = (Ncell )R
Table 3 Scaling groups for two phase NC flow. No
x 0 q1 (0, y+ , t ) ⎞ + q1 (0, y+ , t ) ks Ts ⎠0
⎜
Eq. (15) indicates that the dimension of cell in model should be preserved for similarity of heat transfer. Obviously, the poloidal direction ratio, zo,R, is 1 as well. So the total heat power ratio, qcell,R, also meets Eq. (16). Based on scaling choices, the conservation of energy in a cell yields:
3.3. Loop natural circulation scaling
Equation
x+ = 0
= −⎛ ⎝
Because the initial temperature in model and prototype is the same and the x-direction is along with the direction of flow, these scaling criteria can be derived from Eqs. (12–14):
(9)
dimensionless groups
⎟
(16)
V
(17)
k v, M = k v, SE = 8k v, S = 8k v
(18)
qc′ ′ q0′ ′
(18)
k v, BC = k v, SM = 16k v or24k v
(19)
ΠFi = Πfi + Πoi
(19)
The main components, including FW, CPs, SWs&SPs and manifolds, are preserved. These constitute heat-transferring cells, showed in Fig. 4.
gi Πdi = ⎛ ⎞ ⎝ u0 ⎠i
Πq =
721
Fusion Engineering and Design 146 (2019) 719–722
Z. Liu et al.
as well. It takes about 1681 s in test model before long-term single phase natural circulation rather than 1865 s in the prototype. At 4000 s, the mass flow rates of the prototype and test model are 0.63719 kg/s and 0.11895 kg/s respectively. The actual scaling factor is 1/5.36 approximately. Actually it is unnecessary to match parameters of the prototype and model exactly. The present results are in acceptable range of distortions.
Fig. 4. Poloidal cross-section of the test model for 3# module.
5. Conclusions Table 4 The design of channels in 3# module for test model. Module
3#
kv, BC
1/5
Prototype /Model
P M
Scaling analysis is conducted on the WCCB blanket coolant system for LOFA, and the test model is designed based on scaling criteria. LOFA in WCCB BCS can be divided into three temporal phases, including pump coastdown, steam cavities formation and clearance, and longterm single phase natural circulation and a PPIRT are established to rank the importance of thermal-hydraulic phenomena of each phase. The length scaling factor of 1 and volume scaling factor of 1/120 are chosen. Scaling criteria of pump coastdown and NC are identified and one-dimensional flow still is applied to FW, CPs, and SWs&SPs, but heat transfer in cells is scaled as a multi-dimensional process. Different volume scaling factors generated when merging branches guide the design at each level. The heat-transferring cells should be preserved to ensure the similarities of heat transfer and flow. An ideal model is designed and computational results show that thermal-hydraulic responses are reproduced in the test model. For further work, more engineering details would be considered for the test model.
Number of channels FW
CPs
SWs&SPs
42 8
60 12
60 12
Acknowledgments This study is supported by National Key R&D Program of China (No.2017YFE0300604). This work is also supported by National Natural Science Foundation of China (Grant No. 11305169). Fig. 5. The simulation of 3# module of the test model.
References
However the number of channels is scaled down by kv,BC. An approximate integer, particularly an even number in SWs&SPs, is accepted for the number of channels in components. Table 4 shows the number of channels in 3# module. In 3# module, a CP has 15 channels, and set these data to Eqs. (18 and 19) yields:
qs′,′′R = ks, R = (ρs cps )R = (Ncell, CP )R = 0.8
[1] S. Liu, X. Ma, K. Jiang, et al., Conceptual design of the water cooled ceramic breeder blanket for CFETR based on pressurized water cooled reactor technology, Fusion Eng. Des. 124 (2017) 856–870. [2] D. Bestion, et al., Scaling in System Thermal-hydraulics Applications to Nuclear Reactor Safety and Design: a State-of-the-Art-Report, NEA/CSNI/R(2016)14, Paris, 2017 March. [3] Jose N. Reyes Jr, L. Hochreiter, Scaling analysis for the OSU AP600 test facility (APEX), Nucl. Eng. Des. 186 (1998) 53–109. [4] X. Cheng, K. Huang, S. Liu, et al., Thermal hydraulic responses of the primary heat transfer system of the WCCB blanket to accident cases for CFETR, Fusion Eng. Des. 121 (2017) 50–59. [5] A. Annunziato, H. Glaeser, et al., CSNI Integral Test Facility Validation Matrix for the Assessment of Thermal-Hydraulic Codes for LWR LOCA and Transients 17 NEA/ CSNI/R(96), Paris, 1996 July. [6] H. Gao, F. Gao, X. Zhao, et al., Transient flow analysis in reactor coolant pump systems during flow coastdown period, Nucl. Eng. Des. 241 (2) (2011) 509–514. [7] Ki Yong Choi, et al., Development of a pump performance model for an integral effect test facility, Nucl. Eng. Des. 238 (2008) 2614–2623.
(20)
The cross-sectional area of these channels need to made small modifications to meet the velocity factor and volume factor. Channels are arranged uniformly in each component. 4.2. LOFA simulation for model The LOFA simulation is completed for an ideal test model of 3# module, showed in Fig. 5. Three same temporal phases can be identified
722
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Scaling analysis on LOFA for the test model of WCCB blanket in CFETR a
a
b
Zihan Liu , Yun Guo , Hui Bao , Changhong Peng a b
a,⁎
T
Department of Engineering and Applied Physics, University of Science and Technology of China, Hefei, China Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Scaling analysis WCCB blanket CFETR Loss of flow accident
The water Cooled Ceramic Breeder (WCCB) blanket, as a candidate for Chinese Fusion Engineering Test Reactor (CFETR), must demonstrate its safety before engineering application. Enough data are necessary and the test model should ensure that the data are convincing within reasonable expenses. In this paper, scaling criteria are identified for loss of flow accident (LOFA) in WCCB blanket coolant system, which guides the design scheme of test model that the length scaling factor of 1 and volume scaling factor of 1/120. Scaling analyses are performed to develop similarity criteria for pump coastdown and loop natural circulation in three temporal phases identified by LOFA simulation. The test model only preserves a branch at the sector level and sub-module level, which results in different volume scaling factors at levels. Typical heat-transferring cells, constituted by blanket components, are preserved for heat transfer similarity. By computational simulation of an ideal model, it is testified that the test model can reproduce thermal-hydraulic responses within acceptable range of the distortion.
1. Introduction
2. LOFA analysis for WCCB BCS
CFETR, proposed as a next step fusion facility, is a superconducting tokamak reactor. In CFETR, the blanket is a key component, responsible for producing tritium and removing nuclear heat. As one of three candidates, the WCCB blanket has developed profoundly [1]. Enough experimental data are required to demonstrate the safety of WCCB blanket coolant system (BCS). The expense of direct experiments is so great that it is inevitable to design a simplified and scaled-down model instead of the prototype for experiments with appropriate scaling techniques. Previously, scaling techniques [2,3] were well developed on the aspect of fission reactors. Scaling laws of kinds of thermal-hydraulic phenomena such as natural circulation (NC), heat transfer and flow regime transitions, were proposed. However, scaling criteria derived from fission reactors should be reexamined prudently because of obvious differences of system structure. The main objective for the present paper is to identify scaling criteria for postulated accident in WCCB BCS and to provide basic design scheme of the test model. The loss of flow accident, being a potential initiating accidents, is selected to be performed scaling analysis [4]. Based on the data of fission reactors and computational simulation, important phenomena for LOFA in WCCB BCS can be discerned. By scaling analysis for those phenomena, scaling criteria can be obtained, which can guide the model design.
2.1. WCCB BCS structure
⁎
A conceptual design of WCCB CS [1,4] is formed now. Fig. 1 shows the design for a WCCB sector. A typical sub-module contains the first wall (FW), cooling plates (CPs), side walls (SWs) and stiffening plates (SPs), and manifolds (1–6). In general, the WCCB BCS has the characteristic of multi-hierarchy and multi-branch. The system (S) can be divided downward into sectors (SE), N# module (M), N# sub-module (SM), blanket components (BC), and channels (CH). The upper level usually includes several components of the lower level, which forms the multi-branch structure. For example, a module (inboard or outboard) is linked to two or three submodules. Moreover, the structure and operation conditions of the branches at the same level are similar. 2.2. LOFA simulation The LOFA caused by pump failure in WCCB system is simulated by RELAP5 Mod3.4. Fig. 2 shows the mass flow rate and void fraction of the 3# sub-module outlet during LOFA. Three temporal phases of a prolonged LOFA transient, including pump coastdown, steam cavities formation and clearance, and longterm single phase natural circulation are identified from the scoping
Corresponding author. E-mail address: [email protected] (C. Peng).
https://doi.org/10.1016/j.fusengdes.2019.01.063 Received 7 October 2018; Received in revised form 3 December 2018; Accepted 10 January 2019 Available online 17 January 2019 0920-3796/ © 2019 Elsevier B.V. All rights reserved.
Fusion Engineering and Design 146 (2019) 719–722
Z. Liu et al.
Table 1 PPIRT for WCCB blanket system LOFA. Component Phenomena
Phase
Blanket Pressure drop Decay heat Wall stored heat NC flow Critical heat flux Flow regime transition Flow rate distributing SG NC flow heat transfer Secondary condition Pressurizer surge line Pressure drop - regime transition Piping NC flow HL-Flow regime transition Pump Pump performance
Fig. 1. Conceptual design of WCCB BCS. (a) Multi-pipe manifolds design for a typical sector (b) Sub-module structure.
1
2
3
H H L — — — L
H H P H P P P
H H P H — — L
— — —
H M M
H — —
—
P
—
— —
H H
H —
H
—
—
identification and ranking table (PPIRT) is made to identify the important phenomena in each phase, and showed in Table 1. The importance of phenomena is ranked high (H), plausible (P), moderate (M), low (L) or no impact (—) [3,5]. 3. Scaling laws 3.1. Rationale for scaling choices The working fluid, component materials (except heating material), and operating pressure in test model are the same as the prototype, so the properties of fluids and solids are the same as well. The full-height scaling is adopted to obtain accurate data. The integral scaling ratios of main parameters under the same-property and full-height scaling, can be derived with power-to-volume scaling method [2], and showed in Table 2. The volume scaling factor, kv, for the test model is designed to be 1/120 in consideration of the cost, design and accuracy of the model. 3.2. Pump coastdown scaling Fig. 2. The simulation of 3# sub-module during the LOFA.
When pump coastdown, the energy from the inertia of pump and coolant is consumed by the resistance in the loops [6]. That is:
analysis. During the phase-1, the mass flow rate decreases gradually and single phase NC in the system is still maintained because of the pump coastdown and inertia of the water. When the water velocity reduces to a certain value which the steam cannot be taken out of the inverted u-shaped channels in WCCB blanket, the steam gathers at the upper part of the channels gradually and further prevents water from flowing. When the steam is enough, the driving force, generated by the density variation of coolant in hot leg (HL) and cool leg (CL), makes steam discharge from WCCB blanket, so two phase NC occurs. This process is reduplicative during the phase-2. During the last phase, there is no condition of steam cavities formation, so long-term single phase natural circulation can be maintained.
d (Es + Ep ) dt
+ Pf = 0
(1)
Es = K1 Qm2
(2)
Ep = K2 ω2
(3)
Table 2 Integral scaling ratios of the main parameters. Parameter
ratios
Parameter
ratios
Length Area
1 kv
kv 1
Volume Time Velocity Temperature
kv 1 1 1
Power Power/ volume Pressure Flow rate Diameter of channels Number of channels
2.3. Plausible phenomena identification and ranking Scaling analysis should focus on the phenomena which are important for overall system performance during LOFA. Based on engineering judgments and simulations, the plausible phenomena 720
1 kv 1 kv
Fusion Engineering and Design 146 (2019) 719–722
Z. Liu et al.
Pf = K3 Qm3
(4)
Where Es, Ep, Pf, Qm and ω are the coolant kinetic energy, pump kinetic energy, resistance power, mass flow rate, and rotor angular velocity respectively. K1, K2 and K3 are constant. Introducing the assumption and initial condition that:
ω Q = m ω0 Qm0
(5)
Pf ,0 = Qm0 gH0
(6)
Fig. 3. The schematic of heat transfer in a typical cell.
Where subscript 0 denotes the initial value. Defining τ1/2 as the time during which the mass flow rate is halved. Substituting Eqs. (2–6) into Eq. (1) yields:
τ1/2 =
performed based on the assumption that the heat transfer occurs mainly along radial and toroidal direction, so simplify a cell into a plane, showed in Fig. 3. The following dimensionless partial differential equation and conditions for unique solution (only two) for a cell can be obtained:
2(Es,0 + Ep,0 ) Qm0 gHp,0
(7)
To preserve the similarity of mass flow rate, the following scaling criterion is required:
+
′′ ′′ ks Ts,0 ⎛ 2 ∂2Ts+ ∂Ts+ ∂ 2T + ⎛ q′ ⎞ ⎛ q′ ⎞ = x 0 +2 + y02 +s2 ⎞ + ⎜ s ⎟ ⎜ s ⎟ ∂t ρs cps ⎝ ∂x ∂y ⎠ ρc T ρc ⎝ s ps s ⎠0 ⎝ s ps ⎠
(12)
∂Ts+ ∂x +
⎜
τ1/2, R = t0, R
(8)
Where t0R refers to the time ratio. The subscript R denotes the ratio of the model and prototype. For detail scaling for the pump, three ratios of the dimensionless parameters including specific speed ratio (Ns,R), specific capacity ratio (Qs,R) and specific head ratio (Hs,R) can be identified as follows [7]:
Ns, R =
NR QR1/2 HR3/4
Qs, R =
QR NR dR3
(10)
H = 2R 2 NR dR
(11)
Hs, R
∂Ts+ ∂y+
The scaling criteria for loop natural circulation are well developed based on a one-dimensional formulation [2,3]. In FW, CPs, and SWs& SPs, the fluid has a characteristic of one-dimensional flow, so traditional scaling groups listed in Table 3 are accepted in the aspect of flow. These scaling groups are required to be set as unity in the prototype and model. Moreover, single phase and two phase natural circulation can be reproduced in a test facility for same-property scaling. However, the heat transfer, being an obvious multi-dimensional process, deserves a specialized scaling analysis. The zone of heat transfer is separated into many cells by the FW, CPs and SWs&SPs. A cell is approximately cuboid. Scaling analysis for heat transfer is
Length no. Area no. Zuber no.
Li = li / l 0 Ai = ai / a0
(12) (13) (14)
′
4q ′ l0 ⎞ ⎛ Δρ ⎞ ΠZu = ⎛⎜ 0 ⎟ du ρ i ρ ⎝ 0 f fg ⎠ ⎝ g ⎠ ⎜
Sub-cooling no.
i Δρ Πsub = ⎛ sub ⎞ ⎛ ⎞ ⎝ i fg ⎠ ⎝ ρg ⎠ ⎟⎜
⎜
Froude no.
2
u ΠFr = ⎛ 0 ⎞ gl α ⎝ 0 0⎠ ⎜
Drift-flux no. Heat flux no. Resistance no.
⎟
ρf Δρ
y+ = 0
= −⎛ ⎝
y0 q2 (x +, 0, t ) ⎞ + + q2 (x , 0, t ) ks Ts ⎠0
(14)
⎜
⎟
x 0, R = y0R = 1
(15)
qs′,′′R = ks, R = (ρs cps )R = [q1 (0, y+ , t )]R = [q2 (x +, 0, t )]R
(16)
(17)
Where acell, ucell and Ncell are the flow area, velocity, and number of channels in cell for a specific component, respectively. 4. Model design scheme and simulation 4.1. Model design scheme The model of WCCB BCS can be designed based on following simplifying assumptions: (1) the thermal-hydraulic phenomena at the ‘SE’ level and at the ‘SM’ level are the same, respectively; (2) the thermalhydraulic phenomena of channels at the ‘CH’ level are similar and can be reproduced in heat-transferring cells constituted by fewer channels; (3) the interactions of each sector and each sub-module are negligible for LOFA. The test model only preserves a sector at the ‘SE’ level and a sub-module at the ‘SM’ level, so the branches of sectors and sub-modules are merged into one branch. Ten modules are preserved because of obvious differences of the structure and heat transfer. The following relations among volume scaling factor of branches at different levels can be obtained:
⎟
(15)
⎟
( )
(13)
⎟
qs′,′′R = qcell, R = (ρf acell ucell ΔT )R = (Ncell )R
Table 3 Scaling groups for two phase NC flow. No
x 0 q1 (0, y+ , t ) ⎞ + q1 (0, y+ , t ) ks Ts ⎠0
⎜
Eq. (15) indicates that the dimension of cell in model should be preserved for similarity of heat transfer. Obviously, the poloidal direction ratio, zo,R, is 1 as well. So the total heat power ratio, qcell,R, also meets Eq. (16). Based on scaling choices, the conservation of energy in a cell yields:
3.3. Loop natural circulation scaling
Equation
x+ = 0
= −⎛ ⎝
Because the initial temperature in model and prototype is the same and the x-direction is along with the direction of flow, these scaling criteria can be derived from Eqs. (12–14):
(9)
dimensionless groups
⎟
(16)
V
(17)
k v, M = k v, SE = 8k v, S = 8k v
(18)
qc′ ′ q0′ ′
(18)
k v, BC = k v, SM = 16k v or24k v
(19)
ΠFi = Πfi + Πoi
(19)
The main components, including FW, CPs, SWs&SPs and manifolds, are preserved. These constitute heat-transferring cells, showed in Fig. 4.
gi Πdi = ⎛ ⎞ ⎝ u0 ⎠i
Πq =
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Z. Liu et al.
as well. It takes about 1681 s in test model before long-term single phase natural circulation rather than 1865 s in the prototype. At 4000 s, the mass flow rates of the prototype and test model are 0.63719 kg/s and 0.11895 kg/s respectively. The actual scaling factor is 1/5.36 approximately. Actually it is unnecessary to match parameters of the prototype and model exactly. The present results are in acceptable range of distortions.
Fig. 4. Poloidal cross-section of the test model for 3# module.
5. Conclusions Table 4 The design of channels in 3# module for test model. Module
3#
kv, BC
1/5
Prototype /Model
P M
Scaling analysis is conducted on the WCCB blanket coolant system for LOFA, and the test model is designed based on scaling criteria. LOFA in WCCB BCS can be divided into three temporal phases, including pump coastdown, steam cavities formation and clearance, and longterm single phase natural circulation and a PPIRT are established to rank the importance of thermal-hydraulic phenomena of each phase. The length scaling factor of 1 and volume scaling factor of 1/120 are chosen. Scaling criteria of pump coastdown and NC are identified and one-dimensional flow still is applied to FW, CPs, and SWs&SPs, but heat transfer in cells is scaled as a multi-dimensional process. Different volume scaling factors generated when merging branches guide the design at each level. The heat-transferring cells should be preserved to ensure the similarities of heat transfer and flow. An ideal model is designed and computational results show that thermal-hydraulic responses are reproduced in the test model. For further work, more engineering details would be considered for the test model.
Number of channels FW
CPs
SWs&SPs
42 8
60 12
60 12
Acknowledgments This study is supported by National Key R&D Program of China (No.2017YFE0300604). This work is also supported by National Natural Science Foundation of China (Grant No. 11305169). Fig. 5. The simulation of 3# module of the test model.
References
However the number of channels is scaled down by kv,BC. An approximate integer, particularly an even number in SWs&SPs, is accepted for the number of channels in components. Table 4 shows the number of channels in 3# module. In 3# module, a CP has 15 channels, and set these data to Eqs. (18 and 19) yields:
qs′,′′R = ks, R = (ρs cps )R = (Ncell, CP )R = 0.8
[1] S. Liu, X. Ma, K. Jiang, et al., Conceptual design of the water cooled ceramic breeder blanket for CFETR based on pressurized water cooled reactor technology, Fusion Eng. Des. 124 (2017) 856–870. [2] D. Bestion, et al., Scaling in System Thermal-hydraulics Applications to Nuclear Reactor Safety and Design: a State-of-the-Art-Report, NEA/CSNI/R(2016)14, Paris, 2017 March. [3] Jose N. Reyes Jr, L. Hochreiter, Scaling analysis for the OSU AP600 test facility (APEX), Nucl. Eng. Des. 186 (1998) 53–109. [4] X. Cheng, K. Huang, S. Liu, et al., Thermal hydraulic responses of the primary heat transfer system of the WCCB blanket to accident cases for CFETR, Fusion Eng. Des. 121 (2017) 50–59. [5] A. Annunziato, H. Glaeser, et al., CSNI Integral Test Facility Validation Matrix for the Assessment of Thermal-Hydraulic Codes for LWR LOCA and Transients 17 NEA/ CSNI/R(96), Paris, 1996 July. [6] H. Gao, F. Gao, X. Zhao, et al., Transient flow analysis in reactor coolant pump systems during flow coastdown period, Nucl. Eng. Des. 241 (2) (2011) 509–514. [7] Ki Yong Choi, et al., Development of a pump performance model for an integral effect test facility, Nucl. Eng. Des. 238 (2008) 2614–2623.
(20)
The cross-sectional area of these channels need to made small modifications to meet the velocity factor and volume factor. Channels are arranged uniformly in each component. 4.2. LOFA simulation for model The LOFA simulation is completed for an ideal test model of 3# module, showed in Fig. 5. Three same temporal phases can be identified
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