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Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality
Nuclear Engineering and Design 241 (2011) 4972–4977
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality Jianhua Wang a , Yuliang Sun a,∗ , Jianjun Wang b , E. Laurien c a
Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China College of Nuclear Science and Technology, Harbin Engineering University, Harbin 150001, China c University of Stuttgart, Institute for Nuclear Technology and Energy Systems (IKE), Pfaffenwaldring 31, D-70569 Stuttgart, Germany b
a r t i c l e
i n f o
Article history: Received 13 October 2010 Received in revised form 24 August 2011 Accepted 24 August 2011
a b s t r a c t Based on the one-dimension two-phase drift flow model, the numerical simulation of two-phase flow stability characteristic on the test loop (HRTL-5) for 5 MW heating reactor (developed by the Institute of Nuclear and New Energy Technology of Tsinghua University, Beijing) is performed with and without coupled point neutron kinetics. The density wave oscillation instability is analyzed in the system under low pressure at 1.5 MPa and low steam quality less than 10%. The effect of inlet subcooling and heating flux on the system instability is simulated under the system pressure Psys = 1.5 MPa. The numerical results show that there exist two instability inlet subcooling boundaries at different heat flux. The numerical results show good agreement with the experimental results on HRTL-5 without consideration of point neutron kinetics. If coupled with point neutron kinetics, the system will exhibit little difference on instability boundaries from that without considering the nuclear characteristics. But the amplitude and the phase of the oscillation of the thermal hydraulic parameters of the system will be somehow affected in unstable zone if the system is coupled with point neutron kinetics. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Since the 1950s, with the beginning of commercialization of nuclear reactors, especially boiling water reactors, the interest in two-phase flow instability studies started to grow internationally. Two-phase flow stability has been one of the important safety criterions in thermal–hydraulic design of a reactor. The thermal–hydraulic stability had been one of the most important issues for the design, operation, and safety since the development and commercialization of boiling water reactor (BWR). Two-phase flow instability associated with BWR was always under the conditions with high steam quality and forced circulation. Boure et al. (1973) made a clear classification of flow instability. Most of these instabilities were concerned with forced circulation, and the density wave instability was concerned with high steam quality under BWR conditions. Some supplement was done by Lahey (1980), including nonlinear, multi-dimensional and instant effect. The density wave oscillation instability concerning low steam quality was firstly reported by Fukuda and Koborl (1979). Especially, the severe nuclear accidents of Three-Mile Island (TMI) and Chernobyl, greatly influenced the design concept of the nuclear engineers. The design
∗ Corresponding author. E-mail address: [email protected] (Y. Sun). 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.08.074
concepts of inherent safety and passive safety attracted more and more interests. Because of the highly simplicity of the equipments and the inherent safety characteristic, natural circulation is introduced into the design concepts and has been one important operation mode of the coolant in new advanced reactors. For example, natural circulation is used in residual heat removal system (RHRS) to remove residual heat without any extra pump or electricity power, and it is also employed to transfer heat in the next generation boiling water reactor. However, natural circulation system, similar with the forced circulation system, can also lead to instability phenomenon under some operational conditions. Thus, the designers and the engineers need to know when the instability phenomenon may occur and how to avoid the occurrence of the phenomenon. Fukuda and Koborl (1979) studied both low (type I) and high steam quality (type II) density wave instability for both natural circulation and forced circulation systems. D.D.B. van Bragt investigated flow instability under natural circulation based on the natural circulation Dutch Dodewarrd BWR, and flow oscillation during startup was measured. Jiang et al. (2000) performed a series of experiments on the HRTL-5 (5 MW heating reactor test loop) under different pressures and other operation parameters in a rather wide range. In their work, not only several kinds of two phase flow special instability phenomena were observed and the mechanisms were analyzed, but also the type I density wave instability was reported and analyzed. Numerous
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
experimental investigations on the natural circulation boiling systems were reported in literature. Durga Prasad et al. (2007) made a review of investigations on flow instability in natural circulation loops. Caorso and Lasalle plant events happened in 1984 and 1988, respectively, renewed the interests of many researchers in coupled neutron dynamic thermal hydraulic instability in BWRs (March-Leuba and Rey, 1993), which are generated due to reactivity effect of void generated in the core or the Doppler effect of the fuel rod. Since then, many researchers focused their investigation interests on neutronic and thermal hydraulic coupling characteristics. van Bragt and van der Hagen (1998) interpret the basic mechanism of feedback and co-effect between the neutron dynamic and thermal hydraulic of the boiling water reactor. Durga Prasad et al. (2007) made some revision, expansion and supplement and made a review of the state of the art about natural circulation instability in boiling systems. However, there exist different understandings on the issue and reported results show great differences between each other. For example, van Bragt and van der Hagen (1998) found that an increase in the absolute value of void reactivity coefficient (VRC) had different ways of effect in different types of density wave oscillations (DWO), as so called type-I and type-II DWO regions. However, different from the results given by van Bragt and van der Hagen (1998), increasing the absolute value of VRC has a stabilizing effect in both regions according to Nayak et al. (2000), and a destabilizing effect in both the regions according to Lee and Pan (2005). Similar to the effects of VRC, the effects of the fuel time constant on the stability characteristics of the system show very great differences according to the reported literatures above mentioned. Even though these researchers use different approaches to study the similar problems, but the inconsistent results reported imply that understanding on the issue of the natural circulation instability coupled with neutron kinetics is not clear enough. The 5-MW nuclear heating reactor developed by the Institute of Nuclear Energy Technology (INET), Tsinghua University, has been in operation since 1989. It adopts the concept of integral arrangement and can operate both in pressurized water mode and boiling water mode under low pressure of 1.5 MPa. Different from the systems studied by van Bragt and van der Hagen (1998), Nayak et al. (2000), and Lee and Pan (2005), the present paper deals with the natural circulation instability on HRTL-5 with and without coupled point neutron kinetics. When the coupling between neutron kinetics and thermal hydraulic is considered, both the Doppler effect and void reactivity feedback are taken into account.
2. Approach In this investigation, the drift flux model with four equations is applied to describe the flow characteristics of the system and the point neutron kinetics with six groups of delayed neutron precursor is used to simulate heat generation in the core, based on which the computational code has been developed by ourselves. The features of the HRTL-5 are shown in Fig. 1, the whole loop can be divided into seven flow regions, including single-phase flow region, deep subcooled boiling region, low sub-cooled boiling region, bulk boiling region in the heated section and condensation region, single-phase flow region, void-flashing region in the adiabatic riser, finally the single-phase flow region in the down-comer. Such is the detailed division about the natural circulation. In this investigation, the local resistances concentrate in the inlet and outlet of the heated section. Based on the corresponding experimental data, the resistance coefficient at the inlet and outlet of the heated section is about 33 and 3, respectively. Consequently, the widely validated computer program has been developed
4973
Fig. 1. HRTL – 5 test loop. 1, heated section; 2, riser; 3, steam–water separator; 4, condensator; 5, heat exchanger; 6, downcomer; 7, flow meter; 8, throttle valve; 9, observation window.
successfully, which shows very good agreement with the experimental results performed on HRTL-5. The mathematic model is shown as follows:Mass conservation: ∂ ∂ [(1 − ˛)l + ˛v ] + [(1 − ˛)l ul + ˛v uv ] = 0 ∂t ∂z
(1)
Momentum conservation: ∂ ∂ [(1 − ˛)l u2l + ˛v u2v ] [(1 − ˛)l ul + ˛v uv ] + ∂z ∂t ∂p =− + ∂z
∂p ∂z
+ L
∂p ∂z
+ F
∂p ∂z
(2) G
Energy conservation: ∂ Uq ∂ [(1 − ˛)l hl + ˛v hv ] + [(1 − ˛)l ul hl + ˛v uv hv ] = A ∂t ∂z (3) Steam mass equation: ∂ ∂ (˛v ) + (˛v uv ) = i ∂t ∂t
i = 1, 2, 3
(4)
Drift flux velocity model (Zuber and Findlay, 1965): J = (1 − ˛)ul + ˛uv
(5)
uv = C0 J + uvj
(6)
Sub-cooled boiling model (Marotti, 1977): Qc =
ϕ=
3˛Aq (Ts − T )2 · Rb (TW − T )2 − (TW − TS )2
(TW − TS )2 (TW − T )2
(7)
(8)
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J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
From Eqs. (12) and (13), the following equation can be derived:
(t) − ˇ ˇ dP(t) = P(0) i e−i t P(t) + dt + e−i t
i
i
ˇi i
t
P(t )ei t dt
(14)
0
The reactor kinetics is coupled with the fuel rod dynamics and thermal hydraulics through the reactivity feedback due to fuel temperature and void fraction. The reactivity (t) consists of void and Doppler feedbacks and is given in form as follows: (t) = (0) + CT (Tav − Tav0 ) + C˛ (˛av − ˛av0 )
(15)
More detailed information about the mathematical model and computational format can be found in the literature (Wang et al., 2007). 3. Results and discussions
Fig. 2. The stability map of the system (Psys = 1.5 MPa, Kin = 33, Kout = 3).
3.1. Model verification Uqϕ Qc 1 = − Ar Ar
(9)
Condensation model (Yang, 2002): 2 = −
The model can be used to determine the stability map of a system. The operating point will be considered unstable if the dis-
3˛(TS − T ) rRb [(6z(Cp TS + r))/(u¯ v rl cp )(((TS − Tin )/(2TS + Tin )) + ((TS − T )/(2TS + T )))]
1/2
−
˛uv cpv TS lv r 2 l
·
dp (10) dz
Void flashing model (Jiang and Emendorfer, 1993): 3 =
1 dhS dp · [(1 − ˛)l ul + ˛v uv ] r dp dz
(11)
Point neutron kinetics with six delayed neutron precursor groups: dP(t) (t) − ˇ 1 = P(t) + i Ci (t) dt
(12)
dCi (t) = −i Ci (t) + ˇi P(t), dt
(13)
6
6
i = 1, 2, . . . , 6
turbance of some parameter, such as inlet subcooling and heat flux, makes the flow parameter grow continuously to same amplitude. However, if the disturbance makes the flow parameter perturbation dampen out, the corresponding state is considered stable. Fig. 2 shows the comparison of the marginal stability boundaries obtained from the model evaluation against the experimental results performed on HRTL-5 and the data set of Jiang (1994). It can be seen that the simulation results in this paper agree very well with both the experimental results performed on HRTL-5 and
0.54 0.51 0.48 0.52 0.51
Ule(m/s)
0.50 0.50 0.45 0.5 0.4 0.3 0.40 0.35 0.30 5
10
15
20
25
30
35
t(s) Fig. 3. The time evolution of inlet flow velocity (Psys = 1.5 MPa, q = 200 kW/m2 , Kin = 33, Kout = 3).
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
0.192
4975
ZFDB
0.53 0.52 0.51
0.189
Void Fraction
0.50
0.186
0.20 0.16
0.024
0.183
0.022 0.180
5
10
15
20
25
30
35
0.020
10
20
30
t(s)
t(s)
the results reported by Jiang (1994). It indicates that there are two marginal stability boundaries for some heat flux. With the increase of the heat flux, the inlet subcooling corresponding to the stability boundary increases for both. Fig. 3 shows the time evolution of the flow velocity at the inlet with disturbance of the same amplitude. In this figure, it is clearly indicated that if other operating parameters are fixed, including system pressure, heat flux and the geometry of the system, with the increase of the inlet subcooling from 15.0 K to 26.2 K, the disturbance of the inlet flow velocity will result in different way of development. For example, when the inlet subcooling is 15.0 K, the disturbance dampens slowly out if the time is long enough; but when the inlet subcooling goes to 15.2 K, even though the value of the inlet subcooling only increases by a very small amount, the disturbance makes the inlet flow velocity oscillation grow continuously to a oscillation with same amplitude finally. The similar phenomenon happens when the inlet subcooling is around 26.0 K. Moreover, the final amplitude of the oscillation undergoes a track from low to high then to low with the increase of the inlet subcooling. The results also agree well with the experimental results reported by Jiang et al. (2000). Fig. 4 shows the time evolution of the onset point of fully developed boiling (FDB) when the inlet subcooling is 15.2 K. The figure indicates that ZFDB oscillates from about 0.181 to 0.190 associated with the oscillation of inlet flow velocity, as is shown in the third curve in Fig. 3. Figs. 5 and 6 show the model prediction of time evolution of void fraction at different position in heated section and adiabatic riser respectively. It can be clearly found in the two figures that the void fraction wave at different position in both heated section and adiabatic riser transfer from upstream to downstream during the process of the oscillation. It is also seen that the transfer process of the disturbance of inlet parameter takes longer time to adiabatic riser. In other words, this process can be considered as the transfer process of density wave of the two phase mixture from inlet to outlet. 3.2. Nuclear coupled density wave instability Fig. 7 shows the marginal stability boundary comparison of model evaluation between with and without consideration of coupling of neutron kinetics and thermal–hydraulic. The consideration of the coupling includes Doppler effect and void reactivity feedback. It can be concluded that the nuclear coupled density wave instability has a wider unstable zone than ever, which means that coupling
Fig. 5. the time evolution of void fraction in heated section (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
0.50
Z=1.58m Z=2.58m Z=3.58m
0.49
Void Fraction
Fig. 4. the time evolution of ZFDB (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
0.48
0.47
10
20
30
t(s)
Fig. 6. the time evolution of void fraction in adiabatic riser (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
neutron kinetics with thermal–hydraulic makes the system more unstable around the original boundary. In order to understand the effects of Doppler effect feedback and void reactivity feedback better, the two effects are investigated 54
without neutron feedback nuclear feedback
48 42 36
stable
30
unstable 24 18 12 180
stable
240
300
360
420 2
q(kW/m ) Fig. 7. The stability map of the system (Psys = 1.5 MPa, Kin = 33, Kout = 3).
4976
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
750
Ule(m/s)
0.54
Doppler effect only void reactivity feedback only Doppler effect and void reactivity feedback without nuclear feedback 2
250
''
500
0
q (q -q 0)(W/m )
0.52
''
''
0.50
without nuclear feedback void reactivity feedback only Doppler effect only Doppler effect and void reactivity feedback
0.48
-250 -500
0.46 10.0
12.5
15.0
17.5
20.0
-750 10
t(s) Fig. 8. The time evolution of inlet flow velocity (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
respectively. Fig. 8 shows the time evolution of inlet flow velocity under different consideration modes of the nuclear feedback when inlet subcooling is 15.2 K. It can be observed that for a fixed operation condition, Doppler effect makes the system a little bit more “stable”, the void reactivity feedback makes the system more “unstable”, and the cooperation of Doppler effect and void reactivity makes system stability lie between without consideration of nuclear feedback and only consideration of void reactivity feedback. It is because that those different consideration modes of the nuclear feedback make the amplitude of the oscillation of inlet flow velocity exhibit difference between each other. Fig. 9 shows different feedback reactivity time series based on different consideration modes. As is shown in Fig. 9, the feedback reactivity oscillations are different from each other in both the amplitude and phase. It is because of the following coupling chains, which include the coupling of the fuel temperature, reactivity, thermal power of the reactor, the fuel dynamics and the fuel temperature again, the coupling of the overall void fraction in the core, the reactivity, thermal power of the reactor, the fuel dynamics and the void fraction in the core again, and the coupling of the above two coupling chains, and the time delay of the thermal–hydraulic parameters. The direct effect of the nuclear feedback results in the change of the heat flux transfer from the
20
30
t(s) Fig. 10. The time evolution of relative heat flux (Psys = 1.5 MPa, q0 = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
fuel to the coolant. Fig. 10 shows the time evolution of the relative heat flux (q (t) − q (0)) under different consideration modes of nuclear feedback. It is clearly showed that the relative heat flux caused by Doppler effect takes the smallest value and the biggest by the void reactivity. Even Doppler effect makes the heat flux oscillate around the initial value; the system will have the trend to be stable according to the results shown in Fig. 8. It can be explained by the time delay or phase difference between the feedback reactivity, feedback heat flux and inlet flow velocity as shown in Figs. 8–10. Because the feedback reactivity caused by void reactivity, feedback heat flux and inlet flow velocity are in phase, the consideration of void reactivity feedback makes the system have the trends to be unstable as shown in Fig. 8. Furthermore, the comparison of marginal stability boundaries between different coefficients of nuclear feedback is also studied. Fig. 11 shows the comparison between different void reactivity feedback coefficients. It can be observed that the increase of absolute value of void reactivity feedback coefficient makes the system more unstable. Fig. 12 shows the comparison under different Doppler effect feedback coefficient in the system. It can be observed
54 1.5x10
-5
1.0x10
-5
5.0x10
-6
48 Doppler effect only void reactivity feedback only Doppler effect and void reactivity feedback
42 36 30
0.0
-5.0x10
-6
-1.0x10
-5
-1.5x10
-5
10.0
stable
unstable
24 18 12 180 12.5
15.0
17.5
20.0
t(s) Fig. 9. The time evolution of feedback reactivity (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
stable
240
300
360
420 2
q(kW/m ) Fig. 11. The stability map of the system as function of Doppler coefficient (Ca ) (Psys = 1.5 MPa, Kin = 33, Kout = 3).
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
54
3. Under present structure and operation condition, increasing the absolute value of Doppler effect feedback coefficient has a stabilizing effect on the stability of the system; 4. Under present structure, operation condition and design nuclear feedback coefficient condition, the nuclear feedback makes the system more unstable than without consideration of nuclear feedback; 5. The different effect way of different coupling modes is because of the relative phase difference between the feedback parameters and some thermal–hydraulic parameters.
48 42 36
stable
30 unstable
24 18 12 180
References
stable
240
4977
300
360
420 2
q(kW/m ) Fig. 12. The stability map of the system as function of Doppler coefficient (CT ) (Psys = 1.5 MPa, Kin = 33, Kout = 3).
that the increase of absolute value of Doppler effect feedback coefficient makes the system more stable in the system. 4. Conclusion The 5 MW heating reactor is operated under lower pressure and lower quality, which is very different from the commercial boiling water reactor in service. This paper presents the analysis method of the nuclear coupled two phase flow instability. Analysis results show: 1. The self-developed code can be used to analyze two phase density wave instability; 2. Under present structure and operation condition, increasing the absolute value of void reactivity feedback coefficient has a destabilizing effect on the stability of the system;
Boure, J.A., Bergles, A.E., Tong, S.L., 1973. Review of two-phase flow instability. Nuclear Engineering and Design 25, 165–192. Durga Prasad, G.V., Manmohan Pandey, Kalra, M.S., 2007. Review of research on flow instabilities in natural circulation boiling systems. Progress in Nuclear Energy 49, 429–451. Fukuda, K., Koborl, T., 1979. Classification of two-phase instability by density wave oscillation model. Journal of Nuclear Science and Technology 16 (2), 95–108. Jiang, S.Y., 1994. Instabilitaet untersuchungen am Naturumlauf systemen. Ph.D. Thesis. University of Stuttgart. Jiang, S.Y., Emendorfer, D., 1993. Subcooling boiling and void flashing in a natural circulation system at heating reactor conditions. Kerntechnik 58 (5), 62–67. Jiang, S.Y., Wu, X.X., Zhang, Y.J., 2000. Experimental study of two-phase flow oscillation in natural circulation. Nuclear Science and Engineering 135, 177–189. Lahey, R.T., 1980. An assessment of the literature related to LWR instability modes. NUREG/CR-144. Lee, J.D., Pan, C., 2005. Nonlinear analysis for a nuclear-coupled two-phase natural circulation loop. Nuclear Engineering and Design 235, 613–626. March-Leuba, J., Rey, J.M., 1993. Coupled thermohydraulic–neutronic instabilities in boiling water nuclear reactors: a review of the state of the art. Nuclear Engineering and Design 145, 97–111. Marotti, L., 1977. Axial distribution of void fraction in sub-cooled boiling. Nuclear Technology 34, 8. Nayak, A.K., Vijayan, P.K., Saha, D., Venkat Raj, V., Aritomi, M., 2000. Analytical study of nuclear-coupled density-wave instability in a natural circulation pressure tube type boiling water reactor. Nuclear Engineering and Design 195, 27–44. van Bragt, D.D.B., van der Hagen, T.H.J.J., 1998. Stability of natural circulation boiling water reactors: part II: parametric study of coupled neutronic–thermohydraulic stability. Nuclear Technology 121, 52–62. Wang, J.J. Ph.D. Thesis, Tsinghua University, 2007. Yang, X.T. Study on flow excursion at natural circulation condition. Ph.D. Thesis, Tsinghua University, 2002. Zuber, N., Findlay, J., 1965. Average volumetric concentration in two-phase flow systems. Journal of Heat Transfer 87, 453–468.
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality Jianhua Wang a , Yuliang Sun a,∗ , Jianjun Wang b , E. Laurien c a
Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China College of Nuclear Science and Technology, Harbin Engineering University, Harbin 150001, China c University of Stuttgart, Institute for Nuclear Technology and Energy Systems (IKE), Pfaffenwaldring 31, D-70569 Stuttgart, Germany b
a r t i c l e
i n f o
Article history: Received 13 October 2010 Received in revised form 24 August 2011 Accepted 24 August 2011
a b s t r a c t Based on the one-dimension two-phase drift flow model, the numerical simulation of two-phase flow stability characteristic on the test loop (HRTL-5) for 5 MW heating reactor (developed by the Institute of Nuclear and New Energy Technology of Tsinghua University, Beijing) is performed with and without coupled point neutron kinetics. The density wave oscillation instability is analyzed in the system under low pressure at 1.5 MPa and low steam quality less than 10%. The effect of inlet subcooling and heating flux on the system instability is simulated under the system pressure Psys = 1.5 MPa. The numerical results show that there exist two instability inlet subcooling boundaries at different heat flux. The numerical results show good agreement with the experimental results on HRTL-5 without consideration of point neutron kinetics. If coupled with point neutron kinetics, the system will exhibit little difference on instability boundaries from that without considering the nuclear characteristics. But the amplitude and the phase of the oscillation of the thermal hydraulic parameters of the system will be somehow affected in unstable zone if the system is coupled with point neutron kinetics. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Since the 1950s, with the beginning of commercialization of nuclear reactors, especially boiling water reactors, the interest in two-phase flow instability studies started to grow internationally. Two-phase flow stability has been one of the important safety criterions in thermal–hydraulic design of a reactor. The thermal–hydraulic stability had been one of the most important issues for the design, operation, and safety since the development and commercialization of boiling water reactor (BWR). Two-phase flow instability associated with BWR was always under the conditions with high steam quality and forced circulation. Boure et al. (1973) made a clear classification of flow instability. Most of these instabilities were concerned with forced circulation, and the density wave instability was concerned with high steam quality under BWR conditions. Some supplement was done by Lahey (1980), including nonlinear, multi-dimensional and instant effect. The density wave oscillation instability concerning low steam quality was firstly reported by Fukuda and Koborl (1979). Especially, the severe nuclear accidents of Three-Mile Island (TMI) and Chernobyl, greatly influenced the design concept of the nuclear engineers. The design
∗ Corresponding author. E-mail address: [email protected] (Y. Sun). 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.08.074
concepts of inherent safety and passive safety attracted more and more interests. Because of the highly simplicity of the equipments and the inherent safety characteristic, natural circulation is introduced into the design concepts and has been one important operation mode of the coolant in new advanced reactors. For example, natural circulation is used in residual heat removal system (RHRS) to remove residual heat without any extra pump or electricity power, and it is also employed to transfer heat in the next generation boiling water reactor. However, natural circulation system, similar with the forced circulation system, can also lead to instability phenomenon under some operational conditions. Thus, the designers and the engineers need to know when the instability phenomenon may occur and how to avoid the occurrence of the phenomenon. Fukuda and Koborl (1979) studied both low (type I) and high steam quality (type II) density wave instability for both natural circulation and forced circulation systems. D.D.B. van Bragt investigated flow instability under natural circulation based on the natural circulation Dutch Dodewarrd BWR, and flow oscillation during startup was measured. Jiang et al. (2000) performed a series of experiments on the HRTL-5 (5 MW heating reactor test loop) under different pressures and other operation parameters in a rather wide range. In their work, not only several kinds of two phase flow special instability phenomena were observed and the mechanisms were analyzed, but also the type I density wave instability was reported and analyzed. Numerous
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
experimental investigations on the natural circulation boiling systems were reported in literature. Durga Prasad et al. (2007) made a review of investigations on flow instability in natural circulation loops. Caorso and Lasalle plant events happened in 1984 and 1988, respectively, renewed the interests of many researchers in coupled neutron dynamic thermal hydraulic instability in BWRs (March-Leuba and Rey, 1993), which are generated due to reactivity effect of void generated in the core or the Doppler effect of the fuel rod. Since then, many researchers focused their investigation interests on neutronic and thermal hydraulic coupling characteristics. van Bragt and van der Hagen (1998) interpret the basic mechanism of feedback and co-effect between the neutron dynamic and thermal hydraulic of the boiling water reactor. Durga Prasad et al. (2007) made some revision, expansion and supplement and made a review of the state of the art about natural circulation instability in boiling systems. However, there exist different understandings on the issue and reported results show great differences between each other. For example, van Bragt and van der Hagen (1998) found that an increase in the absolute value of void reactivity coefficient (VRC) had different ways of effect in different types of density wave oscillations (DWO), as so called type-I and type-II DWO regions. However, different from the results given by van Bragt and van der Hagen (1998), increasing the absolute value of VRC has a stabilizing effect in both regions according to Nayak et al. (2000), and a destabilizing effect in both the regions according to Lee and Pan (2005). Similar to the effects of VRC, the effects of the fuel time constant on the stability characteristics of the system show very great differences according to the reported literatures above mentioned. Even though these researchers use different approaches to study the similar problems, but the inconsistent results reported imply that understanding on the issue of the natural circulation instability coupled with neutron kinetics is not clear enough. The 5-MW nuclear heating reactor developed by the Institute of Nuclear Energy Technology (INET), Tsinghua University, has been in operation since 1989. It adopts the concept of integral arrangement and can operate both in pressurized water mode and boiling water mode under low pressure of 1.5 MPa. Different from the systems studied by van Bragt and van der Hagen (1998), Nayak et al. (2000), and Lee and Pan (2005), the present paper deals with the natural circulation instability on HRTL-5 with and without coupled point neutron kinetics. When the coupling between neutron kinetics and thermal hydraulic is considered, both the Doppler effect and void reactivity feedback are taken into account.
2. Approach In this investigation, the drift flux model with four equations is applied to describe the flow characteristics of the system and the point neutron kinetics with six groups of delayed neutron precursor is used to simulate heat generation in the core, based on which the computational code has been developed by ourselves. The features of the HRTL-5 are shown in Fig. 1, the whole loop can be divided into seven flow regions, including single-phase flow region, deep subcooled boiling region, low sub-cooled boiling region, bulk boiling region in the heated section and condensation region, single-phase flow region, void-flashing region in the adiabatic riser, finally the single-phase flow region in the down-comer. Such is the detailed division about the natural circulation. In this investigation, the local resistances concentrate in the inlet and outlet of the heated section. Based on the corresponding experimental data, the resistance coefficient at the inlet and outlet of the heated section is about 33 and 3, respectively. Consequently, the widely validated computer program has been developed
4973
Fig. 1. HRTL – 5 test loop. 1, heated section; 2, riser; 3, steam–water separator; 4, condensator; 5, heat exchanger; 6, downcomer; 7, flow meter; 8, throttle valve; 9, observation window.
successfully, which shows very good agreement with the experimental results performed on HRTL-5. The mathematic model is shown as follows:Mass conservation: ∂ ∂ [(1 − ˛)l + ˛v ] + [(1 − ˛)l ul + ˛v uv ] = 0 ∂t ∂z
(1)
Momentum conservation: ∂ ∂ [(1 − ˛)l u2l + ˛v u2v ] [(1 − ˛)l ul + ˛v uv ] + ∂z ∂t ∂p =− + ∂z
∂p ∂z
+ L
∂p ∂z
+ F
∂p ∂z
(2) G
Energy conservation: ∂ Uq ∂ [(1 − ˛)l hl + ˛v hv ] + [(1 − ˛)l ul hl + ˛v uv hv ] = A ∂t ∂z (3) Steam mass equation: ∂ ∂ (˛v ) + (˛v uv ) = i ∂t ∂t
i = 1, 2, 3
(4)
Drift flux velocity model (Zuber and Findlay, 1965): J = (1 − ˛)ul + ˛uv
(5)
uv = C0 J + uvj
(6)
Sub-cooled boiling model (Marotti, 1977): Qc =
ϕ=
3˛Aq (Ts − T )2 · Rb (TW − T )2 − (TW − TS )2
(TW − TS )2 (TW − T )2
(7)
(8)
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J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
From Eqs. (12) and (13), the following equation can be derived:
(t) − ˇ ˇ dP(t) = P(0) i e−i t P(t) + dt + e−i t
i
i
ˇi i
t
P(t )ei t dt
(14)
0
The reactor kinetics is coupled with the fuel rod dynamics and thermal hydraulics through the reactivity feedback due to fuel temperature and void fraction. The reactivity (t) consists of void and Doppler feedbacks and is given in form as follows: (t) = (0) + CT (Tav − Tav0 ) + C˛ (˛av − ˛av0 )
(15)
More detailed information about the mathematical model and computational format can be found in the literature (Wang et al., 2007). 3. Results and discussions
Fig. 2. The stability map of the system (Psys = 1.5 MPa, Kin = 33, Kout = 3).
3.1. Model verification Uqϕ Qc 1 = − Ar Ar
(9)
Condensation model (Yang, 2002): 2 = −
The model can be used to determine the stability map of a system. The operating point will be considered unstable if the dis-
3˛(TS − T ) rRb [(6z(Cp TS + r))/(u¯ v rl cp )(((TS − Tin )/(2TS + Tin )) + ((TS − T )/(2TS + T )))]
1/2
−
˛uv cpv TS lv r 2 l
·
dp (10) dz
Void flashing model (Jiang and Emendorfer, 1993): 3 =
1 dhS dp · [(1 − ˛)l ul + ˛v uv ] r dp dz
(11)
Point neutron kinetics with six delayed neutron precursor groups: dP(t) (t) − ˇ 1 = P(t) + i Ci (t) dt
(12)
dCi (t) = −i Ci (t) + ˇi P(t), dt
(13)
6
6
i = 1, 2, . . . , 6
turbance of some parameter, such as inlet subcooling and heat flux, makes the flow parameter grow continuously to same amplitude. However, if the disturbance makes the flow parameter perturbation dampen out, the corresponding state is considered stable. Fig. 2 shows the comparison of the marginal stability boundaries obtained from the model evaluation against the experimental results performed on HRTL-5 and the data set of Jiang (1994). It can be seen that the simulation results in this paper agree very well with both the experimental results performed on HRTL-5 and
0.54 0.51 0.48 0.52 0.51
Ule(m/s)
0.50 0.50 0.45 0.5 0.4 0.3 0.40 0.35 0.30 5
10
15
20
25
30
35
t(s) Fig. 3. The time evolution of inlet flow velocity (Psys = 1.5 MPa, q = 200 kW/m2 , Kin = 33, Kout = 3).
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
0.192
4975
ZFDB
0.53 0.52 0.51
0.189
Void Fraction
0.50
0.186
0.20 0.16
0.024
0.183
0.022 0.180
5
10
15
20
25
30
35
0.020
10
20
30
t(s)
t(s)
the results reported by Jiang (1994). It indicates that there are two marginal stability boundaries for some heat flux. With the increase of the heat flux, the inlet subcooling corresponding to the stability boundary increases for both. Fig. 3 shows the time evolution of the flow velocity at the inlet with disturbance of the same amplitude. In this figure, it is clearly indicated that if other operating parameters are fixed, including system pressure, heat flux and the geometry of the system, with the increase of the inlet subcooling from 15.0 K to 26.2 K, the disturbance of the inlet flow velocity will result in different way of development. For example, when the inlet subcooling is 15.0 K, the disturbance dampens slowly out if the time is long enough; but when the inlet subcooling goes to 15.2 K, even though the value of the inlet subcooling only increases by a very small amount, the disturbance makes the inlet flow velocity oscillation grow continuously to a oscillation with same amplitude finally. The similar phenomenon happens when the inlet subcooling is around 26.0 K. Moreover, the final amplitude of the oscillation undergoes a track from low to high then to low with the increase of the inlet subcooling. The results also agree well with the experimental results reported by Jiang et al. (2000). Fig. 4 shows the time evolution of the onset point of fully developed boiling (FDB) when the inlet subcooling is 15.2 K. The figure indicates that ZFDB oscillates from about 0.181 to 0.190 associated with the oscillation of inlet flow velocity, as is shown in the third curve in Fig. 3. Figs. 5 and 6 show the model prediction of time evolution of void fraction at different position in heated section and adiabatic riser respectively. It can be clearly found in the two figures that the void fraction wave at different position in both heated section and adiabatic riser transfer from upstream to downstream during the process of the oscillation. It is also seen that the transfer process of the disturbance of inlet parameter takes longer time to adiabatic riser. In other words, this process can be considered as the transfer process of density wave of the two phase mixture from inlet to outlet. 3.2. Nuclear coupled density wave instability Fig. 7 shows the marginal stability boundary comparison of model evaluation between with and without consideration of coupling of neutron kinetics and thermal–hydraulic. The consideration of the coupling includes Doppler effect and void reactivity feedback. It can be concluded that the nuclear coupled density wave instability has a wider unstable zone than ever, which means that coupling
Fig. 5. the time evolution of void fraction in heated section (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
0.50
Z=1.58m Z=2.58m Z=3.58m
0.49
Void Fraction
Fig. 4. the time evolution of ZFDB (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
0.48
0.47
10
20
30
t(s)
Fig. 6. the time evolution of void fraction in adiabatic riser (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
neutron kinetics with thermal–hydraulic makes the system more unstable around the original boundary. In order to understand the effects of Doppler effect feedback and void reactivity feedback better, the two effects are investigated 54
without neutron feedback nuclear feedback
48 42 36
stable
30
unstable 24 18 12 180
stable
240
300
360
420 2
q(kW/m ) Fig. 7. The stability map of the system (Psys = 1.5 MPa, Kin = 33, Kout = 3).
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J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
750
Ule(m/s)
0.54
Doppler effect only void reactivity feedback only Doppler effect and void reactivity feedback without nuclear feedback 2
250
''
500
0
q (q -q 0)(W/m )
0.52
''
''
0.50
without nuclear feedback void reactivity feedback only Doppler effect only Doppler effect and void reactivity feedback
0.48
-250 -500
0.46 10.0
12.5
15.0
17.5
20.0
-750 10
t(s) Fig. 8. The time evolution of inlet flow velocity (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
respectively. Fig. 8 shows the time evolution of inlet flow velocity under different consideration modes of the nuclear feedback when inlet subcooling is 15.2 K. It can be observed that for a fixed operation condition, Doppler effect makes the system a little bit more “stable”, the void reactivity feedback makes the system more “unstable”, and the cooperation of Doppler effect and void reactivity makes system stability lie between without consideration of nuclear feedback and only consideration of void reactivity feedback. It is because that those different consideration modes of the nuclear feedback make the amplitude of the oscillation of inlet flow velocity exhibit difference between each other. Fig. 9 shows different feedback reactivity time series based on different consideration modes. As is shown in Fig. 9, the feedback reactivity oscillations are different from each other in both the amplitude and phase. It is because of the following coupling chains, which include the coupling of the fuel temperature, reactivity, thermal power of the reactor, the fuel dynamics and the fuel temperature again, the coupling of the overall void fraction in the core, the reactivity, thermal power of the reactor, the fuel dynamics and the void fraction in the core again, and the coupling of the above two coupling chains, and the time delay of the thermal–hydraulic parameters. The direct effect of the nuclear feedback results in the change of the heat flux transfer from the
20
30
t(s) Fig. 10. The time evolution of relative heat flux (Psys = 1.5 MPa, q0 = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
fuel to the coolant. Fig. 10 shows the time evolution of the relative heat flux (q (t) − q (0)) under different consideration modes of nuclear feedback. It is clearly showed that the relative heat flux caused by Doppler effect takes the smallest value and the biggest by the void reactivity. Even Doppler effect makes the heat flux oscillate around the initial value; the system will have the trend to be stable according to the results shown in Fig. 8. It can be explained by the time delay or phase difference between the feedback reactivity, feedback heat flux and inlet flow velocity as shown in Figs. 8–10. Because the feedback reactivity caused by void reactivity, feedback heat flux and inlet flow velocity are in phase, the consideration of void reactivity feedback makes the system have the trends to be unstable as shown in Fig. 8. Furthermore, the comparison of marginal stability boundaries between different coefficients of nuclear feedback is also studied. Fig. 11 shows the comparison between different void reactivity feedback coefficients. It can be observed that the increase of absolute value of void reactivity feedback coefficient makes the system more unstable. Fig. 12 shows the comparison under different Doppler effect feedback coefficient in the system. It can be observed
54 1.5x10
-5
1.0x10
-5
5.0x10
-6
48 Doppler effect only void reactivity feedback only Doppler effect and void reactivity feedback
42 36 30
0.0
-5.0x10
-6
-1.0x10
-5
-1.5x10
-5
10.0
stable
unstable
24 18 12 180 12.5
15.0
17.5
20.0
t(s) Fig. 9. The time evolution of feedback reactivity (Psys = 1.5 MPa, q = 200 kW/m2 , subcooling T = 15.2 K, Kin = 33, Kout = 3).
stable
240
300
360
420 2
q(kW/m ) Fig. 11. The stability map of the system as function of Doppler coefficient (Ca ) (Psys = 1.5 MPa, Kin = 33, Kout = 3).
J. Wang et al. / Nuclear Engineering and Design 241 (2011) 4972–4977
54
3. Under present structure and operation condition, increasing the absolute value of Doppler effect feedback coefficient has a stabilizing effect on the stability of the system; 4. Under present structure, operation condition and design nuclear feedback coefficient condition, the nuclear feedback makes the system more unstable than without consideration of nuclear feedback; 5. The different effect way of different coupling modes is because of the relative phase difference between the feedback parameters and some thermal–hydraulic parameters.
48 42 36
stable
30 unstable
24 18 12 180
References
stable
240
4977
300
360
420 2
q(kW/m ) Fig. 12. The stability map of the system as function of Doppler coefficient (CT ) (Psys = 1.5 MPa, Kin = 33, Kout = 3).
that the increase of absolute value of Doppler effect feedback coefficient makes the system more stable in the system. 4. Conclusion The 5 MW heating reactor is operated under lower pressure and lower quality, which is very different from the commercial boiling water reactor in service. This paper presents the analysis method of the nuclear coupled two phase flow instability. Analysis results show: 1. The self-developed code can be used to analyze two phase density wave instability; 2. Under present structure and operation condition, increasing the absolute value of void reactivity feedback coefficient has a destabilizing effect on the stability of the system;
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