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A simple novel analysis procedure for IVR calculation in core-molten severe accident
Nuclear Engineering and Design 241 (2011) 4634–4642
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A simple novel analysis procedure for IVR calculation in core-molten severe accident Y.P. Zhang, S.Z. Qiu ∗ , G.H. Su, W.X. Tian Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an City 710049, China
a r t i c l e
i n f o
Article history: Received 27 December 2010 Received in revised form 15 March 2011 Accepted 15 March 2011
a b s t r a c t In-Vessel Retention (IVR) of core melt is a key severe accident management strategy adopted by operating nuclear power plants and advanced light water reactors (ALWRs), AP600, AP1000, etc. External Reactor Vessel Cooling (ERVC), which involves flooding the reactor cavity to submerge the reactor vessel in an attempt to cool core debris relocated to the vessel low head, is a novel severe accident management for IVR analysis. In present study, IVR analysis code in severe accident (IVRASA) has been proposed to evaluate the safety margin of IVR in AP600 with anticipative depressurization and reactor cavity flooding in severe accident. For, IVRASA, a simple novel analysis procedure has been developed for modeling the steady-state endpoint of core melt configurations. Furthermore, IVRASA was developed in a more general fashion so that it is applicable to compute various molten configurations such as UCSB Final Bounding State (FIBS). The results by IVRASA were consistent with those of the UCSB and INEEL. Benchmark calculations of UCSB-assumed FIBS indicate the applicability and accuracy of IVRASA and it could be applied to predict the thermal response of various molten configurations. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In-vessel coolability of core melt is an important issue in addressing a postulated inadequate core cooling event in nuclear reactors. In such an event, a significant amount of core material can become molten and relocate downward into the lower head of the reactor vessel, as happened in the Three Mile Island Unit2 (TMI-2) accident. If it is possible to ensure that the lower head remains intact so that relocated core materials are retained, the enhanced safety associated with these plants can reduce concerns about containment failure and associated risk. For example, the Westinghouse Advanced 600 MWe PWR (AP600) adopted ERVC (External Reactor Vessel Cooling) with a flooded reactor cavity as the enhanced safety. Subsequental advanced light water reactors, such as AP1000, APR1400, also adopted this enhanced safety. If the reactor cavity is flooded before melt relocated into the lower head, the vessel wall would be initially cool and the outer vessel wall would remain close to the cavity water saturation temperature. Boiling crisis is the sufficient and necessary condition for lower head failure (Theofanous et al., 1996a). Nucleate poor boiling of the cavity water is an efficient mechanism for heat removal from the molten debris in the lower plenum. If the local heat flux through the vessel wall exceeded the critical heat flux (CHF), vessel failure would be expected.
∗ Corresponding author. Tel.: +86 29 82665607; fax: +86 29 82665607. E-mail address: [email protected] (S.Z. Qiu). 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.03.055
IVR of molten core debris inside reactor pressure vessel (RPV) lower head through external cooling by cavity water has been the subject of numerous numerical and experimental investigations conducted by Kolev (1993), Theofanous et al. (1994a,b, 1996a,b), Asfia and Dhir (1996), Chu et al. (1997), Rempe et al. (1997), Loktinonov et al. (1999), Esmaili and Khatib-Rahbar (2004), and Dinh et al. (2004). Henry and Fauske (1993) investigated the capability of the external cooling of the RPV lower head to prevent failure considering the presence of the RPV insulation. Cheung et al. (1997) developed a subscale boundary layer boiling (SBLB) test facility to study the boundary layer boiling and critical heat flux phenomena on a downward facing cured heating surface, and to measure the spatial variation of the critical heat flux. Knudson and Rempe (2002) established IVR model to simulate heat transfer inside the accumulated molten pool, heat transfer from the molten pool to the reactor vessel, and heat transfer from exterior vessel surfaces using SCDAP/RELAP5-3D (SCDAP/RELAP5-3D Code Development Team, 2002). Theofanous et al. (1996a) and Rempe et al. (1997) used one-dimensional mathematical model to calculate the thermal response of the lower head. They also provided a summary of the various heat transfer correlations for the ceramic pool and the stratified light molten metallic layer. Khatib-Rahbar et al. (1996) adopted a two-dimensional model. A comparison of the one-dimensional and two-dimensional models showed that a onedimensional heat transfer model of the lower head performed adequately.
Y.P. Zhang et al. / Nuclear Engineering and Design 241 (2011) 4634–4642
Nomenclature A
q qh,b
coefficient for estimating heat transfer from the surface of the melt pool, W/m2 K4 Grashoff number, = gˇTmax H3 /2 gravity acceleration, m/s2 height of the metallic layer, vertical size of the cavity, m depth of oxide pool, m thermal conductivity, W/mK Nusselt number, = (q H )/kTmax Prandtl number, = /˛ volumetric heat generation rate, W/m3 average heat flux at pool boundaries, W/m2 heat flux from the bottom of heavy metallic layer,
ql,b
W/m2 heat flux from the top oxidic pool crust into the top
ql,t
light metal layer, W/m2 heat flux from the top light metallic layer into the
ql,w
internal atmosphere of the reactor, W/m2 heat flux from the top metallic layer into the vessel
qo,dn qo,h
wall, W/m2 heat flux towards the bottom of oxidic pool, W/m2 heat flux from the ceramic pool to the heavy metallic
Gr g H H k Nu Pr Q˙
qo,up qves R R Ra Ra S Sdn Sh,b Sl,b Sl,t Sside Sup T Tbh Tbl Tl,b Tl,t Ts,i
Ts,o TV,i TV,o V
layer, W/m2 heat flux towards the top of oxidic pool, W/m2 heat flux from the outer surface of the vessel to water, W/m2 reactor vessel, hemisphere radius, m ratio of the Nusselt number Rayleigh number (metallic layer), = (gˇTmax H3 )/(˛) Rayleigh number (oxide pool), = (gˇQ˙ H 5 )/(k˛) area of the melt pool, m2 area of the bottom of the oxide pool, m2 area of the bottom of the heavy metallic layer, m2 area of the bottom of the light metallic layer, m2 area of the top of the light metallic layer, m2 area of the side of the oxide pool, m2 area of the top of the oxide pool, m2 temperature, K bulk temperature of the heavy metallic layer, K bulk temperature of the light metallic layer, K temperature of the bottom of light metallic layer, K temperature of the top of light metallic layer, K inner surface temperature of the internal structure, K outer surface temperature of the internal structure, K inner surface temperature of the vessel wall, K outer surface temperature of the vessel wall, K volume of the melt pool, m3
ε ε1 h Tmax
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emissivity emissivity of the top light metallic layer angle from the bottom center of the lower head, degree maximum angle of the heavy metallic layer, degree kinematic viscosity, m2 s Stefan-Boltzmann constant (5.67 × 10−8 W/m2 K4 ) maximum bulk-wall temperature difference, K
Subscripts CHF critical heat flux cr ceramic crust dn downward (over the hemispherical boundary) h heavy metallic layer l light metallic layer o oxide pool s upper plenum structures side the side of the oxide pool up upward (over the flat boundary of the oxidic pool) w vessel wall
In the present paper, the main objective is to present a simple novel analysis procedure IVRASA based on the existing constitutive relations, originally developed for AP600 (Theofanous et al., 1996a; Rempe et al., 1997), and to compare the results calculated by IVRASA with those calculated by the University of California–Stanta Barbara (UCSB) (Theofanous et al., 1996a) and the Idaho National Engineering and Environmental Laboratory (INEEL) (Rempe et al., 1997). 2. The model of IVRASA IVRASA model is based on DOE/ID-10460 that the Department of Energy (DOE) contracted the UCSB to produce to support the Westinghouse position on AP600 IVR (Theofanous et al., 1996a) and the technical evaluation of AP600 IVR by INEEL (Rempe et al., 1997). The later was developed by INEEL to independently verify the results of UCSB. The UCSB study regarded configuration A (see Fig. 1) as the final steady state, their postulated Final Bounding State (FIBS). A key assumption in the UCSB study was their assumed debris configuration. And the UCSB study argued that their FIBS bounded thermal loads from any other configurations. However, INEEL’s review suggested that the UCSB FIBS did not bound several possible thermal
Greek characters ˛ thermal diffusivity, m2 /s ˇ thermal expansion coefficient, K−1 ı the thickness, m ıcr oxide crust thickness of the side of the oxide pool, m oxide crust thickness of the bottom of the oxide pool, ıcr,b m oxide crust thickness of the top of the oxide pool, m ıcr,t ıV thickness of the vessel wall, m Fig. 1. Configuration A (UCSB-assumed FIBS debris configuration).
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Fig. 2. Alternate debris configurations evaluated by INEEL (a) configuration B; (b) configuration C.
challenges from other debris configurations. So, INEEL gave other two configurations of core melt (see Fig. 2), which could be more challenging than the UCSB-assumed configuration. Configuration A assumes a molten ceramic pool lies beneath a metallic layer; configuration B represents a hypothesized endstate that is based on configuration A. A middle metallic layer is sandwiched between two molten ceramic layers. Configuration C represents a case where sufficient uranium dissolves into unoxidized zirconium to form a heavier metallic layer of Fe–U–Zr in the bottom and a light metallic layer of Fe–Zr on the top with a molten ceramic pool between the two metallic layers.
IVRASA is a simple analysis procedure that is similar to the model used in the UCSB report (Theofanous et al., 1996a), and IVRASA contains equations similar to the equations reported in the UCSB study (Theofanous et al., 1996a). The governing equations of the IVRASA model can be seen as follows, and more details about the property equations can be seen in UCSB report (Theofanous et al., 1996a). However, IVRASA was developed in a more general manner so that it could calculate Configuration B and Configuration C, besides Configuration A assumed as UCSB FIBS, and some modifications of the Rempe model equations (Rempe et al., 1997) have been shown here. The melt pool Configuration C more bounded thermal loads from other configurations (Rempe et al., 1997). So, the threelayer schematic diagram of the melt pool Configuration C is shown in Fig. 3, and the schematic diagram of the melt pool Configuration A and B is similar with the schematic of the melt pool Configuration C in addition to the different layers of melt. As discussed above, the governing equations of the three layers are shown as follows (these equations are also suitable for the Configuration A and B). Oxidic pool:
qo,dn = R =
Q˙ o Vo Sside + Sdn + Sup R
Nuup Nudn
qo,up =
Q˙ o ı2cr () + ıcr () 2kcr
qo,dn () kcr
Q˙ o ıw () + kw
− To,m +
qo,dn ()ıw () kw
+ Tw,o = 0
ıw () = kw
Tw,m − Tw,o qo,dn () + Q˙ o ıcr ()
qves () = qo,dn () + Q˙ ıcr ()
2.1. IVRASA methodology
Q˙ o Vo = qo,up Sup + qo,dn Sdn
A modification in the Rempe model equations (Eq. (A-106)) (Rempe et al., 1997) has been shown as follow:
Sup
(6)
(7)
Eqs. (5) and (6) were solved iteratively to get the value of the thickness of the ceramic crust, then the heat flux to the water of the outer surface of the vessel could be obtained. Light metallic layer: Q˙ l Vl + ql,b Sl,b = ql,t Sl,t + ql,w Sl,w ql,b = (To,m − Tbl )
Q˙ o ıcr,t kcr + 2 ıcr,t
(1) (2)
(3)
Q˙ o Vo − qo,dn (Sside + Sdn )
(5)
(4) Fig. 3. The schematic of the melt pool Configuration C for IVRASA.
(8) (9)
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Table 1 Comparison of IVRASA with UCSB FIBS. IVRASA
UCSB
Configuration A, B and C Portion of the decay heat in metallic layer Emissivity from the metallic layer may be represented by a point value of 0.29a Some additional heat sources due to oxidation or steel activations exist in the metallic layerb UCSB ACOPO molten pool natural convection correlations apply UCSB ULPU CHF lower bound correlations apply
Configuration A assumed FIBS All the decay heat resides in the ceramic pool Emissivity from the metallic layer may be represented by a point value of 0.45 No additional heat sources exist in the metallic layer
a b
According to the analysis of INEEL (Rempe, 1997), emissivity from the metallic layer was a point value of 0.29, which is a conservative. Power and Behbahani (2004) suggested that there had the potential for inter-metallic reactions in metallic layer. 4 − T4 ] [Tl,t s,i
ql,t = ql,w
2.2. IVRASA-FIBS (10)
(1/εl ) + ((1 − εs )Sl,t /εs Ss )
kw = (Tw,m − Tw,o ) ıw ıs ks
Ts,o = Ts,i −
4 Tw = Ts,o −
(11)
4 − T4 ) (Tl,t s,i
(12)
(Ss /εl Sl,t ) + ((1 − εs )/εs )
0.25
ks (Ts,i − Ts,o ) ıs εs
(13)
ks ıo (Ts,i − Ts,o ) + Tw,o kw ıs
Tw =
(14)
Other two modifications in the Rempe model equations (Eqs. (A121) and (A-122)) (Rempe et al., 1997) have been shown as follow:
Tbl
UCSB Mini-ACOPO molten pool natural convection correlations apply UCSB ULPU CHF lower bound correlations apply
=
4 − T4 ) (Tl,t s,i
1/Al,t ((1/εl ) + ((1 − εs )Sl,t /εs Ss )
Tl,b =
0.25
qo,up
+ Tl,t
(15)
0.25 + Tbl
Al,b
(16)
Heavy metallic layer: Q˙ h Vh + qo,h Sdn = qh,b Sh,b qo,h = qh,b =
Sup Sdn
h
qo,dn () sin() cos() d
(17) (18)
0
kw (Tw,i − Tw,o ) ıw
(19)
qo,h is the heat flux from the ceramic pool to the heavy metallic layer, and the definition of the variable is different from the INEEL model and the UCSB model. The decay heat in the oxidic pool and the heavy metallic layer is calculated in a simple way, that is: Q˙ o + Q˙ h = Pdecay,t
(20)
mU (270/238) Q˙ h Vh = mUO2 Q˙ o Vo
(21)
where mU is the mass of uranium dissolved into the heavy metallic layer, and mUO2 is the mass of mUO2 in the oxidic pool. CHF from vessel outer surface: qCHF () = C1 + C2 + C3 2 + C4 3 + C5 4
(22)
where is the angle from the bottom center of the vessel lower head, and the coefficients C1 through C5 are based on the experimental results for AP600 (Theofanous et al., 1996a). The impact of the decay heat in the metallic layers as the sensitivity study is discussed later. The calculation of the fraction of the decay heat in the metallic layers was same with that in the Rempe model (Rempe et al., 1997).
As discussed before, IVRASA was developed in a more general fashion so that it could calculate configuration A, B and C. However, the UCSB study regarded configuration A (see Fig. 1) as the FIBS, which was a key assumption in the UCSB study (Theofanous et al., 1996a). Configuration A is assumed to represent a two-layer melt pool with a light metallic layer of Fe–Zr on top of a molten ceramic pool of UO2 –ZrO2 as shown in Fig. 1. According to the technical estimate report by INEEL (Rempe et al., 1997), IVRASA concerns about the limitations of the UCSB model, and some important assumptions were modified (as shown in Table 1). The comparison of IVRASA with UCSB FIBS was shown in Table 1. As shown in Table 1, here, the CHF correlations still adopted the CHF correlations used in UCSB study. 2.3. Heat transfer correlations in IVRASA In DOE/ID-10460 (Theofanous et al., 1996a), heat transfer correlations were based on data from the UCSB Mini-ACOPO tests. Further testing was subsequently carried out in the ACOPO facility, which was a larger scale version of Mini-ACOPO. Correlations obtained from the Mini-ACOPO and ACOPO tests differ. IVRASA adopted the heat transfer correlations based on ACOPO data. Heat transfer correlations in molten ceramic pool and metallic layer in IVRASA were compared with those used in UCSB model and INEEL calculations, as shown in Table 2. The constitutive set of empirical heat transfer correlation is used in the same form with some variation as given in Table 2 for different models. 3. Verification and calculation results of IVRASA This section presents IVRASA calculation results. IVRASA calculations for the UCSB-assumed FIBS (as shown in Table 1) were conducted with the UCSB input data and INEEL input data under the condition of successful reactor coolant system depressurization and reactor cavity flooding. And the input data of the UCSB and INEEL were shown in the technical estimate report by INEEL (Rempe et al., 1997). Calculation results of IVRASA were presented as follows. Here, we give that these variables representing IVR margins best, such as heat fluxes, ratios of these vessel heat fluxes to the CHF, oxide crust thickness and vessel wall thickness. 3.1. Benchmark calculation results of IVRASA In order to verifying IVRASA study results, benchmark calculations were conducted with the UCSB input and the UCSB-assumed FIBS. As the UCSB results were verified by INEEL (Rempe et al., 1997), benchmark calculations of IVRASA were compared with the UCSB results and INEEL results as follows. Results from IVRASA were compared with results presented in DOE/ID-10460 Appendix
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Table 2 Heat transfer correlations used in different models. 1. Constitutive correlation set used by IVRASA in a steady state Metal Side wall: Churchill and Chu (1975): Nu =
0.15Ra1/3 [1+(0.492/Pr)9/16 ] 12
16/27
for 0.1 < Ra < 10 and any Pr. Top and bottom: Globe and Dropkin (1959): Nu = 0.069Ra1/3 Pr0.074 for 3 · 105 < Ra < 7 · 109 and 0.02 < Pr < 8750 Ceramic pool Top: Bonnet (1998) ACOPO (3D experiments): Nuup = 1.95Ra 0.18 for 1010 < Ra < 3 · 1016 . Bottom: Mayinger et al. (1975): Nudn = 0.55Ra 0.22 for 7 · 106 < Ra < 5 · 1014 2. Constitutive correlation set used by UCSB in a steady state (Theofanous et al., 1996a) Metal Side wall: Theofanous et al. (1994c): Nu = 0.076Ra1/3 . Top and bottom: Globe and Dropkin (1959) modified to Nu = 0.15Gr1/3 for 3 · 105 < Ra < 7 · 109 and 0.02 < Pr < 8750 Ceramic pool Top: Theofanous et al. (1996b) Mini-ACOPO (1/8 scale): Nuup = 0.345Ra 0.233 for 1012 < Ra < 3 · 1014 and 2.6 < Pr < 10.8 Bottom: Theofanous et al. (1994c) Mini-ACOPO: Nudn = 0.0038Ra 0.35 for 1012 < Ra < 3 · 1014 and 2.6 < Pr < 10.8
Fig. 4. Comparison of IVRASA heat flux with UCSB (DOE/ID-10460) and INEEL heat fluxes assuming UCSB FIBS and input.
3. Constitutive correlation set used by INEEL in a steady state (Rempe et al., 1997) Metal Side wall: Churchill and Chu (1975):
Nu =
0.825 + 0.387Ra1/6 / 1 + (0.492/Pr)
9/16
8/27 2
for 0.1 < Ra < 1012 and any Pr. Top and bottom: Globe and Dropkin (1959): Nu = 0.069Ra1/3 Pr0.074 for 3 · 105 < Ra < 7 · 109 and 0.02 < Pr < 8750 Ceramic pool Top: Theofanous et al. (1996b) ACOPO (1/2 scale): Nuup = 2.4415Ra 0.1722 Bottom: Theofanous et al. (1996b) ACOPO (1/2 scale): 0.25 Nudn = 0.1857Ra 0.2304 (H/R) for 1010 < Ra < 3 · 1016
Q (Theofanous et al., 1996a) and the INEEL calculation results (Rempe et al., 1997). It can be seen from Figs. 4–7 that benchmark calculations indicate that IVRASA correctly interpreted equations in the UCSB analyses and correctly encoded these equations into IVRASA. Fig. 4 compares vessel wall heat fluxes predicted by IVRASA, UCSB, and INEEL; Fig. 5 compare CHF ratios predicted by IVRASA and UCSB; Figs. 6 and 7, respectively, compare oxide crust thickness and vessel wall thickness predicted by IVRASA, UCSB, and INEEL. Figs. 4 and 5 indicate that IVRASA, UCSB model, and INEEL predictions differ slightly at the locations adjacent to ceramic pool (between 0 and ∼76◦ ), and were slightly larger at locations adjacent to the metallic layer (greater than ∼76◦ ). Particularly, at the loca-
Fig. 5. IVRASA and UCSB (DOE/ID-10460) CHF ratios assuming UCSB FIBS and input.
Fig. 6. IVRASA, UCSB (DOE/ID-10460) and INEEL predictions for oxide crust thickness assuming UCSB FIBS and input.
Y.P. Zhang et al. / Nuclear Engineering and Design 241 (2011) 4634–4642
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Fig. 9. Comparison of CHF ratios for UCSB-assumed FIBS. Fig. 7. IVRASA, UCSB (DOE/ID-10460) and INEEL predictions for oxide wall thickness assuming UCSB FIBS and input.
tions adjacent to the metallic layer, IVRASA heat flux prediction is larger than UCSB and INEEL. And INEEL prediction is smallest. Fig. 6 indicates that IVRASA oxide crust thickness prediction is smallest, and INEEL prediction is largest. Fig. 7 indicates that IVRASA vessel wall thickness prediction is similar to UCSB model, but different to INEEL at the locations adjacent to the metallic layer. Hence, differences in these figures may be due to different correlations adopted in different models. 3.2. Calculation results with IVRASA input As the UCSB results were verified by INEEL (Rempe et al., 1997), calculations of configuration A, configuration B and configuration C for UCSB-assumed FIBS were conducted with the IVRASA input recommended by INEEL. Calculation results of IVRASA were compared with those calculated by INEEL. 3.2.1. Calculation results of configuration A Calculation of configuration A for UCSB-assumed FIBS was conducted with the IVRASA input considering the decay heat in the metallic layer. Calculation results were compared with those calculated by INEEL as follows.
Fig. 8. Comparison of heat fluxes for UCSB-assumed FIBS.
It can be seen from Figs. 8 and 9 that IVRASA results of configuration A is similar to those calculated by INEEL, but different from the results calculated by UCSB model. Particularly, apparent differences lie in the locations adjacent to the metallic layer. IVRASA results and INEEL results have a sharply increase at the interface between the oxide ceramic pool and the metallic layer (∼76◦ ), and keep a high value at the locations adjacent to the metallic layer. This is because IVRASA adopts the input data recommended by INEEL considering the decay heat in the metallic layer (Rempe et al., 1997). However, UCSB model did not consider the decay heat in the metallic layer. As shown in Fig. 9, IVRASA predicts that CHF ratios remain below unity when INEEL input is adopted. There is much margin to failure for IVR. 3.2.2. Sensitivity studies of configuration A Although IVRASA predicts that CHF ratios remain below unity, Rempe et al. (1997) suggested that there were uncertainties in several input parameters. Rempe et al. (1997) presented three kinds of uncertainties that were vapor transport effects on natural convection, additional metallic layer sources (due to steel activation or oxidation) and reduced metallic melt mass. The uncertainty analysis of IVRASA input parameters were assumed to change the corresponding values of the parameters or equations that were modified to assess the phenomena of inter-
Fig. 10. Comparison of CHF ratios for UCSB-assumed FIBS.
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Fig. 11. Comparison of CHF ratios for UCSB-assumed FIBS.
Fig. 12. Comparison of CHF ratios for UCSB-assumed FIBS.
est. Modifications required for each analysis and results from each analysis are discussed below. Fig. 10 represents the condition of vapor transport effects on natural convection. When the temperature in the oxide pool exceeds the boiling temperature of one or more molten components, vaporization and pool boiling could occur, enhancing upward heat transfer from the molten pool. The presence of such lower evaporation temperature materials is supported by voids measured in examinations of debris from the TMI-2 vessel (Akers et al., 1992). IVRASA assumed a factor of 10 increase in the upward heat transfer correlation for this uncertainty recommended by INEEL Rempe et al. (1997). It can be seen from Fig. 10 that IVRASA result is similar to that by INEEL and the heat flux from the vessel at location adjacent to the oxide pool are reduced significantly (below ∼76◦ ). This is because increased upward heat losses decreased downward heat fluxes. At vessel locations in contact with the metallic layer (at angles above ∼76◦ ), heat fluxes are nearly 65% higher than values estimated for the base case. This is due to the increased heat input from the oxide pool into the metallic layer. As shown in Fig. 10, IVRASA result is slightly higher than that by INEEL, which is due to two different models adopt different CHF correlations. The CHF correlation based on ULPU-III facility was used by IVRASA model (Theofanous et al., 1994a,b), while the CHF correlation based on SBLB facility was adopted by INEEL model (Cheung et al., 1997). It can be seen that CHF margin is apparently reduced in this case. Fig. 11 represents the condition of additional metallic layer sources. Rempe et al. (1997) suggested that there was a potential for the metallic layer to contain additional heat source due to activation of stainless steel and oxidation of materials in the metallic layer. So IVRASA assumed an additional heat source in the metallic layer that corresponded to 8% of the core’s power at times between 2 and 6 h after shutdown recommended by INEEL (Rempe et al., 1997). Additional heat sources only affect the metallic layer results, which are proved from Fig. 11. It can be seen from Fig. 11 that IVRASA calculation results indicate that this additional heat source increases heat flux ratios at locations adjacent to the metallic layer by approximately 20%, which reduces the CHF margin of IVR. IVRASA result predicts heat flux ratio slightly higher than that by INEEL, which is due to different CHF and heat transfer correlations in the metallic layer adopted by IVRASA model. Fig. 12 represents the condition of reduced metallic melt mass that affects the height of the metallic layer. Because the metallic layer has a higher thermal conductivity, the mass of metals
assumed in the metallic layer significantly affects the estimated magnitude of the heat fluxes focused towards the adjacent vessel sidewall. If metallic melt mass is reduced, the excess of energy which come from the oxide pool and cannot be removed by radiation is focused through the vessel wall causing considerable thermal attack of the vessel. This is so-called focusing effect. This focusing effect may be a challenge to the integrity of the vessel. For IVRASA calculations, respectively, assumed the metallic layer contains approximately 70,000, 19,500 and 10,000 kg of vessel internal structure steel recommended by INEEL (Rempe et al., 1997). It can be seen from Fig. 12 that reductions in the steel relocation mass only affect metallic layer results, because oxide pool heat fluxes are independent of metallic layer mass assumptions. As shown in Fig. 12, CHF ratios at vessel locations in contact with the metallic layer approach unity for steel masses equal to 19,500 kg. When the steel masses are below these values, CHF ratios are greater than unity. This may cause the vessel failure. Particularly, when the steel masses equal to 10,000 kg, CHF ratios calculated by IVRASA reach to 1.6, which is greater than 1.3 calculated by INEEL. This is due to different CHF correlations adopted by IVRASA. According to the point calculations by IVRASA, reduced metallic layer mass may cause the vessel failure. 3.2.3. Calculation results of configuration B As discussed above, configuration B contains a debris configuration that occurs sometime after configuration A. A middle metallic layer is sandwiched between two molten ceramic layers. This configuration may be more challenge to the integrity of the vessel than configuration A. Calculation results of configuration B for UCSB-assumed FIBS were conducted by IVRASA with the input parameters recommended by INEEL (Rempe et al., 1997). Configuration B calculation results using IVRASA are shown in Figs. 13–15. It can be seen from Fig. 13 that peak heat fluxes occur at locations where the vessel is contact with the metallic layer and are approximately a factor of 32 times larger than predicted for configuration A (see Fig. 8). These higher heat fluxes are primarily due to the combined heat load to this metallic layer from the upper and lower oxide pool. As shown in Fig. 13, IVRASA result is lower than that of INEEL, which may be due to corrections in equations and different heat transfer correlations adopted by IVRASA. Fig. 14 results indicate that the ratio of the vessel heat flux to CHF values are predicted to typically be approximately 20 at vessel locations adjacent to the metallic layer (at locations above∼59◦ ).
Y.P. Zhang et al. / Nuclear Engineering and Design 241 (2011) 4634–4642
Fig. 13. Comparison of heat fluxes of configuration B for UCSB-assumed FIBS.
Fig. 14. Comparison of CHF ratios of configuration B for UCSB-assumed FIBS.
IVRASA result is lower than that of INEEL, which may be due to corrections in equations and different CHF correlations adopted by IVRASA. INEEL adopted the CHF Cheung (H/R = 2) correlations (Cheung et al., 1997). Fig. 15 shows the wall thickness of configuration B calculated by IVRASA, and the initial wall thickness is 15 cm.
Fig. 15. IVRASA wall thickness of configuration B for UCSB-assumed FIBS.
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Fig. 16. Comparison of heat fluxes of configuration C for UCSB-assumed FIBS.
3.2.4. Calculation results of configuration C As discussed above, configuration C contains a case where sufficient uranium dissolves into unoxidized zirconium to form a heavier metallic layer beneath a molten ceramic layer. Heat loads from the lower heavier metallic layer are focused to the bottom of the vessel lower head where the potential of the heat removal is a minimum. In this condition, decay heat in the lower heavier metallic layer applied. This configuration may be more challenge to the integrity of the vessel than configuration A. Calculation results of configuration C for UCSB-assumed FIBS were conducted by IVRASA with the input parameters recommended by INEEL (Rempe et al., 1997), considering decay heat in the lower heavier metallic layer. And the volumetric decay heat is 0.88 MW/m3 in the heavier metallic layer. Configuration C calculation results using IVRASA are shown in Figs. 16 and 17. It can be seen from Fig. 16 that peak heat fluxes occur at locations adjacent to the metallic layer (at locations below ∼42◦ ). As shown in Fig. 17, the ratio of the vessel heat flux to CHF values from 3.5 to 6.5 at adjacent to the metallic layer. This result is due to high heat fluxes from the metallic layer (due to decay heat from fission product into the metallic layer) and to lower heat removal rates at lower angles. It can be seen from Figs. 16 and 17 that difference between IVRASA results and those of INEEL is very small, but difference of results between two models is slightly larger at locations adjacent
Fig. 17. Comparison of CHF ratios of configuration C for UCSB-assumed FIBS.
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to the metallic layer. IVRASA predictions of heat fluxes and CHF ratios are all smaller than those predicted by INEEL. This is due to corrections in equations and different heat transfer correlations, as well as different CHF correlations adopted by IVRASA. The CHF correlation based on ULPU-III facility was used by IVRASA model (Theofanous et al., 1994a,b), while the CHF correlation based on SBLB facility was adopted by INEEL model (Cheung et al., 1997). 3.3. Sensitivity analysis of CHF correlations for IVR analysis Rempe et al. (2008) suggested that there was a large uncertainty in the CHF data. So, many uncertainties existed in fitting correlations according to experimental data. Moreover, the CHF correlation used for IVR analysis of AP600 was depended on experimental data of UPLU-III facility (Theofanous et al., 1994a,b). The UPLU-III is a 2D facility and cannot be used to adequately simulate the 3D heat transfer to the hemispherical channel between the reactor vessel and the surrounding insulation structure. SBLB facility (Cheung et al., 1997) is a 3D facility that can simulate the 3D heat transfer and two-phase boundary layer flow behavior in the annular between the reactor vessel and the surrounding insulation. Therefore, 3D ERVC tests should be carried out for IVR analysis of ALWRs, or some existing 3D experimental data should be used to IVR analysis, such as data or correlations of SBLB tests. 4. Conclusions 1. A simple novel analysis procedure-IVRASA was developed to predict the failure margin of the vessel. Benchmark calculations considering the UCSB-assumed FIBS indicate that IVRASA correctly interpreted equations in the UCSB analyses and correctly encoded these equations into IVRASA. IVRASA calculation results for the UCSB-assumed FIBS indicate that the vessel would remain intact, which is similar to the UCSB study and INEEL analyses. 2. According to INEEL evaluation report, INEEL gave other two configurations of core melt, which could be more challenging than the UCSB-assumed configuration. Calculation results of alternate debris configurations were conducted by IVRASA, which were consistent with those calculated by INEEL. This indicated that UCSB assumed FIBS did not bound all the heat loads, and additional analyses should be conducted. 3. This work also investigated the effect of the uncertainties of the CHF correlations on the analysis of IVR. The existing CHF correlation for IVR analysis is based on 2D tests. However, there exists a large uncertainty in the UPLU-III experimental data. Therefore, 3D ERVC tests should be carried out for IVR analysis, or some existing 3D experimental data should be used to IVR analysis.
References Akers, D.W., Jensen, S.M., Scheutz, B.K., 1992. Examination of Relocated Fuel Debris Adjacent to the Lower Head of the TMI-2 Reactor Vessel, NUREG/CR-61995, TMI(92) EG10. Asfia, F.J., Dhir, V.K., 1996. An experimental study of natural convection in a volumetrically heated spherical pool bounded on top with a rigid wall. Nucl. Eng. Des. 163, 333–348. Bonnet, J.M., 1998. Thermal hydraulic phenomena in corium pools: the BALI experiment. In: SARJ Meeting , Tokyo, Japan. Cheung, F.B., Haddad, K.H., Liu, Y.C., 1997. Critical Heat Flux (CHF) Phenomenon on a Downward Facing Curved Surface, NUREG/CR-6507, PSU/ME-97-7321. Chu, T.Y., Bentz, J.H., Slezak, S.E., Pasedag, W.F., 1997. Ex-vessel boiling experiment: 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, 89–99. Churchill, S.W., Chu, H.H.S., 1975. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transfer 18, 1323–1329. Dinh, T.N., Tu, J.P., Theofanous, T.G., 2004. Two-phase natural circulation flow in AP1000, In-vessel retention-related ULPU-V facility experiments. In: Proceedings of the 2004 International Congress on Advances in Nuclear Power Plants, ICAPP’04 , pp. 928–938. Esmaili, H., Khatib-Rahbar, M., 2004. Analysis of In-vessel Retention and Ex-vessel Fuel Coolant Interaction for AP1000. Energy Research, Inc, ERI/NRC 04-21, NUREG/CR-6849. Globe, S., Dropkin, D., 1959. Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below. Heat Transfer 81, 24. Henry, R.L., Fauske, H., 1993. External cooling of a reactor vessel under severe accident conditions. Nucl. Eng. Des. 139, 31–43. Khatib-Rahbar, M., Esmaili, H., Vijaykumar, R., Wagage, H., 1996. An assessment of Ex-vessel Steam Explosions in the AP600 Advanced Pressurized Water Reactor. Energy Research, Inc, ERI/NRC 95-211. Knudson, D.L., Rempe, J.L., 2002. In-vessel retention modeling capabilities of SCDAP/RELAP5-3D. In: Proceedings of ICONE10-22754 , Arlington, VA, USA. Kolev, N.I., 1993. Sicherheitsbericht des geplanten WWER-640 (W-407) Auswertung: System für Erhaltung der Schmelze im RDB, Schmelzfänger, KWU NA-M/93/016, Project GUS-Kooperation. Loktinonov, V.D., Mukhtarov, E.S., Yaroshenko, N.I., Orlov, V.E., 1999. Numerical investigation of the reactor pressure vessel behavior under severe accident conditions taking into account the combined processes of the vessel creep and the molten pool natural convection. Nucl. Eng. Des. 191, 31–52. Mayinger, F., Jahn, M., Reineke, H., Steinberner, U., 1975. Examination of thermohydraulic processes and heat transfer in a core melt, Final Report BMFT RS 48/1. Power, D., Behbahani, A., 2004. Density stratification of core debris. In: Proceedings of the OECD MASCA Seminar , Paris. Rempe, J.L., et al., 1997. Potential for AP600 In-vessel Retention Through Ex-vessel Flooding, Technical Evolution Report, INEEL/EXT-97-0077. Rempe, J.L., Suh, K.Y., Cheung, F.B., Kim, S.B., 2008. In-Vessel Retention Strategy for High Power Reactors, Technical Report, INEEEL/EXT-04-025621. SCDAP/RELAP5-3D Code Development Team, 2002. SCDAP/RELAP5-3D Code Manual, INEEL/EXT-02-00589. Theofanous, T.G., et al., 1994a. Critical heat flux through curved, downwards facing thick wall. In: Proceedings of the OECD/CSNI/NEA Workshop on Large Molten Pool Hear Transfer , Gernoble, France. Theofanous, T.G., et al., 1994b. Experience from the first two integrated approaches to in-vessel retention external cooling. In: Proceedings of the OECD/CSNI/NEA Workshop on Large Molten Pool Hear Transfer , Gernoble, France. Theofanous, T.G., et al., 1994c. In-vessel Cool-ability and Retention of a Core Melt, DOE/ID-10460. U.S. Department of Energy. Theofanous, T.G., et al., 1996a. In-vessel Cool-ability and Retention of a Core Melt, DOE/ID-10460, vol. 1 (revised October). Theofanous, T.G., et al., 1996b. The first results from the ACOPO experiment. In: Proceedings of the Topical Meeting on Probabilistic Safety Assessment (PSA’96) , Park Soty, UT.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
A simple novel analysis procedure for IVR calculation in core-molten severe accident Y.P. Zhang, S.Z. Qiu ∗ , G.H. Su, W.X. Tian Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an City 710049, China
a r t i c l e
i n f o
Article history: Received 27 December 2010 Received in revised form 15 March 2011 Accepted 15 March 2011
a b s t r a c t In-Vessel Retention (IVR) of core melt is a key severe accident management strategy adopted by operating nuclear power plants and advanced light water reactors (ALWRs), AP600, AP1000, etc. External Reactor Vessel Cooling (ERVC), which involves flooding the reactor cavity to submerge the reactor vessel in an attempt to cool core debris relocated to the vessel low head, is a novel severe accident management for IVR analysis. In present study, IVR analysis code in severe accident (IVRASA) has been proposed to evaluate the safety margin of IVR in AP600 with anticipative depressurization and reactor cavity flooding in severe accident. For, IVRASA, a simple novel analysis procedure has been developed for modeling the steady-state endpoint of core melt configurations. Furthermore, IVRASA was developed in a more general fashion so that it is applicable to compute various molten configurations such as UCSB Final Bounding State (FIBS). The results by IVRASA were consistent with those of the UCSB and INEEL. Benchmark calculations of UCSB-assumed FIBS indicate the applicability and accuracy of IVRASA and it could be applied to predict the thermal response of various molten configurations. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In-vessel coolability of core melt is an important issue in addressing a postulated inadequate core cooling event in nuclear reactors. In such an event, a significant amount of core material can become molten and relocate downward into the lower head of the reactor vessel, as happened in the Three Mile Island Unit2 (TMI-2) accident. If it is possible to ensure that the lower head remains intact so that relocated core materials are retained, the enhanced safety associated with these plants can reduce concerns about containment failure and associated risk. For example, the Westinghouse Advanced 600 MWe PWR (AP600) adopted ERVC (External Reactor Vessel Cooling) with a flooded reactor cavity as the enhanced safety. Subsequental advanced light water reactors, such as AP1000, APR1400, also adopted this enhanced safety. If the reactor cavity is flooded before melt relocated into the lower head, the vessel wall would be initially cool and the outer vessel wall would remain close to the cavity water saturation temperature. Boiling crisis is the sufficient and necessary condition for lower head failure (Theofanous et al., 1996a). Nucleate poor boiling of the cavity water is an efficient mechanism for heat removal from the molten debris in the lower plenum. If the local heat flux through the vessel wall exceeded the critical heat flux (CHF), vessel failure would be expected.
∗ Corresponding author. Tel.: +86 29 82665607; fax: +86 29 82665607. E-mail address: [email protected] (S.Z. Qiu). 0029-5493/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2011.03.055
IVR of molten core debris inside reactor pressure vessel (RPV) lower head through external cooling by cavity water has been the subject of numerous numerical and experimental investigations conducted by Kolev (1993), Theofanous et al. (1994a,b, 1996a,b), Asfia and Dhir (1996), Chu et al. (1997), Rempe et al. (1997), Loktinonov et al. (1999), Esmaili and Khatib-Rahbar (2004), and Dinh et al. (2004). Henry and Fauske (1993) investigated the capability of the external cooling of the RPV lower head to prevent failure considering the presence of the RPV insulation. Cheung et al. (1997) developed a subscale boundary layer boiling (SBLB) test facility to study the boundary layer boiling and critical heat flux phenomena on a downward facing cured heating surface, and to measure the spatial variation of the critical heat flux. Knudson and Rempe (2002) established IVR model to simulate heat transfer inside the accumulated molten pool, heat transfer from the molten pool to the reactor vessel, and heat transfer from exterior vessel surfaces using SCDAP/RELAP5-3D (SCDAP/RELAP5-3D Code Development Team, 2002). Theofanous et al. (1996a) and Rempe et al. (1997) used one-dimensional mathematical model to calculate the thermal response of the lower head. They also provided a summary of the various heat transfer correlations for the ceramic pool and the stratified light molten metallic layer. Khatib-Rahbar et al. (1996) adopted a two-dimensional model. A comparison of the one-dimensional and two-dimensional models showed that a onedimensional heat transfer model of the lower head performed adequately.
Y.P. Zhang et al. / Nuclear Engineering and Design 241 (2011) 4634–4642
Nomenclature A
q qh,b
coefficient for estimating heat transfer from the surface of the melt pool, W/m2 K4 Grashoff number, = gˇTmax H3 /2 gravity acceleration, m/s2 height of the metallic layer, vertical size of the cavity, m depth of oxide pool, m thermal conductivity, W/mK Nusselt number, = (q H )/kTmax Prandtl number, = /˛ volumetric heat generation rate, W/m3 average heat flux at pool boundaries, W/m2 heat flux from the bottom of heavy metallic layer,
ql,b
W/m2 heat flux from the top oxidic pool crust into the top
ql,t
light metal layer, W/m2 heat flux from the top light metallic layer into the
ql,w
internal atmosphere of the reactor, W/m2 heat flux from the top metallic layer into the vessel
qo,dn qo,h
wall, W/m2 heat flux towards the bottom of oxidic pool, W/m2 heat flux from the ceramic pool to the heavy metallic
Gr g H H k Nu Pr Q˙
qo,up qves R R Ra Ra S Sdn Sh,b Sl,b Sl,t Sside Sup T Tbh Tbl Tl,b Tl,t Ts,i
Ts,o TV,i TV,o V
layer, W/m2 heat flux towards the top of oxidic pool, W/m2 heat flux from the outer surface of the vessel to water, W/m2 reactor vessel, hemisphere radius, m ratio of the Nusselt number Rayleigh number (metallic layer), = (gˇTmax H3 )/(˛) Rayleigh number (oxide pool), = (gˇQ˙ H 5 )/(k˛) area of the melt pool, m2 area of the bottom of the oxide pool, m2 area of the bottom of the heavy metallic layer, m2 area of the bottom of the light metallic layer, m2 area of the top of the light metallic layer, m2 area of the side of the oxide pool, m2 area of the top of the oxide pool, m2 temperature, K bulk temperature of the heavy metallic layer, K bulk temperature of the light metallic layer, K temperature of the bottom of light metallic layer, K temperature of the top of light metallic layer, K inner surface temperature of the internal structure, K outer surface temperature of the internal structure, K inner surface temperature of the vessel wall, K outer surface temperature of the vessel wall, K volume of the melt pool, m3
ε ε1 h Tmax
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emissivity emissivity of the top light metallic layer angle from the bottom center of the lower head, degree maximum angle of the heavy metallic layer, degree kinematic viscosity, m2 s Stefan-Boltzmann constant (5.67 × 10−8 W/m2 K4 ) maximum bulk-wall temperature difference, K
Subscripts CHF critical heat flux cr ceramic crust dn downward (over the hemispherical boundary) h heavy metallic layer l light metallic layer o oxide pool s upper plenum structures side the side of the oxide pool up upward (over the flat boundary of the oxidic pool) w vessel wall
In the present paper, the main objective is to present a simple novel analysis procedure IVRASA based on the existing constitutive relations, originally developed for AP600 (Theofanous et al., 1996a; Rempe et al., 1997), and to compare the results calculated by IVRASA with those calculated by the University of California–Stanta Barbara (UCSB) (Theofanous et al., 1996a) and the Idaho National Engineering and Environmental Laboratory (INEEL) (Rempe et al., 1997). 2. The model of IVRASA IVRASA model is based on DOE/ID-10460 that the Department of Energy (DOE) contracted the UCSB to produce to support the Westinghouse position on AP600 IVR (Theofanous et al., 1996a) and the technical evaluation of AP600 IVR by INEEL (Rempe et al., 1997). The later was developed by INEEL to independently verify the results of UCSB. The UCSB study regarded configuration A (see Fig. 1) as the final steady state, their postulated Final Bounding State (FIBS). A key assumption in the UCSB study was their assumed debris configuration. And the UCSB study argued that their FIBS bounded thermal loads from any other configurations. However, INEEL’s review suggested that the UCSB FIBS did not bound several possible thermal
Greek characters ˛ thermal diffusivity, m2 /s ˇ thermal expansion coefficient, K−1 ı the thickness, m ıcr oxide crust thickness of the side of the oxide pool, m oxide crust thickness of the bottom of the oxide pool, ıcr,b m oxide crust thickness of the top of the oxide pool, m ıcr,t ıV thickness of the vessel wall, m Fig. 1. Configuration A (UCSB-assumed FIBS debris configuration).
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Fig. 2. Alternate debris configurations evaluated by INEEL (a) configuration B; (b) configuration C.
challenges from other debris configurations. So, INEEL gave other two configurations of core melt (see Fig. 2), which could be more challenging than the UCSB-assumed configuration. Configuration A assumes a molten ceramic pool lies beneath a metallic layer; configuration B represents a hypothesized endstate that is based on configuration A. A middle metallic layer is sandwiched between two molten ceramic layers. Configuration C represents a case where sufficient uranium dissolves into unoxidized zirconium to form a heavier metallic layer of Fe–U–Zr in the bottom and a light metallic layer of Fe–Zr on the top with a molten ceramic pool between the two metallic layers.
IVRASA is a simple analysis procedure that is similar to the model used in the UCSB report (Theofanous et al., 1996a), and IVRASA contains equations similar to the equations reported in the UCSB study (Theofanous et al., 1996a). The governing equations of the IVRASA model can be seen as follows, and more details about the property equations can be seen in UCSB report (Theofanous et al., 1996a). However, IVRASA was developed in a more general manner so that it could calculate Configuration B and Configuration C, besides Configuration A assumed as UCSB FIBS, and some modifications of the Rempe model equations (Rempe et al., 1997) have been shown here. The melt pool Configuration C more bounded thermal loads from other configurations (Rempe et al., 1997). So, the threelayer schematic diagram of the melt pool Configuration C is shown in Fig. 3, and the schematic diagram of the melt pool Configuration A and B is similar with the schematic of the melt pool Configuration C in addition to the different layers of melt. As discussed above, the governing equations of the three layers are shown as follows (these equations are also suitable for the Configuration A and B). Oxidic pool:
qo,dn = R =
Q˙ o Vo Sside + Sdn + Sup R
Nuup Nudn
qo,up =
Q˙ o ı2cr () + ıcr () 2kcr
qo,dn () kcr
Q˙ o ıw () + kw
− To,m +
qo,dn ()ıw () kw
+ Tw,o = 0
ıw () = kw
Tw,m − Tw,o qo,dn () + Q˙ o ıcr ()
qves () = qo,dn () + Q˙ ıcr ()
2.1. IVRASA methodology
Q˙ o Vo = qo,up Sup + qo,dn Sdn
A modification in the Rempe model equations (Eq. (A-106)) (Rempe et al., 1997) has been shown as follow:
Sup
(6)
(7)
Eqs. (5) and (6) were solved iteratively to get the value of the thickness of the ceramic crust, then the heat flux to the water of the outer surface of the vessel could be obtained. Light metallic layer: Q˙ l Vl + ql,b Sl,b = ql,t Sl,t + ql,w Sl,w ql,b = (To,m − Tbl )
Q˙ o ıcr,t kcr + 2 ıcr,t
(1) (2)
(3)
Q˙ o Vo − qo,dn (Sside + Sdn )
(5)
(4) Fig. 3. The schematic of the melt pool Configuration C for IVRASA.
(8) (9)
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Table 1 Comparison of IVRASA with UCSB FIBS. IVRASA
UCSB
Configuration A, B and C Portion of the decay heat in metallic layer Emissivity from the metallic layer may be represented by a point value of 0.29a Some additional heat sources due to oxidation or steel activations exist in the metallic layerb UCSB ACOPO molten pool natural convection correlations apply UCSB ULPU CHF lower bound correlations apply
Configuration A assumed FIBS All the decay heat resides in the ceramic pool Emissivity from the metallic layer may be represented by a point value of 0.45 No additional heat sources exist in the metallic layer
a b
According to the analysis of INEEL (Rempe, 1997), emissivity from the metallic layer was a point value of 0.29, which is a conservative. Power and Behbahani (2004) suggested that there had the potential for inter-metallic reactions in metallic layer. 4 − T4 ] [Tl,t s,i
ql,t = ql,w
2.2. IVRASA-FIBS (10)
(1/εl ) + ((1 − εs )Sl,t /εs Ss )
kw = (Tw,m − Tw,o ) ıw ıs ks
Ts,o = Ts,i −
4 Tw = Ts,o −
(11)
4 − T4 ) (Tl,t s,i
(12)
(Ss /εl Sl,t ) + ((1 − εs )/εs )
0.25
ks (Ts,i − Ts,o ) ıs εs
(13)
ks ıo (Ts,i − Ts,o ) + Tw,o kw ıs
Tw =
(14)
Other two modifications in the Rempe model equations (Eqs. (A121) and (A-122)) (Rempe et al., 1997) have been shown as follow:
Tbl
UCSB Mini-ACOPO molten pool natural convection correlations apply UCSB ULPU CHF lower bound correlations apply
=
4 − T4 ) (Tl,t s,i
1/Al,t ((1/εl ) + ((1 − εs )Sl,t /εs Ss )
Tl,b =
0.25
qo,up
+ Tl,t
(15)
0.25 + Tbl
Al,b
(16)
Heavy metallic layer: Q˙ h Vh + qo,h Sdn = qh,b Sh,b qo,h = qh,b =
Sup Sdn
h
qo,dn () sin() cos() d
(17) (18)
0
kw (Tw,i − Tw,o ) ıw
(19)
qo,h is the heat flux from the ceramic pool to the heavy metallic layer, and the definition of the variable is different from the INEEL model and the UCSB model. The decay heat in the oxidic pool and the heavy metallic layer is calculated in a simple way, that is: Q˙ o + Q˙ h = Pdecay,t
(20)
mU (270/238) Q˙ h Vh = mUO2 Q˙ o Vo
(21)
where mU is the mass of uranium dissolved into the heavy metallic layer, and mUO2 is the mass of mUO2 in the oxidic pool. CHF from vessel outer surface: qCHF () = C1 + C2 + C3 2 + C4 3 + C5 4
(22)
where is the angle from the bottom center of the vessel lower head, and the coefficients C1 through C5 are based on the experimental results for AP600 (Theofanous et al., 1996a). The impact of the decay heat in the metallic layers as the sensitivity study is discussed later. The calculation of the fraction of the decay heat in the metallic layers was same with that in the Rempe model (Rempe et al., 1997).
As discussed before, IVRASA was developed in a more general fashion so that it could calculate configuration A, B and C. However, the UCSB study regarded configuration A (see Fig. 1) as the FIBS, which was a key assumption in the UCSB study (Theofanous et al., 1996a). Configuration A is assumed to represent a two-layer melt pool with a light metallic layer of Fe–Zr on top of a molten ceramic pool of UO2 –ZrO2 as shown in Fig. 1. According to the technical estimate report by INEEL (Rempe et al., 1997), IVRASA concerns about the limitations of the UCSB model, and some important assumptions were modified (as shown in Table 1). The comparison of IVRASA with UCSB FIBS was shown in Table 1. As shown in Table 1, here, the CHF correlations still adopted the CHF correlations used in UCSB study. 2.3. Heat transfer correlations in IVRASA In DOE/ID-10460 (Theofanous et al., 1996a), heat transfer correlations were based on data from the UCSB Mini-ACOPO tests. Further testing was subsequently carried out in the ACOPO facility, which was a larger scale version of Mini-ACOPO. Correlations obtained from the Mini-ACOPO and ACOPO tests differ. IVRASA adopted the heat transfer correlations based on ACOPO data. Heat transfer correlations in molten ceramic pool and metallic layer in IVRASA were compared with those used in UCSB model and INEEL calculations, as shown in Table 2. The constitutive set of empirical heat transfer correlation is used in the same form with some variation as given in Table 2 for different models. 3. Verification and calculation results of IVRASA This section presents IVRASA calculation results. IVRASA calculations for the UCSB-assumed FIBS (as shown in Table 1) were conducted with the UCSB input data and INEEL input data under the condition of successful reactor coolant system depressurization and reactor cavity flooding. And the input data of the UCSB and INEEL were shown in the technical estimate report by INEEL (Rempe et al., 1997). Calculation results of IVRASA were presented as follows. Here, we give that these variables representing IVR margins best, such as heat fluxes, ratios of these vessel heat fluxes to the CHF, oxide crust thickness and vessel wall thickness. 3.1. Benchmark calculation results of IVRASA In order to verifying IVRASA study results, benchmark calculations were conducted with the UCSB input and the UCSB-assumed FIBS. As the UCSB results were verified by INEEL (Rempe et al., 1997), benchmark calculations of IVRASA were compared with the UCSB results and INEEL results as follows. Results from IVRASA were compared with results presented in DOE/ID-10460 Appendix
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Table 2 Heat transfer correlations used in different models. 1. Constitutive correlation set used by IVRASA in a steady state Metal Side wall: Churchill and Chu (1975): Nu =
0.15Ra1/3 [1+(0.492/Pr)9/16 ] 12
16/27
for 0.1 < Ra < 10 and any Pr. Top and bottom: Globe and Dropkin (1959): Nu = 0.069Ra1/3 Pr0.074 for 3 · 105 < Ra < 7 · 109 and 0.02 < Pr < 8750 Ceramic pool Top: Bonnet (1998) ACOPO (3D experiments): Nuup = 1.95Ra 0.18 for 1010 < Ra < 3 · 1016 . Bottom: Mayinger et al. (1975): Nudn = 0.55Ra 0.22 for 7 · 106 < Ra < 5 · 1014 2. Constitutive correlation set used by UCSB in a steady state (Theofanous et al., 1996a) Metal Side wall: Theofanous et al. (1994c): Nu = 0.076Ra1/3 . Top and bottom: Globe and Dropkin (1959) modified to Nu = 0.15Gr1/3 for 3 · 105 < Ra < 7 · 109 and 0.02 < Pr < 8750 Ceramic pool Top: Theofanous et al. (1996b) Mini-ACOPO (1/8 scale): Nuup = 0.345Ra 0.233 for 1012 < Ra < 3 · 1014 and 2.6 < Pr < 10.8 Bottom: Theofanous et al. (1994c) Mini-ACOPO: Nudn = 0.0038Ra 0.35 for 1012 < Ra < 3 · 1014 and 2.6 < Pr < 10.8
Fig. 4. Comparison of IVRASA heat flux with UCSB (DOE/ID-10460) and INEEL heat fluxes assuming UCSB FIBS and input.
3. Constitutive correlation set used by INEEL in a steady state (Rempe et al., 1997) Metal Side wall: Churchill and Chu (1975):
Nu =
0.825 + 0.387Ra1/6 / 1 + (0.492/Pr)
9/16
8/27 2
for 0.1 < Ra < 1012 and any Pr. Top and bottom: Globe and Dropkin (1959): Nu = 0.069Ra1/3 Pr0.074 for 3 · 105 < Ra < 7 · 109 and 0.02 < Pr < 8750 Ceramic pool Top: Theofanous et al. (1996b) ACOPO (1/2 scale): Nuup = 2.4415Ra 0.1722 Bottom: Theofanous et al. (1996b) ACOPO (1/2 scale): 0.25 Nudn = 0.1857Ra 0.2304 (H/R) for 1010 < Ra < 3 · 1016
Q (Theofanous et al., 1996a) and the INEEL calculation results (Rempe et al., 1997). It can be seen from Figs. 4–7 that benchmark calculations indicate that IVRASA correctly interpreted equations in the UCSB analyses and correctly encoded these equations into IVRASA. Fig. 4 compares vessel wall heat fluxes predicted by IVRASA, UCSB, and INEEL; Fig. 5 compare CHF ratios predicted by IVRASA and UCSB; Figs. 6 and 7, respectively, compare oxide crust thickness and vessel wall thickness predicted by IVRASA, UCSB, and INEEL. Figs. 4 and 5 indicate that IVRASA, UCSB model, and INEEL predictions differ slightly at the locations adjacent to ceramic pool (between 0 and ∼76◦ ), and were slightly larger at locations adjacent to the metallic layer (greater than ∼76◦ ). Particularly, at the loca-
Fig. 5. IVRASA and UCSB (DOE/ID-10460) CHF ratios assuming UCSB FIBS and input.
Fig. 6. IVRASA, UCSB (DOE/ID-10460) and INEEL predictions for oxide crust thickness assuming UCSB FIBS and input.
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Fig. 9. Comparison of CHF ratios for UCSB-assumed FIBS. Fig. 7. IVRASA, UCSB (DOE/ID-10460) and INEEL predictions for oxide wall thickness assuming UCSB FIBS and input.
tions adjacent to the metallic layer, IVRASA heat flux prediction is larger than UCSB and INEEL. And INEEL prediction is smallest. Fig. 6 indicates that IVRASA oxide crust thickness prediction is smallest, and INEEL prediction is largest. Fig. 7 indicates that IVRASA vessel wall thickness prediction is similar to UCSB model, but different to INEEL at the locations adjacent to the metallic layer. Hence, differences in these figures may be due to different correlations adopted in different models. 3.2. Calculation results with IVRASA input As the UCSB results were verified by INEEL (Rempe et al., 1997), calculations of configuration A, configuration B and configuration C for UCSB-assumed FIBS were conducted with the IVRASA input recommended by INEEL. Calculation results of IVRASA were compared with those calculated by INEEL. 3.2.1. Calculation results of configuration A Calculation of configuration A for UCSB-assumed FIBS was conducted with the IVRASA input considering the decay heat in the metallic layer. Calculation results were compared with those calculated by INEEL as follows.
Fig. 8. Comparison of heat fluxes for UCSB-assumed FIBS.
It can be seen from Figs. 8 and 9 that IVRASA results of configuration A is similar to those calculated by INEEL, but different from the results calculated by UCSB model. Particularly, apparent differences lie in the locations adjacent to the metallic layer. IVRASA results and INEEL results have a sharply increase at the interface between the oxide ceramic pool and the metallic layer (∼76◦ ), and keep a high value at the locations adjacent to the metallic layer. This is because IVRASA adopts the input data recommended by INEEL considering the decay heat in the metallic layer (Rempe et al., 1997). However, UCSB model did not consider the decay heat in the metallic layer. As shown in Fig. 9, IVRASA predicts that CHF ratios remain below unity when INEEL input is adopted. There is much margin to failure for IVR. 3.2.2. Sensitivity studies of configuration A Although IVRASA predicts that CHF ratios remain below unity, Rempe et al. (1997) suggested that there were uncertainties in several input parameters. Rempe et al. (1997) presented three kinds of uncertainties that were vapor transport effects on natural convection, additional metallic layer sources (due to steel activation or oxidation) and reduced metallic melt mass. The uncertainty analysis of IVRASA input parameters were assumed to change the corresponding values of the parameters or equations that were modified to assess the phenomena of inter-
Fig. 10. Comparison of CHF ratios for UCSB-assumed FIBS.
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Fig. 11. Comparison of CHF ratios for UCSB-assumed FIBS.
Fig. 12. Comparison of CHF ratios for UCSB-assumed FIBS.
est. Modifications required for each analysis and results from each analysis are discussed below. Fig. 10 represents the condition of vapor transport effects on natural convection. When the temperature in the oxide pool exceeds the boiling temperature of one or more molten components, vaporization and pool boiling could occur, enhancing upward heat transfer from the molten pool. The presence of such lower evaporation temperature materials is supported by voids measured in examinations of debris from the TMI-2 vessel (Akers et al., 1992). IVRASA assumed a factor of 10 increase in the upward heat transfer correlation for this uncertainty recommended by INEEL Rempe et al. (1997). It can be seen from Fig. 10 that IVRASA result is similar to that by INEEL and the heat flux from the vessel at location adjacent to the oxide pool are reduced significantly (below ∼76◦ ). This is because increased upward heat losses decreased downward heat fluxes. At vessel locations in contact with the metallic layer (at angles above ∼76◦ ), heat fluxes are nearly 65% higher than values estimated for the base case. This is due to the increased heat input from the oxide pool into the metallic layer. As shown in Fig. 10, IVRASA result is slightly higher than that by INEEL, which is due to two different models adopt different CHF correlations. The CHF correlation based on ULPU-III facility was used by IVRASA model (Theofanous et al., 1994a,b), while the CHF correlation based on SBLB facility was adopted by INEEL model (Cheung et al., 1997). It can be seen that CHF margin is apparently reduced in this case. Fig. 11 represents the condition of additional metallic layer sources. Rempe et al. (1997) suggested that there was a potential for the metallic layer to contain additional heat source due to activation of stainless steel and oxidation of materials in the metallic layer. So IVRASA assumed an additional heat source in the metallic layer that corresponded to 8% of the core’s power at times between 2 and 6 h after shutdown recommended by INEEL (Rempe et al., 1997). Additional heat sources only affect the metallic layer results, which are proved from Fig. 11. It can be seen from Fig. 11 that IVRASA calculation results indicate that this additional heat source increases heat flux ratios at locations adjacent to the metallic layer by approximately 20%, which reduces the CHF margin of IVR. IVRASA result predicts heat flux ratio slightly higher than that by INEEL, which is due to different CHF and heat transfer correlations in the metallic layer adopted by IVRASA model. Fig. 12 represents the condition of reduced metallic melt mass that affects the height of the metallic layer. Because the metallic layer has a higher thermal conductivity, the mass of metals
assumed in the metallic layer significantly affects the estimated magnitude of the heat fluxes focused towards the adjacent vessel sidewall. If metallic melt mass is reduced, the excess of energy which come from the oxide pool and cannot be removed by radiation is focused through the vessel wall causing considerable thermal attack of the vessel. This is so-called focusing effect. This focusing effect may be a challenge to the integrity of the vessel. For IVRASA calculations, respectively, assumed the metallic layer contains approximately 70,000, 19,500 and 10,000 kg of vessel internal structure steel recommended by INEEL (Rempe et al., 1997). It can be seen from Fig. 12 that reductions in the steel relocation mass only affect metallic layer results, because oxide pool heat fluxes are independent of metallic layer mass assumptions. As shown in Fig. 12, CHF ratios at vessel locations in contact with the metallic layer approach unity for steel masses equal to 19,500 kg. When the steel masses are below these values, CHF ratios are greater than unity. This may cause the vessel failure. Particularly, when the steel masses equal to 10,000 kg, CHF ratios calculated by IVRASA reach to 1.6, which is greater than 1.3 calculated by INEEL. This is due to different CHF correlations adopted by IVRASA. According to the point calculations by IVRASA, reduced metallic layer mass may cause the vessel failure. 3.2.3. Calculation results of configuration B As discussed above, configuration B contains a debris configuration that occurs sometime after configuration A. A middle metallic layer is sandwiched between two molten ceramic layers. This configuration may be more challenge to the integrity of the vessel than configuration A. Calculation results of configuration B for UCSB-assumed FIBS were conducted by IVRASA with the input parameters recommended by INEEL (Rempe et al., 1997). Configuration B calculation results using IVRASA are shown in Figs. 13–15. It can be seen from Fig. 13 that peak heat fluxes occur at locations where the vessel is contact with the metallic layer and are approximately a factor of 32 times larger than predicted for configuration A (see Fig. 8). These higher heat fluxes are primarily due to the combined heat load to this metallic layer from the upper and lower oxide pool. As shown in Fig. 13, IVRASA result is lower than that of INEEL, which may be due to corrections in equations and different heat transfer correlations adopted by IVRASA. Fig. 14 results indicate that the ratio of the vessel heat flux to CHF values are predicted to typically be approximately 20 at vessel locations adjacent to the metallic layer (at locations above∼59◦ ).
Y.P. Zhang et al. / Nuclear Engineering and Design 241 (2011) 4634–4642
Fig. 13. Comparison of heat fluxes of configuration B for UCSB-assumed FIBS.
Fig. 14. Comparison of CHF ratios of configuration B for UCSB-assumed FIBS.
IVRASA result is lower than that of INEEL, which may be due to corrections in equations and different CHF correlations adopted by IVRASA. INEEL adopted the CHF Cheung (H/R = 2) correlations (Cheung et al., 1997). Fig. 15 shows the wall thickness of configuration B calculated by IVRASA, and the initial wall thickness is 15 cm.
Fig. 15. IVRASA wall thickness of configuration B for UCSB-assumed FIBS.
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Fig. 16. Comparison of heat fluxes of configuration C for UCSB-assumed FIBS.
3.2.4. Calculation results of configuration C As discussed above, configuration C contains a case where sufficient uranium dissolves into unoxidized zirconium to form a heavier metallic layer beneath a molten ceramic layer. Heat loads from the lower heavier metallic layer are focused to the bottom of the vessel lower head where the potential of the heat removal is a minimum. In this condition, decay heat in the lower heavier metallic layer applied. This configuration may be more challenge to the integrity of the vessel than configuration A. Calculation results of configuration C for UCSB-assumed FIBS were conducted by IVRASA with the input parameters recommended by INEEL (Rempe et al., 1997), considering decay heat in the lower heavier metallic layer. And the volumetric decay heat is 0.88 MW/m3 in the heavier metallic layer. Configuration C calculation results using IVRASA are shown in Figs. 16 and 17. It can be seen from Fig. 16 that peak heat fluxes occur at locations adjacent to the metallic layer (at locations below ∼42◦ ). As shown in Fig. 17, the ratio of the vessel heat flux to CHF values from 3.5 to 6.5 at adjacent to the metallic layer. This result is due to high heat fluxes from the metallic layer (due to decay heat from fission product into the metallic layer) and to lower heat removal rates at lower angles. It can be seen from Figs. 16 and 17 that difference between IVRASA results and those of INEEL is very small, but difference of results between two models is slightly larger at locations adjacent
Fig. 17. Comparison of CHF ratios of configuration C for UCSB-assumed FIBS.
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to the metallic layer. IVRASA predictions of heat fluxes and CHF ratios are all smaller than those predicted by INEEL. This is due to corrections in equations and different heat transfer correlations, as well as different CHF correlations adopted by IVRASA. The CHF correlation based on ULPU-III facility was used by IVRASA model (Theofanous et al., 1994a,b), while the CHF correlation based on SBLB facility was adopted by INEEL model (Cheung et al., 1997). 3.3. Sensitivity analysis of CHF correlations for IVR analysis Rempe et al. (2008) suggested that there was a large uncertainty in the CHF data. So, many uncertainties existed in fitting correlations according to experimental data. Moreover, the CHF correlation used for IVR analysis of AP600 was depended on experimental data of UPLU-III facility (Theofanous et al., 1994a,b). The UPLU-III is a 2D facility and cannot be used to adequately simulate the 3D heat transfer to the hemispherical channel between the reactor vessel and the surrounding insulation structure. SBLB facility (Cheung et al., 1997) is a 3D facility that can simulate the 3D heat transfer and two-phase boundary layer flow behavior in the annular between the reactor vessel and the surrounding insulation. Therefore, 3D ERVC tests should be carried out for IVR analysis of ALWRs, or some existing 3D experimental data should be used to IVR analysis, such as data or correlations of SBLB tests. 4. Conclusions 1. A simple novel analysis procedure-IVRASA was developed to predict the failure margin of the vessel. Benchmark calculations considering the UCSB-assumed FIBS indicate that IVRASA correctly interpreted equations in the UCSB analyses and correctly encoded these equations into IVRASA. IVRASA calculation results for the UCSB-assumed FIBS indicate that the vessel would remain intact, which is similar to the UCSB study and INEEL analyses. 2. According to INEEL evaluation report, INEEL gave other two configurations of core melt, which could be more challenging than the UCSB-assumed configuration. Calculation results of alternate debris configurations were conducted by IVRASA, which were consistent with those calculated by INEEL. This indicated that UCSB assumed FIBS did not bound all the heat loads, and additional analyses should be conducted. 3. This work also investigated the effect of the uncertainties of the CHF correlations on the analysis of IVR. The existing CHF correlation for IVR analysis is based on 2D tests. However, there exists a large uncertainty in the UPLU-III experimental data. Therefore, 3D ERVC tests should be carried out for IVR analysis, or some existing 3D experimental data should be used to IVR analysis.
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