Analysis of Focusing Effect of Light Metallic Layer in Stratified Molten Pool Under IVR-ERVC Condition

Author(s):  
Xi Wang ◽  
Xu Cheng

The main failure mechanism of in-vessel corium retention through external reactor vessel cooling (IVR-ERVC) happens when the local heat flux through reactor pressure vessel (PRV) wall exceeds the critical heat flux (CHF). High local heat flux in the molten pool is usually caused by the metallic layer focusing effect due to stratification. In this paper, depending on experimental correlations, both the lump parameter method and computational fluid dynamic method are used to investigate the mechanism of focusing effect. The concentration factor varying with the height of metallic layer is studied. The results show that the lump parameter method probably overestimates the wall heat flux of metal layer.

Author(s):  
F. Fichot ◽  
L. Carénini ◽  
W. Villanueva ◽  
S. Bechta

The In-Vessel Retention (IVR) strategy for Light Water Reactors (LWR) intends to stabilize and isolate corium and fission products in the reactor pressure vessel and in the primary circuit. This type of Severe Accident Management (SAM) strategy has already been incorporated in the design and SAM guidances (SAMGs) of several operating small and medium capacity LWRs (reactors below 500 MWe, e.g. VVER440) and is part of the SAMG strategies for some Gen III+ PWRs of higher power such as the AP1000 or the APR1400. However, the demonstration of IVR feasibility for high power reactors requires using less conservative models as the safety margins are reduced. In Europe, the IVMR project aims at providing new experimental data and a harmonized methodology for IVR. A synthesis of the methodology applied to demonstrate the efficiency of IVR strategy for VVER-440 in Europe (Finland, Slovakia, Hungary and Czech Republic) was made. It showed very consistent results, following quite comparable methodologies. The main weakness was identified in the evaluation of the heat flux that could be reached in transient situations, e.g. under the “3-layers” configuration, where the “focusing effect” may cause higher heat fluxes than in steady-state (due to transient “thin” metal layer on top). Analyses of various designs of reactors with a power between 900 and 1300 MWe were also made. Different models for the description of the molten pool were used: homogeneous, stratified with fixed configuration, stratified with evolving configuration. The last type of model provides the highest heat fluxes (above 3 W/m2) whereas the first type provides the lowest heat fluxes (around 500 kW/m2) but this model is not realistic due to the immiscibility of molten steel with oxide melt. Obviously, there is a need to reach a consensus about best estimate practices for IVR assessment to be used in the major codes used for safety analysis, such as ASTEC, MELCOR, SOCRAT, MAAP, ATHLET-CD, SCDAP/RELAP, etc. Despite the model discrepancies, and leaving aside the unrealistic case of homogeneous pool, the average calculated heat fluxes can reach, in many cases, values which are well above 1 MW/m2. This could reduce the residual thickness of the vessel considerably and threaten its strength and integrity. Therefore, it is clear that the safety demonstration of IVR in high power reactors requires a more careful evaluation of the situations which can lead to formation of either a very thin top metal layer provoking the focusing effect or significantly overheated metal, e.g. after oxide and metal layer inversion. Both situations are illustrated in this paper. The demonstration also requires an accurate thermo-mechanical analysis of the ablated vessel. The standard approach based on “yield stress” (plastic behaviour) is compared with more detailed calculations made on realistic profiles of ablated vessels. The validity of the standard approach is discussed. The current approach followed by many experts for IVR is a compromise between a deterministic analysis using the significant knowledge gained during the last two decades and a probabilistic analysis to take into account large uncertainties due to the lack of data for some physical phenomena, e.g. associated with molten pool transient behaviour, and due to excessive simplifications of models. A harmonization of the positions of safety authorities on the IVR strategy is necessary to allow decision making based on shared scientific knowledge. Some elements that might help to reach such harmonization are proposed in this paper, with a preliminary revision of the methodology that could be used to address the IVR issue. In the proposed revised methodology, the safety criterion is not based on a comparison of the heat flux and the Critical Heat Flux (CHF) profiles as in the current approaches but on the minimum vessel thickness reached after ablation and the maximum pressure load that is applied to the vessel during the transient. The main advantage of this revised criterion is in consideration of both steady-state and transient loads on the RPV. Another advantage is that this criterion is more straightforward to be used in a deterministic approach.


Author(s):  
L. Carénini ◽  
F. Fichot

The In-Vessel Retention (IVR) strategy for Light Water Reactors (LWR) intends to stabilize and retain the core melt in the reactor pressure vessel. This type of Severe Accident Management (SAM) strategy has already been incorporated in the SAM guidance (SAMG) of several operating small size LWR (reactors below 500MWe, like VVER440) and is part of the SAMG strategies for some Gen III+ PWRs of higher power like the AP1000. One of the main issues for the demonstration of the success of the IVR strategy lies in the evaluation of the transient heat fluxes applied by the corium pool along the vessel wall. Indeed, these transient heat fluxes, during the corium pool stratification evolution, are expected to be higher than the steady-state ones, in particular due to the concentration of the heat flux in the top metal layer when it is thin (so called focusing effect). Another issue appears when a heavy metal is initially formed and rises later to the top (inversion of stratification): in such a situation, the metal goes through the oxide phase and accumulates a significant superheat which is likely to produce a high transient heat flux. Thus, it is of primary importance to be able to evaluate the duration of these transient peaks in order to evaluate the minimal residual vessel thickness after such fast transient ablation and draw conclusions about the vessel integrity. This paper first presents the phenomenology associated to the transient molten pool stratification and the model implemented in the severe accident integral code ASTEC (Accident Source Term Evaluation Code) to evaluate this kinetics. Then, evaluations are presented, based on a typical PWR reactor configuration. A sensitivity study is proposed to consider the impact of the main uncertainties on parameters which govern this kinetics. A particular focus is made on the physical phenomena driving the transient stratification of material layers in the corium pool and on the identification of critical situations with possible consequences in terms of vessel failure. The characteristic times of each individual process (chemistry, stratification, natural convection) are compared. In particular, the limiting cases of very fast chemistry or very slow chemistry are evaluated. This work is performed in the frame of the European H2020 project IVMR (In-Vessel Melt Retention) coordinated by IRSN. This project has been launched in 2015 and gathers 27 organizations with, as main objective, the evaluation of feasibility of IVR strategy for LWR (PWR, VVER, BWR) of total power 1,000MWe or higher.


2020 ◽  
Vol 117 (6) ◽  
pp. 602
Author(s):  
Heping Liu ◽  
Jianjun Zhang ◽  
Hongbiao Tao ◽  
Hui Zhang

In this article, based on the actual monitored temperature data from mold copper plate with a dense thermocouple layout and the measured magnetic flux density values in a CSP thin-slab mold, the local heat flux and thin-slab solidification features in the funnel-type mold with electromagnetic braking are analyzed. The differences of local heat flux, fluid flow and solidified shell growth features between two steel grades of Q235B with carbon content of 0.19%C and DC01 of 0.03%C under varying operation conditions are discussed. The results show the maximum transverse local heat flux is near the meniscus region of over 0.3 m away from the center of the wide face, which corresponds to the upper flow circulation and the large turbulent kinetic energy in a CSP funnel-type mold. The increased slab width and low casting speed can reduce the fluctuation of the transverse local heat flux near the meniscus. There is a decreased transverse local heat flux in the center of the wide face after the solidified shell is pulled through the transition zone from the funnel-curve to the parallel-cure zone. In order to achieve similar metallurgical effects, the braking strength should increase with the increase of casting speed and slab width. Using the strong EMBr field in a lower casting speed might reverse the desired effects. There exist some differences of solidified shell thinning features for different steel grades in the range of the funnel opening region under the measured operating conditions, which may affect the optimization of the casting process in a CSP caster.


Author(s):  
R Tabassum ◽  
Rashid Mehmood ◽  
O Pourmehran ◽  
NS Akbar ◽  
M Gorji-Bandpy

The dynamic properties of nanofluids have made them an area of intense research during the past few decades. In this article, flow of nonaligned stagnation point nanofluid is investigated. Copper–water based nanofluid in the presence of temperature-dependent viscosity is taken into account. The governing nonlinear coupled ordinary differential equations transformed by partial differential equations are solved numerically by using fourth-order Runge–Kutta–Fehlberg integration technique. Effects of variable viscosity parameter on velocity and temperature profiles of pure fluid and copper–water nanofluid are analyzed, discussed, and presented graphically. Streamlines, skin friction coefficients, and local heat flux of nanofluid under the impact of variable viscosity parameter, stretching ratio, and solid volume fraction of nanoparticles are also displayed and discussed. It is observed that an increase in solid volume fraction of nanoparticles enhances the magnitude of normal skin friction coefficient, tangential skin friction coefficient, and local heat flux. Viscosity parameter is found to have decreasing effect on normal and tangential skin friction coefficients whereas it has a positive influence on local heat flux.


Author(s):  
Tom I-Ping Shih ◽  
Srisudarshan Krishna Sathyanarayanan

Convective heat transfer over surfaces is generally presented in the form of the heat-transfer coefficient (h) or its nondimensional form, the Nusselt number (Nu). Both require the specification of the free-stream temperature (Too) or the bulk (Tb) temperature, which are clearly defined only for simple configurations. For complicated configurations with flow separation and multiple temperature streams, the physical significance of Too and Tb becomes unclear. In addition, their use could cause the local h to approach positive or negative infinity if Too or Tb is nearly the same as the local wall temperature (Twall). In this paper, a new Nusselt number, referred to as the SCS number, is proposed, that provides information on the local heat flux but does not use h and hence by-passes the need to define Too or Tb. CFD analysis based on steady RANS with the shear-stress transport model is used to compare and contrast the SCS number with Nu for two test problems: (1) compressible flow and heat transfer in a straight duct with a circular cross section and (2) compressible flow and heat transfer in a high-aspect ratio rectangular duct with a staggered array of pin fins. Parameters examined include: Reynolds number at the duct inlet (3,000 to 15,000 for the circular duct and 15,000 and 150,000 for the rectangular duct), wall temperature (Twall = 373 K to 1473 K for the circular duct and 313 K and 1,173 K for the rectangular duct), and distance from of the inlet of the duct (up to 100D for the circular duct and up to 156D for the rectangular duct). For the circular duct, Nu was found to decrease rapidly from the duct inlet until reaching a minimum and then to rise until reaching a nearly constant value in the “fully” developed region if the wall is heating the gas. If the wall is cooling the gas, then Nu has a constant positive slope in the “fully” developed region. The location of the minimum in Nu and where Nu becomes nearly constant in value or in slope are strong functions of Twall. For the SCS number, the decrease from the duct inlet is monotonic with a negative slope, whether the wall is heating or cooling the gas. Also, different SCS curves for different Twall approach each other as the distance from the inlet increases. For the rectangular duct, Nu tends to oscillate about a constant value in the pin-fin region, whereas SCS tends to oscillate about a line with a negative slope. For both test problems, the variation of SCS is not more complicated than Nu, but SCS yields the local heat flux without need for Tb, a parameter that is hard to define and measure for complicated problems.


2020 ◽  
Vol 2020 (0) ◽  
pp. 0187
Author(s):  
Masanori Morisaki ◽  
Shota Minami ◽  
Koji Miyazaki ◽  
Tomohide Yabuki

2005 ◽  
Vol 128 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Yuan Lin ◽  
Timothy C. Ovaert

The thermal surface distortion of an anisotropic elastic half-plane is studied using the extended version of Stroh’s formalism. In general, the curvature of the surface depends both on the local heat flux into the half-plane and the local temperature variation along the surface. However, if the material is orthotropic, the curvature of the surface depends only on the local heat flux into the half-plane. As a direct application, the two-dimensional thermoelastic contact problem of an indenter sliding against an orthotropic half-plane is considered. Two cases, where the indenter has either a flat or a parabolic profile, are studied in detail. Comparisons with other available results in the literature show that the present method is correct and accurate.


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