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Implicit Eulerian method for analyzing transient phenomena in fast reactors

Description: An Eulerian compressible hydrodynamic method is presented for analyzing transient phenomena in nuclear reactors following hypothetical excursions. The method uses the implicit integration scheme to solve nonlinear equations of fluid dynamics in conjunction with a thin-shell analysis to calculate the response of the wall boundary. Detailed formulations are given. Results are presented for two example problems and compared with available experimental data. 6 references. (auth)
Date: October 1, 1975
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

SHAPS-2: a three-dimensional computer program for linear/non-linear, static/dynamic analyses of piping systems. [LMFBR]

Description: A three-dimensional computer program for linear/non-linear, static/dynamic analyses of reactor-piping systems under various accident loads is described. In the analysis, the hydrodynamic calculation can be performed in the implicit or semi-implicit manner. The structure response can be calculated using either a purely explicit or implicit time-integration scheme. Coupling between the fluid and structure is achieved by utilizing either the implicit-explicit or implicit-implicit link. Thus, a wide range of piping safety problems can be analyzed by the suitable choice of options available in the hydrodynamics and structural analysis. In this paper, several salient features are presented. Sample problems illustrating the versatility of the program are given. The results are discussed in detail.
Date: January 1, 1985
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Analysis of piping response to thermal and operational transients

Description: The reactor piping system is an extremely complex three-dimensional structure. Maintaining its structural integrity is essential to the safe operation of the reactor and the steam-supply system. In the safety analysis, various transient loads can be imposed on the piping which may cause plastic deformation and possible damage to the system, including those generated from hydrodynamic wave propagations, thermal and operational transients, as well as the seismic events. At Argonne National Laboratory (ANL), a three-dimensional (3-D) piping code, SHAPS, aimed for short-duration transients due to wave propagation, has been developed. Since 1984, the development work has been shifted to the long-duration accidents originating from the thermal and operational transient. As a result, a new version of the code, SHAPS-2, is being established. This paper describes many features related to this later development. To analyze piping response generated from thermal and operational transients, a 3-D implicit finite element algorithm has been developed for calculating the hoop, flexural, axial, and torsional deformations induced by the thermomechanical loads. The analysis appropriately accounts for stresses arising from the temperature dependence of the elastic material properties, the thermal expansion of the materials, and the changes in the temperature-dependent yield surface. Thermal softening, failure, strain rate, creep, and stress ratching can also be considered.
Date: January 1, 1987
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Eulerian formulation of fluid-structure interaction in reactor containment system

Description: This paper is concerned with an Eulerian formulation for a fluid-structure interface developed for the nonlinear fluid-structure interaction analysis encountered in the primary containment and piping components of nuclear reactors. The Eulerian finite difference methodology is chosen because of its decisive abilities in: (1) investigating material motion with large distortions, (2) treating fluid flow around internal structures having a geometrical discontinuity, (3) handling wave transients in the vicinity of perforated structures. The ultimate objective is to perform the analysis of the reactor integrity when subject to the transient load. Two types of irregular cells are considered and their formulation corresponding to the ICE technique are described. The first one is for interfaces between a coolant and a deformable structure, where the fluid slides tangentially along the moving boundary. A relaxation equation is derived here, allowing the adjustment of the pressure on the moving boundary of the fluid by an amount proportional to the actual mass flux across the boundary. The second irregular cell is for fluid adjacent to the perforated structure where fluid flow through coolant passage takes place. A modified Poisson equation is obtained to appropriately account for the volume perforation and the flow-area availability of the perforated structure. These two equations, in conjunction with the governing Poisson equation of the ICE technique, are solved iteratively. Convergence is attained when boundary conditions at all interfaces are satisified. The development scheme enables the implicit Eulerian hydrodynamic techniques to be coupled with any structural dynamic program. Presently, a corotational coordinate finite element program, WHAMS, is employed for calculating the structural response. Three sample problems are presented to illustrate the analysis. The results are discussed.
Date: January 1, 1979
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Theory and application of a three-dimensional code SHAPS to complex piping systems. [LMFBR]

Description: This paper describes the theory and application of a three-dimensional computer code SHAPS to the complex piping systems. The code utilizes a two-dimensional implicit Eulerian method for the hydrodynamic analysis together with a three-dimensional elastic-plastic finite-element program for the structural calculation. A three-dimensional pipe element with eight degrees of freedom is employed to account for the hoop, flexural, axial, and the torsional mode of the piping system. In the SHAPS analysis the hydrodynamic equations are modified to include the global piping motion. Coupling between fluid and structure is achieved by enforcing the free-slip boundary conditions. Also, the response of the piping network generated by the seismic excitation can be included. A thermal transient capability is also provided in SHAPS. To illustrate the methodology, many sample problems dealing with the hydrodynamic, structural, and thermal analyses of reactor-piping systems are given. Validation of the SHAPS code with experimental data is also presented.
Date: January 1, 1983
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Three-dimensional method for integrated transient analysis of reactor-piping systems

Description: A three-dimensional method for integrated hydrodynamic, structural, and thermal analyses of reactor-piping systems is presented. The hydrodynamics are analyzed in a reference frame fixed to the piping and are treated with a two-dimensional Eulerian finite-difference technique. The structural responses are calculated with a three-dimensional co-rotational finite-element methodology. Interaction between fluid and structure is accounted for by iteratively enforcing the interface boundary conditions.
Date: January 1, 1981
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Implicit finite element structural dynamic formulation for long-duration accidents in reactor piping systems

Description: This taper describes an implicit three-dimensional finite-element formulation for the structural analysis of reactor piping system. The numerical algorithm considers hoop, flexural, axial, and torsion modes of the piping structures. It is unconditionally stable and can be used for calculation of piping response under static or long duration dynamic loads. The method uses a predictor-corrector, successive iterative scheme which satisfies the equilibrium equations. A set of stiffness equations representing the discretized equations of motion are derived to predict the displacement increments. The calculated displacement increments are then used to correct the element nodal forces. The algorithm is fairly general, and is capable of treating large displacements and elastic-plastic materials with thermal and strain-rate effects. 7 refs., 7 figs.
Date: January 1, 1985
Creator: Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Seismic analysis of a large pool-type LMR (liquid metal reactor)

Description: This paper describes the seismic study of a 450-MWe liquid metal reactor (LMR) under 0.3-g SSE ground excitation. Two calculations were performed using the new design configuration. They deal with the seismic response of the reactor vessel, the guard vessel and support skirt, respectively. In both calculations, the stress and displacement fields at important locations of those components are investigated. Assessments are also made on the elastic and inelastic structural capabilities for other beyond-design basis seismic loads. Results of the reactor vessel analysis reveal that the maximum equivalent stress is only about half of the material yield stress. For the guard vessel and support skirt, the stress level is very small. Regarding the analysis if inelastic structural capability, solutions of the Newmark-Hall ductility modification method show that the reactor vessel can withstand seismics with ground ZPAs ranging from 1.015 to 1.31 g, which corresponds to 3.37 to 4.37 times the basic 0.3-g SSE. Thus, the reactor vessel and guard vessel are strong enough to resist seismic loads. 4 refs., 10 figs., 5 tabs.
Date: January 1, 1989
Creator: Wang, C.Y. & Gvildys, J.
Partner: UNT Libraries Government Documents Department

Structural and seismic analyses of waste facility reinforced concrete storage vaults

Description: Facility 317 of Argonne National Laboratory consists of several reinforced concrete waste storage vaults designed and constructed in the late 1940`s through the early 1960`s. In this paper, structural analyses of these concrete vaults subjected to various natural hazards are described, emphasizing the northwest shallow vault. The natural phenomenon hazards considered include both earthquakes and tornados. Because these vaults are deeply embedded in the soil, the SASSI (System Analysis of Soil-Structure Interaction) code was utilized for the seismic calculations. The ultimate strength method was used to analyze the reinforced concrete structures. In all studies, moment and shear strengths at critical locations of the storage vaults were evaluated. Results of the structural analyses show that almost all the waste storage vaults meet the code requirements according to ACI 349--85. These vaults also satisfy the performance goal such that confinement of hazardous materials is maintained and functioning of the facility is not interrupted.
Date: July 1995
Creator: Wang, C. Y.
Partner: UNT Libraries Government Documents Department

Eulerian method for large-displacement fluid-structure interaction in reactor containments

Description: An Eulerian method for analyzing large-displacement fluid-structure interaction in reactor containments is presented. The emphasis is on the development of a generalized hydrodynamic scheme to treat the irregular cells created by the movement of the structure with respect to the fixed Eulerian coordinates. A relaxation equation is derived from the boundary condition at the fluid-structure interface for the solution of the pressure at the interface. By combining this with the Poisson equation a sufficient set of equations is obtained for the determination of the advanced-time pressures in the fluid region and at the fluid-structure interfaces. Sample problems are given to illustrate the analysis.
Date: January 1, 1977
Creator: Chang, Y.W. & Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Multi-dimensional arbitrary Lagrangian-Eulerian method for dynamic fluid-structure interaction. [LMFBR]

Description: This paper describes an arbitrary Lagrangian-Eulerian method for analyzing fluid-structure interactions in fast-reactor containment with complex internal structures. The fluid transient can be calculated either implicitly or explicitly, using a finite-difference mesh with vertices that may be moved with the fluid (Lagrangian), held fixed (Eulerian), or moved in any other prescribed manner (hybrid Lagrangian Eulerian). The structural response is computed explicitly by two nonlinear, elastic-plastic finite-element modules formulated in corotational coordinates. Interaction between fluid and structure is accounted for by enforcing the interface boundary conditions. The method has convincing advantages in treating complicated phenomena such as flow through perforated structures, large material distortions, flow around corners and irregularities, and highly contorted fluid boundaries. Several sample problems are given to illustrate the effectiveness of this arbitrary Lagrangian-Eulerian method.
Date: January 1, 1982
Creator: Wang, C.Y. & Zeuch, W.R.
Partner: UNT Libraries Government Documents Department

Effects of reactor internals on primary containment response of an LMFBR during an HCDA

Description: Several studies in the past have demonstrated the effects of the upper internal structural (UIS) in altering the flow paths of coolant and in mitigating the effects of slug impact during HCDA's. Results indicate that each slug impact pressure can be reduced significantly when the UIS is introduced into the reactor configuration. It is important to model internal structures in order to present an accurate analytical model of the reactor - one which produces useful design parameters, and one which is not overly conservative in its assumptions. The scoping analysis presented here provides insight into the effects of the various core internals during HCDA conditions and demonstrates the capabilities necessary in an analytic tool to carry out a reliable analysis of structural integrity.
Date: January 1, 1983
Creator: Zeuch, W.R. & Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Quantitative analysis of the effect of complex internals on LMFBR containment during energetic accidents

Description: This paper discusses the effects of complex internals on the containment response of large LMFBRs during energetic accidents. Results of a series of analyses with the ALICE-II code demonstrate quantitative structural and hydrodynamic effects from parametric variation of reactor internal designs. Effects of various upper internal structure treatments, structural stiffness of the upper internal structure and core support structure, and the location and dimensions of internal components are examined. Results indicate that reduction of primary containment loads can be accomplished through such means as confinement of the core region and avoiding over-strengthened, rigid internals. A study of the beneficial and adverse parameters involved in primary containment response should be helpful in optimizing designs for safety purposes.
Date: January 1, 1985
Creator: Zeuch, W.R. & Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Recent developments of the arbitrary Lagrangian-Eulerian containment code ALICE-II. [LMFBR]

Description: The ANL arbitrary Lagrangian Eulerian containment code ALICE was developed for use in fast reactor containment studies and is particularly suited for problems involving complex fluid-structure interactions. Many improvements have been made which has resulted in a second version of the code, ALICE-II. A selection of some important improvements are given in this paper. To realistically analyze the above-core hydrodynamics containing a movable upper internal structure (UIS), a 3-D pipe element has been adopted to calculate the response of the UIS columns that connect the UIS to the vessel head. A corotational coordinate scheme for large displacement, small strain, elastic-plastic structural-dynamic analysis is utilized in the formulation. Both geometric and material nonlinearities are considered. The governing equations are integrated explicitly using a central difference procedure. Many sample problems are presented, including comparisons of ALICE-II and ICECO-CEL results on the APRICOT Phase 3 problems.
Date: January 1, 1983
Creator: Wang, C.Y. & Zeuch, W.R.
Partner: UNT Libraries Government Documents Department

Recent development of three-dimensional piping code SHAPS

Description: This paper describes the recent development of the three-dimensional, structural, and hydrodynamic analysis piping code SHAPS. Several new features have been incorporated into the program, including (1) an elbow hydrodynamic model for analyzing the effect of global motion on the pressure-wave propagation, (2) a component hydrodynamic model for treating fluid motion in the vicinity of rigid obstacles and baffle plates, (3) the addition of the implicit time integration scheme in the structural-dynamic analysis, (4) the option of an implicit-implicit fluid-structural linking scheme, and (5) provisions for two constitutive equations for materials under various loading conditions. Sample problems are given to illustrate these features. Their results are discussed in detail. 7 refs., 8 figs.
Date: January 1, 1985
Creator: Wang, C.Y. & Zeuch, W.R.
Partner: UNT Libraries Government Documents Department

Advanced multi-dimensional method for structural and hydrodynamic analyses of LMFBR piping systems

Description: Maintaining the structural integrity of the piping system of Liquid Metal Fast Breeder Reactors (LMFBRs) is essential to the safe operation of the reactor and steam supply systems. In the safety analysis various transient loads can be imposed on the piping systems, which may pose threats to the integrity of the piping structure. These transient loads can be classified into two categories. The first represents dynamic loads resulting from the hydrodynamic pressure-wave propagation or seismic events. The second represents static or quasi-dynamic loads generated by thermal wave propagation, normal operation transient, or creep phenomena. At Argonne National Laboratory, a multi-dimensional method has been developed for the integrated analysis of piping systems under these transient loading conditions. It utilizes a 2-D implicit finite-difference hydrodynamics in conjunction with a 3-D explicit finite-element structural analysis.
Date: April 9, 1985
Creator: Wang, C.Y. & Zeuch, W.R.
Partner: UNT Libraries Government Documents Department

Analysis of pressure wave transients and seismic response in LMFBR piping systems using the SHAPS code

Description: This paper presents some of the current capabilities of the three-dimensional piping code SHAPS and demonstrates their usefulness in handling analyses encountered in typical LMFBR studies. Several examples demonstrate the utility of the SHAPS code for problems involving fluid-structure interactions and seismic-related events occurring in three-dimensional piping networks. Results of two studies of pressure wave propagation demonstrate the dynamic coupling of pipes and elbows producing global motion and rigorous treatment of physical quantities such as changes in density, pressure, and strain energy. Results of the seismic analysis demonstrate the capability of SHAPS to handle dynamic structural response within a piping network over an extended transient period of several seconds. Variation in dominant stress frequencies and global translational frequencies were easily handled with the code. 4 refs., 10 figs.
Date: January 1, 1985
Creator: Zeuch, W.R. & Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Comparison of ALICE-II code predictions with SRI complex vessel experiments

Description: Several complex vessel experiments on 1/20-scale models of the Clinch River Breeder Reactor Project (CRBR) were performed by SRI International to help evaluate the containment structural integrity subjected to HCDAs. Among these experiments SM-3 is a simple model which consists of a radial shield, core barrel, upper internal structure (UIS), and a primary vessel. Tests SM-4 and SM-5 are more complex models than SM-3. This paper presents comparisons of the ALICE-II code (Arbitrary Lagrangian Implicit-explicit Continuous Fluid Eulerian containment code - second version) with experiments SM-3 through SM-5. Two calculations are performed with ALICE-II on each of these three experiments, using both the pressure-time histories (p-t) and the pressure-volume relationships (p-v) as input to describe the energy source. Pressure profiles, dynamic strains, and vessel deformations are used as the basis of the comparison.
Date: January 1, 1983
Creator: Ku, J.L.; Wang, C.Y. & Zeuch, W.R.
Partner: UNT Libraries Government Documents Department

Mitigation of earthquake hazards using seismic isolation systems

Description: This paper describes mitigation of earthquake hazards using seismic base isolation systems. A numerical algorithm for analyzing system response of base-isolated structures with laminated elastomer bearings is briefly described. Seismic response analyses of both base- isolated and unisolated buildings under earthquakes {number_sign}42 and {number_sign}44 are performed and the results are compared to illustrate the mitigating effect of base-isolated systems.
Date: June 1, 1996
Creator: Wang, C.-Y.
Partner: UNT Libraries Government Documents Department

ICECO-CEL: A Coupled Eulerian-Lagrangian Code for Analyzing Primary System Response in Fast Reactors

Description: This report describes a coupled Eulerian-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit Eulerian method is used to calculate the fluid motion so that large fluid distortion, two-dimensional sliding interface, flow around corners, flow through coolant passageways, and out-flow boundary conditions can be treated. The explicit Lagrangian formulation is employed to compute the response of the containment vessel and other elastic-plastic solids inside the reactor containment. Large displacements, as well as geometrical and material nonlinearities are considered in the analysis. Marker particles are utilized to define the free surface or the material interface and to visualize the fluid motion. The basic equations and numerical techniques used in the Eulerian hydrodynamics and Lagrangian structural dynamics are described. Treatment of the above-core hydrodynamics, sodium spillage, fluid cavitation, free-surface boundary conditions and heat transfer are also presented. Examples are given to illustrate the capabilities of the computer code. Comparisons of the code predictions with available experimental data are also made.
Date: February 1981
Creator: Wang, C. Y.
Partner: UNT Libraries Government Documents Department

Some safety considerations in the selection of redans for pool-type LMR plants

Description: Three basic safety issues in the selection of the redan design for a pool type liquid metal fast breeder reactor plant are examined. The first area examined is the effect of the redan selection on the integrity of the primary system pressure boundary in normal and offset conditions. The second area is on the consequence of the hypothetical core disruptive accident. The third area is on the consequence of the loss of heat sink accident. Some general discussion and numerical results are presented which may help in the selection of an optimum redan design. 3 refs., 7 figs.
Date: January 1, 1985
Creator: Pan, Y.C.; Pedersen, D.R. & Wang, C.Y.
Partner: UNT Libraries Government Documents Department

Eulerian algorithm for analyzing fluid-structure interaction in the fast reactor containment

Description: The Eulerian algorithm described is capable of analyzing two-dimensionally the fluid-structure interaction in a typical LMFBR containment consisting of various structure components. The algorithm has several special features. First, it employs the Eulerian coordinates in the formulation and enables the technique to be applicable to excursions involving large material distortions. Second, it provides rigorous hydrodynamic analyses at the fluid-structure interface and at the geometrical discontinuities, which is very important in the study of wave-transmission and -diffraction problems. Third, the algorithm incorporates a well-developed finite-element structural program that can account for both material and geometrical nonlinearities. The application of this Eulerian algorithm is not limited to fast reactor containment. It can also be applied to the major piping components, such as valve and IHX, where internal baffle plates may play an important role in the wave propagation. Moreover, the treatment of the time-dependent irregular cell can be integrated with the IMF/sup 2/ Method and structural dynamics program for investigating the coupled fluid-structure problems involving two-phase flows.
Date: January 1, 1977
Creator: Wang, C.Y.; Chang, Y.W. & Fistedis, S.H.
Partner: UNT Libraries Government Documents Department

HCDA behavior within the primary containment of a large pool-type LMFBR

Description: This paper discusses, specifically, the primary containment response of a large pool-type reactor under HCDA conditions. A large-diameter, thin-walled, pool-type reactor may have some inherent safety advantages in terms of energy accommodation during HCDA loads. The purpose of this study was to predict the containment response from the energetic excursion and to determine the impact loading on the reactor deck for a more detailed analysis. The essential features of the primary system which were modelled include the reactor core, radial shield, redan (separating the hot and cold pools), core support structure (CSS), upper internal structure (UIS), the sodium coolant, and the reactor vessel. Three different UIS configurations were studied and the effects of flow paths on the primary containment response were noted. In each case the primary systems were identical except for the upper internal structure (UIS) which was parametrically varied to simulate; (1) annular flow, (2) a horizontal guide plate, and (3) a cylindrical shroud with guide plate.
Date: January 1, 1983
Creator: Zeuch, W.R.; Wang, C.Y. & Seidensticker, R.W.
Partner: UNT Libraries Government Documents Department

Analysis of LMFBR primary system response to an HCDA using an Eulerian computer code

Description: Applications of an Eulerian code to predict the response of LMFBR containment and primary piping systems to hypothetical core disruptive accidents (HCDA), and to analyze sodium spillage problems, are described. The computer code is an expanded version of the ICECO code. Sample problems are presented for slug impact and sodium spillage, dynamics of the HCDA bubbles, and response of a piping loop. (JWR)
Date: January 1, 1975
Creator: Chang, Y.W.; Wang, C.Y.; Chu, H.Y.; Abdel-Moneim, M.T. & Gvildys, J.
Partner: UNT Libraries Government Documents Department