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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Review of analytical studies on seismic fluid-structure interaction of base-supported cylindrical tanks

Analytical solutions for seismic fluid-structure interaction (FSI) of tanks are used by analysts and engineers for a number of purposes, including preliminary sizing, risk assessment, and verification of numerical models. Analytical solutions for seismic FSI of tanks were first developed in the 1930s and have been extended and/or modified in the following nine decades to accommodate different seismic inputs and boundary conditions. This report reviews published analytical solutions for rigid and flexible, base-supported, cylindrical tanks subjected to unidirectional horizontal motion of a small amplitude. The studies parsed the fluid-structure (FSI) response into an impulsive and a convective component, and addressed frequencies of lateral motions of the tank (i.e., impulsive frequencies), hydrodynamic pressures, frequencies of waves (i.e., convective frequencies), wave heights, and reactions at the base. The solutions were categorized into exact and approximate solutions based on the methodologies used. Herein, FSI responses are calculated and compared for a range of tank dimensions using the analytical solutions from the different studies. The responses presented here are normalized to be unitless, and can be used for tanks with different dimensions and mechanical properties, and subjected to different input motions. A sample steel water tank is analyzed using the normalized solutions for two earthquake ground motions with different frequency contents. Ignoring tank flexibility may significantly underestimate seismic responses of the tank and its contained fluid. The approximate solutions, which have been widely used for decades, may not be sufficiently accurate in the modern era. Calculation errors in the reviewed studies are identified and corrected, and differences are quantified for the sample tank.

42 ENGINEERING↗
DOE OSTI2021

A process to verify numerical models for seismic fluid-structure interaction in advanced reactor vessels

Seismic design and qualification of a liquid-filled advanced nuclear reactor will have to account for fluid-structure interaction (FSI). Interaction between the tank, internal components, and contained liquid will rely on analysis of numerical models that must be verified and validated. Here this study demonstrates a verification process for models of a base-supported cylindrical tank by comparing numerical predictions and analytical solutions. The numerical models are consistent with the assumptions made to derive analytical solutions, namely, either a rigid or a linear elastic tank, ideal fluid, and small-amplitude, unidirectional, horizontal inputs. One software platform is used to illustrate the process. Seismic FSI analysis is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Reported responses are those used for design, including hydrodynamic pressures on the tank wall, shear forces and moments at the tank base, and wave heights of the contained liquid. The accuracy of the numerical results is discussed. The numerical models are verified for calculating the pressures on the tank wall and reactions at its base. Accurate simulation of wave action is challenging for both solvers. Recommendations for modeling, code development, and steps for verification are provided. Although focused on reactor vessels and one software platform, the verification process described herein is broadly applicable to liquid-filled vessels and other finite element codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Experimental and numerical studies of seismic fluid-structure interaction in a base-supported cylindrical vessel

Seismic design and qualification of advanced reactors will rely heavily on the use of verified and validated numerical models capable of capturing the interaction of the vessel, its contained fluid, and the internal equipment: fluid-structure interaction (FSI) analysis. Analytical solutions can be used for preliminary sizing and design of such vessels but their application is limited to simple geometries and boundary conditions, and small amplitude, translational (and rotational) inputs. To validate numerical models for seismic FSI analysis in finite element codes, a comprehensive set of experiments was performed on a liquid-filled cylindrical vessel, using a 6 degree-of-freedom earthquake simulator. Results in terms of sloshing frequency, damping ratio in sloshing modes, and hydrodynamic responses (wave height, hydrodynamic pressure, base shear, and base moment) for multi-directional earthquake simulator inputs are reported and compared with analytical solutions for liquid-filled vessels. The impact of seismic (base) isolation on hydrodynamic responses was studied using earthquake simulator inputs generated using a virtual isolation system. Data from the experiments are used to validate a numerical model of the fluid-filled vessel using the Arbitrary Lagrangian Eulerian (ALE) solver in the commercial finite element program LS-DYNA. Validation studies are presented for multi-directional seismic inputs, including rocking motions. Lagrangian modeling approaches using an elastic material formulation for the fluid are also investigated and their limitations and possible applications are identified. Here, the results are broadly applicable to the seismic response of base supported, liquid-filled vessels.

58 GEOSCIENCES↗
DOE OSTI2021

Verification of numerical models for seismic fluid-structure interaction analysis of internal components in liquid-filled advanced reactors

Earthquake shaking of a liquid-filled advanced reactor induces fluid-structure interaction (FSI) between the reactor vessel (tank), its internal components, and the contained liquid. Seismic design, qualification, and risk assessment of such reactors must consider fluid-structure responses, their geometries and support conditions, and three-directional seismic inputs, all of which require numerical simulations. Numerical models used for analysis of safety-related nuclear equipment must be verified and validated. Here, this paper verifies numerical models of submerged components using analytical solutions. Seismic FSI analysis of the numerical models is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Prior analytical solutions are reworked in this paper, and calculation errors are identified and corrected. The solutions address frequencies of two concentric cylindrical pipes filled with liquid: the inner pipe is a submerged component, and the outer pipe contains the liquid. A unitless frequency coefficient is defined and presented for pipes of different materials, filled with different liquids, and with a range of dimensions for application to advanced reactors. The numerical models are verified here by comparing the lateral frequencies of submerged components with those calculated using the corrected analytical solutions. Recommendations for verification of numerical models of internal components in advanced reactors for seismic FSI analysis are provided. Although the unitless frequency coefficients and verification procedures are developed for application to advanced nuclear reactors, they are broadly applicable to FSI analysis of submerged components in liquid-filled vessels such as storage tanks, boilers, and steam generators.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Analytical Solutions for Seismic Fluid-Structure Interaction of Head-Supported Cylindrical Tanks

Fluid-structure interaction (FSI) of earthquake shaking is a design consideration in the civil, nuclear, chemical, and mechanical industries. Preliminary sizing of structures and components in these industries will often use analytical solutions because there is insufficient information to warrant the analysis of numerical models. Here, this study extends prior analytical work on seismic FSI of base-supported tanks in the 1980s to accommodate head-supported tanks with geometries similar to those proposed for new-build, liquid (fluid)-filled, advanced reactors. Analytical solutions are derived for flexible, head-supported, cylindrical tanks subjected to small-amplitude, unidirectional, horizontal seismic motion, and address frequencies of lateral motions of the tank, hydrodynamic pressures, frequencies of waves, wave heights, and reactions at the head support. Solutions are presented for a range of tank dimensions and could be used for a) preliminary design of head-supported cylindrical tanks and their supporting structures with idealized seismic input, and b) verification of numerical models to be used for final seismic analysis, design, and probabilistic risk assessment.

42 ENGINEERING↗
DOE OSTI2020

Assessment of Survey Results from Advanced Reactor Industry Domain Experts on Nonlinear Soil-Structure Interaction Analysis Software Verification and Validation

The seismic load case has a significant impact on the design and cost of nuclear power plants. Given the need to substantially reduce cost, advanced reactor designers are looking to leverage numerical tools that enable seismic analysis of an integrated vessel/support/structure/soil system. Modern nonlinear analysis tools provide a solution, capturing dynamic coupling between components (including soil-structure interaction (SSI)) concurrent with nonlinear behavior in one or more parts of the system. Although these methods have a rich history of technical development and implementation, software quality assurance (SQA) following nuclear industry standards remains a significant burden for those wishing to adopt such methods for advanced reactor design and licensing. To reduce the SQA burden, this project will develop the guidance for SQA verification and validation (V&V) of coupled nonlinear SSI analysis tools, to include a test matrix of software features and test problems to support commercial grade dedication (CGD). The guidance is intended to be technology-neutral: supporting designers of all advanced reactors. To maximize the value of the project to reactor designers, the project team performed focused surveys of and interviews with advanced reactor designers. Additionally, the project surveyed members of the broader industry involved in reactor design and licensing. The aggregated industry feedback consists of written survey responses, live polling responses, focused interviews, and informal feedback provided after outreach presentations, collectively referred to as “survey results”. Herein, the survey results are reported, reviewed, and assessed to inform follow-on project activities. The survey results confirmed the familiarity of the industry with the coupled nonlinear SSI analysis. They also affirm the project need based upon the expressed intent to (1) incorporate nonlinear features and (2) pursue the coupled nonlinear SSI analysis to reduce seismic demands and construction costs. All reactor designers indicated their intent to incorporate two or more nonlinear features, and all reactor designer respondents opined that the coupled nonlinear SSI analysis would allow for the optimization of the reactor design and construction. However, the programmatic challenges, whether real or perceived, present a significant barrier to reactor designers. The barrier most commonly identified by the reactor designer population was regulatory risk, with 70% citing this as a reason not to pursue the approach. The perceived regulatory risk identified by the reactor designers underscores the importance of regulator engagement and dialogue in this project. Additionally, half of the reactor designers identified cost and lack of guidance as a deterrent. The survey results also provide insights to tailor specific aspects of the guidance document and test matrix. The project plans to prepare both a formal referenceable guidance document and a collaborative, web-based test matrix and problem set. The project will focus on more complete test problem definitions for the prioritized nonlinear features over shallower problem descriptions for a larger set of features. The nonlinearities prioritized as high based upon survey feedback include fluid-structure interaction and seismic isolation and energy dissipation devices. The nonlinearities prioritized as intermediate include nonlinear geomaterials, nonlinear concrete, nonlinear steel, and interface/contact nonlinearity. Deep embedment and the associated nonlinear phenomena are assigned the lowest priority based upon survey feedback.

42 ENGINEERING↗
DOE OSTI2021

Validation of numerical models for seismic fluid-structure-interaction analysis of nuclear, safety-related equipment

Seismic design, qualification, and risk assessment of nuclear safety-related vessels filled with liquid will have to consider the interaction between the vessel (tank), the contained liquid, and submerged components, if any. Seismic fluid-structure-interaction (FSI) analysis of nuclear vessels will rely on numerical models, which are required to be verified and validated. This study validates previously-verified numerical models using test data generated from earthquake-simulator experiments involving a cylindrical tank. Two solvers in LS-DYNA for FSI simulations are used for the numerical analysis: Arbitrary-Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD). Numerical and test results are compared for responses critical to seismic design of advanced reactor vessels: hydrodynamic pressures on the tank wall, reactions at the support, and wave heights of the contained liquid. Analysis is performed for one-, two-, and three-directional seismic inputs with a range of intensity, and rocking motions. The accuracy of the numerical results and different methods for outputting wave heights are discussed. Recommendations for validation of seismic FSI numerical models of advanced reactors are provided. As a result, the validation exercise presented in this study is broadly applicable to cylindrical tanks, regardless of industry sector.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
NASA NTRS1985

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗
DOE OSTI2022

Development, verification, and validation of comprehensive acoustic fluid-structure interaction capabilities in an open-source computational platform

The acoustic fluid-structure interaction (FSI) formulation is a practical numerical approach for the seismic analysis of fluid-filled tanks. However, there are no verification and validation studies reported in the literature that demonstrate the ability of an acoustic FSI numerical model to predict responses important to structural and mechanical design for intense translational and rotational earthquake inputs. Herein, an acoustic FSI formulation is implemented in the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE), and is formally verified and validated using analytical solutions and code-to-code verification, and experimental data, respectively. The analytical solutions are for small amplitude, unidirectional seismic inputs. The code-to-code verification utilizes a previously verified and validated Arbitrary Lagrangian-Eulerian (ALE) numerical model in the commercial finite element code LS-DYNA. The validation studies utilize a comprehensive data set assembled from results of 3D earthquake-simulator tests of a fluid-filled vessel. The acoustic numerical model in MOOSE is verified and validated for hydrodynamic pressures and support reactions except for cases that involve significant convective response. For small amplitude inputs, numerically predicted wave heights match those of the analytical solutions. The numerical model is not verified and validated for wave height calculations under intense 3D seismic inputs. The run times for the acoustic FSI simulations in MOOSE are an order of magnitude, or more, shorter than for the corresponding ALE simulations in LS-DYNA. The utility of the MOOSE acoustic FSI implementation is demonstrated by seismic analysis of a building equipped with a fluid-filled, advanced nuclear reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Structural modeling and dynamic analysis of condensate storage tanks in nuclear power plants

Condensate storage tanks (CSTs) in nuclear power plants (NPPs) are classified as critical equipment capable of surviving strong shaking in a design basis earthquake to assure the ability to subsequently provide cooling water. Structural modeling and dynamic analysis of CSTs are complicated due to fluid-structure interaction (FSI) and coupling issues, which could have significant effects on seismic response. The capability of a number of approximate models to capture seismic response is investigated using dynamic analysis results from detailed finite element models. Modal analyses and time history analyses are carried out using both 2D and 3D models to predict the dynamic behavior of CSTs as a function of ground motion intensity. Although 2D simplified models can be used to quickly evaluate the dynamic response of CSTs when there is substantial margin to failure, a detailed 3D model is required when it is necessary to examine a limit state associated with the failure mode of the tank. The findings show good agreement between the natural frequencies of convective modes determined from the 2D and 3D CST models. The difference between the frequencies of impulsive modes were found to be equal to or less than 25%.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗