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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Topological Charge Pumping in Excitonic Insulators

Here, we show that in excitonic insulators with s-wave electron-hole pairing, an applied electric field (either pulsed or static) can induce a p-wave component to the order parameter, and further drive it to rotate in the s + ip plane, realizing a Thouless charge pump. In one dimension, each cycle of rotation pumps exactly two electrons across the sample. Higher dimensional systems can be viewed as a stack of one-dimensional chains in momentum space in which each chain crossing the Fermi surface contributes a channel of charge pumping. Physics beyond the adiabatic limit, including in particular dissipative effects is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Measurement of the polarisation of single top quarks and antiquarks produced in the $t$-channel at $ \sqrt{s} $ = 13 TeV and bounds on the $tWb$ dipole operator from the ATLAS experiment

A simultaneous measurement of the three components of the top-quark and top-antiquark polarisation vectors in t-channel single-top-quark production is presented. This analysis is based on data from proton–proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb –1 , collected with the ATLAS detector at the LHC. Selected events contain exactly one isolated electron or muon, large missing transverse momentum and exactly two jets, one being b-tagged. Stringent selection requirements are applied to discriminate t-channel single-top-quark events from the background contributions. The top-quark and top-antiquark polarisation vectors are measured from the distributions of the direction cosines of the charged-lepton momentum in the top-quark rest frame. The three components of the polarisation vector for the selected top-quark event sample are P x' = 0.01 ± 0.18, P y' = –0.029 ± 0.027, P z' = 0.91 ± 0.10 and for the top-antiquark event sample they are P x' = –0.02 ± 0.20, P y' = –0.007 ± 0.051, P z' = 0.79 ± 0.16. Normalised differential cross-sections corrected to a fiducial region at the stable-particle level are presented as a function of the charged-lepton angles for top-quark and top-antiquark events inclusively and separately. These measurements are in agreement with Standard Model predictions. The angular differential cross-sections are used to derive bounds on the complex Wilson coefficient of the dimension-six O tW operator in the framework of an effective field theory. The obtained bounds are C tW ϵ [–0.9, 1.4] and C itW ϵ [–0.8, 0.2], both at 95% confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Practical applications of machine-learned flows on gauge fields

Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open question how flows can improve lattice QCD at state-of-the-art scales. We discuss and demonstrate two applications of flows in replica exchange (parallel tempering) sampling, aimed at improving topological mixing, which are viable with iterative improvements upon presently available flows.

Abbott, Ryan↗
DOE OSTI2020

Communication-Constrained Expansion Planning for Resilient Distribution Systems

Distributed generation and remotely controlled switches have emerged as important technologies to improve the resiliency of distribution grids against extreme weather-related disturbances. Therefore it becomes important to study how best to place them on the grid in order to meet a resiliency criteria, while minimizing costs and capturing their dependencies on the associated communication systems that sustain their distributed operations. This paper introduces the Optimal Resilient Design Problem for Distribution and Communication Systems (ORDPDC) to address this need. The ORDPDC is formulated as a two-stage stochastic mixed-integer program that captures the physical laws of distribution systems, the communication connectivity of the smart grid components, and a set of scenarios that specifies which components are affected by potential disasters. The paper proposes an exact branch-and-price algorithm for the ORDPDC that features a strong lower bound and a variety of acceleration schemes to address degeneracy. The ORDPDC model and branch-and-price algorithm were evaluated on a variety of test cases with varying disaster intensities and network topologies. The results demonstrate the significant impact of the network topologies on the expansion plans and costs, as well as the computational benefits of the proposed approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Motion Control of Hydraulic Actuators In the Presence of Discrete Pressure Rail Switching

Conventional off-highway mobile machines are hydraulically actuated and have poor energy efficiencies. The goal to increase system efficiency and to reap the benefits of electrification have led to the creation of a novel Hybrid Hydraulic-Electric Architecture (HHEA) which could significantly increase efficiency, decrease the sizes and cost of electrical components, and maintain control performance. The key concept is to utilize a set of common pressure rails to provide the majority of power via the power dense hydraulics and to modulate that power by small electric components, which are less power dense, for precise control. The paper presents the motion control strategy for this architecture. The architecture presents a distinct challenge in that as the energy minimization algorithm selects different pressure rails, the system could experience large discrete jumps in pressures that impact control performance, especially when the electric components are torque limited. To meet this challenge, a passivity based back-stepping controller is used as the nominal controller between pressure rail switching events and a separate transition controller is used to deal with the pressure rail switching events. Two transition controllers are proposed, one uses the electric motor torque as the input, and the other also uses valve timing as a second input. For both transition controllers, a least norm control approach is used to steer the system states to the exact desired states at the end of the short transition period (~ 40 ms). The transition controllers are able to reduce the tracking error and the required electric motor torque, and hence achieve better control performance even with smaller electric components.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Foundations of variational discrete action theory

Variational wave functions and Green's functions are two important paradigms for solving quantum Hamiltonians, each having their own advantages. Here we detail the variational discrete action theory (VDAT), which exploits the advantages of both paradigms in order to approximately solve the ground state of quantum Hamiltonians. VDAT consists of two central components: the sequential product density matrix (SPD) ansatz and a discrete action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer $\mathscr{N}$, recovering many well-known variational wave functions, in addition to the exact solution for $\mathscr{N}$ = ∞. The discrete action describes all dynamical information of an effective integer time evolution with respect to the SPD. We generalize the path integral to our integer time formalism, which converts a dynamic correlation function in integer time to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism to integer time, which results in analogous but distinct mathematical structures, yielding integer time versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We prove that the SPD can be exactly evaluated in the multiband Anderson impurity model (AIM) by summing a finite number of diagrams. For the multiband Hubbard model, we prove that the self-consistent canonical discrete action approximation (SCDA), which is the integer time analog of the dynamical mean-field theory, exactly evaluates the SPD for d = ∞. VDAT within the SCDA provides an efficient yet reliable method for capturing the local physics of quantum lattice models, which will have broad applications for strongly correlated electron materials. More generally, VDAT should find applications in various many-body problems in physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Removing Basis Set Incompleteness Error in Finite-Temperature Electronic Structure Calculations: Two-Electron Systems

We investigate the basis-set-size dependence for quantities related to interacting electrons in the canonical ensemble. Calculations are performed using exact diagonalization (finite temperature full configuration interaction method) on two-electron model systems–the uniform electron gas (UEG) and the helium atom. Our data reproduce previous observations of a competition for how the internal energy converges between the ground-state correlation energy and the high-temperature kinetic energy. We explore how this can be related to component parts of the internal energy including kinetic, exchange, and correlation energies and show there is surprising nuance in how this can be broken down into mostly monotonically converging quantities. We also show that separation of the free energy into a free energy with/without correlation allows for monotonic convergence with basis set size due to the variational principle. We find that the free energy convergence matches the previously observed convergence properties of the internal energy. We discuss the free energy divergence that happens when converging a finite basis analytical hydrogen atom to the complete basis set limit and compare this to the energies of a helium atom in a large periodic box. Reducing the box size, we saw convergence trends for the helium atom that were similar to the UEG.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

NGEE Arctic Integrated Modeling (IM3): Improved snow-vegetation interaction

This data product represents the integration of new code capability for arctic tundra snow-vegetation-terrain interactions into the Energy Exascale Earth System Model (E3SM), through the E3SM Land Model (ELM) component. This code integration is the result of collaborative effort between the NGEE Arctic project and the E3SM project. The NGEE Arctic project developed a total of six Integrated Modeling (IM) modules informed by observations and experiments. New ELM capability represented by this data product (IM3) falls into three categories: 1) Downscaling from gridcell to topographic unit level when working through the existing coupler bypass code. 2) Four new parameters (taper, stocking, bendresist, and vegshape) have been added to ELM to allow for flexible definition of snow-vegetation interactions. 3) Vegshape and bendresist parameters are used to calculate the fraction of leaf area and/or stem area buried by snow for a given snow depth. This data record consists of a single document (pdf format) that describes the theoretical basis for the snow-vegetation-terrain interactions added to ELM, and describes the modifications made to the ELM code. The Methods section of this metadata record includes a link to the public E3SM code repository where the exact code modifications as integrated in E3SM can be accessed. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

Thornton, Peter E [ORNL] (ORCID:0000000247595158)↗
DOE OSTI2021

Measurement of the top quark mass using events with a single reconstructed top quark in pp collisions at $$ \sqrt{s} $$ = 13 TeV

A measurement of the top quark mass is performed using a data sample enriched with single top quark events produced in the t channel. The study is based on proton- proton collision data, corresponding to an integrated luminosity of 35.9 fb -1 , recorded at √s = 13 TeV by the CMS experiment at the LHC in 2016. Candidate events are selected by requiring an isolated high-momentum lepton (muon or electron) and exactly two jets, of which one is identified as originating from a bottom quark. Multivariate discriminants are designed to separate the signal from the background. Optimized thresholds are placed on the discriminant outputs to obtain an event sample with high signal purity. The top quark mass is found to be $172.13^{+0.76}_{-0.77}$ GeV, where the uncertainty includes both the statistical and systematic components, reaching sub-GeV precision for the first time in this event topology. The masses of the top quark and antiquark are also determined separately using the lepton charge in the final state, from which the mass ratio and difference are determined to be $0.9952^{+0.0079}_{-0.0104}$ and $0.83^{+1.79}_{-1.35}$ GeV, respectively. The results are consistent with CPT invariance.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

NGEE Arctic Integrated Modeling (IM2): Improved subgrid hillslope hydrologic connectivity

This data product represents the integration of new code capability for arctic tundra hillslope hydrologic processes into the Energy Exascale Earth System Model (E3SM), through the E3SM Land Model (ELM) component. This code integration is the result of collaborative effort between the NGEE Arctic project and the E3SM project. The current ELM represents water movement primarily through vertical processes, such as precipitation, canopy interception, evaporation, infiltration, and soil water movement. Lateral water movement—such as surface runoff, subsurface flow, and river transport—plays a significant role in the hydrological cycle, especially in regions with varied topography. While E3SM includes a runoff routing component representing water transport in the river network, the lateral transport of water at the subgrid scale within the land model has previously not been taken into account. With the recent development of topographic units within the ELM subgrid data structure, there is an opportunity to simulate hillslope hydrologic connectivity by introducing water transport along topographic gradients. We expect that more realistic representation of hillslope hydrologic processes will lead to improved predictions of both soil water content and river network flows. Lateral transport of water at and near the surface is represented as a sub-grid process in this new code development. Water is tracked as it moves from higher to lower elevations within a gridcell. This capability uses the nested hierarchical sub-grid scheme within ELM to connect water fluxes from sub-grid elements with higher elevation to those with lower elevation. This data record consists of a single document (pdf format) that describes the theoretical basis for the hillslope hydrology processes added to ELM, and describes the modifications made to the ELM code. The Methods section of this metadata record includes a link to the public E3SM code repository where the exact code modifications as integrated in E3SM can be accessed. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

Thornton, Peter E [ORNL] (ORCID:0000000247595158)↗
DOE OSTI2021

Modified equilibrium distributions for Cooper-Frye particlization

We introduce a positive-definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence of moderately large viscous corrections. The modified equilibrium distribution function can be constructed with hydrodynamic input from either relativistic viscous fluid dynamics or anisotropic fluid dynamics. We test the modified equilibrium distribution's hydrodynamic output for a stationary hadron resonance gas subject to either shear stress, bulk pressure, or baryon diffusion current at a given freeze-out temperature and baryon chemical potential. While it does not reproduce all components of the net baryon current and energy-momentum tensor exactly, it significantly improves upon the customary linearized approximations for the nonequilibrium correction δf n which typically lead to unphysical negative distribution functions at large particle momenta. A comparison of particle spectra and p T –differential elliptic flow coefficients from the Cooper–Frye formula computed with the modified equilibrium distribution and with linearized δf n corrections is presented, for two different (2 + 1)–dimensional hypersurfaces corresponding to central and noncentral Pb + Pb collisions at the Large Hadron Collider (LHC).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Addressing Consequence within Operational Risk: An Approach for Understanding an Organization’s Unique Infrastructure Environment

The endeavor of tackling operational risk focused on consequences is challenging even for the most resourced entity but can be advanced though a simplified approach: identifying, binning, and prioritizing the infrastructure environment. While no two entities within a single element of the 16 critical infrastructure sectors are exactly alike when it comes to risk, there is a basic process to move toward a greater understanding of operational risk through becoming more informed about the infrastructure landscape in which the entity exists. The process starts with bringing internal and external stakeholders and subject matter experts together to analyze key areas such as Information Technology (IT) and Operational Technology (OT) components and points of convergence, analyzing internal and external cyber and physical dependencies, accounting for explosive growth in devices and wireless technology, and leveraging the contributions of people inside and outside the operational environment. Attaining a common understanding of the infrastructure landscape as part of addressing consequences within operational risk is not easy to do or resource light, but the process outlined provides the framework to further any entity’s efforts in this space.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Addressing Consequence within Operational Risk (O.T. Gagnon III) 9-18-2024

Addressing Consequence within Operational Risk: Why threats and security are just not that important! When dealing with cyber or physical risk within any critical infrastructure (CI) environment, don’t concern yourself with vulnerabilities and threats, at least not at first! Also, don’t be overly fixated on “securing the systems” within the organization. The endeavor of tackling operational risk focused on consequences in any critical infrastructure environment to include the complex Aviation ecosystem is challenging even for the most resourced entity but can be advanced though a simplified approach: identifying, binning, and prioritizing the infrastructure environment. While no two entities within a single element of the 16 critical infrastructure sectors are exactly alike when it comes to risk, there is a basic process to move toward a greater understanding of operational risk through becoming more informed about the infrastructure environment in which the entity exists. The process starts with bringing internal and external stakeholders and subject matter experts together to analyze key areas such as Information Technology (IT) and Operational Technology (OT) components and points of convergence, analyzing internal and external cyber and physical dependencies, accounting for explosive growth in devices and wireless technology, and leveraging the contributions of people inside and outside the operational environment. Attaining a common understanding of the infrastructure environment as part of addressing consequences within operational risk is not easy to do or resource light, but the process outlined provides the framework to further any entity’s efforts in this space. When it comes to cyber risks, before an organization can consider vulnerabilities within and threats to its operations, it must first have a solid understanding of the consequences existing inside its infrastructure environment. Idaho National Lab’s Consequence-Driven, Cyber-Informed Engineering is offered as an example of this approach to effective and efficient cyber risk mitigation.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Electronic structure of α - RuCl 3 by fixed-node and fixed-phase diffusion Monte Carlo methods

Layered material α-RuCl 3 has caught wide attention due to its possible realization of Kitaev's spin liquid and its electronic structure that involves the interplay of electron-electron correlations and spin-orbit effects. Several DFT+U studies have suggested that both electron-electron correlations and spin-orbit effects are crucial for accurately describing the band gap. This work studies the importance of these two effects using fixed-node and fixed-phase diffusion Monte Carlo calculations both in spin-averaged and explicit spin-orbit formalisms. In the latter, the Slater-Jastrow trial function is constructed from two-component spin orbitals using our recent quantum Monte Carlo (QMC) developments and thoroughly tested effective core potentials. Our results show that the gap in the ideal crystal is already accurately described by the spin-averaged case, with the dominant role being played by the magnetic ground state with significant exchange and electron correlation effects. We find qualitative agreement between hybrid DFT, DFT+U, and QMC. In addition, QMC results agree very well with available experiments, and we identify the values of exact Fock exchange mixing that provide comparable gaps. Explicit spin-orbit QMC calculations reveal that the effect of spin-orbit coupling on the gap is minor, of the order of 0.2 eV, which corresponds to the strength of the spin orbit of the Ru atom.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Quench dynamics of two-component dipolar fermions subject to a quasiperiodic potential

Motivated by recent experiments in fermionic polar gases, we study the nonequilibrium dynamics of two-component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a long-range spin-SU(2) symmetric fermionic Hamiltonian by calculating experimentally accessible dynamical observables. To study the nonequilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons |↑↓0↑↓0↑↓0↑↓0↑↓$\rangle$ and (ii) product state with singlons |↑↓↑↓↑↓↑↓↑↓$\rangle$. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization (ED) and the time-dependent variational principle (TDVP) for finite matrix product states (MPS), within experimentally relevant timescales. For the product state with doublons, we observe a delocalized to localized phase transition varying disorder strengths by monitoring the decay of charge imbalance with time. For the long-range interacting Hamiltonian of our focus, and in the presence of strong enough disorder, starting the time evolution with singlons we find a strong reduction in the spin delocalization, contrary to results of previous studies using the disordered short-range (on-site) Hubbard model with SU(2) symmetry. In addition to the quench dynamics, we also demonstrate the localization of charge and spin in the full energy spectrum of the long-range spin-SU(2) symmetric Hamiltonian by monitoring spin and charge autocorrelation functions. Finally, our predictions for localization of both charge and spin should be observable in ultracold experiments with fermionic dipolar atoms subject to a quasiperiodic potential.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Capturing CO 2 in Quadrupolar Binding Pockets: Broadband Microwave Spectroscopy of Pyrimidine-(CO 2 ) n , n = 1,2

Pyrimidine has two in-plane CH(δ+)/N̈(δ–)/CH(δ+) binding sites that are complementary to the (δ–/2δ+/δ–) quadrupole moment of CO 2 . For this study, we recorded broadband microwave spectra over the 7.5–17.5 GHz range for pyrimidine-(CO 2 ) n with n = 1 and 2 formed in a supersonic expansion. Based on fits of the rotational transitions, including nuclear hyperfine splitting due to the two 14 N nuclei, we have assigned 313 hyperfine components across 105 rotational transitions for the n = 1 complex and 208 hyperfine components across 105 rotational transitions for the n = 2 complex. The pyrimidine-CO 2 complex is planar, with CO 2 occupying one of the quadrupolar binding sites, forming a structure in which the CO 2 is stabilized in the plane by interactions with the C–H hydrogens adjacent to the nitrogen atom. This structure is closely analogous to that of the pyridine-CO 2 complex studied previously by (Doran, J. L. J. Mol. Struct. 2012, 1019, 191–195). The fit to the n = 2 cluster gives rotational constants consistent with a planar cluster of C 2v symmetry in which the second CO 2 molecule binds in the second quadrupolar binding pocket on the opposite side of the ring. The calculated total binding energy in pyrimidine-CO 2 is –13.7 kJ mol –1 , including corrections for basis set superposition error and zero-point energy, at the CCSD(T)/ 6-311++G(3df,2p) level, while that in pyrimidine-(CO 2 ) 2 is almost exactly double that size, indicating little interaction between the two CO 2 molecules in the two binding sites. The enthalpy, entropy, and free energy of binding are also calculated at 300 K within the harmonic oscillator/rigid-rotor model. This model is shown to lack quantitative accuracy when it is applied to the formation of weakly bound complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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↗