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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Turbulent Kinetic Energy Budgets over Gentle Topography Covered by Forests

Large-eddy simulations of flow over a “horizontally” uniform model forest are used to investigate the effects of gentle topography on the turbulent kinetic energy (TKE) budget within the canopy roughness sublayer. Despite significant differences between simulations using idealized sinusoidal topography and real topography of the Amazon forest, results indicate that the effects of topography are located predominantly in the upper canopy and above, and are mostly caused by mean advection of TKE. The “horizontally” averaged TKE budget from idealized and real gentle topographies are almost identical to that for flat terrain, including a clear inertial layer above the roughness sublayer in which shear production is balanced by local dissipation. At topography crests, where observational towers are usually located, mean vertical advection of TKE can be as important as horizontal advection. Here, we propose the use on an approximate TKE balance equation to estimate mean advection from single tower measurements, and introduce a new advection index that can be used as a proxy to quantify the importance of the topography on the TKE budget.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Ocean fronts and eddies force atmospheric rivers and heavy precipitation in western North America

Atmospheric rivers (ARs) are responsible for over 90% of poleward water vapor transport in the mid-latitudes and can produce extreme precipitation when making landfall. However, weather and climate models still have difficulty simulating and predicting landfalling ARs and associated extreme precipitation, highlighting the need to better understand AR dynamics. Here, using high-resolution climate models and observations, we demonstrate that mesoscale sea-surface temperature (SST) anomalies along the Kuroshio Extension can exert a remote influence on landfalling ARs and related heavy precipitation along the west coast of North America. Inclusion of mesoscale SST forcing in the simulations results in approximately a 40% increase in landfalling ARs and up to a 30% increase in heavy precipitation in mountainous regions and this remote impact occurs on two-week time scales. The asymmetrical response of the atmosphere to warm vs. cold mesoscale SSTs over the eddy-rich Kuroshio Extension region is proposed as a forcing mechanism that results in a net increase of moisture flux above the planetary boundary layer, prompting AR genesis via enhancing moisture transport into extratropical cyclones in the presence of mesoscale SST forcing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Dimits shift, avalanche-like bursts, and solitary propagating structures in the two-field flux-balanced Hasegawa–Wakatani model for plasma edge turbulence

We show that the recently introduced two-field flux-balanced Hasegawa–Wakatani (BHW) model captures the key features of drift-wave turbulent transport mediated by zonal flows observed in more complete and accurate gyrokinetic simulations, such as the existence of a nonlinear upshift of the threshold for drift wave turbulence driven transport, often called the Dimits shift, as well as non-local transport with avalanche bursts and solitary propagating structures. Because of the approximations made in the BHW model, these observations are made for the particle flux instead of the heat flux more commonly studied in ion temperature gradient (ITG) driven turbulence in fluid or gyrokinetic codes. Many of these features are not seen in other Hasegawa–Wakatani models, which confirm the critical role of the electron dynamics parallel to the magnetic field lines. To address questions regarding the role of boundary conditions on the drift-wave zonal flow dynamics, we apply our model to both a channel domain geometry and the more typical doubly periodic geometry. We only observe strong soliton-like solutions in the particle flux for the channel geometry, in the vicinity of the boundaries, where strong velocity shear and density gradients are generated, which are absent in the doubly periodic simulations. Changing the aspect ratio of the simulation domain also has a significant effect. In domains which are elongated in the radial direction, more complex multi-scale dynamics takes place, with multiple zonal jets interacting with each other, and large scale avalanches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Electrical Resistivity Tomography Monitoring of In Situ Soil Flushing at the Hanford 100-K East Area: 100KE Soil Flushing Monitoring

Former operations in the 100-KE Area at the Hanford Site resulted in vadose zone hexavalent chromium that provides a source of groundwater contamination. Previous efforts to remediate vadose zone chromium involved excavation and offsite treatment of contaminated soils. Although much of the chromium was removed, contamination still exists in native soil between the water table and the bottom of the pit, which has since been backfilled. In-situ soil flushing was tested at the 100-KE Area to accelerate the removal of the remaining hexavalent chromium in the vadose zone. Soil flushing works by applying clean flush water at the surface, which mobilizes and transports chromium as it migrates downward to the water table. Once the chromium reaches the water table, it is hydraulically contained, extracted, and treated through pump and treat operations. The efficacy of soil flushing is directly related to the volume of clean water that infiltrates through contaminated soils. Therefore, performance monitoring requires and understanding of flush water migration through the vadose zone. It is challenging to comprehensively assess soil flushing performance via borehole access due to the limited volume of investigation afforded by a given wellbore. As an alternative, 3D time-lapse electrical resistivity tomography (ERT) was tested as a method of monitoring the distribution of flush water over time within the vadose zone. ERT is a method of imaging the bulk electrical conductivity of the subsurface, which is highly dependent on water saturation levels in unconsolidated and unsaturated sediments. Thus, the timing and location of changes in bulk conductivity caused by soil flushing can be used to infer flush water migration pathways. In this report we present results of 3D time-lapse ERT imaging during two separate soil flushing campaigns conducted during the spring and summer months of 2022 and 2023. Results show generally that: 1) Pit backfill materials appear to nominally have larger permeability than native soils. Consequently, the boundary between pit backfill and native soil had a significant impact on flush water migration, causing some flush water to migrate along the pit boundary to the bottom of the pit. 2) Non-uniform flows, likely caused by variations in hydrogeologic properties, developed in the pit backfill materials, resulting in uneven flush water distribution on the southern margin of the soil flushing zone. 3) Redistribution of water at the interface between backfill materials and Hanford formation materials likely facilitated elevated and uniform distribution of flush water within native soils beneath the deeper parts of the pit boundary beneath the center of the flush zone, which presumably overlie soils with elevated chromium contamination. These areas appear to have been infiltrated by higher volumes of flush water than the northern and southern margins of the flush zone. 4) In comparison to 2022, high flush water application rates significantly improved flush water distribution throughout the target flushing zone. 5) Imaging resolution was limited to a depth of approximate 20 meters below the land surface, due primarily to limitations on the lateral extent of the surface ERT array. The ~10 m region of the vadose zone between approximately 130 meters elevation and the water table at approximately 120 meters elevation was unresolved.

100 Area↗
DOE OSTI2022

Seasonal variations in fire conditions are important drivers in the trend of aerosol optical properties over the south-eastern Atlantic

Abstract. From June to October, southern Africa produces one-third of the global biomass burning (BB) emissions by widespread fires. BB aerosols are transported westward over the south-eastern Atlantic with the mid-tropospheric winds, resulting in significant radiative effects. Ascension Island (ASI) is located midway between Africa and South America. From June 2016 to October 2017, a 17-month in situ observation campaign on ASI found a low single-scattering albedo (SSA) as well as a high mass absorption cross-section of black carbon (MACBC), demonstrating the strong absorbing marine boundary layer in the south-eastern Atlantic. Here we investigate the monthly variations of critical optical properties of BB aerosols, i.e. SSA and MACBC, during the BB seasons and the driving factors behind these variations. Both SSA and MACBC increase from June to August and decrease in September and October. The average SSA during the BB seasons is 0.81 at 529 nm wavelength, with the highest mean ∼ 0.85 in October and the lowest ∼ 0.78 in August. The absorption enhancement (Eabs) derived from the MACBC shows similar trends with SSA, with the average during the whole of the BB seasons at ∼ 1.96 and ∼ 2.07 in 2016 and 2017, respectively. As the Eabs is higher than the ∼ 1.5 commonly adopted value by climate models, this result suggests the marine boundary layer in the south-eastern Atlantic is more absorbing than model simulations. We find the enhanced ratio of BC to CO (ΔBC/ΔCO, equal to BC/ΔCO as the BC background concentration is considered to be 0) is well correlated with SSA and MACBC, providing a simple way to estimate the aerosol optical characteristics in the south-eastern Atlantic. The exponential function we proposed can approximate SSA and MACBC with BC/ΔCO, and when BC/ΔCO is small it can capture the rapid growth of SSA as BC/ΔCO decreases. BC/ΔCO is influenced by combustion conditions and aerosol scavenging. From the analysis of the location of BB, the primary source fuel, the water content in the fuel, combined with the mean cloud cover and precipitation in the transport areas of the BB plume, we conclude that the increase in BC/ΔCO from June to August is likely to be caused by burning becoming more flaming. The reduction in the water content of fuels may be responsible for the change in the burning conditions from June to August. The decrease in BC/ΔCO in September and October may be caused by two factors, one being a lower proportion of flaming conditions, possibly associated with a decrease in mean surface wind speed in the burning area, and the other being an increase in precipitation in the BB transport pathway, leading to enhanced aerosol scavenging, which ultimately results in an increase in SSA and MACBC.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

The holar wind

String theory in AdS 3 with purely NS-NS fluxes and vanishing RR moduli has a continuum of winding string excitations in radial plane wave states. BTZ black holes can emit such strings, which then flow out toward the AdS 3 boundary as a stream of massive quanta, and form a black hole analogue of the solar wind. The winding string sector thus provides a decay channel for the black hole to evaporate without having either to couple the system to an external reservoir or to match the AdS 3 throat onto an asymptotically flat region. We compute the emission amplitude of this “holar wind” in the semi-classical approximation, and consider the associated version of the black hole information paradox.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗
DOE OSTI2020

Kilometer-Scale Hydrologic Exchange Flows in a Gravel Bed River Corridor and Their Implications to Solute Migration

In this work, a well-characterized field site along a major river corridor was used to investigate the dynamic pathways and impacts of subsurface hydrogeologic structures on kilometer-scale hydrologic exchange flows between river water and groundwater. A aqueous uranium (U aq ) plume exists at the site that discharges to the Columbia River. We performed temporally intensive monitoring of specific conductance (SpC) and U aq concentrations within the plume at increasing distances from the river shoreline and at locations both within and outside a presumed subsurface pathway of lateral hydrologic exchange. Specific conductance and U aq were utilized as in-situ tracers of hydrologic exchange and associated groundwater-surface water mixing. Monitoring data was collected for an approximate two year period during which seasonal river elevations varied by more than 2 m causing distinct events of river water intrusion and retreat from the near-shore aquifer, and large temporal variations in well-water analyte concentrations. Statistical clustering analysis was applied to identify well groupings exhibiting common time series behaviors. PFLOTRAN was implemented within a modeling domain of 3.3 x 1.9 km with dynamic flow boundary conditions and accurate subsurface topography for the basal aquitard underlying the aquifer. In-silico calculations of river water tracer behavior were performed to assess predominant flow directions and velocities influenced by river stage variations and variable aquitard topography, and their collective influences on SpC and U aq concentrations. We demonstrate complicated multidirectional flow behaviors at the kilometer scale resulting from hydrologic exchange and subsurface structure that influence plume dynamics and determine the overall system behavior.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

On the differences in the vertical distribution of modeled aerosol optical depth over the southeastern Atlantic

Abstract. The southeastern Atlantic is home to an expansive smoke aerosol plume overlying a large cloud deck for approximately a third of the year. The aerosol plume is mainly attributed to the extensive biomass burning activities that occur in southern Africa. Current Earth system models (ESMs) reveal significant differences in their estimates of regional aerosol radiative effects over this region. Such large differences partially stem from uncertainties in the vertical distribution of aerosols in the troposphere. These uncertainties translate into different aerosol optical depths (AODs) in the planetary boundary layer (PBL) and the free troposphere (FT). This study examines differences of AOD fraction in the FT and AOD differences among ESMs (WRF-CAM5, WRF-FINN, GEOS-Chem, EAM-E3SM, ALADIN, GEOS-FP, and MERRA-2) and aircraft-based measurements from the NASA ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) field campaign. Models frequently define the PBL as the well-mixed surface-based layer, but this definition misses the upper parts of decoupled PBLs, in which most low-level clouds occur. To account for the presence of decoupled boundary layers in the models, the height of maximum vertical gradient of specific humidity profiles from each model is used to define PBL heights. Results indicate that the monthly mean contribution of AOD in the FT to the total-column AOD ranges from 44 % to 74 % in September 2016 and from 54 % to 71 % in August 2017 within the region bounded by 25∘ S–0∘ N–S and 15∘ W–15∘ E (excluding land) among the ESMs. ALADIN and GEOS-Chem show similar aerosol plume patterns to a derived above-cloud aerosol product from the Moderate Resolution Imaging Spectroradiometer (MODIS) during September 2016, but none of the models show a similar above-cloud plume pattern to MODIS in August 2017. Using the second-generation High Spectral Resolution Lidar (HSRL-2) to derive an aircraft-based constraint on the AOD and the fractional AOD, we found that WRF-CAM5 produces 40 % less AOD than those from the HSRL-2 measurements, but it performs well at separating AOD fraction between the FT and the PBL. AOD fractions in the FT for GEOS-Chem and EAM-E3SM are, respectively, 10 % and 15 % lower than the AOD fractions from the HSRL-2. Their similar mean AODs reflect a cancellation of high and low AOD biases. Compared with aircraft-based observations, GEOS-FP, MERRA-2, and ALADIN produce 24 %–36 % less AOD and tend to misplace more aerosols in the PBL. The models generally underestimate AODs for measured AODs that are above 0.8, indicating their limitations at reproducing high AODs. The differences in the absolute AOD, FT AOD, and the vertical apportioning of AOD in different models highlight the need to continue improving the accuracy of modeled AOD distributions. These differences affect the sign and magnitude of the net aerosol radiative forcing, especially when aerosols are in contact with clouds.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Fourier Neural Networks as Function Approximators and Differential Equation Solvers

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a straightforward architecture with a single hidden layer. The simplicity of this network architecture facilitates the integration with any other higher-complexity networks, at a data pre- or postprocessing stage. We validate this FNN on naturally periodic smooth functions and on piecewise continuous periodic functions. We showcase the use of this FNN for modeling or solving partial differential equations with periodic boundary conditions. The main advantages of the current approach are the validity of the solution outside the training region, interpretability of the trained model, and simplicity of use.

Fourier decomposition↗
DOE OSTI2020

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Model-based predictive control of multi-zone commercial building with a lumped building modelling approach

Here this study investigates the applicability of a lumped building modeling approach to model-based predictive control (MPC) to alleviate the complex modeling process of the grey-box multi-zone building model. Based on experimental data, two building models were estimated in this study. The detailed model as a reference case and a lumped model were estimated with decentralized and conventional approaches, respectively. Then, simulations were performed with two boundary conditions, including the comfort bound and electricity cost structure. The performances of the MPC with the detailed and lumped models were analyzed compared to the feedback control. More savings was achieved with a larger comfort bound and more aggressive electricity cost structure. The savings potential of the proposed lumped model approach was not as high as that of the detailed model. However, the proposed method yields good control performance, whose savings was approximately 8.6% over that of feedback control. These results suggest that the proposed method can be used to facilitate MPC implementation in multi-zone building applications.

42 ENGINEERING↗
DOE OSTI2021

Analytic solutions for Asay foil trajectories with implications for ejecta source models and mass measurements

We consider the trajectory of an Asay foil ejecta diagnostic for scenarios where ejecta are produced at a singly shocked planar surface and fly ballistically through a perfect vacuum to the sensor. We do so by building upon a previously established mathematical framework derived for the analytic study of stationary sensors. First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source model. The result is an integrodifferential equation of motion for the foil trajectory. This equation yields an easily calculable closed-form implicit solution for the foil trajectory in instant-production scenarios. From there, we derive a boundary condition that particle velocity distributions must satisfy if their associated foil trajectories are to exhibit a smooth initial acceleration, as occurs in some experiments. This condition is identical to one derived previously from a consideration of piezoelectric voltage data obtained in similar experiments. We also compare techniques for inferring accumulated ejecta masses from foil trajectories, first by deriving the exact solution, and then by quantifying the error imposed by a frequently used approximate solution (both subject to the assumption of instantaneous ejecta production). Finally, we examine the common practice of presenting inferred cumulative ejecta masses as a function of implied ejecta velocity, establishing the conditions under which this methodology is most meaningful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Hazma meets HERWIG4DM: precision gamma-ray, neutrino, and positron spectra for light dark matter

Herein we present a new open-source package, Hazma 2, that computes accurate spectra relevant for indirect dark matter searches for photon, neutrino, and positron production from vector-mediated dark matter annihilation and for spin-one dark matter decay. The tool bridges across the regimes of validity of two state of the art codes: Hazma 1, which provides an accurate description below hadronic resonances up to center-of-mass energies around 250 MeV, and Herwig4DM, which is based on vector meson dominance and measured form factors, and accurate well into the few GeV range. The applicability of the combined code extends to approximately 1.5 GeV, above which the number of final state hadrons off of which we individually compute the photon, neutrino, and positron yield grows exceedingly rapidly. We provide example branching ratios, particle spectra and conservative observational constraints from existing gamma-ray data for the well-motivated cases of decaying dark photon dark matter and vector-mediated fermionic dark matter annihilation. Finally, we compare our results to other existing codes at the boundaries of their respective ranges of applicability. Hazma 2 is freely available on GitHub athttps://github.com/LoganAMorrison/Hazma.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

3D In-situ Stop Action Study of Recrystallization in Additively Manufactured 316L Stainless Steel: Reconstruction Optimization and Observations

A volume of an additively manufactured 316L stainless steel sample has been tracked during its recrystallization using near-and far-field High Energy Diffraction Microscopy (HEDM) and absorption tomography at Advanced Photon Source beamline 1-ID. A nearfield compatible in situ furnace allows monitoring of Bragg diffraction signals as they evolve out of a weak and diffuse background while the sample temperature is approximate to 1250 degrees C. The sample is rapidly cooled to room temperature after observation of significant signal evolution and ti similar to 0.035 mm(3) is mapped by the near-field method. Four cycles of heat treatment follow the structure from a state of small, isolated grains through impingement of domains to near completion of recyrstallization. Here, the experiment and reconstructions are described, and recrystallized fractions, twin domains, and distributions of grain boundary types are discussed.

Liu, He↗
DOE OSTI2022

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale

The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. Here, we present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.

Nguyen, Thien↗
DOE OSTI2022

Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations

The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while B 1g (d x 2 –y 2 ) and B 2g (d xy ) pairing dominates in the absence of repulsive longer-range Coulomb interactions V NN , the latter induces pairing in other symmetry channels, including, e.g., A 2g (g-wave), nodal A 1g (extended s-wave), or nodal E u (p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, V NN < 0, on the superconducting gap structure. Furthermore, depending on the electronic filling, such an attraction boosts E u (p-wave) spin-triplet or B 1g (d x 2 –y 2 ) spin-singlet ordering.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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↗