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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Identification of Dynamic Force Coefficients for an Additively Manufactured Hermetic Squeeze Film Bearing Support Damper Utilizing a Pass-Through Channel

Abstract The following paper presents breakthrough experimental results for a new hermetic squeeze film damper (HSFD) concept that is integrally designed within an externally pressurized tilting-pad radial gas bearing support. The flexibly damped gas bearing module was designed for a 7.2″ (183 mm) diameter shaft and fabricated using direct metal laser melting (DMLM); also known as additive manufacturing. The bearing and HSFD were sized based on ongoing studies for oil-free supercritical carbon dioxide (sCO2) power turbines in the 8.5 MW–10 MW power range. The development of the new damper concept was motivated by past dynamic testing on HSFD, which generated frequency-dependent stiffness and damping force coefficients. In efforts to eliminate the frequency dependency, a new HSFD architecture was conceived that adds accumulator volumes and a pass-through channel to previously conceived HSFD flow network designs. The other motivation for the work is the need to develop a cost-effective and reliable oil-free bearing technology that is scalable to large power turbomachinery applications. There were several objectives for the following work. The first objective was to successfully design and fabricate a single piece bearing-damper using additive manufacturing, while dimensionally controlling critical design features. The paper discusses the manufacturing steps and shows cut-ups that reveal adequate clearance control capability with internal damper clearances. The second objective was to perform experimental testing with the new HSFD design in efforts to extract stiffness and damping coefficients for excitation frequencies within 20–160 Hz and peak vibration amplitudes between 0.25 mils (6.35 microns) to 1 mil (25.4 microns). The test results for a single HSFD bearing module indicated that the design modifications to the HSFD architecture were successful in eliminating nearly all the frequency dependencies for the stiffness force coefficient. The dynamic tests yielded a stiffness coefficient that varied between 112 klb/in. (19.6 MN/m) and 96 klb/in. (16.8 MN/m). The damping force coefficient however, exhibited relatively more variation with frequency with values residing between 175 lb-s/in. (31 kN-s/m) to 214 lb-s/in. (37 kN-s/m). Finally, the paper advances a three-dimensional fluid-structure interaction (FSI) model using transient finite element analysis (FEA) coupled to a computational fluid dynamics (CFD) model. The FSI analysis performed between 20 Hz and 80 Hz was used to predict the stiffness and damping of the HSFD using a quarter-section model of the damper. The FSI analysis was able to support test results by showing only a 6–7.4% change in the magnitude of force coefficients. Stiffness predictions agree reasonably well with experiments whereas damping is underpredicted.

Engineering↗
DOE OSTI2025

Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dynamic response of a freely rotating butterfly valve in the advanced test reactor − dynamic coefficients modeling

Here, in evaluating the water hammer issue pertaining to the primary-coolant-regulating butterfly valve in the Advanced Test Reactor, the dynamic fluid body interaction (DFBI) approach was implemented in the analysis covered in Part I. Although DFBI modeling accurately and simultaneously solved the dynamic motion of the valve’s disk along with the flow field of the surrounding fluid, it shed little light on the reason behind such motion. For Part II, the reacting torque of the fluid on the disk was decomposed into representations of the dynamic coefficients in terms of stiffness, damping, and added mass. These were evaluated via simulations with steady-state static (stiffness), constant angular speed (damping), and variable angular speed (added mass) disks. Substituting the dynamic coefficients into Newton’s second law enabled the response trajectories to be obtained. Stable (by average) and unstable equilibrium positions and thrust tendencies of the valve were determined based on the stiffness coefficient (or static torque), the response amplitude was dampened or enlarged by the damping coefficient (minorly affected by added mass), and the response frequency was altered by the damping and added mass coefficients. Although the dynamic coefficient approach renders slightly different trajectories, due to the averaging effect of the torque in comparison to the DFBI method, the overall trend of the response aligns with the DFBI simulation, thus confirming the conclusion in Part I that a fix to the current butterfly valve is necessary.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Influence of Rigidity–Hydration Coupling on Size-Dependent Diffusion in Hydrated Polymer Membranes

Selective ion transport in polymer membranes depends critically on how penetrant motion couples to polymer dynamics and hydration. Yet, the mechanistic interplay between polymer rigidity, water content, and penetrant size remains poorly understood, especially in the regime where the penetrant diameter, polymer Kuhn length, and correlation length are comparable. Here, we employ coarse-grained molecular dynamics simulations to systematically investigate penetrant diffusion in hydrated polymer networks across a broad range of water volume fractions, chain rigidities, and penetrant sizes. The results reveal a transition from a decoupled regime, where small penetrants diffuse nearly independently of polymer relaxation, to a coupled regime in which large penetrants require cooperative polymer motion for transport. Increasing polymer rigidity amplifies the sensitivity of diffusivity to hydration, particularly at low water content, leading to pronounced deviations from Stokes−Einstein scaling. Comparison with scaling theories and free-volume models shows that classical nanoparticle-based frameworks fail to capture this intermediate regime. To address this gap, we extend the Yasuda model to incorporate polymer rigidity through a single parameter that quantifies the dynamic contribution of chain stiffness to free-volume fluctuations. The resulting model collapses diffusivity data across all sizes, water contents, and rigidities, providing a unified description of penetrant transport in hydrated polymer matrices. Furthermore, these findings establish polymer rigidity as a key, tunable determinant of diffusion and offer a framework for interpreting size-dependent transport in ion-selective membranes.

diffusion↗
DOE OSTI2021

Intramolecular structure and dynamics in computationally designed peptide-based polymers displaying tunable chain stiffness

Here, polymers assembled using computationally designed coiled coil bundlemers display tunable stiffness via control of interbundlemer covalent connectivity as confirmed using small-angle neutron scattering. Neutron spin echo spectroscopy reveals that rigid rod polymers show a decay rate Γ~Q 2 (Q is the scattering vector) expected of straight cylinders. Semirigid polymers assembled using bundlemers linked via 4-armed organic linker show flexible segmental dynamics at mid-Q and Γ~Q 2 behavior at high Q. The results give insight into linker flexibility-dependent interbundlemer dynamics in the hybrid polymers.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Implementation and Verification of Cable Bending Stiffness in MoorDyn: Preprint

Cable bending stiffness capabilities have been added to MoorDyn to enable modeling of dynamic power cables. The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. MoorDyn is a lumped-mass mooring dynamics model that is used for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim). Its existing line elasticity formulation considers axial stiffness only. To properly capture the dynamics of power cables, a cable bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent line elements. The resulting bending moment is realized by applying forces on adjacent nodes, leaving the underlying lumped-mass formulation unchanged. The bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗
DOE OSTI2021

Implementation and Verification of Cable Bending Stiffness in MoorDyn

The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. Bending stiffness capabilities have recently been added to the lumped-mass mooring dynamics model MoorDyn to enable simulation of dynamic power cables. MoorDyn is a common modeling choice for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim) but the model’s previous line elasticity formulation only considered axial stiffness. To properly capture the dynamics of power cables, a bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent elements. The resulting bending moment is realized by applying forces on adjacent nodes, enabling cable modeling while leaving the underlying lumped-mass formulation unchanged. In this paper, the new bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with the commercial simulator OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗
DOE OSTI2024

Integration and validation of some modules for modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures

Three modules are integrated into the built-in OpenFOAM rhoCentralFoam solver towards accurate and efficient modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures within the OpenFOAM 10.0 framework. The first module is the mixture-averaged diffusion model. The second module is the built-in OpenFOAM Lagrangian solver coupled with optimised droplet drag coefficient and convective heat transfer coefficient sub-models. The last module is a sparse stiff chemistry solver based on dynamic adaptive hybrid integration (AHI-S). The optimised droplet sub-models are first verified in correct implementation for subsequent simulations in this work. Further, they show good accuracy against experimental and analytical data in the modelling of ammonia droplet acceleration and cooling in the flowing and/or low-temperature air. The accuracy and efficiency gains related to the mixture-averaged diffusion model and the AHI-S chemistry solver are examined by simulating 1-D detonation propagation in ammonia droplet-free/laden ammoniaoxygen mixtures. Numerical results of detonation propagation speed, gaseous temperature, density, and species distributions around the induction zone show good agreement with experimental data and analytical solutions. Compared to the built-in OpenFOAM diffusion model, the mixture-averaged diffusion model provides different numerical predictions of pulsating instabilities in detonation propagation. It shows better accuracy in depicting the detonation structure within the droplet-free section attributed to improved multi-component diffusion modelling. Compared to the built-in OpenFOAM solver EulerImplicit (backward Euler), the AHI-S chemistry solver reduces the computational cost by around 50%. It achieves satisfactory accuracy in calculating detonation propagation speed within the droplet-free section with the optimal efficiency when the safety factor, β, equals 0.5.

42 ENGINEERING↗
DOE OSTI2024

Tailored ultrasound propagation in microscale metamaterials via inertia design

The quasi-static properties of micro-architected (meta)materials have been extensively studied over the past decade, but their dynamic responses, especially in acoustic metamaterials with engineered wave propagation behavior, represent a new frontier. However, challenges in miniaturizing and characterizing acoustic metamaterials in high-frequency (megahertz) regimes have hindered progress toward experimentally implementing ultrasonic-wave control. Here, we present an inertia design framework based on positioning microspheres to tune responses of 3D microscale metamaterials. We demonstrate tunable quasi-static stiffness by up to 75% and dynamic longitudinal-wave velocities by up to 25% while maintaining identical material density. Using noncontact laser-based dynamic experiments of tunable elastodynamic properties and numerical demonstrations of spatio-temporal ultrasound wave propagation, we explore the tunable static and elastodynamic property relation. This design framework expands the quasi-static and dynamic metamaterial property space through simple geometric changes, enabling facile design and fabrication of metamaterials for applications in medical ultrasound and analog computing.

42 ENGINEERING↗
DOE OSTI2022

Hydrogen-Bonding Bottlebrush Networks: Self-Healing Materials from Super-Soft to Stiff

The impact of polymer architecture on network dynamics and self-healing is presented using bottlebrushes containing side chains that are end-functionalized with 2-ureido-4[1H]-pyrimidinone (UPy). The synthesis of these materials is straightforward through a three-step process: (1) synthesizing rubbery poly(4-methylcaprolactone) macromonomers (p4MCL–OH) with a norbornene-based initiator, (2) functionalizing the terminal hydroxyl group with UPy–isocyanate (p4MCL–UPy), and (3) statistically copolymerizing p4MCL–OH and p4MCL–UPy via ring-opening metathesis polymerization (ROMP) to form hydrogen-bonding bottlebrushes having a fraction (p) of side chains functionalized with UPy. Attaching UPy to the free end of bottlebrush side chains dilutes the impact of friction from complementary UPy interactions on segmental dynamics, leading to a much weaker dependence of the glass-transition temperature (T g ) on p than observed in linear analogues, while the activation energy to dissociate UPy–UPy bonds (41–47 kJ/mol) remains mostly unchanged. Longer side chains result in a competition between reducing T g and inducing entanglements that influence hydrogen-bonded network dynamics. Increasing the backbone length extends the sticky Rouse region without affecting the network modulus (G x ) or UPy–UPy dissociation time (τ s ). Gx scales linearly with p and ranges from 27 kPa to 1.6 MPa, while τs remains nearly constant in contrast to linear telechelic ionomers, implying a similar self-healability across bottlebrush networks containing different amounts of UPy. Furthermore, these stretchable networks with p ≤ 0.25 undergo self-healing upon repeated rupture and melt pressing at ≤100 °C while retaining similar tensile properties. In summary, decorating bottlebrush polymers with hydrogen bonds creates opportunities to independently manipulate associative network dynamics and mechanical moduli.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Slow dynamics in a single bead with mechanical conditioning and transient heating

The contact stiffness of an aluminum bead confined between two slabs diminishes upon mechanical conditioning, and then recovers like log(t) after the conditioning ceases. Here that structure is evaluated for its response to transient heating and cooling, with and without accompanying conditioning vibrations. It is found that, under heating or cooling alone, stiffness changes are mostly consistent with temperature dependent material moduli; there is little or no slow dynamics. Hybrid tests in which vibration conditioning is followed by heating or cooling lead to recoveries that begin like log(t) and then become more complex. On subtracting the known response to heating or cooling alone we discern the influence of higher or lower temperatures on slow dynamic recovery from vibrations. It is found that heating accelerates the initial log(t) recovery, but by an amount more than predicted by an Arrhenius model of thermally activated barrier penetrations. Furthermore, transient cooling has no discernable effect, in contrast to the Arrhenius prediction that it slows recovery.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Amplifying Nanoparticle Reinforcement through Low Volume Topologically Controlled Chemical Coupling

Here, we present a streamlined method to covalently bond hydroxylated carbon nanotubes (CNOH) within a polyphenol matrix, all achieved through a direct, solvent-free process. Employing an extremely small concentration of CNOH (0.01% w/w) along with topologically contrasting linkers led to a maximum of 5-fold increase in modulus and a 25% enhancement in tensile strength compared to the unaltered matrix, an order of magnitude greater reinforcement (w/w) compared to state-of-the-art melt-processed nanocomposites. Through dynamic mechanical analysis, low field solid-state nuclear magnetic resonance spectroscopy, and molecular dynamics simulations, we uncovered the profound influence of linker’s conformational degrees of freedom on the segmental dynamics and therefore the material’s properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Simulations of Glass Transition and Mechanical Behavior of Off-Stoichiometric Crosslinked Polymers

Here, this work explores the influence of blend composition, network architecture, and hydrogen bonding on the material properties of crosslinked epoxy networks, focusing on the glass transition temperature (T g ) and Young’s modulus (Y). We used coarse-grained molecular dynamics simulations to simulate varying compositions of stiff and flexible components in epoxy monomer blends with varying excess of curative. We find that, without hydrogen bonding, networks of any composition show a monotonically increasing T g with decreasing excess curative, consistent with theory. In contrast, we find that when hydrogen bonding is introduced, the binary blend networks show significant enhancement in T g for lightly crosslinked systems. This result contributes to an explanation of the anomalous T g behavior observed experimentally in these systems. We further find that Y is generally enhanced by hydrogen bonds, especially below T g , demonstrating that hydrogen bonding has a significant influence on mechanical properties and can allow access to other desirable dynamic behavior, especially self-healing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Stiff neural ordinary differential equations

Neural Ordinary Differential Equations (ODEs) are a promising approach to learn dynamical models from time-series data in science and engineering applications. This work aims at learning neural ODEs for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODEs in the classical stiff ODE systems of Robertson’s problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson’s problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODEs. The success of learning stiff neural ODEs opens up possibilities of using neural ODEs in applications with widely varying time-scales, such as chemical dynamics in energy conversion, environmental engineering, and life sciences.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stiffness anisotropy coordinates supracellular contractility driving long-range myotube-ECM alignment

The ability of cells to organize into tissues with proper structure and function requires the effective coordination of proliferation, migration, polarization, and differentiation across length scales. Skeletal muscle is innately anisotropic; however, few biomaterials can emulate mechanical anisotropy to determine its influence on tissue patterning without introducing confounding topography. Here, we demonstrate that substrate stiffness anisotropy coordinates contractility-driven collective cellular dynamics resulting in C2C12 myotube alignment over millimeter-scale distances. When cultured on mechanically anisotropic liquid crystalline polymer networks (LCNs) lacking topography, C2C12 myoblasts collectively polarize in the stiffest direction. Cellular coordination is amplified through reciprocal cell-ECM dynamics that emerge during fusion, driving global myotube-ECM ordering. Conversely, myotube alignment was restricted to small local domains with no directional preference on mechanically isotropic LCNs of the same chemical formulation. These findings provide valuable insights for designing biomaterials that mimic anisotropic microenvironments and underscore the importance of stiffness anisotropy in orchestrating tissue morphogenesis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Dynamic inflow and unsteady aerodynamics models for modal and stability analyses in OpenFAST

This work presents two aerodynamic models that are used to perform modal and stability analyses of wind turbines. Including aerodynamic effects in stability analyses is important to capture aerodynamic inertia, stiffness, and damping. The two models consist of a dynamic inflow model based on Øye’s model and an unsteady aerodynamics model based on a simplified Beddoes-Leishman dynamic stall model. Both models are written in a continuous-time state-space form, which is the form needed to perform linearizations within OpenFAST. In this article, we present the new models, perform some simple verifications against HAWC2 results, and then perform stability analyses. We investigate the contribution of the aerodynamic effects on the turbine modes, particularly the flapwise modes, which are the most affected. Because of the development presented in this work, Campbell diagrams accounting for dynamic stall and dynamic wake effects were generated for the first time using OpenFAST.

17 WIND ENERGY↗
DOE OSTI2021

Electromagnetic Transient (EMT) Simulation Algorithm for Evaluation of Photovoltaic (PV) Generation Systems

Use of inverter-based resources facilitating renewable energy resources such as photovoltaic (PV) generation is increasing rapidly with decreasing costs and reduced emissions associated. To accommodate such rapid growth of inverter-based resources like PV systems, electromagnetic transient (EMT) simulation models of both PV systems and grids are required to analyze the interaction of PVs in the grid (like the post-event analysis). In addition, the EMT simulation would help with the planning of future power grid with a large number of PVs as well as other inverter-based distributed generation systems. In this paper, the EMT simulation models of PV systems and grids are developed based on the differential algebraic equations (DAEs) representing their EMT dynamics. Furthermore, advanced simulation algorithms including numerical stiffness-based hybrid discretization, DAE clustering and aggregation, multi-order integration, and matrix splitting approaches are applied to accelerate the EMT simulation. The proposed algorithm was applied to 125 PV inverters within 52-bus medium-voltage (MV) distribution grid.

Choi, Jongchan↗
DOE OSTI2021

Relationship between the contact force strength and numerical inaccuracies in piecewise-smooth systems

This work studies the different types of behavior and inaccuracies that can occur when contact is not adequately accounted for in a dynamical system with freeplay, as the strength of the contact stiffness increases. The MATLAB® ode45 time integration solver, with the built-in Event Location capability, is first validated using past experimental data from a forced Duffing oscillator with freeplay. Next, numerical results utilizing event location are compared to results neglecting event location in order to highlight possible numerical errors and effects on multistable dynamical responses. Inaccuracies tend to occur in two different ways. First, neglecting event location can affect the boundaries between basins of attraction. Second, neglecting event location has little effect on the behaviors of the attractor solutions themselves besides merely resembling poorly converged solutions. Errors are less pronounced at the limits of soft or hard contact stiffness. Finally, this study shows the importance of accurately solving piecewise-smooth systems and the existing correlation between the strength of the contact force and possible numerical inaccuracies.

42 ENGINEERING↗