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DOE OSTI2025

Effect of artificial viscosity on shocked particle-laden flows for staggered grid Lagrangian methods

Abstract Shocked particle-laden flows are important to many natural and industrial processes. When simulating these systems, artificial viscosity is often required to prevent numerical artifacts, such as ringing, from arising in the pressure and density fields. The linear and quadratic coefficients of the artificial viscosity determine the amount of smoothing that occurs in these fields. For particle-laden flows, however, many of the fluid–particle interaction forces, for example, the pressure gradient force and unsteady forces, depend on gradients in the fluid fields. Furthermore, while the shock passes over a particle, these forces can be more dominant than drag. This means that the artificial viscosity coefficients affect how a particle and fluid interact when simulating shocked particle systems. Here this effect is investigated for isolated particles and for a particle curtain using a staggered grid Lagrangian approach. The artificial viscosity coefficients have a significant impact on the maximum force that a fluid imparts to a particle, which is important for determining whether a particle will break up in response to the shock. Furthermore, it is found that the density ratio between the particle and the fluid is important in determining whether the artificial viscosity coefficients have a significant impact on the particle’s motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Shock-driven dispersal of a corrugated finite-thickness particle layer

A research area emerging in the multiphase flow community is the study of shock-driven multiphase instability (SDMI), a gas–particle analog of the traditional fluid-fluid Richtmyer–Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian–Lagrangian approach. One objective of this study is to compare the simulated particle curtains to a comparable set of shock tube experiments performed to analyze traditional RMI of a gas curtain. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while also matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. Varying particle diameters are tested in the simulations to explore the impact of particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of the multiphase Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that the comparison depends on the diameter of the particles (thus, dependent on the Stokes number of the flow). A second objective of this study is to analyze the effect of the initial particle volume fraction on the evolution of the curtain and the behavior of the instability. This is done through analyzing the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.

42 ENGINEERING↗

DOE OSTI2025

Spatially resolved measurements of plasma ion velocity distributions in a dipole magnetic field

The equilibrium flows of a plasma discharge in a dipole magnetic field are a topic of interest in low temperature plasma physics. Experimentalists typically rely on probe-based and line-integrated diagnostic techniques in these environments to describe plasma behavior. Presented here are measurements of argon ion dynamics with laser induced fluorescence techniques to provide insight into plasma dynamics in dipole magnetic fields with nonperturbative, spatially localized measurements. Simulation results from a Lagrangian approach to track particle orbits are compared to measured density profiles and provide evidence to support the mechanism distinguishing experimental configurations is the initial approach of particles. Applying a negative DC bias to the magnet induces strong E×B flows around the magnet, even exceeding the ion acoustic speed as measured far from the magnet. A strong enough bias also produces two distinct ion populations and provides a method for controlling the density gradient on the equator.

McLaughlin, Jacob W. (ORCID:0000000152661888)↗

DOE OSTI2022

Gravitational wave modes in matter

Here, a general linear gauge-invariant equation for dispersive gravitational waves (GWs) propagating in matter is derived. This equation describes, on the same footing, both the usual tensor modes and the gravitational modes strongly coupled with matter. It is shown that the effect of matter on the former is comparable to diffraction and therefore negligible within the geometrical-optics approximation. However, this approximation is applicable to modes strongly coupled with matter due to their large refractive index. GWs in ideal gas are studied using the kinetic average-Lagrangian approach and the gravitational polarizability of matter that we have introduced earlier. In particular, we show that this formulation subsumes the kinetic Jeans instability as a collective GW mode with a peculiar polarization, which is derived from the dispersion matrix rather than assumed a priori. This forms a foundation for systematically extending GW theory to GW interactions with plasmas, where symmetry considerations alone are insufficient to predict the wave polarization.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Galaxy bias in the era of LSST: perturbative bias expansions

Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the Rubin Observatory Legacy Survey of Space and Time (LSST) bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Year 10 (Y10) data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian perturbation theory (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. Here, we consider a variety of different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of k max = 0.4 Mpc -1 for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Analysis of Σ* via isospin selective reaction 𝐾 𝐿 ⁢𝑝 →𝜋 + ⁢Σ 0

The isospin-selective reaction 𝐾 𝐿 ⁢𝑝 →𝜋 + ⁢Σ 0 provides a clean probe for investigating 𝐼 =1 Σ* resonances. In this work, we perform an analysis of this reaction using an effective Lagrangian approach for the first time, incorporating the well-established Σ⁡(1189)⁢1/2 + , Σ⁡(1385)⁢3/2 + , Σ⁡(1670)⁢3/2 − , and Σ⁡(1775)⁢5/2 − states, while also exploring contributions from other unestablished states. By fitting the available differential cross-section and recoil polarization data, adhering to partial-wave phase conventions same as the Particle Data Group, we find that besides the established resonances, contributions from Σ⁡(1660)⁢1/2 + , Σ⁡(1580)⁢3/2 − , and a Σ*⁢(1/2 − ) improve the description. Notably, a Σ*⁢(1/2 − ) resonance with mass around 1.54 GeV, consistent with Σ⁡(1620)⁢1/2 − , is found to be essential for describing the data in this channel, a stronger indication than found in previous analyses focusing on 𝜋⁢Λ final states. While providing complementary support for Σ⁡(1660)⁢1/2 + and Σ⁡(1580)⁢3/2 − , our results highlight the importance of the Σ⁡(1620)⁢1/2 − region in 𝐾 𝐿 ⁢𝑝 →𝜋 + ⁢Σ 0 . Future high-precision measurements are needed to solidify these findings and further constrain the Σ* spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Propagator Zeros and Lattice Chiral Gauge Theories

Symmetric mass generation (SMG) has been advocated as a mechanism to render mirror fermions massive without symmetry breaking, ultimately aiming for the construction of lattice chiral gauge theories. It has been argued that in an SMG phase, the poles in the mirror fermion propagators are replaced by zeros. Using an effective Lagrangian approach, we investigate the role of propagator zeros when the gauge field is turned on, finding that they act as coupled ghost states. In four dimensions, a propagator zero makes an opposite-sign contribution to the one-loop beta function as compared to a normal fermion. In two dimensional Abelian theories, a propagator zero makes a negative contribution to the photon mass squared. In addition, propagator zeros generate the same anomaly as propagator poles. Thus, gauge invariance will always be maintained in an SMG phase, in fact, even if the target chiral gauge theory is anomalous, but unitarity of the gauge theory is lost. Published by the American Physical Society 2024

Physics↗

DOE OSTI2022

Parallel-in-Time Integration for Nonlinear Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to diffusion-dominated PDEs, with some recent success in scalar linear hyperbolic PDEs. Given the ubiquity of numerical simulations of hyperbolic PDEs throughout the sciences, in particular, nonlinear hyperbolic systems, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems beyond simple scalar and linear cases, which is the main topic of this subcontract. The main focus of the work was to further develop and perfect coarse-grid operators for the Multigrid Reduction-inTime (MGRIT) method applied to hyperbolic PDEs that were recently proposed in PhD thesis, based on a modified semi-Lagrangian approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Dataset for "Bioaerosols are the dominant source of warm-temperature immersion-mode INPs and drive uncertainties in INP predictability

Ice nucleating particles (INPs) are a rare subset of atmospheric aerosol that can initiate primary ice formation and thus trigger cloud glaciation. The re is a significant gap between our ability to measure INPs and to predict their concentrations and variability in large-scale weather and climate models. Accurate simulation of I NPs requires simulation of their major particle sources, as well as representative parameterizations of IN efficiency. Thus, there is a need for measurements of INP concentrations , delineated by particle type, to validate and improve model prediction of INP concentrations. Here we present a novel method for speciating INP concentrations into the relative c ontributions from dust, sea spray aerosol (SSA), and bioaerosol using single particle measurements. In a field campaign at Bodega Bay (coastal California), we find that bioaerosol s were the primary source of INPs between -12 and -20 ?C, while dust was a relatively minor source and SSA did not contribute significantly. We show that recent INP parameterizati ons for dust and SSA accurately predict ambient INP concentrations for these particle types. Finally, we use the speciated INP concentrations to evaluate the simulation of INPs at Bodega Bay, using a Lagrangian approach to connect the locally-observed aerosol with regionally-widespread emissions parameterizations. We find that we can skillfully simulate du st and SSA INPs, but not bioaerosol INPs. This points to a need for additional research to identify the major factors controlling the emissions and INP efficiency of bioaerosol IN Ps in order to develop improved parameterizations and enable their improved representation in models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1973

Effect of steady state coning angle and damping on whirl flutter stability

The main object of this investigation is to find the effect of the steady state coning angle and the damping at the flapping hinge of the blades on the whirl flutter stability boundary and thus to determine the role they can play in narrowing down the gap between theory and experiment. The governing equations of motion, with these two parameters included are derived by the classical Lagrangian approach using quasi-steady blade element theory for aerodynamic forces. A linearized analysis of these equations is applied to two of the wind tunnel models of the previous investigations. The results indicate that these parameters have a marked effect on stability boundary and they may even change the mode of flutter from backward whirl to forward whirl.

Kaza, K. R. V.↗

NASA NTRS1977

A special purpose symbolic manipulation program for the derivation of the equations of motion for large flexible structures

This paper outlines a computer program especially tailored to the task of deriving explicit equations of motion for structures with point-connected substructures. The special purpose program is written in FORTRAN and is designed for performing the specific algebraic operations encountered in the derivation of explicit equations of motion. The derivation is by the Lagrangian approach. Using an orderly kinematical procedure and a discretization and/or truncation scheme, it is possible to write the kinetic and potential energy of each substructure in a compact vector-matrix form. Then, if each element of the matrices and vectors encountered in the kinetic and potential energy is a known algebraic expression, the computer program performs the necessary operations to evaluate the kinetic and potential energy of the system explicitly. Lagrange's equations for small motions about equilibrium can be deduced directly from the explicit form of the system kinetic and potential energy.

Hale, A. L.↗

NASA NTRS1978

Derivation of the equations of motion for complex structures by symbolic manipulation

Hale, A. L.↗

NASA NTRS1979

Analysis of solar radiation pressure induced coupled librations of a gravity stabilized axisymmetric satellite

This paper presents an analysis of solar radiation pressure induced coupled librations of gravity stabilized cylindrical spacecraft with a special reference to geostationary communication satellites. The Lagrangian approach is used to obtain the corresponding equations of motion. The solar induced torques are assumed to be free of librational angles and are represented by their Fourier expansion. The response and periodic solutions are obtained through linear and nonlinear analyses, using the method of harmonic balance in the latter case. The stability conditions are obtained using Routh-Hurwitz criteria. To establish the ranges of validity the analytic response is compared with the numerical solution. Finally, values of the system parameters are suggested to make the satellite behave as desired. Among these is a possible approach to subdue the solar induced roll resonance. It is felt that the approximate analysis presented here should significantly reduce the computational efforts involved in the design and stability analysis of the systems.

Shrivastava, S. K.↗

NASA NTRS1980

On maneuvering large flexible spacecraft using an annular momentum control device

A scheme for the control and maneuvering of a large flexible spacecraft by means of two flexible AMCD's using noncontacting magnetic suspension is presented. The system consists of a flexible vehicle, two flexible rings and a magnetic suspension and driving assembly. The necessary skewing of the rings for maneuvering of the vehicle is accomplished by moving the pairs of magnets along tracks distributed around the circumference of the vehicle. The equations of motion for each subsystem are derived by the Lagrangian approach. Attitude motions are described in terms of quasi-coordinates. For small vehicle angular rates and rings attitude motions, an ordering scheme can be used to separate the equations of motion according to the magnitude of the terms. The ordered equations of motion lead to a linear time-variant optimal control problem for the maneuvering of the spacecraft.

Oz, H.↗

NASA NTRS1982

Natural frequency of rotating beams using non-rotating modes

A Lagrangian approach is formulated for predicting the rotating natural frequencies of a beam from the nonrotating modes and frequencies. Using the first two nonrotating mode shapes in one case and the first four such modes in the other case the frequencies of the rotating modes are calculated for a short tapered beam and a typical helicopter blade, respectively. In each case the beam is represented by lumped parameters. The number of mass points representing the beam and the accuracy of the calculated slopes of the nonrotating mode shapes at those points are both shown to affect the accuracy of the resulting frequencies, but the number of stations is shown to be more important.

Loewy, R. G.↗

NASA NTRS1983

Structural optimization - Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1983

Blade loss transient dynamics analysis with flexible bladed disk

The transient dynamic response of a flexible bladed disk on a flexible rotor in a two rotor system is formulated by modal synthesis and a Lagrangian approach. Only the nonequilibrated one diameter flexible mode is considered for the flexible bladed disk, while the two flexible rotors are represented by their normal modes. The flexible bladed disk motion is modeled as a combination of two one diameter standing waves, and is coupled inertially and gyroscopically to the flexible rotors. Application to a two rotor model shows that a flexible bladed disk on one rotor can be driven into resonance by an unbalance in the other rotor, and at a frequency equal to the difference in the rotor speeds.

Gallardo, V. C.↗

NASA NTRS1984

Structural optimization: Challenges and opportunities

Sobieszczanski-Sobieski, J.↗