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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

MHD aspects of magnetotail dynamics

The equations of ideal MHD represent the conservation of mass, momentum, and energy; thus, MHD must, in some broad sense, provide a correct description of large-scale structure of the earth's magnetosphere. However, steady-state, ideal MHD (the simplest description) allows only a static interaction between the solar wind and the magnetosphere. Hence an MHD theory of magnetospheric dynamics must involve unsteady flow turbulence, such as might be generated by Kelvin-Helmholtz turbulence at the magnetopause, and dissipative transport, such as reconnection, which violates ideal MHD. This brief review summarizes recent theoretical efforts to explore and extend the early MHD magnetospheric models of Axford and Petschek. Analytic calculations show that steady convection in the magnetotail is nearly impossible. Global magnetospheric simulations exhibit substorm reconnection phenomena for southward IMF and predict a novel convection pattern for northward IMF. Reconnection simulations show plasmoid formation and field-aligned current flows in the tail. The Kelvin-Helmholtz instability can provide a strong anomalous viscosity which can drive the viscous convection system.

Coroniti, F. V.↗
NASA NTRS2005

Modeling of Turbulence Effects on Liquid Jet Atomization and Breakup

Recent experimental investigations and physical modeling studies have indicated that turbulence behaviors within a liquid jet have considerable effects on the atomization process. This study aims to model the turbulence effect in the atomization process of a cylindrical liquid jet. Two widely used models, the Kelvin-Helmholtz (KH) instability of Reitz (blob model) and the Taylor-Analogy-Breakup (TAB) secondary droplet breakup by O Rourke et al, are further extended to include turbulence effects. In the primary breakup model, the level of the turbulence effect on the liquid breakup depends on the characteristic scales and the initial flow conditions. For the secondary breakup, an additional turbulence force acted on parent drops is modeled and integrated into the TAB governing equation. The drop size formed from this breakup regime is estimated based on the energy balance before and after the breakup occurrence. This paper describes theoretical development of the current models, called "T-blob" and "T-TAB", for primary and secondary breakup respectivety. Several assessment studies are also presented in this paper.

Trinh, Huu P.↗
NASA NTRS2007

GRMHD/RMHD Simulations and Stability of Magnetized Spine-Sheath Relativistic Jets

A new general relativistic magnetohydrodynamics (GRMHD ) code "RAISHIN" used to simulate jet generation by rotating and non-rotating black holes with a geometrically thin Keplarian accretion disk finds that the jet develops a spine-sheath structure in the rotating black hole case. Spine-sheath structure and strong magnetic fields significantly modify the Kelvin-Helmholtz (KH) velocity shear driven instability. The RAISHIN code has been used in its relativistic magnetohydrodynamic (RMHD) configuration to study the effects of strong magnetic fields and weakly relativistic sheath motion, cl2, on the KH instability associated with a relativistic, Y = 2.5, jet spine-sheath interaction. In the simulations sound speeds up to ? c/3 and Alfven wave speeds up to ? 0.56 c are considered. Numerical simulation results are compared to theoretical predictions from a new normal mode analysis of the RMHD equations. Increased stability of a weakly magnetized system resulting from c/2 sheath speeds and stabilization of a strongly magnetized system resulting from d 2 sheath speeds is found.

Hardee, Philip↗
DOE OSTI2024

The inviscid incompressible limit of Kelvin–Helmholtz instability for plasmas

The Kelvin–Helmholtz Instability (KHI) is an interface instability that develops between two fluids or plasmas flowing with a common shear layer. KHI occurs in astrophysical jets, solar atmosphere, solar flows, cometary tails, planetary magnetospheres. Two applications of interest, encompassing both space and fusion applications, drive this study: KHI formation at the outer flanks of the Earth’s magnetosphere and KHI growth from non-uniform laser heating in magnetized direct-drive implosion experiments. Here, we study 2D KHI with or without a magnetic field parallel to the flow. We use both the GAMERA code, which solves the compressible Euler equations, and the STRATOSPEC code, which solves the Navier-Stokes equations under the Boussinesq approximation, coupled with the magnetic field dynamics. GAMERA is a global three-dimensional MHD code with high-order reconstruction in arbitrary nonorthogonal curvilinear coordinates, which is developed for a large range of astrophysical applications. STRATOSPEC is a three-dimensional pseudo-spectral code with an accuracy of infinite order (no numerical diffusion). Magnetized KHI is a canonical case for benchmarking hydrocode simulations with extended MHD options. An objective is to assess whether or not, and under which conditions, the incompressibility hypothesis allows to describe a dynamic compressible system. For comparing both codes, we reach the inviscid incompressible regime, by decreasing the Mach number in GAMERA, and viscosity and diffusion in STRATOSPEC. Here, we specifically investigate both single-mode and multi-mode initial perturbations, either with or without magnetic field parallel to the flow. The method relies on comparisons of the density fields, 1D profiles of physical quantities averaged along the flow direction, and scale-by-scale spectral densities. We also address the triggering, formation and damping of filamentary structures under varying Mach number or Atwood number, with or without a parallel magnetic field. Comparisons show very satisfactory results between the two codes. The vortices dynamics is well reproduced, along with the breaking or damping of small-scale structures. We end with the extraction of growth rates of magnetized KHI from the compressible regime to the incompressible limit in the linear regime assessing the effects of compressibility under increasing magnetic field. The observed differences between the two codes are explained either from diffusion or non-Boussinesq effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗
NASA NTRS1972

Generation and development of a viscous vortex ring.

The vorticity transport and definition of vorticity equations are derived for an axisymmetric incompressible viscous vortex ring. The coupled system is solved numerically by the Peaceman-Rachford method and the method of successive over-relaxation. Instantaneous streaklines, velocity vector fields, vorticity contours, and streamline patterns offer a detailed picture of vortex ring generation. Results compare well with experimental observations of the behavior of viscous vortex rings. The radius, trajectory, and velocity of the ring are calculated and employed to predict the propagation velocity of the vortex ring using the vortex models of Helmholtz and Hill.

Whitehead, K. D.↗
DOE OSTI2025

A Polar Scaling Technique for the Regularization of Strongly Singular and Strongly Near-Singular Helmholtz Surface Integrals Evaluated Over 2-D Domains

The numerical integration of expressions containing strong singularities or strong near-singularities has long been a challenging problem in the electromagnetics community. Much attention has been paid to this problem, as strong $1/R^{{2}}$ singularities routinely appear when implementing electromagnetic simulation techniques like the method of moments (MoM). To date, several techniques, from singularity extraction to singularity cancellation (SC), have been employed to deal with problems that require the evaluation of 2-D strongly singular integrals. However, no single technique has been proposed that can deal with both strong singularities and strong near-singularities in a fully numerical manner for arbitrary 2-D domains. Moreover, it has been claimed that the Helmholtz-type strongly singular integral found in the MoM is convergent in a principal value sense, but this convergence value has yet to be proven mathematically. In this work, we will conduct the convergence proof and introduce a “polar scaling” change of variables method that may be used to evaluate Helmholtz integrals with both strong and weak singularities/near-singularities. The technique is fully numerical and can in principle be applied to any planar or curved polygon and any nonsingular basis function. We will also provide numerical results showing useful convergence behavior for integrals involving both exact and near-singularities.

47 OTHER INSTRUMENTATION↗
NASA NTRS1984

A Lagrangian method for a two layer shallow water model

One of the biggest drawbacks of Eulerian methods is the presence of the nonlinear convective terms which leads to inaccurate representations of advection and fronts. An alternative and conceptually simpler approach is the Lagrangian approach in which the fluid particles themselves are tracked and equations are derived based on local spatial interaction. In this formulation the nonlinear convective terms do not appear. The main drawback with the Lagrangian formulation, however, is that the local spatial interactions are time dependent. That is, at each time level, one must know the current neighbors of a given particle to accurately compute the forces acting on the particle. The Voroni Mesh which is continuously deforming and always linking nearest neighbors is needed. The effectiveness of a simple Lagrangian method for simulating the onset of a Kelvin-Helmholtz instability in a 2 layer fluid is demonstrated.

Augenbaum, J. M.↗
DOE OSTI2022

Fully Distributed Multi-Material Magnetic Sensing Structures for Multiparameter DAS Applications

This dissertation demonstrates the first of its kind distributed magnetic field sensor based on a fiber optic distributed acoustic sensing (DAS) scheme. Ferromagnetic nickel and Metglas® were dispersed internally within a fiber optic preform and then drawn on an in-house fiber optic draw tower to lengths in the kilometers. Due to the close proximity of the ferromagnetic metals and fiber optic core, the magnetostrictive strain response of the ferromagnetic materials when exposed to a magnetic field would perturbate within the fiber cladding and transfer that strain, internally, to the fiber optic core. Strain resulting from the magnetostrictive effect allows the DAS based sensor to accurately translate strain into readable magnetic field data. Due to the high sensitivity seen in this sensor design, multiparameter sources, acoustic and magnetic fields, were tested and validated and a three dimensional magnetic-field vector sensor was proposed. Numerical analysis of the novel sensor design was first implemented using COMSOL Multiphysics, where inputs such as magnetostrictive element shape, size, distance, and number were first investigated. Upon optimizing system constraints, the sensor design was further modified such that single mode operation was consistent across multiple fiber draws while retaining high strain transfer from the ferromagnetic elements to the fiber optic core. Ferromagnetic material selection was evaluated as a function of the saturation magnetostriction constants and a total of 4 modules were used to fully characterize the complex physics involved in this sensor design. All fabrication and testing were performed in-house using a full scale 3-story fiber draw tower and custom environmental testing stations to imitate naturally occurring events such as magnetic or acoustic point sources. A unique stacking method was used to embed ferromagnetic nickel and Metglas® into a fiber optic preform which when combined with a custom fiber draw process resulted in consistent multi-material fibers drawn to lengths of 1-km. In-house testing facilities included different types of electromagnetic generators, in addition to a soil test bed, and an outdoor test bed which allowed 100 meters of fiber to be tested simultaneously. All tested sensors demonstrated high strain transfer capabilities on the order of 0.01-10 μϵ depending on the materials used, ferromagnetic rod number, and core to metal spacing. Due to the sensitivity of the system the difference between AC and DC was distinct, and directional magnetostriction was studied. Transverse and longitudinal magnetic wave propagation was controlled through a solenoid and rectangular Helmholtz coil, both built in-house. A three-dimensional magnetic field vector sensor was proposed due to the success of the magnetic field sensor, and a design was proposed and initially tested to validate direction as a function of field strength and distance. To summarize, this dissertation explores the first fully distributed magnetic field sensor using DAS based techniques and one of the first multi-material fiber draw processes which can produce consistent single mode fiber up to 1-km. Due to extensive FEA modeling, multiple iterations of the magnetic sensor were fully characterized and an equation describing the relationship between sensor design and strain transfer has been created and validated experimentally. Multi-parameter tests including acoustic and magnetic fields were implemented and an algorithm was developed to separate the mixed signals. Finally, a test was performed to demonstrate the feasibility of sensing magnetic fields directionally. Cumulative results demonstrate a high-quality sensor alternative to current designs which may surpass other magnetic sensors due to innate multi-parameter capabilities, in addition to the inexpensive production cost and extremely long operating lengths.

02 PETROLEUM↗
DOE OSTI2020

Structure formation in turbulence as an instability of effective quantum plasma

Structure formation in turbulence can be understood as an instability of “plasma” formed by fluctuations serving as effective particles. These “particles” are quantumlike in the sense that their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding “kinetic equation” describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we show how to systematically extend it to more complex systems using compressible Navier–Stokes turbulence as an example. In this case, the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an illustration, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin–Helmholtz-type instability that is a generalization of the known zonostrophic instability. Our calculations are readily extendable to other types of turbulence, for example, magnetohydrodynamic turbulence in plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2004

The Role of Instability Waves in Predicting Jet Noise

There has been an ongoing debate about the role of linear instability waves in the prediction of jet noise. Parallel mean flow models, such as the one proposed by Lilley, usually neglect these waves because they cause the solution to become infinite. The resulting solution is then non-causal and can, therefore, be quite different from the true causal solution for the chaotic flows being considered here. The present paper solves the relevant acoustic equations for a non-parallel mean flow by using a vector Green s function approach and assuming the mean flow to be weakly non-parallel, i.e., assuming the spread rate to be small. It demonstrates that linear instability waves must be accounted for in order to construct a proper causal solution to the jet noise problem. . Recent experimental results (e.g., see Tam, Golebiowski, and Seiner,1996) show that the small angle spectra radiated by supersonic jets are quite different from those radiated at larger angles (say, at 90deg) and even exhibit dissimilar frequency scalings (i.e., they scale with Helmholtz number as opposed to Strouhal number). The present solution is (among other things )able to explain this rather puzzling experimental result.

Goldstein, M. E.↗
DOE OSTI2025

Understanding the Transport Properties of Methane–Hydrogen Mixtures under the Interior Conditions of Ice Giants

Inaccuracy in our knowledge of the transport properties of relevant mixtures under planetary interior conditions is a roadblock in predicting the observable properties of planets in our solar system and beyond. In this work, we investigate methane–hydrogen mixtures using data sets obtained from density functional theory calculations for the electronic structure, combined with molecular dynamics simulations for the ions for a wide range of pressure and temperature. Hydrogen concentration significantly affects the equation of state (EOS) but has little influence on transport properties. We provide an analytical expression to model thermal EOS and transport properties as a function of hydrogen content, with the maximum deviation observed at low P–T conditions. These insights are particularly relevant to improve the planetary models and enhance our ability to predict the properties of “ice” giants and beyond.

Methane↗
NASA NTRS1975

Coupling of Helmholtz resonators to improve acoustic liners for turbofan engines at low frequency

An analytical and test program was conducted to evaluate means for increasing the effectiveness of low frequency sound absorbing liners for aircraft turbine engines. Three schemes for coupling low frequency absorber elements were considered. These schemes were analytically modeled and their impedance was predicted over a frequency range of 50 to 1,000 Hz. An optimum and two off-optimum designs of the most promising, a parallel coupled scheme, were fabricated and tested in a flow duct facility. Impedance measurements were in good agreement with predicted values and validated the procedure used to transform modeled parameters to hardware designs. Measurements of attenuation for panels of coupled resonators were consistent with predictions based on measured impedance. All coupled resonator panels tested showed an increase in peak attenuation of about 50% and an increase in attenuation bandwidth of one one-third octave band over that measured for an uncoupled panel. These attenuation characteristics equate to about 35% greater reduction in source perceived noise level (PNL), relative to the uncoupled panel, or a reduction in treatment length of about 24% for constant PNL reduction. The increased effectiveness of the coupled resonator concept for attenuation of low frequency broad spectrum noise is demonstrated.

Dean, L. W.↗
NASA NTRS1990

Stability of an oscillated fluid with a uniform density gradient

Instabilities in a fluid with a constant density gradient that is subject to arbitrarily oriented oscillatory accelerations are considered. With the Boussinesq approximation and for the case of an unbounded fluid, transformation to Lagrangian coordinates allows the reduction of the problem to an ordinary differential equation for each three-dimensional wavenumber. The problem has three parameters: the nondimensional amplitude R of the base-state oscillation, the nondimensional level of background steady acceleration, which for some cases can be represented in terms of a local (in time) Richardson number Ri, and the Prandtl number Pr. Some general bounds on stability are derived. For Pr = 1 closed-form solutions are found for impulse (delta function) accelerations and a general asymptotic solution is constructed for large R and general imposed accelerations. The asymptotic solution takes advantage of the fact that at large R wave growth is concentrated at 'zero points'. These are times when the effective vertical wavenumber passes through zero. Kelvin-Helmholtz instabilities are found to dominate at low R, while Rayleigh-Taylor instabilities dominate at high R. At high R, the uniform shear of the Kelvin-Helmholtz case tends to distort and weaken instability waves. With unsteady flows, Ri = 1/4 is no longer an instability limit. Significant instabilities have been found for sinusoidal forcing for Ri up to 0.6.

Jacqmin, David↗
DOE OSTI2025

Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

Density Functional Theory↗
NASA NTRS1986

Helmholtz decomposition revisited: Vorticity generation and trailing edge condition. I - Incompressible flows

Using the decomposition for the infinite-space, the issue of the nonuniqueness of the Helmholtz decomposition for the problem of the three-dimensional unsteady incompressible flow around a body is considered. A representation for the velocity that is valid for both the fluid region and the region inside the boundary surface is employed, and the motion of the boundary is described as the limiting case of a sequence of impulsive accelerations. At each instant of velocity discontinuity, vorticity is shown to be generated by the boundary condition on the normal component of the velocity, for both inviscid and viscous flows. In viscous flows, the vorticity is shown to diffuse into the surroundings, and the no-slip conditions are automatically satisfied. A trailing edge condition must be satisfied for the solution to the Euler equations to be the limit of the solution of the Navier-Stokes equations.

Morino, L.↗
DOE OSTI2020

An analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure

The objective of this paper is to develop an analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure. This expression for the temperature is obtained for both constant and variable specific heat models and can be used in common models for the material yield strength that include thermal softening due to increase in temperature. Additionally, the material parameters in the model can easily be calibrated to match known experimental data and the model has been used to determine the value of the shock pressure at the onset of melting during shock loading.

42 ENGINEERING↗
DOE OSTI2023

Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence

To comprehensively understand the saturation of two-dimensional (2D) magnetized Kelvin–Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasi-linear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are an explosive large-scale vortex separation instead of the well-known merger of 2D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length scale. These show the critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses.

Physics↗