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NASA NTRS2008

Nonstandard Analysis and Jump Conditions for Converging Shock Waves

Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.

Baty, Roy S.↗

NASA NTRSDate not supplied

Surface Instability of Liquid Propellants in Microgravity During Pulsed Settling Operations

Pulsing reaction control system (RCS) thrusters, vent valves, or other propulsion devices can preserve propellant resources in space, but this operation also effectively introduces a vibration to the vehicle. When the vibration is perpendicular to the liquid propellant surface, Faraday waves may be generated at the liquid-vapor interface. These Faraday instabilities can perturb or break up the liquid surface of cryogenic tanks, leading to inefficiencies in thermal management or even ullage collapse. Drawing from theory and experiments, an engineering model defining the allowable design regions for pulsed settling in microgravity was assembled and verified with computational fluid dynamics (CFD) simulations. A traditional settling metric, the Bond number, was also overlaid in the model to indicate which duty cycles were insufficient to overcome surface tension and aggregate propellant. Mission planners and engineers can consult the tool to rapidly evaluate the stability of a liquid-vapor interface given the pulse frequency and the excitation acceleration. Expressions developed for Faraday waves induced by a sinusoidal forcing input at standard gravity were found to provide excellent predictive capabilities for pulsed, or rectangular, waveforms in the absence of a consistent gravitational acceleration. This study extends the usage of these equations to an alternative forcing function and microgravity environments for the purpose of estimating natural frequencies, surface mode shapes, surface wave amplitudes, and the onset of droplet ejection. CFD simulations with the Loci/STREAM-VoF (Volume of Fluid) solver were initially validated against experimental results in standard gravity. Discrete points on the design map were then investigated with CFD and confirmed that the engineering model reliably indicates surface stability and most Faraday wave characteristics without requiring higher-fidelity tools. The engineering model is highly extensible and can be adapted for various propellant fill fractions, fluid properties, and tank sizes.

Faraday Waves↗

NASA NTRS2011

Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics: Basic Concepts and Operations - Part 1

This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.

Farassat, Fereidoun↗

NASA NTRS1991

A Local Condensation Analysis Representing Two-phase Annular Flow in Condenser/radiator Capillary Tubes

NASA's effort for the thermal environmental control of the Space Station Freedom is directed towards the design, analysis, and development of an Active Thermal Control System (ATCS). A two phase, flow through condenser/radiator concept was baselined, as a part of the ATCS, for the radiation of space station thermal load into space. The proposed condenser rejects heat through direct condensation of ATCS working fluid (ammonia) in the small diameter radiator tubes. Analysis of the condensation process and design of condenser tubes are based on the available two phase flow models for the prediction of flow regimes, heat transfer, and pressure drops. The prediction formulas use the existing empirical relationships of friction factor at gas-liquid interface. An attempt is made to study the stability of interfacial waves in two phase annular flow. The formulation is presented of a stability problem in cylindrical coordinates. The contribution of fluid viscosity, surface tension, and transverse radius of curvature to the interfacial surface is included. A solution is obtained for Kelvin-Helmholtz instability problem which can be used to determine the critical and most dangerous wavelengths for interfacial waves.

Karimi, Amir↗

NASA NTRS2023

Breaking Wave Field Statistics With A Multi-Layer Model

The statistics of breaking wave fields are characterised within a novel multi-layer framework, which generalises the single-layer Saint-Venant system into a multi-layer and non-hydrostatic formulation of the Navier–Stokes equations. We simulate an ensemble of phase-resolved surface wave fields in physical space, where strong nonlinearities, including directional wave breaking and the subsequent highly rotational flow motion, are modelled, without surface overturning. We extract the kinematics of wave breaking by identifying breaking fronts and their speed, for freely evolving wave fields initialised with typical wind wave spectra. The Λ(c) distribution, defined as the length of breaking fronts (per unit area) moving with speed c to c + dc following Phillips (J. Fluid Mech., vol. 156, 1985, pp. 505–531), is reported for a broad range of conditions. We recover the Λ(c) ∝ c−6 scaling without wind forcing for sufficiently steep wave fields. A scaling of Λ(c) based solely on the root-mean-square slope and peak wave phase speed is shown to describe the modelled breaking distributions well. The modelled breaking distributions are in good agreement with field measurements and the proposed scaling can be applied successfully to the observational data sets. The present work paves the way for simulations of the turbulent upper ocean directly coupled to a realistic breaking wave dynamics, including Langmuir turbulence, and other sub-mesoscale processes.

Jiarong Wu↗

DOE OSTI2021

Vortex-sheet modeling of hydrodynamic instabilities produced by an oblique shock interacting with a perturbed interface in the HED regime

In this work, we consider hydrodynamic instabilities produced by the interaction of an oblique shock with a perturbed material interface under high-energy-density (HED) conditions. During this interaction, a baroclinic torque is generated along the interface due to the misalignment between the density and pressure gradients, thus leading to perturbation growth. Our objective is to understand the competition between the impulsive acceleration due to the normal component of the shock velocity, which drives the Richtmyer–Meshkov instability, and the shear flow across the interface due to the tangential component of the shock velocity, which drives the Kelvin–Helmholtz instability, as well as its relation to perturbation growth. Since the vorticity resulting from the shock-interface interaction is confined to the interface, we describe the perturbation growth using a two-dimensional vortex-sheet model. We demonstrate the ability of the vortex-sheet model to reproduce roll-up dynamics for non-zero Atwood numbers by comparing to past laser-driven HED experiments. We determine the dependence of the interface dynamics on the tilt angle and propose a time scaling for the perturbation growth at early time. Eventually, this scaling will serve as a platform for the design of future experiments. This study is the first attempt to incorporate into a vortex-sheet model the time-dependent interface decompression and the deceleration (as well as the corresponding Rayleigh–Taylor instability) arising from laser turn-off.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A generalized effective potential for differentially rotating plasmas

Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi and Pharr [Astrophys. J. 936, 145 (2022)]), confined either between two Alfvénic resonances or an Alfvénic resonance and a boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Numerical relativity simulations of prompt collapse mergers: Threshold mass and phenomenological constraints on neutron star properties after GW170817

We determine the threshold mass for prompt (no bounce) black hole formation in equal-mass neutron star (NS) mergers using a new set of 227 numerical relativity simulations. We consider 23 phenomenological and microphysical finite-temperature equations of state (EOS), including models with hyperons and first-order phase transitions to deconfined quarks. We confirm the existence of EOS-insensitive relations between the threshold mass, binary tidal parameter at the threshold (Λth), maximum mass of nonrotating NSs, and radii of reference mass NSs. We combine the EOS-insensitive relations, phenomenological constraints on NS properties, and observational data from GW170817 to derive an improved lower limit on radii of maximum mass and a 1.6 M ⊙ NS of 9.81 and 10.90 km, respectively. We also constrain the radius and quadrupolar tidal deformability (Λ) of a 1.4 M ⊙ NS to be larger than 10.74 km and 172, respectively. We consider uncertainties in all independent parameters—fitting coefficients as well as GW170817 masses while reporting the range of radii constraints. We discuss an approach to constrain the upper as well as lower limit of NS maximum mass using future binary NS detections and their identification as prompt or delayed collapse. With future observations, it will be possible to derive even tighter constraints on the properties of matter at and above nuclear density using the method proposed in this work.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Geometric and thermodynamic characterization of binary neutron star accretion discs

Accretion disks formed in binary neutron star mergers play a central role in many astrophysical processes of interest, including the launching of relativistic jets or the ejection of neutron-rich matter hosting heavy element nucleosynthesis. In this work we analyze in detail the properties of accretion disks from 44 ab initio binary neutron star merger simulations for a large set of nuclear equations of state, binary mass ratios, and remnant fates, with the aim of furnishing reliable initial conditions for disk simulations and a comprehensive characterization of their properties. We find that the disks have a significant thermal support, with an aspect ratio decreasing with the mass ratio of the binary from ~0.7 to 0.3. Even if the disk sample spans a broad range in mass and angular momentum, their ratio is independent from the equation of state and from the mass ratio. This can be traced back to the rotational profile of the disk, characterized by a constant specific angular momentum (as opposed to a Keplerian one) of 3 – 5×10 16 cm 2 s –1 . The profiles of the entropy per baryon and of the electron fraction depend on the mass ratio of the binary. For more symmetric binaries, they follow a sigmoidal distribution as a function of the rest mass density, for which we provide a detailed description and a fit. Furthermore, the disk properties discussed in this work can be used as a robust set of initial conditions for future long-term simulations of accretion disks from binary neutron star mergers, posing the basis for progress in the quantitative study of the outflow properties.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1971

Ion-acoustic instability of a two-temperature, collisional, fully-ionized plasma.

From a perturbation analysis of the fluid equations for a homogeneous unmagnetized plasma, it is shown that long wavelength ion waves are unstable when the electron temperature exceeds the ion temperature. Thus, the temperature difference can drive a resistive-type ion wave instability in a plasma which on a collisionless basis is stable. The additional destabilizing effect of a current is also investigated.

Rognlien, T. D.↗

NASA NTRS1972

Model for energy transfer in the solar wind: Formulation of model

The two-fluid solar-wind model is extended by including the collisionless dissipation of hydromagnetic waves originating at the sun. A series of solar wind models is generated, parameterized by the total energy flux of hydromagnetic waves at the base of the model. The resulting properties of propagation and dissipating of hydromagnetic waves on this model are presented.

Hartle, R. E.↗

NASA NTRS1982

Geophysical fluid flow cell experiment

The primary purpose of the geophysical flow experiments is to simulate large-scale baroclinic (density-stratified) flows which occur naturally in the atmospheres of rotating planets and stars and to gain insights and obtain answers to crucial questions concerning the large-scale nonlinear mechanics of the global geophysical flows. Those external conditions related to fluid viscosity, rotation, gravity are identified, which allow qualitatively different modes of instability or waves in the model.

Hart, J. E.↗

NASA NTRS1988

Numerical methods for turbulent flow

It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.

Turner, James C., Jr.↗

NASA NTRS1990

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

Young, David P.↗

NASA NTRS1991

Formation of intermediate shocks in both two-fluid and hybrid models

Intermediate shocks are studied in a two-fluid model that includes finite ion inertia dispersion and in a hybrid model in which the full ion dynamics is retained while the electrons are treated as a massless fluid. It is shown that in both models intermediate shocks can be formed through wave steepening, meaning that they are stable and possess shock structures.

Wu, C. C.↗

NASA NTRS1990

The flow of a thin liquid film on a stationary and rotating disk. I - Experimental analysis and flow visualization

The mean thickness of a thin liquid film of deionized water with a free surface on a stationary and rotating horizontal disk has been measured with a nonobtrusive capacitance technique. The measurements were taken when the rotational speed was 0-300 RPM and the flow rate was 7.0-15.0 LPM. A flow visualization study of the thin film was also performed to determine the characteristics of the waves on the free surface. When the disk was stationary, a circular hydraulic jump was present on the disk. Surface waves were found in the supercritical and subcritical regions at all flow rates studied. When the rotational speed of the disk is low, a standing wave at the edge of the disk was present. As the rotational speed increased, the surface waves changed from the wavy-laminar region to a region in which the waves ran nearly radially across the disk on top of a thin substrate of fluid.

Thomas, S.↗

NASA NTRS1995

A procedure for automating CFD simulations of an inlet-bleed problem

A procedure was developed to improve the turn-around time for computational fluid dynamics (CFD) simulations of an inlet-bleed problem involving oblique shock-wave/boundary-layer interactions on a flat plate with bleed into a plenum through one or more circular holes. This procedure is embodied in a preprocessor called AUTOMAT. With AUTOMAT, once data for the geometry and flow conditions have been specified (either interactively or via a namelist), it will automatically generate all input files needed to perform a three-dimensional Navier-Stokes simulation of the prescribed inlet-bleed problem by using the PEGASUS and OVERFLOW codes. The input files automatically generated by AUTOMAT include those for the grid system and those for the initial and boundary conditions. The grid systems automatically generated by AUTOMAT are multi-block structured grids of the overlapping type. Results obtained by using AUTOMAT are presented to illustrate its capability.

Chyu, Wei J.↗

NASA NTRS2001

Dynamic Magnetic Field Applications for Materials Processing

Magnetic fields, variable in time and space, can be used to control convection in electrically conducting melts. Flow induced by these fields has been found to be beneficial for crystal growth applications. It allows increased crystal growth rates, and improves homogeneity and quality. Particularly beneficial is the natural convection damping capability of alternating magnetic fields. One well-known example is the rotating magnetic field (RMF) configuration. RMF induces liquid motion consisting of a swirling basic flow and a meridional secondary flow. In addition to crystal growth applications, RMF can also be used for mixing non-homogeneous melts in continuous metal castings. These applied aspects have stimulated increasing research on RMF-induced fluid dynamics. A novel type of magnetic field configuration consisting of an axisymmetric magnetostatic wave, designated the traveling magnetic field (TMF), has been recently proposed. It induces a basic flow in the form of a single vortex. TMF may find use in crystal growth techniques such as the vertical Bridgman (VB), float zone (FZ), and the traveling heater method. In this review, both methods, RMF and TMF are presented. Our recent theoretical and experimental results include such topics as localized TMF, natural convection dumping using TMF in a vertical Bridgman configuration, the traveling heater method, and the Lorentz force induced by TMF as a function of frequency. Experimentally, alloy mixing results, with and without applied TMF, will be presented. Finally, advantages of the traveling magnetic field, in comparison to the more mature rotating magnetic field method, will be discussed.

Mazuruk, K.↗