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NASA NTRS1995

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

NASA NTRS1992

An investigation of DTNS2D for use as an incompressible turbulence modelling test-bed

This paper documents an investigation of a two dimensional, incompressible Navier-Stokes solver for use as a test-bed for turbulence modelling. DTNS2D is the code under consideration for use at the Center for Modelling of Turbulence and Transition (CMOTT). This code was created by Gorski at the David Taylor Research Center and incorporates the pseudo compressibility method. Two laminar benchmark flows are used to measure the performance and implementation of the method. The classical solution of the Blasius boundary layer is used for validating the flat plate flow, while experimental data is incorporated in the validation of backward facing step flow. Velocity profiles, convergence histories, and reattachment lengths are used to quantify these calculations. The organization and adaptability of the code are also examined in light of the role as a numerical test-bed.

Steffen, Christopher J., Jr.↗

NASA NTRS1947

Calculation of the Pressure Distribution on Bodies of Revolution in the Subsonic Flow of a Gas: Axially Symmetrical Flow - Part 1

The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.

Bilharz, Herbert↗

DOE OSTI2021

Spatially Quasi-Periodic Water Waves of Infinite Depth

Abstract We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

Wilkening, Jon (ORCID:0000000327827596)↗

NASA NTRS1987

Numerical simulations of trailing vortex bursting

Solutions of the steady-state Navier-Stokes equations for the axisymmetric bursting of a laminar trailing vortex are computed with Newton's method and the pseudo-arc length continuation method for wide ranges of vortex strength and Reynolds number. The results indicate that a trailing vortex can undergo a transition from a state in which the core slowly diffuses to a state marked by large amplitude, spatial oscillations of core radius and core axial velocity. At the transition point the core grows rapidly in size. This event is interpreted as vortex bursting. The results also suggest that when the maximum core swirl velocity is sufficiently large the centerline axial flow downstream of transition will be reversed.

Beran, Philip S.↗

NASA NTRS2019

A Dissection of Spatially Resolved AGN Feedback across the Electromagnetic Spectrum

We present optical SuperNova Integral Field Spectrograph integral field spectroscopy, Hubble Space Telescope optical imaging, Chandra X-ray imaging, and Very Large Array radio interferometry of the merging galaxy 2MASX J04234080+0408017, which hosts a Seyfert 2 active galactic nucleus (AGN) at z = 0.046. Our observations reveal that radiatively driven, ionized gas outflows are successful to distances >10 kpc due to the low mass of the host system, encompassing the entirety of the observed optical emission. We also find that at large radii, where observed velocities cannot be reproduced by radiative driving models, high-velocity kinematics are likely due to mechanical driving from AGN winds impacting high-density host material. This impacting deposits sufficient energy to shock the host material, producing thermal X-ray emission and cosmic rays, which in turn promote the formation of in situ radio structure in a pseudo-jet morphology along the high-density lanes.

Travis Fischer↗

DOE OSTI2023

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

The growing significance of shales and tight formations in the transition to less carbon-intensive and clean energy drives the research endeavor to understand the physics of gas flow within these systems. However, shales are composed of massively heterogeneous physical and chemical features. Most nano-sized pores connect to millimeter-scale fractures, leading to multiscale transport. These nano-scale pore throats demonstrate non-classical flow behavior, such as non-negligible slip velocities and adsorbed gas layers at the boundary. As a result, classical computational fluid dynamics models do not capture the physics. In this work, we develop a coupling scheme for the multiple-relaxation-time (MRT) lattice Boltzmann (LB) method that integrates the Peng-Robinson equation of state into a pseudo-potential interaction model to capture the physics of methane flow in irregular networks of channels that represent nano-scale porous media. We use atomistic simulations to calibrate and validate our model in slit nano-channels. We propose a preconditioning scheme to initialize the coupled transport and adsorption simulation of methane in complex porous media. The results of this implementation of LB agree with Direct Simulation Monte Carlo (DSMC) and Molecular Dynamics (MD) simulations. We then scale up the LB implementation through vectorization and indirect addressing. We parallelize it using Message Passing Interface (MPI) and OpenMP frameworks to simulate transport and adsorption in complex media with a million lattices. Additionally, we analyze the differences between coupled and transport-only simulations in two case studies and show that considering phase behavior, i.e., adsorption, can significantly change the flow behavior. This work constitutes an important step towards bridging the gap between molecular flow and system-scale behavior of complex disordered porous media.

42 ENGINEERING↗

NASA NTRS2001

GPS/Magnetometer Based Satellite Navigation and Attitude Determination

In recent years algorithms were developed for orbit, attitude and angular-rate determination of Low Earth Orbiting (LEO) satellites. Those algorithms rely on measurements of magnetometers, which are standard, relatively inexpensive, sensors that are normally installed on every LEO satellite. Although magnetometers alone are sufficient for obtaining the desired information, the convergence of the algorithms to the correct values of the satellite orbital parameters, position, attitude and angular velocity is very slow. The addition of sun sensors reduces the convergence time considerably. However, for many LEO satellites the sun data is not available during portions of the orbit when the spacecraft (SC) is in the earth shadow. It is here where the GPS space vehicles (SV) can provide valuable support. This is clearly demonstrated in the present paper. Although GPS measurements alone can be used to obtain SC position, velocity, attitude and angular-rate, the use of magnetometers improve the results due to the synergistic effect of sensor fusion. Moreover, it is possible to obtain these results with less than three SVs. In this paper we introduce an estimation algorithm, which is a combination of an Extended Kalman Filter (EKF) and a Pseudo Linear Kalman Filter (PSELIKA).

Deutschmann, Julie↗

NASA NTRSDate not supplied

100 kHz High-Spectral-Resolution NO-PLIF Measurements for Compressible Flows

In the present work, we use a burst-mode laser and optical parametric oscillator system to perform high-spectral resolution NO-PLIF measurements of an underexpanded jet at a repetition-rate of 100 kHz, with the motivation of multi-parameter measurements of temperature, pressure, and velocity. The laser frequency of the 1064 nm seed laser for the burst-mode laser was scanned during the burst to cover two neighboring absorption line pairs near 226 nm. The peak PLIF signal intensity varies along the axial (z) direction of the underexpanded jet as the laser frequency is scanned, which we attribute to the collisional shift induced by the flow and only revealed due to the narrow linewidth of the laser. A pseudo-Voight fit is applied to the LIF excitation spectra on a pixel-by-pixel basis to measure the spectral position of the peak intensity for the two transition pairs and their amplitude. The spectral position of the peak intensity is used to derive a frequency shift, which is separated into its collisional and Doppler components using the axisymmetric nature of the flow field. The amplitude of the measured peaks is used for two-line rotational thermometry. Challenges for quantitative measurements using such an approach are discussed, including measuring the spatial variations in the energy distribution of the laser sheet at a 100 kHz repetition rate and uncertainty/variability in the step size during the fast frequency scan.

laser induced fluorescence↗

NASA NTRSDate not supplied

100 kHz High-Spectral-Resolution NO-PLIF Measurements for Compressible Flows

laser induced fluorescence↗

NASA NTRS1997

Multiwavelength Modeling of Nova Atmospheres

We have analyzed the early optically thick ultraviolet spectra of Nova OS And 1986 using a grid of spherically symmetric, non-LTE, line-blanketed, expanding model atmospheres and synthetic spectra with the following set of parameters: 5,000 less than or equal to T(sub model) less than or equal to 60,000K, solar abundances, (rho)(alpha) r(sup -3), v(sub max) = 2000 km/s, L = 6 x 10(exp 4) solar luminosity, and a statistical or microturbulent velocity of 50 km/s. We used the synthetic spectra to estimate the model parameters corresponding to the observed IUE spectra. The fits to the observations were then iteratively improved by changing the parameters of the model atmospheres, in particular T(sub model) and the abundances, to arrive at the best fits to the optically thick pseudo-continuum and the features found in the IUE spectra. The IUE spectra show two different optically thick subphases. The earliest spectra, taken a few days after maximum optical light, show a pseudo-continuum created by overlapping absorption lines. The later observations, taken approximately 3 weeks after maximum light, show the simultaneous presence of allowed, semi-forbidden, and forbidden lines in the observed spectra. Analysis of these phases indicate that OS And 86 had solar metallicities except for Mg which showed evidence of being underabundant by as much as a factor of 10. We determine a distance of 5.1 kpc to OS And 86 and derive a peak bolometric luminosity of approximately 5 x 10(exp 4) solar luminosity. The computed nova parameters provide insights into the physics of the early outburst and explain the spectra seen by IUE. Lastly, we find evidence in the later observations for large non-LTE effects of Fe II which, when included, lead to much better agreement with the observations.

Hauschildt, P. H.↗

NASA NTRS1996

Development of a Vorticity-Velocity Navier-Stokes Formulation for the Study of Compressibility Effects on Dynamic Stall

The first major area of this study was to develop a vorticity-velocity formulation and numerical solution algorithms suitable for the analyses of incompressible as well as low-to- moderate-speed compressible flows. Research performed towards contributing to the determination of the appropriate vorticity and dilation creation boundary conditions suggested to temporarily set aside this approach and use a primitive-variable approach other than the pseudo-compressibility approach used. The second major area of study was initiated to comprehensively examine the INS-2D and INS-3D programs from the point of view of boundary conditions. The research carried out was documented in the form of two technical papers which are included in Appendices A and B; the boundary-condition related issues for INS-3D are briefly mentioned.

Ghia, K. N.↗

NASA NTRS2017

A Minimal State Augmentation Algorithm for Vision-Based Navigation without Using Mapped Landmarks

This paper describes MAVeN (Minimal State Augmentation Algorithm for Vision-Based Navigation), which is a new algorithm for vision-based navigation that has only 21 states, yet is able to track features in successive camera images and use them to propagate estimates of the spacecraft position and velocity. The filter dimension drops to 12 if attitude information is already available. The low filter dimension makes MAVeN a very reliable and practical algorithm for real-time flight implementation. The main idea is to project observed features onto a rough shape model of the ground surface, which are then used by the filter as pseudo-landmarks. The shape model is assumed to be known beforehand, as would be obtained from prior surveillance of the landing site from orbit. MAVeN does not require pre-mapped landmarks, so it is able to navigate terrain that has not been previously observed up close. This property is especially important for close proximity operations in small body missions where ground surface features are being seen for the first time at close range. MAVeN is also able to hover motionless above the ground without position error growth, which is unusual for this class of vision-based navigation algorithms.

San Martin, A. Miguel↗

NASA NTRS1994

On the Two-Dimensionalization of Homogeneous Rotating Turbulence

Large-eddy simulation of the incompressible Navier-Stokes equations has been used to examine the long-time development of initially isotropic turbulence subjected to solid-body rotation. The simulations were carried out using a pseudo-spectral method with 128 x 128 x 512 collocation points in a computational domain that is four times larger along the rotation axis than in the other directions; subgrid-scale motions were parameterized using a spectral eddy viscosity model modified for system rotation. Simulation results show that the correlation length along the rotation am's of velocities orthogonal to the rotation vector exhibits rapid growth while the integral length-scale of velocities aligned with the rotation axis is relatively unaffected by rotation. Examination of the energy spectrum of two-dimensional, two-component motions indicates the presence of an inverse cascade of energy. System rotation also causes an alignment of vorticity along the rotation axis with relatively stronger cyclonic vorticity than anticyclonic. The onset of anisotropic effects are well characterized by Rossby numbers defined in terms of both macroscopic and microscopic quantities.

Squires, K. D.↗

NASA NTRS1984

Impact experiments in viscous fluid media

Available phase and group velocity data are inverted by a procedure which includes the effects of transverse anisotropy, anelastic dispersion, sphericity, and gravity. The resulting models, for average Earth, average ocean, and oceanic regions divided according to the age of the ocean floor, are quite different from previous results which ignore the above effects. The models show a low-veocity zone with age dependent anisotropy and velocities higher than derived in previous surface wave studied. The correspondence between the anisotropy variation with age and a physical model based on flow aligned olivine is suggestive. For most of the Earth SHSV in the vicinity of the low-velocity zone. Near the East Pacific Rise, however, SVSH at depth, consistent with ascending flow. Anisotropy is as important as temperature in causing radial and lateral variations in velocity. The models have a high velocity nearly isotropic layer at the top of the mantle that thickens with age. This layer defines the LID, or seismic lithosphere. In the Pacific, the LID thickens with age to a maximum thickness of about 50 km. This thickness is comparable to the thickness of the elastic lithosphere. The LID thickness is thinner than derived using isotropic or pseudo-isotropic procedures A new model for Average Earth is obtained which includes a thin LID. This model extends the fit of a P.R.E.M. type model to shorter period surface waves.

Greeley, R.↗

NASA NTRS1994

Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence

We study weak Alfvenic turbulence of an incompressible, magnetized fluid in some detail, with a view to developing a firm theoretical basis for the dynamics of small-scale turbulence in the interstellar medium. We prove that resonant 3-wave interactions are absent. We also show that the Iroshnikov-Kraichnan theory of incompressible, magnetohydrodynamic turbulence -- which is widely accepted -- describes weak 3-wave turbulence; consequently, it is incorrect. Physical arguments, as well as detailed calculations of the coupling coefficients are used to demonstrate that these interactions are empty. We then examine resonant 4-wave interactions, and show that the resonance relations forbid energy transport to small spatial scales along the direction of the mean magnetic field, for both the shear Alfven wave and the pseudo Alfven wave. The three-dimensional inertial-range energy spectrum of 4-wave shear Alfven turbulence guessed from physical arguments reads E(k(sub z), k(sub perpendicular)) approximately V(sub A)v(sub L)L(exp -1/3)k(sub perpendicular)(exp -10/3), where V(sub A) is the Alfven speed, and v(sub L) is the velocity difference across the outer scale L. Given this spectrum, the velocity difference across lambda(sub perpendicular) approximately k(sub perpendicular exp -1) is v(sub lambda (sub perpendicular)) is approximately v(sub L)(lambda(sub perpendicular)/L)(exp 2/3). We derive a kinetic equation, and prove that this energy spectrum is a stationary solution and that it implies a positive flux of energy in k-space, along directions perpendicular to the mean magnetic field. Using this energy spectrum, we deduce that 4-wave interactions strengthen as the energy cascades to small, perpendicular spatial scales; beyond an upper bound in perpendicular wavenumber, k(sub perpendicular)L is approximately (V(sub A)/v(sub L))(exp 3/2), weak turbulence theory ceases to be valid. Energy excitation amplitudes must be very small for the 4-wave inertial-range to be substantial. When the excitation is strong, the width of the 4-wave inertial-range shrinks to zero. This seems likely to be the case in the interstellar medium.

Sridhar, S.↗

NASA NTRS2018

Application of a First-Principles Anomalous Transport Model for Electrons to Multiple Hall Thrusters and Operating Conditions

We have developed a physics-based model based on a pseudo-particle description of the electron cyclotron drift instability. A key improvement of the model with respect to previous work is that linear theory is not applied in the event of wave saturation and deviations of electrons or ions from a Maxwellian distribution function. In the acceleration region, the anomalous collision frequency is computed as the minimum value necessary to prevent the electron drift velocity from exceeding the thermal velocity. A functional based on the electron equilibration time is defined to control the transition from high to low resistivity regions. The model was previously applied to a single Hall thruster at its nominal operating condition, showing promising results that captured accurately the location of the thruster’s acceleration region. In this paper, we extend the use of this firstprinciples models to two additional thrusters, also considering multiple operating conditions for each of them. Numerical results are compared to experimental measurements obtained with non-invasive laser induced fluorescence. In general, the agreement between experiments and simulations is good. The model is able to predict the location of the acceleration region for all cases. We observe however that fine details, such as changes in the plasma potential gradient within the acceleration regions, are not captured. The model is also insensitive to changes in the magnetic field strength while experiments show that small shifts in location (of less than 5% of the acceleration channel length) occur. We plan to address the weaknesses of our method with the help of physical insight gained from kinetic simulations of the acceleration region.

Chaplin, Vernon H.↗

NASA NTRS1984

A solution procedure for three-dimensional incompressible Navier-Stokes equation and its application

An implicit, finite-difference procedure is presented for numerically solving viscous incompressible flows. For convenience of applying the present method to three-dimensional problems, primitive variables, namely the pressure and velocities, are used. One of the major difficulties in solving incompressible flows that use primitive variables is caused by the pressure field solution method which is used as a mapping procedure to obtain a divergence-free velocity field. The present method is designed to accelerate the pressure-field solution procedure. This is achieved by the method of pseudocompressibility in which the time derivative pressure term is introduced into the mass conservation equation. The pressure wave propagation and the spreading of the viscous effect is investigated using simple test problems. The present study clarifies physical and numerical characteristics of the pseudo-compressible approach in simulating incompressible flows. Computed results for external and internal flows are presented to verify the present procedure. The present algorithm has been shown to be very robust and accurate if the selection of the pseudo-compressibility parameter has been made according to the guidelines given.

Kwak, D.↗