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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS1987

Study of non-equilibrium transport phenomena

Nonequilibrium phenomena due to real gas effects are very important features of low density hypersonic flows. The shock shape and emitted nonequilibrium radiation are identified as the bulk flow behavior parameters which are very sensitive to the nonequilibrium phenomena. These parameters can be measured in shock tubes, shock tunnels, and ballistic ranges and used to test the accuracy of computational fluid dynamic (CFD) codes. Since the CDF codes, by necessity, are based on multi-temperature models, it is also desirable to measure various temperatures, most importantly, the vibrational temperature. The CFD codes would require high temperature rate constants, which are not available at present. Experiments conducted at the NASA Electric Arc-driven Shock Tube (EAST) facility reveal that radiation from steel contaminants overwhelm the radiation from the test gas. For the measurement of radiation and the chemical parameters, further investigation and then appropriate modifications of the EAST facility are required.

Sharma, Surendra 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 NTRS1988

Design and dynamic testing of an instrumented spacecraft component

Details relating to the design and subsequent vibration and shock tests of a spacecraft component for a severe vibration and shock environment are presented. The design process and analysis method involve the use of finite element analysis coupled with the Modal Strain Energy method with risk graphs to determine the adequacy of the design. The vibration levels experienced by box parts are reduced by the application of passive constrained layer viscoelastic treatments that significantly improve component reliability. All significant internal components were fully instrumented in both the random vibration and shock tests, the latter being done on a mechanical impact pyro simulator. Correlation between analysis and test data is good, validating the modeling and analysis techniques.

Dwyer, Thomas J.↗
NASA NTRS1995

Computations of Axisymmetric Flows in Hypersonic Shock Tubes

A time-accurate two-dimensional fluid code is used to compute test times in shock tubes operated at supersonic speeds. Unlike previous studies, this investigation resolves the finer temporal details of the shock-tube flow by making use of modern supercomputers and state-of-the-art computational fluid dynamic solution techniques. The code, besides solving the time-dependent fluid equations, also accounts for the finite rate chemistry in the hypersonic environment. The flowfield solutions are used to estimate relevant shock-tube parameters for laminar flow, such as test times, and to predict density and velocity profiles. Boundary-layer parameters such as bar-delta(sub u), bar-delta(sup *), and bar-tau(sub w), and test time parameters such as bar-tau and particle time of flight t(sub f), are computed and compared with those evaluated by using Mirels' correlations. This article then discusses in detail the effects of flow nonuniformities on particle time-of-flight behind the normal shock and, consequently, on the interpretation of shock-tube data. This article concludes that for accurate interpretation of shock-tube data, a detailed analysis of flowfield parameters, using a computer code such as used in this study, must be performed.

Sharma, Surendra P.↗
NASA NTRS2014

High Order Numerical Methods for LES of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing explicit subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. In this work we perform a comparative study of different approaches to reduce this loss of accuracy within the framework of the dynamic Germano SGS model. One of the possible approaches is to apply Harten's subcell resolution procedure to locate and sharpen the shock, and to use a one-sided test filter at the grid points adjacent to the exact shock location. The other considered approach is local disabling of the SGS terms in the vicinity of the shock location. In this study we use a canonical shock-turbulence interaction problem for comparison of the considered modifications of the SGS filtering procedure. For the considered test case both approaches show a similar improvement in the accuracy near the shock.

High Order↗
NASA NTRS2015

High Order Numerical Methods for LES of Turbulent Flows with Shocks

Simulation of turbulent flows with shocks employing explicit subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. In this work we perform a comparative study of different approaches to reduce this loss of accuracy within the framework of the dynamic Germano SGS model. One of the possible approaches is to apply Harten’s subcell resolution procedure to locate and sharpen the shock, and to use a one-sided test filter at the grid points adjacent to the exact shock location. The other considered approach is local disabling of the SGS terms in the vicinity of the shock location. In this study we use a canonical shock-turbulence interaction problem for comparison of the considered modifications of the SGS filtering procedure. For the considered test case both approaches show a similar improvement in the accuracy near the shock.

LES↗
NASA NTRS1992

Kinetic structure of slow shocks - Effects of the electromagnetic ion/ion cyclotron instability

The structure of slow magnetosonic shocks in the low beta regime is analyzed with attention given to ion heating and the effects of waves upstream of the electromagnetic ion/ion cyclotron (EMIIC) instability. Shock formation is assessed by means of three methods - a relaxation method and two based on dynamic flow interactions - to determine the effects of initialization and boundary conditions on the formation. Good solutions are found with the piston method and the similar flow-flow method in which the plasma is injected from two boundaries to form two slow shocks. Plasma parameters and shock normal angle are found to be the key variables dictating the structure of the magnetosonic shocks. Four unique classes of resultant shock structures are described in which classical, steady, or nonsteady behavior is found. The analysis also yields insight into the relationship between EMIIC instability and ion dissipation.

Omidi, N.↗
NASA NTRS1991

Quasi-perpendicular/quasi-parallel divisions of earth's bow shock

Computer-drawn diagrams of the boundaries between quasi-perpendicular and quasi-parallel areas of earth's bow shock are displayed for a few selected cone angles of static interplanetary magnetic field (IMF). The effect on the boundary of variable IMF in the foreshock is also discussed and shown for one nominal case. The boundaries demand caution in applying them to the realistic, dynamic conditions of the solar wind and in interpreting the effects of small cone angles on the distributions of structures at the shock. However, the calculated, first-order boundaries are helpful in defining areas of the shock where contributions from active structures inherent in quasi-parallel geometry may be distinguishable from those derived secondarily from upstream reflected ion dynamics. The boundaries are also compatible with known behavior of daytime ULF geomagnetic waves and pulsations according to models postulating that cone angle-controlled, time-dependent ULF activity around the subsolar point of the bow shock provides the source of geomagnetic excitation.

Greenstadt, E. W.↗
NASA NTRS1994

The evolution of cosmic-ray-mediated magnetohydrodynamic shocks: A two-fluid approach

We study the shock structure and acceleration efficiency of cosmic-ray mediated Magnetohydrodynamic (MHD) shocks both analytically and numerically by using a two-fluid model. Our model includes the dynamical effect of magnetic fields and cosmic rays on a background thermal fluid. The steady state solution is derived by following the technique of Drury & Voelk (1981) and compared to numerical results. We explore the time evolution of plane-perpendicular, piston-driven shocks. From the results of analytical and numerical studies, we conclude that the mean magnetic field plays an important role in the structure and acceleration efficiency of cosmic-ray mediated MHD shocks. The acceleration of cosmic-ray particles becomes less efficient in the presence of strong magnetic pressure since the field makes the shock less compressive. This feature is more prominent at low Mach numbers than at high Mach numbers.

Jun, Byung-Il↗
NASA NTRS2012

Quasi One-Dimensional Unsteady Modeling of External Compression Supersonic Inlets

The AeroServoElasticity task under the NASA Supersonics Project is developing dynamic models of the propulsion system and the vehicle in order to conduct research for integrated vehicle dynamic performance. As part of this effort, a nonlinear quasi 1-dimensional model of an axisymmetric external compression supersonic inlet is being developed. The model utilizes compressible flow computational fluid dynamics to model the internal inlet segment as well as the external inlet portion between the cowl lip and normal shock, and compressible flow relations with flow propagation delay to model the oblique shocks upstream of the normal shock. The external compression portion between the cowl-lip and the normal shock is also modeled with leaking fluxes crossing the sonic boundary, with a moving CFD domain at the normal shock boundary. This model has been verified in steady state against tunnel inlet test data and it s a first attempt towards developing a more comprehensive model for inlet dynamics.

Kopasakis, George↗
NASA NTRS1988

Fluid dynamic modeling and numerical simulation of low-density hypersonic flow

The concept of a viscous shock-layer and several related versions of continuum theories/methods are examined for their adequacy as a viable framework to study flow physics and aerothermodynamics of relevance to sustained hypersonic flights. Considering the flat plate at angle of attack, or the wedge, as a generic example for the major aerodynamic component of a hypersonic vehicle, the relative importance of the molecular-transport effects behind the shock (in the form of the 'shock slip') and the wall-slip effects are studied. In the flow regime where the shock-transition-zone thickness remains small compared to the shock radius of curvature, a quasi-one-dimensional shock structure under the Burnett/thirteen-moment approximation, as well as particulate/collisional models, can be consistently developed. The fully viscous version of the shock-layer model is shown to provide the crucial boundary condition downstream the shock in this case. The gas-kinetic basis of the continuum description for the flow behind the bow shock, and certain features affecting the non-equilibrium flow chemistry, are also discussed.

Cheng, H. K.↗
NASA NTRS1995

The 3D Navier-Stokes analysis of a Mach 2.68 bifurcated rectangular mixed-compression inlet

The supersonic diffuser of a Mach 2.68 bifurcated, rectangular, mixed-compression inlet was analyzed using a three-dimensional (3D) Navier-Stokes flow solver. A two-equation turbulence model, and a porous bleed model based on unchoked bleed hole discharge coefficients were used. Comparisons were made with experimental data, inviscid theory, and two-dimensional Navier-Stokes analyses. The main objective was to gain insight into the inlet fluid dynamics. Examination of the computational results along with the experimental data suggest that the cowl shock-sidewall boundary layer interaction near the leading edge caused a substantial separation in the wind tunnel inlet model. As a result, the inlet performance may have been compromised by increased spillage and higher bleed mass flow requirements. The internal flow contained substantial waves that were not in the original inviscid design. 3D effects were fairly minor for this inlet at on-design conditions. Navier-Stokes analysis appears to be an useful tool for gaining insight into the inlet fluid dynamics. It provides a higher fidelity simulation of the flowfield than the original inviscid design, by taking into account boundary layers, porous bleed, and their interactions with shock waves.

Mizukami, M.↗
NASA NTRS1992

An experimental examination of the effects of incoming boundary layer modifications on the dynamics of a turbulent compression corner interaction

This experimental study examines the effects of modifications to the incoming turbulent boundary layer on the highly separated shock wave/boundary layer interaction generated by an unswept compression corner. Particular focus is placed on the motion of the unsteady separation shock wave. The flowfield was generated by a 28 deg ramp in a Mach 5 flow with a freestream Reynolds number of 50 x 10 exp 6/m. The incoming turbulent boundary layer transitioned naturally and developed under near-adiabatic wall conditions. Modification of the flow entering the interaction was effected through either a single plate boundary layer manipulator (BLM) or riblets. The BLM reduced the length of separation by 35-45 percent and reduced the streamwise extent of the separation shock motion by 36-74 percent. Examination of the flowfield downstream of the BLM showed this result to be due to the inviscid preturning of the flow by the BLM, and not by changes to the boundary layer dynamics. The riblets had no measurable effect on the compression corner interaction.

Mcclure, W. B.↗
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

Solar wind dynamic pressure variations and possible ground signatures of flux transfer events

The effects of a series of solar wind dynamic pressure pulses are followed through the solar wind, across the bow shock and magnetosheath, into the magnetosphere, and down to the dayside ionosphere. Each pressure pulse had an intrinsic solar wind origin, i.e., was not generated by processes occurring at the earth's bow shock. Both upstream and downstream of the earth's bow shock, the pulses were identified by depressed magnetic field strengths and enhanced plasma densities. The pulses compressed the magnetosheath and magnetosphere, causing satellites in the magnetosphere to briefly observe enhanced magnetic field strengths, and/or enter the low-latitude boundary layer or magnetosheath. Satellites already in the magnetosheath observed a brief burst of enhanced magnetosheath flow caused by the relative inward motion of magnetosheath flow patterns. Alfven and fast mode compressional waves propagated rapidly down to the polar ionosphere, where they produced transient ionospheric flows at latitudes equatorward of the convection reversal boundary. The flow patterns moved westward around the auroral oval.

Sibeck, D. G.↗
NASA NTRS1993

Analysis of unsteady wave processes in a rotating channel

The impact of passage rotation on the gas dynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel. Initial conditions are prescribed by assuming homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. The results suggest possible criteria for assessing the consequences of passage rotation on the wave processes, and they may therefore be applicable to pressure-exchange wave rotors. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface as well as the hub-to-tip radius ratio. Rarefaction fronts, shocks, and contact interfaces are observed to propagate faster with increasing wheel Mach number.

Larosiliere, L. M.↗