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Results for “infinite dimensional symmetries”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Shih, Tso-Shin↗
NASA NTRS1993

Symmetry algebra of a generalized anisotropic harmonic oscillator

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

Castanos, O.↗
NASA NTRS1992

Observations on the Proper Orthogonal Decomposition

The Proper Orthogonal Decomposition (P.O.D.), also known as the Karhunen-Loeve expansion, is a procedure for decomposing a stochastic field in an L(2) optimal sense. It is used in diverse disciplines from image processing to turbulence. Recently the P.O.D. is receiving much attention as a tool for studying dynamics of systems in infinite dimensional space. This paper reviews the mathematical fundamentals of this theory. Also included are results on the span of the eigenfunction basis, a geometric corollary due to Chebyshev's inequality and a relation between the P.O.D. symmetry and ergodicity.

Berkooz, Gal↗
NASA NTRS1985

Vortex studies relating to boundary layer turbulence and noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Futher, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.

Adelman, J. L.↗
NASA NTRS1985

Vortex Studies Relating to Boundary Layer Turbulence and Noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Further, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.

Adelman, J. L.↗
NASA NTRS1993

Remarks about massive and massless particles in supersymmetry

The internal space-time symmetry and simple supersymmetry of relativistic particles are briefly discussed in terms of the little group of the Poincare group. The little group generators in a finite-dimensional matrix representation of the N = 1 super-Poincare algebra are explicitly constructed. The supergeometry of a massive case continuously becomes that of a massless case in the infinite-momentum limit. The origin of the gage transformations associated with the massless supermultiplets becomes transparent in that limit.

Ketov, S. V.↗
NASA NTRS1978

Sound propagation through a subsonic jet due to a source near the duct exit

Matched asymptotic solutions are constructed for the acoustic potentials of a periodic point source located in a two-dimensional subsonic jet near the exit of the duct with the ratio of the duct thickness to the acoustic wave length as the small parameter. The leading term of the far field solution has the same directionality effect as that for an infinite jet without the duct and that when the plane at the duct exit is considered to be a plane of symmetry. However, the intensity is different because of the wave propagation into the duct and is dependent on the location of the source.

Ting, L.↗
NASA NTRS1972

Flow field measurements for space-shuttle-related cylindrical configurations in hypersonic streams.

Use of surface pressures, heat-transfer rates, and flow-visualization photographs to define the flowfields for simulated infinite cylinders. Four cylindrical cross sections were studied in the experimental program, which was conducted at free-stream Mach numbers of 5 to 15, free-stream unit Reynolds numbers from 2 to 20 million per foot, and angles of attack from 30 to 90 deg. Although swept-cylinder theory provides a reasonable correlation of the measured laminar heat-transfer rates in the plane of symmetry, improved correlation with the measurements is obtained if the three-dimensional nature of the flow is taken into account. In cases where the boundary layer on the windward forebody was turbulent, the large velocity gradients near the chines produced relaminarization of the boundary layer prior to separation. The average heat-transfer-rate in the separated region, which is weakly dependent on the free-stream conditions, was found to be a linear function of the angle of attack. For a given flow condition the effect of the leeward geometry on heat transfer can be correlated by a single geometric parameter which is dependent on the location of separation.

Bertin, J. J.↗
NASA NTRS1990

Time-optical spinup maneuvers of flexible spacecraft

Attitude controllers for spacecraft have been based on the assumption that the bodies being controlled are rigid. Future spacecraft, however, may be quite flexible. Many applications require spinning up/down these vehicles. In this work the minimum time control of these maneuvers is considered. The time-optimal control is shown to possess an important symmetry property. Taking advantage of this property, the necessary and sufficient conditions for optimality are transformed into a system of nonlinear algebraic equations in the control switching times during one half of the maneuver, the maneuver time, and the costates at the mid-maneuver time. These equations can be solved using a homotopy approach. Control spillover measures are introduced and upper bounds on these measures are obtained. For a special case these upper bounds can be expressed in closed form for an infinite dimensional evaluation model. Rotational stiffening effects are ignored in the optimal control analysis. Based on a heuristic argument a simple condition is given which justifies the omission of these nonlinear effects. This condition is validated by numerical simulation.

Singh, G.↗
NASA NTRS1984

Acoustic-radiation stress in solids. I - Theory

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

Cantrell, J. H., Jr.↗
NASA NTRS1999

Experimental Observations on a Low Strain Counter-Flow Diffusion Flame: Flow and Bouyancy Effects

Diffusion flames are of great interest in fire safety and many industrial processes. The counter-flow configuration provides a constant strain flow, and therefore is ideal to study the structure of diffusion flames. Most studies have concentrated on the high velocity, high strain limit, since buoyantly induced instabilities will disintegrate the planar flame as the velocity decreases. Only recently, experimental studies in microgravity conditions have begun to explore the low strain regimes. Numerical work has shown the coupling between gas phase reaction rates, soot reaction rates, and radiation. For these programs, size, geometry and experimental conditions have been chosen to keep the flame unaffected by the physical boundaries. When the physical boundaries can not be considered infinitely far from the reaction zone discrepancies arise. A computational study that includes boundary effects and accounts for the deviations occurring when the major potential flow assumptions are relaxed was presented by Borlik et al. This development properly incorporates all heat loss terms and shows the possibility of extinction in the low strain regime. A major constraint of studying the low strain regime is buoyancy. Buoyant instabilities have been shown to have a significant effect on the nature of reactants and heat transport, and can introduce instabilities on the flow that result in phenomena such as flickering or fingering. The counter-flow configuration has been shown to provide a flame with no symmetry disrupting instabilities for inlet velocities greater than 50 mm/s. As the velocity approaches this limit, the characteristic length of the experiment has to be reduced to a few millimetres so as to keep the Rayleigh number (Ra L = (β g 0 L 3 ∆T)/(𝑎v)) below 2000. In this work, a rectangular counter-flow burner was used to study a two-dimensional counter-flow diffusion flame. Flow visualisation and Particle Image Velocimetry served to describe the nature of the stagnation plane for strain rates smaller than 100 (1/s). These experiments were conducted with a non-reacting flow. Video images of a propane air diffusion flame were used to describe the behaviour of a diffusion flame in this regime. Flame geometry and pulsation frequency are described.

J. A. Sutula↗
NASA NTRS2003

Radiant Extinction Of Gaseous Diffusion Flames

The absence of buoyancy-induced flows in microgravity (mu:g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and :g flames have been reported in experiments on candle flames [1, 2], flame spread over solids [3, 4], droplet combustion [5,6], and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (i) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation, and (ii) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the Aweak@ (low burning rate per unit flame area) :g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in :g will burn indefinitely [1]. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the :g experiments and modeling because: (i) It reduces the complexity by making the problem one-dimensional. (ii) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame. (iii) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in :g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in :g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Berhan, S.↗
NASA NTRS1999

Radiant Extinction of Gaseous Diffusion Flames

The absence of buoyancy-induced flows in microgravity (mu-g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and mu-g flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion, and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (1) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation; and (2) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the "weak" (low burning rate per unit flame area) mu-g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in mu-g will burn indefinitely. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the mu-g experiments and modeling because: (1) It reduces the complexity by making the problem one-dimensional; (2) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame; (3) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in mu-g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in mu-g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Berhan, Sean↗
NASA NTRS2001

Unsteady Spherical Diffusion Flames in Microgravity

The absence of buoyancy-induced flows in microgravity (mu-g) and the resulting increase in the reactant residence time significantly alters the fundamentals of many combustion processes. Substantial differences between normal gravity (ng) and (mu-g) flames have been reported in experiments on candle flames, flame spread over solids, droplet combustion, and others. These differences are more basic than just in the visible flame shape. Longer residence times and higher concentration of combustion products in the flame zone create a thermochemical environment that changes the flame chemistry and the heat and mass transfer processes. Processes such as flame radiation, that are often ignored in ng, become very important and sometimes even controlling. Furthermore, microgravity conditions considerably enhance flame radiation by: (i) the build-up of combustion products in the high-temperature reaction zone which increases the gas radiation, and (ii) longer residence times make conditions appropriate for substantial amounts of soot to form which is also responsible for radiative heat loss. Thus, it is anticipated that radiative heat loss may eventually extinguish the "weak" (low burning rate per unit flame area) mu-g diffusion flame. Yet, space shuttle experiments on candle flames show that in an infinite ambient atmosphere, the hemispherical candle flame in mu-g will burn indefinitely. This may be because of the coupling between the fuel production rate and the flame via the heat-feedback mechanism for candle flames, flames over solids and fuel droplet flames. Thus, to focus only on the gas-phase phenomena leading to radiative extinction, aerodynamically stabilized gaseous diffusion flames are examined. This enables independent control of the fuel flow rate to help identify conditions under which radiative extinction occurs. Also, spherical geometry is chosen for the mu-g experiments and modeling because: (i) It reduces the complexity by making the problem one-dimensional; (ii) The spherical diffusion flame completely encloses the soot which is formed on the fuel rich side of the reaction zone. This increases the importance of flame radiation because now both soot and gaseous combustion products co-exist inside the high temperature spherical diffusion flame. (iii) For small fuel injection velocities, as is usually the case for a pyrolyzing solid, the diffusion flame in mu-g around the solid naturally develops spherical symmetry. Thus, spherical diffusion flames are of interest to fires in mu-g and identifying conditions that lead to radiation-induced extinction is important for spacecraft fire safety.

Atreya, Arvind↗