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At least 1,099 records · Page 61
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NASA NTRS1994

The stability of thick, self-gravitating disks in protostellar systems

Using numerical hydrodynamics techniques, we perform a nonlinear stability analysis of accretion disk systems that contain thick, self-gravitating disks. The systems are initially represented by a point mass M(sub c) at the center and a geometrically thick, axisymmetric disk of mass M(sub d) that supports uniform specific angular momentum and obeys an n = 3/2, polytropic equation of state. The equilibrium disk structure is uniquely defined upon the specification of two key dimensionless system parameters: M(sub d)/M(sub c) and T/absolute value of W (the ratio of rotational kinetic energy if the disk to the gravitational potential energy of the system). The focus of this work is on the identification of systems within this two-dimensional parameter space that are marginally unstable toward the development of nonaxisymmetric distortions. The geometric form and relative pattern speed of the disk's distortion as well as the likelihood of disk fragmentation as a result of such instabilities is examined, particularly in the context of protostellar systems. The value of T/absolute value of W at which thick disks first become dynamically unstable to nonaxisymmetric distortions is found to vary significantly with the mass ratio of the accertion disk system. Nonaxisymmetric eigenmodes with four distinctly different characters are identified in systems with mass ratios in the range 0.2 less than or equal to (M(sub d)/M(sub c)) less than or equal to 5.

Woodward, John W.↗
NASA NTRS1993

Intraseasonal variability in a barotropic model with seasonal forcing

It has recently been suggested that oscillatory topographic instability could contribute to low-frequency variability over the Northern Hemisphere midlatitudes. A barotropic potential vorticity model, with a hierarchy of forcing and topography configurations on the sphere, is used to investigate the nature of low-frequency oscillations induced by such instabilities. Steady-state solutions of the model include multiple unstable equilibria that sustain oscillatory instabilities with periods of 10 - 15 days, and 150 - 180 days, for a realistic forcing pattern, Time-dependent solutions exhibit chaotic behavior with episodic oscillations, featuring both the intraseasonal (35 - 50 day) and biweekly (10 - 15 day) modes. The former is dominated by standing spatial patterns, the latter by traveling wave patterns. The phases of the intraseasonal oscillation are robust for all cases, exhibiting a clear oscillatory exchange of atmospheric angular momentum with the solid earth via mountain troque. It is demonstrated, through linear stability analysis on the sphere, that the intraseasonal oscillations are induced by topographic instabilities. The role of the seasonal cycle is studied by prescribing an annual cycle in the forcing. In this case, the winter forcing is more favorable than the summer for the occurrence of episodic intraseasonal oscillations. Recent observations are consistent with this model result.

Strong, Christopher M.↗
NASA NTRS1995

An instability in planetary rings due to ballistic transport

Ballistic transport in planetary rings is the net radial transport of mass and angular momentum due to exchanges of meteoroid impact ejecta between neighboring ring regions. The detailed linear stability analysis in this paper demonstrates that ballistic transport causes wavelike disturbances to grow and propagate in an otherwise uniform ring. The growth is strongest for intermediate values of the normal ring optical depth tau = 0.1 to 1.0 and goes to zero as tau approaches 0 and tau approaches infinity. For nominal values of various physical parameters, the minimum e-folding time is approximately 10(exp 5) years for tau approximately 0.4. The direction of propagation is opposite to the sense of any asymmetry that may exist in the ejecta direction distribution (inward for prograde ejecta and outward for retrograde ejecta). The additional effect of viscous transport tends to damp wavelike perturbations strongly at short wavelengths and at high values of tau. The quantitative agreement between this analytic work and numerical simulations reported elsewhere is generally quite good. As applied to Saturn's rings, the results in this paper strengthen the earlier conclusion from numerical calculations that the 100-km structure in the inner B Ring is caused by ballistic transport. However, it is also clear that ballistic transport cannot produce the complex structure seen in the outer two-thirds of the B Ring where tau greater than or approximately 1.5. Wavelike structures in the C Ring might also be attributed to ballistic transport; but this requires further study.

Durisen, Richard H.↗
NASA NTRS1996

Heat and Momentum Transfer Studies in High Reynolds Number Wavy Films at Normal and Reduced Gravity Conditions

We examined the effect of the gas flow on the liquid film when the gas flows in the countercurrent direction in a vertical pipe at normal gravity conditions. The most dramatic effect of the simultaneous flow of gas and liquid in pipes is the greatly increased transport rates of heat, mass, and momentum. In practical situations this enhancement can be a benefit or it can result in serious operational problems. For example, gas-liquid flow always results in substantially higher pressure drop and this is usually undesirable. However, much higher heat transfer coefficients can be expected and this can obviously be of benefit for purposes of design. Unfortunately, designers know so little of the behavior of such two phase systems and as a result these advantages are not utilized. Due to the complexity of the second order boundary model as well as the fact that the pressure variation across the film is small compared to the imposed gas phase pressure, the countercurrent gas flow affect was studied for the standard boundary layer model. A different stream function that can compensate the shear stress affect was developed and this stream function also can predict periodic solutions. The discretized model equations were transformed to a traveling wave coordinate system. A stability analysis of these sets of equations showed the presence of a Hopf bifurcation for certain values of the traveling wave velocity and the shear stress. The Hopf celerity was increased due to the countercurrent shear. For low flow rate the increases of celerity are more than for the high flow rate, which was also observed in experiments. Numerical integration of a traveling wave simplification of the model also predicts the existence of chaotic large amplitude, nonperiodic waves as observed in the experiments. The film thickness was increased by the shear.

Balakotaiah, V.↗
NASA NTRS1995

Effects of Meteoroid Erosion in Planetary Rings

This grant supported continuing studies of the effects of ballistic transport on the evolution of Saturn's rings. Ballistic transport, as used in this context, refers to the net transport of mass and angular momentum caused by the exchange of meteoroid impact ejecta between neighboring ring regions (Ip 1983, 1984, Morfill et al. 1983, Lissauer 1984, Durisen 1984a,b). The characteristic time scale associated with this process is the gross erosion time t(sub g) the time it would take a ring region to be completed eroded if all impact ejecta were lost. This time scale is estimated to be about 10(exp 5) to 10(exp 6) years for a ring region with normal optical depth tau approximately 1. Earlier work by myself and collaborators developed the physical theory and simulation techniques to model this process (Durisen et al. 1989, Cuzzi and Durisen 1990). Detailed simulations, supported in part by this grant, have demonstrated that ballistic transport can produce observed structures in Saturn's rings, especially at and near the inner edges of the A and B Rings (Durisen et al. 1992, 1996). The structures of interest in the real rings are illustrated in Figures 1 and 2. Most of these structures were previously unexplained. The computational results plus analytic treatments place useful constraints on fundamental ring properties, including the indication of a relatively young ring age less than or equal 10(exp 8) years (see reviews by Nicholson and Dones 1991, Esposito 1993, Cuzzi 1995, and Porco 1995). This grant also supported development of the faster computational algorithms necessary to permit longer evolutions. Resulting simplications in the ballistic transport equations permitted an analytic linear stability analysis (Durisen 1995), which has provided considerable insight into ballistic transport processes and applications to Saturn's rings. All these accomplishments are described in more detail below.

Durisen, Richard H.↗
NASA NTRS1997

Effects of Acoustically Lined Cylindrical Ducts on Instability Waves in Confined Supersonic Jets

The pressure disturbances generated by an instability wave in the shear layer of a supersonic jet are studied for an axisymmetric jet inside a lined cylindrical duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions. These values are used to determine the growth rates and phase velocities of the instability waves and the radial pressure disturbance patterns. The study is confined to the dominant Kelvin-Helmholtz instability mode and to the region just downstream of the nozzle exit where the shear layer is growing but is still small in size compared to the radius of the duct. Numerical results are used to study the effects of changes in the outer flow, growth in the shear layer thickness, wall distance, wall impedance, and frequency. Results indicate that the effects of the duct wall on shear layer growth rates diminish as the outer flow increases. Also, wall reflections cause variations in growth rates depending on wall height and Strouhal number. These variations are due to the phase relationship between the outgoing and the reflected incoming pressure disturbances at the shear layer. The growth rate variations can be reduced and the maximum growth rate minimized by keeping the imaginary part of the impedance negative.

Dahl, Milo D.↗
NASA NTRS1997

The Stability of Radiatively Cooling Jets. 2: Nonlinear Evolution

We use two-dimensional time-dependent hydrodynamical simulations to follow the growth of the Kelvin-Helmholtz (K-H) instability in cooling jets into the nonlinear regime. We focus primarily on asymmetric modes that give rise to transverse displacements of the jet beam. A variety of Mach numbers and two different cooling curves are studied. The growth rates of waves in the linear regime measured from the numerical simulations are in excellent agreement with the predictions of the linear stability analysis presented in the first paper in this series. In the nonlinear regime, the simulations show that asymmetric modes of the K-H instability can affect the structure and evolution of cooling jets in a number of ways. We find that jets in which the growth rate of the sinusoidal surface wave has a maximum at a so-called resonant frequency can be dominated by large-amplitude sinusoidal oscillations near this frequency. Eventually, growth of this wave can disrupt the jet. On the other hand, nonlinear body waves tend to produce low-amplitude wiggles in the shape of the jet but can result in strong shocks in the jet beam. In cooling jets, these shocks can produce dense knots and filaments of cooling gas within the jet. Ripples in the surface of the jet beam caused by both surface and body waves generate oblique shock "spurs" driven into the ambient gas. Our simulations show these shock "spurs" can accelerate ambient gas at large distances from the jet beam to low velocities, which represents a new mechanism by which low-velocity bipolar outflows may be driven by high-velocity jets. Rapid entrainment and acceleration of ambient gas may also occur if the jet is disrupted. For parameters typical of protostellar jets, the frequency at which K-H growth is a maximum (or highest frequency to which the entire jet can respond dynamically) will be associated with perturbations with a period of - 200 yr. Higher frequency (shorter period) perturbations excite waves associated with body modes that produce internal shocks and only small-amplitude wiggles within the jet. The fact that most observed systems show no evidence for large-amplitude sinusoidal oscillation leading to disruption is indicative that the perturbation frequencies are generally large, consistent with the suggestion that pro- tostellar jets arise from the inner regions (r less than 1 AU) of accretion disks.

Stone, James M.↗
NASA NTRS1998

Supersonic Coaxial Jets: Noise Predictions and Measurements

The noise from perfectly expanded coaxial jets was measured in an anechoic chamber for different operating conditions with the same total thrust, mass flow, and exit area. The shape of the measured noise spectrum at different angles to the jet axis was found to agree with spectral shapes for single, axisymmetric jets. Based on these spectra, the sound was characterized as being generated by large turbulent structures or fine-scale turbulence. Modeling the large scale structures as instability waves, a stability analysis was conducted for the coaxial jets to identify the growing and decaying instability waves in each shear layer and predict their noise radiation pattern outside the jet. When compared to measured directivity, the analysis identified the region downstream of the outer potential core, where the two shear layers were merging, as the source of the peak radiated noise where instability waves, with their origin in the inner shear layer, reach their maximum amplitude. Numerical computations were also performed using a linearized Euler equation solver. Those results were compared to both the results from the instability wave analysis and to measured data.

Dahl, Milo D.↗
NASA NTRS1998

Dendritic Growth of Hard-Sphere Crystals

Recent observations of the disorder-order transition for colloidal hard spheres under microgravity revealed dendritic crystallites roughly 1-2 mm in size for samples in the coexistence region of the phase diagram. Order-of-magnitude estimates rationalize the absence of large or dendritic crystals under normal gravity and their stability to annealing in microgravity. A linear stability analysis of the Ackerson and Schaetzel model for crystallization of hard spheres establishes the domain of instability for diffusion-limited growth at small supersaturations. The relationship between hard-sphere and molecular crystal growth is established and exploited to relate the predicted linear instability to the well-developed dendrites observed.

Russel, W. B.↗
NASA NTRS1996

Nonlinear Response of Layer Growth Dynamics in the Mixed Kinetics-Bulk-Transport Regime

In situ high-resolution interferometry on horizontal facets of the protein lysozyme reveal that the local growth rate R, vicinal slope p, and tangential (step) velocity v fluctuate by up to 80% of their average values. The time scale of these fluctuations, which occur under steady bulk transport conditions through the formation and decay of step bunches (macrosteps), is of the order of 10 min. The fluctuation amplitude of R increases with growth rate (supersaturation) and crystal size, while the amplitude of the v and p fluctuations changes relatively little. Based on a stability analysis for equidistant step trains in the mixed transport-interface-kinetics regime, we argue that the fluctuations originate from the coupling of bulk transport with nonlinear interface kinetics. Furthermore, step bunches moving across the interface in the direction of or opposite to the buoyancy-driven convective flow increase or decrease in height, respectively. This is in agreement with analytical treatments of the interaction of moving steps with solution flow. Major excursions in growth rate are associated with the formation of lattice defects (striations). We show that, in general, the system-dependent kinetic Peclet number, Pe(sub k) , i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe(sub k) can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities under steady bulk nutrient crystallization conditions.

Vekilov, Peter G.↗
NASA NTRS1999

A Numerical Study of Low-Reynolds-Number Separation Bubbles

The present study uses two dimensional numerical simulations to study unsteady low-Reynolds-number separation bubbles. The numerical study is in two parts: (1) a two dimensional time-accurate Navier-Stokes solver is used to simulate flows over the APEX airfoil, and (2) a numerical procedure is developed for localized simulations of transitional separation bubbles. The 2-D computations of flow over the APEX airfoil show that the flow is unsteady with periodic vortex shedding. A linear stability analysis of the separated flow shows that the vortex shedding is caused due to the instability of the separated flow. For transonic flows over the APEX airfoil the vortex shedding is additionally influenced by the presence of shocks. The flowfield has two characteristic time scales, one corresponding to the vortex shedding and another corresponding to the movement of the shocks. The two dimensional (2-D) airfoil simulations also showed the presence of nonlinear effects in the separated region. To better understand the characteristics of separation bubbles a numerical procedure has been developed for localized separation bubble calculations. This procedure is used to perform computations for a flat plate separation bubble test case. The separation bubble is induced by specifying a velocity gradient in the freestream. The growth of disturbances in the separation bubble is analyzed by introducing disturbances upstream of the separation bubble.

Tatineni, Mahidhar↗
NASA NTRS1999

Magnetic Field Effect on the Stability of Flow Induced by a Rotating Magnetic Field

A linear stability analysis has been performed for the flow induced by a rotating magnetic field in a cylindrical column filled with electrically conducting fluid. The first transition is time-independent and results in the generation of Taylor vortices. The critical value of the magnetic Taylor number has been examined as a function of the strength of the transverse rotating magnetic field, the strength of an axial static magnetic field, and thermal buoyancy. Increasing the transverse field increases the critical magnetic Taylor number and decreases the aspect ratio of the Taylor vortices at the onset of instability. An increase in the axial magnetic field also increases the critical magnetic Taylor number but increases the aspect ratio of the Taylor vortices. Thermal buoyancy is found to have only a negligible effect on the onset of instability.

Mazuruk, K.↗
NASA NTRS1999

Magnetic Field Effect on the Stability of Flow Induced by a Rotating Magnetic Field

A linear stability analysis has been performed for the flow induced by a rotating magnetic field in a cylindrical column filled with electrically conducting fluid. The first transition is time- independent and results in the generation of Taylor vortices. The critical value of the magnetic Taylor number has been examined as a function of the strength of the transverse rotating magnetic field, the strength of an axial static magnetic field, and thermal buoyancy. Increasing the transverse field increases the critical magnetic Taylor number and decreases the aspect ratio of the Taylor vortices at the onset of instability. An increase in the axial magnetic field also increases the critical magnetic Taylor number but increases the aspect ratio of the Taylor vortices. Thermal buoyancy is found to have only a negligible effect on the onset of instability.

Mazuruk, K.↗
NASA NTRS1999

Exploring Mars: the Ares Payload Service (APS)

In last year's Mars Society convention we introduced the results of five years of studies of space launch capability for the second millennium. We concluded that Single Stage to Orbit (SSTO) vehicles such as the Delta Clipper X33, and X34 cannot make it to orbit from the Earth's surface. Whether taking off vertically or horizontally or landing vertically or horizontally, the rocket equations, the performance of available fuels, and the realities of the weight and strength of materials leave no margin for payload. The promised savings from SSTO systems are illusory. However, a configuration that is able to deliver useful payload to orbit is the Single step to Orbit, SsTO, a rocket plane that is released fully fueled, from 35,000 to 40,000 feet altitude. Three approaches have been proposed. The Hot'l and Molnya Corporation designs carry the fueled rocket plane to altitude on the back of a carrier aircraft. In this design the carrier aircraft is Russia's Antonov 225 the world's largest cargo plane. The rocket plane is a modified version of the Buran, Russia's own space shuttle. Another configuration is Kelly Aviation's concept in which the fully fueled rocket plane is towed to altitude by the cargo plane and then released. A third approach is based on the early "X" planes, which were dropped from the belly of the carrier plane. While the rocket equations indicate that these three concepts can deliver useful payloads, the Stanford review found significant advantages to the approach of Pioneer Rocket, in which the rocket plane flies up to the carrier plane with conventional jet engines, docks, and then loads on the oxidizer for the flight to orbit. This architecture has more reasonable abort modes in case of system failure in either aircraft and can deliver a larger final payload to orbit for a given sized carrier. The Stanford recommendation is that the carrier aircraft be the Antonov 225. A design based on this was presented in a report last year. Refinements to the design notably an improved re-entry cooling system and fueling stability analysis were done this year. More technical detail and a proposed international consortium to develop the SSTO is presented in another session of this year's Mars convention. We believe that there will be no human exploration of Mars based on the Shuttle or Expendable launch vehicles, and no resources available except for a cooperative international program. However, just as the world is learning to cooperate in peacekeeping, we hold out the hope that similar cooperation will develop for Mars exploration. With that in mind, this year we asked the question- "How will the human mission get to Mars if it has to use the SsTO for transportation?"

Bowen, Justin↗
NASA NTRS1999

Magnetic Control of Convection in Electrically Nonconducting Fluids

Inhomogeneous magnetic fields exert a body force on electrically nonconducting, magnetically permeable fluids. This force can be used to compensate for gravity and to control convection. The effects of uniform and nonuniform magnetic fields on a laterally unbounded fluid layer heated from below or above are studied using a linear stability analysis of the Navier-Stokes equations supplemented by Maxwell's equations and the appropriate magnetic body force. For a uniform oblique field, the analysis shows that longitudinal rolls with axes parallel to the horizontal component of the field are the rolls most unstable to convection. The corresponding critical Rayleigh number and critical wavelength for the onset of such rolls are less than the well-known Rayleigh-Benard values in the absence of magnetic fields. Vertical fields maximize these deviations, which vanish for horizontal fields. Horizontal fields increase the critical Rayleigh number and the critical wavelength for all rolls except longitudinal rolls. For a nonuniform field, our analysis shows that the magnetic effect on convection is represented by a dimensionless vector parameter which measures the relative strength of the induced magnetic buoyancy force due to the applied field gradient. The vertical component of this parameter competes with the gravitational buoyancy effect, and a critical relationship between this component and the Rayleigh number is identified for the onset of convection. Therefore, Rayleigh-Benard convection in such fluids can be enhanced or suppressed by the field. It also shows that magnetothermal convection is possible in both paramagnetic and diamagnetic fluids. Our theoretical predictions for paramagnetic fluids agree with experiments. Magnetically driven convection in diamagnetic fluids should be observable even in pure water using current technology.

Huang, Jie↗
NASA NTRS1999

Material Instabilities in Particulate Systems

Following is a brief summary of a theoretical investigation of material (or constitutive) instability associated with shear induced particle migration in dense particulate suspensions or granular media. It is shown that one can obtain a fairly general linear-stability analysis, including the effects of shear-induced anisotropy in the base flow as well as Reynolds dilatancy. A criterion is presented here for simple shearing instability in the absence of inertia and dilatancy.

Goddard, J. D.↗
NASA NTRS1999

Electrohydrodynamic Stability of a Liquid Bridge: The "ALEX" Experiment

To provide insight into the roles of electrical forces, experiments on the stability of a liquid bridge were carried out during the 1996 Life And Microgravity Science Mission on the space shuttle Columbia. In terrestrial laboratories a Plateau configuration (where the bridge is surrounded by a matched density liquid) is necessary to avoid deformation due to buoyancy. This complicates the electrical boundary conditions, since charge is transported across the liquid-liquid interface. In the microgravity environment, a cylindrical bridge can be deployed in a gas which considerably simplifies the boundary condition. Nevertheless, to provide a tie-in to terrestrial experiments, two-phase experiments were carried out. The agreement with previous work was excellent. Then several experiments were conducted with a bridge deployed in a dielectric gas, SF6. In experiments with steady fields, it was found that the bridge was less stable than predicted by a linearized stability analysis using the Taylor-Melcher leaky dielectric model.

Burcham, C. L.↗
NASA NTRS2001

Lamellar Spacing Selection in Al-Si Eutectic System: a Theoretical Investigation

It is well known that irregular eutectics such as Al-Si and Fe-C exhibit larger lamellar spacings and undercoolings compared to the predictions made by the Jackson and Hunt (JH) theory. In this paper, we reexamine the JH theory and relax some of the assumptions used in that treatment. The modified theoretical model has enhanced capabilities to predict the lamellar spacing in both regular and irregular eutectics. For the Al-Si system in particular we identified two different spacing selection mechanisms:a) for a particular growth rate, a nearly isothermal interface can be achieved at a unique minimum spacing lambda(sub I); b) the average spacing in the microstructure (lambda(sub av) greater than lambda(sub I)) is essentially dictated by the undercooling of the faceted phase. Based on the modified theoretical model a semi-empirical expression has been developed to account for the influence of the temperature gradient. Application of a Mullin and Sekerka type stability analysis for eutectics will also be presented and the results compared to the modified JH model. It will be shown that the both theoretical approaches are in good agreement with each other and also with the published experimental measurements.

Catalina, Adrian V.↗