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At least 163 records · Page 9
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NASA NTRS1994

The behavior of unsteady thermocapillary flows

The thermocapillary-driven flow of a liquid in a shallow slot provides a simple model to explore the effects of free-surface deflection and end walls on the stability of the flow. Such an investigation may be useful in understanding the complex flow seen in processes such as the float-zone refining of single crystals. A linear stability analysis of the viscously-dominated slot flow indicates stable basic states to both tow- and three-dimensional infinitesimal disturbances for capillary numbers below 43.3. Above this capillary number steady solutions do not exist. We also discuss current work involving the development of an inertially-dominated slot-flow model using singular perturbation methods. If these flows are unstable, inertial effects would be the only possible cause of the instability.

Vrane, David R.↗
NASA NTRS1994

Shear stabilization of solidification fronts

A linear-stability analysis is performed on the interface formed during the directional solidification of a dilute binary alloy in the presence of a time-periodic flow. In general, the flow is generated by the elliptical motion of the crystal parallel to the interface. The presence of the flow can either stabilize or destabilize the system relative to the case without flow with the result depending on the frequency and amplitude of the oscillations as well as the properties of the material. In the particular, we find that the morphological instability present in the absence of flow can be entirely suppressed with respect to disturbances of the same frequency as the oscillation.

Davis, Stephen H.↗
NASA NTRS1994

Two-layer viscous instability in a rotating couette device

A novel experiment to study the interfacial shear instability between two liquids is described. Density-matched immiscible liquids are confined between concentric cylinders such that the interface is parallel to the cylinder walls. Interfacial waves that develop because of viscosity differences between the shearing fluids are studied as a function of rotation rate and depth ratio using optical techniques. Conditions neutral stability and the most unstable wavenumber agree reasonably well with predictions from linear stability analysis of the Navier-Stokes equations. Illumination using laser sheets allows precise measurement of the interface shape. Future experiments will verify the correctness of weakly nonlinear theories that describe energy transfer and saturation of wave growth by nonlinear effects. Measurements of solitary wave shapes, that occur far above neutral stability, will be compared to similar measurements for systems that have gravity as an important force to determine how gravity effects large disturbances. These results will be used to interpret slug and annular flow data that have been obtained in other mu g studies.

Gallagher, Christopher↗
NASA NTRS1992

Role of cross-field current instability in substorm onsets and intensifications

A cross field current instability is investigated as a potential mechanism for current reduction/disruption during substorm onsets and intensifications. Linear stability analysis shows that, for sufficiently strong current density, the instability can occur in the plasma sheet with a growth time comparable to the substorm onset time and excite waves with a significant electromagnetic component. Nonlinear analysis shows that the wave growth reaches the nonlinear stage in less than one ion gyroperiod and can reduce the cross tail current by approximately 15 to 28 of its initial value at saturation. The resulting anomalous resistivity is 11 to 12 orders of magnitude above the classical value. For a typical current reduction, the plasma in the disruption region is subjected to an earthward force. The substorm development scenario constructed based on this instability can readily account for a large number of substorm features.

Lui, Anthony T. Y.↗
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 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 NTRS1995

Hydrodynamic Stability of Multicomponent Droplet Gasification in Reduced Gravity

This investigation addresses the problem of hydrodynamic stability of a two-component droplet undergoing spherically-symmetrical gasification. The droplet components are assumed to have characteristic liquid species diffusion times that are large relative to characteristic droplet surface regression times. The problem is formulated as a linear stability analysis, with a goal of predicting when spherically-symmetric droplet gasification can be expected to be hydrodynamically unstable from surface-tension gradients acting along the surface of a droplet which result from perturbations. It is found that for the conditions assumed in this paper (quasisteady gas phase, no initial droplet temperature gradients, diffusion-dominated gasification), surface tension gradients do not play a role in the stability characteristics. In addition, all perturbations are predicted to decay such that droplets were hydrodynamically stable. Conditions are identified, however, that deserve more analysis as they may lead to hydrodynamic instabilities driven by capillary effects.

Aharon, I.↗
NASA NTRS1996

The Effects of Acoustic Treatment on Pressure Disturbances From a Supersonic Jet in a Circular Duct

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 circular duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions at each axial location. These values are used to determine the growth rates and phase velocities of the instability waves and the near field 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, and wall impedance, and the effects of these changes on non-axisymmetric modes. The primary results indicate that the effects of the duct wall on stability characteristics diminish as the outer flow increases and as the jet azimuthal mode number increases. Also, wall reflections are reduced when using a finite impedance boundary condition at the wall; but in addition, reflections are reduced and growth rates diminished by keeping the imaginary part of the impedance negative when using the negative exponential for the harmonic dependence.

Dahl, Milo D.↗
NASA NTRS1997

Stability of Thin Liquid Sheet Flows

A two-dimensional, linear stability analysis of a thin nonplanar liquid sheet flow in vacuum is carried out. A sheet flow created by a narrow slit of W and tau attains a nonplanar cross section as a consequence of cylinders forming on the sheet edge under the influence of surface tension forces. The region where these edge cylinders join the sheet is one of high curvature, and this is found to be the location where instability is most likely to occur. The sheet flow is found to be unstable, but with low growth rates for symmetric wave disturbances and high growth rates for antisymmetric disturbances. By combining the symmetric and antisymmetric disturbance modes, a wide range of stability characteristics is obtained. The product of unstable growth rate and flow time is proportional to the width-to-thickness ratio of the sift generating the sheet Three-dimensional effects can alter these results, particularly when the sheet length-to-width ratio is not much greater than unity.

McConley, Marc W.↗
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 NTRS1999

Potential Flow Interactions With Directional Solidification

The effect of convective melt motion on the growth of morphological instabilities in crystal growth has been the focus of many studies in the past decade. While most of the efforts have been directed towards investigating the linear stability aspects, relatively little attention has been devoted to experimental and numerical studies. In a pure morphological case, when there is no flow, morphological changes in the solid-liquid interface are governed by heat conduction and solute distribution. Under the influence of a convective motion, both heat and solute are redistributed, thereby affecting the intrinsic morphological phenomenon. The overall effect of the convective motion could be either stabilizing or destabilizing. Recent investigations have predicted stabilization by a flow parallel to the interface. In the case of non-parallel flows, e.g., stagnation point flow, Brattkus and Davis have found a new flow-induced morphological instability that occurs at long wavelengths and also consists of waves propagating against the flow. Other studies have addressed the nonlinear aspects (Konstantinos and Brown, Wollkind and Segel)). In contrast to the earlier studies, our present investigation focuses on the effects of the potential flow fields typically encountered in Hele-Shaw cells. Such a Hele-Shaw cell can simulate a gravity-free environment in the sense that buoyancy-driven convection is largely suppressed, and hence negligible. Our interest lies both in analyzing the linear stability of the solidification process in the presence of potential flow fields, as well as in performing high-accuracy nonlinear simulations. Linear stability analysis can be performed for the flow configuration mentioned above. It is observed that a parallel potential flow is stabilizing and gives rise to waves traveling downstream. We have built a highly accurate numerical scheme which is validated at small amplitudes by comparing with the analytically predicted results for the pure morphological case. We have been able to observe nonlinear effects at larger times. Preliminary results for the case when flow is imposed also provide good validation at small amplitudes.

Buddhavarapu, Sudhir S.↗
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

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.↗