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NASA NTRS1991

A comparison of numerical methods for the Rayleigh equation in unbounded domains

A second-order finite difference and two spectral methods, including a Chebyshev tau and a Chebyshev collocation method were implemented to determine the linear hydrodynamic stability of an unbounded shear flow. The velocity profile of the basic flow in the stability analysis mimicks that of a one-stream free mixing layer. Local and global eigenvalue solution methods are used to determine individual eigenvalues and the eigenvalue spectrum, respectively. The calculated eigenvalue spectrum includes a discrete mode, a continuous spectrum associated with the equation singularity and a continuous spectrum associated with the domain unboundedness. The efficiency and the accuracy of these discretization methods in the prediction of the eigensolutions of the discrete mode were evaluated by comparison with a conventional shooting procedure. Their capabilities in mapping out the continuous eigenvalue spectra are also discussed.

Liou, W. W.↗

NASA NTRS1990

Instability of a supersonic shock-free elliptic jet

A comparison of the measured and the computed spatial stability properties of an aspect ratio 2, supersonic, shock free, elliptic jet is presented. The shock free nature of the elliptic jet furnishes a perfect test of the validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with the linear hydrodynamic stability theory. Aerodynamic and acoustic data are measured to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. The measured mean velocity profiles are employed to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles utilized in the stability analysis. It is shown that the measured frequency associated with peak amplitude noise radiation agrees with that frequency predicted to dominate the large scale structure near the end of the potential core.

Baty, Roy S.↗

NASA NTRS1990

Morphological instability in a float zone

This paper examines the morphological instability of the freezing interface of the float zone in a crystal sheet for which the height of the liquid zone L = Lf + Lm (where Lf and Lm are the planar positions of the solidifying and melting interfaces) is smaller than the width and the thickness of the sheet. The Lf and Lm positions are calculated, and basic state concentration profiles are determined for a planar interfacial system. A linear stability analysis of this system is performed showing that the growth rate of disturbances is a modified version of the growth rate for a directional solidification system. It was found that shorter melt zone configurations are less susceptible to long wavelength morphological instability, indicating that, to suppress morphological instability in a float zone system, it is necessary to decrease the liquid zone height.

Humphreys, Laura B.↗

NASA NTRS1990

Modeling and stability of segmented reflector telescopes - A decentralized approach

The decentralization of a segmented reflector telescope based on a finite-element model of its structure is considered. The decentralization of the system at the panel level is considered. Each panel is originally treated as an isolated subsystem so that the controller design is performed independently at the local level, and then applied to the composite system for stability analysis. The panel-level control laws were designed by means of pole placement using local output feedback. Simulation results show a better 1000:1 vibration attenuation in panel position when compared to the open-loop system. It is shown that the overall closed-loop system is exponentially stable provided that certain conditions are met. The advantage to the decentralized approach is that the design is performed in terms of the low-dimensionality subsystems, thus drastically reducing the design computational complexities.

Ryaciotaki-Boussalis, Helen A.↗

NASA NTRS1991

Robust controller designs for second-order dynamic systems - A virtual passive approach

A robust controller design is presented for second-order dynamic systems. The controller is model-independent and itself is a virtual second-order dynamic system. Conditions on actuator and sensor placements are identified for controller designs that guarantee overall closed-loop stability. The dynamic controller can be viewed as a virtual passive damping system that serves to stabilize the actual dynamic system. The control gians are interpreted as virtual mass, spring, and dashpot elements that play the same roles as actual physical elements in stability analysis. Position, velocity, and acceleration feedback are considered. Simple examples are provided to illustrate the physical meaning of this controller design.

Juang, Jer-Nan↗

NASA NTRS1991

On the viscous modes of instability of a trailing line vortex

A viscous linear stability analysis of a trailing line (Batchelor) vortex is presented. Employing a staggered Chebyshev spectral collocation technique, very accurate results were obtained. The destabilizing role of viscous forces has been shown to produce two types of viscous instability modes. These viscous disturbances consist of an axisymmetric mode and an asymmetric mode. Both disturbances are long-wave instabilities with maximum growth rates which are orders of magnitude smaller than the inviscid modes which have been found by others. Comparison with experimental results and condensation trail observations are found to be in good qualitative agreement with the present study.

Khorrami, Mehdi R.↗

NASA NTRS1991

Asynchronous, macrotasked relaxation strategies for the solution of viscous, hypersonic flows

A point-implicit, asynchronous macrotasked relaxation of the steady, thin-layer, Navier-Stokes equations is presented. The method employs multidirectional, single-level storage Gauss-Seidel relaxation sweeps, which effectively communicate perturbations across the entire domain in 2n sweeps, where n is the dimension of the domain. In order to enhance convergence the application of relaxation factors to specific components of the Jacobian is examined using a stability analysis of the advection and diffusion equations. Attention is also given to the complications associated with asynchronous multitasking. Solutions are generated for hypersonic flows over blunt bodies in two and three dimensions with chemical reactions, utilizing single-tasked and multitasked relaxation strategies.

Gnoffo, Peter A.↗

NASA NTRS1991

On spatial instability of a swirling jet - Theory and experiment

The spatial instability of a swirling jet is investigated both experimentally and theoretically. A hydrodynamic stability analysis is applied to an inviscid incompressible top-hat jet, with a swirl distribution of solid-body rotation and free vortex in and outside the vortex core, respectively. Both plane and helical instability modes are examined. It is found that the top-hat jet with swirl distribution of Rankine vortex type is unstable in all the modes studied. The higher the positive helicity, the less spatially unstable the jet behavior; the higher the negative helicity, the more spatially unstable this behavior becomes. A comparison is made between theoretical results and experimental data on a low-intensity swirling jet. The trend of the initial growth of the instability waves in the near field is captured.

Wu, C.↗

NASA NTRS1991

Numerical simulation of shock-induced combustion/detonation in a premixed H2-air mixture using Navier-Stokes equations

A numerical study was conducted to address the structural stability of the oblique detonation wave. An attempt was made to isolate the structural instability predicted by Buckmaster's (1990) linear stability analysis. For this study a detailed viscous flowfield with finite-rate chemistry was computed past a 20-deg wedge. The finite-rate chemistry was modeled by using a seven-species and seven-reaction model. Instability modes were isolated by analyzing the Fourier power spectrum of the H2O mass fraction at selected sample stations. No unstable temporal modes with dominant frequency were isolated. It was concluded that the instability which is predicted by the Buckmaster work was a high-frequency low-amplitude phenomenon. For engineering purposes, the oblique detonation wave is a stable phenomenon as long as sufficient levels of overdrive are present.

Singh, D. J.↗

NASA NTRS1991

Isothermal, Compton-heated coronae above accretion disks

The structure of Compton-heated coronae above accretion disks is studied here by using analytic and numerical approaches are used here to determine the direct and scattered radiation reaching the base of the corona for a range of central source luminosities. It is found that the outer region of the corona is unaffected by multiple scattering in the interior, provided that the luminosity of the central source is sufficient below the Eddington limit. How attenuation and scattering by the corona affects the strength of chromospheric emission lines is determined, as is the condition for which the irradiation due to the central source exceeds the locally generated flux from the disk. Finally, it is shown that the stability analysis for irradiated accretion disks of Tuchman et al. is not substantially altered by the corona.

Ostriker, Eve C.↗

NASA NTRS1992

A numerical model for atomization-spray coupling in liquid rocket thrust chambers

The physical process of atomization is an important consideration in the stable operation of liquid rocket engines. Many spray combustion computational fluid dynamics (CFD) codes do not include an atomization sub-model but assume arbitrary drop size distributions, drop initial locations, and velocities. A method of coupling an atomization model with the spray model in a REFLEQS CFD code is presented. This method is based on a jet-embedding technique in which the equations governing the liquid jet core are solved separately using the surrounding gas phase conditions. The droplet initial conditions are calculated using a stability analysis appropriate for the atomization regime of liquid jet break-up. This novel coupling model is used to analyze the SSME fuel preburner single injector flow. Results of the diffusion flame characteristics in a single injection element will be presented. The effect of relative velocity, mixture ratio and droplet initial conditions will be shown. The predictions of present atomization model is compared with that of the widely used CICM correlation. The results are also compared with the predictions of volume-of-fluid method.

M. G. Giridharan↗

NASA NTRS1992

Comparison between the PISO algorithm and preconditioning methods for compressible flow

Two widely used family of algorithms, pressure-based and density-based methods, have been developed for computational fluid dynamics (CFD) problems over the years. Pressure-based methods (such as SIMPLE and PISO) use a Poisson-like equation for updating pressure instead of the continuity equation, while density-based methods use the continuity equation to update density (an equation of state is used to provide density in pressure based schemes and pressure in density based schemes). Pressure-based methods were developed originally for incompressible flows at low Reynolds numbers and were then extended to high Reynolds numbers and compressible applications. On the other hand, density based methods were originally developed for transonic flows and have been extended down to low Mach numbers through the use of preconditioning techniques. We compare these two very different approaches to solving the Navier-Stokes equations in order to gain an understanding of their similarities and differences. Specifically, we consider the PISO scheme as a representative pressure-based method and contrast it with a recently developed preconditioning scheme. We also compare the relative performance of the PISO algorithm with a Euler implicit algorithm that is employed to solve the preconditioned equations by means of a vector stability analysis.

Merkle, Charles L.↗

NASA NTRS1991

The radial-azimuthal stability of accretion disks - Gas pressure contributions

A radial-azimuthal stability analysis of a thin, alpha disk accretion flow is presented. The proportion of radiation pressure, Pr, of the unperturbed flow is allowed to vary according to the parameter beta = Pr/P, where P is the total pressure. As is the case for a purely radial analysis, the disk is stable for beta equal to or less than 0.6. However, the coupling of radial and azimuthal perturbations eliminates the viscous instability for such nonradial modes for all values of beta. The group velocity of the retrograde thermal mode is calculated as a function of beta.

Mckee, M. R.↗

NASA NTRS1990

Instability during directional solidification - Gravitational effects

After an elementary introduction to solidification, recent research that attempts to understand the interaction of fluid flow with a crystal-melt interface under gravitational influence using linear stability analysis is reviewed. Recent numerical calculations of fluid flow and interface morphology during alloy solidification are briefly discussed.

Coriell, S. R.↗

NASA NTRS1992

Fluid flow in a jet and the Ca XIX line profiles observed during solar flares

The present study considers two types of fluid models as methods for reproducing the blueshifts and line broadening observed in soft X-ray lines during the rise of solar flares. The fluid models representing the laminar flow of material in a jet and through a pipe were used to derive the velocity at each location in the flow. The optimal values for the free parameters in the jet model were within the ranges expected for solar flare conditions. The jet was much smaller than typical flare volumes estimated from spatial images, but the resulting densities were consistent with the upper limit of densities derived using density-sensitive line ratios. This supports previous reports of small filling factors and is interpreted as evidence for a chromospheric origin for the flow. Stability analysis indicates that, although the laminar jet can reproduce the observations, instabilities may cause the flow to become turbulent, and that this laminar treatment is not strictly valid.

Bornmann, P. L.↗

NASA NTRS1992

Morphological instability of a thermophoretically growing deposit

The stability of the planar interface of a structureless solid growing from a depositing component dilute in a carrier fluid is studied when the main solute transport mechanism is thermal (Soret) diffusion. A linear stability analysis, carried out in the limit of low growth Peclet number, leads to a dispersion relation which shows that the planar front is unstable either when the thermal diffusion factor of the condensing component is positive and the latent heat release is small or when the thermal diffusion factor is negative and the solid grows over a thermally-insulating substrate. Furthermore, the influence of interfacial energy effects and constitutional supersaturation in the vicinity of the moving interface is analyzed in the limit of very small Schmidt numbers (small solute Fickian diffusion). The analysis is relevant to physical vapor deposition of very massive species on cold surfaces, as in recent experiments of organic solid film growth under microgravity conditions.

Castillo, Jose L.↗

NASA NTRS1992

Radiative instabilities and 1000 second fluctuations in astrophysical masers

A stability analysis for small (linear) perturbations is presented for the radiation in astrophysical masers treated in the usual, linear maser approximation. Instabilities that oscillate with a period of about L/c, where L is the length of the maser are found. They occur (1) when the maser is partly but not heavily saturated, (2) when the decay rate Gamma for the molecular states is near c/L, and (3) when the product of the brightness temperature T sub 0 of the incident radiation and the angle for the beaming is less than a critical value that depends upon the particular masing transition. A fourth parameter, the fractional inversion in the pumping multiplied by (T sub 0/frequency), determines the importance of spontaneous emission which can eliminate the instabilities. These instabilities are a likely cause for the fluctuations in the radiation from the 18 cm OH masers that have been reported to occur on time scales as short as 1000 s. The calculations are applicable to other types of astrophysical masers as well, and suggest that spontaneous emission will prevent similar instabilities in the H2O and SiO masers.

Scappaticci, Gerardo A.↗

NASA NTRS1992

Break-down of a planar liquid-solid interface during directional solidification - Influence of convection

The influence of convection on the development of morphological instability at the liquid-solid interface during directional solidification in a positive thermal gradient has been examined in Pb-10 wt pct Sn and succinonitrile-1.9 wt pct acetone. The onset of interfacial breakdown occurs at higher growth speeds in the presence of convection. The linear stability analysis due to Favier and Rouzaud which uses the 'deformable' mass flow boundary layer concept shows a good agreement with the experimentally observed behavior.

Tewari, S. N.↗