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Results for “stability theory”

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At least 289 records · Page 16

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NASA NTRS1982

Influence of diffusion and convective transport on dendritic growth in dilute alloys

Experimentation has been carried out in which the kinetics and morphology of dendritic growth were measured as a function of thermal supercooling, solute concentration, and spatial orientation of the dendritic growth axis. The crystal growth system studied is succinonitrile, NC(CH2)2CN, with additions of argon (up to 0.1 mole percent). This system is especially useful as a model for alloy studies because kinetic data are available for high purity (7-9's) succinonitrile. The influence of the solute, at fixed thermal supercooling, is to increase the growth velocity and correspondingly decrease intrinsic crystal dimensions. Morphological measurements are described in detail relating tip size, perturbation wavelength, supercooling, and solute concentration. The analysis of these effects based on morphological stability theory is also discussed, and experiments permitting the separation of convective and diffusive heat transport during crystal growth of succinonitrile are described. The studies underscore the importance of gravitationally-induced buoyancy effects on crystal growth.

Glicksman, M. E.↗

NASA NTRS1984

Alternative experiments using the geophysical fluid flow cell

This study addresses the possibility of doing large scale dynamics experiments using the Geophysical Fluid Flow Cell. In particular, cases where the forcing generates a statically stable stratification almost everywhere in the spherical shell are evaluated. This situation is typical of the Earth's atmosphere and oceans. By calculating the strongest meridional circulation expected in the spacelab experiments, and testing its stability using quasi-geostrophic stability theory, it is shown that strongly nonlinear baroclinic waves on a zonally symmetric modified thermal wind will not occur. The Geophysical Fluid Flow Cell does not have a deep enough fluid layer to permit useful studies of large scale planetary wave processes arising from instability. It is argued, however, that by introducing suitable meridional barriers, a significant contribution to the understanding of the oceanic thermocline problem could be made.

Hart, J. E.↗

NASA NTRS1984

Instability and transition in supersonic boundary layers

Recently obtained flight transition data for a 5-deg half-angle cone at Mach numbers of 1.2, 1.35, 1.6, and 1.92, together with 'quiet' tunnel data at Mach 3.5, are analyzed by linear compressible stability theory. The results obtained indicate that the exponent N ranges in value between 9 and 11, which is in keeping with values previously determined for subsonic flows. Computations show that the transition in both the flight and quiet wind tunnel experiments was due to oblique first-mode disturbances.

Malik, M. R.↗

NASA NTRS1984

Impurity effects in dendritic solidification

A quantitative calculation of growth rates and tip radii is presented for dendrites growing in undercooled dilute solutions. Included in the calculations are the capillary corrections to the steady-state Ivantsov needle-crystal solutions. The results show good agreement with available experimental data and support the validity of the marginal-stability theory of dendritic growth.

Karma, A.↗

NASA NTRS1985

The wave pattern produced by a point source on a rotating disk

It is pointed out that the boundary layer on a rotating disk is important in stability theory because it provides a particularly simple way to study the important phenomenon of crossflow instability. This type of instability is responsible for early transition on sweptback wings. Mack and Kendall (1983) have studied the wave patterns formed by harmonic point sources in a Blasius boundary layer on the basis that the source uniformly excites all oblique normal modes of the source frequency. The calculation procedure for planar boundary layers was modified to fit the different geometry of the rotating disk and the lack of an axis of symmetry. Calculations were performed of the wave pattern produced by a zero-frequency point source located at the Reynolds number of the artificial roughness element in an experiment conducted by Wilkinson and Malik (1983). The results provided in the present investigation confirm that the experimental wave pattern is a superposition of the complete azimuthal wavenumber spectrum of zero-frequency normal modes with uniform initial amplitude and phase.

Mack, L. M.↗

NASA NTRS1985

Analysis of transitional separation bubbles on infinite swept wings

A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. A series of two-dimensional calculations are presented as a verification of the prediction capability of the interaction technique with this transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

Davis, R. L.↗

NASA NTRS1986

Analysis of transitional separation bubbles on infinite swept wings

A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

Davis, R. L.↗

NASA NTRS1986

Disturbance functions of the Goertler instability on an airfoil

Goertler vortices arise in boundary layers along concave surfaces due to centrifugal effects. This paper presents some results of an experiment conducted to study the development of these vortices on an airfoil with a pressure gradient in the concave region where an attached laminar boundary layer was insured with suction through a perforated panel. A sublimating chemical technique was used to visualize Goertler vortices and the velocity field was measured by laser velocimetry. Experimental disturbance functions are compared with those predicted by the linear stability theory. The trend of vortex amplification in the concave zone and damping in the following convex region is shown to essentially follow the theoretical predictions.

Dagenhart, J. R.↗

NASA NTRS1986

A methodology for designing robust multivariable nonlinear control systems

A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.

Grunberg, D. B.↗

NASA NTRS1987

Spatially growing disturbances in a high velocity ratio two-stream, coplanar jet

The influence of cold and heated secondary flow on the instability of a two-stream, coplanar jet having a 0.7 Mach number heated primary jet for a nominal fan to primary velocity ratio of 0.68 was investigated by means of inviscid linearized stability theory. The instability properties of spatially growing axisymmetric and first order azimuthal disturbances were studied. The instability characteristics of the two-stream jet with a velocity ratio of 0.68 are very different from those of a single stream jet, and a two-stream, coplanar jet having a 0.9 Mach number heated primary jet and a cold secondary jet for a fan to primary velocity ratio of 0.30. For X/D = 1 and in comparison to the case where the velocity ratio was 0.3, the presence of the fan stream with a velocity ratio of 0.68 enhanced the instability of the jet and increased the unstable frequency range. However, the axisymmetric mode (m = 0) and the first order azimuthal mode (m = 1) have similar spatial growth rates where the velocity ratio is 0.68 while for a velocity ratio of 0.3 the growth rate of the first order azimuthal mode (m = 1) is greater. Comparing the cold and hot secondary flow results showed that for a velocity ratio of 0.68 the growth rate is greater for cold.

Miles, J. H.↗

NASA NTRS1986

Spatially growing disturbances in a two-stream, coplanar jet

The influence of the outer stream on the instability of a two-stream, coplanar jet with only the primary (central) stream heated for a nominal outer-to-primary velocity ratio of 0.3 was investigated by means of inviscid linearized stability theory. The instability properties of spatially growing axisymmetric and first order azimuthal disturbances were studied. It was found that the instability characteristics of the two stream jet are very different from those of a single stream jet. The presence of the outer stream enhanced the instability of the jet and increased the unstable frequency range for the first order azimuthal mode.

Miles, Jeffrey H.↗

NASA NTRS1987

Influence of suction and curvature on the growth of Goertler vortices on an airfoil

Laser velocimetry (LV) was used to study the development of Goertler vortices in a laminar boundary layer on a 1.83 m chord airfoil model. The vortex pattern was visualized using a sublimating chemical technique. A fixed, essentially uniform vortex spacing was observed throughout the test region for any given freestream velocity but the vortex wavelength varied significantly with change in freestream velocity. An appreciable, abrupt decrease in streak contrast indicated vortex damping in the convex region and was confirmed by disturbance functions determined from LV measurements. Moderate variation in suction levels did not alter the vortex spacing but appreciably modified the vortex strength. The experimental results on the growth of Goertler vortices along the concave surface and the effect of suction are compared with results from linear stability theory.

Mangalam, S. M.↗

NASA NTRS1987

Spatially growing disturbances in a high velocity ratio two-stream, coplanar jet

Miles, Jeffrey H.↗

NASA NTRS1986

Some insights into the stability of difference approximations for hyperbolic initial-boundary-value problems

This paper states a conjecture which relates Lax-Richmyer stability to the algebraic test of the stability theory of Gustafsson, Kreiss, and Sundstrom (1972), developed for difference approximations to initial boundary value problems where the matrix size J increases linearly with n as n goes to infinity. This corresponds to mesh refinement in both space and time for t = n x delta t = constant.

Warming, Robert F.↗

NASA NTRS1987

Absolute instability of the Gaussian wake profile

Linear parallel-flow stability theory has been used to investigate the effect of viscosity on the local absolute instability of a family of wake profiles with a Gaussian velocity distribution. The type of local instability, i.e., convective or absolute, is determined by the location of a branch-point singularity with zero group velocity of the complex dispersion relation for the instability waves. The effects of viscosity were found to be weak for values of the wake Reynolds number, based on the center-line velocity defect and the wake half-width, larger than about 400. Absolute instability occurs only for sufficiently large values of the center-line wake defect. The critical value of this parameter increases with decreasing wake Reynolds number, thereby indicating a shrinking region of absolute instability with decreasing wake Reynolds number. If backflow is not allowed, absolute instability does not occur for wake Reynolds numbers smaller than about 38.

Hultgren, Lennart S.↗

NASA NTRS1988

Design and fabrication requirements for low-noise supersonic/hypersonic wind tunnels

Analyses of NASA Langley experimental results obtained from efforts to develop a low disturbance wind tunnel by means of linear stability theory have shown that the amplification of Gortler vortices on the concave walls of nozzles at Mach numbers from 3 to 5 are the cause of transition. The theory is used to design advanced nozzles for Mach numbers of 3.5 and 6 which can generate substantially longer quiet test regions. Transition on the nozzle walls is noted to be extremely sensitive to nozzle wall roughness and contamination.

Beckwith, I. E.↗

NASA NTRS1988

Comparison of boundary-layer transition on a cone and flat plate at Mach 3.5

NASA-Langley's Pilot Low-Disturbance Tunnel has been used to obtain boundary layer transition data on a cone and flat plate at Mach 3.5. The transition Reynolds numbers measured under these low noise conditions are higher than those in conventional noisy tunnels by a factor of 3 in the case of the cone and of seven in that of the flat plate. Transition predictions based on compressible linear stability theory and the e exp N method, for N=10, are in excellent agreement with the measured locations with transition onset for both the cone and flat plate under these low noise conditions.

Chen, F.-J.↗

NASA NTRS1987

Stability of three-dimensional boundary layers

The computational modeling of the transition process characteristic of flows over swept wings is discussed. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full three-dimensional Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that regular stability theory is insufficient to explain the discrepancies between experiments and between theory and experiment. The leading edge region of a swept wing will be considered in a three-dimensional spatial simulation with random disturbances as the initial conditions.

Reed, Helen L.↗