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NASA NTRS1983

On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid

The stability of the two-dimensional flow induced by the tranverse oscillation of a cylinder in a viscous fluid is investigated in both the linear and weakly nonlinear regime. The major assumption that is made to simplify the problem is that the oscillation frequency is large in which case an unsteady boundary layer is set up on the cylinder. Results are given for cylinders of elliptic cross section and it is found that for any given eccentricity the most dangerous configuration is when the cylinder oscillates parallel to its minor axis. Some discussion of nonlinear effects is also given and for the circular cylinder it is shown that the steady streaming boundary layer of the basic flow is significantly altered by the instability.

Hall, P.↗

NASA NTRS1984

On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid

The stability of the two-dimensional flow induced by the transverse oscillation of a cylinder in a viscous fluid is investigated in both the linear and weakly nonlinear regime. The major assumption that is made to simplify the problem is that the oscillation frequency is large in which case an unsteady boundary layer is set up on the cylinder. Results are given for cylinders of elliptic cross section and it is found that for any given eccentricity the most dangerous configuration is when the cylinder oscillates parallel to its minor axis. Some discussion of nonlinear effects is also given and for the circular cylinder it is shown that the steady streaming boundary layer of the basic flow is significantly altered by the instability.

Hall, P.↗

NASA NTRS1989

On the interaction of stationary crossflow vortices and Tollmien-Schlichting waves in the boundary layer on a rotating disc

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete among themselves. The interaction is considered of two types of instability mode (at an asymptotically large Reynolds number) which can occur in the flow above a rotating disc. In particular, the interaction is examined between lower branch Tollmien-Schlichting (TS) waves and the upper branch, stationary, inviscid crossflow vortex whose asymptotic structure has been described by Hall (1986). This problem is studied in the context of investigating the effect of the vortex on the stability characteristics of a small TS wave. Essentially, it is found that the primary effect is felt through the modification to the mean flow induced by the presence of the vortex. Initially, the TS wave is taken to be linear in character and it is shown (for the cases of both a linear and a nonlinear stationary vortex) that the vortex can exhibit both stabilizing and destabilizing effects on the TS wave and the nature of this influence is wholly dependent upon the orientation of this latter instability. Further, the problem is examined with a larger TS wave, whose size is chosen so as to ensure that this mode is nonlinear in its own right. An amplitude equation for the evolution of the TS wave is derived which admits solutions corresponding to finite amplitude, stable, traveling waves.

Bassom, Andrew P.↗

NASA NTRS1990

On the interaction of stationary crossflow vortices and Tollmien-Schlichting waves in the boundary layer on a rotating disc

Bassom, Andrew P.↗

NASA NTRS1986

The nonlinear development of Gortler vortices in growing boundary layers

The development of Gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion whilst the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflection character as the flow moves downstream. The latter result suggests that the major effect of Gortler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗

NASA NTRS1988

The nonlinear development of Goertler vortices in growing boundary layers

The development of Goertler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion while the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflectional character as the flow moves downstream. The latter result suggests that the major effect of Goertler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗

NASA NTRS1986

On the secondary instability of Taylor-Goertler vortices to Tollmien-Schlichting waves in fully-developed flows

There are many flows of practical importance where both Tollmien-Schlichting waves and Taylor-Goertler vortices are possible causes of transition to turbulence. The effect of fully nonlinear Taylor-Goertler vortices on the growth of small amplitude Tollmien-Schlichting waves is investigated. The basic state considered is the fully developed flow between concentric cylinders driven by an azimuthal pressure gradient. It is hoped that an investigation of this problem will shed light on the more complicated external boundary layer problem where again both modes of instability exist in the presence of concave curvature. The type of Tollmein-Schlichting waves considered have the asymptotic structure of lower branch modes of plane Poisseulle flow. Whilst instabilities at lower Reynolds number are possible, the latter modes are simpler to analyze and more relevant to the boundary layer problem. The effect of fully nonlinear Taylor-Goertler vortices on both two-dimensional and three-dimensional waves is determined. It is shown that, whilst the maximum growth as a function of frequency is not greatly affected, there is a large destabilizing effect over a large range of frequencies.

Bennett, James↗

NASA NTRS1988

On the secondary instability of Taylor-Goertler vortices to Tollmien-Schlichting waves in fully developed flows

There are many flows of practical importance where both Tollmien-Schlichting waves and Taylor-Goertler vortices are possible causes of transition to turbulence. The effect of fully nonlinear Taylor-Goertler vortices on the growth of small amplitude Tollmien-Schlichting waves is investigated. The basic state considered is the fully developed flow between concentric cylinders driven by an azimuthal pressure gradient. It is hoped that an investigation of this problem will shed light on the more complicated external boundary layer problem where again both modes of instability exist in the presence of concave curvature. The type of Tollmien-Schlichting waves considered have the asymptotic structure of lower branch modes of plane Poiseuille flow. Whilst instabilities at lower Reynolds number are possible, the latter modes are simpler to analyze and more relevant to the boundary layer problem. The effect of fully nonlinear Taylor-Goertler vortices on both two-dimensional and three-dimensional waves is determined. It is shown that, whilst the maximum growth as a function of frequency is not greatly affected, there is a large destabilizing effect over a large range of frequencies.

Bennett, James↗

NASA NTRS1985

The application of the detection filter to aircraft control surface and actuator failure detection and isolation

The performance of the detection filter in detecting and isolating aircraft control surface and actuator failures is evaluated. The basic detection filter theory assumption of no direct input-output coupling is violated in this application due to the use of acceleration measurements for detecting and isolating failures. With this coupling, residuals produced by control surface failures may only be constrained to a known plane rather than to a single direction. A detection filter design with such planar failure signatures is presented, with the design issues briefly addressed. In addition, a modification to constrain the residual to a single known direction even with direct input-output coupling is also presented. Both the detection filter and the modification are tested using a nonlinear aircraft simulation. While no thresholds were selected, both filters demonstrated an ability to detect control surface and actuator failures. Failure isolation may be a problem if there are several control surfaces which produce similar effects on the aircraft. In addition, the detection filter was sensitive to wind turbulence and modeling errors.

Bonnice, W. F.↗

NASA NTRS1993

On the nonlinear interfacial instability of rotating core-annular flow

The interfacial stability of rotating core-annular flows is investigated. The linear and nonlinear effects are considered for the case when the annular region is very thin. Both asymptotic and numerical methods are used to solve the flow in the core and film regions which are coupled by a difference in viscosity and density. The long-term behavior of the fluid-fluid interface is determined by deriving its nonlinear evolution in the form of a modified Kuramoto-Sivashinsky equation. We obtain a generalization of this equation to three dimensions. The flows considered are applicable to a wide array of physical problems where liquid films are used to lubricate higher or lower viscosity core fluids, for which a concentric arrangement is desired. Linearized solutions show that the effects of density and viscosity stratification are crucial to the stability of the interface. Rotation generally destabilizes non-axisymmetric disturbances to the interface, whereas the centripetal forces tend to stabilize flows in which the film contains the heavier fluid. Nonlinear affects allow finite amplitude helically travelling waves to exist when the fluids have different viscosities.

Coward, Aidrian V.↗

NASA NTRS1987

The fully nonlinear development of Goertler vortices in growing boundary layers

The fully nonlinear development of small wavelength Goertler vortices in a growing boundary layer is investigated using a combination of asymptotic and numerical methods. The starting point for the analysis is the weakly nonlinear theory of Hall (1982b) who discussed the initial development of small amplitude vortices in a neighborhood of the location where they first become linearly unstable. That development is unusual in the context of nonlinear stability theory in that it is not described by the Stuart-Watson approach. In fact the development is governed by a pair of coupled nonlinear partial differential evolution equations for the vortex flow and the mean flow correction. Here the further development of this interaction is considered for vortices so large that the mean flow correction driven by them is as large as the basic state. Surprisingly it is found that such a nonlinear interaction can still be described by asymptotic means. It is shown that the vortices spread out across the boundary layer and effectively drive the boundary layer. In fact the system obtained by writing down the equations for the fundamental component of the vortex generate a differential equation for the basic state. Thus the mean flow adjusts so as to make these large amplitude vortices locally neutral. Moreover in the region where the vortices exist the mean flow has a square-root profile and the vortex velocity field can be written down in closed form. The upper and lower boundaries of the region of vortex activity are determined by a free-boundary problem involving the boundary layer equations. In general it is found that this region ultimately includes almost all of the original boundary layer and much of the free-stream. In this situation the mean flow has essentially no relationship to the flow which exists in the absence of the vortices.

Hall, Philip↗

NASA NTRS1998

Annual Research Briefs, 1998

The topics contained in this progress report are direct numerical simulation of turbulent non-premixed combustion with realistic chemistry; LES of non-premixed turbulent reacting flows with conditional source term estimation; measurements of the three-dimensional scalar dissipation rate in gas-phase planar turbulent jets; direct simulation of a jet diffusion flame; on the use of interpolating wavelets in the direct numerical simulation of combustion; on the use of a dynamically adaptive wavelet collocation algorithm in DNS (direct numerical simulation) of non-premixed turbulent combustion; 2D simulations of Hall thrusters; computation of trailing-edge noise at low mach number using LES and acoustic analogy; weakly nonlinear modeling of the early stages of bypass transition; interactions between freestream turbulence and boundary layers; interfaces at the outer boundaries of turbulent motions; largest scales of turbulent wall flows; the instability of streaks in near-wall turbulence; an implementation of the v(sup 2) - f model with application to transonic flows; heat transfer predictions in cavities; a structure-based model with stropholysis effects; modeling a confined swirling coaxial jet; subgrid-scale models based on incremental unknowns for large eddy simulations; subgrid scale modeling taking the numerical error into consideration; towards a near-wall model for LES of a separated diffuser flow; on the feasibility of merging LES with RANS (Reynolds Averaging Numerical simulation) for the near-wall region of attached turbulent flows; large-eddy simulation of a separated boundary layer; numerical study of a channel flow with variable properties; on the construction of high order finite difference schemes on non-uniform meshes with good conservation properties; development of immersed boundary methods for complex geometries; and particle methods for micro and macroscale flow simulations.

Spinks, Debra↗

NASA NTRS1985

Instability of time-periodic flows

The instabilities of some spatially and/or time-periodic flows are discussed, in particular, flows with curved streamlines which can support Taylor-Gortler vortices are described in detail. The simplest flow where this type of instability can occur is that due to the torsional oscillations of an infinitely long circular cylinder. For more complicated spatially varying time-periodic flows, a similar type of instability can occur and is spatially localized near the most unstable positions. When nonlinear effects are considered it is found that the instability modifies the steady streaming boundary layer induced by the oscillatory motion. It is shown that a rapidly rotating cylinder in a uniform flow is susceptible to a related type of instability; the appropriate stability equations are shown to be identical to those which govern the instability of a boussinesq fluid of Prandtl number unity heated time periodically from below.

Hall, P.↗

NASA NTRS1987

Instability of time-periodic flows

The instabilities of some spatially and/or time-periodic flows are discussed, in particular, flows with curved streamlines which can support Taylor-Gortler vortices are described in detail. The simplest flow where this type of instability can occur is that due to the torsional oscillations of an infinitely long circular cylinder. For more complicated spatially varying time-periodic flows, a similar type of instability can occur and is spatially localized near the most unstable positions. When nonlinear effects are considered it is found that the instability modifies the steady streaming boundary layer induced by the oscillatory motion. It is shown that a rapidly rotating cylinder in a uniform flow is susceptible to a related type of instability; the appropriate stability equations are shown to be identical to those which govern the instability of a Boussinesq fluid of Prandtl number unity heated time periodically from below.

Hall, Philip↗

NASA NTRS1996

On the Effect of Feedback Control on Benard Convection in a Boussinesq Fluid

The effect of nonlinear feedback control strategies on the platform of convection in a Boussinesq fluid heated from below is investigated. In the absence of the control, given that non-Boussinesq effects may be neglected, it is well known that convection begins in the form of a supercritical bifurcation to rolls. Non-Boussinesq behaviour destroys the symmetry of the basic state, and through a subcritical bifurcation leads to the formation of hexagonal cells. Here we discuss the influence of regulation of the lower surface temperature by means of a control mechanism, made up of a combination of a proportional linear and nonlinear controller, on the stability of the hexagonal cell pattern.

Shortis, Trudi A.↗

NASA NTRS1984

The evaluation of failure detection and isolation algorithms for restructurable control

Three failure detection and identification techniques were compared to determine their usefulness in detecting and isolating failures in an aircraft flight control system; excluding sensor and flight control computer failures. The algorithms considered were the detection filter, the Generalized Likelihood Ratio test and the Orthogonal Series Generalized Likelihood Ratio test. A modification to the basic detection filter is also considered which uses secondary filtering of the residuals to produce unidirectional failure signals. The algorithms were evaluated by testing their ability to detect and isolate control surface failures in a nonlinear simulation of a C-130 aircraft. It was found that failures of some aircraft controls are difficult to distinguish because they have a similar effect on the dynamics of the vehicle. Quantitative measures for evaluating the distinguishability of failures are considered. A system monitoring strategy for implementing the failure detection and identification techniques was considered. This strategy identified the mix of direct measurement of failures versus the computation of failure necessary for implementation of the technology in an aircraft system.

Motyka, P.↗

NASA NTRS2009

Discharge Oscillations in a Permanent Magnet Cylindrical Hall-Effect Thruster

Measurements of the discharge current in a cylindrical Hall thruster are presented to quantify plasma oscillations and instabilities without introducing an intrusive probe into the plasma. The time-varying component of the discharge current is measured using a current monitor that possesses a wide frequency bandwidth and the signal is Fourier transformed to yield the frequency spectra present, allowing for the identification of plasma oscillations. The data show that the discharge current oscillations become generally greater in amplitude and complexity as the voltage is increased, and are reduced in severity with increasing flow rate. The breathing mode ionization instability is identified, with frequency as a function of discharge voltage not increasing with discharge voltage as has been observed in some traditional Hall thruster geometries, but instead following a scaling similar to a large-amplitude, nonlinear oscillation mode recently predicted in for annular Hall thrusters. A transition from lower amplitude oscillations to large relative fluctuations in the oscillating discharge current is observed at low flow rates and is suppressed as the mass flow rate is increased. A second set of peaks in the frequency spectra are observed at the highest propellant flow rate tested. Possible mechanisms that might give rise to these peaks include ionization instabilities and interactions between various oscillatory modes.

Polzin, K. A.↗

NASA NTRS1988

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

The nonlinear reaction between two oblique 3-D Tollmein-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an imcompressible boundary layer. The same theory applies to the destabilization of an incident vortex motion by subharmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlionear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial differential system for the vortex flow coupled with an ordinary-differential one for the TS pressure. The solution properties found sometimes produce a breakup within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasi-parallel ones governed by the full nonlinear triple-deck response.

Hall, P.↗