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NASA NTRS1994

Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow

It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer.

Wundrow, David W.↗

NASA NTRS1992

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically by employing two distinct computational implementations of Floquet theory. Results for materials with large Schmidt number are presented, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, Bruce T.↗

NASA NTRS2018

In-Line Electromagnetic Actuator for Fuel Modulation

An in-line electromagnetic actuator with normally-open configuration has been developed for the purpose of exploring its application as a fuel modulator for the active control of combustor thermo-acoustic instabilities. The actuator is based on the spring-coil-plunger mechanism with the plunger designed to be suspended by crossed cantilever beam springs. Operational specification was set for a 1000 psi maximum inlet fuel pressure and modulation for a broad frequency bandwidth that encompasses frequencies that are typically associated with combustor thermo-acoustic instabilities. Various test results demonstrated fuel modulation up to 1200 Hz for coil excitation voltage between 2.3 and 4.6 V and current between 16 and 48 mA, respectively. The initial goal of this work was to demonstrate fuel modulation based on the concept of a normally-open fuel modulator with tethered plunger displacement.

Actuator↗

NASA NTRS2018

In-Line Electromagnetic Actuator for Fuel Modulation

Okojie, Robert S.↗

NASA NTRS2003

Control of Thermo-Acoustics Instabilities: The Multi-Scale Extended Kalman Approach

"Multi-Scale Extended Kalman" (MSEK) is a novel model-based control approach recently found to be effective for suppressing combustion instabilities in gas turbines. A control law formulated in this approach for fuel modulation demonstrated steady suppression of a high-frequency combustion instability (less than 500Hz) in a liquid-fuel combustion test rig under engine-realistic conditions. To make-up for severe transport-delays on control effect, the MSEK controller combines a wavelet -like Multi-Scale analysis and an Extended Kalman Observer to predict the thermo-acoustic states of combustion pressure perturbations. The commanded fuel modulation is composed of a damper action based on the predicted states, and a tones suppression action based on the Multi-Scale estimation of thermal excitations and other transient disturbances. The controller performs automatic adjustments of the gain and phase of these actions to minimize the Time-Scale Averaged Variances of the pressures inside the combustion zone and upstream of the injector. The successful demonstration of Active Combustion Control with this MSEK controller completed an important NASA milestone for the current research in advanced combustion technologies.

Le, Dzu K.↗

NASA NTRS1999

Fluid Physics in a Fluctuating Acceleration Environment

Our program of research aims at developing a stochastic description of the residual acceleration field onboard spacecraft (g-jitter) to describe in quantitative detail its effect on fluid motion. Our main premise is that such a statistical description is necessary in those cases in which the characteristic time scales of the process under investigation are long compared with the correlation time of g-jitter. Although a clear separation between time scales makes this approach feasible, there remain several difficulties of practical nature: (i), g-jitter time series are not statistically stationary but rather show definite dependences on factors such as active or rest crew periods; (ii), it is very difficult to extract reliably the low frequency range of the power spectrum of the acceleration field. This range controls the magnitude of diffusive processes; and (iii), models used to date are Gaussian, but there is evidence that large amplitude disturbances occur much more frequently than a Gaussian distribution would predict. The lack of stationarity does not constitute a severe limitation in practice, since the intensity of the stochastic components changes very slowly during space missions (perhaps over times of the order of hours). A separate analysis of large amplitude disturbances has not been undertaken yet, but it does not seem difficult a priori to devise models that may describe this range better than a Gaussian distribution. The effect of low frequency components, on the other hand, is more difficult to ascertain, partly due to the difficulty associated with measuring them, and partly because they may be indistinguishable from slowly changing averages. This latter effect is further complicated by the lack of statistical stationarity of the time series. Recent work has focused on the effect of stochastic modulation on the onset of oscillatory instabilities as an example of resonant interaction between the driving acceleration and normal modes of the system, and on cavity flow as an example of how an oscillatory response under periodic driving becomes diffusive if the forcing is random instead. This paper describes three different topics that illustrate behavior that is peculiar to a stochastic acceleration field. In the first case, we show that g-jitter can induce effective attractive or repulsive forces between a pair of spherical particles that are suspended in an incompressible fluid of different density provided that the momentum diffusion length is larger than the interparticle separation (as in the case in most colloidal suspensions). Second, a stochastic modulation of the control parameter in the vicinity of a pitchfork or supercritical bifurcation is known not to affect the location of the threshold. We show, however, that resonance between the modulation and linearly stable modes close to onset can lead to a shift in threshold. Finally, we discuss the classical problem of vorticity diffusion away from a plane boundary that is being vibrated along its own plane. Periodic motion with zero average vorticity production results in an exponential decay of the vorticity away from the boundary. Random vibration, on the other hand, results in power law decay away from the boundary even if vorticity production averages to zero.

Drolet, Francois↗

NASA NTRS2004

Systems Characterization of Combustor Instabilities With Controls Design Emphasis

This effort performed test data analysis in order to characterize the general behavior of combustor instabilities with emphasis on controls design. The analysis is performed on data obtained from two configurations of a laboratory combustor rig and from a developmental aero-engine combustor. The study has characterized several dynamic behaviors associated with combustor instabilities. These are: frequency and phase randomness, amplitude modulations, net random phase walks, random noise, exponential growth and intra-harmonic couplings. Finally, the very cause of combustor instabilities was explored and it could be attributed to a more general source-load type impedance interaction that includes the thermo-acoustic coupling. Performing these characterizations on different combustors allows for more accurate identification of the cause of these phenomena and their effect on instability.

Kopasakis, George↗

NASA NTRS1985

Recent research on magnetospheric wave-particle interactions

Highlights of recent Stanford University VLF research in the Antarctic include new observations of wave-induced particle precipitation and controlled experiments on nonlinear wave growth phenomena. Higher-than-expected levels of burst precipitation have been discovered inside the plasmasphere, near L = 2, using subionospheric signal perturbations called 'Trimpi events'. Studies of burst precipitation have been extended to the region poleward of the plasmapause using the Siple transmitter signal as a waveguide probe. Experiments on the 'coherent wave instability', using the amplitude and frequency modulation capability of the new Siple transmitter, have produced exciting new results. Examples are: (1) better definition of the power threshold for the stimulation of temporal wave growth, (2) generation of strong sidebands by unamplified 'beat' waves and (3) generation of chorus-like elements within a band of simulated hiss. Using a new digital processing technique developed at Stanford, new features of the phase behavior of growing waves have been found. Opportunities for extending these experiments are discussed.

Helliwell, R. A.↗

NASA NTRS1993

Numerical simulation of plasma processes driven by transverse ion heating

The plasma processes driven by transverse ion heating in a diverging flux tube are investigated with numerical simulation. The heating is found to drive a host of plasma processes, in addition to the well-known phenomenon of ion conics. The downward electric field near the reverse shock generates a doublestreaming situation consisting of two upflowing ion populations with different average flow velocities. The electric field in the reverse shock region is modulated by the ion-ion instability driven by the multistreaming ions. The oscillating fields in this region have the possibility of heating electrons. These results from the simulations are compared with results from a previous study based on a hydrodynamical model. Effects of spatial resolutions provided by simulations on the evolution of the plasma are discussed.

Singh, Nagendra↗

NASA NTRS2008

Effect of Excess Lead and Bismuth Content on the Electrical Properties of High-Temperature Bismuth Scandium Lead Titanate Ceramics

Aeronautic and aerospace applications require piezoelectric materials that can operate at high temperatures. The air-breathing aeronautic engines can use piezoelectric actuators for active combustion control for fuel modulation to mitigate thermo-acoustic instabilities and/or gas flow control to improve efficiency. The principal challenge for the insertion of piezoelectric materials is their limitation for upper use temperature and this limitation is due low Curie temperature and increasing conductivity. We investigated processing, microstructure and property relationship of (1-x)BiScO3-(x)PbTiO3 (BS-PT) composition as a promising high temperature piezoelectric. The effect of excess Pb and Bi and their partitioning in grain boundaries were studied using impedance spectroscopy, ferroelectric, and piezoelectric measurement techniques. Excess Pb addition increased the grain boundary conduction and the grain boundary area (average grain size was 24.8 m, and 1.3 m for compositions with 0at.% and 5at.% excess Pb, respectively) resulting in ceramics with higher AC conductivity (tan d= 0.9 and 1.7 for 0at.% and 5at.% excess Pb at 350 C and at 10kHz) that were not resistive enough to pole. Excess Bi addition increased the resistivity (rho= 4.1x10(exp 10) Omega cm and 19.6 x10(exp 10) Omega.cm for compositions with 0at.% and 5at.% excess Bi, respectively), improved poling, and increased the piezoelectric coefficient from 137 to 197 pC/N for 5at.% excess Bi addition. In addition, loss tangent decreased more than one order of magnitude at elevated temperatures (greater than 300 C). For all compositions the activation energy of the conducting species was similar (approximately equal to 0.35-0.40 eV) and indicated electronic conduction.

Sehirlioglu, Alp↗

NASA NTRS2024

Eddy-Mediated Turbulent Mixing of Oxygen in the Equatorial Pacific

In the tropical Pacific, weak ventilation and intense microbial respiration at depth give rise to a low dissolved oxygen (O 2 ) environment that is thought to be ventilated primarily by the equatorial current system (ECS). The role of mesoscale eddies and vertical mixing as potential pathways of O 2 supply in this region, however, remains poorly known due to sparse observations and coarse model resolution. Using an eddy resolving simulation of ocean circulation and biogeochemistry, we assess the contribution of these processes to the O 2 budget balance and find that vertical mixing of O 2 , which is modulated by the surface wind speed and the vertical shear of the eddying currents, contributes substantially to the replenishment of O 2 in the upper equatorial Pacific thermocline, complementing the advective supply of O 2 by the ECS and meridional circulation at depth. These transport processes vary seasonally in conjunction with the wind: mixing of O 2 into the upper thermocline is strongest during boreal summer and fall when the vertical shear and eddy kinetic energy are intensified. The relationship between eddy activity and the downward mixing of O 2 arises from the modulation of equatorial turbulence by Tropical Instability Waves via their impacts on the vertical shear. This interaction of processes across scales sustains a local pathway of O 2 delivery into the equatorial Pacific interior and highlights the need for adequate observations and models of turbulent mixing and mesoscale processes for understanding and predicting the fate of the tropical Pacific O 2 content in a warmer and more stratified ocean.

Eddy-Mediated↗

NASA NTRS1999

Hydrodynamic Stability and Magnetic Reconnection in Disks and Stars

The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period.

Goodman, Jeremy↗

NASA NTRS1993

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy-driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time-periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time-periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically employing two distinct computational implementations of Floquet theory. Results are presented for materials with large Schmidt number, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, B. T.↗

NASA NTRS1992

The effect of gravity modulation on thermosolutal convection

In a gravitational field, the opposing effects of components of different diffusivities, for example, temperature and solute, in the density profile in a fluid may produce convective instabilities that exhibit a broad range of dynamical behavior. The effect of time periodic vertical gravity modulation on the onset of these instabilities in an infinite horizontal layer with stress free boundaries is examined. This work is viewed as a first step in expanding previous results in solidification to the full problem of characterizing the effects of gravity modulation in thermosolutal convection during the directional solidification of binary alloys. Calculations carried out both with and without steady background acceleration are presented, the latter results being relevant to microgravity conditions.

Saunders, Bonita V.↗

NASA NTRS1991

Nonlinear dynamics near the stability margin in rotating pipe flow

The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

Yang, Z.↗

NASA NTRS2000

Mesosphere Dynamics with Gravity Wave Forcing: Diurnal and Semi-Diurnal Tides - 1

We present results from a nonlinear, 3D, time dependent numerical spectral model (NSM), which extends from the ground up into the thermosphere and incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GW). Our focal point is the mesosphere that is dominated by wave interactions. We discuss diurnal and semi-diurnal tides ill the present paper (Part 1) and planetary waves in the companion paper (Part 2). To provide an understanding of the seasonal variations of tides, in particular with regard to gravity wave processes, numerical experiments are performed that lead to the following conclusions: 1. The large semiannual variations in tile diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. 2. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength. 3.Variations in eddy viscosity associated with GW interactions tend to peak in late spring and early fall and call also influence the DT. 4. The semidiurnal semidiurnal tide (SDT), and its phase in particular, is strongly influenced by the mean zonal circulation. 5. The SDT, individually, is amplified by GW's. But the DT filters out GW's such that the wave interaction effectively reduces the amplitude of the SDT, effectively producing a strong nonlinear interaction between the DT and SDT. 6.) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT.

Mayr, H. G.↗

NASA NTRS2000

Modeling the Dynamics of the Middle Atmosphere and Lower Thermosphere Under the Influence of Gravity Waves

Our Numerical Spectral Model (NSM), which extends from the ground up into the thermosphere, is non-linear, time-dependent and has been employed for 2D and 3D applications. The standard version of the NSM incorporates Hines' Doppler Spread Parameterization for small scale gravity waves (GW), but planetary waves generated in the troposphere have also been incorporated. The NSM has been applied to describe: (1) the anomalous seasonal variations of the zonal circulation and temperature in the upper mesosphere, (2) the equatorial oscillations (quasi-biennial and semi-annual oscillations (QBO and SAO)) extending from the stratosphere into the upper mesosphere, (3) the diurnal and semi-diurnal tides, and (4) the planetary waves that are excited in the mesosphere. With the emphasis to provide understanding, we present here results from numerical experiments with the NSM that shed light on the GW processes that are of central importance in the mesosphere and lower thermosphere. These are our conclusions: (1) The large semiannual variations in the diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength, but variations in eddy viscosity associated with GW interactions are also important. (2) The semidiurnal tide (SDT) and its phase in particular, is strongly influenced by the mean zonal circulation. The SDT, individually, is also amplified by GW. But the DT filters out GW such that the GW interaction effectively reduces the amplitude of the SDT, producing a strong nonlinear interaction between the DT and SDT. (3) Without external time dependent energy or momentum sources, planetary waves (PW) are generated in the model for zonal wavenumbers 1 to 4, which have amplitudes in the mesosphere above 50 km as large as 40 m/s and periods between 50 and 2 days. The waves are generated primarily during solstice conditions, which indicates that the baroclinic instability (associated with the GW induced reversal in the latitudinal temperature gradient) is playing an important role. Numerical experiment show that GW, directly, also greatly amplify the PW. A common feature of the PW generated in summer and winter is that their vertical wavelengths throughout the mesosphere are large, which indicates that the waves are not propagating freely but are generated throughout the region. Another common feature is that the PW propagate preferentially westward in summer and eastward in winter, being launched from the westward and eastward zonal winds that prevail respectively in summer and winter at altitudes below 80 km. (4) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT. In summary we conclude that GW play major roles in generating and amplifying the dynamical components in the MLT region and, acting principally through wave filtering, produce important non-linear interactions between the components.

Mayr, H. G.↗

NASA NTRS2007

Receptivity of Supersonic Boundary Layers Due To Acoustic Disturbances Over Blunt Cones

Receptivity and stability of supersonic boundary layers over a 5-degree straight cone with a blunt tip are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The linear stability results showed that bluntness has less stabilizing effects on the stability of boundary layers over cones than on flat plates and wedges. The unsteady simulations of the interaction of plane threedimensional acoustic waves with the cone showed that the modulation of wavelength and the generation of instability waves first occurred near the leading edge in the plane where the constant acoustic phase lines are perpendicular to the cone axis. Further downstream, this instability region spreads in the azimuthal direction from this plane.

Balakumar, P.↗