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NASA NTRS1989

Nonlinear interactions in mixing layers and compressible heated round jets

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Jarrah, Yousef Mohd↗

NASA NTRS1984

Line sources of instability waves in a Blasius boundary layer

Numerical solutions of the instability wave pattern behind a harmonic point source in a Blasius boundary layer are used to form line sources by superposition. For infinite-length spanwise line sources of constant amplitude and phase, the result is just the two-dimensional normal mode of the same frequency; for a sinusoidal amplitude or linear phase distribution, the result is an oblique normal mode of the same spanwise wavenumber. A finite-length spanwise source simulates a vibrating ribbon. In a study of the influence of the source length on the downstream amplitude, the effective field of view is found to have a half-angle of about 16 deg. If the source tips are within this field, the amplitude may be either greater than or less than the comparable normal-mode amplitude, depending on the distance from the source and the spanwise location. For an oblique line source, the downstream wave development at each spanwise location is found to be close to, but not identical with, that of an oblique normal mode which originates at the source with the initial wave angle of the source and satisfies the irrotationality condition on the wavenumber vector.

Mack, L. M.↗

NASA NTRS1994

Numerical simulation of the edge tone phenomenon

Time accurate Navier-Stokes computations were performed to study a class 2 (acoustic) whistle, the edge tone, and to gain knowledge of the vortex-acoustic coupling mechanisms driving production of these tones. Results were obtained by solving the full Navier-Stokes equations for laminar compressible air flow of a two dimensional jet issuing from a slit interacting with a wedge. Cases considered were determined by varying the distance from the slit to the wedge. Flow speed was kept constant at 1,750 cm/s as was the slit thickness of 0.1 cm, corresponding to conditions in the experiments of Brown. The analytical computations revealed edge tones to be present in four harmonic stages of jet flow instability over the wedge as the jet length was varied from 0.3 to 1.6 cm. Excellent agreement was obtained in all four edge tone stage cases between the present computational results and the experimentally obtained frequencies and flow visualization results of Brown. Specific edge tone generation phenomena and further confirmation of certain theories and empirical formulas concerning these phenomena were brought to light in this analytical simulation of edge tones.

Dougherty, N. S.↗

NASA NTRS1999

Vortex/Flame Interactions in Microgravity Pulsed Jet Diffusion Flames

The problem of vortex/flame interaction is of fundamental importance to turbulent combustion. These interactions have been studied in normal gravity. It was found that due to the interactions between the imposed disturbances and buoyancy induced instabilities, several overall length scales dominated the flame. The problem of multiple scales does not exist in microgravity for a pulsed laminar flame, since there are no buoyancy induced instabilities. The absence of buoyant convection therefore provides an environment to study the role of vortices interacting with flames in a controlled manner. There are strong similarities between imposed and naturally occurring perturbations, since both can be described by the same spatial instability theory. Hence, imposing a harmonic disturbance on a microgravity laminar flame creates effects similar to those occurring naturally in transitional/turbulent diffusion flames observed in microgravity. In this study, controlled, large-scale, axisymmetric vortices are imposed on a microgravity laminar diffusion flame. The experimental results and predictions from a numerical model of transient jet diffusion flames are presented and the characteristics of pulsed flame are described.

Bahadori, M. Y.↗

NASA NTRS1973

Stabilization of electron streams in type 3 solar radio bursts

It is shown that the electron streams that give rise to Type 3 solar radio bursts are stable and will not be decelerated while propagating out of the solar corona. The stabilization mechanism depends on the parametric oscillating two stream instability. Radiation is produced near the fundamental and second harmonic of the local electron plasma frequency. Estimates of the emission at the second harmonic indicate that the wave spectra created by the oscillating two stream instability can account for the observed intensities of Type 3 bursts.

Papadopoulos, K.↗

NASA NTRS1985

Beam-driven ion cyclotron harmonic resonances in the terrestrial foreshock

A terrestrial upstream wave event which demonstrates multiple, ion cyclotron harmonic resonances between the interplanetary wave population and an observed proton beam is analyzed. The techniques and parameters employed in the data analysis are discussed, including the use of differential and band-pass filters. An upstream wave event demonstrating multiple harmonic waves is examined, and the instability analysis relevant to the ion beam observations thought to be responsible for that event is discussed. It is shown that an observed bi-Maxwellian ion beam is capable of generating right and left-hand polarized waves through ion cyclotron harmonic resonance.

Smith, C. W.↗

NASA NTRS1998

Second Harmonic Hectometric Radio Emission at Jupiter

Galileo has been in orbit around Jupiter since December 1995. The plasma wave instrument on board the spacecraft has occasionally detected a rotationally modulated attenuation band in the hectometric (HOM) emission that most likely is due to scattering of the radiation from density fluctuations along the Io L-shell, as reported earlier. The occurrence of the attenuation band is likely to be dependent on Io activity and the presence of density scattering centers along the Io L-shell as well as the location of the source region. Some of the attenuation bands show clear indications of second harmonic emission. Without polarization measurements, it is difficult to place constraints on the local generation conditions based on the cyclotron maser instability, but the results imply that second harmonic emission could be present in the decametric (DAM) radiation as well. A survey of the data has revealed about 30 examples of second harmonic HOM.

Menietti, J. D.↗

NASA NTRS1998

Second Harmonic Hectometric Radio Emission at Jupiter

Galileo has been in orbit around Jupiter since December 1995. The plasma wave instrument on board the spacecraft has occasionally detected a rotationally modulated attenuation band in the hectometric (HOM) emission that most likely is due to scattering of the radiation from density fluctuations along the Io L-shell, as reported earlier. The occurrence of the attenuation band is likely to be dependent on Io activity and the presence of density scattering centers along the Io-L-shell as well as the location of the source region. Some of the attenuation bands show clear indications of second harmonic emission. Without polarization measurements, it is difficult to place constraints on the local generation conditions based on the cyclotron maser instability, but the results imply that second harmonic emission could be present in the decametric (DAM) radiation as well. A survey of the data has revealed about 30 examples of second harmonic HOM.

Menietti, J. D.↗

NASA NTRS1989

Three-dimensional wave packets and instability waves in free shear layers and their receptivity

A study is made of the evolution of strongly three-dimensional disturbances which are generated by a point force in a parallel mixing layer. When the input force is a pulse, a wave packet develops whose wavefronts are approximately parallel to the spanwise direction. This is in sharp contrast to a wave packet in a wall boundary layer for which the wavefronts are strongly curved. On the other hand, when the input disturbance is oscillating harmonically in time, a spatially growing instability wave develops in a downstream wedge of (x, z)-space. The size of this wedge, as a function of excitation frequency and velocity ratio, is determined. The receptivity of the shear layer to pulse-type and harmonic excitation is also studied. It is found that the shear layer is especially sensitive to relatively high-frequency forcing on its centreline.

Balsa, Thomas F.↗

NASA NTRS1974

Stabilization of electron streams in type III solar radio bursts

We show that the electron streams that give rise to type III solar radio bursts are stable and will not be decelerated while propagating out of the solar corona. The stabilization mechanism depends on the parametric oscillating two-stream instability. Radiation is produced near the fundamental and second harmonic of the local electron plasma frequency. Estimates of the emission at the second harmonic indicate that the wave spectra created by the oscillating two-stream instability can account for the observed intensities of type III bursts.

Papadopoulos, K.↗

NASA NTRS1994

Instabilities orginating from suction holes used for Laminar Flow Control (LFC)

A small-scale wind tunnel previously used for turbulent boundary layer studies has been modified for experiments in laminar flow control. The facility incorporates suction through interchangeable porous test surfaces which are used to stabilize the boundary layer and delay transition to turbulent flow. The thin porous test surfaces are supported by a baffled plenum chamber box which also acts to gather the flow through the surface into tubes which are routed to a high pressure fan. An elliptic leading edge is attached to the assembly to establish a new layer on the test plate. A slot is used to remove the test section flow below the leading edge. The test section was lengthened and fitted with a new ceiling. Substantial modifications were also made to the 3D probe traverse. Detailed studies have been made using isolated holes to explore the underlying instability mechanisms. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance. Conditions corresponding to strong suction and without suction have been studied. In both cases, 3D contour surfaces in the vicinity of the hole show highly three-dimensional T-S waves that fan out away from the hole with streamwise distance. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the far field is similar to the case without suction. Downstream the contour surfaces of the bow-shaped TS waves develop spanwise irregularities which eventually form into clumps. The contours remain smooth when suction is not applied. Even without suction, the harmonic point source is challenging for CFD; e.g. DNS has been used for streamwise growth. With suction, grid resources are consumed by the hole and this makes DNS even more expensive. Limited DNS results so far indicate that the vortices which emanate from suction holes appear to be stable. The spanwise clumping observed in the experiment is evidence of a secondary instability that could be associated with suction vortices. A typical porous surface for LFC consists of 0.002 inch diameter holes with 0.020 inch grid spacing L, which is too small to resolve disturbances. A 20:1 scale porous test surface has been machined for improved spatial resolution while the L/d is still representative of flight conditions. Designers of porous surfaces use Goldsmith's criterion to minimize crossstream interaction. However nothing is known about the streamwise interactions. Results using two holes, aligned but displaced in the streamwise direction, indicate that partial TS wave cancellation is possible, depending on the hole spacing and disturbance frequency. Using DNS for streamwise interaction studies will be prohibitively expensive if linear superposition cannot be used for the multiple holes.

Watmuff, Jonathan H.↗

NASA NTRS1998

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

Lee, Sang Soo↗

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 NTRS1965

Drift instabilities and electron cyclotron oscillations for arbitrary plasma pressure

DRIFT↗

NASA NTRS1986

Electron-cyclotron maser and solar microwave millisecond spike emission

An intense solar microwave millisecond spike emission (SMMSE) event was observed on May 16, 1981 by Zhao and Jin at Beijing Observatory. The peak flux density of the spikes is high to 5 x 100,000 s.f.u. and the corresponding brightness temperature (BT) reaches approx. 10 to the 15th K. In order to explain the observed properties of SMMSE, it is proposed that a beam of electrons with energy of tens KeV injected from the acceleration region downwards into an emerging magnetic arch forms so-called hollow beam distribution and causes electron-cyclotron maser (ECM) instability. The growth rate of second harmonic X-mode is calculated and its change with time is deduced. It is shown that the saturation time of ECM is t sub s approx. equals 0.42 ms and only at last short stage (delta t less than 0.2 t sub s) the growth rate decreases to zero rather rapidly. So a SMMSE with very high BT will be produced if the ratio of number density of nonthermal electrons to that of background electrons, n sub s/n sub e, is larger than 4 x .00001.

Li, Hong-Wei↗

NASA NTRS1994

Dynamics and efficiency of type III solar radio emission

Existing calculations of nonlinear coupling coefficients for fundamental and harmonic emission via three-wave interactions are refined and used to calculate the conversion efficiency of Langmuir energy into electromagnetic waves when the Langmuir waves have the observed bursty form. Resulting field strengths for harmonic emission are found to be consistent with typical International Sun Earth Explorer 3 (ISSE 3) observations at 1 AU. Fundamental emission at 1 AU is found to proceed only when stimulated by the presence of a source of ion sound waves. However, it is argued that electrostatic decay of Langmuir waves can supply the necessary waves provided the driving electron beam is sufficiently fast. Under these conditions, the predicted fundamental field strengths can account for both the highest and typical fields observed; they also dominate the predicted harmonic fields, consistent with observations. This mechanism is also consistent with previous observations that fundamental emission generally occurs early in type III events, when the beam is fastest. For typical parameters it is shown that neither fundamental nor harmonic emission saturates its respective source instability, contrary to previous assumptions. However, saturation cannot be ruled out under particularly favorable conditions.

Robinson, P. A.↗

NASA NTRS1979

Microscale instabilities in stream interaction regions

The microstructure of solar wind stream interaction regions is considered theoretically with emphasis on the role of several electrostatic kinetic instabilities which may be important within the stream interface and the compression region. Inside of 1 AU, the interface is likely to be stable against the electrostatic streaming instabilities considered. Between 1 and 2 AU, the interface will excite the magnetized ion-ion instability. The compression region is also found to be unstable beyond 1 AU where the modified two-stream instability, beam-cyclotron instability, and ion-acoustic instability are important in determining the structure of the compressive pulses as they evolve into forward and reverse shocks. It is concluded that the modified two-stream instability and beam-cyclotron instability predominately play a role in heating the electrons to the threshold for the ion-acoustic instability. Various electrostatic plasma waves, ranging in frequency from the lower-hybrid to harmonics of the electron cyclotron frequency, would be produced by these instabilities. Their signature should also be seen by high time resolution measurements of the temperature of the various plasma species.

Eviatar, A.↗

NASA NTRS1991

Ion cyclotron harmonic resonances driven by ion ring-beam distributions

Enhanced magnetic fluctuations with frequencies peaking at the ion cyclotron frequency and its harmonics have been observed at Comet Halley and also in the upstream regions of planetary bow shocks. It is thought that these waves are generated at comets by pickup ions that are unstable to the generation of waves at harmonics of the ion cyclotron wave number. In the spacecraft frame of reference these waves are observed as harmonics of the ion cyclotron frequency. In this report, it is shown that the ring-beam distributions of pickup ions observed in the cometary environment are capable of generating these waves if the beam speed component of the distribution (parallel to the ambient magnetic field) is much larger than the ring speed (perpendicular to the magnetic field). As the ring speed increases relative to the beam speed, other instabilities occur at the same wave number which have even larger growth rates. These additional instabilities do not lead to generation of harmonics.

Wong, H. K.↗