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NASA NTRS1987

Research in millimeter wave techniques

The areas of millimeter wave (MMW) research include atmospheric propagation and radiometry, advanced MMW component design with emphasis on quasi-optical techniques, and the development of MMW receivers, especially those using subharmonic mixers. Calculations of atmospheric attenuation and radiometric antenna temperature were made in the range 100 to 700 GHz, together with measurements of atmospheric antenna temperature near 95 and 183 GHz. Quasi-optical components designed include lenses, mirrors, and wire grid devices, as well as feedhorns for interference with waveguide components. Subharmonic mixers with state-of-the-art performance at 183 GHz were also developed. Each of these areas of research is summarized.

Mcmillan, R. W.↗

NASA NTRS1987

Effect of a bulge on the secondary instability of boundary layers

The influence of a two-dimensional hump on the three-dimensional (3-D) subharmonic secondary instability on a flat plate is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for the inviscid/viscous interaction. The primary wave is taken in the form of a two-dimensional (2-D) Tollmien-Schlichting (T-S) wave. The secondary wave is taken in the form of a 3-D subharmonic T-S wave.

Nayfeh, Ali H.↗

NASA NTRS1987

Numerical study of ribbon-induced transition in Blasius flow

The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.

Spalart, Philippe R.↗

NASA NTRS1987

Nonlinear binary-mode interactions in a developing mixing layer

This paper presents the formulation and results of two-wave interactions in a spatially developing shear layer, directed at understanding and interpreting the physical mechanisms that underlie the results of quantitative observation. The study confirms the existence of Kelly's (1967) mechanism that augments the growth of a subharmonic disturbance by extracting energy from its fundamental or vice versa. This mechanism is shown to be strongest in the region where the fundamental begins to return energy to the mean flow and the two wave modes are of comparable energy levels. It is found that the initial conditions and, especially, the initial phase angle between the two disturbances play a very significant role in the modal development and that of the shear layer itself. A doubling of the shear-layer thickness is shown to take place; the two successive plateaux in its growth are attributed to the peaking in the energy production rates of the fundamental and subharmonic fluctuations.

Nikitopoulos, D. E.↗

NASA NTRS1988

Forced periodic vibration of unsymmetric piecewise-linear systems

The forced steady response of a single degree of freedom system involving a large nonlinearity, represented by unsymmetric piecewise-linear stiffness, is determined by a harmonic balance Newton-Raphson method with the application of the fast Fourier transformation (FFT) algorithm. All possible subharmonic, harmonic, and superharmonic responses are sought. The responses of two systems involving subharmonic and superharmonic dominant motions are calculated by the newly developed method and compared with previously published findings. The results obtained by using this method reveal the details of the response of the systems more efficiently than previous methods.

Choi, Y. S.↗

NASA NTRS1989

Spatial three-dimensional secondary instability compressible boundary-layer flows

Three-dimensional linear secondary instability theory is extended for compressible and high Mach number boundary layer flows. The small but finite amplitude compressible Tollmien-Schlichting wave effect on the growth of 3-D perturbations is investigated. The focus is on principal parametric resonance responsible for the strong growth of subharmonic in low disturbance environment. The effect of increasing Mach number on the onset, growth, the shape of eigenfunctions of the subharmonic is assessed, and the resulting vortical structure is examined.

El-Hady, Nabil M.↗

NASA NTRS1989

On the secondary instability in plane Poiseuille flow

Numerical experiments were performed to clarify apparent differences between experimental observations and a theoretical prediction of the secondary instability in plane Poiseuille flow. It is shown that subharmonic breakdown is unlikely in natural transition as a result of the initial growth of what we call the 'minus' modes and consequent forcing of Orr-Sommerfeld modes present in the background noise. Subharmonic breakdown was achieved only when these minus modes were continuously suppressed.

Kim, John↗

NASA NTRS1990

Optical synchronization of millimeter-wave oscillators for distributed architecture

A review of various methods of phase and frequency synchronization of active MMIC based transmit/receive modules is presented, and particular emphasis is placed on the synchronization of oscillators through the use of an indirect subharmonic optical injection locking technique. In this approach, the nonlinear behavior of large-signal modulated laser diodes and solid-state oscillators is exploited to extend the bandwidth of the synchronizing link to the millimeter-wave frequency range. Experimental results of the phase and frequency coherency of two 21.5 GHz FET oscillators are reported. Optimum performance is achieved at a subharmonic factor of 1/4, with a locking range of 84 MHz and a phase noise degradation of only 14 dB. The phase coherency measurement of two injection-locked oscillators points to a phase shift, which is introduced as a result of the frequency detuning between the slave and master oscillator signals. A scheme to correct for this phase error is presented.

Daryoush, Afshin S.↗

NASA NTRS1990

Wave-interactions in supersonic and hypersonic flows

Work completed under the current grant comprises the start of a theoretical and computational attack on the subharmonic route to secondary instabilities in compressible flows. The total flow field in this problem is made up of the following components: (1) a steady streamwise mean boundary layer flow which depends only on the normal space component y; (2) a two-dimensional time dependent T-S wave which moves with wavespeed c and has no spanwise dependence; and (3) a fully three-dimensional, time dependent T-S wave whose streamwise wavenumber is half of the streamwise wavenumber associated with the two-dimensional T-S wave in b. If a frame of reference is adopted which moves with the wavespeed c of the 2-D T-S wave, the time dependence of this portion of the flow can be eliminated. The effective steady mean flow in this problem is now the sum of the original parallel steady mean flow and the initial 2-D T-S instability. Dependence on the streamwise coordinate x in this mean flow can be extracted by assuming normal mode expansions involving complex exponentials and the streamwise wavenumber a. However, it is important to note that, because this is a wave-wave interaction problem, unlike the usual linear instability case, both the complex exponential, and its complex conjugate, must be retained in describing the 2-D T-S wave. The role of the perturbation to the steady mean flow is now played by the 3-D time dependent T-S wave. In treating this wave, normal modes in the streamwise and spanwise directions and time may be used. Consistent with the subharmonic nature of this transition route, the streamwise wavenumber is a/2, and complex conjugates of the complex exponential must be employed. This is not the case with the modes giving z and t dependence with wavespeed o and spanwise wavenumber B as the effective mean flow quantities are independent of z and their time dependence is accounted for by the moving frame of reference. Consequently, the wave-wave interaction which will produce mean flow modification occurs only through the streamwise exponentials.

Lakin, William D.↗

NASA NTRS1991

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. David↗

NASA NTRS1991

An experimental study of natural and forced modes in an axisymmetric jet

The experiment consisted of two parts. The first part was an effort to study naturally occurring instability modes in the axisymmetric shear layer of a high Reynolds number turbulent jet. Untripped (transitional) and tripped (turbulent) nozzle exit conditions, both with 0.1 percent core turbulence, were studied. For the turbulent nozzle exit boundary layer case, the core turbulence, was varied systematically from 0.1 to 5 percent of the jet exit velocity. The region up to the end of the potential core was dominated by the axisymmetric mode. The azimuthal modes grew rapidly but dominated only downstream of the potential core region. For the jet excited by natural disturbances, the energy content of the higher order modes (m is less than 1) was significantly lower than that of the axisymmetric and m = +/-1 modes. The initial boundary layer had a profound effect on the natural jet evolution and its excitability. The shorter potential core allowed the jet in the transitional case to support helical disturbances closer the nozzle exit than the turbulent case. The natural jet evolution was found to remain unaffected for varying initial core turbulence over the range of 0.15 to 5 percent of the jet velocity. Target modes for efficient excitation of the jet were determined from the results of the naturally occurring jet instability mode experiments. The second part of this work describes an effort to control the axisymmetric shear layer by artificially exciting target modes. Under optimum conditions, two-frequency excitation is indeed more effective than single frequency plane wave excitation as far as jet mixing is concerned. At high amplitudes of fundamental and subharmonic forcing, the subharmonic augmentation and the axial location of the peak were independent of the initial phase difference. Two-frequency excitation also has its limitations, since axisymmetric waves are damped beyond the potential core. Higher spreading rates are obtained when multi-modal forcing is applied.

Raman, Ganesh↗

NASA NTRS1990

Control of the vortical structure in the early stages of transition in boundary layers

The effect of suction and pressure gradient on controlling the production of the three-dimensional vortical structure due to secondary instability is investigated for a boundary layer in the presence of small but finite amplitude Tollmien-Schlichting wave. The subharmonic instability is the focus of the study due to its realistic application in low disturbance flight environment. The spanwise wavelength of the most unstable secondary subharmonic disturbance increases with the increase of control indicating possible alteration of the flow structure from H-type to C-type.

El-Hady, Nabil M.↗

NASA NTRS1991

Secondary instability of high-speed flows and the influence of wall cooling and suction

The periodic streamwise modulation of the supersonic and hypersonic boundary layers by a two-dimensional first-mode or second-mode wave makes the resulting base flow susceptible to a broad-band spanwise-periodic three-dimensional type of instability. The principal parametric resonance of this instability (subharmonic) has been analyzed using Floquet theory. The effect of Mach number and the effectiveness of wall cooling or wall suction in controlling the onset, the growth rate, and the vortical structure of the subharmonic secondary instability are assessed for both a first-mode and a second-mode primary wave.

El-Hady, Nabil M.↗

NASA NTRS1991

Limit cycle vibrations in turbomachinery

The focus is on an examination of rotordynamic systems which are simultaneously susceptible to limit cycle instability and subharmonic response. Characteristics of each phenomenon are determined as well as their interrelationship. A normalized, single mass rotor model is examined as well as a complex model of the high pressure fuel turbopump and the Space Shuttle Main Engine. Entrainment of limit cycle instability by subharmonic response is demonstrated for both models. The nonuniqueness of the solution is also demonstrated.

Ryan, S. G.↗

NASA NTRS1992

Direct numerical simulation of laminar breakdown in high-speed, axisymmetric boundary layers

Temporal direct numerical simulation of laminar breakdown via subharmonic secondary instability in high-speed axisymmetric boundary layers has been accomplished using a highly accurate, fully explicit algorithm which combines spectral collocation and high-order compact-difference techniques. Numerical test cases confirm that subharmonic secondary instability is confirmed to be a viable path to transition in high-speed boundary-layer flow. Secondary instability is shown to account for peaks in the Reynolds stresses at or near the critical layer which are not possible from the second-mode primary instability alone. Reynolds stresses spatially reconstructed from the temporal model via the Gaster transformation show a 'spreading angle' of about 12 deg, in qualitative agreement with experimental findings. The rate of broadening of the Reynolds stress peak is a strongly nonlinear phenomenon which cannot be reproduced by secondary instability theory.

Pruett, C. D.↗

NASA NTRS1992

The 77 day periodicity in the flare rate of cycle 22

The ocurrence times of major flares of solar cycle 22 are analyzed to detect periodicities. It is found that a periodicity of 77 d was in operation in the 15-m interval from 1988 November to 1990 February for six cycles. During the rest of 1990 no periodicity was discernible; however, it seems that the 77-d periodicity resumed in 1991. This 77-d period is interpreted as the third subharmonic of the fundamental period of about 25.5 d. In this interpretation, the 154-d periodicity is the sixth subharmonic. It is also found that when the 77-d periodicity or the 154-d periodicity is in operation the occurrence rate of major flares is much higher than is expected form the relative sunspot number.

Bai, T.↗

NASA NTRS1991

Investigation of supersonic modes and three-dimensionality in bounded, free shear flows

It is found through two-dimensional temporal simulations of high-speed free shear layers that mean flow distortion is significantly increased when supersonic disturbances are introduced as initial conditions. The shear layer exhibits no subharmonic growth or roll-up, but rather a spectral broadening as energy is distributed into higher harmonics. Increasing the velocity of one side of the mixing layer (u2) to roughly 1/5 the speed of the high speed side (u1), allows a slight subharmonic growth at a very slow rate for two-dimensional modes. A first look at three-dimensional free shear flows is also presented for M = 2. No effect is seen for incompressible flow; however, stabilization is seen with respect to maximum temporal growth rates as the transverse velocity is increased. A much stronger, but similar effect is seen if u2 is increased. The wave direction of maximum growth for u2 is greater than 0.4 is found to be the direction of the faster stream (u1) over a broad range of transverse velocities.

Macaraeg, Michele G.↗

NASA NTRS1992

Dynamics and control of coherent structure in turbulent jets

Current understanding of coherent structure dynamics in incompressible turbulent jets as explained by the nonlinear stability theory is reviewed, focusing on nonswirling turbulent jets. Topics addressed include hydrodynamic stability theory and coherent structures; dynamics of energy transfers among different scales of motion; nonlinear development of amplitude; development of single-frequency coherent mode; fundamental-subharmonic interaction and vortex pairing; and reversal of Reynolds stresses. Attention is also given to the effect of initial phase-difference angle between fundamental and subharmonic, conditions for resonance interaction, modulation of spreading rate by controlling coherent structure, turbulence enhancement or suppression due to excitation, 3D effects, jet noise, and swirling jets.

Mankbadi, Reda R.↗