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NASA NTRS1989

Unstable vortices in the near region of an internal flow cavity

This paper presents experimental data taken in the forward region of a separated internal free-shear layer produced in an internal cavity flowfield. It has been found that in the region very near the forward restrictor, experimental velocity profiles agree closely with the exact Stuart instability velocity profile with various values of a steepness parameter. Reynolds shear-stress profiles suggest the presence of counter-rotating longitudinal vortices. Spectral analysis by the maximum entropy method of the time samples within the vortices indicates subharmonic and harmonic components of the fundamental frequency, with a weak indication of the fundamental frequency itself.

Isaacson, L. K.↗

NASA NTRS1990

Numerical simulation of 3-D Benard convection with gravitational modulation

In this numerical study, randomly and sinusoidally modulated gravitational fields imposed on three-dimensional Rayleigh-Benard convection are investigated in an effort to understand the effects of vibration (G-Jitter) on fluid systems. The time-dependent, Navier-Stokes equations and the energy equation with Boussinesq approximations are solved by a semi-implicit, pseudospectral procedure. An analysis of energy balances indicates that with increasing modulation amplitude, transition from synchronous to relaxation oscillation goes through the subharmonic response. Random modulations are found to be less stabilizing than sinusoidal and are shown to impose three-dimensionality on the flow for some parameter ranges both at terrestrial and zero base gravity conditions.

Biringen, S.↗

NASA NTRS1990

Coherence properties of a doubly resonant monolithic optical parametric oscillator

A doubly resonant optical parametric oscillator (DRO) pumped with the second harmonic of a narrow-linewidth Nd:YAG laser is described. The linewidth of the DRO signal was less than 13 kHz, the DRO was shown to generate a phase-locked subharmonic of the pump at degeneracy, and the signal and the idler were shown to be mutually coherent with the pump and to be phase-anticorrelated with each other away from degeneracy. The signal-idler heterodyne linewidth was 500 Hz, and pump phase modulation was shown to transfer to the DRO phase at degeneracy.

Nabors, C. D.↗

NASA NTRS1990

Period and phase of the 88-year solar cycle and the Maunder minimum - Evidence for a chaotic sun

The problem of whether the solar dynamo is quasi-periodic or chaotic is addressed by examining 1500 years of sunspot, geomagnetic, and auroral activity cycles. Sub-harmonics were found of the fundamental solar cycle period during the years preceding the Maunder minimum and loss of phase of the subharmonic on emergence from it. These phenomena are indicative of chaos. They indicate that the solar dynamo is chaotic and is operating in a region close to the transition between period doubling and chaos. Since Maunder-type minima reoccur irregularly for millennia, it appears that the sun remains close to this transition to and from chaos. This is postulated to be a universal characteristic of solar type stars caused by feedback in the dynamo number.

Feynman, J.↗

NASA NTRS1989

Numerical simulation of nonlinear development of instability waves

The nonlinear interactions of high amplitude instability waves in turbulent jets are described. In plane shear layers Riley and Metcalf (1980) and Monkewitz (1987) have shown that these interactions are dependent, among other parameters, on the phase-difference between the two instability waves. Therefore, here researchers consider the nonlinear development of both the amplitudes and the phase of the instability waves. The development of these waves are also coupled with the development of the mean flow and the background turbulence. In formulating this model it is assumed that each of the flow components can be characterized by conservation equations supplemented by closure models. Results for the interactions between the two instability waves under high-amplitude forcing at fundamental and subharmonic frequencies are presented here. Qualitative agreements are found between the present predictions and available experimental data.

Mankbadi, Reda R.↗

NASA NTRS1990

Critical-layer nonlinearity in the resonance growth of three-dimensional waves in boundary layers

The nonlinear interactions of a triad of initially linear stability waves are addressed. The triad consisted of a single two-dimensional mode at a given frequency and two oblique modes with equal and opposite spanwise wave numbers. The oblique waves were at half the frequency and streamwise wave number of the two-dimensional mode. Attention was focused on the boundary-layer transition at low frequencies and high Reynolds numbers. A five-zoned structure and low-frequency scaling were used to derive the nonlinear-interaction equations. The initial nonlinear development of the waves was analyzed; the results indicated that the two-dimensional wave behaves according to linear theory. Nonlinear interactions caused exponential-of-an-exponential growth of the oblique modes. This resonant amplification of the subharmonic depended on the initial amplitude of the two-dimensional wave and on the initial phase angle between the two-dimensional wave and the oblique waves. The resonant growth of the oblique modes was more pronounced at lower frequencies than at higher frequencies. The results are in good agreement with experimental results and offer explanations of the observed process.

Mankbadi, Reda R.↗

NASA NTRS1991

Design and status of the RF-digitizer integrated circuit

An integrated circuit currently under development samples a bandpass-limited signal at a radio frequency in quadrature and then performs a simple sum-and-dump operation in order to filter and lower the rate of the samples. Downconversion to baseband is carried out by the sampling step itself through the aliasing effect of an appropriately selected subharmonic sampling frequency. Two complete RF digitizer circuits with these functions will be implemented with analog and digital elements on one GaAs substrate. An input signal, with a carrier frequency as high as 8 GHz, can be sampled at a rate as high as 600 Msamples/sec for each quadrature component. The initial version of the chip will sign-sample (1-bit) the input RF signal. The chip will contain a synthesizer to generate a sample frequency that is a selectable integer multiple of an input reference frequency. In addition to the usual advantages of compactness and reliability associated with integrated circuits, the single chip will replace several steps required by standard analog downconversion. Furthermore, when a very high initial sample rate is selected, the presampling analog filters can be given very large bandwidths, thereby greatly reducing phase and delay instabilities typically introduced by such filters, as well as phase and delay variation due to Doppler changes.

Rayhrer, B.↗

NASA NTRS1991

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Mankbadi, Reda R.↗

NASA NTRS1991

Resonant Triad in Boundary-Layer Stability: Composite Solution and Comparison with Observations - Part 2

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Mankbadi, Reda R.↗

NASA NTRS1990

Non-linear dynamics of a spur gear pair

The backlash nonlinearity excited primarily by transmission error between spur gear pairs is studied for both external and internal excitations. The digital simulation technique and the method of harmonic balance are used to develop steady state solutions for the internal sinuosidal excitations. The analytic predictions agreed well with available experimental data. Digital simulation is used to observe that at the chaotic and subharmonic resonances may exist in a gear pair depending on the mean or design load, mean to alternating force ratio, damping, and backlash.

Kahraman, A.↗

NASA NTRS1991

The effect of compliant walls on secondary instabilities in boundary layer transition

The effect of compliant walls on the stage of transition where three-dimensional secondary instabilities (SIs) are excited is studied. A theory developed by Herbert (1983) to represent SIs for two-dimensional primary instabilities is extended to allow for oblique waves. The effects of the variations in primary amplitude, spanwise, wavenumber, and Reynolds number on the SIs are examined. As in the rigid-wall case, the subharmonic mode of SI dominates for low-amplitude disturbances over compliant walls. Both isotropic and nonisotropic compliant walls lead to reduced SI growth rates as compared to the rigid-wall results. Calculations show that, for high frequencies, the nonisotropic wall suppresses the amplification of the SIs, while for the isotropic wall SIs grow with an explosive rate similar to the rigid-wall results. For lower frequencies, both types of compliant wall suppress the amplification of SIs.

Joslin, Ronald D.↗

NASA NTRS1991

International Symposium on Space Terahertz Technology, 1st, University of Michigan, Ann Arbor, Mar. 5, 6, 1990, Proceedings

Problems, proposed solutions, and recent results related to the development of solid-state oscillators, detectors, mixers, diode multipliers, and antennas at THz frequencies are addressed. Individual topics considered include: submillimeter heterodyne remote sensing of upper atmospheric gases, planar dipole array antenna with an elliptical lens, twin slot antenna structures integrated with microbolometer detectors for 94-GHz imaging. Also discussed are: quantum-well and quantum-barrier diodes for generating submillimeter wave power, planar Schottky barrier mixer diodes for space applications at submillimeter wavelengths, GaAs Schottky barrier varactor diodes for submillimeter wavelength power generation, planar doped barrier devices for subharmonic mixers.

Ulaby, Fawwaz↗

NASA NTRS1991

Periodic response of multi-disk rotors with bearing clearances

The forced steady state response of a multi-disk rotor system involving a clearance at one of the bearings is determined by using a harmonic balance approach. The impedance method is applied to each of the harmonic steady state components in order to reduce the system to its displacement at the nonlinear bearing support. The results reveal the interrelated roles of the bearing clearance, mass eccentricity and side force in producing dangerous subharmonics. The significant effects of the strong nonlinearity of a bearing clearance are studied as related to the various system parameters. The results show that the approach developed in this study is computationally superior to numerical integration methods in analyzing multi-disk rotor systems with strong nonlinearity.

Kim, Y. B.↗

NASA NTRS1991

Effect of suction on controlling the secondary instability of boundary layers

The effect of suction on controlling the three-dimensional secondary instability is investigated for a boundary layer with a pressure gradient in the presence of a small but finite-amplitude Tollmien-Schlichting wave. The focus is on the principal parametric resonance responsible for the strong growth of subharmonics in a low disturbance environment. Calculations are presented for the effect of suction on the onset and amplification of the secondary instability in Blasius and Falkner-Skan flows, as well as its effect on controlling the production of the vortical structure.

El-Hady, Nabil M.↗

NASA NTRS1990

Analysis of three-dimensional structures in boundary layers

A perturbation scheme, based on the simultaneous expansion of primary and secondary modes, is used to study the prebreakdown flow field. Results of the analysis are in good agreement with experiments for amplitudes in excess of 5 percent. For peak-valley splitting, the analysis captures the development of the high shear layer associated with breakdown. Subharmonic modes evolve differently, with the region of high shear concentrated near the wall.

Crouch, Jeffrey D.↗

NASA NTRS1990

Bounded free shear flows - Linear and nonlinear growth

The physics of bounded free shear flows is studied at supersonic Mach numbers. Wall locations are at 1500 momentum thicknesses away from the shear layer center line. Intrinsic to this flow are high multiplicities of supersonic modes not present in the unbounded case. It is seen that these supersonic modes are resistant to subharmonic growth, a necessary precursor for efficient mixing. Previous results (Eberhardt et al., 1988) with wall locations at less than one half momentum thickness away from the shear layer center indicate that modes resembling channel modes (maximum amplification at the walls) did not roll up in numerical simulations. The similarity between these two cases is pointed out.

Macaraeg, Michele G.↗

NASA NTRS1991

Compressible stability of growing boundary layers using parabolized stability equations

The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

Chang, Chau-Lyan↗

NASA NTRS1990

Steady-state analysis of a nonlinear rotor-housing system

The periodic steady state response of a high pressure oxygen turbopump (HBOTP) of a Space Shuttle main engine (SSME), involving a clearance between the bearing and housing carrier, is sought. A harmonic balance method utilizig Fast Fourier Transform (FFT) algorithm is developed for the analysis. An impedance method is used to reduce the number of degrees of freedom to the displacements at the bearing clearance. Harmonic and subharmonic responses to imbalance for various system parameters are studied. The results show that the computational technique developed in this study is an effective and flexible method for determining the stable and unstable periodic response of complex rotor-housing systems with clearance type nonlinearity.

Noah, S. T.↗